Evaluation of the Biaxial Mechanical Properties of the Mitral Valve

EVALUATION OF THE BIAXIAL MECHANICAL PROPERTIES OF THE MITRAL
VALVE ANTERIOR LEAFLET UNDER PHYSIOLOGICAL LOADING CONDITIONS
by
Jonathan Sayer Grashow
BS, University of Pittsburgh, 2002
Submitted to the Graduate Faculty of
The School of Engineering in partial fulfillment
of the requirements for the degree of
Master of Science
University of Pittsburgh
2005
UNIVERSITY OF PITTSBURGH
SCHOOL OF ENGINEERING
This thesis was presented
by
Jonathan Sayer Grashow
It was defended on
April 12, 2005
and approved by
Dr. Richard Debski,
Assistant Professor, Department of Bioengineering
Assistant Professor, Department of Orthopedic Surgery
Dr. Jiro Nagatomi,
Research Assistant Professor, Department of Bioengineering
Dr. Michael Sacks,
William Kepler Whiteford Professor, Department of Bioengineering
Thesis Advisor
ii
EVALUATION OF THE BIAXIAL MECHANICAL PROPERTIES OF THE MITRAL
VALVE ANTERIOR LEAFLET UNDER PHYSIOLOGICAL LOADING CONDITIONS
Jonathan Sayer Grashow, MS
University of Pittsburgh, 2005
It is a fundamental assumption that a repaired mitral valve (MV) or MV replacement
should mimic the functionality of the native MV as closely as possible. Thus, improvements in
valvular treatments are dependent on the establishment of a complete understanding of the
mechanical properties of the native MV.
In this work, the biaxial mechanical properties,
including the viscoelastic properties, of the MV anterior leaflet (MVAL) were explored. A novel
high-speed biaxial testing device was developed to achieve stretch rates both below and beyond
in-vitro values reported for the MVAL (Sacks et al, ABME, Vol. 30,pp. 1280-90, 2002).
Experiments were performed with this device to assess the effects of stretch rate (from quasistatic to physiologic) on the stress-stretch response in the native leaflet. Additionally, stressrelaxation and creep tests were performed on the MVAL under physiologic biaxial loading
conditions.
The results of these tests showed that the stress-stretch responses of the MVAL during
the loading phases were remarkably independent of stretch rate. The results of the creep and
relaxation experiments revealed that the leaflet exhibited significant relaxation, but unlike
traditional viscoelastic biological materials, exhibited negligible creep.
These results suggested that the MVAL may be functionally modeled as an anisotropic
quasi-elastic material and highlighted the importance of performing creep experiments on soft
iii
tissues. Additionally, this study underscored the necessity of performing biaxial experiments in
order to appropriately determine the mechanical properties of membranous tissues.
iv
TABLE OF CONTENTS
1.0
INTRODUCTION .............................................................................................................. 1
1.1
ANATOMY AND PHYSIOLOGY OF THE HEART................................................... 1
1.2
MITRAL VALVE ANATOMY ..................................................................................... 4
1.3
MITRAL VALVE HISTOLOGICAL STRUCTURE .................................................... 7
1.3.1
Tri-layered leaflet structure..................................................................................... 7
1.3.2
Passive components of the mitral valve.................................................................. 8
1.3.2.1
Collagen. ............................................................................................................. 8
1.3.2.2
Elastin. .............................................................................................................. 11
1.3.2.3
Glycosaminoglycans. ........................................................................................ 11
1.3.3
Active components of the mitral valve ................................................................. 12
1.3.4
Small angle light scattering analysis of collagen architecture .............................. 14
1.4
MITRAL VALVE DISEASE ....................................................................................... 16
1.4.1
Mitral valve stenosis ............................................................................................. 16
1.4.2
Mitral valve regurgitation ..................................................................................... 17
1.5
PROSTHETIC VALVE REPLACEMENTS ............................................................... 21
1.6
VALVULAR COORDINATE SYSTEM..................................................................... 23
1.7
MITRAL VALVE DYNAMICS .................................................................................. 24
1.7.1
Surface stretches of the anterior leaflet................................................................. 27
1.8
MECHANICAL PROPERTIES OF MITRAL VALVE LEAFLETS.......................... 31
1.9
VISCOELASTIC BEHAVIOR .................................................................................... 36
v
1.9.1
Stress-relaxation testing ........................................................................................ 37
1.9.2
Creep testing ......................................................................................................... 38
1.9.3
Hysteresis.............................................................................................................. 40
1.9.4
Modeling viscoelastic behavior - the Boltzmann superposition principle............ 40
1.9.5
Modelling viscoelastic behavior - quasilinear viscoelasticity .............................. 41
1.9.6
Stretch rate sensitivity in soft tissues .................................................................... 43
1.9.7
Creep and stress-relaxation in soft tissues ............................................................ 44
1.10
MOTIVATION FOR THE CURRENT STUDY & STUDY AIMS ............................ 46
1.10.1
2.0
Specific study aims ............................................................................................... 48
METHODS ....................................................................................................................... 49
2.1
HIGH-SPEED BIAXIAL TESTING DEVICE ............................................................ 49
2.1.1
Device specifications ............................................................................................ 49
2.1.1.1
Displacements and displacement rates.............................................................. 49
2.1.1.2
Maximum loads ................................................................................................ 50
2.1.1.3
Stretch & load measurement frequency............................................................ 51
2.1.2
Device design........................................................................................................ 53
2.1.2.1
Device overview ............................................................................................... 53
2.1.2.2
Actuation components. ..................................................................................... 56
2.1.2.3
Specimen attachments....................................................................................... 58
2.1.2.4
Specimen bath................................................................................................... 60
2.1.2.5
Stretch and load measurement .......................................................................... 60
2.1.3
2.1.3.1
Device software .................................................................................................... 63
Marker identification. ....................................................................................... 63
vi
2.1.3.2
Stretch calculation............................................................................................. 65
2.1.3.3
Quasi-static control ........................................................................................... 68
2.1.3.4
High stretch rate testing. ................................................................................... 70
2.1.3.5
Stress-relaxation testing. ................................................................................... 70
2.1.3.6
Creep testing ..................................................................................................... 71
2.2
CHARACTERIZATION OF DEVICE PERFORMANCE.......................................... 72
2.2.1
Stretch measurement system................................................................................. 72
2.2.2
Load cell calibration ............................................................................................. 73
2.2.3
Ability to reach quasi-static peak loads ................................................................ 75
2.2.4
Load cell momentum sensitivity........................................................................... 75
2.2.5
System relaxation.................................................................................................. 76
2.3
BIAXIAL TESTING OF THE MV ANTERIOR LEAFLET....................................... 77
2.3.1
Specimen preparation............................................................................................ 77
2.3.2
Quasi-static biaxial testing.................................................................................... 80
2.3.3
High-speed biaxial testing..................................................................................... 82
2.3.4
Kinematic analysis ................................................................................................ 84
2.3.5
Statistical methods ................................................................................................ 85
3.0
RESULTS ......................................................................................................................... 86
3.1
CHARACTERIZATION OF DEVICE PERFORMANCE.......................................... 86
3.1.1
Stretch Measurement Accuracy ............................................................................ 86
3.1.2
Load cell calibration ............................................................................................. 87
3.1.3
Ability to reach peak loads ................................................................................... 87
3.1.4
Load cell momentum sensitivity........................................................................... 88
vii
3.1.5
3.2
System relaxation.................................................................................................. 91
EFFECTS OF STRETCH RATE ................................................................................. 92
3.2.1
Device Control ...................................................................................................... 92
3.2.2
Effects of Stretch Rate on Stress-Stretch Response.............................................. 95
3.2.3
Effects of Stretch Rate on Hysteresis.................................................................... 98
3.3
STRESS-RELAXATION AND CREEP .................................................................... 103
3.3.1
Device control..................................................................................................... 103
3.3.2
Biaxial Stress-Relaxation.................................................................................... 105
3.3.3
Uniaxial Stress-Relaxation.................................................................................. 108
3.3.4
Reduced Relaxation Function Fit........................................................................ 109
3.3.5
Creep ................................................................................................................... 110
4.0
DISCUSSION ................................................................................................................. 113
4.1
RELEVANCE OF STUDY ........................................................................................ 113
4.2
MECHANICAL ANISOTROPY................................................................................ 114
4.3
STRETCH RATE EFFECTS...................................................................................... 115
4.4
STRESS-RELAXATION ........................................................................................... 117
4.5
CREEP ........................................................................................................................ 123
4.6
RELATIONSHIP OF STRESS-RELAXATION AND CREEP ................................ 124
4.7
COMPARISONS TO SMALL ANGLE X-RAY SCATTERING RESULTS........... 125
4.8
STUDY LIMITATIONS ............................................................................................ 129
4.9
CONCLUSIONS......................................................................................................... 130
4.10
RECOMMENDATIONS FOR FUTURE STUDY .................................................... 131
5.0
THESIS SUMMARY ..................................................................................................... 133
viii
APPENDIX A............................................................................................................................. 134
APPENDIX B ............................................................................................................................. 136
APPENDIX C ............................................................................................................................. 166
BIBLIOGRAPHY....................................................................................................................... 182
ix
LIST OF TABLES
Table 1. Specimen database......................................................................................................... 78
Table 2. Stretch measurement accuracy....................................................................................... 86
Table 3. Peak loads for the ten cycle test using a latex test sample.............................................. 88
Table 4. Circumferential and radial membrane tensions ± STDEV for all creep tests after the
initial loading phase. ........................................................................................................... 105
x
LIST OF FIGURES
Figure 1. A cross section of the heart looking down on the four heart valves from the atria.
Reproduced from Otto CM. Valvular Heart Disease. Elsevier Inc. 2004............................. 3
Figure 2. A photograph of the MV leaflets. (A) anterior leaflet (P) posterior leaflet. Reproduced
from Otto CM. Valvular Heart Disease. Elsevier Inc. 2004................................................. 5
Figure 3. Diagram from a pathological perspective with division of the septum illustrating the
fibrous continuity between the mitral and aortic valves. Reproduced from Anderson RH,
Wilcox BR: The anatomy of the mitral valve, in Wells FC, Shapiro LM (eds): Mitral Valve
Disease. Oxford, England, Butterworth-Heinemann, 1996. ................................................... 6
Figure 4. The organization of tropocollagen molecules to for collagen fibrils. Reproduced from
Fung, Y.C., Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. 1993, New
York: Springer Verlag. 568..................................................................................................... 8
Figure 5. Schematic showing the hydrogen bonding between strands that is responsible for
collagen’s strength (A) and the tri-helical structure that the three collagen strands take when
they assemble into a collagen fiber (B). Reproduced from Voet, Biochemistry, 1995 ....... 10
Figure 6. Picture illustrates the extensive branching characteristic of GAG molecules which
account for their ability to attract and retain water molecules to enhance their molecular
volume. Reproduced from Alberts, Molecular Biology of the Cell, 1994. ......................... 13
Figure 7. A map of the collagen fiber architecture of the MV anterior leaflet. Colors from red
(highly aligned) to blue (randomly aligned) represent the degree of collagen alignment. ... 15
Figure 8. (A, B) 2D echocardiographic images of mitral valve regurgitation in diastole and
systole respectively. (C) Color flow Doppler image showing the eccentric jet of
regurgitation. Reproduced from Otto CM. Valvular Heart Disease. Elsevier Inc. 2004... 19
Figure 9. Typical Pressure-Volume loops for the normal heart, mitral regurgitation, and aortic
regurgitation. Reproduced from Otto CM. Valvular Heart Disease. Elsevier Inc. 2004... 20
Figure 10. On-X bileaflet pyrolytic carbon mechanical aortic valve (MCRI Inc.)...................... 21
Figure 11. Porcine aortic valve (Edwards Lifesciences) ............................................................. 22
xi
Figure 12. A drawing, looking down on the mitral orifice, showing the circumferential and
radial specimen axes. Reproduced from Reproduced from May-Newman and Yin. Biaxial
Mechanical Properties of the Mitral Valve leaflets. American Journal of Physiology, 1995.
............................................................................................................................................... 23
Figure 13. Drawing of balance of forces in mitral apparatus in the left panel. In the right panel,
potential effect of papillary muscle displacement to restretch leaflet closure, causing mitral
regurgitation. Reproduced from Liel-Cohen N, Guerrero JL, Otsuji Y. Design of a new
surgical approach for ventricular remodeling. Circulation, 2000; 101: 2756...................... 25
Figure 14. Motion of marker placed on free edge of anterior leaflet. Reproduced from Tsakiris
AG, Gordon DA, Mathieu Y, et al: Motion of both mitral valve leaflets: a
cineroentgenographic study in intact dogs. J Appl Physiol 1975; 39:359............................ 26
Figure 15. Left-heart simulating flow loop used by Sacks et al to quantify the surface stretches
of the MV anterior leaflet. Reproduced from Sacks et al. Surface stretches in the anterior
leaflet of the functioning mitral valve................................................................................... 28
Figure 16. Principle stretches observed in left heart-simulating flow loop (closed symbols) and
in vivo using sonomicrometry method (open symbols). Reproduced from Sacks MS et al.
In-vivo dynamic deformation of the mitral valve leaflet. Annals of Thoracic Surgery.
Submitted 2005. .................................................................................................................... 29
Figure 17. Principle stretch rates versus time for the MV anterior leaflet under normal
physiologic conditions. Reproduced from Sacks MS et al. In-vivo dynamic deformation of
the mitral valve leaflet. Annals of Thoracic Surgery. Submitted 2005. .............................. 30
Figure 18. Experimental setup for biaxial mechanical testing of the MV leaflet. Reproduced
from May-Newman and Yin. Biaxial Mechanical Properties of the Mitral Valve leaflets.
American Journal of Physiology, 1995................................................................................. 32
Figure 19. Membrane stress-stretch relations from porcine anterior (A) and posterior (B) leaflets
comparing equibiaxial (open symbols) and strip biaxial (filled symbols) protocols. Circles,
circumferential axis: triangles, radial axis. Reproduced from May-Newman and Yin.
Biaxial Mechanical Properties of the Mitral Valve leaflets. American Journal of
Physiology, 1995................................................................................................................... 33
Figure 20. Pressure - areal stretch relationship of the MV anterior leaflet measured in left heartsimulating flow loop. Reproduced from Sacks et al. Surface stretches in the anterior leaflet
of the functioning mitral valve............................................................................................. 34
Figure 21. (a) The seven loading protocols used to characterize the biaxial stress-stretch
response, and (b) response to all loading protocols for an AV cusp (open circles), along with
the structural model fit, demonstrating an excellent fit. ....................................................... 35
xii
Figure 22. (b) The stress-relaxation responses to three different stretch histories (a). Reproduced
from Wineman AS, Rajagopal KR, Mechanical Response of Polymers. Cambridge
University Press. 2000. ......................................................................................................... 38
Figure 23. The creep responses (b) to three different stress histories (a). Reproduced from
Wineman AS, Rajagopal KR, Mechanical Response of Polymers. Cambridge University
Press. 2000. ........................................................................................................................... 39
Figure 24. The high-speed biaxial testing device mounted on a vibration isolation table........... 53
Figure 25. Overhead schematic of the high speed biaxial testing device; a) stepper motors; b)
screw-driven linear actuators; c) load cells; d) specimen bath outlet; e) specimen bath inlet;
f) heating element maintained bath temperature at 37°C; g) high speed digital camera; h)
standard digital camera; i) beam splitter; j) sub specimen mirror. ....................................... 55
Figure 26. Two computers used to control the biaxial testing device. ......................................... 57
Figure 27. A CAD model of one suture attachment arm. (A) Custom suture attachments were
designed to balance the force applied by each carriage through all four suture lines. (B)
Specimens were mounted to these attachment arms in a trampoline fashion by attaching two
loops of 000 nylon suture to each side of the specimen via four stainless steel surgical
staples. (C) Specimen............................................................................................................ 59
Figure 28. A CAD model of the cross-shaped specimen bath with specimen window/stand. .... 61
Figure 29. The dual biaxial testing device dual camera system. ................................................. 62
Figure 30. A sample bitmap showing four markers (black) and the user-defined marker
subregions (green)................................................................................................................. 64
Figure 31. Marker coordinates were mapped into an isoparametric coordinate system.............. 66
Figure 32. A photograph of the calibration fixture mounted on the bath. ................................... 74
Figure 33. Diagram of the native mitral valve. Square specimens were taken from the anterior
leaflet with sides parallel to the circumferential and radial axes of the leaflet centered
circumferentially and extending radially from just below the annulus to just above the first
chordae tendineae attachment site. ....................................................................................... 79
Figure 34. Biaxial stretch rate sensitivity, creep, stress-relaxation, and uniaxial stress-relaxation
protocols................................................................................................................................ 81
Figure 35. Specimens were mounted in the biaxial testing device with the circumferential and
radial specimen axes aligned with the device axes............................................................... 82
xiii
Figure 36. Load versus time curves for the loaded axis (closed symbols) and unloaded axis
(open symbols) showed that the load cell on the unloaded axis was not affected by rapid
motions.................................................................................................................................. 89
Figure 37. Residuals versus time for the unloaded axis showed no clear trend, further indicating
that the unloaded axis was not affected by rapid motions. ................................................... 90
Figure 38. Relaxation of the biaxial test system and sutures. Both device axes (open symbols:
device axis 1, closed symbols: device axis 2) showed minimal relaxation and were
indistinguishable from each other......................................................................................... 91
Figure 39. Typical tension-stretch curves for the initial and final 1s loading/unloading protocols.
............................................................................................................................................... 93
Figure 40. Typical (a)Load versus time and (b)stretch versus time curves for 1s and 0.1s
loading periods. The load versus time and stretch versus time curves were similar for the
full range of cycle periods. As displayed above, the device was able to accurately control
rise time for different cycle periods. Note the different time scales between the 1s and 0.1s
plots....................................................................................................................................... 94
Figure 41. Typical tension-stretch curves for each loading cycle period (15s, 1s, 0.5s, 0.1s, and
0.05s) for the circumferential (a) and radial (b) specimen directions. Curves generally
showed no apparent stretch rate-dependence. Note the different stretch scales between the
circumferential and radial plots. ........................................................................................... 96
Figure 42. The circumferential and radial stretches of the leaflet at the 90 N/m equitension state.
............................................................................................................................................... 97
Figure 43. Loading and unloading membrane tension (T) vs. stretch curves for 15, 1, 0.5 and 0.1
second loading and unloading of a single specimen........................................................... 100
Figure 44. Membrane stretch energy versus membrane tension for a typical loading cycle. Note
the larger amount of energy storage in the tissue at lower tension levels due to the relatively
higher tissue extensibility at low stretch levels................................................................... 101
Figure 45. Energy stored or dissipated within the leaflet specimens during loading and
unloading phases with different cycle times....................................................................... 102
Figure 46. Typical membrane tension versus time curves for the first 500 ms of a biaxial stressrelaxation experiment. The biaxial stretching mechanism was able to load the specimens
within the allotted 100 ms rise time with minimal vibrations and overshoot..................... 104
Figure 47. Membrane tension versus time curves for a typical stress-relaxation experiment.
Membrane tension levels at 3 hours were statistically less than those immediately after
loading (100 ms) for both specimen axes. .......................................................................... 106
xiv
Figure 48. Relaxation percentage for different test groups and specimen axes. Relaxation was
observed in both uniaxial and biaxial experiments, however, the amount of radial relaxation
was significantly greater in the biaxial experiments and the circumferential and radial
relaxation percentages were not statistically different in the uniaxial experiments as they
were in the biaxial experiments. ......................................................................................... 107
Figure 49. The one phase reduced relaxation model fit both the uniaxial (pictured) and biaxial
relaxation data very well for both the circumferential and radial (pictured) axes. ............. 109
Figure 50. Stretch versus time curves for a typical biaxial creep experiment. Minimal relaxation
was observed on either axis. Note the anisotropic leaflet behavior exhibited by the
relatively higher radial stretch required to maintain the 90 N/m membrane tension.......... 111
Figure 51. Creep percentages were not statistically different from zero for any time point on the
circumferential or radial axes.............................................................................................. 112
Figure 52. Changes in stretch over the three hour duration of the stress relaxation experiments
compared to the changes in stretch required to reach the same membrane tension in quasistatic unloading cycle.......................................................................................................... 118
Figure 53. In uniaxial stress-relaxation experiments, stretch levels increased for axes under
tension and decreased on the free axis. Data presented as mean ± SEM........................... 120
Figure 54. Changes in collagen D-spacing as a function of membrane tension (left). Membrane
tension versus areal stretch % for the same MVAL specimen. Reproduced from Liao, J.
