CZECH TECHNICAL UNIVERSITY IN PRAGUE Faculty of Electrical Engineering Department of Measurement Inverse Problems of Magnetometry – Theory and Applications DOCTORAL THESIS 2009 Jiří Tomek Czech Technical University in Prague Faculty of Electrical Engineering Department of Measurement Inverse Problems of Magnetometry – Theory and Applications DOCTORAL THESIS Ph.D. Program: Electrical Engineering and Information Technology Branch of study: Measurement and Instrumentation Supervisor: Supervisor-Specialist: 2009 Prof. Ing. Pavel Ripka, CSc. Ing. Antonín Platil, Ph.D. Jiří Tomek PODĚKOVÁNÍ Mé velké díky patří všem, kteří mě podporovali ve všech směrech a to zejména psychicky, byť pochopitelně bez finančního zázemí by také nic být nemohlo. Nástrah, překážek a problémů se vždy najde nesčetně a na mnohé je člověk sám příliš slabý, tím se i tato práce stává týmovým dílem a to ne exkluzivně jen co se týče přímých spolupracovníků na jejích jednotlivých částech. Těm samozřejmě vděčím za mnohé. Při dokončování práce nastaly navíc komplikace nepředpokládané, spojené s koncem studia, přinášející značné množství stresu. Zde zaúřadovali rodiče, má úžasná přítelkyně a jistě i přes dva roky praktikovaná jóga, zřízená bývalou spolužačkou a kamarádkou. Role kamarádů a kolegů na pracovišti, ale i milých známých, je rovněž nezastupitelná. Není možné zde zmínit všechna jména, vděk patří všem kolem mě ☺ I těm, co si myslí, že ani nějak významněji pomoci nemohli. Za nedocenitelnou pomoc při opravách faktických, formálních a jazykových velice děkuji Pavlu Ripkovi - svému školiteli, Antonínu Platilovi a Harveymu Cookovi. ACKNOWLEDGEMENT My great thanks belong to everyone, who supported me in any way but primarily psychologically, though without the financial backing there would also be nothing. Innumerous constrictions, obstructions and problems always turn-up and one is too weak to cope with them alone, thus they made this work a team product and not just in means of taking into account the direct co-workers dealing with particular tasks, to whom I am bound for much. During the completion of this work some unexpected complications arose with the end of my studies, bringing a dose of stress. Here, my thanks go mainly to my parents, to my wonderful girl-friend and certainly also to yoga, which I have practised for more than two years and which was established by my friend and former classmate. A great part was also played by my friends and my helpful colleagues at school. It is impossible to name all the people here. My thanks go to everybody around me ☺ even to the ones who think that they could not help significantly. Many thanks for invaluable help with corrections of the thesis - issue-of-fact ones, formal ones and in language go to my supervisor Pavel Ripka, Antonín Platil and Harvey Cook. Doktorská práce vznikla ve spolupráci s těmito institucemi: The research was performed in collaboration with the following institutions: Veterans Research Foundation in Oklahoma City, USA JanasCard – Ing. Vojtěch Janásek, CSc Výzkum (a)nebo autor disertace byli finančně podpořeni následujícími granty: The research and/or the author of the thesis were funded by: Kontakt Me756 (2005-2007) CTU 06 10-86216 (2006) Fond ČVUT, CTU foundation (2006 a 2007) Výzkumný záměr MSM6840770012 "Transdisciplinary Research in the Area of Biomedical Engineering II" Introduction Jiří Tomek Contents 1. INTRODUCTION...........................................................................................1 1.1 2 ORGANISATION OF THE THESIS ......................................................................1 STATE OF THE ART ....................................................................................3 2.1 CONTACTLESS MEASUREMENT OF DISTANCE .................................................5 2.1.1 Electronic devices in medicine.............................................................6 2.2 MEASUREMENT OF MAGNETIC MOMENT ........................................................7 2.2.1 Measurements of the magnetic moment of solid samples containing magnetic materials ...............................................................................7 2.2.2 Magnetic field of the lungs...................................................................8 3 OBJECTIVES .................................................................................................9 3.1 RESEARCH TASK I..........................................................................................9 3.1.1 Magnetopneumography......................................................................10 3.2 RESEARCH TASK II.......................................................................................10 3.2.1 On-demand gastric pacer – basic analysis ........................................11 3.2.2 Volume measurements for AGES (Active Gastric Electrical Stimulation)........................................................................................12 4 MAGNETOPNEUMOGRAPHY (MPG)....................................................13 4.1 MAGNETIZATION PROBLEM - AN ELECTROMAGNET .....................................13 4.2 SCANNING DEVICE .......................................................................................15 4.2.1 Probe setups & noise .........................................................................20 4.2.1.1 4.2.1.2 4.2.1.3 4.2.1.4 Separate (reference) gradiometer sensing the outer fields ......................... 21 Probe array ................................................................................................ 23 More coaxial first order gradients ............................................................. 24 Higher order gradients, averaging, statistical analysis of the field in the measurement region and compensation..................................................... 34 4.2.2 Video controlled positioning ..............................................................34 4.3 FORWARD MODELLING ................................................................................35 4.4 INVERSE PROBLEM .......................................................................................36 4.4.1 Basic overview of some techniques ....................................................37 4.4.1.1 4.4.1.2 4.4.1.3 4.4.2 4.4.3 4.4.3.1 4.4.3.2 4.4.3.3 4.4.3.4 Neural networks ........................................................................................ 39 Automatic differentiation of the forward model for optimization ............. 40 Newest optimization methods ................................................................... 40 Estimation of total dust load ..............................................................41 Neural network inversion in MPG .....................................................47 Restraints & limitations............................................................................. 47 Localized sources ...................................................................................... 48 General problem........................................................................................ 54 General problem with more scanning planes............................................. 59 4.4.4 More probes & fitting to model function............................................68 4.5 DISCUSSION .................................................................................................68 5 MEASUREMENT OF THE STOMACH VOLUME.................................71 5.1 THE TASKS ...................................................................................................71 Introduction Jiří Tomek 5.2 METHOD...................................................................................................... 71 5.3 OVERVIEW OF SOME APPLICABLE METHODS ................................................ 72 5.4 IN-VIVO APPLICABLE SYSTEMS .................................................................... 78 5.4.1 First version....................................................................................... 78 5.4.1.1 5.4.1.2 5.4.1.3 5.4.1.4 5.4.1.5 5.4.1.6 5.4.2 5.4.2.1 5.4.2.2 5.5 6 Summary ................................................................................................... 78 The principle of the sensors and the system .............................................. 79 How it is designed and made..................................................................... 83 Final measurements ................................................................................... 88 Practical application on laboratory animals............................................... 90 Possibility of a three-axial probe introduction........................................... 98 Second version – tri-axial system .................................................... 105 Practical application on laboratory animals............................................. 106 Examples of the in-vivo measurements ................................................... 107 DISCUSSION............................................................................................... 109 CONCLUSIONS ......................................................................................... 111 6.1 6.2 ACHIEVED OBJECTIVES.............................................................................. 112 OUTLOOK .................................................................................................. 113 7 REFERENCES ........................................................................................... 115 8 APPENDIX.................................................................................................. 122 8.1 PUBLICATIONS .......................................................................................... 122 8.1.1 Articles in SCI journals ................................................................... 122 8.1.2 Papers in other journals .................................................................. 122 8.1.3 Papers in international conference proceedings ............................. 122 8.1.4 Papers in other conference proceedings.......................................... 122 8.2 ABBREVIATIONS ........................................................................................ 122 Introduction Jiří Tomek 1. Introduction In general, an inverse problem can be considered as an interpretation of measured data (e.g. magnetic field values) for the purpose of finding sources (or information about them) creating, for example, a tested field. The determination of sources plays crucial role in all branches of science. Everyone wants to interpret measured data sets and wants to know their sources, no matter if some background or “a priori” knowledge is available or not, we have or do not have the domain of the possible solutions or whatever solution-specifying information. What is more, the inverse problems are usually ill-posed (under-determined), which means that more variables should be assessed out of a small collection of measurements. Thus, any realistic solution has to first match various constraints and empirical knowledge of the specific problem. Solutions are usually obtained iteratively, not in one step by mathematical calculations. In case of an electromagnetic field, which we are going to deal with, there is inherent non-uniqueness arising from the basic definition given by Maxwell’s Equations (partial derivatives, thus the constants of integration). Definitely, the subject of this thesis is not the argumentation about the fundamentals of physics and proven theories, the aim is to try to show, on two different cases, how I, together with my colleagues (and others), coped with the inverse problem of magnetometry. The primary target will be thus forward modelling necessary for the simulation of the problem, the methodology and the software for the realization of the inversion, in which a number of estimated parameters depends strongly on the amount of acquired independent data. This thesis is not focused too much on the sensors and their principles. However, to a certain depth it is necessary to reveal even this aspect as the methods depend partially on the means of data acquisition. Therefore, processing electronics and software are to be discussed too. One relatively small problem is going to be solved. It is severely limited by the feasible set of hardware that could be utilized, as it is intended as an implantable device in human medicine; therefore, the dependability and the ease of surgery are the main goals. Another problem, on the contrary, is a bulky one, comparable in size with the problems solved in geoscience and also in the disciplines of medical imaging, within which in fact it falls. It utilizes a DC field, though in the established applications, alternating fields are mostly employed. Measurement techniques and sometimes even inverse strategies, which are the main target, are thus different than those we can utilize in this static problem. 1.1 Organisation of the thesis The work is written as an accompanying text to scientific publications that were issued in reputable journals or submissions to journals that came from papers -1- Introduction Jiří Tomek in international conference proceedings. I have rewritten and included a report to our US partner - demanded for the purpose of a new US grant application - and also included the scientific parts of the final report of an international grant from which comes the second presented application described in this thesis. The scientific papers and respective documentation pieces are inserted into the corresponding chapters. The thesis consists of four main chapters besides this one and the concluding section. The following Chapter 2 is devoted to the magnetic measurements with respect to the inversion aspect. It also mentions several branches of science using the respective state-of-the-art inversion methodologies and tries to provide background information for the applications described later. Chapter 3 reveals the motivation and objectives of the thesis. And then, in Chapter 4, comes a complex problem of magnetopneumography with the description of our experiments (probes, their configurations, positioning device, magnetometers and processing software) and the development in the inversion strategy, while dealing with the project. The next Chapter 5 is devoted to a relatively easier grant task being concurrently solved. It deals with an implantable device enabling the measurement of the distension of a stomach wall. The main challenge was, naturally, the practical application and the selection of the most effective solution to track the wall relaxation and motility. Besides the chosen method and the in-vitro experiments, the sensors and processing electronic units as well as several in-vivo testing results will be described there also. Finally, the conclusion is provided in the last chapter, which summarises the whole work and proposes the tasks to be dealt with next. -2- Inverse Problems of Magnetometry Jiří Tomek 2 State of the Art Inverse problems, i.e. the determination of certain parameters of sources out of the measured data, are one of the basic tasks of measuring processes. In magnetometry, the interpretation of the data is usually not trivial. Usually, we have the problem posed badly and there is an inherent non-uniqueness of D and H coming directly from Maxwell’s Equations that describe electromagnetism. In case of magnetostatic measurements, further problems turn-up, especially in the case of a general problem, where we do not know the direction of magnetization of the sources, etc. [Shearer 2004, Lelièvre 2006, He 1998, Forsman 1998]. We are speaking about the non-uniqueness of the inversion as there can be a number of solutions for the acquired data. [Shearer 2005] speaks about the concept of nonuniqueness such that a particular set of the observed data could be reproduced by an infinite number of models. Such a complication arises because there is a finite amount of inaccurate data describing the subsurface. To support the idea, she cites [Menke 1989; Parker 1994 and Scales 1997]. This non-uniqueness may be overcome to a certain extent by simplifications and empirical knowledge incorporated into the models. The scanning of the magnetic field or its point measurement is used in many branches for the purpose of determining some information. There are several applications in geosciences, such as metal ore location. Additionally, many applications are in industry, including flux leakage inspections or eddy current testing of imperfections or cracks in metals. Others still are plenty of applications in medicine. Many methods are still in the stage of research like MEG (Magnetoencephalography), MCG (Magnetocardiography) as well as MPG (Magnetopneumography) which we are also going to deal with. A method that is widely used in non destructive testing of metals and experimentally in medicine is MIT (Magnetic Induction Tomography), which is an imaging technique used to show electromagnetic properties of an object by using the eddy current effect. It is also called electromagnetic tomography (EMT), eddy current tomography or eddy current testing [Griffiths 2001, Telford 1976, Korjenevsky 2000]. Another one still more or less an experimental medical application, is the measurement of susceptibility for the determination of iron retention in the liver. Though the detected fields are also low, as in the case of MPG, it can even be realized by a room temperature device [Avrin 2007], however cryogenic superconducting quantum interference devices (SQUIDs) are more established, e.g. [Carneiro 2002]. On the contrary, one very effective application has been commonly used for more than a decade, NMR (Nuclear magnetic resonance) or more often called MRI (Magnetic Resonance Imaging), which belongs to the best imaging methods in medicine. -3- Inverse Problems of Magnetometry Jiří Tomek The fields used by the above mentioned methods vary a great deal, anywhere from fT of the fields created by the human body sensed by SQUIDs to the present 7T steady field electromagnets of the NMRs with extremely good resolution. The measurement of magnetic fields is excellent for the possibility of noninvasive contactless examination of sources; moreover, there is no clinically detectable adverse effect on human health. There are even appliances for magnetotherapy based mainly on an AC magnetic field. This work also concentrates on applications of contactless magnetic methods in biomedicine and deals with the inverse problem Inversion in magnetometry depends on the known parameters of the sources, which are usually reduced to discrete magnetic moments representing a certain volume of the examined object. Measurements of magnetic moments (either DC or AC) can be then divided into the following basic cases, according to the parameters of the moments - magnitude (strength), position and orientation. At first, let us concentrate on the case that we have a single magnetic source: • The magnetic moment of the source is known (both size and its orientation) – we can measure the distance by a single coil. • Just the magnitude of the moment is known, but not the orientation – the distance cannot be measured precisely without an array of detectors, but e.g. when sensing the vector of its field, the distance can be determined with maximum error less than 26% (the base is the smallest distance from a dipole with given field intensity), as the difference between the intensities of signals that can be measured in the 1st and 2nd Gaussian position is one half, thus the proportionality constant is 3 2 , thanks to the cube inverse proportionality between the measured field and the distance from a magnetic dipole. applied in the measurement of the distension of the stomach wall for determination of the volume changes for the purpose of active gastric electrical stimulation (AGES) – obesity treatment method – see Chapter 5. • The position of the moment is known as well as its orientation – the size is measured precisely used e.g. in perhaps one of the most interesting medical applications: MRI (Magnetic Resonance Imaging) where the position is given by different Larmor frequencies in voxels given by gradients of the strong DC field and by phase coding. -4- Inverse Problems of Magnetometry • Jiří Tomek Position of the moment is not known, but we know its orientation – the estimation of the size and position of the measured moment is possible depending on the measured field maps of the moment applied in Magnetopneumography (MPG), but there is usually a need to determine more than one moment. However, even determination of the total moment of the ferromagnetic particles in the lungs may be useful. This was my first goal in the task concerning the MPG (Chapter 4). More moments have to be determined by some optimization procedure, which is dealt with in the latter parts of Chapter 4. • Nothing is known about the moment, altogether there are all six degrees of freedom (3 for position in space, 2 spatial angles for orientation and 1 for size). For the detection arrays of sensors are needed. This is the most general case applied e.g. in tracking of magnetic markers in space or the centre of the electrical activity responsible for some simple action in the MEG. Such general problems are solved for multiple moments e.g. in geoscience. 