Modeling organs, tissues, cells and devices: using MATLAB and COMSOL multiphysics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
[2017]
|
| Series: | Lecture notes in bioengineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Physical Description: | xiii, 502 Seiten Illustrationen, Diagramme |
| ISBN: | 9783642548000 |
Staff View
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Record in the Search Index
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| adam_text |
CONTENTS
PART I BIOENGINEERING MODELLING PRINCIPLES, METHODS AND THEORY
1 INTRODUCTION TO MODELLING IN BIOENGINEERING
.
3
1.1 MODELLING AND SIMULATION IN MEDICINE AND B IO LO G Y
.
3
1.2 THE MODELLING
PROCESS.
4
1.3 MATHEMATICAL MODEL T Y P E S
. 5
1.3.1 LINEAR VERSUS N
ON-LINEAR. 6
1.3.2 DYNAMIC VERSUS S TA TIC
.
7
1.3.3 DETERMINISTIC VERSUS S
TOCHASTIC. 7
1.3.4 CONTINUOUS VERSUS D ISCRETE
.
9
1.3.5 RULE-BASED
.
12
1.4 DIMENSIONAL
ANALYSIS.
16
1.4.1 DIMENSIONS AND
UNITS. 16
1.4.2 BUCKINGHAM TT-THEOREM
.
19
1.5 MODEL S CALIN G
.
21
PROBLEMS.
23
REFERENCES.
27
2 LUMPED PARAMETER MODELLING WITH ORDINARY DIFFERENTIAL
EQUATIONS.
29
2.1 OVERVIEW OF ORDINARY DIFFERENTIAL
EQUATIONS. 29
2.2 LINEAR
ODES.
31
2.3 ODE
SYSTEMS.
35
2.3.1 EXAMPLE MODEL 1: CARDIAC M
ECHANICS. 37
2.3.2 EXAMPLE MODEL 2: HODGKIN-HUXLEY MODEL OF NEURAL
E
XCITATION.
42
2.4 FURTHER R
EADING.
46
PROBLEMS.
46
REFERENCES.
53
3 NUMERICAL INTEGRATION OF O RDINARY DIFFERENTIAL EQUATIONS
.
55
3.1 TAYLOR*S THEOREM
.
55
3.2 ONE-STEP M
ETHODS.
60
3.2.1 BACKWARD-EULER M
ETHOD. 63
3.2.2 TRAPEZOIDAL M ETH O D
. 65
3.2.3 RUNGE-KUTTA METHODS
.
66
3.2.4 THE GENERALIZED-A M
ETHOD. 73
3.3 MULTISTEP M
ETHODS.
82
3.3.1 PREDICTOR-CORRECTOR M ETHODS
.
86
3.3.2 BACKWARD DIFFERENTIATION FORMULAS
.
93
3.3.3 NUMERICAL DIFFERENTIATION FORMULAS
.
96
3.4 ODE SOLVER IMPLEMENTATIONS IN MATLAB AND COMSOL
.
97
3.5 FURTHER R
EADING.
100
PROBLEMS.
100
REFERENCES.
103
4 DISTRIBUTED SYSTEMS MODELLING
WITH P ARTIAL DIFFERENTIAL EQUATIONS
.
105
4.1 MODELLING WITH PD F
S.
105
4.1.1 THE
GRADIENT.
105
4.1.2 THE
DIVERGENCE.
108
4.1.3 THE C U
RL.
112
4.1.4 THE DIVERGENCE THEOREM
. 113
4.1.5 CONSERVATION LAW
FORMULATION. 117
4.1.6 THE
LAPLACIAN.
119
4.1.7 PDE BOUNDARY C
ONDITIONS. 120
4.2 BASIC ANALYTICAL AND NUMERICAL SOLUTION TECHNIQUES
.
123
4.2.1 SEPARATION OF VARIABLES
.
123
4.2.2 FINITE DIFFERENCE M E TH O D
. 139
4.2.3 METHOD OF L INES
.
147
4.3 FURTHER R
EADING.
153
PROBLEMS.
153
REFERENCES.
157
5 THE FINITE ELEMENT M E TH O D
.
159
5.1 FINITE ELEMENTS FOR ID
SYSTEMS. 159
5.1.1 WEAK FORM PDE EQUIVALENT
.
160
5.1.2 BASIS FUNCTION
APPROXIMATION. 164
5.1.3 HIGHER-ORDER BASIS FUNCTIONS
.
