Eng. MIHAELA PLEŞA (CREłU) CONSIDERATIONS REGARDING THE STUDY OF THE MAGNETIC FUNCTIONAL STIMULATION OVER THE SPINAL CORD

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1 Eng. MIHAELA PLEŞA (CREłU) CONSIDERATIONS REGARDING THE STUDY OF THE MAGNETIC FUNCTIONAL STIMULATION OVER THE SPINAL CORD PhD Evaluation Commission: PRESIDENT: SUPERVISOR: MEMBERS: Prof. dr. eng. Ioan G. TÂRNOVAN Dean, Faculty of Electrical Engineering, Technical University of Cluj-Napoca Prof. dr. eng. Radu V. CIUPA Faculty of Electrical Engineering, Technical University of Cluj-Napoca Prof. dr. eng. Alexandru M. MOREGA Faculty of Electrical Engineering, Politehnica University of Bucharest Prof. dr. eng. Mirela TOTH TAŞCĂU Faculty of Mechanical Engineering, Politehnica University of Timisoara Conf. dr. eng. Laura DĂRĂBANT Faculty of Electrical Engineering, Technical University of Cluj-Napoca 2012

2 SUMMARY LIST OF CONTENTS 1 STIMULATION BY ELECTRIC OR MAGNETIC FIELD 1.1 CLASSIFICATION OF ELECTROMAGNETIC WAVES 1.2 PRINCIPLES OF INDUCTION OF THE ELECTRIC FIELD 1.3 PRINCIPLES OF INDUCTION OF THE LOW-FREQUENCY MAGNETIC FIELD VARIABLE IN TIME. INTERACTION MECHANISM 1.4 THEORETICAL ANALYSIS METHODS 1.5 APPLICATIONS OF THE ELECTRIC AND MAGNETIC FIELDS IN MEDICINE Medical applications of the electric field Medical applications of the magnetic field Medical applications of the magnetic stimulation of the nervous tissue 1.6 STIMULATION BY ELECTRIC OR MAGNETIC FIELD THEORETICAL COMPARISON. ADVANTAGES AND DIS-ADVANTAGES Example of practical application of the electric stimulation as a treatment method 1.7 CONCLUSIONS AND CONTRIBUTIONS 2 THE ACTUAL PHASE OF THE INVESTIGATIONS REGARDING THE MAGNETIC STIMULATION IN MEDICINE. MODELING THE STIMULATION COILS IN A REALISTIC MANNER 2.1 MAGNETIC STIMULATION HISTORY OF HUMAN TISSUE 2.2 MAGNETIC STIMULATION MECHANISM 2.3 TRANSIENT REGIME OF THE STIMULATION CIRCUIT 2.4 CALCULATION OF THE ELECTRIC FIELD INDUCED IN THE TISSUE Calculation of the electric scalar potential Determination of the electric field induced by magnetic stimulation in tissues, modeled by cylindrical or spherical conductors 2.5 COILS OPTIMIZATION CIRCUIT STIMULATION Focus criteria 2.6 SHAPE OF STIMULATION COILS. INFLUENCE OF TURNS POSITION INSIDE THE COIL OVER THE INDUCED ELECTRIC FIELD AND ACTIVATION FUNCTION Circular coil Eight coil Cloverleaf coil disc and solenoid Slinky coils D differential coil Comparing the results 2.7 MAGNETIC STIMULATION OF THE NERVE FIBERS IN THREE DIFFERENT OPERATING PROCEDURES Solving the circuit transient stimulation Determining the temporal component of the electric field induced in the tissue and the activation function 2.8 CONCLUSIONS AND CONTRIBUTIONS 3 CABLE MODEL FOR THE NERVOUS FIBER IN MAGNETIC STIMULATION 3.1 EQUATION DEDUCTION FOR PASSIVE CABLE OF THE NERVE FIBER 3.2 HODGKIN HUXLEY MODEL 3.3 NUMERICAL MODELLING OF PASSIVE RESPONSE DURING MAGNETIC STIMULATION OF NERVE FIBER 3.4 NUMERICAL MODELLING OF THE ACTIVE MEMBRANE CELL BEHAVIOUR DURING MAGNETIC STIMULATION 1