2.1 Contactless measurement of distance As the above states, the examination of the magnetic field is usually performed in order to determine the distance of a source or distribution of sources from a measurement probe or from their array. Such contactless distance measurement is important in analysing the vibration, alignment, position or bending. It is practical in applications, where the motion of an object would be damped or otherwise affected by a coupled mass or force exerted by a measurement device; when sensitive surfaces must not be damaged; or when rapid motion must be tracked or simply when tested objects cannot be removed and measured another way like it is with magnetic particles deposited in the lungs. Such testing and measurement tasks are commonplace in research and development, automation, quality control, machine control applications and naturally in various biomedical applications. Besides the magnetic field, other phenomena are often utilized for contactless testing including: ultrasound, capacitive principle, optical triangulation or interferometric principle, etc. Magnetic phenomena are based on the inductive principle (induction of the voltage in a sensing coil), the induction principle (change of induction of the magnetic circuit e.g. eddy current principle, etc.) -5- Inverse Problems of Magnetometry Jiří Tomek 2.1.1 Electronic devices in medicine As I am going to deal with applications for medical purposes I would like to add more details about this branch. There is a relatively long history of biomedical applications of electronic devices from simple ones like digital thermometers to high resolution functional MRI (Magnetic Resonance Imaging) devices. Now we cannot even imagine specialized medical investigation without the use of sophisticated imaging instruments like an ultrasound, a CT (Computed Tomography), an MRI, a SPECT (Single Photon Emission Computed Tomography) and many others. Between these diagnostic imaging methods we could classify even an MPG which we are going to deal with in Section 3.1. MPG is in the stage of experiments, on the one hand with extremely sensitive but expensive SQUID technology, on the other with not such sensitive types of sensors like fluxgates. It has just been used for several studies of workers e.g. [Zheng 2004] and mostly for estimation of the total amount of dust in lungs e.g. [Huvinen 1997] so it is not as a pure imaging technique. But there is still continuous progress. The development in the sphere of implantable devices is more rapid. They sometimes incorporate quite complicated electronics and firmware. When just counting the commonly used ones, not various intensively developing artificial organs, there are pacemakers [Mediline Plus] and cochlear implants (a detailed description of the development at [Tomek 2004a]). Nevertheless, just the devices in development or research employ sensors for distance measurement, usually as a control or for feedback of their function or as a kind of switching mechanism or measurement of deformation, etc., e.g. in measurement of the deformation using laser triangulation in dentistry [Lukas 2001]. Use of implants naturally struggles with the biocompatibility of used materials and their mechanical and chemical durability. No one is surprised when the implants use noble metals and materials that arise from space exploration, thus manufacturing them is expensive not just because of the sophisticated electronics and firmware inside and long development and testing time. New methods of treatment of obesity [Chen 2004] and of gut motility disorders [McCallum 1998, Ouyang 2003, Zhang 2006, Familoni 2006] plan to use implants similar to cardiac pacemakers. For treatment of gastroparesis [Xing 2004], a stimulating device and method of its use was already approved by the FDA (Food & Drug Administration - USA) for ordinary treatment. A series of experiments have been performed by several research groups with the stimulation of the stomach or intestine [Zhang 2006]. Currently, there is also the task of controlling the stimulation according to the food intake instead of the continuous operation of the device, not only in order to save power of the implant but also to make its function more effective and efficacious. Measurement of the distance in the abdominal cavity is quite a challenging task, but it can be used not only in future obesity treatment but can also help a great deal in gastric studies. -6- Inverse Problems of Magnetometry Jiří Tomek 2.2 Measurement of magnetic moment The magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic dipole moment is defined as: m = I ∫ da (1.1) where a is the area of the current loop. This is the definition for Ampere’s magnetic moment. The direction of the vector of the magnetic moment is given by the right-hand rule according to the direction of current (I) flowing through the loop. In the more complicated case of a spinning, charged solid, the magnetic dipole moment can be found by the following equation: m= 1 r × JdV ∫ 2 (1.2) Where dV = r2sinθ·dr·dθ·dφ (r, θ, φ are coordinates in spherical coordinate system) is a volume element, r is the position vector pointing from the origin to the volume element and J is the current density at the location of the element. In case of a static magnetization M of a volume element we can integrate the overall moment of such magnetized body using the expression (1.3). m = ∫ MdV (1.3) 2.2.1 Measurements of the magnetic moment of solid samples containing magnetic materials Among various applications, there are some used, e.g. in occupational medicine to examine aerosols in the working environment – i.e. testing the magnetic moment of ferromagnetic dust or fumes. An interesting biomedical application connected to this task is the measurement of deposited dusts in human lungs that have suitable magnetic properties. It is an examination method mentioned several times before: Magnetopneumography [e.g.: Cohen 1975, Ripka 1997, Forsman 1998, Tipek 2002, Tomek 2005a, Tomek 2006a], which was being developed as a possible substitution of a less sensitive X-ray; moreover, it does not load the patients with radiation. -7- Inverse Problems of Magnetometry Jiří Tomek There are several possibilities how to measure the magnetic moment of the solid samples containing magnetic materials (which we consider ferromagnetic except for the last point) after their magnetization in a strong DC field: • Measurement (AC) in a rotating sample magnetometer in the case of small samples usually up to 1cm3 • Integration of induced voltage (semi-DC) in Helmholtz coils when rotating the measured sample by 180°, according to Equation (1.4) [Trout 1988, Stupak 1995, Tomek 2006] mA = u dt Φ = ∫ k H ⋅ µ0 k H ⋅ µ 0 (1.4) • Computation of the moment from the measurements of the magnetic field (magnetic induction (B) or gradient of B) created by the magnetized material. This method is, naturally, well applicable even on subjects in medicine. • Measurement of the susceptibility of ferrimagnetic materials stored in tissues by SQUID magnetometers [Brittenham 2003] or by utilization of AC fields by a room temperature susceptometer of special design [Avrin 2007]. These methods are used, e.g. for the detection of an iron overload in the liver. It is possible not only to compute the total magnetic moment of the measured sample but also using some inverse methods, to estimate the distribution of the detected content in it [Tomek 2005a, Tomek 2007a]. This is the primary aim in geological prospecting [Li 1996, Lelièvre 2003], MEG and of course in the already mentioned Magnetopneumography. 2.2.2 Magnetic field of the lungs Magnetopneumography as a non-invasive technique to measure the amount of magnetisable dust deposited in the lung tissue has been or is still being dealt with by the research groups of Högstedt [e.g. Högstedt 1995, Forsman 1998] Freedman [e.g. Freedman 1982] Kalliomäki [e.g. Kalliomäki 1983], Bohákova [e.g. Boháková 2003 and 2006], Ripka [e.g. Ripka 1997 and 2000] and others. Their works have proven its high sensitivity in assessing the amount of retained magnetisable dust and in [Ripka 1997] even the applicability of fluxgate probes has been demonstrated. In this thesis, we continue with the utilization of these sensors and prepare new configurations. MPG could be used in examinations of welders, metal -8- Inverse Problems of Magnetometry Jiří Tomek grinders or even miners. In most of the works mentioned, just the estimation of the total dust amount based on various methods had been performed, e.g. mean value and multipolar expansion methods [Forsman 1998]. Attempts were by Kotani and Chiyotani and others with the multi-dipole model, however not providing stable solutions [Kotani 1985]. Important to note are the works using SQUID magnetometers, which provide a much higher sensitivity, thus do not need such high magnetising fields [e.g. Boháková 2003 and 2006], however, not too much accent is put on the estimates of dust distribution. The problem of the non-uniqueness of the analytical solution to such complex static magnetic problems [He 1998, Lelièvre 2003, De Lange 2003 and Shearer 2005] leads to discretization of the space and utilization of multiple-dipole models for inversion. 3 Objectives The objective of this thesis is first to develop new methods of solving the inverse problem of magnetometry and second to test them in two different applications: I. magnetopneumography, where the location and magnitude of the source is not known, while its orientation is given by the static magnetization in strong magnetic field. II. distance measurement, where in general case only the magnitude of the source is known. The following text gives a more detailed description of the objectives together with the motivation. 3.1 Research task I During my study at CTU FEE I have dealt with the long term project of Magnetopneumography (MPG). Our approach to the measurements is based on fluxgate gradiometers used for mapping of weak remanent field of ferromagnetic dust deposited in lungs. Nowadays, the project continues under the research project Transdisciplinary Research in the Area of Biomedical Engineering II No. MSM6840770012. The development of the methodology is mostly carried out on verified models or in-vitro scans. We will describe primarily the progress in scanning of potential patients and in suppression of noise from distant sources. A lot of space is to be dedicated to the forward modelling and particularly to my main task - inversion of the MPG data. -9- Inverse Problems of Magnetometry Jiří Tomek 3.1.1 Magnetopneumography For the inversion in this task, we have adopted the idea of a multiple-dipole model. We are going to describe successes using artificial neural network (NN) models, including a novel approach of their application in a direct one step inversion, not an iterative one mostly presented in literature. Promising results on phantoms and computer models are to be shown. All this, except the last step revealed, is in a relatively rough resolution and in small tested volumes. The most recent work increases the examined volumes and shows the applicability of the approach to a whole volume of lungs, though further steps are to be made to reduce inversion artefacts, etc. The limits are to be revealed and the magnetic fields that we can measure are to be described in details. For the inverse task we need a perfectly working forward model as well as a system for the real measurements to support and verify our results. During the work, a special positioning bed has been built for subjects enabling the scanning of field maps. Several setups of gradiometers for the bed have been proposed and are to be dealt with here. Naturally, the computer forward models had to be improved according to these configurations. The main objective is definitely a complete experimental magnetopneumographic system, which also includes an air-gap electromagnet for magnetization of subjects. It is to be briefly described, including the models intended for improvements of its construction to obtain a better homogeneity of the magnetizing field. For future automatic reading, or better determination of the scanning position, we are going to mention first steps dealing with video tracking using a camera and an appropriate system of control points in the view, as well as a small array of six-probe gradiometers for the next generation of the scanning system that should integrate our experience and enable in-vivo data inversion relevant even for practise. 3.2 Research task II As has been outlined the second focus of my Ph.D. study concerns measurement of distance by means of a magnetic field. Particularly, it is a special medical application of stomach volume/distension and motility measurement for the purpose of active gastric electrical stimulation (AGES). This is proposed for obesity treatment. This project was part of international grant of cooperation with a team of Professor Chen from the Department of Gastroenterology at the University of Texas Medical Branch who leads the research group of the Veterans Research Foundation at the Veterans Affairs Medical Centre, Oklahoma City, dealing with various studies of the gastrointestinal tract. The targets are: working on the development of a gastric pacer that is controlled by means of measurement of the elongation of the gastric wall - 10 - Inverse Problems of Magnetometry Jiří Tomek proportional to the volume of the stomach and also to analyse the gastric motility according to chymus (food content) composition - this especially for research purposes. Unfortunately, the mechanisms of gastric wall function and also the effects of various kinds of stimuli to different regions on its activity, are still not well known [Zhang 2006]. The tasks in this part are to: • suggest a proper method of measurement of the stomach size and motility using magnetic moment • design applicable implantable sensors that can be used during in-vivo testing • test electronics that drives the sensors and process the measured data • develop software for data recording and further processing 3.2.1 On-demand gastric pacer – basic analysis Continuous electrical stimulation still used in the research of our US partner and other groups unfortunately results in the adaptation and resistance to stimuli and so its efficiency gradually decreases. The proposed on-demand stimulation should be more effective and less energy consuming. The final system should help in the treatment of obesity and gastro-intestinal malfunctions. This idea is supported by several previous studies of the American partner showing the positive effects of chronic gastric electrical stimulation on weight reduction and on the gastric motility disorders [Zhang 2006]. Chronic electrical stimulation led, in the case of healthy animals, to the reduction of the daily food intake and therefore, may lead, especially in obese subjects, to a significant weight reduction, without adverse yo-yo effects of fasting or the not always long lasting effects of the gastric bandage [Chen 2004]. The problem is of course more complex, the diet has to be well-balanced in order to provide all the essential nutrients. Obesity is unfortunately not just a matter of high consumption but also of bad food composition and this device may only provide help in the reduction of the food intake. Similar to heart pacemakers, the surgery concerning implantation is miniinvasive and it does not intervene any organ except for small sutures on the outer layer of the stomach wall; moreover, stimulation of the stomach wall by different frequencies and voltages has been approved by the FDA for treatment of one of gastric diseases - gastroparesis [Tomek 2009b]. - 11 - Inverse Problems of Magnetometry Jiří Tomek 3.2.2 Volume measurements for AGES (Active Gastric Electrical Stimulation) Our US colleagues suggested, at first, ultrasound for the measurement of the distension of the stomach; however they did not succeed because of the varying speed of sound in different media, which was varying too much during operation to get some relevant data for volume estimates. Another reason for the failure was the large power consumption. We are going to reveal a method that uses magnetic field sensors. Again it is based on the measurement of the distension of the stomach wall, which provides information about the volume of the consumed food; furthermore, the setup should give good enough signal for analysis of an action of the stomach wall corresponding to different stages during the food intake. Electrical activity beyond this movement can also be measured by EGG (Electrogastrogram), which was analysed by our colleagues in parallel during our lab experiments in November 2007. The motility of the stomach is, however, quite complex and needs further analysis. There is also some action without the food and before the meal, etc. For more information, the reader should see some publications about Gastroenterology [Friedman 2002, Butcher 2003] as this exceeds the range of this thesis - 12 - Inverse Problems of Magnetometry Jiří Tomek 4 Magnetopneumography (MPG) Many publications are dedicated to Magnetopneumography, an experimental diagnostic method for determination of ferromagnetic dust load in lungs. Some of the papers of mine are included in this thesis, see Sections 4.2.1.3, 4.4.2, 4.4.3.2, 4.4.3.3 and 4.4.3.4. Others are just in the references [Tomek 2003, Tomek 2005a, Tomek 2005b and Tomek 2007c]. Many others have been written by my former colleagues e.g. [Navrátil 1999, Tipek 2002] and other teams as have already been mentioned in Chapter 3. MPG deals with very weak steady magnetic fields, usually detected by SQUID magnetometers however, it has been proven that fluxgate probes can be utilized too, as the amounts of ferromagnetic particles in the lungs, especially of certain heavy industry workers can reach several grams [Tipek 2002]. Much about this task is also written in the introduction of the paper in Section 4.2.1.3. During the project several improvements have been made even with the measuring system, which is going to be described in Section 4.2 and in the papers in the further chapters. The set-ups exhibited many changes as well as the forward and inverse models that were developed according to them or several times it was also vice versa. The last and most progressive modification described in Sections 4.2.1.3 was inspired by a lack of data for the purpose of determining the problem and also to study the fields of the measured sources more. Unlike the state-of-the-art in geosciences, we do not have so much a priori information about the task which could reduce the non-uniqueness of the badly posed inversion task. In order to be able to measure content of the ferromagnetic dust in the lungs, these dust particles have to be primarily magnetized in a strong DC field. This may be performed in an electromagnet which was modified for this purpose already during [Navrátil 1995]. Some modelling of the field of the magnet is to be revealed in Section 4.1. When the subject or a phantom is magnetized we can perform scanning on a special bed with a separate portal for fixing the probes arranged in gradiometric configurations. These are described in Section 4.2. The crucial task is modelling. Forward modelling is foreshadowed in Section 4.3. Inverse tasks in general and our several approaches are the most extensive in Section 4.4., where my most important published papers describing the work over MPG are also included. 