Modeling and simulation in medicine and the life sciences:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2004
|
| Ausgabe: | 2. ed., corr. print. |
| Schriftenreihe: | Texts in applied mathematics
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 1. Aufl. u.d.T.: Hoppensteadt, Frank C.: Mathematics in medicine and the life sciences |
| Beschreibung: | XIV, 354 S. Ill., graph. Darst. |
| ISBN: | 0387950729 9780387950723 |
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| 250 | |a 2. ed., corr. print. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2004 | |
| 300 | |a XIV, 354 S. |b Ill., graph. Darst. | ||
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| 500 | |a 1. Aufl. u.d.T.: Hoppensteadt, Frank C.: Mathematics in medicine and the life sciences | ||
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Datensatz im Suchindex
| _version_ | 1804132889300828160 |
|---|---|
| adam_text | Contents
Series
Preface
vii
Preface
ix
Introduction
1
1
The Heart and Circulation
5
1.1
Plan of the Circulation
................... 5
1.2
Volume, Flow, and Pressure
................ 7
1.3
Resistance and Compliance Vessels
............ 8
1.4
The Heart as a Pair of Pumps
............... 10
1.5
Mathematical Model of the Uncontrolled Circulation
. . 14
1.6
Balancing the Two Sides of the Heart and
the Two Circulations
.................... 18
1.7
The Need for External Circulatory Control Mechanisms
. 20
1.8
Neural Control: The Baroreceptor Loop
.......... 21
1.9 Autoregulation........................ 25
1.10
Changes in the Circulation Occurring at Birth
...... 28
1.11
Dynamics of the Arterial Pulse
.............. 33
1.12
Computer Simulation of Pulsatile Blood Flow
...... 39
1.13
Suggestions for Computing Projects Concerning
the Circulation
....................... 63
1.14
Annotated References
.................... 68
Exercises
.............................. 69
xii Contents
2 Gas Exchange in
the Lungs
75
2.1 The Ideal Gas
Law and the Solubility of Gases
...... 76
2.2
The Equations of Gas Transport in One Alveolus
.... 78
2.3
Gas Transport in the Lung
................. 82
2.4
Optimal Gas Transport
................... 83
2.5
Mean Alveolar and Arterial Partial Pressures
...... 85
2.6
Transport of O2
....................... 87
2.7
Computer Solution of the Equations for O2 Transport
in the Lung
......................... 91
2.8
Computing Projects Concerning Oxygen Transport
by the Lung
......................... 104
2.9
Annotated References
.................... 107
Exercises
.............................. 107
3
Control of Cell Volume and Electrical Properties of
Cell Membranes
109
3.1
Osmotic Pressure and the Work of Concentration
.... 109
3.2
A Simple Model of Cell Volume Control
......... 113
3.3
The Movement of Ions Across Cell Membranes
...... 115
3.4
The Interaction of Electrical and Osmotic Effects
.... 118
3.5
The Hodgkin-Huxley Equations for the
Nerve Action Potential
................... 124
3.6
Computer Simulation of the Nerve Action Potential
. . . 132
3.7
Suggestions for Computing Projects Concerning
the Nerve Impulse
...................... 139
3.8
Annotated References
.................... 143
Exercises
.............................. 144
4
The Renal Countercurrent Mechanism
147
4.1
The Nephron
......................... 147
4.2
Dynamics of Na+ and H2O: Transport along the Renal
Tubules
............................ 150
4.3
The Loop of Henle
..................... 152
4.4
The Juxtaglomerular Apparatus and the Renin-Angiotensin
System
............................ 155
4.5
The Distal Tubule and Collecting Duct: Concentrating and
Diluting Modes
....................... 157
4.6
Remarks on the Significance of the Juxtaglomerular
Apparatus
.......................... 158
4.7
How Nephrons Do Better Than a Factor of
e
....... 159
4.8
Computing Project on the Interacting Nephron
Population Model
...................... 166
4.9
Annotated References
.................... 168
Exercises
.............................. 169
Contents xiii
5
Muscle
Mechanics
171
5.1
The Force-Velocity Curve
................. 171
5.2
Crossbridge Dynamics
................... 173
5.3
Computer Simulation of Crossbridge Attachment
and Detachment
....................... 179
5.4
Suggested Computing Projects on Crossbridge Dynamics
188
5.5
Annotated References
.................... 190
Exercises
.............................. 190
6
Neural Systems
193
6.1
Guttman s Experiments on Phase Locking
........ 195
6.2
Biological Rhythms
..................... 197
6.2.1
Modulating the Clock on the Wall
......... 198
6.2.2
Biological Clocks
.................. 199
6.2.3
Electronic Clocks: Voltage-Controlled Oscillators
200
6.3
Model Neural Networks
................... 200
6.3.1
A Thalamocortical Circuit
.............. 201
6.3.2
Hippocampus