Unpublished Communication. ............................................................................................ 126
Figure 55. D-spacing as a function of creep experiment duration (left). Areal stretch as a
function of creep test duration for the same specimen (right). Reproduced from Liao, J.
Unpublished Communication. ............................................................................................ 127
Figure 56. Normalized membrane tension versus stress-relaxation test duration (top). Collagen
D-spacing as a function of stress-relaxation test duration for the same specimen (bottom).
Reproduced from Liao, J. Unpublished Communication. ................................................. 128
xv
ACKNOWLEDGEMENTS
Although I have worked at the Engineered Tissue Mechanics Laboratory (ETML) for five
years, sometimes I feel like it has only been a week, and other times I feel like I can’t remember
what it was like to do anything else. My time at ETML was spent with many great people whom
I could not have survived without. I would like to thank ( in no particular order) Dan Hildebrand,
Thanh Lam, Claire Gloeckner, Wei Sun, W. David Merryman, Hiroatsu Sugimoto, Ajay Abad,
Khashayar Toosi, John Stella and George Engelmayr for all of their help. I would also like to
thank my committee members, Drs. Debski, Nagatomi and Sacks for all of their advice and help
with my thesis.
Outside of the laboratory, I also owe many thanks to my parents for the plethora of
positive energy and pixie dust that have fueled my most important achievements. Also, I would
like to thank to Kathryn Beardsley and Sol Dostilio for moral support and for convincing me
that, “yes, I would actually finish my thesis one day.”
xvi
1.0 INTRODUCTION
1.1 ANATOMY AND PHYSIOLOGY OF THE HEART
The heart propels blood through the circulation, providing necessary nutrients and removing
waste products from the many organ systems throughout the body. The mammalian heart
consists of four chambers: the left and right atria and the left and right ventricles (Figure 1). The
walls of these chambers are composed of myocardium which contracts, allowing each chamber
to function as a positive displacement pump. The right atrium fills with blood from the systemic
and coronary circulation via the superior and inferior vena cava. From the right atrium blood
moves into the right ventricle which, in turn, pumps the blood into the pulmonary circulation
where it is oxygenated in the lungs.
The left atrium fills with blood returning from the
pulmonary circulation via the pulmonary veins. This blood is pumped into the left ventricle
which, in turn, pumps the blood through the systemic and coronary circulation via the aorta and
coronary arteries.
Each cardiac chamber pumps blood through a one way valve. The mitral and tricuspid
valves, are known as the atrioventricular valves due to their location between the atria and
ventricles. These valves prevent retrograde flow from the left and right ventricles respectively
during ventricular contraction or “systole.” The mitral valve has two leaflets while the tricuspid
1
valve, as its name denotes, has three leaflets. The leaflets of the atrioventricular valves are
tethered to papillary muscles, located within the respective ventricles, via thin tendinous
structures known as chordae tendineae. A second pair of valves, the aortic and pulmonary
valves, are known as the semi-lunar valves. These valves each have three leaflets, but the
leaflets lack the chordal attachments present on the atrioventricular valves. The aortic valve is
located between the left ventricle and the aorta, while the pulmonary valve is located between the
right ventricle and the pulmonary arteries.
2
Figure 1. A cross section of the heart looking down on the four heart valves from the atria.
Reproduced from Otto CM. Valvular Heart Disease. Elsevier Inc. 2004.
3
1.2 MITRAL VALVE ANATOMY
The mitral valve (MV) serves to prevent blood regurgitation into the left atrium during left
ventricular contraction. The complete valve apparatus consists of a saddle-shaped annulus that
adjoins the base of the left atrium to the two valve leaflets (anterior and posterior), which extend
into the ventricle where they are connected to the papillary muscles via an intricate arrangement
of chordae tendineae [1-5]. The mitral annulus consists of both fibrous and muscular tissue. The
two major collagenous structures within the annulus are referred to as fibrous trigones. (Figure 3)
Thin collagen bundles called the fila of Henle stretch circumferentially from each trigone into the
mitral orifice. The annular muscle, predominant in the posterior region of the annulus, is
primarily oriented orthogonally to the annulus. When the MV is opened by cutting one of the
leaflets as in (Figure 2), no distinct separation is observed between the two leaflets. The anterior
leaflet is generally somewhat larger and has a smooth appearance while the posterior leaflet
tends to be smaller and has a scalloped texture.
4
Figure 2. A photograph of the MV leaflets. (A) anterior leaflet (P) posterior leaflet.
Reproduced from Otto CM. Valvular Heart Disease. Elsevier Inc. 2004.
5
Figure 3. Diagram from a pathological perspective with division of the septum illustrating
the fibrous continuity between the mitral and aortic valves. Reproduced from Anderson
RH, Wilcox BR: The anatomy of the mitral valve, in Wells FC, Shapiro LM (eds): Mitral
Valve Disease. Oxford, England, Butterworth-Heinemann, 1996.
6
1.3 MITRAL VALVE HISTOLOGICAL STRUCTURE
1.3.1
Tri-layered leaflet structure
The MV leaflets are composed of three membranous layers [6]. Beginning on the atrial side, the
first layer, termed the spongiosa, consists of proteoglycans, elastin, and a variety of connective
tissue cells. The spongiosa contains a relatively small number of collagen fibers when compared
to the other two layers. The core of the leaflets is named the fibrosa due to its large collagenous
content. This layer is thought to bear the majority of the loads applied to the leaflets evidenced
by the fact that collagen fibers from this layer have been shown to extend directly into the
chordae tendineae. Both the spongiosa and the fibrosa are wrapped in a thin fibrous layer
composed of densely packed elastin fibers. On the atrial side of the leaflet, covering the
spongiosa, this layer is termed the atrialis while on the ventricular side of the leaflet this layer is
termed the ventricularis. The ventricularis predominantly covers the anterior leaflet and contains
higher collagen content than the atrialis. Additionally, the ventricularis may thicken with age
due to increases in collagen and elastin content.
7
1.3.2
1.3.2.1
Passive components of the mitral valve
Collagen.
The term collagen fiber describes an intricately arranged set of
tropocollagen molecules. Three single chains are wound around each other in a left handed αhelix. Each of these chains contains approximately one third glycine, one third proline and
hydroxyproline, and one third other amino acids. These left-handed helices are then wrapped
together to form a right-handed super helix (Figure 4). The integrity of this helical structure is
maintained by the interactions of proline and glycine amino acid residues.
Additionally,
hydroxylated proline and lysine residues serve to further stabilize the structure via hydrogen
bonding interactions. These tropocollagen molecules are then assembled into collagen fibrils
(Figure 5) which are organized fibers with diameter on the scale of a single micrometer.
Figure 4. The organization of tropocollagen molecules to for collagen fibrils. Reproduced
from Fung, Y.C., Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. 1993,
New York: Springer Verlag. 568.
8
To date, over 30 distinct types of collagen have been identified. Valve leaflets are
composed mainly of type I collagen with some type III collagen. Collagen is strongest in tension
and primarily serves as a load bearing mechanism. Collagen fibers are typically crimped in their
stress-free configuration [7]. Due to this arrangement, in some cases collagen fibers may not
develop their full load bearing capacity until they are sufficiently distended.
9
Figure 5. Schematic showing the hydrogen bonding between strands that is responsible for
collagen’s strength (A) and the tri-helical structure that the three collagen strands take
when they assemble into a collagen fiber (B). Reproduced from Voet, Biochemistry, 1995
10
1.3.2.2
Elastin. Elastin fibers are composed of proline and glycine rich amino acid linkages
that do not possess the stabilizing hydroxylated or glycosylated residues present in collagen.
Elastin fibers are known to be highly distensible when compared to collagen and therefore the
mechanical contribution of elastin to load bearing is most noticeable when the collagen fibers are
not fully recruited. The highly branched structure of elastin typically contains many coiled
fibers. This coiling is hypothesized to allow the elastin fibers to retain elastic mechanical
properties even when highly distended.
1.3.2.3
Glycosaminoglycans. Glycosaminoglycans (GAGs) are composed of a series of are
negatively charged unbranched polysaccharides attached to a protein core (Figure 6). The
negative charges of the GAGs cause these molecules to be highly hydrophilic. This property
allows GAGs to retain a relatively large volume of water given their molecular weight. Because
of the GAG content, valve leaflets typically contain a large amount of water which enables them
to resist compressive forces due to the incompressibility of water.
11
1.3.3
Active components of the mitral valve
In addition to the previously mentioned passive components, the MV leaflets contain cells that
may actively contribute to the leaflets’ mechanical properties such as myocardium, smooth
muscle and contractile interstitial cells.
These cells are supplied with blood by a sparse
arrangement of blood vessels which runs throughout the leaflets. The MV leaflets are innervated
with both adrenergic and cholinergic nerves [8, 9] and recent evidence has shown that neural
control may play a role in controlling some of the finer motions of the leaflets such as regulating
the precise leaflet deformations necessary for proper leaflet coaptation.
12
Figure 6. Picture illustrates the extensive branching characteristic of GAG molecules
which account for their ability to attract and retain water molecules to enhance their
molecular volume. Reproduced from Alberts, Molecular Biology of the Cell, 1994.
13
1.3.4
Small angle light scattering analysis of collagen architecture
The orientation of collagen fibers within the MV anterior leaflet has been examined using a
small angle light scattering (SALS) technique (Figure 7). This technique consists of directing a
helium neon laser through dehydrated tissue specimens and recording the subsequent beam
diffraction [10]. According to the principles of Fraunhofer Diffraction, the laser light scatters in
a direction orthogonal to the fibers within the beam envelope. Based on this principle, the
collagen fiber orientations can be reconstructed from the recorded diffraction pattern.
14
Figure 7. A map of the collagen fiber architecture of the MV anterior leaflet. Colors from
red (highly aligned) to blue (randomly aligned) represent the degree of collagen alignment.
15
1.4 MITRAL VALVE DISEASE
Diseases of the MV can be logically separated into two categories: those that cause left
ventricular inflow obstruction, termed MV stenosis, and those that allow retrograde flow from
the left ventricle during systole, termed MV regurgitation.
1.4.1
Mitral valve stenosis
The most widely recognized symptoms of MV stenosis are associated primarily with pulmonary
venous congestion or low cardiac output. Additionally, systemic thromboembolism may occur.
In general, thromboembolic events are much more common in patients with MV stenosis or a
combination of MV stenosis and regurgitation than they are in patients with MV regurgitation
alone. The most common cause of MV stenosis is rheumatic heart disease which causes
occlusion of the mitral orifice due to structural changes, such as scarring, to the valve leaflets
[11]. 20 million cases of rheumatic fever are reported annually, with this condition being
particularly prevalent in third world countries [12]. It is believed that rheumatic MV stenosis
typically begins before the age of twenty, but may take up to thirty years to fully develop into a
clinically important condition.
Other causes of MV stenosis include MV calcification,
congenital mitral valve deformities, thrombus formation within the left atrium, and certain
inherited metabolic diseases.
Although this condition develops with a relatively long time course, preemptive treatment
is generally not performed since the primary treatment is surgical intervention. Surgical options
16
include both valvular repair and replacement. In order to repair the stenotic valve, a surgeon
typically removes the leaflet-like regions between the anterior and posterior leaflets known as
commisures in order to create a larger mitral orifice. Replacement of the MV with a prosthetic
valve may be superior to repair in this case. Patients who undergo MV replacement have a
reduced need for additional procedures in the first ten years following implantation [13].
1.4.2
Mitral valve regurgitation
The most common valve disorder, affecting five to twenty percent of the population [14], is
mitral valve prolapse (MVP) (Figs. 8, 9), in which the MV leaflets coapt improperly and allow
leakage from the ventricle into the atrium during systole. In MVP one or both of the leaflets
typically extend above the plane of the atrioventricular junction during ventricular contraction.
In the United States, MVP results in 4000 mitral valve surgical procedures (25% of all cases),
1000 cases of endocarditis (10% of all cases), and 4000 cases of sudden death [3]. Symptoms of
MV prolapse may include chest pain, palpitations, dyspnea, fatigue, and dizziness. Acute cases
of MV leakage may trigger the onset of cardiogenic shock, while chronic mitral regurgitation
may affect the geometric structure of the ventricle [15] and may lead to pulmonary edema [16].
MVP is often correlated with symptoms of myxomatous mitral valve disease such as opaque and
thickened leaflets and chordal elongation, thinning, and rupture.
Current treatment for the diseased MV includes surgical repair and valve replacement.
Repair techniques include partial leaflet resection, chordal transplantation, chordal shortening,
insertion of artificial chordae, and edge-to-edge leaflet apposition [17-21]. These methods are
17
usually accompanied with annuloplasty [22, 23] which, is thought to increase the durability of
the repair by stabilizing the valve [24].
18
Figure 8. (A, B) 2D echocardiographic images of mitral valve regurgitation in diastole and
systole respectively.
(C) Color flow Doppler image showing the eccentric jet of
regurgitation. Reproduced from Otto CM. Valvular Heart Disease. Elsevier Inc. 2004.
19
Figure 9. Typical Pressure-Volume loops for the normal heart, mitral regurgitation, and
aortic regurgitation. Reproduced from Otto CM. Valvular Heart Disease. Elsevier Inc.
2004.
20
1.5 PROSTHETIC VALVE REPLACEMENTS
In many instances, damage to the MV is too severe for the valve to be effectively repaired and
the valve must be replaced with a prosthetic valve. Mechanical valves are completely fabricated
from synthetic materials (Figure 10).
These implants pose an increased risk of
thromboembolism, so that patients require continuous anticoagulation therapy for the lifetime of
the implant.
Additionally, the hemodynamic characteristics of mechanical valves do not
perfectly duplicate those of the native valve, often causing hemolysis.
Figure 10. On-X bileaflet pyrolytic carbon mechanical aortic valve (MCRI Inc.)
21
“Bioprosthetic” alternatives (Figure 11) (made of biologically-derived, chemically modified
collagenous tissues) greatly reduce the risks associated with mechanical valves, but have limited
durability and may require anti-calcification treatment to prevent material failure [25].
Figure 11. Porcine aortic valve (Edwards Lifesciences)
22
1.6 VALVULAR COORDINATE SYSTEM
The coordinate system used to describe orientation with respect to the valve, is typically based
on the circumferential and radial specimen axes (Figure 12). The circumferential direction
describes the axis that would be created by following the mitral orifice about its circumference,
while the radial direction is defined as the direction orthogonal to the circumferential axis which
typically is parallel to the path from the atrium into the ventricle.
Figure 12. A drawing, looking down on the mitral orifice, showing the circumferential and
radial specimen axes. Reproduced from Reproduced from May-Newman and Yin. Biaxial
Mechanical Properties of the Mitral Valve leaflets. American Journal of Physiology, 1995.
23
1.7 MITRAL VALVE DYNAMICS
The proper and coordinated action of each of the components of the MV apparatus
(Figure 13) is critical to the normal function of the valve [26-28]. The majority of blood flow
through the MV occurs at the beginning of diastole. This flow is driven primarily by passive
forces supplemented with relaxation of the left ventricular myocardium and active movement of
the mitral annulus.[24]. In order to properly regulate the left ventricular volume, the mitral
orifice must become enlarged beyond the size of the aortic valve. Typically, enlargement of the
mitral orifice starts just before the end of systole and the orifice returns to its original, smaller
size at the end of diastole [2].
During ventricular systole valve closure occurs when the two leaflets coapt to form an
arc-shaped closure line. While the valve is closed, both the anterior and posterior MV leaflets
are generally shaped with a concave curvature to the left ventricle [29]. After ventricular systole
is completed, the valve leaflets open starting from the center of the leaflets [30] and quickly
reverse their curvature into a convex formation with respect to the left ventricle. Subsequently,
the leaflets straighten and the edges of the valve separate. The larger anterior leaflet then
continues to open, reaching a position more widely open than that of the posterior leaflet As
systole becomes eminent, the anterior leaflet then moves towards the closed configuration at a
much faster rate than the posterior leaflet ensuring that the leaflets coapt properly and then return
to the concave closed configuration.
Analysis of MV leaflet dynamics was performed by
Tsakiris et al [31], who measured the motions of both the anterior and posterior leaflets by
tracking radiopaque markers sutured onto the valve leaflets and annulus using film angiograms
and correlated the marker displacements with an electrocardiogram. Of particular relevance is
24
their analysis of the anterior leaflet (Figure 14) which showed the closing time of the leaflet to be
approximately 63 milliseconds and the opening time to be approximately 42 seconds.
Figure 13. Drawing of balance of forces in mitral apparatus in the left panel. In the right
panel, potential effect of papillary muscle displacement to restretch leaflet closure, causing
mitral regurgitation. Reproduced from Liel-Cohen N, Guerrero JL, Otsuji Y. Design of a
new surgical approach for ventricular remodeling. Circulation, 2000; 101: 2756.
25
Figure 14. Motion of marker placed on free edge of anterior leaflet. Reproduced from
Tsakiris AG, Gordon DA, Mathieu Y, et al: Motion of both mitral valve leaflets: a
cineroentgenographic study in intact dogs. J Appl Physiol 1975; 39:359.
26
1.7.1
Surface stretches of the anterior leaflet
A recent study by Sacks et al [32] measured the surface stretches of the anterior leaflet under
physiologic conditions by tracking graphite markers glued onto the surface of the valve leaflet in
a left-heart simulating flow loop (Figure 15). This study made use of two high speed digital
cameras that were both focused on the leaflet, but were oriented at thirty degrees to one another
such that 3D spatial coordinates could be determined from the two camera images using a direct
linear transform method. [33]. The results of this analysis confirmed that the anterior leaflet
opened in approximately 70 milliseconds and closed in approximately 40 milliseconds, and
additionally confirmed that the leaflet deformation occurred faster during opening than they did
in closure.
In this study, the authors were able to quantify the surface stretches (Figure 16) as well as
the surface stretch rates of the anterior leaflet (Figure 17). Additionally, this study showed that
after valve closure, the leaflet stretch state remained constant while the valve was held closed for
approximately 0.3 seconds during systole, before finally returning to its original configuration as
the valve opened. The surface stretches observed by Sacks et al in vitro were confirmed in vivo
in an unpublished study by Sacks et al in which sonomicrometry crystals were tracked on the
MV leaflets of living sheep (Figures. 16, 17).
27
Resistance
Atrial
Reservoir
Compliance
High-Speed Cameras
LV Simulator
Flow
Probe
Pump
Pressure Transducer
Data Acquisition System
Figure 15. Left-heart simulating flow loop used by Sacks et al to quantify the surface
stretches of the MV anterior leaflet. Reproduced from Sacks et al. Surface stretches in the
anterior leaflet of the functioning mitral valve.
28
1.2
Closed
Closing
0.8
Openin
0.6
g
Normalized major
principal stretch
1.0
In-Vitro
In-Vivo
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Normalized time
Figure 16. Principle stretches observed in left heart-simulating flow loop (closed symbols)
and in vivo using sonomicrometry method (open symbols). Reproduced from Sacks MS et
al. In-vivo dynamic deformation of the mitral valve leaflet. Annals of Thoracic Surgery.
Submitted 2005.
29
Closing
Normalized d∆/dt
1.0
0.5
Closed
0.0
-0.5
In-Vitro
In-Vivo
-1.0
Opening
0.0
0.2
0.4
0.6
0.8
1.0
Normalized time
Figure 17. Principle stretch rates versus time for the MV anterior leaflet under normal
physiologic conditions. Reproduced from Sacks MS et al. In-vivo dynamic deformation of
the mitral valve leaflet. Annals of Thoracic Surgery. Submitted 2005.
30
1.8 MECHANICAL PROPERTIES OF MITRAL VALVE LEAFLETS
May-Newman and Yin measured the mechanical properties of the MV leaflets in response to a
series of different biaxial leaflet stretch states [34]. In this study, MV leaflets were mounted in a
biaxial stretching mechanism (Figure 18) using a series of suture loops on 3 of the four leaflet
edges and directly tethering the leaflet chordae tendineae on the final edge. In this study, cyclic
stretching was applied with displacement ramp times of 10 seconds corresponding to stretch
rates of 4-12% per second.
Results of this study showed that the mechanical properties of the valve leaflets were
highly anisotropic with the circumferential axis much less distensible than the radial axis.
Additionally this study revealed that the mechanical behavior each specimen axis was highly
dependent on the stretch state of the alternate specimen axis (Figure 19). The stress-stretch
responses of both specimen axes were found to be highly nonlinear. The authors of this study
attributed this nonlinear behavior to the stretch dependent recruitment of collagen fibers.