4.1 Magnetization problem - an electromagnet For several experiments with human subjects, we have utilized an electromagnet for magnetization of the volume of their lungs. It is a big electromagnet between whose pole pieces the subject can stand. The device is not perfect for this purpose, because the created field is not very homogenous and even not as strong as we would need. The picture of the electromagnet without insulation - 13 - Inverse Problems of Magnetometry Jiří Tomek that was used during the magnetization of the subjects is shown in Figure 4.1 and in Figures 4.2 and 4.3 the drawings of the device are shown. A photo during magnetization of one volunteer is visible in the paper in Section 4.4.3.2. Fig. 4.1. The electromagnet without insulation Fig. 4.2. Top view cross-section of the electromagnet [Hlaváček 2007] Fig. 4.3. Side view of the electromagnet [Hlaváček 2007] During my doctoral studies two BSc. students dealt with the modelling of the field of the electromagnet. The first one measured the field between the yoke ends and tried a simple 2D extended model in Gemini [Hlaváček 2007] and the second - 14 - Inverse Problems of Magnetometry Jiří Tomek one under my supervision has completed more valuable work in the 3D software ANSYS and has also proposed one relevant modification of the yoke to obtain a bigger volume of more homogenous and stronger field [Janský 2008]. Both these works are included in an attached DVD (/Works). 4.2 Scanning device In previous works [Navrátil 1999, Tipek 2002, Tomek 2003] a measuring table was used, which was just suitable for measurements on models. I have proposed and partially designed a glass fibre reinforced composite positioning bed [Tomek 2005a]. It has been built and a great deal of testing and improvements have been made during the four years of my cooperation on the research program No. MSM6840770012 of the Ministry of Education of the Czech Republic - branch concerning Magnetopneumography. This device is suitable for general use, especially for measurements in vivo. It is modular, having several separable parts: a table, a base module, a support frame, a bed, a portal in which tubes with probes are fixed and a box for added weight screwed to the bottom of the portal. This weight is there together with some rubber at the bottom to damp vibrations and to give stability to the portal. The bed enables, without any problem, the scanning of people, which has also been performed with several metal workers during practical exercises with students at the faculty (Figure 4.4). Unfortunately, when considering the application of our methodology on real data we have to say that we are still in the phase of modelling and preparing of the methodology, so there is no sophisticated interpretation of the data that were measured in-vivo. Fig. 4.4: A scanned volunteer – a metal worker - 15 - Inverse Problems of Magnetometry Jiří Tomek The bed is composed entirely of non-magnetic materials. In fact no metals were used. The complete documentation that describes the construction, materials and our testing of its magnetic cleanliness is in [Tomek 2005a], which is included on the DVD (/Works). Utilization of glass fibre reinforced composites in electromagnetic applications is quite common: the cases of the transmitting antennas of broadcasters for cellular and wireless networks use these materials, etc. One very famous application in the Czech Republic is also the housing of the broadcasting tower on Ještěd. The material can have interesting properties depending on its composition. Its matrix can be various fibres of glasses, carbon, basalt, etc. and different resins are used as fillers: polyester, epoxy, vinylester, etc. It can be light but extremely tough. The original design had been substantially changed during the development and construction, not everything was economically feasible or mechanically optimal. The final concept is rational and meets the desired properties. During my Ph.D. study there have only been changes made on the portal and naturally several innovations of the gradiometers have been implemented. Schematic pictures showing the main dimensions of the system are shown in Figures 4.5 - 4.7. Photographs of some of the important parts are given in Figures 4.8 – 4.10 and on the DVD appendix (/Photos). Detailed documentation is not part of this thesis and can be found in [Tomek 2005a]. Fig. 4.5: The positioning bed – scheme[Tomek 2005a] - 16 - Inverse Problems of Magnetometry Jiří Tomek Fig. 4.6: The portal [Tomek 2005a] Fig. 4.7: Tubes for fixing the sensors [Tomek 2005a] The bed moves on rails in two axes using special, double helix, trapezoid screws with a rise of 12 millimetres. The range of movement is 445 millimetres in length (y-axis) and 460 millimetres in width (x-axis), which is enough for testing of human lungs. The bed is laid on two rails placed on a frame that runs in four rails embodied to the base, respectively to the square pultruded profiles. This layout provides enough space for putting additional weight onto the base in order to preclude movement during scanning. The current portal can bear two tubes holding sensors or other equipment. The sensors can be adjusted to the proper positions on glass fibre tubes elsewhere in a calibrating field and then fixed to the portal without any disassembling of their set-up. One of the tubes was intended originally for two probes that were measuring the first order gradient [Tomek 2006, Tomek 2007a], but later we have introduced four more sensors forming a coaxial multi probe gradiometer to pick-up more information at once. This set-up can still use the same holder. Some gradiometer can also be placed under the bed [Tomek 2009a] as it is magnetically “transparent”. An array of the first order gradiometers based on the PCB fluxgate sensors [Kubík 2006, Janošek 2008] is planned as an option for the second generation of the positioning device that has been recently built for a project in 2008 [Pribula 2008]. This needed a new stronger holder. The tube in it can be tilted by screws, into an ideal perpendicular position independently from the base. All the sensors – an array of them – may be fastened to the holding tube together with a camera on a new boom enabling simultaneous adjustment of their height above the bed. The camera is intended for tracking the position of the object on the bed, which was pioneered even during [Nováček 2006]. Also some reference sensors can be fastened to the - 17 - Inverse Problems of Magnetometry Jiří Tomek second tube. The system is quite versatile and enables various experiments and the proper settings to the right distance from the measured object and a good adjustment of the probes. In the case when we need more space above the bed, the portal can be supported to a higher position as it is completely independent from the positioning table. Separation was necessary to ensure the least amount of transmission of vibrations caused by the moving bed, see Figures 4.8, 4.10. with the old design of the portal. The damping of vibrations is solved by 4 centimetres of rubber and the weight of 18 – 26 bricks that can be placed into the box base. This also disables any unwanted movement of the configuration during the measurements. The bed is heavily ribbed and U-shaped to minimise deflections while the test object or person is laid on. It moves on 6 wheels in two rows in rails on a strong frame made from square profiles that has 8 wheels in 4 rows on the bottom side moving in rails on supports on the base of the bed. The base is freely placed over a sandwich table and secured by long margins of the base that overreach the table. Manual scanning is very time consuming as in 1 centimetre resolution there are 2025 positions so we use usually 4 centimetre resolution with just 144 positions. Actuators for automation could be added thanks to the design which counts with that, but it is a rather complicated and expensive task. The number of scanning positions can be sufficiently reduced using the intended probes’ array for the mentioned project [Pribula 2008] together with the sophisticated video control of the object’s position. - 18 - Inverse Problems of Magnetometry Jiří Tomek Figure 4.8: Completed positioning bed, bricks just at the base of the portal, two probes fixed to the holders and then to the tube Fig. 4.9: Probe and parts of the holder used for the two-probe gradiometer [Tomek 2005a] - 19 - Inverse Problems of Magnetometry Jiří Tomek Fig. 4.10: Portal with the tubes, two sensors and boom [Tomek 2005a] The product does not have many accessories for precise adjustment of position of the portal, gradiometers or the bed, but it is a robust, rigid device that can be easily set once and work without constant interventions, until a different setup is to be assembled. 4.2.1 Probe setups & noise The most obvious problem of the performed weak magnetic fields’ scanning is the magnetic disturbances during the measurements for which the utilized first-order gradiometric measurement is not usually sufficient (more on this problem is also written in the paper [Tomek 2009a] in Section 4.2.1.3). This can be - 20 - Inverse Problems of Magnetometry Jiří Tomek solved by the location of the lab faraway from the sources of disturbance, i.e. not in the city but in the country side. Better background noise suppression is possible with shorter gradiometric bases (or baselines, i.e. the distances between the probes); however it is always a question of optimization of the noise suppression and intensity of the wanted signal from the considered source types [Braginski 2004a]. SQUID magnetometry (MEG, MCG, etc.) can be a good source of inspiration how to deal with noise in such medical applications thanks to extensive practical and experimental knowledge. The principles are similar, but our sources are stronger and moreover, we do not have shielding that is common to SQUID applications. The noise of the probes and electronics itself is also higher. One of the main limits, why we cannot fully automatically adopt the established MEG techniques is the fact that our sensors contain high permeability materials and have compensating feedback. Thus, not such short baselines and the presence of the sensors extremely close to each other as in the case of SQUIDs are possible. Higher order gradients realized by more coaxial probes can partially help as well as having the same gradiometer placed as close to the measuring one but also far enough away not to be affected much by the scanned object. Magnetic shielding of the necessary size is very costly, so we have not even tried it. Moreover, our aim is in fact a system that can be used elsewhere and will be more or less movable. 4.2.1.1 Separate (reference) gradiometer sensing the outer fields This is the method of using a reference gradiometer to suppress variations of the background field. Together with the other methods it is extensively described, mainly in the works devoted to SQUID magnetometry, e.g. Magnetoencephalography [Vrba 2002, Vrba 2004 and Braginski 2004]. Some more references are revealed in the paper [Tomek 2009a] in Section 4.2.1.3. We have tried that with another first-order gradiometer placed about 1.5 meters (at the same height above the ground) sideways from the measuring gradiometer in order to have a reference almost not influenced by the measured object. Considering the distance, we cannot suppose that even with the same gradiometer the detected gradients should be the same because of the nonhomogeneity of the field in the measurement region. This gradiometer was supposed to track the background during the period of the measurement. By this means, we could keep information about the level of the background gradient in time and subtract it from the gradients taken over the objects. It would also be necessary to optimize the distance and relative position to the measuring gradiometer and to find the appropriate constants for the chosen sites in the room as the fields are supposed to have different intensities due to the different distances from the sources and different angles to them. This is a problem - 21 - Inverse Problems of Magnetometry Jiří Tomek independent of the facts that the gradiometers are identical, properly aligned and calibrated. The measured signals should be well correlated if we want to use such a method. One overnight measurement presented at the conference OIPE 2006 is presented. It shows a calm period between 1 and 4 o’clock in the morning, see Figures 4.11 and 4.12. “Grad 1” is the signal from gradiometer over the measurement node and “Grad 2” is the reference signal coming from the same gradiometer 1.5 meters sideways. The distance between the probes of these two first order gradiometers was 40 cm. One can observe an excellent correlation between the signals, however the amplitudes are not the same and due to the different closer sources of disturbances, there are significant differences in amplitude variations. The situation would be far better in a place where the field is nearly homogenous, like in the countryside away from ferromagnetic rocks or inside some shielding system. We could consider a similar shielding as is used for SQUID MEG (Magnetoencephalography), however it is costly. There is a question of optimization of the distance between the two gradiometers and the distance of the reference from the object. It is similar to the task of finding the best gradiometric base between the probes of the individual gradiometers. Again, one can find much about it in [Braginski 2004a], which is focussed on SQUID magnetometry. This method has not been closely examined further until now, because we have focused more to other perspective solutions. -8 x 10 Gradient [T/m] 4 2 0 Grad 1 Grad 2 -2 19:00 0:00 5:00 Time [hr:min] 10:00 15:00 Fig. 4.11: Overnight measurement that maps the background field during the day in our lab. The noisier the signal is from the measuring gradiometer Grad 1,the less noise comes from the reference gradiometer Grad 2. In both tracks there is the calm period approximately from 1 to 4 o’clock AM also reported in [Tipek 2002]. The differences are mainly due to the different positions of the gradiometers in the room and slightly different alignment of the sensors. Both gradients are filtered by a 0.67 mHz high-pass filter and a 30nT/m gradient field has been added to Grad 2 in order to visually separate the two traces. - 22 - Inverse Problems of Magnetometry Jiří Tomek -8 x 10 Gradient [T/m] 4 Grad 1 Grad 2 2 0 -2 4:50 4:55 5:00 Time [hr:min] 5:05 Fig. 4.12: Detail of the measurement, showing a perfect correlation of the signals 4.2.1.2 Probe array An array of probes, respectively of the first order gradiometers, is one of the key parts of the already mentioned ‘FRVŠ’ project for the year 2008. By scanning of the interesting region in one moment with a well calibrated assembly of sensors connected to separate channels of a new magnetometer based on [Janošek 2007], we can get rid of the problem of magnetic disturbances in time, however others arise. The sensors inevitably influence each other so we cannot have the array too dense. Also, these probes contain ferromagnetic cores and work in a compensating feedback loop cancelling the field in the core region as is discussed in the paper in Section 4.2.1.3. The minimal cross-axial spacing of the sensors is planned to be 2 cm and the standard one 4 cm, which still suggests several successive readings in order to obtain a higher resolution. The optimum axial distance, i.e. the gradiometric base, is to be determined experimentally while getting the best ratio between the useful signal from the object and the background field suppression [Braginski 2004a]. The details of the realization are subject to the project itself and are available in the final report [Pribula 2008]. The main problem that remains is the non-homogeneity of the background gradient field in the scanning region. Definitely, the map of the non-homogeneity can be obtained by a number of measurements without the tested object and by averaging. Averaging of the data obtained in a certain period of sampling during examination is supposed to suppress the stochastic field variations satisfactorily, however extending scanning time, which is problematic. We even plan to test an array of gradiometers having more probes in one axis to measure in several heights simultaneously and to test one method, revealed later on. It applies a mathematical calculation of a magnetic field function for the tested object eliminating some noise sources and to a certain extent also the imperfections of the probes alignment. The suggested approach unfortunately needs, e.g. 6 or even more, sensors coaxially - 23 - Inverse Problems of Magnetometry Jiří Tomek aligned over one scanning node (see next chapter). This alignment also enables the further investigation of efficiency of a reference gradiometer technique discussed in the previous Section 4.2.1.1. 