Simulation of bioelectric fields: the forward and inverse problem of electro-encephalographic source analysis
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| Format: | Book |
| Language: | English |
| Published: |
Erlangen
Inst. für Informatik
2004
|
| Series: | Arbeitsberichte des Instituts für Informatik, Friedrich-Alexander-Universität Erlangen-Nürnberg
37,6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Erlangen-Nürnberg, Univ., Diss, 2004. - Enth. dt. und engl. Zsfassung |
| Physical Description: | XII, 297 S. Ill., graph. Darst. |
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ARBEITSBERICHTE DES INSTITUTS FUR INFORMATIK
FRIEDRICH-ALEXANDER-UNIVERSITAT ERIANGEN NURNBERG BAND 37 * NUMMER 6 *
DEZEMBER 2004 MARCUS MOHR SIMULATION OF BIOELECTRIC FIELDS: THE FORWARD
AND INVERSE PROBLEM OF ELECTRO-ENCEPHALOGRAPHIC SOURCE ANALYSIS
DISSERTATION HERAUSGEBER: M. DAL CIN, R. GERMAN, G. GORZ, G. GREINER, U.
HERZOG, F. HOFMANN, J. HORNEGGER, S. JABLONSKI, K. LEEB, ULB DARMSTADT *
MULLER - H - N'EMANN, IE, F. SAGLIETTI, KSCHAT, M. STAMMINGER,
"16641556"'" WEDEKIND DIE REIHE DER ARBEITSBERICHTE DES INSTITUTS FUR
INFORMATIK (EHEM. INSTITUT FUR MATHEMATISCHE MASCHINEN UND
DATENVERARBEITUNG) DER UNIVERSITAT ERLANGEN-NUMBERG ERSCHEINT SEIT 1967.
BEGRUNDET VON PROF. DR. DR. H. C. MULT. WOLFGANG HANDLER CONTENTS I
BACKGROUND AND MOTIVATION 1 1 PRELIMINARIES 3 1.1 MEDICAL IMAGING AND
DATA ACQUISITION TECHNIQUES 3 1.2 BASIC STAGES OF BIOELECTROMAGNETIC
FIELD SIMULATION 4 1.3 APPLICATION AREAS OF SOURCE ANALYSIS 8 1.4 THE
INVERSE PROBLEM AND ITS ILL-POSEDNESS 9 2 BIOPHYSICAL MODELLING 11 2.1
THE EEG AND ITS GENERATORS 11 2.2 DIPOLES AND MONOPOLES AS BASIC
ELEMENTS OF BIOELECTRIC SIMULATION 15 2.3 THE BIOELECTRIC FIELD EQUATION
16 2.4 LEAD FIELD THEORY AND RECIPROCITY THEOREM 18 2.4.1 LEAD VECTORS
AND LEAD FIELD 19 2.4.2 THE RECIPROCITY THEOREM 20 2.4.3 RECIPROCAL
ELECTRIC FIELD AND LEAD FIELD 23 2.4.4 EXPLOITING RECIPROCITY FOR
NUMERICAL SIMULATION 25 3 SOLUTION APPROACHES FOR THE FORWARD EEG
PROBLEM 27 3.1 SPHERICAL HEAD MODELS 27 3.2 NUMERICAL DISCRETISATION
TECHNIQUES 29 4 STATE OF THE ART AND CURRENT TRENDS 35 4.1 CURRENT
TRENDS 35 4.2 SCOPE OF THIS THESIS 38 II THE FORWARD EEG PROBLEM 41 5
DISCRETISATION 43 5.1 DISCRETE HEAD MODEL 43 5.2 FINITE VOLUME APPROACH
44 5.3 PROPERTIES OF THE DISCRETISATION MATRIX AND REGULARISATION 46 6
ITERATIVE SOLVERS 51 6.1 DIRECT VERSUS ITERATIVE SOLVERS 51 6.2 TOOLS
FROM THE THEORY OF ITERATIVE METHODS 53 6.3 DESCRIPTION OF THE DIFFERENT
METHODS 57 CONTENTS 6.3.1 SUCCESSIVE OVER-RELAXATION 57 6.3.2 CONJUGATE
GRADIENTS 58 6.3.3 PRECONDITIONED CONJUGATE GRADIENTS 60 6.3.4 SSOR
PRECONDITIONER 64 6.3.5 ILU / IC PRECONDITIONER 65 6.3.6 FSAI