31
Figure 18.
Experimental setup for biaxial mechanical testing of the MV leaflet.
Reproduced from May-Newman and Yin. Biaxial Mechanical Properties of the Mitral
Valve leaflets. American Journal of Physiology, 1995.
32
Figure 19. Membrane stress-stretch relations from porcine anterior (A) and posterior (B)
leaflets comparing equibiaxial (open symbols) and strip biaxial (filled symbols) protocols.
Circles, circumferential axis: triangles, radial axis. Reproduced from May-Newman and
Yin. Biaxial Mechanical Properties of the Mitral Valve leaflets. American Journal of
Physiology, 1995.
33
The nonlinear behavior measured in the quasi-static biaxial testing was similar to the
nonlinear pressure-areal stretch relationship observed by Sacks et al in their left heart-simulating
flow loop (Figure 20). In the May-Newman study, differences in the loading and unloading
stress-stretch curves were observed, though no attempt was made to quantify this behavior. In
addition to the 10 displacements, a select number of specimens were tested at higher stretch
rates, up to 40% per second for comparison. The mechanical properties of these specimens were
not found to be different from the specimens tested at the slower speeds.
Figure 20. Pressure - areal stretch relationship of the MV anterior leaflet measured in left
heart-simulating flow loop. Reproduced from Sacks et al. Surface stretches in the anterior
leaflet of the functioning mitral valve.
34
This characteristic nonlinear stress-stretch response has been observed for other valvular
materials as well. In their study on the biaxial mechanical properties of the aortic valve cusp,
Billiar and Sacks [35] reported similar nonlinearity, anisotropy and mechanical coupling (Figure
21).
Protocol 1
Protocol 2
Radial membrane stress (N/m)
Lagrangian Membrane Stress (N/m)
60
50
40
30
7
6
5
4
60
60
50
50
3
50
40
2
30
40
40
20
1
10
30
30
0
0
20
10
20
30
40
50
60
20
Circumferential membrane stress (N/m)
10
0
-0.2
20
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0
-0.2
10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0
-0.2
60
60
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0.0
0.2
0.4
0.6
0.2
0.8
1.0
1.2
0
-0.2
0.0
0.2
0.4
0.6
0.8
E
E
0.4
0.6
0.8
1.0
1.2
Protocol 7
60
0
-0.2
0.0
Protocol 6
Protocol 4
Lagrangian Membrane Stress (N/m)
Protocol 3
60
1.0
1.2
0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
E
Figure 21. (a) The seven loading protocols used to characterize the biaxial stress-stretch
response, and (b) response to all loading protocols for an AV cusp (open circles), along with
the structural model fit, demonstrating an excellent fit.
35
1.9 VISCOELASTIC BEHAVIOR
The term “viscoelastic” implies that the mechanical properties of such a material are composed
of both a time dependent (or viscous) and a time-independent (or elastic) component. Much of
the pioneering work on the viscoelasticity of living tissues was done by Fung, who summarized
the time dependence of biological tissues: “When a body is suddenly stretched and then the
stretch is maintained constant afterward, the corresponding stresses induced in the body decrease
with time: this phenomenon is called “stress-relaxation.” If the body is suddenly stressed and
then the stress is maintained constant afterward, the body continues to deform: this phenomenon
is called “creep.” If the body is subjected to a cyclic loading, the stress-stretch relationship in the
loading process is usually somewhat different from that in the unloading process: this
phenomenon is called “hysteresis.” These behaviors are all features of a mechanical property
called “viscoelasticity.” [36]
On its most basic level, viscoelasticity suggests that the time-dependent mechanical
properties of a material are dependent on the deformations to which the particular specimen has
been previously subjected; a classification often termed “stretch-history dependence.” Currently,
the viscoelastic properties of the MV leaflets remain largely unstudied, mainly due to the
complexity of the necessary experimental protocols.
36
Generally, one of three main theories is used to describe the viscoelastic mechanisms in
soft tissues.
1. Time-dependent reorientation of collagen fibers within a viscous matrix.
2. Molecular relaxations within the GAG matrix.
3. Molecular relaxations within the collagen fibers themselves.
The following subsections give information on viscoelastic testing in general.
1.9.1
Stress-relaxation testing
Stress-relaxation experiments (Figure 22) typically include a rapid loading phase to a desired
stretch level, after which, the material stretch state is held constant. The maintenance of a
constant stretch state has special implications for typical biological materials including the MV
leaflet; the lack of change in the stretch state of the material limits the ability of the fibers within
a tissue to reorient themselves for the duration of the test. Thus, changes in the specimen loading
state required to maintain the constant stretch state can be assumed to be independent of fiber
rotations. It should be noted that currently many membranous tissues are subjected to uniaxial
“stress-relaxation” tests. These tests, while important in their own right, are not true stressrelaxation experiments since deformations are possible on the free specimen axis.
37
Figure 22.
(b) The stress-relaxation responses to three different stretch histories (a).
Reproduced from Wineman AS, Rajagopal KR, Mechanical Response of Polymers.
Cambridge University Press. 2000.
1.9.2
Creep testing
In a creep test (Figure 23), a specimen is loaded to a desired load or stress level, then the loading
state is maintained for the duration of the test by adjusting the specimen stretch state. In many
instances the creep experiment provides more physiologically relevant data for bodily tissues
than are provided by the stress-relaxation test since, in vivo, most tissues are generally loaded
with a certain force rather than stretched to a certain stretch state. One disadvantage of the creep
experiment is that, unlike the stress-relaxation case, the fibers within a tissue specimen are free
38
to rotate and changes in the mechanical properties of the tissue cannot be isolated from the
dynamic rearrangements of fibers within the material.
Figure 23. The creep responses (b) to three different stress histories (a). Reproduced from
Wineman AS, Rajagopal KR, Mechanical Response of Polymers. Cambridge University
Press. 2000.
39
1.9.3
Hysteresis
Hysteresis represents the energy lost when a material is loaded. Hysteresis is typically calculated
as the ratio of the change in energy between the loading and unloading cycles to the total energy
stored in the loading cycle. Energy storage is usually determined by calculating the area beneath
the loading versus displacement curves.
1.9.4
Modeling viscoelastic behavior - the Boltzmann superposition principle
The superposition principle, developed by Boltzmann, states that the total stretch response of a
material to the application of individual stress histories is the sum of the effect of applying each
stress separately. In the one-dimensional case, we may consider a simple bar subjected to a force
F(t) and elongation u(t). The elongation u(t) is caused by the total stress history before the
current time, t. If the function F(t) is continuous and differentiable, then in a small time interval
dτ at time τ the increment of loading is (dF/dτ)dτ. This increment acts on the bar and contributes
an element du(t) to the elongation at time t, with a proportionality constant c:
du(t) = c(t − τ )
dF(τ )
dτ
dτ
(1)
If the origin of time corresponds with the beginning of motion and loading, then, by the
contributions of all loading for all time, we obtain:
t
dF(τ )
dτ
u(t) = ∫ c(t − τ )
dτ
0
40
(2)
A similar argument, with the role of F and u interchanged, gives
t
du(τ )
F(t) = ∫ k(t − τ )
dτ
dτ
0
(3)
These laws are linear. Scaling the load by a given factor causes the elongation to be scaled by
the identical amount, and vice versa. The functions c(t-τ) and k(t-τ) are the creep and relaxation
functions, respectively. The application of the Boltzmann principle of superposition allows the
use of a limited amount of experimental data, from both static and time dependent experiments,
to predict the mechanical response of a tissue to a wide number of loading conditions.
1.9.5
Modelling viscoelastic behavior - quasilinear viscoelasticity
In order to adequately model the viscoelastic properties of soft tissues under finite deformations,
the non-linear stress-stretch characteristics of the tissue must be considered [37]. For this reason
Fung has developed a theory known as quasi-linear viscoelasticity (QLV) in which the relaxation
function, K(ε,t), is dependent on time (as in the linear viscoelasticity formulation) as well as
stretch level. This theory is termed “quasi-linear” because the relaxation function may be
separated into a reduced relaxation function, G(t) that is a function of time only and an elastic
response, σ (e) (ε) that is a function of stretch only.
41
K (ε , t ) = G (t )σ ( e ) (ε )
(4)
In this formulation, the generalized form of G(t) proposed by Fung is given by:
−
∞
G (t ) =
t
1 + ∫ S (τ )e τ dτ
0
∞
1 + ∫ S (τ )dτ
0
(5)
where S(τ) is defined based on the stress response of the material to be modeled. Experimental
evidence has shown that the relaxation of soft tissues tends to decrease with time. This behavior
can be modeled simply using the following formulation:
S (t ) =
c
τ
(6)
for τ1 ≤ t ≤ τ2 where c is the magnitude of relaxation, τ1 is the short time constant and τ2 is the
long time constant.
QLV has been used previously to model many soft tissues such as ligament [38], bladder
[39] and valvular materials [40] to name just a few. QLV is analysis is very attractive because
the QLV formulation is formed from continuous functions and the viscoelastic behavior may be
described using only three physically meaningful mathematical parameters.
42
1.9.6
Stretch rate sensitivity in soft tissues
The hypothesis that the mechanical properties of the MV anterior leaflet may be sensitive to
stretch-rate, necessitating the need to define the mechanical properties of the valve under
physiologic stretch rates, is based on several observations of the stretch rate sensitivity of the
MV leaflet and other soft tissues throughout the biomechanical literature. The dynamic
viscoelasticity of the MVAL was investigated by Lim et al. [41] who measured the bulge height
of the MV leaflet in response to sinusoidal pressure gradients applied at frequencies varying
from 0.5 to 5.0 Hz. Their results suggested that the mechanical properties of the valve were
dependent on stressing frequency. This finding was supported by a study by Leeson-Deitrich et
al. [42] who used a uniaxial tension testing mechanism to test porcine pulmonary and aortic
valve leaflet strips and reported that the average leaflet stiffness increased with stretch rate.
Results for other soft tissues have revealed varying behaviors among different tissues.
Naimark et al. [43] explored the effects of uniaxial loading rate on mammalian pericardia and
showed that the stress-stretch relationship for pericardia was not dependent on stretch rate. Woo
et al. [38] found that the stress-stretch relationship for the canine medial collateral ligament was
only slightly affected by stretch rate while a study by Lydon et al. [44] measured the affects of
elongation rate on the rabbit anterior cruciate ligament and found that the stress-stretch response
of the ligament was highly dependent on elongation rate. Haut and Little [45] explored the
effects of stretch rates on rat tail tendon and observed that the stiffness of the tendon was
affected slightly by stretch rate, but that the failure stretch increased dramatically with stretch
rate.
43
Additional studies have explored the effects of loading rate on biologically derived
valvular materials, again with varying results. Lee et al. [46] performed uniaxial experiments on
glutaraldehyde-stabilized porcine aortic valve leaflet strips and found that the stress-stretch
relationship was dependent on stretch rate in the circumferential direction and independent of
stretch rate in the radial direction.
Overall, the stretch rate sensitivity of soft tissues appears to be highly tissue specific and
dependent on the specific experimental protocol. The variation in the findings of these studies
underscores the necessity for characterization of the MV leaflet mechanical properties under the
physiologic condition.
1.9.7
Creep and stress-relaxation in soft tissues
In addition to the stretch rate sensitivity, the creep and relaxation aspects of MV leaflet
mechanical behavior remain to be explored. These tests are particularly relevant to the 300
millisecond constant stretch phase observed in the leaflet surface during valve closure.
Of particular relevance to this study is a recent study by Liao and Vesely [40], in which
uniaxial stress relaxation experiments were performed on the porcine MV chordae tendineae.
This study reported relaxation percentages between 30% and 60% after 100 seconds and went on
to link the amount and rate of relaxation to the glycosaminoglycan (GAG) content of the
individual chordae. Although the investigations into the stress-relaxation and creep response of
the MV leaflets are non-existent to the author’s knowledge, the creep and relaxation literature for
soft tissues reveals some interesting behaviors that should be investigated in the MV.
44
Provenzano et al [47] explored the relaxation and creep behavior of the rat medial
collateral ligament (MCL) and found that the rate of relaxation was nonlinearly inversely
proportional to the stretch level and that the rate of creep was nonlinearly directly proportional to
the applied stress. Dunn and Silver [48] showed that the amounts of relaxation in aorta, skin,
tendon, dura matter and pericardium were all dependent on stretch level. In contrast to these two
studies, Lee et al [46] found that the percentage of stress remaining in glutaraldehyde-stabilized
porcine aortic valve strips after a 1000 second uniaxial stress-relaxation test was independent of
initial load. In their study of the rabbit MCL, Thornton et al observed an imbalance between
stress-relaxation and creep rates of MCL specimens initially loaded to the same level [49]. To
quantify their results, Thornton et al fit the MCL relaxation data with a quasilinear viscoelastic
(QLV) model and used this model to predict the MCL creep behavior. A comparison to the
actual creep data showed that the QLV formulation predicted much higher creep percentages
than those actually observed (150% predicted versus 115% observed). These findings were
supported by the findings of the previously mentioned study by Provenzano et al [47] in which
the rate of stress-relaxation proceeded approximately two times faster than the creep rate in the
rat MCL when contralateral ligaments were tested simultaneously. Vesely et al [50] expanded
on these findings by showing that the stress-relaxation behavior of porcine aortic valve cusps
was highly dependent on the initial rise time. As seen in the stretch rate sensitivity literature, it is
clear that the creep and relaxation responses in different studies are highly tissue specific.
Additionally, the experimental factors such as initial rise time, initial stretch/load level and test
duration heavily influence the results.
45
1.10
MOTIVATION FOR THE CURRENT STUDY & STUDY AIMS
The ultimate goal for any MV repair or replacement is to permanently reproduce the functional
properties of the native valve. Studying the mechanical properties of the native valve will
provide the necessary data for the qualification of suitable prosthetic materials. Additionally, an
in-depth understanding of the relationship between the valvular function, macrostructure, and
microstructure may provide motivation for the progression of novel repair techniques as well as
the development of suitable tissue-engineered replacement materials. The primary objective of
any biomechanical study should be to first describe the functional properties of the valve. The
investigation of biomaterial behavior under non-physiologic conditions does supply useful
information and may provide insight into the inner workings of a given material, but this
information is of much greater value when it complements a complete understanding of the
physiologically relevant material properties.
In the case of the MV, the valve leaflet is a thin and nearly incompressible membrane.
Therefore, planar biaxial testing can be used to quantitatively characterize its mechanical
properties [51]. In the work by May-Newman and Yin discussed previously [34], quasi-static
(stretch rates of 4% to 12 %/second) biaxial experiments were performed on the MV leaflets.
This work provided biomechanical data by subjecting MV leaflet specimens to a range of biaxial
stretch-based protocols and this data was later used to develop a stretch energy-based
constitutive model for a generalized loading state [52]. This study provided a valuable data, but
was performed before a complete understanding of MV surface stretches was available. The
recent study by Sacks et al [32], in which the surface stretches of the leaflet were measured in a
left heart-simulating flow loop, showed that the stretch rates of the MV anterior leaflet were on
46
the order of 1000% per second, more than an order of magnitude greater than the maximum
stretch rates employed in the May-Newman study. In addition to the stretch rate analysis, the
study by Sacks and colleagues reported the stretch states of the leaflet under physiological
conditions, thus providing the necessary data to reasonably replicate the in vivo loading
condition of the valve leaflet under controlled conditions in a biaxial stretching mechanism. It is
critical to determine if previously reported quasi-static biomechanical data can be used to model
the behavior of the valve in the physiological condition, since the application of any such model
(i.e. to optimize MV repair or replacement techniques) would be used to predict behavior under
physiological conditions.
47
1.10.1
Specific study aims
The goal of this work was to expand on previous studies by quantifying the biaxial viscoelastic
properties of the MV anterior leaflet under physiological conditions. Specific aims were:
1. To develop a biaxial testing device capable of testing MV leaflet specimens under
physiologic stretch and loading conditions at physiological stretch rates.
2. To determine the stretch rate sensitivity of the MV anterior leaflet when loaded to
physiologic stretch levels at stretch rates ranging from quasi-static to physiological.
3. To determine the stress-relaxation and creep responses of the MV anterior leaflet at a
physiologic stretch or loading state with physiologic initial rise times.
48
2.0 METHODS
2.1 HIGH-SPEED BIAXIAL TESTING DEVICE
2.1.1
Device specifications
The following section describes the factors taken into account in the design of the high-speed
biaxial testing device. These specifications were deemed to be those necessary to adequately
represent the physiological properties of the MV leaflet.
2.1.1.1
Displacements and displacement rates. In order to adequately reproduce the stretch
rates experienced by the MVAL in vivo, the necessary displacements and displacement rates for
the actuation components were determined based on the in vitro findings of Sacks et al in their
left heart-simulating flow loop [32]. In this study, the mean circumferential and radial stretches
were 1.11 and 1.33 respectively (refer to INTRODUCTION as necessary). To calculate the
maximum stretches for the device requirements, the standard deviations of the circumferential
and radial stretches, 0.07 and 0.16 respectively, were multiplied by three and added to the mean
values. This stretch range was chosen in order to encompass 99% of the MVAL specimens. The
specification for the maximum specimen stretches calculated in this manner were 1.31
(circumferential) and 1.80 (radial). To translate the maximum stretches into displacements, they
49
were multiplied by the appropriate maximum expected specimen dimension.
Maximum
specimen dimensions were estimated to be 3 cm x 3cm based on previous experience. These
dimensions resulted in maximum displacements of 0.93 cm (circumferential) and 2.40 cm
(radial). These displacements were divided by two to account for the fact that each specimen
axis would be stretched by two actuators (one on each free edge) for maximum displacements of
0.47 cm (circumferential) and 1.20 cm (radial) per actuator.
Using the calculated displacements, the maximum necessary displacement rates were
calculated by dividing the necessary displacements by the shortest required loading time. The in
vitro data showed the physiological opening and closing times to be approximately 0.07 seconds,
so the shortest desired loading time was chosen to be 0.05 seconds to provide sub-physiological
loading rates.
This resulted in maximum required displacement rates of 0.093 m/s
(circumferential) and 0.24 m/s (radial) per actuator.
These displacement rates were then
multiplied by a safety factor of 2 in order to account for the influence of edge effects on the
overall loading.
This provided a final displacement rate specification of 0.19 m/s
(circumferential) and 0.48 m/s (radial) for each actuator.
2.1.1.2
Maximum loads. The maximum loads on the device carriages were calculated by
estimating the membrane tension, T (defined as the load per unit length over which it is applied),
on the leaflet under physiological conditions. Assuming the valve was roughly spherical with a
radius of 10 mm when loaded, the Law of Laplace was used to calculate T:
T=
PR
2
(7)
50
where P is the transvalvular pressure and R is the radius. Substituting a transvalvular pressure
value of 120 mmHg [3] into this equation yielded a T=79.99 N/m. It was preferable for this
estimate to slightly overestimate the physiological condition because this would make it more
likely that the physiologic condition would be included in the load range, so this estimate was
rounded up to 90 N/m (+10%). This peak membrane tension level was converted to axial load
by multiplying by the largest expected specimen dimension (3 cm). This yielded a peak load
value of 2.7 N. This was converted to grams by multiplying by unit conversion factor of 101.97
g/N to yield peak loads in grams of 275.32. Because the stretch rate sensitivity of the MV tissue
was unknown at this point in the design process, this value was rounded up to 1000g to account
for any stretch rate sensitivity in the stress response of the leaflets.
2.1.1.3
Stretch & load measurement frequency.
Using the 0.05 second minimum
loading/unloading time, the maximum necessary stretch and load measurement frequencies were
calculated by dividing the minimum number of data points desired by the 0.05 second duration.
The minimum number of desired data points was estimated at 25. Approximating the stretch
response of the MV leaflet to be roughly linear with respect to time during loading and unloading
(see INTRODUCTION), 25 data points would allow a maximum stretch step of 0.032 between
image acquisitions.
Dividing 25 by the 0.05 second minimum loading duration yielded a
necessary stretch measurement frequency of 500 Hz.
The load frequency was calculated by multiplying the stretch acquisition frequency by
10. This was done to allow each load data point to represent the average of 10 load acquisitions.
51
This technique was employed successfully on the previous biaxial testing device to reduce noise
levels in the load signal.
52
2.1.2
Device design
The following section describes the specific components used in the design of the testing
apparatus in order to meet the design specifications provided in the previous section.