.................... 203
6.4
Annotated References
.................... 207
Exercises
.............................. 208
7
Population Dynamics
215
7.1
Bacterial Cultures
...................... 216
7.1.1
Batch Culture Growth
............... 217
7.1.2
Least-Squares Estimation of the Growth Rate
. . 221
7.2
Age Structures
........................ 222
7.2.1
Cohort Analysis
................... 223
7.2.2
Birth Rates
..................... 224
7.2.3
Age Distributions
.................. 228
7.3
Microbial Ecology
...................... 230
7.3.1
Uptake of Nutrients
................. 230
7.3.2
Growth and Quiescence
............... 232
7.3.3
Biofilms
and Growth in a Continuous Flow
.... 234
7.3.4
A Solutivory Food Chain
.............. 236
7.4
Nonlinear Reproduction Curves
.............. 237
7.4.1
Compensatory Growth: Verhulst s Model
..... 238
7.4.2
Chaos
........................ 243
7.5
Controlling Populations
................... 248
7.5.1
Cell Synchronization
................ 249
7.5.2
Cohort Dynamics near the Limits of Growth
. . . 250
7.5.3
Harvesting: Economics of Populations
....... 252
7.6
Annotated References
.................... 256
Exercises
.............................. 257
xiv Contents
8
Genetics
267
8.1 Population
Genetics
..................... 269
8.1.1
Natural Selection
.................. 269
8.1.2
Slow Selection
.................... 272
8.1.3
Genotype Frequencies
................ 273
8.1.4
Random Genetic Drift
............... 275
8.2
Biotechnology
........................ 277
8.2.1
Plasmids
....................... 277
8.2.2
Control of Plasmid Replication
.......... 281
8.2.3
Regulation of Gene Expression
........... 286
8.2.4
Stoichiometry of Metabolic Pathways
....... 290
8.3
Annotated References
.................... 291
Exercises
.............................. 292
9
A Theory of Epidemics
295
9.1
Spread of Infection Within a Family
............ 296
9.2
The Threshold of an Epidemic
............... 300
9.3
Predicting the Severity of an Epidemic
.......... 303
9.4
Annotated References
.................... 306
Exercises
.............................. 306
10
Patterns of Population Growth and Dispersal
311
10.1
Random Walks and the Process of Diffusion
....... 312
10.1.1
Random Walks
................... 313
10.1.2
Boundary Conditions
................ 314
10.1.3
Sample Paths
.................... 316
10.1.4
Diffusion Approximation
.............. 317
10.1.5
Two-Dimensional Diffusion
............ 318
10.1.6
Sample Paths in Two-Dimensions
......... 319
10.1.7
Numerical Solutions: The Method of Lines
.... 320
10.2
Bacterial Growth on
a Petri
Plate
............. 321
10.2.1
Diffusion of a Drop of Substrate
.......... 321
10.2.2
Bacterial Growth Due to Diffusing Nutrition
... 323
10.2.3
Growth Patterns Due to Two Nutrients
...... 323
10.3
Concluding Remarks
.................... 325
10.4
Annotated References
.................... 326
Exercises
.............................. 326
Appendix A Getting Started with Matrices and
MATLAB
335
Appendix
В
Background on Random Processes
343
Index
349
Mathematical modeling and computer simulation are emerging as
major themes of the
biomedical
sciences. This book lays a solid foun¬
dation by working through simple examples in which elementary math¬
ematics can be used to gain profound biological insight. The two main
subjects of the book are physiology and population biology. Topics
covered include the heart and circulation, gas exchange in the lungs,
control of cell volume, electrophysiology of neurons, the countercurrent
mechanism of the kidney, crossbridge dynamics in muscle, neural net¬
works, dynamics of microbial populations, genetics, epidemics, and
the patterns of population growth and dispersal. Each of these topics
can also be studied in a more traditional, descriptive manner, but the
student who reads this book, and does the exercises and computing
projects, will emerge with a different level of understanding of the kind
that can only be achieved through modeling and simulation.
The book is written primarily for students who have had one semester
of calculus, but parts can be read with even less mathematical back¬
ground, and other parts touch on more advanced methods, so the
book can be useful at many levels. Numerous exercises are included
many of which expand on themes developed in the text.
In this new edition, computer simulation is a central theme of the book,
with detailed
MATLAB®
programs embedded in the text. Unlike canned
software, these programs are meant to be modified by the students,
and are therefore extensively documented by comments and surround¬
ed by explanatory text. Computing projects are suggested in special
sections devoted to that purpose. The open-ended nature of these pro¬
jects makes them well suited to independent study.