PRECONDITIONER 68 6.3.7 ALGEBRAIC MULTIGRID 75 6.4 CONVERGENCE PROOFS 83
NUMERICAL EXPERIMENTS 89 7.1 IMPLEMENTATION 89 7.2 DATA SETS 92 7.3 WORK
ESTIMATES 97 7.4 OPTIMAL PARAMETERS 98 7.4.1 SOR 99 7.4.2 PCG(SSOR) 99
7.4.3 PCG(IC) 101 7.4.4 PCG(FSAI) 102 7.4.5 AMG 106 7.5 COMPARISON OF
METHODS 110 7.5.1 ARITHMETIC COSTS ILL 7.5.2 RUN TIMES 112 7.5.3
DISCUSSION 115 7.6 QUALITY OF THE DISCRETISATION 119 7.7 ANISOTROPIC
HEAD MODELS 124 CELL-CENTRED MULTIGRID 131 8.1 BASIC CONCEPTS AND
HISTORICAL DEVELOPMENT 131 8.2 TRANSFER OPERATORS 133 8.3 GALERKIN
COARSE GRID OPERATORS 140 8.4 TREATMENT OF THE GEOMETRY 146 8.5
NUMERICAL EXPERIMENTS 148 8.6 DISCUSSION 153 III THE INVERSE EEG PROBLEM
155 9 NUMERICAL TECHNIQUES 157 9.1 STANDARD SOLUTION APPROACHES 157
9.1.1 DIPOLE LOCALISATION 157 9.1.2 DEVIATION SCAN 158 9.1.3 BRAIN
IMAGING 158 9.2 GAIN FUNCTION FOR MINIMISATION 159 9.2.1 RELATIVE
RESIDUAL ENERGY 159 9.2.2 SINGLE TIME SAMPLE 160 9.2.3 MULTIPLE TIME
SAMPLES 163 9.3 NELDER-MEAD ALGORITHM FOR NON-LINEAR OPTIMISATION 166
CONTENTS 10 SENSITIVITY ANALYSIS 173 10.1 ERROR SOURCES IN THE
RECONSTRUCTION 173 10.2 RECONSTRUCTION ALGORITHM AND QUALITY MEASURES
176 10.3 VALIDATION OF THE RECONSTRUCTION ALGORITHM 178 10.3.1
MOTIVATION AND SETUP OF THE STUDY 178 10.3.2 EXPERIMENTAL RESULTS 179
10.4 LEAD SENSITIVITY 182 10.5 INFLUENCE OF REFERENCING 190 10.6
ACCURACY OF FORWARD SOLUTIONS 201 10.6.1 MOTIVATION AND SETUP OF THE
STUDY 201 10.6.2 EXPERIMENTAL RESULTS 201 10.7 ANISOTROPY OF THE SKULL
204 10.7.1 MOTIVATION AND SETUP OF THE STUDY 204 10.7.2 EXPERIMENTAL
RESULTS 206 10.8 SUMMARY AND DISCUSSION 209 IV APPENDIX 213 A STANDARD
MODEL PROBLEMS 215 B SOBOLEV SPACES AND INTEGRATION BY PARTS FORMULAS
219 C MODEL PROBLEM ANALYSIS FOR THE SEMI-DEFINITE ID CASE 223 C.I
INTRODUCTION 223 C.2 MODEL PROBLEM 224 C.2.1 FORMULATION AND
DISCRETISATION 224 C.2.2 NOTATION AND DEFINITIONS 225 C.2.3 SOLVABILITY
AND SOLUTION 226 C.2.4 SEMI-CONVERGENCE 228 C.3 SMOOTHERS 229 C.3.1
GENERAL REMARKS 229 C.3.2 WEIGHTED JACOBI 229 C.3.3 SUCCESSIVE
OVER-RELAXATION 233 C.4 GRID TRANSFER OPERATORS 245 C.4.1 PROLONGATION
245 C.4.2 RESTRICTION 247 C.5 COARSE GRID CORRECTION 251 C.5.1
SOLVABILITY ISSUE 251 C.5.2 SOLUTION OF COARSE GRID PROBLEM 252 C.5.3
OPERATOR OF COARSE GRID CORRECTION 252 C.6 TWO-LEVEL-CYCLE 254 C.7
CONCLUSIONS 257 D COLOR PLATES 259 BIBLIOGRAPHY 269 CONTENTS V GERMAN
PART INHALT S VER ZEICHNIS ZUSAMMENFASSUNG 287 291 295 |