2.1.2.1
Device overview
Figure 24. The high-speed biaxial testing device mounted on a vibration isolation table.
53
The high-speed biaxial testing device (Figures 24, 25) consisted of four linear positioners,
each driven by a stepper motor. The positioners were arranged around a central specimen bath,
with each specimen carriage arm reaching into the bath from a direction orthogonal to its axis of
travel. The positioners and bath were mounted on a custom-designed support fixture that was
built to be mounted on a vibration isolation tabletop. This fixture raised the bath and positioners
6” above the tabletop so that the specimens could be imaged from below using a 45° mirror
configuration. Cameras were mounted separately on a single camera stand that allowed precise,
spatial adjustments on 3 axes. In addition to holding the specimen and fluid, the bath had inflow
and outflow tubing connectors that allowed the bath fluid to be pumped into a heat exchanger so
that fluid temperatures could be maintained at physiologic levels. The device was controlled
with a dual computer system (Figure 26), with one computer designated for high-speed imaging.
54
a
d
b
a
b
f
i
h
j
C
C
g
e
b
b
a
a
Figure 25. Overhead schematic of the high speed biaxial testing device; a) stepper motors;
b) screw-driven linear actuators; c) load cells; d) specimen bath outlet; e) specimen bath
inlet; f) heating element maintained bath temperature at 37°C; g) high speed digital
camera; h) standard digital camera; i) beam splitter; j) sub specimen mirror.
55
2.1.2.2
Actuation components. The new biaxial stretching device was designed to meet the
displacement requirements while accelerating smoothly and stopping precisely in order to
prevent overstretching and to minimize excessive vibrations associated with rapid accelerations
and decelerations that could potentially result in specimen damage and generally decrease the
levels of test repeatability and validity.
To accomplish this, four ball-screw driven linear positioners (404XR, Parker Hannafin
Corp., Irwin, PA), each equipped with a 20mm lead capable of achieving a maximum carriage
velocity of 1 m/s and maximum carriage acceleration of 25 m/s2 were mounted in an opposing
fashion such that one pair of positioners was aligned to stretch a centered tissue sample along
one device axis and a second pair of positioners was aligned, with orientation orthogonal to the
first pair, to stretch the sample along the second device axis. These linear positioners were
coupled with rotary stepper motors (OS22B-SNL10, Parker Hannafin Corp., Irwin, PA). Each
stepper motor was driven with a microstepping drive (E-AC, Parker Hannafin Corp., Irwin, PA)
that provided a step resolution of 50,800 steps per revolution, which, when coupled to each
aforementioned linear positioner resulted in a spatial resolution of approximately 0.394 µm for
each positioner carriage. All stepper motors were controlled via a 4-axis PCI motion controller
card (DMC 1840, Galil Motion Control Inc., Rocklin, CA) that was installed in the device
control PC (Precision 550, Dell Inc., Round Rock, TX) (Figure 26).
56
Stepper
Motors
Motion
Controller
Load
Cells
Analog/Digital
Converter
Camera
IEEE 1394
Port
Control Computer
High-Speed
Camera Trigger
High-Speed
Digital Camera
Frame
Grabber
Frame
Grabber
Frame
Grabber
High-Speed
Camera Computer
Figure 26. Two computers used to control the biaxial testing device.
57
2.1.2.3
Specimen attachments. Custom attachment arms (Figure 27) were mounted onto the
carriage of each linear positioner in order to provide a mechanism for specimen attachment.
Leaflet specimens were mounted to these attachment arms in a trampoline fashion by attaching
two loops of 000 nylon suture to each side of the specimen via four stainless steel surgical
staples. The attachment arms were designed to fasten the two specimen suture loops and to
transmit the total load applied by each actuator evenly through all of the attached suture lines.
To accomplish this, each attachment arm was furnished with a pair of custom stainless steel
pulleys which were free to rotate, ensuring that the forces applied through each pulley were
balanced between both of the surgical staple attachments for the attached suture loop. Both
pulleys were mounted symmetrically on either side of a central stainless steel ball bearing. This
mechanism distributed the total force applied by the positioner equally between both pulleys.
This attachment mechanism was based on the previously reported suture attachment pulley
system, but improved on that mechanism by ensuring that the orientation of each suture line was
aligned with the specimen plane.
58
A
B
C
Figure 27. A CAD model of one suture attachment arm. (A) Custom suture attachments
were designed to balance the force applied by each carriage through all four suture lines.
(B) Specimens were mounted to these attachment arms in a trampoline fashion by
attaching two loops of 000 nylon suture to each side of the specimen via four stainless steel
surgical staples. (C) Specimen.
59
2.1.2.4
Specimen bath. The cross-shaped specimen bath (Figure 28) was designed to allow
room for the carriage arm/specimen attachment travel required to achieve the necessary
specimen displacements. The cross shape was used because it minimized the volume of the bath
while still allowing adequate travel lanes for the portions of the specimen attachments that
reached into the bath. The central portion of the bath base contained a custom acrylic specimen
viewing window. Unlike the rest of the bath, this window was highly polished, allowing a clear
image to be taken from beneath the bath. The window doubled as a specimen stand. This stand
supported the specimen so that it did not move vertically when the applied membrane tensions
were not high enough to keep the specimen perfectly taut. The original prototype specimen
window was thin and level with the bottom of the bath, but it was discovered in testing that small
vertical specimen motions could cause problems with image focus and could introduce some
stretch measurement error since, from the camera viewpoint, the markers appeared to move apart
as the specimen moved closer to the camera, thus increasing the size of the specimen in the
camera image.
2.1.2.5
Stretch and load measurement. Leaflet deformations were measured optically with
a dual camera digital imaging system (Figure 29). The first camera (XCD-X700, Sony, Tokyo,
Japan) acquired images with a pixel resolution of 1024 x 768 at an acquisition rate of 15 frames
per second. These images were stored in the device computer memory in real-time via a
Firewire (IEEE 1394) port and were used for control purposes during quasi-static preloading
cycles and to acquire data in the later portions of stress-relaxation and creep experiments.
During high-speed cycles and the initial loading phases of stress-relaxation and creep
experiments an auxiliary high-speed digital imaging system (FastCamera 13, Fast Vision,
60
Nashua, NH) was engaged. This imaging system made use of a 4 megapixel complementary
metal oxide semiconductor (CMOS) image sensor with a maximum resolution of 1240 x 1024
and acquisition speed of 1000 frames per second. This high speed camera was controlled with a
second PC that contained 3 high-speed frame grabbers (FastFrame 1300, Fast Vision, Nashua,
NH) (Figure 26). Because of the high frame rates, images from the high-speed imaging system
were not available in real-time and could not be used for control purposes.
Figure 28. A CAD model of the cross-shaped specimen bath with specimen window/stand.
61
Figure 29. The dual biaxial testing device dual camera system.
These images were downloaded after each test and analyzed separately. Both cameras were
equipped with 55mm telecentric lenses (H52-271, Edmund Optics, Barrington, NJ) which were
focused through a 60-40 beam splitter in order to ensure that both cameras maintained identical
specimen views. The greater portion (60%) of the light was directed towards the high-speed
62
imaging system since this system was more sensitive to light intensity levels due to the rapid
image acquisition rates it employed. The specimens were mounted with an orientation parallel to
the specimen plane and a sub-specimen 45° angled first-surface mirror was used to direct the
camera views to the lower specimen surface. In addition to acquiring images, the high-speed
frame grabbers received an image acquisition trigger signal from an analog/digital converter
(PCI-6036E, National Instruments, Austin, TX) within the device control computer. This trigger
signal served to synchronize the acquired images with load measurements that were acquired by
the device control computer from a pair (one on each device axis) of load cells (Model 31,
Honeywell Sensotec, Columbus, OH) via the analog/digital converter. The specification for
hysteresis in each load cell was 0.5%. All data acquisition and image analysis was accomplished
using custom software routines (see Device Algorithms) written using the LabView virtual
instrumentation package (Version 6.i, National Instruments, Austin, TX).
2.1.3
2.1.3.1
Device software
Marker identification. All images were recorded as 8-bit grayscale images. This
resolution provided 256 image intensity increments from black (intensity = 0) to white (intensity
= 255). In order to facilitate the location of the graphite markers within the specimen images, an
intensity threshold was defined for each experiment which transformed the grayscale specimen
images into black and white bitmaps (Figure 30). This was convenient because the graphite
markers were typically much darker than the leaflet surface.
63
Figure 30. A sample bitmap showing four markers (black) and the user-defined marker
subregions (green).
This image thresholding technique did not always perform perfectly since, occasionally, the
intensity levels of dark markings on the tissue surface or small shadows caused by leaflet surface
textures were similar to those of the graphite markers. To correct for this, two additional
algorithms were used to identify the markers. First, image subregions were defined for each
marker. Once defined, detection of a given marker was only performed within the specified
image subregion. The main purpose of this technique was to eliminate the detection of erroneous
marker-like shapes that were sufficiently spatially separate from the markers themselves.
Because the marker positions within the image moved throughout the test, once a marker was
identified within a subregion, the subregion was translated such that it was re-centered on the
marker. By translating the subregions with the markers in this way, markers always stayed
within the defined subregion as long as they did not translate out of the image subregion in the
time duration between individual frames (approximately 0.1 seconds for the device control
64
camera and 0.002 seconds for the high speed digital camera). To reduce the chances of this
occurring, the size of each individual marker subregion was increased to a level that
accommodated the motions of the particular marker between frames.
After the marker
subregions were defined, a size threshold was applied to any markers that were identified within
the subregions. This was helpful due to the fact that discolorations on the surface of the leaflets
were usually much larger than the graphite markers and had the added benefit of reducing the
sensitivity of the marker tracking system to image noise, which occasionally caused small image
areas (usually in the single pixel range) to become dark. Marker subregions and detected
markers from the device control camera were plotted in green on the device computer monitor
specimen image display in real-time so that marker tracking could be visually confirmed. Once
markers were located, their precise image coordinates were calculated as the center of area of the
pixels below the image intensity threshold.
2.1.3.2
Stretch calculation. The stretch calculation method used is well documented for soft
tissues [53, 54]. First, consider this generalized homogenous biaxial deformation:
(8)
where X and x are the location of a particular material particle in the reference and deformed
configurations respectively, λ is the stretch ratio, and κ describes the in-plane shear angle.
65
Figure 31. Marker coordinates were mapped into an isoparametric coordinate system.
In the biaxial testing protocol, Xn (where n is the marker number) are the pixel coordinates of the
marker positions in the reference configuration and xn, are the time-dependent marker
coordinates calculated during the test. Shape functions are used to map the real pixel coordinates
into an isoparametric coordinate system (Figure 31) such that the marker displacements u, can be
calculated as the linear sum of the isoparametric shape functions:
(9)
66
where f is the set of isoparametric shape functions, m is the total number of markers, n denotes a
specific marker in the set of m markers, and r and s are the isoparametric coordinates. The
spatial derivatives of u with respect to r and s can then be calculated as:
(10)
which can be substituted into:
(11)
to calculate the spatial derivatives of u with respect to x. These spatial derivatives form the basis
of the deformation gradient tensor, F, from which λ and κ can be determined by:
(12)
This procedure was used to calculate the stretch state of at the center of the marker array,
(0,0) is the isoparametric coordinate system.
All reported stretch levels were the levels
interpolated at this location. For this study, four markers (a 2 by 2 array) were used, providing a
bi-linear interpolation of the displacement field. It should be noted that, although it was not
used, the biaxial device also included provisions for 9 marker (3 x 3 array) interpolation that
could allow bi-quadric variation of the displacement field.
67
2.1.3.3
Quasi-static control.
Due to the non-linear and highly variable mechanical
properties of the MV anterior leaflets, the only variables that could realistically be controlled in
the quasi-static testing were the loading and unloading time and the upper (peak tensions) and
lower (tare configuration) tension limits. In a typical quasi-static loading and unloading cycle,
the device carriages moved with constant velocities for the prescribed loading period in order to
stretch the centered specimen from the tare configuration to the peak tension limit, reversed
direction after the prescribed loading period, then stopped after returning to their original
location. Pairs of opposing carriages always moved with the same velocity in order to prevent
the specimen from moving out of the camera view, but the two pairs of carriages usually had
different velocities in order to account for anisotropic specimen behavior. In the first quasi-static
cycle of a given specimen, the carriage velocities were calculated based on stretch estimates
input by the user. In this study, these guesses were based on pilot studies of other leaflets as well
as experience with other test specimens within the study.
Because the carriage velocities
required to reach the 90 N/m tension state were highly variable, it was rare that the initial
carriage velocity guesses were sufficient. For this reason automated corrections were made to
the carriage velocities between cycles. Corrections for each axis were made independently,
without considering the correction made on the opposing axis. If the desired peak tension was
not reached for a given specimen axis in the desired loading period the following correction was
made to the carriage velocity:
desired
⎛ T peak
vc = vo ⎜ measured
⎜T
⎝ peak
⎞
⎟(C f
⎟
⎠
)
(13)
68
In this formulation, vo is the corrected carriage velocity, vc is the corrected carriage velocity,
Tpeak is the peak membrane tension, and Cf is a user defined correction factor (typically 0.3 for
the MV leaflet). The correction factor was used in many of the correction algorithms as a
method to decrease the magnitude of the correction. This factor allowed the user to tune the
correction algorithms and was very helpful when making corrections to the MV leaflet due to its
highly nonlinear mechanical behavior. In essence, the correction factor allowed this linear
velocity correction to incrementally make the necessary nonlinear correction over a number of
cycles while reducing the propensity of the correction algorithm become stuck in over- and
under-correction patterns that are common when linear corrections are made and nonlinear
corrections are necessary. Additionally, this correction factor helped reduce the propensity of
the correction algorithm to become stuck in over- and under-correction patterns due to the
simultaneous corrections (and therefore related coupling effects) on both specimen axes. If,
instead of underestimating, the system overestimated the required carriage velocities a different
correction was made. If the carriage velocities were too high, the specimen was not stretched for
the entire prescribed loading period. Instead, the carriages were stopped once one (or both) of
the specimen axes reached the desired peak tension limit. This was done as a safety measure to
prevent specimen damage from over-distension. Once the carriages were stopped, they were
held for the duration of the loading time before returning to their original configuration. In this
case the carriage velocity correction was given by:
⎛ t measured
peak
vc = vo ⎜ desired
⎜ t
⎝ peak
⎞
⎟(C f
⎟
⎠
)
(14)
69
In this formulation, tpeak is the time to reach the peak tension level in the loading cycle. The
effectiveness of these correction algorithms was obviously highly dependent on both the initial
carriage velocity guesses and the correction factor. Generally, the 90 N/m equitension level was
reached in the proper loading duration (15 seconds in this experiment) by the third
loading/unloading cycle. In addition to correcting the initial carriage velocity guesses, the
correction algorithms allowed the carriage velocities to adapt as the specimen properties shifted
due to preconditioning in the initial cycles.
2.1.3.4
High stretch rate testing. The high stretch rate testing was always performed after
an initial set of 20 quasi-static cycles. Unlike the quasi-static cycles, corrections were not made
between the high stretch rate cycles. Instead the carriage velocities from the final quasi-static
cycle were simply scaled to accommodate the higher loading times. For instance, the carriage
velocity on a given device axis for the first, 1 second high-speed cycle was calculated by
multiplying the carriage velocity used in the final 15 second quasi-static cycle by the ratio of
quasi-static cycle time to the high-speed cycle time (or 15 in this case). This control method
ensured only that the specimen would be loaded and unloaded over the desired high-speed
duration to the same carriage displacements reached at the peak of the final quasi-static cycle and
back to the tare configuration. Only if the specimen under test did not exhibit any stretch rate
sensitivity, would this control method load the specimen to the 90 N/m equitension state.
2.1.3.5
Stress-relaxation testing. The algorithms used to control the stress-relaxation test
were very similar to those used to control the high stretch rate testing. As in the high-speed
70
cycles, a stress-relaxation experiment always followed a set of quasi-static cycles and the
carriage velocities used in the final quasi-static cycle were simply scaled to calculate the carriage
velocities required to load the specimen in the 0.1 second rise time. The difference between the
stress-relaxation and high-speed loading/unloading cycles was that, after loading the specimen,
the carriages were simply held at the peak load configuration for the duration of the test in the
case of stress-relaxation.
2.1.3.6
Creep testing. As in the high-speed loading/unloading and stress-relaxation tests, the
creep test was always performed after a set of quasi-static cycles. The carriage velocities
required for the initial 0.1 second loading in the creep test were again calculated by appropriately
scaling the quasi-static carriage velocities. The difference between the creep experiment and the
stress-relaxation experiment was that, after the initial loading was completed, another algorithm
was used to move the device carriages such that the 90 N/m equitension state was maintained for
the duration of the test. The creep algorithm recalculated this carriage velocity approximately 10
times per second using the following formula:
V = (90 − Tmeasured )( S f )
(15)
where V is the carriage velocity, Tmeasured is the current membrane tension and Sf is a scaling
factor that converts the membrane tension difference into the appropriate velocity. In this
formulation, negative carriage velocities corresponded to compressions while positive carriage
velocities corresponded to stretches. As in the quasi-static tension control, the carriage velocity
71
for each axis was evaluated separately, ignoring any mechanical coupling effects between
specimen axes.
The creep algorithm relied heavily on the fact that the MV was not sensitive to stretch
rate. Had this not been the case, the initial loading would not have brought the specimen to the
desired 90 N/m equi-tension state and the effectiveness of the creep control algorithm to
effectively correct such a possibly large discrepancy is questionable.
2.2 CHARACTERIZATION OF DEVICE PERFORMANCE
2.2.1
Stretch measurement system
In order to measure the performance of the stretch measurement system, artificial marker arrays
with known deformations were created using SolidWorks CAD software. The prescribed
stretches were chosen to be representative of the physiologic stretch levels observed in the MV
anterior leaflet. These marker arrays were printed onto paper and the individual printed paper
marker arrays were placed on the specimen window facing down. All of the marker tracking
methods that were used on actual specimens (see Marker tracking) were carried out on the paper
marker arrays. The specimen stretches calculated by the biaxial testing software were then
compared to the prescribed stretches to evaluate the accuracy of the marker tracking method.
72
2.2.2
Load cell calibration
Load cells were calibrated using a custom calibration fixture (Figure 32) which allowed weight
standards to be applied to the specimen attachments. This custom fixture attached to the side of
the specimen bath and contained 2 pulleys. Using these two pulleys, the weight of a standard
could be redirected, via suture similar to that used in actual testing, to the specimen attachment
suture pulleys. A two point calibration procedure was carried out using weights of 1 kg and no
weight (0 load condition) until the calibration was repeatable, then the linearity of the load cells
was tested by hanging a 500 g weight. The weight of the paper clip attachment was 1.3 g and
was compensated for in the calibration and measurement results.
73
Figure 32. A photograph of the calibration fixture mounted on the bath.
74
2.2.3
Ability to reach quasi-static peak loads
The ability of the device of reach desired peak loading state was evaluated using a latex
specimen. For this experiment, peak loads were set at 300g for both axes. Peak specimen loads
were measured for 10 quasi-static cycles to assess the ability of the device to reach the desired
peak loads.
2.2.4
Load cell momentum sensitivity
In order to assess the effects of rapid motion on the load cells, carriage displacements similar to
those predicted for testing were performed without any loads on the load cells. This test
measured the sensitivity of the load cells to rapid motions. In this test, one axis was totally
unloaded while the other axis was sutured with a latex sample and was loaded to a stretch of 1.1
over 0.2 seconds.
75
2.2.5
System relaxation
In order to ensure that any stress-relaxation observed in the leaflet testing was real and not
simply a relaxation in the test system components, a relaxation test was performed with the
opposing sutures hooked to each other without any specimen. By performing a test in this way,
the relaxation of the system was quantified and any relaxation greater than that observed in the
system itself could be considered real. Suture sets were loaded to a tension of 200g in 0.1
seconds and subsequent relaxation was measured for 3 hours.
76
2.3 BIAXIAL TESTING OF THE MV ANTERIOR LEAFLET
2.3.1
Specimen preparation
One set of eight (designated for stretch-rate sensitivity analysis), a second set of eight
(designated for biaxial stress-relaxation experiments), a third set of six (designated for uniaxial
stress-relaxation experiments) and a fourth set of six (designated for biaxial creep experiments)
fresh porcine anterior MV leaflets were obtained from a local slaughterhouse (Table 1). Hearts
were obtained immediately after slaughter whereupon the anterior leaflets were removed from
each heart and were then stored in a phosphate buffered saline (PBS) solution and frozen for no
longer than one week for later use. Prior to testing, each leaflet was thawed at 37°C and trimmed
to provide a square specimen with sides parallel to the circumferential and radial axes of the
leaflet (Figure 33). Specimens were carefully cut out so that each specimen was centered
circumferentially on the anterior leaflet and extended radially from just below the annulus to just
above the first chordae tendineae attachment site.