4.2.1.3 More coaxial first order gradients During experiments with a mathematical description of the fields above the sources, we have come to an interesting idea having several benefits. If the noise levels are not too high and affect the measured gradients almost equally, it may help to separate the background fields from the desired close ones. The fitting method revealed below provides a relatively simple description of the measured functions (the decay of the field of the source with distance) and for smaller compact homogenous sources, it directly calculates the position of such a source even out of the measurements over a single node. Naturally, the bad homogeneity of the background has the biggest effect on the performance. We have built a coaxial six-probe gradiometer providing 5 successive first order gradients. These gradients, above a magnetic dipole, should be described at a given scanning node by a relatively simple equation based on the Biot-Savart law [Fitzpatrick 2006] applied on Ampere’s magnetic moment of an ideal point source. By means of fitting of the data acquired at a moment above one of the nodes, we can mathematically derive what is the value of gradient due to the distant sources that appear between the probes at that moment. This background gradient changes in time as much as is reported in the Figures 4.11, 4.12. So when we are scanning the map in successive steps, we need to keep the information about the background or have to be able to derive it. The presented configuration is quite effective. It preserves data from five scanning heights above the measured object so there is much more data for inversion with an acceptable resolution and we can still separate the level of the additive field from background in scanning moments, thus the data may be less biased. The truth is that in an ordinary environment, this component of the background field is not the only one that disturbs the measurement. The fitting may also suppress, to a certain extent, noise and differences from the ideal measurement caused by the non-homogeneities of the field from the distant sources and differences caused by the non-perfect mutual alignment of individual probes. Something should also be written about the algorithm itself. In order to obtain a good fit of the measured data by our function, appropriate initial conditions have to be used. Otherwise the algorithm stops at the local minimum and the fitting is bad. This is one of the features of the chosen Nelder-Mead procedure [Rowan 1990, Bogacz 2003]. Some more sophisticated minimization method can definitely be utilized, however, that would be a task for another work. With the five gradients, a good fit is possible with just the parameters that are close to the ideal solution. In the case of the total outliers (data too biased), the fitting performs badly. - 24 - Inverse Problems of Magnetometry Jiří Tomek The most important thing is that such a gradient function can be found even for sources that cannot be interpreted as dipoles because of the very short distances of the closest probe from the phantom. The function is then the same for a fictive dipole that would act as if the source fields were summed and located at an appropriate distance. The idea, configuration of the gradiometer and some supporting experiments were published at IEEE Sensors 2007 Conference, Atlanta, Georgia, USA and are dealt with more in the extended paper published in IEEE Sensors Journal [Tomek 2009a] which can be seen on the following pages. - 25 - Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 26 - 1 Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 27 - 2 Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 28 - 3 Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 29 - 4 Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 30 - 5 Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 31 - 6 Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 32 - 7 Inverse Problems of Magnetometry Jiří Tomek IEEE Sensors Journal – accepted paper, 2009 - 33 - 8 Inverse Problems of Magnetometry Jiří Tomek 4.2.1.4 Higher order gradients, averaging, statistical analysis of the field in the measurement region and compensation During the “Project in team” [Křížová-Huňka 2008, included on the DVD/Works] we have been analysing the suppression of a strong disturbing artificial field created by small Helmholtz coils, which were formerly intended to create a field over distances where they could have been interpreted as a dipole. However, the students have also experimented themselves with very short distances, where the coils produced strong non-homogeneities of the disturbing field. The six probe gradiometer has been used in the way reported in the paper in Section 4.2.1.3, but with the averaging of several subsequent measurements of the same phantom at the same node above it. They tried two approaches: Subtraction of an averaged measurement without the tested phantom (i.e. just the background) from the phantom measurement and calculating of the second order gradients using the last gradient as the reference. The experiments would require more study, but show that averaging and especially subtraction of the averaged gradient levels without the presence of the phantom seem to be more helpful than we have assumed. Unfortunately, some compromise between scanning time and acceptable noise would be necessary. The length of scanning has to be cut down for real applications at least because of various artefacts and gradual decrease in the remanet field after magnetization of the subject. An array of gradiometers should be introduced if we wanted to adopt longer term averaging to suppress the background variances. It should be clearly stated that all the presented testing utilizes averaging, but only by means of the integration times of the ADC that were 0.2 s or 2 s, not by averaging of a defined number of readings. 4.2.2 Video controlled positioning For better repeatability of the measurements and especially for optimal placement of the subjects and tracking of their movement on the bed in the examination area, we have proposed to use a camera and image processing tools to determine the relative position of the object to the probes. The first step has been completed during the thesis [Nováček 2006]. Further work with a higher resolution CMOS chip and software including calibration based on the fixed points (spot lights or reflex reflectors) in the scene was made during [Pribula 2008]. Utilization of the camera is going to eliminate the positioning errors caused by the subjective reading of the meters and errors caused by accidental displacement of the bed or the portal. Three non-colinear spots on the moving bed would be sufficient for calibration as well as to reveal any displacement. This is - 34 - Inverse Problems of Magnetometry Jiří Tomek possible only if the camera is fastened to a tube on the portal, i.e. having rigid connection with probes. If it is independent, also the portal position has to be tracked. In order to keep the distance of the camera the same from the measured object, the construction plan is to have the camera and the probes on a single tube that can be moved in the portal vertically in the necessary range, i.e. a subject with a bigger chest will need the probes higher above the bed and the focus of the camera has to also be higher by that distance, because we are tracking the subject not the bed below him. 4.3 Forward modelling The most crucial part of most inversion techniques besides obtaining proper sets of data, is to develop a good forward model of the examined problem. Usually we need to make a computer model that replaces our physical measurements for the purpose of generation of representative sets of measurements that could be processed to obtain the inverse model or very often to use it to determine the error for the calculated measurement of the certain estimate of the sources while using iterative approaches. The model quality has to be proven by several sets of physical measurements. The forward model is an excellent tool for analysis of the possibilities of various inverse processes or for modelling of the efficiency of the different measurement setups, i.e. whether more information from scanning (data in better resolution or from different sensors layout) would be more effective, etc. It enables one to first simulate various experimental configurations before choosing improvements of the older setup that should be realized physically. The model we use utilizes an ordinary summation of fields of point dipoles representing the total magnetic moment of the lungs in discretized voxels each having a volume of 8 cm3. We apply the Biot-Savart Law to calculate the fields. The software has formerly been programmed in Matlab even during [Tomek 2003] but many significant improvements have been made during my Ph.D. studies. For details, see [Tomek 2006a, Tomek 2007a] or an older version in [Tomek 2005a]) and the code on DVD appendix (/Software/Matlab/ForwardMPGsolver) The described approach was mainly chosen for better versatility of the model and better applicability in the inversion which is not the primary purpose of the specialized software for FEM (finite element modelling) like ANSYS and COMSOL or others. The problem itself is not very complicated thanks to the measurements in air and of non-magnetic tissues, which have susceptibilities almost zero. The created PC solver is in perfect accord with the physical measurements, as is confirmed by the included papers in Sections 4.4.3.2 and 4.4.3.3 and also in [Tomek 2005b]. The forward problem is unique thus, it is possible to create a weight matrix using the solver for a defined distance or distances of the probes from the phantom and make - 35 - Inverse Problems of Magnetometry Jiří Tomek the field calculation without program cycles, thus, the quickest possible. We can also use tools like artificial neural networks [Tomek 2005a], etc. However, in our case multiplication of a proper weight matrix by a vector describing the source seems to be the ideal method. Such a matrix can be can be implemented as a fast solver for the purpose of an iterative optimization, e.g. using genetic algorithms (GAs) see the paper in Section 4.4.3.4 [Platil 2008]. The program for GAs has been created by the co-author. The described matrix can be obtained using the phantom model. Imagine that we put a single magnetic cube having a magnetic moment of one unit to the first phantom position. This creates the respective unit field matrix that we scan. This matrix is then reshaped to the first row of the weight matrix. This is done for all possible cube positions, so we obtain unit constants of the scanned magnetic field in all scanning positions we need, meaning the complete weight matrix. When such constants are multiplied by the respective moments of the cubes of the phantom and summed up at the respective scanning nodes we get the right simulated field data. For a mathematic explanation of the process, again see the paper [Platil 2008] in Section 4.4.3.4. 4.4 Inverse problem The inverse problem, as we have it defined here, i.e. the determination of the sources of the measured signal no matter if on a DC or AC base, is usually solved as an optimization task, if there is no direct mathematical solution. Inversion of such complex magnetic data that we have in this case, is unfortunately non-unique and not only because of the fact that we have a smaller set of measurements than is the number of sources to be determined. This comes from the inherent nonuniqueness of D (electric flux density) and H (magnetic field intensity) in Maxwell’s Equations [De Lange 2003, Li 1996] thus, the range of the possible solutions has to be limited by the constraints of the model and a priori knowledge, like the positivity of susceptibilities, no thin layers of high susceptibility, etc. Experience with the characteristics of the given problem is thus crucial. An overview of various techniques applied mostly in geophysics can be found, e.g. in [Oldenburg 1990, Lelièvre 2003]. The more data and conditions of the problem we have and incorporate into our models, the more it reduces the available degrees of freedom. This is, e.g. the reason for utilization of measurements in several layers above the tested object revealed in Section 4.2.1.3. Most of the other theoretical aspects of our DC MPG inverse problem has also been revealed in [Tomek 2005a at DVD/Works] to which I would like to refer the reader for more details. - 36 - Inverse Problems of Magnetometry Jiří Tomek Our problem even when discretized in relatively rough resolution is not well conditioned; furthermore, there is the mentioned non-uniqueness of the magnetic inverse problems generally. We have added more scanning heights reducing the number of degrees of freedom or we even have reduced the region where the possible source unit could be calculated in case of the general solution (3D inversion of a model containing multiple sources, which are randomly distributed). In the task of the general problem, we have performed experiments that imply the possibility to obtain a good solution by means of direct inversion utilizing multiplication of the measured values in each scanning node in each layer (height) by their respective weights. The basic idea is to calculate an inverse matrix and use it for the inverse calculations. The computation then enables one to compose the right value of the respective magnetic moments in the voxels of the lung phantom. These weights can be found by the Least Square Method utilizing the Singular Value Decomposition (SVD), such a technique is common for linear neural networks, which we have tested several times on smaller problems. The idea has unfortunately serious mathematical and computational limitations as the data is bulky. Little bit better results are supposed after forcing the positivity of the magnetic moments. However, this needs non-trivial modification of the process. One idea is to also experiment with this tool iteratively. The method is further described including several experiments in Section 4.4.3.4. Some problems, not having much clear interpretation or being as bulky as ours, are solved by artificial neural networks (NNs) very often or other evolution algorithms or iteratively by various techniques. Neural networks have been thus extensively examined, partially also genetic algorithms, again see paper [Platil 2008] in Section 4.4.3.4. 4.4.1 Basic overview of some techniques In practice the inversion of magnetostatic data is widely used in geology [Li 1996, Lelièvre 2003, Shearer 2005], in some non-destructive testing [Chelouah 2000, Pechenkov 2001, Ramuhalli 2002], in detection of metal objects either in industry or e.g. in some landmine locators and several other applications. An alternating field is utilized much more often. Many such applications are again, in non-destructive testing, based either on eddy-currents or flux leakage, but great research in this field is taking place in medicine: in Magnetoencephalography (MUSIC algorithm [Mosher 1999, Juany 2007], an explicit identification method for electric dipoles in a conducor [Popov 2002]), examination of iron in the liver (biomagnetic susceptometry based on SQUIDs) [Carneiro 2002, Brittenham 2003], a technique called magnetic induction tomography (MIT) [Korjenevsky 2000, Merwa 2005 is also being developed]. - 37 - Inverse Problems of Magnetometry Jiří Tomek We can think about three concepts of solving inverse problems: o Direct mathematical solution if we can derive the proper formulas o Iterative optimization procedure o Evolution algorithms (NNs, Genetic algorithms…) The iterative optimization procedures utilize many specialized techniques to search for the optimal solution. Some are gradient based, where it is usually necessary to know the first and also mostly the second derivative of an error function, others do not need such information. Some guarantee finding of the global extreme of such a function, thus the best possible solution, others unfortunately not. Examples of the optimization techniques are e.g. Nelder-Mead technique (one of the simplex methods) [Lagarias 1995, Chelouah 2000] which does not need the derivatives or BFGS (Broyden-Fletcher-Goldfarb-Shannon) method, belonging to Gauss-Newton gradient methods [Avriel 2003, netlib 2008]. Gauss-Newton global optimization methods are used in tasks in geology that are generally similar to our MPG problem, though stronger fields are detected and the resolution is in several units of meters [Li 1996, Oldenburg 1999, Shearer 2004, Lelièvre 2006]. They utilize problem specific simplifications and incorporate geo-specific constraints and experience (depth weighting, etc.). But also relatively simple problems like the detection of a magnetic marker in space can be realized by such a technique [Hashi 2005 and 2008]. The evolution or genetic algorithms (GAs) are in fact also iterative, but use specific methods originating from their inspiration in natural processes and the evolution theory of the survival of the fittest. They are general-purpose global optimization techniques based on randomized search and incorporating some aspects of iterative algorithms [Caponetto 1997]. GAs can tolerate noisy and discontinuous function evaluations [Chipperfield 1997], which would be excellent for us as our data is always pretty noisy. I am mentioning this technique, because its utilization is subject of our further research whose first part has already been published in [Platil 2008]. The paper is also in Section 4.4.3.4. After mastering the fast forward solver, we have also tried this approach. For some more descriptive information about the GA, the reader can see [Tomek 2005a at DVD/Works] and the references mentioned there. For all types of iterative methods, the fast forward solver is essential to cut down the iteration periods. In cases where the model cannot be realized so effectively by direct mathematic computation, models are estimated commonly by trained neural networks. I have also worked on it earlier [Tomek 2005a]. NN derives solutions very quickly in comparison to the more complex e.g. iterative forward solvers and is thus used to determine the fields corresponding to the estimate of the sources during the iterative optimizations to achieve better computational efficiency even though a certain error is present in the neural network estimates [Ramuhalli 2002]. - 38 - Inverse Problems of Magnetometry Jiří Tomek 4.4.1.1 Neural networks As has been partially revealed, I have used this “evolution” technique for the inversion of our MPG data. There has been continuous progress from the inversion of the simple compact sources [Tomek 2005a, Tomek 2006a and Tomek 2007a] to the more complex multi-source phantoms to the latest adoption of the simplest NN algorithm to calculate an inverse matrix for processing of appropriately formatted data by a direct one step mathematical calculation [Platil 2008 (Section 4.4.3.4)]. Thus, artificial neural networks are in this thesis the most important tool in the means of the inversion of the magnetic field data. Neural networks (NNs) have been quite a popular tool for several decades, various types and techniques have been developed and are used as a powerful tool to find relations in complex data, where we do not see a clear interpretation and moreover, they are able to generalize, meaning their ability to find the correct result even for unknown (i.e. not trained for) inputs. NNs are practically used in medicine for diagnostics, control of devices; in banking for investment risk estimation, in weather forecasting and several other areas. Their ability to successfully solve strongly non-linear problems belongs to the advantages of NNs, moreover in multidimensional space [Jiřina 2004]. They can be used for classification problems or for, in our case, the needed, regression ones. They can solve both discrete and continuous problems. The biggest deal, except for obtaining representative set of data for learning process, is to choose the right type of network. Only the suitable type will enable one to reach the best possible results. Usually, one has to do it by trial and error though there are nowadays software tools (MATLAB’s Neural Network Toolbox by Mathworks, STATISTICA by StatSoft, Inc., etc.) that enable one to test the datasets at least with the most typical configurations. Usually, one finds that the simplest solution is the most effective one and probably even the best one. Which is coincidentally an idea formulated long ago by William Ockham living in 1285–1349. NNs are also usually utilized to realize the forward problem as has been already mentioned above and then the inversion is performed in an iterative loop utilizing some of the optimization methods. This is possible, because the trained network performs the calculations quickly. However, the possibility to apply the tool directly on the inverse problem if enough data is provided exists as the inverse problems are usually undetermined, so we cannot want a better resolution than enables the provided data. If so, iterative procedures are the only choice. - 39 - Inverse Problems of Magnetometry Jiří Tomek 4.4.1.2 Automatic differentiation of the forward model for optimization We should mention here a method that would enable one to apply gradient optimization methods to our problem, which we unfortunately have not examined much even after creating a far more efficient forward model, that is discussed more in Section 4.4.3.4 and [Platil 2008] for which the discrete differences would be easier to calculate than it was with the old model based on the program cycles [Tomek 2005a]. Automatic differentiation provides an excellent possibility to calculate the gradients or better differences of the error functions with multiple unknowns in a reasonable time, which is crucial during iterative inversion tasks. Analytical calculation of the gradients of such problems is very elaborate, sometimes even impossible. The basic function describing the relation between the single magnetic dipole moment and the magnitude of the gradient of the magnetic induction, which is derived form the Maxwell’s Equations is not so complicated, but in general we need derivatives at each measuring point by the position and magnetic moment of every single cube of the source. There exists software in Fortran, C and also in Matlab for this purpose. The Matlab package ADiMat (developed by Andre Vehreschild - Institute for Scientific Computing Aachen University, Germany) redesigns the prepared Matlab function to provide differences with respect to the input parameters. The old model from [Tomek 2005a] has been realized, where the reader can find more details and the derived software is available on [DVD appendix at DVD/Software/AdiMat]. 