175
5.2 FINITE ELEMENTS FOR 2D/3D SYSTEM S
.
179
5.2.1 WEAK FORM D
ESCRIPTION. 180
5.2.2 BASIS FUNCTION
APPROXIMATION. 183
CONTENTS XI
5.3 FEM NUMERICAL
IMPLEMENTATION.
190
5.3.1 ASSEMBLY OF SYSTEM
MATRICES. 191
5.3.2 GAUSSIAN
QUADRATURE.
192
5.3.3 NON-LINEAR SYSTEM
S. 194
5.4 FURTHER R
EADING.
195
PROBLEMS.
196
REFERENCES.
197
P ART II BIOENGINEERING APPLICATIONS
6 MODELLING ELECTRICAL STIMULATION OF T IS S U E
.
201
6.1 ELECTRICAL
STIMULATION.
201
6.1.1 MAXWELL*S
EQUATIONS.
201
6.1.2 ELECTROSTATIC
FORMULATIONS. 203
6.1.3 VOLUME CONDUCTOR T HEORY
.
204
6.1.4 EXAMPLE: CELL CULTURE ELECTRIC FIELD STIMULATOR
.
207
6.1.5 EXAMPLE: ACCESS RESISTANCE OF ELECTRODE D ISC
.
210
6.2 MODELLING ELECTRICAL ACTIVITY OF
TISSUES. 215
6.2.1 CONTINUUM MODELS OF EXCITABLE TISSUES
.
215
6.2.2 EXAMPLE: MODELLING SPIRAL-WAVE REENTRY
IN CARDIAC T ISSU E
.
217
6.2.3 MODELLING PDES/ODES ON BOUNDARIES,
EDGES AND
POINTS.
225
6.2.4 EXAMPLE: AXONAL STIMULATION USING NERVE CUFF
ELECTRODES
.
226
6.3 FURTHER R
EADING.
234
PROBLEMS
.
234
REFERENCES.
235
7 MODELS OF DIFFUSION AND H EAT T RA N SFE
R. 237
7.1
DIFFUSION.
237
7.1.1 PICK'S LAWS OF
DIFFUSION. 237
7.1.2 EXAMPLE: DIFFUSION AND UPTAKE INTO A SPHERICAL C ELL
.
238
7.1.3 CONVECTIVE T RANSPORT
.
241
7.1.4 EXAMPLE: DRUG DELIVERY IN A CORONARY S TENT
.
242
7.2 HEAT T
RANSFER.
247
7.2.1 HEAT CONDUCTION AND CONVECTION
.
248
7.2.2 THE BIOHEAT EQUATION
.
250
7.2.3 EXAMPLE: RF ATRIAL A B LATIO N
. 251
7.3 FURTHER R
EADING.
258
PROBLEMS.
258
REFERENCES.
260
XII CONTENTS
8 SOLID M
ECHANICS.
263
8.1
BIOMECHANICS.
263
8.2 TENSOR
FUNDAMENTALS.
263
8.2.1 TENSOR D EFINITION
.
263
8.2.2 INDICIAL
NOTATION.
265
8.2.3 TENSOR TRANSFORMATION L A W
.
266
8.2.4 TENSOR
INVARIANTS.
268
8.3 MECHANICS
PRINCIPLES.
271
8.3.1 S TRE S S
.
271
8.3.2 S TRA IN
.
275
8.4 LINEAR
ELASTICITY.
281
8.4.1 EXAMPLE: DETECTING TENSION IN A RESPIRATOR S TRA P
.
284
8.5 LINEAR
VISCOELASTICITY.
290
8.6 HYPERELASTIC M
ATERIALS.
291
8.6.1 EXAMPLE: MYOCARDIAL S H E A R
.
294
8.7 FURTHER R
EADING.
299
PROBLEMS.
300
REFERENCES.
302
9 FLUID M EC H AN
ICS.
305
9.1 FLUID M O TIO N
.
305
9.1.1 EXAMPLE: LAMINAR FLOW THROUGH A CIRCULAR T U B E
.
306
9.2 NAVIER-STOKES EQUATIONS
.
311
9.2.1 EXAMPLE: DRUG DELIVERY IN A CORONARY STENT REVISITED . . . 314
9.3 NONDAMINAR
FLOW.
321
9.4 MODELLING BLOOD F LOW
.
324
9.4.1 ELECTRIC CIRCUIT ANALOGUES FOR BLOOD F LOW
.