Trimmed specimens had dimensions of
9.9±0.6 mm x 9.5±0.9 mm x 0.75±0.05 mm (thickness measured in the center of the specimen);
specimen dimensions were measured by hand using calipers.
In order to attach the square
specimen to the biaxial testing device, four evenly spaced suture lines were hooked through each
side of the specimen with stainless steel surgical staples (for uniaxial experiments 2 edges were
left free). To provide a basis for optical stretch measurement 4 small graphite markers (~ 250
µm in diameter) were glued to the specimen center using a cyanoacrylate adhesive (Permabond,
Somerset, NJ) in a 2 x 2 array formation with dimensions of approximately 3mm x 3mm.
77
Table 1. Specimen database
Specimen
HS1
HS2
HS3
HS4
HS5
HS6
HS7
HS8
BSR1
BSR2
BSR3
BSR4
BSR5
BSR6
BSR7
BSR8
CSR1
CSR2
CSR3
RSR1
RSR2
RSR3
C1
C2
C3
C4
C5
C6
Test
High Stretch Rate
High Stretch Rate
High Stretch Rate
High Stretch Rate
High Stretch Rate
High Stretch Rate
High Stretch Rate
High Stretch Rate
Biaxial Stress-relaxation
Biaxial Stress-relaxation
Biaxial Stress-relaxation
Biaxial Stress-relaxation
Biaxial Stress-relaxation
Biaxial Stress-relaxation
Biaxial Stress-relaxation
Biaxial Stress-relaxation
Circumferential Stress-relaxation
Circumferential Stress-relaxation
Circumferential Stress-relaxation
Radial Stress-relaxation
Radial Stress-relaxation
Radial Stress-relaxation
Creep
Creep
Creep
Creep
Creep
Creep
78
Circ (mm) Rad (mm) Thickness (mm)
10
10
0.7366
9
9
0.635
11
10
0.8128
12
11
0.7874
9
9
0.762
9
8
0.6096
10
9
0.7112
10
10
0.8128
10
9
0.80
10
9
0.72
10
10
0.69
11
11
0.75
10
9
0.78
9
9
0.80
10
9
0.79
10
9
0.65
9
10
0.81
9
10
0.76
10
11
0.75
9
10
0.83
10
10
0.67
11
9
0.78
10
9
0.74
11
11
0.75
11
11
0.71
10
11
0.82
9
9
0.81
9
9
0.70
Figure 33. Diagram of the native mitral valve. Square specimens were taken from the
anterior leaflet with sides parallel to the circumferential and radial axes of the leaflet
centered circumferentially and extending radially from just below the annulus to just
above the first chordae tendineae attachment site.
79
2.3.2
Quasi-static biaxial testing
Specimens were mounted in the biaxial testing device with the circumferential and radial
specimen axes aligned with the device axes (Figure 35) within a specimen bath which was filled
with PBS and maintained at a temperature of 37° C for the duration of testing. Each leaflet
underwent 20 preconditioning cycles (Figure 34) in which the specimen was stretched such that
the membrane tension (T) (defined as the force per unit length of tissue over which it was
applied) along each specimen edge was increased to 90 N/m over a cycle period of 15 seconds,
then was returned to its original configuration over an additional period of 15 seconds. To
increase test repeatability, all loading cycles were initiated at a tare load of 0.5g and all presented
stretch data were referenced to the preconditioned tare configuration which was taken at the 0.5g
tare load after the 20 preconditioning cycles.
After the preconditioned tare reference was
recorded, specimens underwent either a high-speed stretch rate sensitivity testing protocol, a
stress-relaxation protocol or a creep protocol.
80
Specimen Mounted
in Biaxial Tester
Preload of 0.5g
20 preconditioning cycles
from 0.5g to 90 N/m with
15s half-cycle time
Preconditioned tare
reference
Strain Rate
High-speed
loading/unloading cycles
with half-cycle periods of 1,
0.5, 0.1, 0.05 and 1 sec
Loading/Unloading to 90
N/m strain state determined
in preconditioning cycles
Strain Rate / Creep / Relaxation
Creep
Loading from 0.5g to 90
N/m with rise time of 0.1
sec
Loading state
maintained at 90 N/m
for 3 hours
Relaxation
Loading from 0.5g to 90
N/m with rise time of 0.1
sec
Displacements held
constant for
3 hours
Figure 34. Biaxial stretch rate sensitivity, creep, stress-relaxation, and uniaxial stressrelaxation protocols.
81
Radial Specimen Axis
Device Axis 2
Circumferential Specimen Axis
Device Axis 1
Figure 35. Specimens were mounted in the biaxial testing device with the circumferential
and radial specimen axes aligned with the device axes.
2.3.3
High-speed biaxial testing
For the stretch rate sensitivity testing, the carriage displacements required to stretch the specimen
to the 90 N/m equitension state in the preconditioning cycles were recorded and repeated for 5
additional high speed cycles in which the specimen was stretched and unstretched in loading and
unloading cycle periods of 1 second, 0.5 seconds, 0.1 seconds, 0.05 seconds and finally again in
1 second to assess test repeatability. For the relaxation and creep protocols, the device carriages
82
were returned to displacements required to stretch the specimen to the 90 N/m equitension state
in the preconditioning cycles in a rise time of 0.1 seconds. The 0.1 second rise time was chosen
because it was very close to the physiologic rise time and was slow enough that any vibrations
associated with rapid carriage decelerations at the peak loading state were limited (± 2% of the
peak load).
In the stress-relaxation protocol the device carriages were then locked in the
displaced positions and the specimens were allowed to relax for 3 hours. For the creep protocols,
after reaching the 90 N/m equitension state, the membrane tensions in both the circumferential
and radial directions were sustained for 3 hours by adjusting the carriage positions at a rate of
approximately 10 Hz in order to maintain the desired membrane tensions.
This was
accomplished by displacing each axis independently at a rate V given by V = C (90 - Tm), where
C is a tuning constant and Tm is the measured membrane tension on the axis to be adjusted.
For this formulation, positive values of V corresponded to stretches while negative values of V
corresponded to compressions. Satisfactory maintenance of the 90 N/m equitension state (see
RESULTS Table 4) was achieved by evaluating and adjusting each axis independently, ignoring
any mechanical coupling between the circumferential and radial specimen axes. Each specimen
was used for only one stretch rate sensitivity, stress-relaxation or creep protocol.
83
2.3.4
Kinematic analysis
and λrpeak , were used to quantify
The leaflet stretches at the 90 N/m equitension state, λ peak
c
leaflet extensibility. In the stretch rate sensitivity protocols, leaflet hysteresis was evaluated by
comparing the energy stored in the loading phase to the energy dissipated in the unloading phase
for each loading rate. Energy stored/dissipated was calculated as the area beneath the T vs.
stretch curve. Areas were calculated using a trapezoidal rule numerical integration.
For the stress-relaxation protocols, membrane tension data were normalized to the peak
membrane tension observed for each leaflet. For all specimens, this peak membrane tension was
reached immediately after the initial 0.1 second loading.
The relaxation percentage was
calculated as R(%) = (Tpeak - T3hr)/Tpeak for each axis. Relaxation data was thinned to 20 data
points evenly distributed through the duration of testing reduce processing time, and then fit with
a reduced relaxation function for long relaxation periods with a single phase relaxation
distribution.
Where c was the magnitude of the relaxation distribution, τ1 was the short
relaxation time constant and τ2 was the long relaxation time constant. Creep data was analyzed
by comparing the circumferential and radial stretches at four time points: immediately after the
initial loading (λ100ms), 300 milliseconds (λ300ms), 1 second (λ1s), and 3 hours (λ3h). Creep
percentage C(%) was calculated as C(%) = (λ – λ100ms)/ (λ100ms – 1).
84
2.3.5
Statistical methods
For all tests, the circumferential and radial data groups were considered separately and the
uniaxial and biaxial stress-relaxation groups were considered separately. To determine the
effects of stretch rate on each biomechanical parameter in the stretch rate sensitivity protocols
(i.e. λ peak
, λrpeak , and hysteresis), comparisons between all loading times were performed using
c
one way Analysis of Variance (ANOVA). The Holm-Sidak method was then used to perform
pair wise comparisons between loading time groups to further elucidate any significant
differences. Student’s t-test was used to assess any directional differences between specimen
axes in both creep and relaxation experiments and to compare uniaxial and biaxial relaxation
percentages. Additional comparisons between creep percentages at 100 ms, 300 ms, 1s and 3 hr
were performed using one way ANOVA for both the circumferential and radial creep data sets.
All tests were performed with a commercial statistics software package (SigmaStat; SPSS Inc.,
Chicago, IL). All data values are presented as the mean ± the standard error of the mean (SEM).
85
3.0 RESULTS
3.1 CHARACTERIZATION OF DEVICE PERFORMANCE
3.1.1
Stretch Measurement Accuracy
The stretch measurement system was found to be accurate to within a stretch of ± 0.001 (Table
2) and shear angle was measured to within 0.1 degrees.
Table 2. Stretch measurement accuracy
Stretch 1
Prescribed Measured
1.200
1.199
1.200
1.200
1.200
1.199
Stretch 2
Prescribed Measured
1.600
1.600
1.600
1.600
1.600
1.600
86
Shear Angle (°)
Prescribed Measured
30.0
29.9
30.0
29.8
30.0
29.9
3.1.2
Load cell calibration
After a repeatable calibration was completed, the mean load measurement of the 500g standard
was 501.3±0.4 g.
3.1.3
Ability to reach peak loads
The ability of the device to reach the desired equibiaxial tension state of 300 g using a latex test
sample is presented in Table 3. The first two cycles were not close to the desired peak loads due
to the initial guesses used for the first cycle. These results show the ability of the device
correction algorithms to correct for inaccurate initial displacement guesses (see METHODS for
details). After the second cycle, the peak loads were reached with a high degree of accuracy.
The mean absolute differences between the desired and measured peak loads were 0.94±0.83 g
(circumferential) and 0.12±0.12 g (radial).
87
Table 3. Peak loads for the ten cycle test using a latex test sample.
Cycle
1
2
3
4
5
6
7
8
9
10
3.1.4
Peak Load (g)
Axis 1
Axis 2
210.3
215.9
290.8
295.5
299.3
301.5
301.1
299.7
298.8
300.9
301.0
299.9
299.0
300.8
298.9
299.4
301.2
299.6
299.8
298.0
Load cell momentum sensitivity
The unloaded device axis showed no sensitivity to high-speed motion (Figure 36). Very little
change was observed in the load data from the unloaded axis. This was demonstrated by a linear
function which was fit to the load data from the unloaded axis with a slope of 0.006 g/s over the
0.2 second duration. A plot of the residuals showed no clear pattern, indicating that the unloaded
axis was not affected by the high speed, rapid acceleration, or sudden deceleration of the carriage
displacement.
88
Loaded Axis (latex sample)
Unloaded Axis
30
Load (g)
20
10
0
-10
0
200
400
600
800
1000
Time (ms)
Figure 36. Load versus time curves for the loaded axis (closed symbols) and unloaded axis
(open symbols) showed that the load cell on the unloaded axis was not affected by rapid
motions.
89
1.0
Residual (g)
0.5
0.0
-0.5
-1.0
0
200
400
600
800
1000
Time (ms)
Figure 37. Residuals versus time for the unloaded axis showed no clear trend, further
indicating that the unloaded axis was not affected by rapid motions.
90
3.1.5
System relaxation
The suture-only relaxation test (Figure 38) showed that the level of relaxation in the system itself
was minimal. After the three hour test duration relaxation percentages were 1.2 percent on the
first device axis and 1.6 percent on the second device axis.
1.2
Normalized Tension
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time (hrs)
Figure 38. Relaxation of the biaxial test system and sutures. Both device axes (open
symbols: device axis 1, closed symbols: device axis 2) showed minimal relaxation and were
indistinguishable from each other.
91
3.2 EFFECTS OF STRETCH RATE
3.2.1
Device Control
Tension and stretch vs. time loading curves were similar among the full range of cycle periods
(Figure 40), demonstrating that the biaxial device was able to accurately control loading and
unloading time for the different cycle periods. Additionally, the level of test repeatability was
found to be quite high as displayed by the close agreement between the first and final 1 second
loading/unloading protocols (Figure 39). Between these two protocols, the mean change in
λ peak
was found to be 0.006±0.002 and the mean change in λrpeak was 0.010±0.005,
c
demonstrating a high degree of accuracy and reproducibility.
92
Figure 39. Typical tension-stretch curves for the initial and final 1s loading/unloading
protocols.
93
Figure 40. Typical (a)Load versus time and (b)stretch versus time curves for 1s and 0.1s
loading periods. The load versus time and stretch versus time curves were similar for the
full range of cycle periods. As displayed above, the device was able to accurately control
rise time for different cycle periods. Note the different time scales between the 1s and 0.1s
plots.
94
3.2.2
Effects of Stretch Rate on Stress-Stretch Response
The shapes of the tension vs. stretch loading curves for all loading protocols (15s, 1s, 0.5s, 0.1s,
0.05s) were very similar for each specimen tested (Figure 41). To better present the stretch rate
and λrpeak for each cycle period were pooled for all specimens (Figure 42).
effects, mean λ peak
c
No significant differences were found between any of the loading time protocols in both the
and λrpeak for all
circumferential (p=0.987) and radial (p=0.996) directions. In addition, λ peak
c
loading times were very similar to, but generally were slightly greater than, the peak stretches
observed in left ventricle-simulating flow loop [32]. Moreover the ratio of the mean
λpeak
/ λrpeak =0.86 was very close in value (0.83) to the same ratio observed under simulated
c
physiologic conditions. These results suggest that the 90 N/m peak tensions used in the present
study were comparable to actual physiological stress levels.
95
Circumferential
120
15s
1s
0.5s
0.1s
0.05s
100
(a)
80
60
T
40
i
(N/ )
20
0
1.00
1.05
1.10
1.15
1.20
1.25
Stretch
Radial
120
15s
1s
0.5s
0.1s
0.05s
100
80
60
(b)
T
40
i
(N/ )
20
0
1.0
1.1
1.2
1.3
1.4
Stretch
Figure 41. Typical tension-stretch curves for each loading cycle period (15s, 1s, 0.5s, 0.1s,
and 0.05s) for the circumferential (a) and radial (b) specimen directions. Curves generally
showed no apparent stretch rate-dependence. Note the different stretch scales between the
circumferential and radial plots.
96
1.6
λCpeak
λRpeak
1.5
1.4
1.3
St t h
1.2
1.1
1.0
15s
1s
0.5s
0.1s
0.05s
Loading Time
Figure 42. The circumferential and radial stretches of the leaflet at the 90 N/m equitension
state.
97
3.2.3
Effects of Stretch Rate on Hysteresis
Typical loading and unloading curves for a set of stretch rate protocols on a single leaflet are
shown in the four separate panes of Figure 43. Stretch energy storage during loading and
dissipation during unloading were minimal due to the extremely nonlinear mechanical behavior
of the MV leaflet. As shown in Figure 44, larger amounts of energy were stored in the leaflet at
lower tension levels due to the relatively higher level of extensibility of the leaflet tissue at lower
stretch levels.
The area beneath the membrane tension versus areal stretch curves (Figure 45) were not
statistically among different cycle times for either the loading or unloading phases. Hyteresis
levels, loading energy minus unloading energy, were significantly greater than zero for the 15s
and 0.1s cycle times only (p<0.01).
98
15 seconds
100
T (N/m)
80
60
40
20
0
1.0
1.1
1.2
1.3
1.4
1.3
1.4
Stretch
1 second
100
T (N/m)
80
60
40
20
0
1.0
1.1
1.2
Stretch
99
0.5 seconds
100
T (N/m)
80
60
40
20
0
1.0
1.1
1.2
1.3
1.4
Stretch
0.05 seconds
100
T (N/m)
80
60
40
20
0
1.0
1.1
1.2
1.3
1.4
Stretch
Figure 43. Loading and unloading membrane tension (T) vs. stretch curves for 15, 1, 0.5
and 0.1 second loading and unloading of a single specimen.
100
0.10
Energy (N/m)
0.08
0.06
0.04
0.02
0.00
0
20
40
60
80
100
T (N/m)
Figure 44. Membrane stretch energy versus membrane tension for a typical loading cycle.
Note the larger amount of energy storage in the tissue at lower tension levels due to the
relatively higher tissue extensibility at low stretch levels.
101
12
Membrane strain energy (N/m)
Loading
Unloading
10
8
6
4
2
0
15s
1s
0.5s
0.1s
Cycle Period
Figure 45. Energy stored or dissipated within the leaflet specimens during loading and
unloading phases with different cycle times.
102
3.3 STRESS-RELAXATION AND CREEP
3.3.1
Device control
The stretching device was able to load the MVAL specimens to the 90 N/m uniaxial or
equibiaxial state smoothly, with minimal vibrations, over the initial 100 ms rise time (Figure 46).
Due to the rapid speeds required to load the tissue within the 100 ms rise time and the high level
of stiffness in the MVAL at the 90 N/m membrane tension level, the stretching mechanism
occasionally slightly overshot the 90 N/m target.
Due to the rapid speeds required to load the tissue within the 100 ms rise time and the
high level of stiffness in the MVAL at the 90 N/m membrane tension level, the stretching
mechanism occasionally slightly overshot the 90 N/m target. Mean peak realized membrane
tensions were 93.2±2.1 N/m on the circumferential axis and 97.1±2.5 N/m on the radial axis for
uniaxial stress-relaxation experiments and 102.2±2.8 N/m on the circumferential axis and
103.4±3.4 N/m on the radial axis for biaxial experiments. Despite this overshoot, the ratio of the
peak circumferential and radial membrane tensions was always maintained near 1 (0.99±0.01) in
biaxial experiments.
For stress-relaxation experiments, the overshoot was not corrected; however, as stated in
the methods section, stress-relaxation results were calculated and normalized for each specimen
based on the peak membrane tension measured for the proper individual experiment. In cases
where overshoot occurred during creep experiments, the membrane tension state was corrected
within the first second of the test by the same device control algorithm that maintained the 90
N/m equibiaxial tension state for the duration of the test. The creep algorithm was able to
103
maintain the 90 N/m membrane tensions very well over the entire duration of the creep tests
(Table 4).
120
100
Circumferential
80
Radial
60
40
20
0
0
100
200
300
400
500
Time (ms)
Figure 46. Typical membrane tension versus time curves for the first 500 ms of a biaxial
stress-relaxation experiment.
The biaxial stretching mechanism was able to load the
specimens within the allotted 100 ms rise time with minimal vibrations and overshoot.
104
Table 4. Circumferential and radial membrane tensions ± STDEV for all creep tests after
the initial loading phase.
Specimen
1
2
3
4
5
6
Mean
3.3.2
Circumferential (N/m)
89.96
89.97
89.88
89.97
90.03
89.94
89.96
± Radial (N/m)
0.34
89.87
0.24
89.92
0.58
89.75
0.31
89.94
0.71
89.88
0.13
89.91
0.39
89.88
±
0.37
0.30
0.93
0.15
0.48
0.21
0.41
Biaxial Stress-Relaxation
Relaxation was observed on both the circumferential and radial axes (Figure 47). The most
drastic relaxation was observed within the first 15 minutes of testing, but specimens continued to
relax up to and beyond the 3 hour time point.
The change in membrane tension from
immediately after initial loading (at 100 ms) to 3 hrs was statistically different for each specimen
axis (P<0.001 for both specimen axes). Relaxation was always greater in the radial direction.
The ratio of circumferential to radial membrane tensions at 3 hours, 1.10±0.02, was statistically
different from the same ratio at 100 ms, 0.99±0.01 (P<0.001) and the relaxation percentage in the
circumferential direction, 24.67±0.93 was statistically different from the relaxation percentage in
the radial direction, 32.09±0.77 (P<0.001) (Figure 48).
105
1.0
0.8
Circumferential
Radial
0.6
0.4
0.2
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time (hrs)
Figure 47.
Membrane tension versus time curves for a typical stress-relaxation
experiment.