4.4.1.3 Newest optimization methods Faster and better optimisation methods are constantly being developed. I had the possibility to get acquainted with research in this branch at the Czech Academy of Sciences. As we now have a very precise mathematical description of the problem, finally formulated into a relatively simple equation, we can on one hand realize the differences and on the other hand apply some new efficient gradient based optimisation method. There was also suggestion to apply a SUBPLEX technique, for which we have found a basic code that could be applied after several modifications to our task [netlib 2008 (http://www.netlib.org/opt/)] New sophisticated methods are also used for alternating signals; however these are usually not adaptable to our task. - 40 - Inverse Problems of Magnetometry Jiří Tomek 4.4.2 Estimation of total dust load The most common task in magnetopneumography is the estimation of the total amount of deposited dust. There have been several approaches in the past, which are briefly mentioned later on in an application oriented paper [Tomek 2006a]. I have come up with an idea to use the integral (summation) of the individual gradients measured in multiple nodes of a single plane lattice over the subject or phantom. The best solution would be to sum the total gradients over the biggest plane possible, ideally by the definition over the area all-around the measured object, which is suggested for good determination of EEG source proposed by [Popov 2002]. We have mathematically modelled our ordinary set-up with the basic first order gradiometer and tried to model the situation. We have generated random distributions of the magnetite contaminated model cubes in the phantom volume and summed the calculated gradients. This has been done for several cases where the magnetite amount in each of the distributed cubes was always the same and just the number of them varied. As is shown in the graphs in the paper below (page 3 figure 2) the estimate error is about ±10 cubes mainly depending on the distance of the measuring plane from the phantom. The necessary prerequisite for the estimate of the dust load is the knowledge of the magnetic properties of the expected dust in the locations where work and live the examined subjects. This is a major subject of the following paper. The paper also deals with related topic concerning the dynamic characterization of ferromagnetic nanoparticles intended for hyperthermia cancer therapy, when heat is induced in the region of the concentrated particles by a high frequency magnetic field. - 41 - Inverse Problems of Magnetometry Jiří Tomek Sensor Letters 2007 – extended paper - 42 - 1 Inverse Problems of Magnetometry Jiří Tomek Sensor Letters 2007 – extended paper - 43 - 2 Inverse Problems of Magnetometry Jiří Tomek Sensor Letters 2007 – extended paper - 44 - 3 Inverse Problems of Magnetometry Jiří Tomek Sensor Letters 2007 – extended paper - 45 - 4 Inverse Problems of Magnetometry Jiří Tomek Sensor Letters 2007 – extended paper - 46 - 5 Inverse Problems of Magnetometry Jiří Tomek 4.4.3 Neural network inversion in MPG As has already been mentioned above, the idea of utilization of the artificial neural networks for our problem comes even from [Ripka 2004] (then [Tomek 2004b]). It has been more deeply examined in [Tomek 2005a] and continuous progress has been recorded in three SCI journal papers [Tomek 2006a, Tomek 2007c (from a conference in 2005) and Tomek 2007a]. The two more important works are included later in respective chapters. 4.4.3.1 Restraints & limitations We have already said that just the discrete model of the problem is feasible. The primary question is thus the resolution we would like to achieve. Then we need to prepare a measurement set-up that can feed the inversion with enough data to reduce the non-uniqueness of such complex magnetic inversion problems, together with the fact that the individual measured gradients themselves are nonunique. Furthermore, we just use a component of the total vector of magnetic field that is in the sensitive axis of the gradiometric probes, thus again there is less information from the testing. Just one first order gradient in a rational resolution of 2 cm provides 552 scan locations (44x46 cm surface) however, we would need to determine up to 574 magnetized sources distributed in the space of the lung phantom. Introduction of five coaxial 1st order gradients in the new set-up improves the situation, but the data cannot be independent when obtained in such a configuration. The phantom of the lungs is simplified for the modelling purposes not only in the resolution to the cubes of 8cm3 but also in the direction and size of their magnetic moments. The direction of magnetization is known – in the sensitive axis of the gradiometer – and the moment can be either zero or a given value, so we just deal with a binary problem, however the moments of the cubes are calculated in a continuous range. Another reduction of the degrees of freedom is the known position of the phantom in relation to the probes. To sum it up, in the most general problem, we deal with the need to determine the positions of randomly distributed magnetized cubes in the phantom. Their number may vary from 0 to 574. It may even happen that there is a nonmagnetic cube surrounded by magnetic ones. Mathematically, the position of each cube is defined by three unknowns, its moment is another unknown though in the simplified phantom it is zero or one. This implies that the inverse problem is in a mathematical and physical point of view badly determined, thus non-unique. Moreover, in real data some noise is present which disturbs the inversion techniques. - 47 - Inverse Problems of Magnetometry Jiří Tomek The above briefly listed limitations of the inversion are also valid for neural networks and others are added with the fact that required number of the representative sets of the training data is high. The problem can therefore, be hardly handled using standard desktop computers and software, see the problems reported in the papers [Tomek 2006a and 2007a and 2007c]. Either the software cannot deal with so much data or so many variables or there is not a long enough nonfragmented memory space for processing memory-intensive problems like singular value decomposition (SVD) [Platil 2008]. The first experiments just used the single scanning plane and were aimed to determine the dimensions of a single homogenous compact source in the phantom’s volume, see Section 4.4.3.2. To further simplify the neural network applied on the inverse problem, we have chosen an approximate function to fit the measured gradient. That reduced the number of inputs, however, it was also causing a bad estimate of the source when having noisy data. From the beginning, the mentioned general distribution has been examined. We have found out to what number of phantom cubes the inversion works in the case of single 1st order gradient, see Section 4.4.3.3. As the number (just 64 cubes) was totally unsatisfactory, more measurements in more planes were introduced and a relatively successful inversion for 100 cubes was presented [Platil 2008], see Section 4.4.3.4. Noise, set-up inaccuracies, background noise and the noise of the electronics itself are the most important limitations for the real application. We have experienced serious noise sensitivity with all of the already tested neural network models, the last one is no exception. Nevertheless, this is common for almost any inversion technique, so we need to cope with that and reduce the noise levels in real data. A lot about this has been already discussed in Section 4.2.1. 4.4.3.2 Localized sources The basic simplification of the problem was to recognize the single localized compact source in the lung phantom. Certain diseases (e.g. lung emphysema) may result in a higher concentration of the deposited particles in the place where the lung tissue is damaged, where the air with diffused particles is cumulating and it cannot easily pass away. However, our experiment is totally artificial. The presented method could also be applied well for the total dust amount estimate, but this aspect was not examined as the primary reason was to test the neural network inversion process with all the possible dimensions and positions of one source in a clear phantom. The forward model was programmed to generate the training data in a cube scribed over the phantom’s volume. The maximum dimension of a source was 10x10x10 cm, the minimum was a single cube. The placement was random in all three dimensions. A trained network (e.g. MLP – multiple layer perceptron one) - 48 - Inverse Problems of Magnetometry Jiří Tomek was supposed to realize our goal, which was an estimate of an unknown source (its size and position) from any measurement, even the one which was not in the training set. The chosen fitting that compresses numerous data from a measured map into several parameters that become inputs of the neural network was surprisingly quite sensitive to noise. More on this is presented in the included papers [Tomek 2006a, Tomek 2007a]. The first inverse model has been developed for the old system with phantom between two fluxgates [Tomek 2005a, Tomek 2005b]. A Gaussian-like function has been used for the approximation of the measured fields to compress the measurements in order to have less inputs of the neural network and thus simplify the training process. It was a generalized 2D Gaussian. Generalized, because of the fact that the exponents were also between the fitted unknowns together with the amplitude, mean values (location of the peak) and generalized dispersion (defining the “width” of the lobe) see Chapter 4 in the next paper [Tomek 2006a]. The same approach remained even with the new measurement setup, where the gradient matrix is being measured in two or more levels just above the phantom, which is placed horizontally. The reason for utilizing this function comes from the fact that we fit the data that is a difference of two planar cross-section measurements of a source that acts almost like a dipole. This gradient distribution is a certain combination of goniometric functions, thus it has this exponential character. The chosen function provides a very effective fit for the wanted simplified purpose. For the fitting, we have chosen the Nelder-Mead Simplex method embedded in Matlab to find the optimum coefficients of the Gaussian. This software (Matlab script) is included on the DVD – see folder [/Software/Matlab/Fitting_Gaussian]. The following paper published in Sensors & Actuators – Physical [Tomek 2006a] describes most of the work done with the MPG until experiments with multiple sources, including the improvements of our forward model, which is compared with real phantom data there. In the paper, a method of measurement of magnetic moment of a magnetized sample using Helmholtz coils and fluxmeter is also revealed. This measurement had to be performed to determine the moment of phantom cubes, which could not be measured more precisely by our other laboratory equipment because of too strong fields. The source was too strong for a geological rock-sample generator, i.e. rotating sample magnetometer. Some further experiments with these localized sources, but in this case without fitting the Gaussian like function are in the paper [Tomek 2007a] in Section 4.4.3.3. We have utilized a far bigger network there, a four layer perceptron one, and have achieved very encouraging results even with a smaller training data set (10 000). The number of examples was limited by the software utilized for the inverse model experiments (StatSoft’s Statistica 6). The results of the same sources, as were presented with the fitting, are closer to the ideal values, especially thanks to the elimination of the inaccurate fitting. - 49 - Inverse Problems of Magnetometry Jiří Tomek - 50 - Inverse Problems of Magnetometry Jiří Tomek - 51 - Inverse Problems of Magnetometry Jiří Tomek - 52 - Inverse Problems of Magnetometry Jiří Tomek - 53 - Inverse Problems of Magnetometry Jiří Tomek 4.4.3.3 General problem Though the problem is not well conditioned we have tried to estimate the smaller subsets of the lung phantom composed from 574 cubes of a volume of 8cm3. As was already mentioned, we have reduced the problem to a binary one so that there could be either magnetic or non-magnetic cubes, however randomly distributed. Such a resolution may seem realizable, however the problem is still quite bulky and we may reach the limits of the used hardware or software in means of computational demands. Our software had problems even with 552 (24x23) input parameters for the neural network, when we wanted to use single scanning height in resolution of 2 cm. [Tomek 2007a]. We needed to make several improvements and especially prepare some custom software, which would only have the limit in size of the non-fragmented memory for the necessary mathematical operations. The first attempts are described already in [Tomek 2005a]. Further experiments are then in the paper below where we reveal that in a relatively small volume of the phantom – 64 model cubes, we can distinguish the magnetic and nonmagnetic cubes/voxels quite well and what is more, even in several layers. Again one-step inversion based on neural networks was used. The best performance provided a simple linear NN [Jirina 2004]. Other NNs were considerably worse. The presented results give us the suggestion that with even more examples for teaching or for the inversion done on the mathematical basis of SVD (which is the algorithm used for calculation of weights of the linear network, explained more in Section 4.4.3.4) and incorporating some more a priori knowledge we could achieve even better results. How much added data would be optimal, has not been fully tested yet. But in the next chapter, we are going to describe results while adding more heights in which the gradients are measured. The paper below [Tomek 2007a] describes the lung phantom and the models and gives another example of a single planar measurement of the magnetic field that is processed by the NN inverse model. - 54 - Inverse Problems of Magnetometry Jiří Tomek IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290 - 55 - Inverse Problems of Magnetometry Jiří Tomek IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290 - 56 - Inverse Problems of Magnetometry Jiří Tomek IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290 - 57 - Inverse Problems of Magnetometry Jiří Tomek IJAEM Vol. 26, ISSN 1383-5416, No. 3-4 (2007) 285-290 - 58 - Inverse Problems of Magnetometry Jiří Tomek 4.4.3.4 General problem with more scanning planes With the availability of better PC configurations and while having more data from the measurements due to the innovation with 5 coaxial 1st order gradients [Tomek 2009a] we have decided to make further steps in the work concerning the inverse problem applied to the multiple source general problem. The main progress was the realization of a custom software based on the simplified experiments as the commercially available programs can readily process only much smaller problems. The paper [Tomek 2009a] in Section 4.2.1.3 deals with, for the first time, the new setup with six coaxial fluxgates. Thus five synchronous first order gradient scans above the object are available, which provides a bigger quantity of data for experimenting with gradiometric setups and mathematical processing and of course reducing the degrees of freedom with the inverse problem. The paper again mentions the approaches in geology where scientists can utilize a lot of empirical knowledge to obtain good estimates also in badly posed tasks. I deal there however, mainly with the analysis of the fields and some practical proofs of my hypothesis about noise suppression and utilization of the fitting for processing of the rough data for inversion. However, in the next paper [Platil 2008] we again deal with the inversion of the general problem and compare 2 approaches. We utilize not only the algorithm adopted from a linear neural network but also try a simple genetic algorithm. The extension of the work concerning the general problem was a logical move after the previous unsatisfactory results on larger volumes of the lung phantom. We have stayed with the already well described phantom model with cubes of 8 cm3 volumes and synthetic, usually random, configurations of the sources in the non-magnetic environment, so there are still reserves in the feasible source arrangements and their real properties. The aspects of the real cases could not be studied on the subjects, nor is such knowledge included into the models. The primary task was again to recognize the magnetic and nonmagnetic cubes. We have started with just a single layer of the phantom, respectively 50 cubes in both lung lobes. So we had 100 cubes altogether. The development of the method for complete lungs should be the subject of further work. We have made several experiments with different spatial resolutions of the scanned data. At first, the resolution in the horizontal plane was 4 cm, thus we had 144 nodes, each with five 1st order gradients and we have generated 60 000 training cases. Then we came with an idea that the smallest effective training set would be represented by an identity matrix of possible sources and the respective fields computed in the nodes of the measured planes. So we have generated data for a resolution of 2cm, which means 5x529 (23x23) nodes and finally also in a - 59 - Inverse Problems of Magnetometry Jiří Tomek resolution of 1 cm which means 5x2025 nodes. Then there was the question how to process the SVD by the available PC and software. In Statistica, we had a problem with processing of just 276 nodes (Section 4.4.3.2) so a custom software was the only solution. It was realized as a script in Matlab according to the definition of the analytical solution of the least square problem which is described in the next paper [Platil 2008]. By this means, we obtained the weights of each measuring node mapping its value to the cubes