324
9.4.2 EXAMPLE: AORTIC BLOOD F LO W
.
325
9.4.3 BLOOD AS A NON-NEWTONIAN
FLUID. 329
9.4.4 EXAMPLE: AXIAL STREAMING OF A BLOOD C ELL
.
330
9.5 FURTHER R
EADING.
339
PROBLEMS.
339
REFERENCES.
341
APPENDIX A: M ATLAB FUNDAM
ENTALS.
343
APPENDIX B: OVERVIEW OF COMSOL M ULTIPHYSICS
.
355
S O LU TIO N
S.
381
IN D E X
.
495 |
| any_adam_object | 1 |
| author | Dokos, Socrates |
| author_GND | (DE-588)1138237574 |
| author_facet | Dokos, Socrates |
| author_role | aut |
| author_sort | Dokos, Socrates |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 681 - Precision instruments and other devices 660 - Chemical engineering |
| dewey-raw | 681.7610113 660.60113 |
| dewey-search | 681.7610113 660.60113 |
| dewey-sort | 3681.7610113 |
| dewey-tens | 680 - Manufacture of products for specific uses 660 - Chemical engineering |
| discipline | Chemie / Pharmazie Handwerk und Gewerbe / Verschiedene Technologien Informatik Medizin |
| format | Book |
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| id | DE-604.BV044424312 |
| illustrated | Illustrated |
| indexdate | 2024-09-10T02:16:09Z |
| institution | BVB |
| isbn | 9783642548000 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029825852 |
| oclc_num | 871183836 |
| open_access_boolean | |
| owner | DE-703 DE-29T |
| owner_facet | DE-703 DE-29T |
| physical | xiii, 502 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Springer |
| record_format | marc |
| series2 | Lecture notes in bioengineering |
| spelling | Dokos, Socrates Verfasser (DE-588)1138237574 aut Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics Socrates Dokos Berlin ; Heidelberg Springer [2017] xiii, 502 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in bioengineering Biomedizinische Technik (DE-588)4006882-1 gnd rswk-swf Biotechnologie (DE-588)4069491-4 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Multiphysics (DE-588)7675978-7 gnd rswk-swf Research UFM Bioengineering Computational Modeling Excitable Tissues Multiphysics Modeling Matlab Cardiovascular Dynamics Fluid-structure Interaction Vestibular Implant Vision Prosthesis Comsol Biomedizinische Technik (DE-588)4006882-1 s Biotechnologie (DE-588)4069491-4 s Computersimulation (DE-588)4148259-1 s MATLAB (DE-588)4329066-8 s Multiphysics (DE-588)7675978-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-54801-7 B:DE-101 application/pdf http://d-nb.info/1047725711/04 Inhaltsverzeichnis X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4601581&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029825852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dokos, Socrates Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics Biomedizinische Technik (DE-588)4006882-1 gnd Biotechnologie (DE-588)4069491-4 gnd Computersimulation (DE-588)4148259-1 gnd MATLAB (DE-588)4329066-8 gnd Multiphysics (DE-588)7675978-7 gnd |
| subject_GND | (DE-588)4006882-1 (DE-588)4069491-4 (DE-588)4148259-1 (DE-588)4329066-8 (DE-588)7675978-7 |
| title | Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics |
| title_auth | Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics |
| title_exact_search | Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics |
| title_full | Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics Socrates Dokos |
| title_fullStr | Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics Socrates Dokos |
| title_full_unstemmed | Modeling organs, tissues, cells and devices using MATLAB and COMSOL multiphysics Socrates Dokos |
| title_short | Modeling organs, tissues, cells and devices |
| title_sort | modeling organs tissues cells and devices using matlab and comsol multiphysics |
| title_sub | using MATLAB and COMSOL multiphysics |
| topic | Biomedizinische Technik (DE-588)4006882-1 gnd Biotechnologie (DE-588)4069491-4 gnd Computersimulation (DE-588)4148259-1 gnd MATLAB (DE-588)4329066-8 gnd Multiphysics (DE-588)7675978-7 gnd |
| topic_facet | Biomedizinische Technik Biotechnologie Computersimulation MATLAB Multiphysics |
| url | http://d-nb.info/1047725711/04 http://deposit.dnb.de/cgi-bin/dokserv?id=4601581&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029825852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dokossocrates modelingorganstissuescellsanddevicesusingmatlabandcomsolmultiphysics |
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