The book is an outgrowth of courses taught by the authors and their
colleagues at New York University, the University of Utah, Michigan
State University, and Arizona State University.
|
| any_adam_object | 1 |
| author | Hoppensteadt, Frank C. 1938- Peskin, Charles S. 1946- |
| author_GND | (DE-588)11268792X (DE-588)108882160X |
| author_facet | Hoppensteadt, Frank C. 1938- Peskin, Charles S. 1946- |
| author_role | aut aut |
| author_sort | Hoppensteadt, Frank C. 1938- |
| author_variant | f c h fc fch c s p cs csp |
| building | Verbundindex |
| bvnumber | BV019423562 |
| classification_rvk | SK 950 SK 990 ST 640 WC 7000 WD 9200 |
| classification_tum | MED 001f DAT 780f BIO 110f |
| ctrlnum | (OCoLC)180003934 (DE-599)BVBBV019423562 |
| dewey-full | 570/.1/51 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 570 - Biology |
| dewey-raw | 570/.1/51 |
| dewey-search | 570/.1/51 |
| dewey-sort | 3570 11 251 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Informatik Mathematik Medizin |
| edition | 2. ed., corr. print. |
| format | Book |
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| id | DE-604.BV019423562 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:59Z |
| institution | BVB |
| isbn | 0387950729 9780387950723 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012885159 |
| oclc_num | 180003934 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-526 DE-11 DE-20 |
| owner_facet | DE-29T DE-703 DE-526 DE-11 DE-20 |
| physical | XIV, 354 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Hoppensteadt, Frank C. 1938- Verfasser (DE-588)11268792X aut Modeling and simulation in medicine and the life sciences Frank C. Hoppensteadt ; Charles S. Peskin 2. ed., corr. print. New York [u.a.] Springer 2004 XIV, 354 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 10 1. Aufl. u.d.T.: Hoppensteadt, Frank C.: Mathematics in medicine and the life sciences Mathematik Biomathematics Population biology Mathematics Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Medizin (DE-588)4038243-6 gnd rswk-swf Biologie (DE-588)4006851-1 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Physiologie (DE-588)4045981-0 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Modellierung (DE-588)4170297-9 s Computersimulation (DE-588)4148259-1 s Medizin (DE-588)4038243-6 s DE-604 Physiologie (DE-588)4045981-0 s Mathematisches Modell (DE-588)4114528-8 s Populationsbiologie (DE-588)4046800-8 s Biomathematik (DE-588)4139408-2 s Mathematik (DE-588)4037944-9 s 1\p DE-604 Biologie (DE-588)4006851-1 s 2\p DE-604 Peskin, Charles S. 1946- Verfasser (DE-588)108882160X aut Texts in applied mathematics 10 (DE-604)BV002476038 10 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012885159&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012885159&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hoppensteadt, Frank C. 1938- Peskin, Charles S. 1946- Modeling and simulation in medicine and the life sciences Texts in applied mathematics Mathematik Biomathematics Population biology Mathematics Populationsbiologie (DE-588)4046800-8 gnd Modellierung (DE-588)4170297-9 gnd Medizin (DE-588)4038243-6 gnd Biologie (DE-588)4006851-1 gnd Biomathematik (DE-588)4139408-2 gnd Computersimulation (DE-588)4148259-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Physiologie (DE-588)4045981-0 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4046800-8 (DE-588)4170297-9 (DE-588)4038243-6 (DE-588)4006851-1 (DE-588)4139408-2 (DE-588)4148259-1 (DE-588)4114528-8 (DE-588)4045981-0 (DE-588)4037944-9 |
| title | Modeling and simulation in medicine and the life sciences |
| title_auth | Modeling and simulation in medicine and the life sciences |
| title_exact_search | Modeling and simulation in medicine and the life sciences |
| title_full | Modeling and simulation in medicine and the life sciences Frank C. Hoppensteadt ; Charles S. Peskin |
| title_fullStr | Modeling and simulation in medicine and the life sciences Frank C. Hoppensteadt ; Charles S. Peskin |
| title_full_unstemmed | Modeling and simulation in medicine and the life sciences Frank C. Hoppensteadt ; Charles S. Peskin |
| title_short | Modeling and simulation in medicine and the life sciences |
| title_sort | modeling and simulation in medicine and the life sciences |
| topic | Mathematik Biomathematics Population biology Mathematics Populationsbiologie (DE-588)4046800-8 gnd Modellierung (DE-588)4170297-9 gnd Medizin (DE-588)4038243-6 gnd Biologie (DE-588)4006851-1 gnd Biomathematik (DE-588)4139408-2 gnd Computersimulation (DE-588)4148259-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Physiologie (DE-588)4045981-0 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Biomathematics Population biology Mathematics Populationsbiologie Modellierung Medizin Biologie Biomathematik Computersimulation Mathematisches Modell Physiologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012885159&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012885159&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT hoppensteadtfrankc modelingandsimulationinmedicineandthelifesciences AT peskincharless modelingandsimulationinmedicineandthelifesciences |