3 3.5 SIMULATION OF PASSIVE AND ACTIVE BEHAVIOUR IN MAGNETIC STIMULATION OF NERVE FIBER - DETERMINATION OF TRANSMEMBRANE POTENTIAL Stimulation coil placed above a flat surface Stimulation coil placed over a cylindrical surface 3.6 INFLUENCE OF CHANGES CELL MEMBRANE ELECTRICAL PARAMETERS ON THE RESPONSE TO ELECTRIC AND MAGNETIC STIMULATION OF NERVE FIBER Modeling of nerve fiber stimulation with a train of pulses Modeling of active behavior of the nerve fiber to the variation of electrical parameters 3.7 CONCLUSIONS AND CONTRIBUTIONS 4 EXPERIMENTAL ANALYSIS CONCERNING THE MAGNETIC STIMULATION OF THE SPINAL CORD 4.1 MATERIALS AND METHODS 4.2 RESULTS AND DISCUSSIONS Identification techniques of recorded CMAP responses Double stimulus paradigm Tendons vibration technique Long latency response in spinal cord magnetic stimulation 4.3 CONCLUSIONS AND CONTRIBUTIONS 5 MODELING AND SIMULATION THE MAGNETIC STIMULATION OF THE SPINAL CORD 5.1 BUILDING SIMULATION MODEL 5.2 SOLVINF THE LAPLACE EQUATION USING FINITE DIFFERENCE METHOD Creating the system of equations corresponding tofinite Difference Method Determination of potential points on the boundary Determination of potential points in the vicinity of the boundary General cases (inside the domain) Forming the corresponding matrix equation system 5.3 RESULTS Comparison of own software with COMSOL Simulation of magnetic stimulation of spinal cord 5.4 CONCLUSIONS AND CONTRIBUTIONS 6 CONCLUSIONS, CONTRIBUTIONS AND FUTURE RESEARCH TOPICS 6.1 THESIS STRUCTURE 6.2 CONTRIBUTIONS 6.3 DIRECTIONS TO PROCEED THE RESEARCH 7 REFERENCES 2

4 Abstract of the Thesis The PhD thesis developed by the author is liable to be framed in the large context of the influence of electromagnetic fields over the living beings. On these lines, presently, a subject of interest in international prospecting has been approached, namely the functional stimulation. The functional stimulation forms a scientific department of the newly arrived interdisciplinary analysis, blending remarkable elements from engineering, mathematics, physics, informatics, and so on. It offers treatment solutions to persons who suffer of certain disabilities, determined by accidents, by stimulating the nervous lay-outs or, in case these are damaged, the muscles of the patient. There are two directions of functional stimulation: electrical way or magnetic way. The present essay studies especially the magnetic one, due to the extended application area, but, for comparison and in order to underline its utility and importance, some references to the electrical stimulation have been made here and there. The interdisciplinary character of the present thesis may be observed, as it combines, in a beautiful manner, fundamentals of the electromagnetic field s Theory, Theory of electric circuits, Numerical Methods, using models of analytical calculus, 2D and 3D numerical calculus and, not at least, programming languages for solving calculus software algorithms. Keywords: functional stimulation of spinal cord, coil design, cable model, magnetic stimulator circuit, vibration technique in magnetic stimulation Structure and Contents Chapter 1, entitled Stimulation by electric or magnetic field, frames the thesis in the large context of the electromagnetic field s influence over the living beings. The investigations in this chapter lean towards the electromagnetic interference sources, offering a methodic presentation of the electromagnetic fields the living beings are exposed to, taking in consideration the nature and the domain of frequencies. A short introduction in the magnetic stimulation technique of the nervous tissue is, also, presented. Some medical applications of this technique in treating and diagnosing various affections are passed in review. There has been made a comparative research, in a detailed manner, concerning each type of functional stimulation known up to the present: electrical and magnetic stimulation. There are mentioned the advantages and disadvantages of each method apart and the performance of a new type of electric stimulator is being tested, in order to be introduced in the market. Chapter II, entitled The actual phase of the investigations regarding the magnetic stimulation in medicine. Modeling the stimulation coils in a realistic manner, sustains briefly and comprehensive all the aspects interfering with the functional magnetic stimulation, creating a clear actual phase of the analysis in domain. One of the main objectives of this chapter is to bring improvements concerning the focalization of the electric field induced towards the target tissue, having as a scope the selective activation of a certain nervous fiber from a bunch. Going from this point, the coil shapes used the most in stimulation are described, and a proposal of a realistic research regarding their projection is made, based on the possible way of placing the turn inside the inductive coil, as a disc or solenoid, having a number equal or different of turn on every layer. For that purpose, there have been considered five different geometric configurations of coils, having the same number of turn (circular, 8-shape, clover leaf, Slinky-3 and 3D differential coil). The last part of this chapter refers to the distribution in time of the induced electric field and the spatial derivation of its axial component on the fiber direction. There has been evidenced that, in time, two phases of the stimulation can be distinguished: the primary 3