Membrane tension levels at 3 hours were statistically less than those
immediately after loading (100 ms) for both specimen axes.
106
50
Circumferential
Radial
P=0.057
40
P<0.001
30
20
St
10
R l
0
ti
Uniaxial
Biaxial
(
Figure 48. Relaxation percentage for different test groups and specimen axes. Relaxation
was observed in both uniaxial and biaxial experiments, however, the amount of radial
relaxation was significantly greater in the biaxial experiments and the circumferential and
radial relaxation percentages were not statistically different in the uniaxial experiments as
they were in the biaxial experiments.
107
3.3.3
Uniaxial Stress-Relaxation
Specimens tested uniaxially also exhibited relaxation on both the circumferential and radial
specimen axes. As observed in the biaxial stress-relaxation experiments, the peak membrane
tensions in both the circumferential and radial directions were statistically greater than the
membrane tensions measured at the 3 hour time point (P<0.001 for each specimen axis).
However, unlike the biaxial relaxation experiments, the relaxation percentages observed in the
circumferential (25.2±2.2) and radial (28.5±1.8) experimental groups were not statistically
different from each other (P=0.305) and a comparison between the uniaxial and biaxial
relaxation percentages revealed that the biaxial relaxation was significantly greater (p<0.05) in
the radial direction, while the uniaxial and biaxial relaxation percentages were not statistically
different in the circumferential direction (p=0.78) .
108
3.3.4
Reduced Relaxation Function Fit
Both the uniaxial and biaxial relaxation data for both the circumferential and radial axes were fit
quite well (Figure 49) with the one phase reduced relaxation model with an r2 value of 0.996 ±
0.002 for all specimens. Model parameters for all specimen fits are presented in appendix A.
Time (s)
Figure 49. The one phase reduced relaxation model fit both the uniaxial (pictured) and
biaxial relaxation data very well for both the circumferential and radial (pictured) axes.
109
3.3.5
Creep
The high degree of mechanical anisotropy in the leaflet, as seen in the stretch rate sensitivity
protocols, was also observed in the creep experiments. Specifically, peak stretches at the 100 ms
time point were 1.12±0.014 in the circumferential direction and 1.36±0.048 in the radial
direction.
In sharp contrast to the relaxation results, the observed creep was minimal in both the
circumferential and radial specimen axes (Figure 50). Mean stretches in the circumferential
direction stayed constant over the entire three hour test duration, and were minimal in the radial
direction. Creep percentages (Figure 51) were not statistically different from zero at any time
point in the circumferential direction and were statistically different from zero only for the 3
hour time point in the radial direction (Table 5).
110
1.4
Radial
1.3
1.2
1.1
Circumferential
1.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Time (Hours)
Figure 50. Stretch versus time curves for a typical biaxial creep experiment. Minimal
relaxation was observed on either axis. Note the anisotropic leaflet behavior exhibited by
the relatively higher radial stretch required to maintain the 90 N/m membrane tension.
111
3.0
Circumferential
Radial
2.5
Creep %
2.0
1.5
1.0
0.5
0.0
0.03 seconds
1 second
3 hours
Figure 51. Creep percentages were not statistically different from zero for any time point
on the circumferential or radial axes.
112
4.0 DISCUSSION
4.1 RELEVANCE OF STUDY
This work details the first known study of the effects of stretch rate on the biaxial mechanical
properties of the MVAL, and indeed for any valve leaflet tissue. These studies are the first to
report the application of high stretch rate studies under biaxial loading for any soft tissue.
Furthermore, this is the first study known to the authors to report biaxial creep results for any
soft tissue and is the first relaxation study to incorporate physiological loading times and a
physiological biaxial loading condition. These findings are of particular importance to the
development of time dependent constitutive models for valve leaflet tissues because they
demonstrate tissue properties at physiologic stretch levels and rates. This characterization of the
material properties of the native valve will provide an improved basis for the comparison and
qualification of potential replacement materials and repair techniques and is a necessary step in
the development of future computational models and material simulations [55].
113
4.2 MECHANICAL ANISOTROPY
The classic nonlinear stress-stretch relationship exhibited by the MVAL leaflet observed in the
present study was consistent with previous biaxial findings of May-Newman and Yin [34], as
well as the transvalvular pressure-areal stretch relationship observed by Sacks et al [32]. The
three-phase curve consisted of a roughly linear toe region, in which the leaflet deformed
extensively while developing minimal membrane tension, followed by a highly nonlinear
transition region, in which leaflet stiffness increased rapidly before reaching a plateau and
entering a second linear region. Efforts have been made to explain this phenomena using
collagen fiber recruitment theories [56, 57], but the microstructural details remain to be
elucidated for the MVAL.
In the present study, for all leaflet specimens the circumferential axis exhibited lower
stretch levels for a given tension level than did its radial counterpart. This result supported the
finding that the marker region used in this study consisted predominantly of circumferentially
oriented collagen fibers [58], since collagen fibers primarily resist only axial loads. This finding
was also consistent with the stretches observed by Sacks et al. [32] in a left-heart simulating flow
loop. The close agreement of the peak stretches observed at the 90 N/m equitension state and the
peak stretches observed in the left-heart simulating flow loop when the MVAL was in the closed
configuration suggested that the 90 N/m peak equitension biaxial loading state was reasonably
representative of the maximum physiologic stress state. The close agreement observed between
the ratio of circumferential and radial stretches at the 90 N/m equitension state compared to those
observed in-vitro for the functioning MVAL was of particular importance because it implied that
114
the rotational kinematics of the underlying fiber structure were comparable to those of the
MVAL in vivo.
4.3 STRETCH RATE EFFECTS
One of the primary findings of this study was that the stress-stretch behavior of the anterior
MVAL was independent of stretch rate in both the circumferential and radial directions over the
full range of cycle periods from 15 seconds to 0.05 seconds studied. This result was in close
agreement with the results reported by Naimark et al. [59] that showed no significant stretch ratedependence in the stress-stretch relationship of mammalian pericardia for stretch rates between 1
and 100%/second. Naimark suggested that the lack of stretch rate dependence may be due to the
pseudo-plastic shear-thinning of the glycosaminoglycan matrix surrounding the collagen fibers.
Conversely, this result differed from those detailed in the work of Leeson-Deitrich [42]
for aortic and pulmonary valves who reported significant differences in the stress-stretch
response at different stretch rates. Our results also differed from the results reported by Lee et al.
[60] who observed stretch rate sensitivity of the glutaraldehyde-stabilized porcine aortic valve in
the circumferential axis only. Lee et al. linked the explanation of this behavior to the presence of
major collagen bundles, which were observed to span the valve parallel to the circumferential
leaflet axis. It should be noted that a similar collagen arrangement has been observed in the
anterior MV leaflet [58] and we observed no directional differences in stretch rate sensitivity. It
is unclear whether the differences between our results and those reported in these two studies
115
were derived from differences in material, or if they were a product of the differences in loading
condition (biaxial tension versus uniaxial tension).
The hysteresis of the MVAL was difficult to compare between different
loading/unloading cycle times due to the extremely small amount of energy stored within the
MVAL. The traditional definition of hysteresis: the difference between the areas beneath the
loading and unloading curves may not be appropriate for biaxially loaded specimens because,
due to coupling effects, one axis may actually contract at high tension levels, creating an
undefined integration of the stress versus stretch relationship. Differences in the stretch energy
beneath the stress-stretch curves were different for the circumferential and radial specimen axes
due to the relatively higher distensibility of the radial axis. The slight differences in the areas
beneath the loading and unloading curves for the 0.1 second loading time were not significant,
and furthermore, could have been a reflection of the hysteresis of the load cells themselves which
was specified as 0.5 percent.
116
4.4 STRESS-RELAXATION
The stress-relaxation exhibited in the MVAL was consistent with findings for other collagenous
soft tissues [47, 48, 50, 61, 62] including findings for the MV chordae tendineae [40]. However,
due to the relatively large change in membrane tension that corresponded to extremely small
changes in stretch on both axes near the 90 N/m equitension level (i.e. high stiffness), further
analysis of the results is necessary. The main goal of this analysis is to show that the observed
stress-relaxation was real and was not an artifact caused by small changes in the specimen
attachments (i.e. specimen sutures pulling out slightly from the specimen edges) that could cause
minute reductions in the specimen stretches. To do this, the change in stretch observed over the
three hour duration of the biaxial stress-relaxation experiments was compared to the change in
stretch observed in the unloading phase of the final preconditioning cycle for the same specimens
from the peak membrane tension to the same membrane tension observed after the three hour
duration of the stress-relaxation experiments (Figure 52).
The results of this analysis showed that the specimen stretches for the relaxation
experiments were markedly different from those seen in the quasi-static unloading cycles.
Specimen stretches observed in the relaxation experiments were statistically different from those
observed in the quasi-static unloading cycles in both the circumferential (p=0.02) and radial
(p<0.01) directions. As expected, the quasi-static results showed a negative change, or decrease
in stretch to reach the relaxed membrane tension. Conversely, the stretches over the duration of
the stress-relaxation experiment actually increased slightly. The increase in stretch was quite
small, however it did occur in all but one specimen.
117
0.008
0.006
Stress-relaxation
Quasi-static unloading
Change in Stretch
0.004
0.002
0.000
-0.002
-0.004
-0.006
-0.008
-0.010
-0.012
Circumferential
Figure 52.
Radial
Changes in stretch over the three hour duration of the stress relaxation
experiments compared to the changes in stretch required to reach the same membrane
tension in quasi-static unloading cycle.
The increased stretches over the stress-relaxation duration indicate that a portion of the
total specimen stretch may be redistributed into the central marker region as the specimen
relaxes. For comparison, a similar analysis was done using the uniaxial stress-relaxation and
quasi-static unloading data. As seen in the biaxial analysis, stretch levels for specimen axes
118
under tension increased over the duration of the stress-relaxation tests, while the quasi-static
unloading cycles showed decreased stretch levels for the equivalent relaxed membrane tension
state. Interestingly, the stretches on the unloaded axes in the stress-relaxation experiments all
decreased (Figure 53) over the duration of the stress-relaxation experiments. This result was
expected due to the mechanical coupling between specimen axes, however, and also showed that
the stretch measurement system was not biased towards positive changes in stretch in the stressrelaxation experiments. The changes in stretch observed, while extremely small, were within the
capabilities of the optical measurement system which was able to calculate stretches to with
0.001 (see RESULTS).
This result underscores the importance of performing biaxial experiments on
membranous tissues. The difference between the change of stretch of the free and loaded axes
indicates that the mechanism of relaxation may be different in uniaxial and biaxial experiments.
In uniaxial experiments increases in stretch level on the loaded axis may be due to timedependent Poisson-like effects minimizing the areal tissue stretch, while this cannot be the case
in biaxial experiments since the stretch on both axes increases. In biaxial experiments, the
observed relaxation was greater in the radial direction than the circumferential direction. This
discrepancy may be linked to the higher distensibility of the MVAL in the radial direction; in
order to achieve the desired 90 N/m equitension state, the required stretches in the radial
direction were generally approximately 3 times greater than those required in the circumferential
direction.
119
0.015
Circumferential Specimen Axis
Radial Specimen Axis
Change in Stretch
0.010
0.005
0.000
-0.005
-0.010
-0.015
Circumferential Stress-relaxation
Radial Stress-relaxation
Figure 53. In uniaxial stress-relaxation experiments, stretch levels increased for axes under
tension and decreased on the free axis. Data presented as mean ± SEM.
In their study on ligament viscoelasticity, Provenzano et al [47] found that the uniaxial
relaxation of the rat medial collateral ligament (MCL) was highly dependent on stretch level.
However, in contrast to our findings, the observed relaxation decreased as the initial stretch level
increased.
Additionally, the results of Provenzano et al showed that the influence of stretch
level on the relaxation behavior diminished after stretch levels increased to a level beyond the
transition phase generally attributed to collagen recruitment in collagenous soft tissues; as shown
in our earlier work the 90 N/m equitension state was achieved in the MVAL well after this
120
transition phase.
In accord with this finding, Lee et al [46] observed that the amount of
relaxation in the glutaraldehyde-stabilized porcine aortic valve leaflet was independent of initial
load. Interestingly, this study noted relaxation differences between specimens tested in uniaxial
tension in the circumferential and radial directions, but these differences were opposite to our
findings, possibly due to the large amount of collagen cross-linking that resulted from the
glutaraldehyde treatment. In contrast to the studies by Provenzano and Lee, a study by Dunn and
Silver [48] reported increased relaxation levels in several soft tissues, including parietal
pericardium, with increased stretch level. However, comparisons with this study are less direct
since relaxations were calculated at 5% sequential stretch increments without returning to the
original unloaded stretch state between relaxations. Another factor that could potentially play a
role in the relaxation behavior observed in our study is the stretch rate differences between
specimen axes. Due to the relatively greater stretch required to load the MVAL to the 90 N/m
membrane tension in the radial direction and the fact that the rise times for the circumferential
and radial axes were the same, the stretch rate in the radial direction was necessarily higher than
that observed in the circumferential direction. In their study on the uniaxial relaxation behavior
of porcine aortic valve (AV) cusps [50], Vesely et al observed that the relaxation percentage and
the rate of relaxation were dependent on stretch rate. However, in this case, the relaxation of the
AV decreased as the displacement rate in the initial loading phase increased. Although the
results of Provenzano and Vesely seem contradictory to our results, these comparisons should be
interpreted with caution since these studies reported the effects of stretch and stretch rate on a
single specimen axis under uniaxial load. Because our result describes differences between two
axes of the same specimen, the structural differences between specimen axes must also be
considered.
121
Previous Small Angle Light Scattering studies [32] have shown that the leaflet subsection
used in our experiments consists predominantly of circumferentially oriented fibers.
This
suggests that a larger portion of the 90 N/m membrane tension was borne by collagen fibers in
the circumferential direction than in the radial direction since collagen most effectively resists
axial loads. In their uniaxial stress relaxation study on the porcine MV chordae tendineae [40],
Liao and Vesely linked decreases in relaxation rate and relaxation percentage to increased GAG
content, hypothesizing that interfibrillar GAG linkages decreased relaxation by resisting shearing
between collagen fibers. Using our result, we may expand on this hypothesis to state that, for the
MVAL, the increased relaxation in the radial direction may be due to the fact that a relatively
larger percentage of the total stress on the radial axis is borne by the GAGs, suggesting that
interfibrillar GAG connections may preferentially resist shearing forces between individual
fibrils, related to circumferential relaxation in the MVAL, and may be weaker when stressed
orthogonally to the preferred collagen orientation, as they would be in response to radial stretch.
Additional support for this idea may be supplied by our uniaxial stress-relaxation data. In the
uniaxial case we observed significantly less radial relaxation than was observed for the biaxial
relaxation protocols. This may be due to the fact that fiber rotations were not restricted in the
uniaxial experiments allowing fibers to reorient themselves in a direction more parallel to the
loaded specimen axis. This fibrillar reorientation would also reorient the proteoglycan linkages
allowing them to resist shearing relaxations. Another hypothesis is that the GAG resistance to
relaxation is not directionally dependent at all, but instead is dependent on areal stretch level. If
this is the case, uniaxial stress-relaxation may not be as sensitive to stretch level because the free
dimension may contract as the tissue is loaded, effectively minimizing the areal stretch. In either
122
case it is clear that the proper biaxial loading condition is critical when evaluating the
physiologically functional viscoelastic properties of soft tissues.
4.5 CREEP
The results of our creep experiments showed that, despite the observed relaxation behavior, the
MVAL did not exhibit a functionally significant degree of creep. The small amount of creep that
was observed over the three hour time period was statistically insignificant for all time points
except 3 hours on the radial specimen axis only. However, creep at this distant time point is
irrelevant to the physiologic loading cycle of the valve, which occurs over approximately 0.5
seconds during ventricular systole. The lack of creep observed in the MVAL was inconsistent
with previous findings for ligament [47, 49], pericardium [62] and AV leaflet [46], which all
exhibited a much greater degree of creep than that observed in the MVAL. It should be noted
again, that these experiments were all performed under uniaxial tension and that it is unclear
whether the differences observed in our creep experiments are due to material differences or due
to differences in loading condition.
123
4.6 RELATIONSHIP OF STRESS-RELAXATION AND CREEP
The presence of disproportionate degrees of creep and relaxation behavior has been observed,
although to a lesser degree than was observed in this study, previously. Provenzano et al
observed that the rate of relaxation proceeded faster than the rate of creep in contralateral
ligaments, while Thornton et al reported a similar finding and showed that ligament creep could
not be predicted from relaxation data using quasilinear viscoelastic assumptions [49]. In contrast
to our study, in which the observed behavior occurred after stretching the MVAL through the
transition phase of the stress-stretch relationship, Thornton et al observed this relaxation-creep
imbalance at low stress and were able to properly relate creep and relaxation by incorporating
fiber recruitment. Our findings suggest that the mechanisms responsible for creep and relaxation
in the MVAL may be functionally independent.
124
4.7 COMPARISONS TO SMALL ANGLE X-RAY SCATTERING RESULTS
Recent small angle x-ray scattering studies (SAXS) [63], also from the University of Pittsburgh
by Liao et al may shed some light on the microstructural mechanisms responsible for the
behavior observed in this study. For quasi-static loading of the MVAL, SAXS results (Figure
54) show that the D-spacing (see INTRODUCTION on collagen structure) of the collagen
molecules does not increase until the specimen has been stretched into the stress-stretch
transition zone and collagen fiber uncrimping has been initiated. This suggests that components
other than collagen itself are primarily responsible for bearing specimen loads at low stretch
levels.
In addition to dynamic loading, this study included SAXS analysis of biaxial creep
(Figure 55) and stress-relaxation behavior (Figure 56). Our finding that the MVAL did not creep
was supported by this SAXS study, which also found no appreciable creep in the MVAL over a
one hour test duration. The SAXS creep results show that the collagen D-spacing does not
change, as would be expected since the specimen does not deform. The SAXS stress-relaxation
results, like our stress-relaxation results, are somewhat paradoxical.
These results showed
relaxation behavior similar to that observed in our biaxial study, but showed that the collagen Dspacing diminished extensively during relaxation. This suggests that the mechanism of stressrelaxation may depend on a non-collagenous component of the MVAL microstructure such as
elastin or GAGs.
125
Figure 54.
Changes in collagen D-spacing as a function of membrane tension (left).
Membrane tension versus areal stretch % for the same MVAL specimen. Reproduced
from Liao, J. Unpublished Communication.
126
Figure 55. D-spacing as a function of creep experiment duration (left). Areal stretch as a
function of creep test duration for the same specimen (right). Reproduced from Liao, J.
Unpublished Communication.
127
Figure 56. Normalized membrane tension versus stress-relaxation test duration (top).
Collagen D-spacing as a function of stress-relaxation test duration for the same specimen
(bottom). Reproduced from Liao, J. Unpublished Communication.
128
4.8 STUDY LIMITATIONS
One limitation of this study was the optical stretch measurement system. This system could only
track four or nine markers in the central belly region of the leaflet. A more thorough analysis of
the stretch state, in the entire specimen would provide insight into both the stress-relaxation and
creep mechanisms. In addition to the stretch measurement system, the actuation components
provided some study limits. While these actuation components provided a major improvement
over previous biaxial testing devices, the component stability at the extremely high speeds
necessary for the 0.05 second loading/unloading cycles was not sufficient.
In addition to limits of the device itself, in the current study it was assumed that the
mechanical properties of the MVAL leaflet were dominated by its passive structural elements:
collagen, elastin, and polysaccharides, which constitute 85-95% of the leaflet dry wt [64, 65].
No attempt was made to maintain cell viability within any of the test samples nor was there any
effort to trigger an active response from the leaflet with an appropriate chemical stimulus. It was
recently demonstrated in flexure that native aortic valve interstitial cells can contribute to leaflet
stiffness [66]. However, the forces generated here are at several orders of magnitude lower than
those experienced by the MVAL ECM components. However, changes in leaflet deformation in
an in-situ preparation [8] suggest some contribution by the leaflet cells. While additional work
in this is required to clarify issue, it is unlikely that cellular forces contribute substantially to the
MVAL mechanical response. We note finally that only equitension protocols were performed in
the present study. However, given the close agreement with normal physiologic stretches, this
should be sufficient for characterizing the physiologically relevant viscoelastic properties of the
MVAL.