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| spelling | Mohr, Marcus Verfasser aut Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis Marcus Mohr Erlangen Inst. für Informatik 2004 XII, 297 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Arbeitsberichte des Instituts für Informatik, Friedrich-Alexander-Universität Erlangen-Nürnberg 37,6 Zugl.: Erlangen-Nürnberg, Univ., Diss, 2004. - Enth. dt. und engl. Zsfassung Bioelektronische Funktionsdiagnostik (DE-588)4128784-8 gnd rswk-swf Echoencephalographie (DE-588)4302467-1 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Bioelektrisches Signal (DE-588)4131877-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Bioelektronische Funktionsdiagnostik (DE-588)4128784-8 s Bioelektrisches Signal (DE-588)4131877-8 s Simulation (DE-588)4055072-2 s Echoencephalographie (DE-588)4302467-1 s DE-604 Arbeitsberichte des Instituts für Informatik, Friedrich-Alexander-Universität Erlangen-Nürnberg 37,6 (DE-604)BV013391036 37,6 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013018830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mohr, Marcus Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis Arbeitsberichte des Instituts für Informatik, Friedrich-Alexander-Universität Erlangen-Nürnberg Bioelektronische Funktionsdiagnostik (DE-588)4128784-8 gnd Echoencephalographie (DE-588)4302467-1 gnd Simulation (DE-588)4055072-2 gnd Bioelektrisches Signal (DE-588)4131877-8 gnd |
| subject_GND | (DE-588)4128784-8 (DE-588)4302467-1 (DE-588)4055072-2 (DE-588)4131877-8 (DE-588)4113937-9 |
| title | Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis |
| title_auth | Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis |
| title_exact_search | Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis |
| title_full | Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis Marcus Mohr |
| title_fullStr | Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis Marcus Mohr |
| title_full_unstemmed | Simulation of bioelectric fields the forward and inverse problem of electro-encephalographic source analysis Marcus Mohr |
| title_short | Simulation of bioelectric fields |
| title_sort | simulation of bioelectric fields the forward and inverse problem of electro encephalographic source analysis |
| title_sub | the forward and inverse problem of electro-encephalographic source analysis |
| topic | Bioelektronische Funktionsdiagnostik (DE-588)4128784-8 gnd Echoencephalographie (DE-588)4302467-1 gnd Simulation (DE-588)4055072-2 gnd Bioelektrisches Signal (DE-588)4131877-8 gnd |
| topic_facet | Bioelektronische Funktionsdiagnostik Echoencephalographie Simulation Bioelektrisches Signal Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013018830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013391036 |
| work_keys_str_mv | AT mohrmarcus simulationofbioelectricfieldstheforwardandinverseproblemofelectroencephalographicsourceanalysis |