5 phase, of proper stimulation and the secondary phase, when the stimulation stops. As a conclusion, the stimulation appears at the beginning of the time frame, right in the moment of the stimulus application. Chapter III, entitled Cable model for the nervous fiber in the magnetic stimulation, presents a study concerning the way the nervous fiber responds effectively to the magnetic stimulation. In order to do this, three aspects must be taken in consideration within the same model: the shape of the stimulation impulse, the distribution of the induced electric field and the interaction between the electric field and the nervous fiber. There has been made a program, in the scientific calculus environment Matlab, permitting the solving of the passive cable equation in subliminal non-steady regime and the procurement of the trans-membrane potential. Using the Finite Differences Method, the active model of membrane has been solved, too, and the momentum of the stimulation appearance, the nervous excitability threshold, for every case and every coil type have been evidenced, and the action potential has been determined. It was studied how membrane cell electrical parameters variation influences the nerve fiber response. Significant changes are seen in the active fiber model. At a variation of the electric parameters along the fiber of more than 20%, the excitability threshold is higher, but the stimulation appears much more rapidly (the latency period is shorter). Chapter IV, entitled Experimental analysis concerning the magnetic stimulation of the spinal cord, has as a main objective the investigation of the neuronal structures activated by the transcutaneous magnetic stimulation of the spinal cord, by electromiographic examination of the answers given in the inferior limbs. For comparison and reference, in every analyzed case, electrical stimulation has been applied, too. The stimulation has been made by the 8-shape coil, which proved to be more useful in the stimulation of the nervous spinal roots. It s evidenced that, both the electric and magnetic stimulation of the spinal cord, can activate the efferent fibers, generating M waves in the muscles of the interior limbs or PRM reflexes can be obtained, due to the activation of the associated fibers. PRM reflexes, through electric stimulation, came up to all the subjects, while, by magnetic stimulation, they could not be generated in more than one of the 7 tested subjects. The question was if, by applying magnetic stimulation at the backbone level, the lay-out of the efferent fibers was activated or the associated fibers were stimulated. To condition the answers and to avoid the misinterpreting of the data, some identifying neurophysiologic methods have been used, such as the double stimuli paradigm or the vibration of the tendons. The double stimuli paradigm proved, though, to be inefficient in interpreting the muscular responses in the magnetic stimulation, because the first stimulus produces a considerable bending (movement) of the spinal cord, due to the muscular contractions of the loin, changing thus the stimulation conditions. Applying the second technique for cancelling the PRM reflexes, namely the vibration at the tendons level, one noticed that these can easily be cancelled. Hence, the tendons vibration is a faultless method for identifying the reflexes, in case of applying each of the two stimulation techniques. Chapter V, entitled Modeling and simulating the magnetic stimulation of the spinal cord, follows the simulation of the magnetic stimulation process of the spinal cord, in order to establish whether the intensity of the electric field induced in the spinal cord during the stimulation and the activating function are intense enough to produce the activation of the cortical spinal lay-out. Thus, there s looking for an answer to some questions come up during the experimental research, wedded to the nature of the muscular responses with a short latency, appeared as a following of the magnetic stimulation of the lumbar area of the backbone. These might be due to the direct activation of the spinal cord or might be generated by the spinal nerves stimulation, situated on the both sides of the backbone. 4

6 In order to find the answers and for the final validation of some conclusions formulated based on the measurements achieved, a simplified calculus model was created, intercepting the properties of the biological environment took in consideration (thorax, spinal cord only 6 vertebrae and the spinal cord). The designed geometric scheme became, then, discreet, in order to make the associated electric field calculus (determination of the total induced electric field in the tissue and its axial component derivate on z direction) using the Finite Differences Method. Knowing the approximation laplacian mode, the boundary conditions and the passing conditions using the Finite Differences Method, the step by step implementation of the established calculus algorithm started, in the calculus program MATLAB Then, the experimental cases have been correctly simulated, using three different placements of the stimulation coil (M90, M0, R270). Finnaly, the conclusion consisted in the fact that, for all the three cases, the activity in the muscles of the inferior limbs was due to the activation of the spinal nerves situated two-sided and not to the direct activity of the nerves situated inside the spinal cord. Original Contributions in this Thesis All the results were published in journals and at international conferences. Based on the conducted research we will present, in the following paragraph, the main contributions of this work to a better knowledge of this thematic: Testing a prototype electrical stimulator to be introduced to market medical devices, for denervated muscle stimulation, in order to improve its performance in treatment; Design, implementation, modeling and interpretation of results for realistic configurations proposed for induction coil - 24 configurations tested - to establish the optimal design that meets the criteria set focus. It is outlined the advantages and disadvantages of each configuration set; Analysis of the variation in time of induced electric field and its spatial derivative, using all three operating modes for stimulating circuit, and especially critical aperiodic regime, which has not been studied; Simulation of nerve cell functioning, using an algorithm implemented in MATLAB; Analysis and interpretation of passive and active response to magnetic stimulation of the nerve fiber with clear evidence of correspondence between stimulus intensity applied when triggering action potential; Creating a SPICE circuit with variable parameters, which models the transmission of nerve impulses along an inhomogeneous fiber; Simulation and interpretation of passive and active response of nerve fiber if the membrane electrical properties along the nerve fiber are no longer considered constant (situation taking into account its possible heterogeneity). Two models were created (in SPICE and MATLAB). Making experimental determinations referred to in Chapter IV (activity in the team in Vienna and Cluj); Taking the electromyograph experimental data in ASCII format and processed (creation of Matlab data files); Analysis of experimental data by creating Matlab programs for automatic generation of graphs for each experiment (each experiment was conducted 10 times to ensure repetability, and the graph obtained is the average of 10 tests); 5