in the phantom. The performance can be shown e.g. on the inversion of the identity matrix sources. Ideally, we should obtain a diagonal matrix with ones on the main diagonal and zeros elsewhere. However, because of not utilizing enough independent data, we obtained the results that are full of artefacts (see Figure 1 in the next paper and Figures 4.13-4.15). There are false images like when the sampling theorem is not fulfilled or like when we reconstruct the images with an incomplete set of Fourier series coefficients. Figures comparing the values over the diagonal for the three mentioned cases are presented in Figures 4.13 - 4.15. X-Z projections of the result of the inversions of the unit sources composing an identity matrix – ideally, there should be a straight plane without any waves. Fig. 4.13: Weight matrix was derived from 60000 Fig. 4.14: Weight matrix was derived from 100 randomly generated cases. Scanning resolution unit cases. Scanning resolution 4 cm. 4 cm. - 60 - Inverse Problems of Magnetometry Jiří Tomek Fig. 4.15: Weight matrix derived from 100 unit cases. Scanning resolution 2 cm. The last case was in a resolution of 1 cm, but could not be processed as we could not reserve enough defragmented space of the memory, including the virtual memory on the disk. The process is unfortunately very memory demanding, so we should deal with the representation of the data in more memory saving formats, if it does not have a bad effect on the precision. We could work only with 2 layers out of 5 which means 4050 nodes, and the result was identical to Figure 4.15 where the resolution is 2cm with 2645 nodes, which means that not much more linearly independent data was added. The utilization of the identity matrix set of sources is definitely effective; however it is still like calculating the weight matrix for any set of 100 cases, so the inversion works best on these cases and should have worse performance on other more complex examples. The inclusion of several more representative cases should help the quality of the inversion matrix without any effect on the needed memory for the computation, as the dimension of the matrix undergoing SVD is always limited just by the number of scanning nodes and not by the number of cases. The early results were published at the EMSA 2008 conference [Platil 2008] and we have prepared an extended paper for Sensor Letters journal. It comes next. - 61 - Inverse Problems of Magnetometry Jiří Tomek EMSA 2008 - paper for Sensor Letters, accepted - 62 - Inverse Problems of Magnetometry Jiří Tomek EMSA 2008 - paper for Sensor Letters, accepted - 63 - Inverse Problems of Magnetometry Jiří Tomek EMSA 2008 - paper for Sensor Letters, accepted - 64 - Inverse Problems of Magnetometry Jiří Tomek EMSA 2008 - paper for Sensor Letters, accepted - 65 - Inverse Problems of Magnetometry Jiří Tomek EMSA 2008 - paper for Sensor Letters, accepted - 66 - Inverse Problems of Magnetometry Jiří Tomek EMSA 2008 - paper for Sensor Letters, accepted - 67 - Inverse Problems of Magnetometry Jiří Tomek 4.4.4 More probes & fitting to model function As it has already been shown in the paper [Tomek 2009a] in Section 4.2.1.3 with several coaxial gradients, we can perform the task of determining some compact source quite well with data coming just from a single scanning node. The difference from the task discussed in Chapter 4 is that we just obtain its overall magnetic moment (amplitude) and relative position in the cylindrical coordinate system, which means the distance of the source from the closest probe and the radius from the scanning node. From the single scan, the dimensions of the source cannot be determined well. The absolute coordinates of a source centre can be derived by eliminating the degrees of freedom by using the data obtained in two nodes. What can be actually calculated is a centre of the magnetic moment corresponding to the measured signals not the centre of the source in the case that the source cannot be interpreted as a dipole from the scanning distance. The data obtained in these multiple scanning heights can also be used in a neural network inversion similar to the one described in Section 4.4.3.2, ideally without any fitting or using a lower compression of the input data than is described in Section 4.4.3.1. The mathematical optimization used for determining the best analytical gradient function describing the measurement partially suppresses certain sources of errors in the data. Between them are: imperfect probe alignment and also outliers, which is excellent for in-vivo experiments. Time variations in the field coming from the background, that result in the same 1st order gradient changes in all the measured heights can be also subtracted from the scanned matrices; however the differences that appear between the coaxial gradiometers cannot be suppressed. The configuration and its properties have not been fully studied yet. A more detailed investigation over the performance of the algorithm and effectiveness of again applied Nelder-Mead optimization technique is to be made. 4.5 Discussion In this task we have made many successive steps in the development of all parts of the magnetopneumographic system. Except for the magnetizing device, whose modelling I was just supervising, the other parts are mostly my work. Demands for better inversion results lead to changes in the scanning device, mainly of the gradiometers. That lead to the need of modifying the forward models and the inverse processing was then developed by means of trial and error to achieve the optimum. The experiments with the localized sources proved applicability of neural networks to the inverse processing and lead us to their further application. The most important experiments were done with general distribution of magnetized and non-magnetized phantom cubes in one layer. We have obtained - 68 - Inverse Problems of Magnetometry Jiří Tomek very satisfactory results using tailor-made software utilizing the SVD algorithm, applied in one type of artificial neural networks. Utilization of this type of “evolution algorithm” may be arguable, but iterative mathematical gradient based optimization or other iterative procedures were not seen as applicable in the beginning. Now, as we have a relatively simple description of the forward problem, which enables fast single step calculations, the door is opening. There has been made also a first trial by my colleague with the genetic algorithms, which showed their applicability, though the results were not precise. Some experiments should be made even with the gradient based methods, which were just briefly touched. We now have an ideal linear equation describing the problem, though the number of variables may easily exceed 1000, but such mathematical description is one of the conditions for the sophisticated gradient methods. I have mentioned complications with high numbers of variables that bring problems with processing, especially in the means of the operational memory of the computers as the datasets and matrices are large. In such big problems, a successful inversion, as has been discussed, needs the maximum possible reduction of the degrees of freedom. We have made much progress in the acquisition of more data describing the sources but could not analyse enough real cases, where the distributions are different Definitely, if we had sufficient data available from real measurements of subjects’ lungs, we may have found similarities and could define what constraints the inversion results have to respect (a priori information), etc. In this respect, improvements of the measurement method according to practical needs - including e.g. video control of body position during scanning – should be made also, which would help improving the reproducibility of the measurements. This naturally needs a representative set of volunteers and are costly and extremely time consuming. The scanning method utilizing fluxgates and up to now, just step by step measurement of the field maps over magnetized phantoms, especially in the presented DC mode, may be disputed because of the relaxation (the effect of the rotation of the formerly aligned particles to random low-energy directions) and long scanning periods during which the subject may move and the background disturbing field may change a great deal. The system may be relatively easily adapted to AC enabling the measurement of even ferrimagnetic oxides, which do not preserve remanent field after magnetization. This change should help with the problematic suppression of low-frequency disturbing fields, moreover, the measurement in the AC mode may be more attractive for practical applications. The adaptation would require just slight changes in the signal filtration and synchronous detection of the signal from magnetometers. The mentioned probe arrays should reduce the time necessary for scanning. The proposed inverse processing is quite universal as well as the principle of the forward model, thus in this theoretical point of view the system, may be applied to various tasks. - 69 - Inverse Problems of Magnetometry Jiří Tomek An altogether different situation is with the magnetization device, which would have to be built as a part of the scanning bed. It should be made from Helmholtz coils of proper size enabling the creation of strong enough fields. Work on the inversion, utilizing the least squares has not stopped with 100 volume elements of the lungs but continues with 600 to which both lung lobes are inscribed, though it again requires a higher computing power because of the increasing size of the matrices to be inverted. We are also considering methods of compensation for the errors arising from discretization and pseudo-inversion of the almost singular matrices. The question arises whether we should not introduce some iterative processing to this method. The one step inversion provides a very good estimate (model) of the distribution of the ferromagnetic cubes and the errors could be decreased by several successive improvements to this model. - 70 - Inverse Problems of Magnetometry Jiří Tomek 5 Measurement of the stomach volume The inverse problem solved in this medical application is in its theory a relatively simple task, however as common during work on the instruments for practical use, many problems rolled out. We had to especially cope with several contradictory requirements and needed to reach an optimal solution in the contemporary conditions and budget. Nevertheless, the work has been welcomed at three prestigious international conferences (including two oral presentations) and two smaller conferences and there are even now two publications in excerpted journals plus one minor journal and we have material for at least one further medical paper. I am going to reveal the important steps of the development, the technical details including even the manufacture and naturally to provide the data measured in-vivo and try to show some interpretation of them and outline targets of future research. 5.1 The tasks This task was part of the Project of International Cooperation (1P05ME756) with a team falling within the University of Texas Medical Branch. Here are the main points concerning the system intended for treatment of obesity or various gastric dysfunctions: • • • • Development of a new generation of experimental implant enabling “ondemand” stimulation. Thus, the device giving impulses to the stomach wall just at the specifically detected moments, i.e. after detection of food consumption (gastric pacing). o Implantable system for stomach volume (or distention) measurement – minimal number of sensors o Potentiality of estimation of stomach chymus composition – mostly liquid vs solid food o Selection of the most suitable sensors Design of the system utilizable for in-vitro experiments and verification of its function Appliance for measurements in-vivo (dogs) Testing in the USA, Veterans Administration Hospital in Oklahoma City 5.2 Method There were many suggestions how to solve the measurement task, however we have chosen the measurement of the voltage induced to (a) solenoid pickup coil(s) from an AC magnetic source – another solenoid. This basic system has many imperfections and may fail to detect reasonable signals because of misalignments. - 71 - Inverse Problems of Magnetometry Jiří Tomek Thus eventually we came up with a compromise between the system complexity and reliable function. It is also relatively little dependent on the alignment of the transmitter and receiver. The following chapters and papers thoroughly describe the reasons for selecting the magnetic induction method as well as the considered configurations of coils, see Section 5.3 and Section 5.4.1.6. 5.3 Overview of some applicable methods In one less important Czech journal (Acta Polytechnica) arising from an international student conference Poster 2007, I have published an overview of the possibilities how to measure the distance of two points in space by means of the magnetic induction principle from the simplest one to those enabling higher precision [Tomek 2007b]. Considered, are mainly such alternatives that could be or are well applicable in our task. Two of them were employed in our successive experiments. In the submission included below, those methods are highlighted that are not only independent from the environmental properties a great deal, but they can also be made for relatively low power and the data processing from those systems would not be too complicated. - 72 - Inverse Problems of Magnetometry Jiří Tomek - 73 - Inverse Problems of Magnetometry Jiří Tomek - 74 - Inverse Problems of Magnetometry Jiří Tomek - 75 - Inverse Problems of Magnetometry Jiří Tomek - 76 - Inverse Problems of Magnetometry Jiří Tomek - 77 - Inverse Problems of Magnetometry Jiří Tomek 5.4 In-vivo applicable systems Except for the relatively short work with the laboratory instruments and the first home-made sensors, there were directly two generations of in-vivo applicable systems. The task needed to be solved quickly, as the first in-vivo experiments were planned in a short time. The first system is well described in the report for our partner, which is reedited and follows in the next section and in two papers included in Sections 5.4.1.5 and 5.4.1.6. Our partners were quite satisfied with the first tested module and the sensors and even applied for a grant on the further development, which made us continue our work on a more reliable device. The gained experience has opened several tasks which we have tried to fulfil in the next generation utilizing more channels and a three-axial sensor. The description of it is in the paper in Section 5.4.1.6 and in the whole Section 5.4.2 and also back in the overview in Section 5.3. 5.4.1 First version The first applicable system was the simplest one possible, utilizing a single transmitting and a single receiving coil. This system is described in detail in the following chapters up to Section 5.4.1.5. We have described the materials used, the way the coils were manufactured, electronics built and also the firmware and software for data acquisition and processing. The appropriate parts of the report are revealed below, including references to the electronic appendices. Fig. 5.1 Single axial distance measurement module with probes 5.4.1.1 Summary • The developed system measures distance by using induction method. Distance range: 2 to 10 cm - 78 - Inverse Problems of Magnetometry Jiří Tomek • Accuracy: 5% below 7 cm, 10% from 7 to 10 cm One transmitting and one sensing coil can be attached to the surface of the stomach. The external electronic box powers the transmitting coil by peak to peak 3 mA/3.025kHz sine-wave and the signal induced in the sensing coil is amplified and converted to distance. The electronic module is powered by a USB from the attached PC. It requires individual calibration of each coil pair plugged in. 5.4.1.2 The principle of the sensors and the system 2a) The coils (solenoids) - one driving coil (air core) o excited by 3025Hz, 3 mA p-p sine-wave o serial inductance at driving frequency approx. 1 mH* o serial resistance approx. 205 Ohm* - one sensing coil (ferrite core, material H11) o serial inductance approx. 13 mH* o serial resistance approx. 215 Ohm* * measured by an RLC meter HP 4284 A, see file: /Measurements/Coil_measurements.xls – set of measurements including the first final coils’ experiments in a saline solution. The magnetic field created is decreasing by the third power of the distance (Fig. 5.4); therefore, the dynamic range of the device has to be wide. Furthermore, from the character of the magnetic field, if the coils are not aligned in one axis, angular mismatch and displacement (perpendicular shift between coils) cause significant errors, see Fig. 5.5 and 5.6, though ± 10° distortion and ±10mm do not cause big deviations in the distance determination as the third power reduces the error. pick-up coil driving coil distance Fig. 5.2. Schematic picture of the sensors - 79 - Inverse Problems of Magnetometry Jiří Tomek Fig. 5.3. Photo of the first sensors in comparison to a 3.5mm jack connector Distance - Induced Voltage 160 140 Uind [microV] 120 100 80 60 40 20 0 0 2 4 6 8 10 12 Distance [cm] Fig. 5.4. Measurements using laboratory equipment, axially aligned coils - 80 - 14 Inverse Problems of Magnetometry Jiří Tomek Effect of lateral displacement 3 Uind [mV] 2,5 2 1,5 1 0,5 0 -80 -60 -40 -20 0 20 40 60 80 Position [mm] 30mm 40mm 50mm Fig. 5.5. Effect of the lateral displacement (Illustrative measurements with an older experimental system) Angular mismatch - induced voltage 5 Uind [mV] 4 3 2 1 0 -100 -50 0 50 Angle [°] 25mm 30mm 40mm 50mm Fig. 5.6. Effect of the angular misalignment (Illustrative measurements with an older experimental system) - 81 - 100 Inverse Problems of Magnetometry Jiří Tomek 2b) The system - Consists of analogue and digital boards Distance evaluation made in the PC software, with graphical user interface o USB interface o EXEcutable file Programmed micro-processor of the device o Data acquisition o Averaging o Communication with PC Basic description: A sine-wave generator excites the driving coil. The magnetic field produced is picked-up by the sensing coil (with a ferrite core). The induced voltage is shifted in phase by approximately 90° in comparison to the exciting signal. Therefore, the generator also provides a correspondingly shifted reference signal for the synchronous detector. The signal from the sensing coil is AC-amplified by 2000x, processed by synchronous detector and DC-amplified by 7x. The higher harmonic frequencies from the detector are suppressed by the low pass filter. The amplified voltage is sampled by a 24-bit ADC. Samples are picked by the micro-processor and averaged. The number of the averages is user selectable from 1 to 128 samples in powers of two. The data is then sent using a FIFO/USB converter to the PC to be processed further, see Figure 5.7. Fig. 5.7. Block scheme of the system - 82 - Inverse Problems of Magnetometry Jiří Tomek 5.4.1.3 How it is designed and made 3a) Sensors Coils (solenoids): - 2000 turns (bigger experimental coils have 2500 turns) - about 2 mm in diameter without leads and coating - 8.5 mm in length - core diameter 1 mm - wound by company TRONIC s.r.o., Prague, CZ Materials: • Paint used for reinforcement and fixing of coils: o Dispersed acrylic varnish lacquer or similar - dull (e.g. SPORTAKRYL-mat by TEBAS, CZ) - several extra thin layers (cca 60% of water added) and high temperature drying, several layers also after a coat of plastic spray o plastic spray, rapidly drying protective varnish (PRF 202 by Taerosol Oy/Ltd. - GES electronics, CZ) - 1 or 2 layers after soldering the leads to the cables and one after attaching them to the coil • Cores: o Ferrite cores Fonox, material H11 – company DOE s.r.o., CZ o Diameter 1 mm, length 8 mm • Winding: o Enamelled Copper wires - ERMEG s.r.o., CZ – (Electrisola http://www.elektrisola.com/, Germany) o Product name: Butybond alcohol 155 o Product code: Ba155 o Base coat: mod. Polyurethane o Bond coat: Polyvinylbutyral o Standards: IEC 60317-35, IEC 60317-2 o Wire used: Cu 0.034 mm in diameter • Coating: o ChronoFlex AR solution - medical grade polyurethane (PUR) by Cardiotech International Inc., USA http://cardiotech-inc.com/ o A minimum of 3 thin layers of cca 70°C solution - 83 - Inverse Problems of Magnetometry Cable: o Jiří Tomek 2 conductor shielded cable STC-32T-2 by BLH, Germany, silvered copper wires, PTFE (Teflon) insulation, www.blh.de, VISHAY The biocompatible polyurethane (ChronoFlex AR) layer gives a very high insulation resistance even after being in a saline solution for more than 1 month. 