129
4.9 CONCLUSIONS
The results of this study highlight the need to perform creep tests on soft tissues. Although,
generally more difficult to perform, creep experiments are more representative of the physiologic
conditions of most soft tissues, and as demonstrated by our results, creep behavior may be
radically different from relaxation behavior. Furthermore, our results underscore the importance
of performing mechanical tests on soft tissues using the appropriate loading condition, which, in
the case of membranous soft tissues, usually consists of a biaxial loading state.
This study has provided insight into the dynamic mechanical properties of the MVAL.
The combination of the stretch rate insensitivity of the stress level observed within the leaflet, the
lack of an appreciable level of tissue hysteresis at physiologic stretch rates, and the lack of creep
implies that the MVAL may be functionally modeled as a nonlinear quasi-elastic anisotropic
biological material. The structural basis for this behavior is as yet unknown, but is likely an
important functional aspect of native MV tissues and warrants further study. Also, additional
studies using small angle X-ray scattering on MV leaflet collagen molecular structure under
creep and relaxation, as done for recently for pericardium [63], may help to provide a structural
basis for the mechanical behavior observed in this study.
130
4.10
RECOMMENDATIONS FOR FUTURE STUDY
The results of this study have provided novel and important data on the MVAL, but much
remains to be studied before our understanding of mitral mechanics is complete. Recommended
future studies include:
1. A duplication of the current study for the posterior mitral valve leaflet.
o This study would provide necessary data for the modeling of the posterior leaflet
and would elucidate differences between the two leaflets.
2. Stress-relaxation study of the MV leaflet using a high resolution camera and
magnifying lens.
o By studying the changes in the stretch state of all regions of the leaflet (as
opposed to only the central region used in the current study) the details of the
paradoxical stress-relaxation behavior may be further explored.
131
3. Creep experiments on the MV chordae tendineae.
o Current studies of the MV chordae tendineae include only dynamic loading and
stress-relaxation.
Since it may be more representative of the physiological
condition, creep experiments on the MV chordae tendineae may provide useful
data.
132
5.0 THESIS SUMMARY
The list below summarizes the major findings of this study for the MVAL:
1. Dynamic biaxial loading and unloading cycles revealed that the stress-stretch relationship
of the MVAL showed no dependence on stretch rate and indicated that the MVAL tissue
may be functionally modeled as an anisotropic quasi-elastic material.
2. Creep experiments revealed that creep in the MVAL at a physiological load state was
functionally insignificant, particularly when considered with respect to physiological
creep duration of approximately 0.5 seconds.
3. Although the MVAL showed no creep, stress-relaxation experiments showed significant
relaxation from the physiological loading state. This result underscored the necessity of
performing creep experiments on soft tissues since creep may be more representative of
the physiological loading condition and cannot be satisfactorily described using stressrelaxation data.
133
APPENDIX A
REDUCED RELAXATION FUNCTION FIT PARAMETERS
134
CIRC
Sample
C
T1
T2
Biaxial
1
2.13E-02 1.06E-02 1.00E+08
2
2.62E-02 1.05E-02 1.04E+08
3
3.22E-02 1.27E-02 7.91E+07
4
3.00E-02 1.20E-02 9.72E+07
5
2.09E-02 1.00E-02 9.45E+07
6
4.25E-02 1.18E-01 7.87E+07
7
5.88E-02 1.47E+00 7.91E+07
8
2.25E-02 1.02E-02 1.00E+08
Mean
3.18E-02 2.06E-01 9.17E+07
SEM
4.61E-03 1.80E-01 3.83E+06
Uniaxial (Circumferential)
1
2.01E-02 1.03E-02 1.00E+08
2
2.71E-02 1.02E-02 1.00E+08
3
6.64E-02 6.37E+00 2.35E+06
Mean
3.79E-02 2.13E+00 6.76E+07
SEM
1.44E-02 2.12E+00 3.26E+07
Uniaxial (Radial)
1
2
3
Mean
SEM
RAD
R^2
C
T1
T2
R^2
9.82E-01
9.90E-01
9.91E-01
9.95E-01
9.87E-01
9.91E-01
9.99E-01
9.80E-01
9.89E-01
2.23E-03
5.93E-02
1.15E-01
1.22E-01
5.97E-02
8.25E-02
1.31E-01
1.46E-01
9.92E-02
1.02E-01
1.14E-02
8.92E-01
1.20E+00
5.70E-01
3.51E+00
3.52E+00
5.28E+00
8.07E+00
4.85E+00
3.49E+00
9.12E-01
2.33E+07
7.48E+08
1.51E+09
1.22E+06
2.37E+07
6.87E+07
1.88E+08
9.30E+07
3.32E+08
1.89E+08
9.98E-01
1.00E+00
9.98E-01
9.99E-01
9.97E-01
9.98E-01
1.00E+00
9.98E-01
9.98E-01
3.73E-04
3.59E-02
1.08E-01
4.36E-02
6.24E-02
2.28E-02
1.35E-02
3.58E+00
4.26E-01
1.34E+00
1.12E+00
8.03E+07
2.76E+08
3.10E+08
2.22E+08
7.15E+07
9.89E-01
1.00E+00
9.89E-01
9.92E-01
3.66E-03
9.78E-01
9.97E-01
9.98E-01
9.91E-01
6.31E-03
135
APPENDIX B
BIAXIAL TESTING DEVICE USER’S MANUAL
136
Biaxial Testing Manual
Author(s): Jonathan Grashow
Version: 1.1
Original Release Date: 3/17/05
Last Revision Date: 3/24/05
137
Contents
Section 1: Background material
Section 2: Biaxial Tester Description
Section 3: Biaxial Testing Software Screens
3.1: Load Cell Calibration Screen
3.2: Image Setup Screen
3.3: Specimen Positioning Screen
3.4: Test Settings Screen (Load Control)
3.5: Test Settings Screen (Stretch Control)
3.6: Run Test Screen
Section 4: Biaxial Testing Protocols
4.1: General Notes
4.2: Setting Up the Biaxial Testing Device
4.3: Preparing the Specimen
4.4: Mounting the Specimen in the Biaxial Testing Device
4.5: Setting Up the Imaging System
4.6: Setting a Preload
4.7: Running a Test
Section 5: Biaxial Tester Output Files
Section 6: Software, Drivers & Virtual Channels
Section 7: System Diagrams
7.1: System Overview
7.2: System Orientation
7.3: Motor Wiring Diagram
7.4: Load Cell Wiring Diagram
7.5: Software Overview
Section 8: System Specifications
138
Section 1: Background Material
Biaxial testing and analysis is a complicated and delicate process. The following
articles are strongly suggested for anyone planning to perform biaxial
experiments:
For General Information on Biaxial Testing:
1. Sacks MS, Sun W. Multiaxial mechanical behavior of biological materials.
Annu Rev Biomed Eng. 2003;5:251-84. Epub 2003 Apr 18. Review.
2. Sacks MS.A method for planar biaxial mechanical testing that includes inplane shear. J Biomech Eng. 1999 Oct;121(5):551-5.
For Information on Optical Stretch Measurement Technique:
1. Hoffman AH, Grigg P. A method for measuring stretches in soft tissue.
J Biomech. 1984;17(10):795-800.
For Examples of Biaxial Experiments:
2. Gloeckner DC, Sacks MS, Fraser MO, Somogyi GT, de Groat WC,
Chancellor MB. Passive biaxial mechanical properties of the rat bladder
wall after spinal cord injury. J Urol. 2002 May;167(5):2247-52.
3. Billiar KL, Sacks MS. Biaxial mechanical properties of the natural and
glutaraldehyde treated aortic valve cusp--Part I: Experimental results. J
Biomech Eng. 2000 Feb;122(1):23-30.
4. Wells SM, Sacks MS. Effects of fixation pressure on the biaxial mechanical
behavior of porcine bioprosthetic heart valves with long-term cyclic
loading. Biomaterials. 2002 Jun;23(11):2389-99.
For Examples of High-Speed Biaxial Experiments:
1. Nagatomi J, Gloeckner DC, Chancellor MB, DeGroat WC, Sacks MS.
Changes in the biaxial viscoelastic response of the urinary bladder
following spinal cord injury. Ann Biomed Eng. 2004 Oct;32(10):1409-19.
139
Section 2: Biaxial Tester Description
Figure 1. Overhead schematic of the high speed biaxial testing device; a)
stepper motors; b) screw-driven linear actuators; c) load cells; d) specimen bath
outlet; e) specimen bath inlet; f) heating element maintained bath temperature
at 37°C; g) high speed digital camera (high speed systems only); h) standard
digital camera; i) beam splitter (high speed systems only); j) sub specimen
mirror.
The actuation components of the biaxial testing device (Fig. 1) are four
ball-screw driven linear positioners (404XR, Parker Hannafin Corp., Irwin, PA).
Each of these linear positioners is equipped with a 20mm lead capable of
achieving a maximum carriage velocity of 1 m/s and maximum carriage
acceleration of 25 m/s2.
These four linear positioners are mounted in an
opposing fashion such that one pair of positioners is aligned to stretch a
140
centered tissue sample along each device axis. Each linear positioner is driven
by a rotary stepper motor (OS22B-SNL10, Parker Hannafin Corp., Irwin, PA) and
each stepper motor is controlled with a microstepping drive (E-AC, Parker
Hannafin Corp., Irwin, PA) that provides a step resolution of 50,800 steps per
revolution, which, when coupled to each aforementioned linear positioner
results in a spatial resolution of approximately 0.394 µm for each positioner
carriage. All the microstepping drives are controlled via a 4-axis PCI motion
controller card (DMC 1740, Galil Motion Control Inc., Rocklin, CA) that is installed
in the device control PC (Precision 550, Dell Inc., Round Rock, TX).
Custom attachment arms are mounted onto the carriage of each linear
positioner in order to provide a mechanism for specimen attachment. Leaflet
specimens are mounted to these attachment arms in a trampoline fashion by
attaching two loops of 000 nylon suture to each side of the specimen via four
stainless steel surgical staples (see specimen mounting procedure).
The
attachment arms are designed to fasten the two specimen suture loops and to
transmit the total load applied by each actuator evenly through all of the
attached suture lines. To accomplish this, each attachment arm is furnished
with a pair of custom stainless steel pulleys which are free to rotate, ensuring that
the forces applied through each pulley are balanced between both of the
surgical staple attachments for the attached suture loop.
Both pulleys are
mounted symmetrically on either side of a central stainless steel ball bearing.
141
This mechanism distributes the total force applied by the positioner equally
between both pulleys.
Leaflet deformations are measured optically with a digital camera (see
background material for references on biaxial stretch measurement). Load
measurements are acquired by the device control computer from a pair (one
on each device axis) of load cells (Model 31, Honeywell Sensotec, Columbus,
OH) via an analog/digital converter (PCI-6036E, National Instruments, Austin, TX).
142
Section 3: Biaxial Testing Software Screens
3.1 – Load Cell Calibration
143
3.2 – Image Setup
144
3.3 – Specimen Positioning
145
3.4 – Test Settings (Load Control)
146
3.5 – Test Settings (Stretch Control)
147
3.6 – Running a Test
148
Section 4: Biaxial Testing Protocols
4.1 - General Notes
1. The program can be run by pressing the LabView arrow in the upper left
corner of the program window.
2. In order to properly shutdown the program, press the “Stop Program”
button at the bottom of the screen while the program is in an idle state.
3. In case of an emergency, turn off power to the motors and stop the
program by clicking the LabView arrow in the upper left corner of the
program window.
4. Throughout the manual gray numbers in parentheses: (X.X) correspond to
labels in the Biax Software Screens section.
149
4.2 - Setting up the Biaxial Testing Device
Notes:
1. This protocol assumes that the device is properly installed and affixed to
the testing tabletop.
2. During this protocol, care should be taken to limit contact and forces
applied to the load cells. Applying forces greater than 150% of full scale
to the load cells will result in permanent damage.
3. Caution should always be used around the biaxial testing device. Limit
switches are in place to prevent the device from damaging itself, not you.
4. Power to the motors may be turned off to allow the device carriages to
be moved manually. Power to the motors must be restored before setting
either the low or high calibration points.
Protocol:
1. Turn on power to all components: computer, motors, light, load cells, and
camera.
2. Turn on device computer
3. Launch Biax software
a. Load Control 1.0 (load based test)
b. Stretch Control 1.0 (stretch based test)
4. Click on the “Load Cell” tab (1.1) at the top of the screen
5. Perform steps 6-10 independently on each load cell
6. Check to make sure that nothing is touching the load cell, and proceed
to adjust the zero for each load cell within the inline amplifier until the
voltage (1.2) for the cell reads ~0.
7. Using the calibration arm, hang a weight and adjust the load cell gain
within the amplifier (See amplifier manual for details) such that the span of
the load cell output voltage is maximized for the load range for your test.
a. If it is necessary, it is possible to mechanically amplify the load signal
by mounting the load cell closer to the carriage arm pivot. Rough
150
amplifications are (from upper to lower mounting position): 1:1,
1.14:1, 1.33:1, 1.6:1
8. With no force on the load cell, check to make sure that 0 is entered next
to the “low” indicator (1.3) for the appropriate axis and click the “set”
button.
9. Hang an appropriate weight from the calibration arm, enter the weight
next to the “high” indicator (1.3) for the appropriate axis and click the
“set” button.
10. Repeat steps 8 and 9 until the loads displayed in the “Loads” graph (1.4)
are correct and repeatable.
11. Click the “Save” button (1.5) to save the calibration file. If you choose not
to save the calibration file and the computer crashes or freezes, you will
have to repeat the load cell calibration.
a. You can reload any calibration file by click the “Load” button (1.6)
and selecting the desired calibration file.
151
4.3 - Preparing the Specimen
Notes:
1. The biaxial tester is designed to test specimens that range in size from 0.7 x
0.7cm to 4.0 x 4.0 cm
2. Specimens should be properly hydrated throughout preparation
procedure by submerging them in the appropriate fluid as needed
Protocol:
1. Prepare specimen for dissection
• Thaw frozen specimens at the appropriate temperature
• Rinse and clean specimens if needed
2. Cutout region for biaxial testing from sample
• Biaxial specimens should be rectangular in shape
3. Insert suture staples along each side of the specimen
• 2 suture loops (consisting of a total of 4 suture staples) should be
attached to each side of the specimen
• Care should be taken to space the 4 suture staples evenly across
each specimen edge
• Insert suture staples at least 1 mm away from the edge to prevent
sutures from ripping out during testing. This spacing
recommendation is a general rule and may have to be increased
for materials that rip easily.
4. Glue or otherwise attach markers to the central region of the biaxial
testing sample
• The biaxial software can track either 4 (in a 2 x 2 array) or 9 (in a 3 x
3 array) markers
• The marker array should be applied to the central region of the
sample, spaced away from the suture staples to ensure an even
stress distribution within the marker region.
• Markers can be dark (on a light specimen) or light (on a dark
specimen). Adequate contrast between the specimen and the
markers is crucial to the success of the experiment.
152
4.4 - Mounting the Specimen in the Biaxial Testing Device
Notes:
1. The mounting process is considered by many to be the crux of biaxial
testing. It requires patience and practice. You can do it!
2. The suture attachment pulley pieces can be removed by unscrewing the
thumbscrew located above each pulley attachment. When twisting the
thumbscrew on a carriage that contains a load cell, be careful to hold
the metal load cell-contacting arm away from the load cell to prevent
from accidentally applying a force to the load cell.
3. It may be helpful to turn the power to the motors off in order to allow
manual carriage position adjustment during the mounting procedure.
Protocol:
1. Steps 2-5 can be completed before preparing the specimen if desired.
2. Fill the specimen bath with the appropriate fluid
3. Begin external bath flow loop (if applicable)
4. Wait for bath parameters (i.e. temperature, gas concentrations) to reach
appropriate stable condition.
5. Attach suture loops to device pulleys by lifting pulley caps, looping suture
around pulley and dropping pulley cap over suture line.
6. Once the specimen is successfully mounted, make sure the power to the
motors is on.
7. Click the “Positioning” tab (3.1) at the top of the software screen.
8. Adjust the motor speed on the “Motor Speed (mm/s)” scroll bar (3.3).
9. Using the “Free Movement” buttons (3.2), center the specimen within the
bath. Note that the free movement directions should correspond to
directions relative to the image window.
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4.5 - Setting Up the Imaging System
Notes:
1. If the markers are lost by the software at any time after they are initialized,
disable the “lock subregions” feature (2.2) and repeat steps 5-10.
2. Once the imaging system is properly setup, you can save a reference file
(X & Y marker positions) for reference or to use in your testing protocols by
clicking the “Save Reference File” (2.5) in the lower right corner of the
imaging tab.
3. The “Compare References” button (2.6) allows you to automatically
calculate the stretches between two reference files that you will be
prompted to select after clicking the “Compare References” button.
4. Clicking any of the “Set” buttons (2.4) next to the “Marker Positions” graph
(2.3) allows you to plot marker positions on the graph for comparison. It
does NOT save the marker positions as a reference file and will not allow
you to use the current marker positions as a reference for a test. See note
3 for details on saving reference files.
Protocol:
1. Position and focus the camera such that the markers are centered in the
image window and leave enough room so that the markers will not move
out of the camera field of view during testing.
2. Select the “Imaging” tab (2.1) at the top of the screen.
3. Click the “Threshold Image” button in step 1 of the image setup box (2.2)
and adjust the threshold value using the scroll bar until the markers are
clearly visible and the thresholded image is clean and free of noise and
image specks.
4. Move to step 2 of the image setup box and select the number of markers
you would like to track (4 or 9).
5. Move to step 3 of the image setup box and click the “initialize” button to
launch the subregion initialization.
6. Using the mouse, draw a box around each marker in the image window
that appears, clicking the “OK” button after drawing each box. A textual
154
description of the marker you should be selecting is written in the upper
right hand corner of the marker initialization window. Note that the
marker subregions should not overlap and the markers should be the only
objects in each subregion.
7. Upon returning to the main screen after completing the marker
initialization, the marker subregions that you drew should be overlayed in
green on the image window.
8. Move to step 5 of the image setup box and click the “turn on marker
tracking button.”
9. Move to step 6 of the image setup box and adjust the upper and lower
marker size thresholds until the software recognizes all markers. You can
tell if the software recognizes a marker by looking for the presence of a
small green cross in the center of the marker. Additionally, recognized
markers should be plotted on the “Marker Positions” graph (2.3).
10. Move to step 7 of the image setup box and click the “Lock Subregions”
button. This will center the marker subregions on the markers and force
the marker subregions to translate with the markers such that the markers
remain centered within their respective subregions.
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4.6 - Setting a Preload
Notes:
1. The automatic preload feature works best if you first manually (Using the
“Free Movement” buttons (3.2)) stretch the specimen such that the loads
displayed on the “Loads” graph (3.8) on the bottom of the “Positioning”
tab (3.1) are close to the desired loads.
2. The autoloading feature is used during an actual test in order to ensure
that the specimen returns to the proper tare loads between test cycles,
using the autoloading feature will give you an idea how this feature will
perform during the actual test.
3. Selecting a tare load that is too low (typically below 0.5g) or an allowable
error that is too small (typically below 0.05g) can cause errors in the
autoloading algorithm.
Protocol:
1. Click on the “Test Settings” tab (4.1 or 5.1) at the top of the screen
2. Enter the specimen dimensions in the provided input boxes (4.2 or 5.2).
3. Click on the “Positioning” tab at the top of the screen (3.1).
4. Select the desired units in the “Preload Units” selection box (3.5).
5. Enter the Allowable Error, X1 Preload and X2 Preload (3.6)
6. If desired, manually stretch the specimen until it is close to the desired tare
loads using the “Free Movement” buttons (3.2).
7. Click the “Apply Load Button” (3.7)
8. The “Program Status” bar (3.9) at the bottom of the screen will display
complete when the autoloading algorithm has finished.
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4.7 - Running a Test
Notes:
1. During or before the test, a live image can be toggled on or off by
clicking the “Update Image” button (6.3) at the top of the “Run Test” tab
(6.1).
2. A test can be cancelled by clicking the “cancel” button (6.3) at the top
of the “Run Test” tab. If the device does not respond to this action and
the device needs to stop immediately, shut off power to the motors.
3. During or before a test, you can choose to view the data for the current
test cycle only or for all test cycles with the toggle (6.2) in the upper right
corner of the “Run Test” tab.
Protocol:
1. Click the “Test Settings” tab (4.1 or 5.1) at the top of the screen.
2. Input all test parameters
a. Specimen dimensions (4.2 or 5.2): insert the specimen dimensions in
mm
b. Number of Cycles (4.3 or 5.3)
c. ½ Cycle Time (4.3 or 5.3): The time in seconds that the specimen will
be loaded (or unloaded). The duration of one cycle will be 2 x “1/2
Cycle Time).
d. Correction Gain (4.8 or 5.8): The testing device makes corrections
between cycles based on the assumption that the material is linear.