7 Analysis and application of suppression techniques of PRM reflexes and interpretation of results obtained; Report of a new type of muscle response, low intensity and long latency, which was not been described in the literature for spinal cord stimulation; Creating a simplified geometric model of the spine that takes into account the environmental properties; Implementing the proper calculation algorithm, based on Finite Difference Method, a mathematical model for determining the electric field induced in the spinal cord and adjacent areas, during magnetic stimulation (solving the Laplace equation with Neumann type boundary conditions in cylindrical and cartesian coordinates and considering sub-areas of different electrical properties calculation); Providing significant results related to considered tissue heterogeneity over the induced electric field; Testing and comparison of the own model with Comsol; Comparison of experimental results with those obtained by simulation and interpretation of short-latency muscle responses occurring during magnetic stimulation of spinal cord. REFERENCES - selection [1]. Ciupa R. V., Dărăbant Laura, Pleşa Mihaela, CreŃ O., Micu D. D., Design Of Efficient Magnetic Coils For Repetitive Stimulation, Revue Roumaine d Electrotechnique, Vol.55, No.3, pp , [2]. Contract de cercetare TD_283/2007, ContribuŃii privind studiul teoretic şi experimental al stimulării magnetice funcńionale, Director: Pleşa Mihaela. [3]. Contract Bilateral Romania-Austria, nr. 224/2009, Stimularea FuncŃională a Măduvei Spinării, Director: Prof. dr. ing. Ciupa R. V., membru în colectivul de cercetare CreŃu Mihaela. [4]. CreŃu Mihaela, Ciupa R. V., Dărăbant Laura, Active Behavior of Peripheral Nerves during Magnetic Stimulation, IFMBE Proceedings of the XII Mediterranean Conference on Medical and Biological Engineering and Computing, Chalkidiki, Greece, Springer Verlag, ISSN , ISBN , Vol.29, pp , MEDICON, May [5]. Dărăbant Laura., Pleşa Mihaela, Micu D. D., ŞteŃ Denisa, Ciupa R. V., Dărăbant A., Energy Efficient Coils for Magnetic Stimulation of Peripheral Nerves, IEEE Transactions on Magnetics, Vol. 45, No. 3, pp , Digital Object Identifier: /TMAG , ISSN: , March [6]. Minassian K, Persy I., Rattay F., Dimitrijevic M. R., Hofer C., Kernet H., Posterior Root Muscle Reflexes Elicited by Transcutaneous Stimulation of the Human Lumbosacral Cord, Muscle&Nerve Vol. 35, No. 3, pp , [7]. Pleşa Mihaela, Dărăbant Laura, Ciupa R. V., Dărăbant A., A Medical Application of Electromagnetic Fields: the Magnetic Stimulation of Nerve Fibers Inside a Cylindrical Tissue, Proceedings of OPTIM 2008, Vol. 1, pp , IEEE Catalogue number 08EX1996C, ISBN , [8]. Pleşa Mihaela, Dărăbant Laura, Ciupa R. V., Nicu Anca, Curta C., Matlab Modelling of Nerve Fiber Activation by Magnetic Stimulation, MEDITECH, Cluj-Napoca, România, ISBN , ISSN , Springer Verlag Berlin, pp , September [9]. Pleşa Mihaela, Dărăbant Laura, Ciupa R. V., CreŃu T., Modelling the Magnetic Stimulation of Nerve Fibers Inside a Cylindrical Tissue, Acta Electrotehnica, Vol. 50, No. 2, pp , ISSN , [10]. Rattay F., Resatz S., Dipole Distance for Minimum Threshold Current to Stimulate Unmyelinated Axons with Microelectrodes, IEEE Transactions on Biomedical Engineering, Vol.54, No. 1, pp.74-77, January [11]. Schnabel V., Struijk J., Calculation of Electric Fields in a Multiple Cylindrical VolumeCconductor Induced by Magnetic Coils, IEEE Transactions on Biomedical Engineering, Vol. 48, No. 1, [12]. Struijk J. J., Schnabel V., Influence of Parameter Variability on Stimulus Thresholds in Nerve Fiber Models, Proceedings of the 5 th conf. of the IFESS, pp ,