3b) The system • Analogue part of the electronics The analogue part of the electronics in blocks is shown in Figure 5.7 up to the LP (low pass filter) block. As it has been finally designed and built by an external company JanasCard, Prague, CZ, I am including it rather for the purpose of completing the description of the system. It consists of the oscillator with a frequency of 3.025 kHz which drives the transmission coil. The signal from the input (pick-up) coil comes to the low-noise amplifier with a gain of 20x and the second-order band-pass active filter with gain of 100x. The output from the filter is fed into the synchronous detector and the signal then comes to the low-pass active filter with a corner frequency of 1 Hz and gain of 7x. A detailed scheme which follows the block diagram above, together with a PCB layout is in the file on the DVD Appendix (/Schemes/syncdet.pdf and ../pcbsyncdet.pdf). In Figure 5.8 just the part of the scheme without the oscillator is presented, which provides a clear sine-wave powering a driving coil by a signal which has its amplitude set to 600 mVp-p and it also provides a square signal produced by a comparator for a synchronous detector. The input amplifier consists of U14 and has a gain of 20x, the second order band-pass consists of U1 and U2A and has a total gain of 200x, U2B and U4 forms the synchronous detector, U3 with R1, C2, R3, R4, C3 forms an output low pass filter with a corner frequency of 1 Hz and gain of 7x. The total gain of the whole input part is approximately 14000x. - 84 - Jiří Tomek Inverse Problems of Magnetometry Fig. 5.8. A detailed scheme of the analogue circuitry based on the JanasCard company documentation - 85 - Inverse Problems of Magnetometry • Jiří Tomek Digital part of the electronics The block scheme starts from the ADC (analogue to digital converter) in Figure 5.7. This was designed, built and programmed by Ing. Pavel Mlejnek, my colleague from the department. The full scheme of the circuitry is included on the DVD Appendix (/Schemes/Schema_dig.pdf). The digital board consists of three main parts. The first part is the 24 bit analogue-digital converter ADS1210, which samples the input voltage with a rate of 300 Sa/s. The sampled data is processed in the microcontroller ATMEL AT89S51. . Next, the data is sent to the PC via a USB. The integrated circuit FTDI FT245BM is used for the communication between the microcontroller and the USB. Finally the digital value of the voltage is converted to the value of distance in the PC. The source code files are stored at /Files/uController and /Files/PD_V_1_0.zip. An update of the firmware and software that is in /Files/DMM_20_install has been made, which includes a necessary installation guide. Fig. 5.9. The electronics with connected probes, without the case. • Software The software is developed in National Instruments’ LabWindows/CVI. It can be compiled to an EXE file that works on any USB equipped PC with the OS MS Windows XP. No additional libraries or programs are needed. - 86 - Inverse Problems of Magnetometry Jiří Tomek Fig. 5.10. User interface of the program Features: • • • • • • automatically establishing a connection with the device after plug-in. setting the calibration information for a given pair of coils setting the identification of the connected pair of coils conversion of the data (voltage levels) to the distances distance in centimetres and inches range of measurement approx. 2-10 cm Data processing in the PC consists of several steps: 1. Sampled 24bit data is converted to voltage value 2. Voltages are converted to distance values o 1/d3 characteristic is not satisfactory due to the non-negligible size of the coils and imperfect alignment o Calibration over several distances necessary o Fitting to power function by Levenberg-Marquardt method (implemented in LabWindows) – still not sufficient o Deviations fitted by polynomial of 3rd order good linearity - 87 - Inverse Problems of Magnetometry Measured distance (mm) 120 Jiří Tomek 110 100 90 80 70 60 50 40 30 20 10 Real distance (mm) 0 0 10 20 30 40 50 60 70 80 90 100 110 120 Fig. 5.11. Mutual characteristics and data dispersion Fig. 5.12. Linearity deviation 5.4.1.4 Final measurements We have manufactured several pairs of sensors. All were in saline solution for at least for 14 days and the insulation resistance of the PUR coating did not - 88 - Inverse Problems of Magnetometry Jiří Tomek show big changes. The expected minimal acceptable 1MΩ value was highly exceeded. For testing and calibration measurements, we use a plastic positioning device that can be easily used even in the saline solution. The sensors and their leads are coated by biocompatible materials. The system is designed to measure distances from 2 to 10 cm. Lower distances than 1 cm overload the electronics, for higher ones the signal to noise ratio is low. This is due to relatively low inductances of the coils and the necessity of using relatively low frequency 3025 Hz because of the presence in a conductive environment, where the signals would be too sensitive to the parasitic capacitances and eddy currents if the frequencies were higher. Noise measurements - several measurements of the complete circuitry made (one pair of coils) Table 5.1. showing noise dependency on averaging o Noise of the digital part and ADC (input of the ADC in short) o Noise of the electronics, equivalent resistor connected instead of a pick-up coil o Noise of the whole electronics with pick-up coil perpendicular to the driving one at a distance of 12 centimetres Tab. 5.1. Noise values measured at the ADC output. The sampling frequency was 300 Sa/s. Values “Max – Min” record the maximum deviations of the measured dataset. “RMS” value was calculated after removal of the DC offset - 89 - Inverse Problems of Magnetometry Jiří Tomek Fig. 5.13. Measurement device with probes on a calibration device 5.4.1.5 Practical application on laboratory animals We had an opportunity to test the performance on living animals. For this purpose we have made tests and calibrations in a warm saline solution and also tested the probes in it for a certain period. Several sets of probes and two electronic boxes were used for in vivo experiments on laboratory dogs by the US partner. Experiments were conducted at the Veterans’ Administration Hospital in Oklahoma City, where there are some research labs of the University of Texas – Medical Branch. During the first phase just one dog was implanted with two pairs of probes and a relatively little set of experiments was conducted. Some of the data was officially authorised for publication at the submission to a World Congress on Biomedical Engineering 2006 [Tomek 2006b] from which a later paper results. It was revised several times as there was not enough statistically relevant supporting data for proper publication. Finally, it was submitted to a specialised journal about Gastroenterology [Tomek 2009b]. I describe, in the paper, the motivation for this new method, include many references to similar experiments, to statistical data about obesity and, of course, the - 90 - Inverse Problems of Magnetometry Jiří Tomek applied system is again briefly described. The crucial part is the description of the in-vivo experiments and an example of the measurements with a statistical graph. The simple system showed to be very dependent on the quality of the surgery as the coils need to be oriented as co-axially as possible and not changing their angular tilt much on the stomach wall. This cannot be assured however. It even happened that the mutual position of one pair after surgery was totally skew and the signals were not reliable. Thus, we have started to develop a more complicated system later on. - 91 - Inverse Problems of Magnetometry Jiří Tomek - 92 - Inverse Problems of Magnetometry Jiří Tomek - 93 - Inverse Problems of Magnetometry Jiří Tomek - 94 - Inverse Problems of Magnetometry Jiří Tomek - 95 - Inverse Problems of Magnetometry Jiří Tomek - 96 - Inverse Problems of Magnetometry Jiří Tomek - 97 - Inverse Problems of Magnetometry Jiří Tomek 5.4.1.6 Possibility of a three-axial probe introduction Further experiments and analysis of the data appeared in the paper finally published in Sensors & Actuators A - Physical 2008 [Tomek 2008]. This paper resulted from a Eurosensors 2006 conference submission. There is also a frequency analysis of the measured signal and longer experimental curve for liquid intake. After the first in-vivo tests there was a strong demand for smaller probes utilizable even on rats, thus less noisy and far more sensitive electronics. The new version of analogue part has been thus developed and tested. Then it was decided to use this more sensitive variant to build a three-channel version of the analogue part that could work with smaller coils composing a three-axial receiver. We demonstrate here the benefits of the later completed three-channel system. The pick-up probe scheme with three smaller orthogonal solenoids is revealed and the in-vitro experimental data is depicted. - 98 - Inverse Problems of Magnetometry Jiří Tomek - 99 - Inverse Problems of Magnetometry Jiří Tomek - 100 - Inverse Problems of Magnetometry Jiří Tomek - 101 - Inverse Problems of Magnetometry Jiří Tomek - 102 - Inverse Problems of Magnetometry Jiří Tomek - 103 - Inverse Problems of Magnetometry Jiří Tomek - 104 - Inverse Problems of Magnetometry Jiří Tomek 5.4.2 Second version – tri-axial system Fig. 5.14. Three-channel electronic box with accumulators Fig. 5.15. Electronics connected to a NI A/D converter As has been written above in Section 5.4.1.6, this is the more sensitive and less noisy version of the electronics. But here, we use three totally separate analogue channels with similar parameters. Amplification of the channels is 42 000x and the noise at output is 25µV with 200Ω resistor at input. Table 5.1. compares the parameters of the tri-axial and the single-axial system. version single axial system tri-axial system turns of (ø 34µm Cu wire) 2000 1000 coil length 8.5 mm 5 mm coil diameter 2 mm 2 mm inductance with H11/without 13mH/1mH 3mH/0,6mH core diameter 1 mm 1 mm 14 000 42 000 250 µV 25 µV amplification of the electronics Output noise rms value (0.1Hz-1kHz) Table 5.1. Parameters of the two versions of the electronics and of the utilized sensors. The driving coil for the in-vivo testing even in the second version had 2000 turns. - 105 - Inverse Problems of Magnetometry Jiří Tomek For the experiments, we have introduced a four channel high speed USB A/D converter by National Instruments (Hi-Speed USB Carrier “NI USB-9162” with module “NI 9215 with BNC”) enabling simultaneous sampling, which is a feature absolutely necessary for our purpose. Data from the tri-axial sensors digitalized by the converter was processed by the newly developed software in LabView environment (Fig. 5.16, see DVD appendix /Software/LabView {the ADC converter has to be installed first}). Recalculation of the acquired voltages to the distance has been realized by an expression whose constants have been derived from the calibration data. This optimization has been performed by a Matlab script based on the Nelder-Mead simplex algorithm (see DVD appendix /Software/Matlab/3axialExample). The module enabled direct on-line monitoring of the last 10 minutes of the measurement of the distance as well as of the voltages and calculated magnitude corresponding to the size of the total vector of the measured field. The program, naturally, also saves the data into a default or selected file for the purpose of offline processing. Fig. 5.16. Window of the data acquisition and display software. Analysis of the induced signals, recalculation to the distance and storage of the data. Redesigned during the in-vivo tests in the USA 5.4.2.1 Practical application on laboratory animals Just at the end of the project we were able to arrange a second session in the USA with another set of experiments. We have applied the new device and probes presented in the above Section from 5.4.1.6. After onsite testing I assisted during the surgery of the same race of dog as two years ago. Two pairs of sensors were sewed on its stomach wall. One was fixed to the bottom part “antrum” where quite regular contractions originate after a meal and second to “fundus” where the wall relaxes a lot with food ingestion, see the Figure 5.17. - 106 - Inverse Problems of Magnetometry Jiří Tomek Fig. 5.17 Scheme of the regions to which the coils were sewed As has been mentioned, the two regions differ in their relaxation and muscular action before and during food digestion. In the antrum, the coils were sewed in parallel, the pickup coils were in the 2nd Gaussian position in respect to the transmitter and in the fundus, the alignment was with probe in the 1st Gaussian position. The reason for this was the size of the stomach in the respective areas and the possibility to attach the cables in the proper way. The contractions that can be observed better in the antrum can be even studied in the means of the food composition – percentage of fats, sugars and proteins or just liquid e.g. water, that is not processed by the stomach. Such studies have not been started yet. Big sets of repeated measurements are necessary and for this there is still little finance and support. 5.4.2.2 Examples of the in-vivo measurements The data presented below was recorded on November 8th 2007 in the USA on the stomach of the laboratory dog. As we did not have two devices to record both stomach parts simultaneously we had to do it in succession which does not give complete information. However, the doctors have chosen this procedure, though we could also use the one channel older type of module to record at least one channel of the second system. At first we started in the fundus, where we were tracking the baseline for 20 minutes, i.e. signal without any food. However, the dog definitely, by Pavlov’s reflex, knew that some feeding experiment was coming so there was some action seen by the team. Then the dog drank in one minute cca 270 ml of the condensed sweet milk and we could observe how much the wall relaxed. The complete measurement is in the graph in Figure 5.18. - 107 - Inverse Problems of Magnetometry Jiří Tomek 26 Distance [mm] 24 22 20 LP filtered Raw data 18 16 0 5 10 15 20 25 30 35 40 45 50 Time [minutes] Fig. 5.18. Stomach distension after drinking 273 ml of the condensed milk 55 Afterwards the fundus sensors were disconnected and a new experiment with the antrum probes was conducted. We waited for 35 minutes and the dog was fed with solid food. At the antrum, the elongation of the wall is not so obvious, however, after the meal there appear distinct relatively regular contractions of the stomach wall which result in the mixing of the chyme inside. The whole low-pass digitally filtered measurement is drawn in the Graph 5.19. The eating lasted approximately 4 minutes. A detail of the record just after eating the 375g of canned meat, when the regular contractions start, is in the next Figure 5.20. 21.5 Distance [mm] 21 20.5 20 19.5 19 18.5 0 10 20 30 40 Time [minutes] 50 60 70 Fig. 5.19. Baseline in the antrum and eating 375 grams of the dog food - 108 - Inverse Problems of Magnetometry Jiří Tomek 23 Distance [mm] 22 21 20 19 BP filtered Raw data 18 17 37.5 38 38.5 39 39.5 40 40.5 Time [minutes] Fig. 5.20. A detail of the signal just after eating the meat – the relatively regular contractions start. Without the meal the stomach activity is irregular in short periods with occasional strong contraction and not food-induced volume changes e.g. like in Figure 5.18. This detail is joined because of the planned counting of the contractions in certain period. This is supposed to provide information about chyme composition – mostly fat, sugars or proteins and especially to decide if it is water or some non energetic liquid or ordinary mainly solid food, for which the simulation is specifically designed and should be switched on. The response of the planned gastric pacemaker implant to the detected status would differ accordingly. Naturally, this is just the subject of further experiments. We have repeated this experiment also the next day and the results were very similar. The measured data and timing is in files on the DVD (/Measurements/3axial) 5.5 Discussion The tests on the lab animals are unfortunately very expensive and for even some preliminary but relevant study we would need a series of repeatable tests on a group of animals, which is nowadays impossible. The presented work however, showed suitability of the chosen method for detection of food ingestion by means of measuring the distension of a gastric wall. The tri-axial system especially deserves confidence for its simplicity and relatively low errors in calculation of the distance between the probes caused by rotations of the transmitter - Section 5.3 (Figure 8 in the inserted paper). More complicated systems are questionable, though they would enable higher precision, while further reducing the degrees of freedom in this inverse task. Section 5.3 had already outlined some interesting options. We have not discussed various wireless systems, e.g. with resonant markers and transmitter(s) working on several frequencies in the case of the implant, where the implantation would be easier and no additional cables would be necessary. Such - 109 - Inverse Problems of Magnetometry Jiří Tomek an idea would require processing using the correlation analysis and either more separate channels than in the three-axial version or quite a sophisticated processing of the signals from the multi-axial markers. Utilization of a permanent magnet and detection of just the static magnetic field that is modulated by the wall contractions would possibly not be so reliable because similar signals may appear in the surroundings. And again the processing seems to be too difficult. One may argue even about implantability of the presented design, however the technologies of the production of the cables and connectors for pacemakers could be applied and the circuitry could be made at least partially on a custom designed chip with low power consumption and minimizing the size. The distension measurement part even does not need to work continuously and may remain switched off totally in certain periods. Experiments with pulse driving of the transmitters have also been made, which may substantially reduce the consumption as well [Humr 2008, Ripka 2008] (for this testing, even samples of factory-made small tri-axial probes were used). The cables would possibly need to use different materials than is usual for pacemakers. The reason could be the permeability of nickel-cobalt alloy utilized in cables of electrodes. We were thinking about silverplatinum wires of similar