The more nonlinear your material is, the lower your correction gain
should be to prevent overshoot. A typical correction gain for valve
materials is 0.3.
3. Parameters in Load Control Only (4.1)
a. Control (4.5): Determine the units and type of control for the load
test
b. Axis 1 & Axis 2 (4.6): Input the desired peak loads for each axis in
the units specified in “Control”
c. Estimated Stretch 1 & 2 (4.7): Initial guesses for the stretches that will
be required to stretch the specimen to the desired peak loads.
d. Allowable Stretch 1 & 2 (4.4): Safety limits for the stretches on each
axis. If an axis is stretched beyond the allowable stretch the test will
be stopped immediately.
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4. Parameters in Stretch Control Only (5.1)
a. Stretch Ratio (5.4): the ratio of (stretch1-1) to (stretch2-1) desired for
the peak stretches
b. Use Load Limits for this Test (5.5): If this option is selected, the test
protocol will consist of the specimen being stretched at the ratio
specified in “Stretch Ratio” until one of the load limits is reached on
one axis (or both simultaneously). This option cannot be used in
conjunction with “Use Stretch Limits for this Test,” and should be
unselected before selecting that option.
i. Max Loads (5.5): select the units for the max loads
ii. Axis 1 & 2 (5.6): the load limits that will be used if “Use Load
Limits for this Test” is selected.
c. Use Stretch Limits for this Test (5.7): if this option is selected the test
protocol will consist of the specimen being stretched at the ratio
specified in “Stretch Ratio” until the stretch limit is reached on one
axis (or both simultaneously). This option cannot be used in
conjunction with “Use Load Limits for this Test,” and should be
unselected before selecting that option.
i. Stretch 1 & 2 (5.7): stretch limits that will be used if “Use Stretch
Limits for this Test” is selected.
5. Click the “Run Test” tab (6.1) at the top of the screen.
6. Click the green “Start Test” button (6.3)at the top of the tab.
7. When prompted, enter a base file name for the test. The software will
automatically write test data for each test cycle in a file named: <user
entered base file name>_<cycle #>.bx
8. When prompted, select a reference file to use for the test.
9. Sit back and watch the show.
158
Section 5: Biaxial Tester Output Files
BX Files
Each file that is automatically generated during the biaxial test procedure (.bx
file) is a tab delimited file that can be opened in Microsoft Excel or most other
spreadsheet programs or text editors. The headings for these files are:
Time (ms), Stretch 1, Stretch 2, Shear Angle, Load 1 (g), Load 2 (g), Tension 1
(N/m), Tension 2 (N/m), Stress 1 (kPa), Stress 2 (kPa), x1, x2, x3, x4, x5, x6, x7, x8, x9,
y1, y2, y3, y4, y5, y6, y7, y8, y9
REF Files
REF files are saved reference files that are saved by the user and used by the
Biax software during test protocols. Each REF file is a tab delimited file that can
be opened in Microsoft Excel or most other spreadsheet programs or text editors
if further analysis is necessary. The field order is:
X1, X2, X3, X4, X5, X6, X7, X8, X9, Y1, Y2, Y3, Y4, Y5, Y6, Y7, Y8, Y9
159
Section 6: Software, Drivers and Virtual Channels
Software & Drivers:
Manufacturer
Name
Version
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
National Instruments
Galil Motion Control
Measurement & Automation Explorer
IMAQ Vision
IVI Engine
Labview Run-Time
Labview
NI-Spy
NI-488.2 Software
NI-DAQ
NI-IMAQ Software
NI-IMAQ for 1394
NI-PAL Software
NI-VISA
DMC-18x0 Motion Controller Driver
3.0.0.3014
6.0
1.6
6.0
6.0
2.0.0.16
1.60
6.9.3f3
2.5.5
1.5
1.6.3f0
3.0
4.0.3.0
Virtual Channels:
Channel Type
Analog Input
Analog Input
Name
X-Axis Load Cell
Y-Axis Load Cell
Analog Output
negative trigger
Analog Output
positive trigger
Description
Differential Channel 0
Differential Channel 1
Channel 0: DAC0OUT,
High-Speed System Only
Channel 1: DAC1OUT,
High-Speed System Only
Biaxial Software Versions:
Load Control 1.0: Quasi-static load control
Load Control 2.0: Quasi-static load control + Stress Relaxation
Load Control 3.0: Quasi-static load control + High stretch rate testing
Load Control 4.0: Quasi-static load control + Biaxial Creep
Stretch Control 1.0: Quasi-static stretch control
160
Section 7: System Diagrams
7.1 System Overview
Device Control PC
Biaxial Testing Device
Load Cells
Stepper Motors
Load Cell
Amplifiers
Motor Drivers
Data Acquisition
Card
ICM/AMP
Motion Controller
Card
Firewire (IEEE
1394) Card
Limit Switches
Digital Camera
High-Speed Imaging PC
High-Speed
Digital Camera
Frame Grabber
Frame Grabber
Frame Grabber
*Items in red are only included in the High-Speed Systems
161
7.2 Setup Orientation
Motor B
Load Cell 2
Motor A
Motor C
Mirror
Load Cell 1
Motor D
162
7.3 Motor Wiring Diagram
Green &
Yellow
Motor
Driver
Pin 1: +5V
Pin 2: +5V
Ground
Pin 14: PWM
Red
Motor
Parallel Cable Pins to
ICM/AMP:
A+
Black
A-
White
Pin 15: SIGN
Parallel
Cable
Pin 16: +5V
Pin 17: AMPEN
B+
Green
B-
See Galil Application Note
#1425 for ICM/AMP Terminal
numbers.
*Connect Orange & Brown motor cables to each other.
**Connect Blue and Yellow motor cables to each other.
7.4 Load Cell Wiring Diagram
AC/DC Converter +
Load 1: DAQ Pin 66
Inline Amplifier
Blue
Load 2: DAQ Pin 34
AC/DC Converter -
White
1
A
Red
2
B
Black
3
C
4
D
Green
White
Load 1: DAQ Pin 33
Load 2: DAQ Pin 68
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Load Cell
7.5 Software Overview
Use this diagram as a map of the LabView Wiring Diagram
Main Program Loop
Image Setup/
Reference Files
Load Cell
Calibration
System
Initialization
Manual Specimen
Positioning
Quasi-Static
Loading Loop
Quasi-Static
Unloading Loop
High-Speed
Functions
Auto Loading
*High-Speed functions are present only in Load Control 2.0, 3.0 and 4.0
164
Section 8: System Specifications
Load Range
Actuator Max Speeds
Actuator Acceleration
Actuator Displacements
Displacement Precision
Camera Resolution
Specimen Size Range
0-1kg per carriage
1 m/s
25 m/s^2
5 cm
0.4 µm
1024 x 960
0.5 x 0.5 to 4 x 4 cm
165
APPENDIX C
HIGH-SPEED BIAXIAL TESTING MANUAL
166
Biaxial Testing Manual
Speed Testing Supplement
Author(s): Jonathan Grashow
Version: 1.0
Original Release Date: 3/16/05
Last Revision Date: N/A
167
High-
Contents
Section 1: General Information
1.1 Warning
1.2 Program Descriptions
Section 2: High-Speed Biaxial Testing Software Screens
2.1 Load Control 2.0 – Stress Relaxation
2.2 Load Control 3.0 – High Stretch Rate Testing
2.3 Load Control 4.0 - Creep
Section 3: High-Speed Biaxial Testing Protocols
3.1 Stress Relaxation
3.2 High Stretch Rate Testing
3.3 Creep
Section 4: High-Speed Biaxial Tester Output Files
Need to Add
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Section 1: General Information
1.1 - Warning
Please note that the high-speed biaxial testing programs (Load Control
2.0: Stress-Relaxation, Load Control 3.0: High stretch rate testing, and Load
Control 4.0: Creep) are much more involved than the standard quasi-static
Biaxial Testing programs. These three programs were all used to complete highspeed testing on the native Mitral Valve leaflet and their performance has not
been qualified for other materials. It is strongly suggested that anyone who uses
these programs have a good knowledge of LabView programming so that
adjustments to the programs can be made as necessary.
The high speeds
involved in these tests increase the need for the user to be familiar with the
device and its capabilities. Always make sure that limit switches are properly
installed to avoid device damage.
1.2 - Program Descriptions
Each of the three high-speed testing programs works in a manner very
similar to the quasi-static load control biaxial testing program (Load Control 1.0).
Generally, each program is set up to run through a series of quasi-static test
cycles (exactly like those in Load Control 1.0) then to perform a designated
high-speed test at the end of the quasi-static testing based to the
displacements determined in the quasi-static cycles.
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Load Control 2.0: Stress-Relaxation
This program runs a series of quasi-static cycles to user-defined load limits.
After the final quasi-static cycle the program can be set to perform a stressrelaxation test, in which the specimen will be stretched from the preload state to
the displacements that were determined to correspond to the load limits in the
final quasi-static cycle. The specimen will be loaded in a user defined time and
the carriage positions will then be locked for the duration of the experiment. This
program triggers the high-speed camera to acquire stretch data in the loading
phase of testing, then engages the standard digital camera to measure stretchs
for the remainder of the test.
Load Control 3.0: High-Speed Loading/Unloading
This program runs a series of quasi-static cycles to user-defined load limits.
After the final quasi-static cycle the program can be set to rapidly load and
unload the specimen from the preload state to the displacements that were
determined to correspond to the load limits in the final quasi-static cycle. The
specimen will be subsequently loaded and unloaded in 1s, 0.5s, 0.25s, 0.1s, 0.05s
and 1s ½ cycle times. This program triggers the high-speed camera to acquire
stretch data during the high-speed testing.
Load Control 4.0: Creep
170
This program runs a series of quasi-static cycles to user-defined load limits.
After the final quasi-static cycle the program can be set to perform a creep test,
in which the specimen will be stretched from the preload state to the
displacements that were determined to correspond to the load limits in the final
quasi-static cycle. The specimen is loaded in a user defined time after which a
loading algorithm is engaged to maintain the specimen loads at user defined
levels for the duration of testing. This program triggers the high-speed camera to
acquire stretch data in the loading phase of testing, then engages the standard
digital camera to measure stretchs for the remainder of the test.
171
Section 2: High Speed Biaxial Testing Software Screens
2.1 – Load Control 2.0: Stress Relaxation
172
2.2 – Load Control 3.0: High Stretch Rate Testing
173
2.3 – Load Control 4.0: Creep
174
Section 3: High-Speed Biaxial Testing Protocols
3.1 – Stress Relaxation
Notes:
1. Load Control 2.0 is simply an expansion of Load Control 1.0. All quasistatic protocols can be run using Load Control 2.0.
2. The displacements used in the stress-relaxation loading are based on the
displacements of the final quasi-static loading cycle. If anything is unusual
with the final quasi-static cycle it is not recommended to proceed with
the stress-relaxation test.
3. It is strongly recommended that all stress-relaxation tests are preceded by
a standard quasi-static biaxial protocol to ensure that no abnormal
characteristics are present in the test sample.
4. Currently a bug in the software causes every second stress-relaxation
experiment to stop prematurely. For this reason it is recommended that
you save all necessary calibration files and reference files, and manually
shut down and restart the program between sequential stress-relaxation
experiments; or fix this bug.
Protocol:
1. Input the desired quasi-static test settings (Refer to Biax Manual for
instructions).
2. Click the “High Speed Test” Tab. (1.1)
3. Enter the desired loading time (in seconds) in the loading time input box.
(1.6)
4. Enter the desired duration for the stress-relaxation portion of the
experiment in the test duration input. (1.7)
5. Click the High-Speed Test toggle (1.5) such that the indicator light turns to
bright green. Clicking this toggle will direct the biaxial testing software to
perform the stress-relaxation test after completing the quasi-static
protocol. Make sure to disable this toggle (by clicking the toggle again
such that the indicator light is black) before proceeding with any
additional quasi-static only experiments.
175
6. Select the Test Settings tab and run a quasi-static experiment as detailed
in the Biax Manual.
7. After the quasi-static protocol is completed, the software will wait for the
user to click the “Trigger Test” button (1.3) on the High Speed Test tab.
Before you trigger the test check the final cycle of the quasi-static
protocol to ensure that nothing abnormal occurred and that the carriage
displacements resulted in a condition very close to the desired loads. If
you are using the high-speed camera to track stretchs during the initial
loading phase, ensure that the camera is ready to receive the analog
trigger signal from the biaxial testing software.
8. Press the “Trigger Test” button.
9. The specimen should be loaded in the user defined duration and the
stretches as loads should be plotted in real-time on the screen.
10. The test will continue for the user specified duration unless you select the
“Stop Test” button (1.2).
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3.2 High Stretch Rate Testing
Notes:
1. Load Control 3.0 is simply an expansion of Load Control 1.0. All quasistatic protocols can be run using Load Control 3.0.
2. The displacements used in the rapid loading and unloading cycles are
based on the displacements of the final quasi-static loading cycle. If
anything is unusual with the final quasi-static cycle it is not recommended
to proceed with the high-speed test.
3. It is strongly recommended that all high stretch rate tests are preceded by
a standard quasi-static biaxial protocol to ensure that no abnormal
characteristics are present in the test sample.
4. The “Axis Return Factors” (2.8) allow the user to multiply the return stroke
during the high-speed testing by the appointed return factor in order to
account for overshoot or instabilities in the high speed protocols. Though
these factors are present, no correction was ever needed (return factors =
1) in the mitral valve testing. Take care that a large number is not
accidentally input into one of these fields as this could be devastating to
your sample and the device if the limit switches are improperly installed.
5. The “Recalibrate LC” button allows the user to recalibrate the load cells
between high-speed cycles. This was found to be unnecessary and this
toggle should not be used since it was never fully qualified.
6. The “Apply Preload” toggle causes the testing software to reapply the
specified preload (See Specimen Positioning in the Biax Manual) between
high speed cycles. Better results were obtained in mitral valve testing
when this feature was disabled (indicator light black).
Protocol:
1. Input the desired quasi-static test settings (Refer to Biax Manual for
instructions).
2. Click the “High Speed Test” Tab. (2.1)
3. Enter 1.0 in both of the “Axis Return Factor Inputs” (2.8)
177
4. Verify that the “Recalibrate LC” (2.7) and “Apply Preload” (2.9) toggles
are deactivated (indicator lights black).
5. Click the High-Speed Test toggle (1.5) such that the indicator light turns to
bright green. Clicking this toggle will direct the biaxial testing software to
perform the high stretch rate tests after completing the quasi-static
protocol. Make sure to disable this toggle (by clicking the toggle again
such that the indicator light is black) before proceeding with any
additional quasi-static only experiments.
6. Select the Test Settings tab and run a quasi-static experiment as detailed
in the Biax Manual.
7. After the quasi-static protocol is completed, the software will wait for the
user to click the “Trigger Test” button (1.3) on the High Speed Test tab.
Before you trigger the test check the final cycle of the quasi-static
protocol to ensure that nothing abnormal occurred and that the carriage
displacements resulted in a condition very close to the desired loads. If
you are using the high-speed camera to track stretchs during the high
speed cycles, ensure that the camera is ready to receive the analog
trigger signal from the biaxial testing software.
8. Press the “Trigger Test” button.
9. The specimen should be loaded and unloaded in 1s and the load vs time
curve should be plotted on the screen after the motion has completed.
10. If everything in the high-speed cycle went normally repeat steps 7-10 for
each high speed protocol. Make sure to setup the high speed camera to
receive the analog trigger before triggering each test.
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3.3 – Creep
Notes:
1. Load Control 4.0 is simply an expansion of Load Control 1.0. All quasistatic protocols can be run using Load Control 4.0.
2. The displacements used in the creep initial loading are based on the
displacements of the final quasi-static loading cycle. If anything is unusual
with the final quasi-static cycle it is not recommended to proceed with
the creep test.
3. It is strongly recommended that all creep tests are preceded by a
standard quasi-static biaxial protocol to ensure that no abnormal
characteristics are present in the test sample.
4. Currently a bug in the software causes every creep experiment to stop
prematurely. For this reason it is recommended that you save all
necessary calibration files and reference files, and manually shut down
and restart the program between sequential creep experiments; or fix this
bug.
5. The creep loading algorithm is used after the initial loading phase to
maintain the desired specimen loads. This algorithm was tuned to prevent
large loading oscillations for the mitral valve and may require adjustment
for other materials.
6. Unlike the stress-relaxation software, the creep software does not allow
the user to define the loading time. All loading is done in 100ms unless
modified on the programming level.
7. The creep algorithm automatically loads the specimen to the peak levels
defined in the Test Settings Tab (See Biax Manual). This was convenient for
the mitral valve since the valve was stretch-rate insensitive, but this may
need to be modified for other materials since loading the specimen in
100ms instead of quasi-statically may result in much higher load levels.
Protocol:
1. Input the desired quasi-static test settings (Refer to Biax Manual for
instructions).
179
2. Click the “High Speed Test” Tab. (3.1)
3. Enter the desired duration for the creep portion of the experiment in the
test duration input. (3.6)
4. Enter the desired “Creep Stretch Limits” (3.7). This is a safety function. If
these limits are reached, the software will automatically stop the test.
5. Click the High-Speed Test toggle (3.5) such that the indicator light turns to
bright green. Clicking this toggle will direct the biaxial testing software to
perform the creep test after completing the quasi-static protocol. Make
sure to disable this toggle (by clicking the toggle again such that the
indicator light is black) before proceeding with any additional quasi-static
only experiments.
6. Select the Test Settings tab and run a quasi-static experiment as detailed
in the Biax Manual.
7. After the quasi-static protocol is completed, the software will wait for the
user to click the “Trigger Test” button (3.3) on the High Speed Test tab.
Before you trigger the test check the final cycle of the quasi-static
protocol to ensure that nothing abnormal occurred and that the carriage
displacements resulted in a condition very close to the desired loads. If
you are using the high-speed camera to track stretchs during the initial
loading phase, ensure that the camera is ready to receive the analog
trigger signal from the biaxial testing software.
8. Press the “Trigger Test” button.
9. The specimen should be loaded in the user defined duration and the
stretches and loads should be plotted in real-time on the screen.
10. The test will continue for the user specified duration unless you select the
“Stop Test” button (1.2).
180
Section 4: High Speed Biaxial Tester Output Files
Stress Relaxation:
“<Filename)>_first_second.hsbx”: This file contains the first second of data from
stress-relaxation test. File column headings are: Time (ms), Load 1 (units selected
in Test Settings Tab), Load 2 (units selected in Test Settings Tab).
“<Filename>_entire_test.hsbx”: This file contains all data from the stressrelaxation test. File column headings are: Time (ms), Stretch 1, Stretch 2, Shear
Angle (degrees), Load 1 (N or g), Load 2 (N or g), Tension 1 (N/m), Tension 2
(N/m), Stress 1 (kPa), Stress 2 (kPa).
High Stretch-Rate Testing:
Each data file for the High Stretch Rate testing includes time and load data for
approximately 2 x the half cycle time + 1 additional second of data all at the
noted acquisition rate. File Headings for each file are: Time (ms), Load 1 (units
selected in Test Settings Tab), Load 2 (units selected in Test Settings Tab).
“<Filename)>_HS 0.hsbx”: 1 second ½ cycle time, 50 Hz acquisition rate.
“<Filename)>_HS 1.hsbx”: 0.5 second ½ cycle time, 100 Hz acquisition rate.
“<Filename)>_HS 2.hsbx”: 0.1 second ½ cycle time, 500 Hz acquisition rate.
“<Filename)>_HS 3.hsbx”: 0.05 second ½ cycle time, 500 Hz acquisition rate.
“<Filename)>_HS 4.hsbx”: 1 second ½ cycle time, 50 Hz acquisition rate.
Creep:
“<Filename)>_first_second.hsbx”: This file contains the first second of data from
creep test. File column headings are: Time (ms), Load 1 (units selected in Test
Settings Tab), Load 2 (g or N).
“<Filename>_entire_test.hsbx”: This file contains all data from the creep test. File
column headings are: Time (ms), Stretch 1, Stretch 2, Shear Angle (degrees),
Load 1 (N or g), Load 2 (N or g), Tension 1 (N/m), Tension 2 (N/m), Stress 1 (kPa),
Stress 2 (kPa).
181
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