composition to leads of cochlear implants (Cochlear Ltd., Australia). Silver would be also good material for winding of the coils. Unfortunately copper, as has been mentioned in the presented papers, is toxic for the human body and would not be accepted even when perfectly insulated. - 110 - Conclusions Jiří Tomek 6 Conclusions This chapter is going to summarize the achieved goals and give an overview of the work done as well as propose the directions of further research. During my study, in the general point of view, I have dealt with various inverse problems in magnetometry, particularly the estimation of size, position and orientation of magnetic moment(s) out of the measured data sets. Based on the known techniques I have come up with a non-traditional approach to determine the multiple magnetic moments, which was fully applied in the first of my two main projects – the measurement of the magnetic field of the lungs or magnetopneumography. Basically, it is the utilization of the direct (one step) inversion of the measured data. Quite commonly, just the iterative techniques with the forward model in the feedback loop are used. This task naturally involved a complete magnetopneumographic system, thus a magnetization device, scanning bed, gradiometers, forward and inverse modelling. We have managed substantial progress in all these tasks. The main effort has been headed to inversion of the measured data and improvements of the measurement setup to achieve better inversion results. For the inversion, I have chosen an artificial neural network approach and a very unusual direct one step estimate of the sources out of the data sets measured above the tested object. Results of simulations and modelling have shown that the described approach (and also the conventional ones) require an excessive amount of experimental data to achieve good resolution in the estimation of the ferromagnetic dust, thus several gradiometric configurations of sensors were tried and forward modelled. I have finally achieved a quick one step calculation of the forward model, which was validated by real measurements over phantoms. Having this final model, a self-programmed software for calculation of an inverse model applicable to general distributions, could be developed. Inversion of several types of simplified model cases have been performed (i.e. localized homogenous sources or general distribution of magnetized elementary phantom sources in a limited volume). Some final types of trained neural networks were also successfully applied to the data measured over the physical lung phantom. The determination of position of magnetic moments based again on inversion of measured data has also been applied in my second project - contactless magnetic measurement of the gastric volume that is necessary for switching the gastric pacing implant intended for obesity treatment. In this case, the inverse problem can be solved quite precisely and directly by mathematical calculation as it is just a practical application of the distension measurement, however, in a non-traditional environment. Though the task may seem simple, with the limitation of the number - 111 - Conclusions Jiří Tomek of sensors and the demand on the simplicity of electronics and surgery, specific problems have arisen. The problem has especially been, from practical reasons, reduced to a single AC dipole estimation. Beside the power consumption optimization of the future implant, the project was also an optimization task of the determination of the distance with satisfactory precision with the minimum number of applied sensors. We have prepared and successfully tested two in-vivo applicable systems. 6.1 Achieved objectives • Design of the non-magnetic positioning bed for magnetopneumography – tests with volunteers, video control of positioning tried; • Magnetization device – projects of two students concerning modelling of the field and possible improvements to achieve more homogeneous fields between the pole pieces of electromagnet; • Gradiometers – six probe gradiometer introduced; reduction of the non-uniqueness thanks to adding more information to the inverse processing; • Software for fitting of the measured gradients to feasible values according to an empirical formula, helping in the reduction of the measurement errors and decreasing impact of variations of the gradient of background sources; • Direct neural network inversion of the localized homogenous sources, showing excellent performance on the models but quite sensitive to noise; • Estimate of the total dust load in the lungs by integration of the measured data of the field maps; • Software for the inverse processing of the bulky data, utilizing a pseudoinversion algorithm limited only by size of free nonfragmented memory of the computer; • Successful single step inversion in a volume of 1000 cm3 (100 cubes + 20 always clear between two model blocks) out of 2645 measured gradients; - 112 - Conclusions Jiří Tomek • Testing of the genetic algorithm based inversion showing their applicability with the new fast forward model; • We have proposed a feasible methodology of the measurement of the stomach distension by means of the magnetic induction principle; • Proper implantable sensors were designed, tested and manufactured, both single axial and tri-axial; • Quite a simple prototype of the second generation of the in-vivo applicable device utilizing a three axial receiver and single coil transmitter has been made and tested on laboratory animals. It has shown good performance; • Two generations of software for recording the measured data. The second one enabling on-line monitoring of the distension in a graphical user interface; • Short-term in-vivo studies were performed. 6.2 Outlook In both of the application tasks, there are many issues of further research and improvements. In magnetopneumography, there we deal with development of the system for video control of the position of the subject on the bed. This required several changes to the portal, thus holders for the arrays of sensors were simultaneously incorporated. This all is to be tested and evaluated. Arrays of sensors will help to reduce the time necessary for scanning and reduce the observed variations in the measured gradients due to the distant sources. Further expansion of the sensory part could be in the placement of the probe, also below the tested subject. Concerning the inverse problem, other inversion possibilities could be examined especially when we finally have a differentiable continuous forward model. It could act as an excellent basis for gradient based optimization techniques, suggested several times in the thesis. Utilization of genetic algorithms could be examined more, too. There is also a question whether the estimate provided by the single step inversion could not be improved by further application of some of the iterative methods. As there is the quick forward model, their utilization is feasible. The incorporation of more background knowledge based on examination of real data is also very important. Further research should also be directed to more attractive applications nowadays, this means particularly AC measurements able to - 113 - Conclusions Jiří Tomek detect ferrimagnetic oxides also. Except for the magnetization device, this would not require drastic changes of the presented methodology for low frequencies. With gastric distension and motility sensing implantable device there would be a lot of work with long term studies on animals and then with the development of proper algorithms for switching the electrical stimulation. Interestingly, from the research point of view, this would be a correlation of volume and motility with electrogastrogram (EGG). However, what concerns the measuring part, there would be the necessity to decrease the power consumption of the electronics (it could use square wave excitation at the proper frequency, etc.) and decrease its size, so that it could be eventually placed into an implant housing. It would be necessary to change the materials of the coils and cables to biocompatible ones. For example we could use silver and/or platinum as even the silvered copper is considered toxic, regardless of the insulation, and the traditionally used nickel-cobalt wires are not acceptable for magnetic measurements because of their permeability. A Teflon (PTFE) coating is also not acceptable for long term use inside the body so that appropriate silicon insulation of the standard leads of the pacemakers should be introduced. Higher precision setups of sensors could also be examined as well as the practical limits of the driving frequency. The experiments suggest that we were relatively sceptic concerning the AC-excitation of the implant surrounded by a current conducting media on almost the same potential. There the frequency could probably be increased, which would further reduce the power consumption. - 114 - References Jiří Tomek 7 References Avriel M., Nonlinear Programming: Analysis and Methods. Dover Publishing. (2003) ISBN 0-486-43227-0 46 Avrin W.F. et al., Non-invasive liver-iron measurements with a room-temperature susceptometer, Physiol. 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Tipek A., Vector magnetometers and their calibration, Ph.D. thesis, Faculty of Electrical Engineering, Czech Technical University in Prague, supervisor: Pavel Ripka (2002) - 119 - References Jiří Tomek Tomek J., Modelování magnetického pole plic, bachelor thesis, Faculty of Electrical Engineering, Czech Technical University in Prague, supervisor: Pavel Ripka (2003) Tomek J. and Konarski, J., Cochlear Implants, web presentation, (2004a), [online] http://cochlear.euweb.cz Tomek J., Ripka P., Tipek A., Magnetic Field of Human Lungs: Models and Inversion, Magnetic Measurements 2004. Praha: Czech Technical University in Prague, (2004b) 7172, ISBN 80-01-02994-8 Tomek J., Magnetic field of the lungs, diploma thesis, Faculty of Electrical Engineering, Czech Technical University in Prague, supervisor: Pavel Ripka (2005a) Tomek J., Platil A., Ripka P., Magnetic Field of the Lungs – Neural Network Inverse models, IFMBE Proc. (EMBEC´05), Volume 11, (2005b) ISSN: 1727 – 1983 Tomek J., Platil A., Ripka P., Kašpar P., Application of Fluxgate Gradiometer in Magnetopneumography, Sensors and Actuators, vol. 132, no. 1, (2006a) 214-217. ISSN 0924-4247 Tomek J., Mlejnek P., Janásek V., Ripka P., Kašpar P. and Chen J.,: Volume and Motility Sensing for Implantable Gastric Pacemaker. In IFMBE Proceedings World Congress on Medical Physics and Biomedical Engineering 2006, Aug. 27.-Sept. 1., COEX Seoul, Korea [CD-ROM]. Berlin: Springer-Verlag, Vol. 14 (2006b) 4943, ISBN 3-540-36839-6 Tomek J., Platil A., Ripka P., Application of Neural Networks Inversion in Magnetopneumography, IJAEM Volume 26, Special volume on OIPE 2006, ISSN 13835416, Number 3-4 (2007a) 285-290 Tomek J., Inductive contactless distance measurement intended for a gastric electrical implant, Acta Polytecnica Vol.47, No. 4-5(2007b) ISSN 1210-2709 Tomek J., Platil A., Ripka P., Magnetopneumography - Advances in Measurement Procedure, Modelling and Inversion Using Artificial Neural Networks, IJAEM Volume 25, Special volume on ISEM 2005, Numbers 1-4 (2007c) 401 - 406, ISSN 1383-5416, ISBN 978-1-58603-746-8 Tomek J., Mlejnek P., Janásek V, Ripka P., Kašpar P. and Chen, J., The precision of gastric motility and volume sensing by implanted magnetic sensors, Sensors and Actuators A 142 (2008) 34-39 Tomek J., Platil A., Ripka., Multiple Layer Scanning in Magnetopneumography, IEEE Sensors Journal Vol. 9, Issue 4, 383-389, ISSN 1530-437X (2009a) Tomek J., Mlejnek P., Janásek V., Ripka P., Kašpar P., Zhu H., Chen J.D.Z., Gastric Distention Sensing for Implantable Gastric Pacemaker, Journal of Gastroenterology (2009b) - submitted Trout S.R., Use of Helmholtz coils for magnetic measurements, IEEE Trans. Magn. 24, (4) (1988) 2108–2111. - 120 - References Jiří Tomek Vrba J. and Robinson S.E., SQUID sensor array configurations for Magnetoencephalography applications, Superconductor Science and Technology, Vol. 15, Number 9 (2002) R51-R89(1) Vrba J., Robinson S.E., McCubbin J., “How Many Channels are Needed for MEG?”, Neurology and Clinical Neurophysiology, (2004), No. 99, (online) http://www.neurojournal.com/article/viewArticle/313, doi:10.1016/j.ics.2007.01.061 Xing J. and Chen J., Alterations of Gastrointestinal Motility in Obesity, Obes Res. Nov, 12 (11) (2004) 1723-32. Zhang J. and Chen, J.D.Z. Systematic review: applications of gastric electrical stimulation, Aliment. Pharmacol.Ther. 24, (2006) 991-1002 Zheng, Y., Kotani, M., Utsukawa, Y., Nakadate, T., Development of a Portable Pneumomagnetic Measurement Device, Neurology and Clinical Neurophysiology (2004) 10 - 121 - Appendix 8 Appendix 8.1 Publications 8.1.1 Articles in SCI journals 2009 Tomek J., Platil A., Ripka., Multiple Layer Scanning in Magnetopneumography, In IEEE Sensors Journal Vol. 9, Issue 4, 383-389, ISSN 1530-437X (2009) Tomek J. - Platil A., Magnetic Field Inversion for Magnetopneumography, In Sensor Letters 7 (3) - Special issue on EMSA 2008 - 8th European Magnetic Sensors & Actuators Conference. Caen: Université de Caen 2008, ISSN: 1546-187X (2009) Tomek J., Mlejnek P., Janásek V., Ripka P., Kašpar P., Zhu H, Chen J.D.Z., Gastric Distention Sensing for Implantable Gastric Pacemaker, Journal of Gastroenterology (2009) submitted 2008 Tomek J., Mlejnek P., Janásek V, Ripka P., Kašpar P. and Chen, J., The precision of gastric motility and volume sensing by implanted magnetic sensors, Sensors and Actuators A 142 (2008) 34-39 Platil A. - Tomek J., Magnetic Field Inversion for Magnetopneumography. In EMSA'08 8th European Magnetic Sensors & Actuators Conference. Caen: Université de Caen (2008) 108 2007 Tomek J, Mlejnek P, Janasek V, et al.: Gastric motility and volume sensing by implanted magnetic sensors Sensor Letters 5 (1): 276-278, Special issue on EMSA 2006, ISSN 1546198X, 2007, Platil, A. - Tomek, J. - Kašpar, P.: Characterization of Ferromagnetic Powders for Magnetopneumography and Other Applications. In Sensor Letters Vol. 5, No. 1, p. 311-314 - Special issue on EMSA 2006, ISSN 1546-198X, 2007 Platil, A. - Tomek, J.: Simple Digitalization of Fluxgate Sensor. In Sensor Letters Vol. 5, No. 1, p. 200-203 - Special issue on EMSA 2006, ISSN 1546-198X, 2007 - 122 - Appendix Tomek J, Platil A, Ripka P: Magnetopneumography - Advances in measurement procedure, modelling and inversion using artificial neural networks IJAEM Special volume on ISEM 2005, Numbers 1-4 / 2007, pp. 401 – 406, ISSN 1383-5416, ISBN 978-1-58603-746-8 25 Tomek J., Platil A., Ripka P.: Application of Neural Networks Inversion in Magnetopneumography, IJAEM Volume 26, Number 3-4/2007 pp. 285-290, ISSN 13835416 2006 Tomek J., Platil A., Ripka P., Kašpar P., Application of Fluxgate Gradiometer in Magnetopneumography, Sensors and Actuators, vol. 132, no. 1, (2006a) 214-217. ISSN 0924-4247 8.1.2 Papers in other journals Tomek J., Inductive contactless distance measurement intended for a gastric electrical implant, Acta Polytecnica Vol.47, No. 4-5(2007) ISSN 1210-2709 8.1.3 Papers in international conference proceedings 2008 Platil, A. - Tomek, J.: Magnetic Field Inversion for Magnetopneumography. In EMSA'08 8th European Magnetic Sensors & Actuators Conference. Caen: Université de Caen, 2008, p. 108. 2007 Tomek, J. – Platil, A. Magnetopneumography – Suppression of Background Field Variations in Scanned Data for Inversion Using Multiple Fluxgates. In The Sixth IEEE Conference on Sensors IEEE SENSORS 2007Final Program &Book of Abstracts, Atlanta, Georgia, USA, 2007, pp. 523-524 & extended: In The Sixth IEEE Conference on Sensors, IEEE SENSORS 2007, October 28-31, 2007, Atlanta, Georgia, USA, pp.1020-1023, ISBN: 1-4244-1262-5, ISSN: 1930-0395 2006 Tomek, J. - Mlejnek, P. - Janásek, V. - Ripka, P. - Kašpar, P. – Chen, J.: Gastric Motility and Volume Sensing by Implanted Magnetic Sensors. In EMSA '06 - 6th European Magnetic Sensors and Actuators Conference. Bilbao (Spain): University of the Basque Country, 2006, p. 35. - 123 - Appendix Platil, A. - Tomek, J.: Simple Digitalization of Fluxgate Sensor. In EMSA '06 - 6th European Magnetic Sensors and Actuators Conference. Bilbao (Spain): University of the Basque Country, 2006, p. 146. Platil, A. - Tomek, J. - Kašpar, P.: Characterization of Ferromagnetic Powders for Magnetopneumography and Other Applications. In EMSA '06 - 6th European Magnetic Sensors and Actuators Conference. Bilbao (Spain): University of the Basque Country, 2006, p. 45. Tomek J., Mlejnek P., Janásek V., Ripka P., Kašpar P. and Chen J.,: Volume and Motility Sensing for Implantable Gastric Pacemaker. In IFMBE Proceedings World Congress on Medical Physics and Biomedical Engineering 2006, Aug. 27.-Sept. 1., COEX Seoul, Korea [CD-ROM]. Berlin: Springer-Verlag, Vol. 14 (2006) 4943, ISBN 3-540-36839-6 Tomek, J. - Platil, A. - Ripka, P.: Application of Neural Networks Inversion in Magnetopneumography. In OIPE 2006 - the 9th Workshop on Optimization and Inverse Problems in Electromagnetism. Sorrento (Italy): Seconda Universita degli Studi di Napoli, 2006, p. 243-244. ISBN 88-7146-733-7 Tomek, J. - Mlejnek, P. - Janásek, V. - Kašpar, P. - Ripka, P. - et al. The Precision of Gastric Motility and Volume Sensing by Implanted Magnetic Sensors In: XX Eurosensors, 20th Anniversary. Göteborg: Eurosensors, 2006, p. 254-255. ISBN 91-631-9280-2 Tomek, J. - Platil, A. - Ripka, P.: Optimization of Magnetopneumographic System for Successful Inversion. In Magnetic Measurements '06 - The Book of Abstracts (Závažná Poruba 2006). Bratislava: Slovak University of Technology, 2006, p. 65-66. ISBN 80-2272452-1. 2005 Tomek, J. - Platil, A. - Ripka, P. Advances in Measurement, Modelling and Inversion for Magnetopneumography, In ISEM 2005 Short Paper Proc. Bad Gastein 09/2005 pp.218-219, ISBN:3-902105-00-1 Tomek, J. - Platil, A. - Ripka, P. - Kašpar, P. Fluxgate Gradiometer in Magnetopneumography In Eurosensors XIX Proc. Vol II, WPb49, Barcelona 09/2005 Tomek, J. - Platil, A. - Ripka, P. Magnetic Field of the Lungs – Neural Network Inverse models In IFMBE Proc. (EMBEC´05), Volume 11, 2005, Prague 11/2005, ISSN: 1727 – 1983 2004 Tomek, J. - Ripka, P. - Tipek, A.: Magnetic Field of Human Lungs: Models and Inversion. In Magnetic Measurements 2004. Praha: Czech Technical University in Prague, 2004, s. 7172. ISBN 80-01-02994-8 P. Ripka, J. Tomek, A. Tipek: Magnetic field of Human lungs: Models and measurement, In Proc. JEMS 2004, Abstracts p. 163 - 124 - Appendix 8.1.4 Papers in other conference proceedings Tomek J., Options for inductive contactless distance measurement intended for gastric implant In Poster 2007 Proc. [CD-ROM] Prague: CTU 2007 Tomek J., Mlejnek P. Volume Sensing for On-demand Gastric Electrical Stimulation In Poster 2006 Proc. [CD-ROM] Prague: CTU 2006 Tomek, J. Neural Networks Application in Modelling of Magnetic Field of the Lungs In Poster 2005 Proc. [CD-ROM] Prague: CTU 2005 - 125 - Appendix B Abbreviations 8.2 Abbreviations AC BFGS CT CTU DC EGG EMT GA LVDT MCG MEG MIT MPG MRI NMR MUSIC PLCD SPECT SQUID – – – – – – – – – – – – – – – – – – – alternating current Broyden-Fletcher-Goldfarb-Shanno (optimization method) computed tomography Czech Technical University direct current electrogastrography electromagnetic tomography genetic algorithm linear variable differential transformer magnetocardiography magnetoencephalography magnetic induction tomography magnetopneumography magnetic resonance imaging nuclear magnetic resonance multiple signal classification permanent magnetic linear contactless displacement single photon emission computed tomography superconducting quantum interference device - 126 -

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