Mathematical modelling of dynamic biological systems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Letchworth
Reserach Studies Pr. <<[u.a.]>>
1986
|
| Edition: | 2. ed., repr. |
| Series: | Medical computing series
3 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 355 S. |
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| 100 | 1 | |a Finkelstein, Ludwik |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical modelling of dynamic biological systems |c Ludwik Finkelstein and Ewart R. Carson |
| 250 | |a 2. ed., repr. | ||
| 264 | 1 | |a Letchworth |b Reserach Studies Pr. <<[u.a.]>> |c 1986 | |
| 300 | |a XII, 355 S. | ||
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| 490 | 1 | |a Medical computing series |v 3 | |
| 700 | 1 | |a Carson, Ewart R. |e Sonstige |4 oth | |
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Record in the Search Index
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|---|---|
| adam_text | Mathematical Modelling
of Dynamic
Biological Systems
SECOND EDITION
Ludwik_Finkelstein
and
Ewart R Carson
The City University, London, England
RESEARCH STUDIES PRESS LTD
Letchworth, Hertfordshire, England
JOHN WILEY amp; SONS INC
New York • Chichester • Toronto - Brisbane • Singapore
Table of Contents
1 Dynamics and Control in Biology 1
2 Dynamics of 1st and 2nd Order Linear Systems 7
2 1 Introduction 7
2 2 First-order linear time-invariant systems 7
2 3 The behaviour of first-order linear
time-invariant dynamic systems 15
2 4 Second-order linear time-invariant
systems 24
2 5 The behaviour of second-order linear
time-invariant systems 36
3 Time Domain Analysis 47
3 1 Introduction 47
3 2 General linear time-invariant systems 47
3 3 The natural response of linear time-
invariant systems Stability 49
3 4 The unit impulse response 51
3 5 System response to a general input
Convolution 53
3 6 Deconvolution 57
3 7 The concept-of state 61
4 Transfer Functions 65
4 1 Introduction 65
4 2 The Fourier series 67
4 3 The Fourier transform , 70
4 4 The Laplace transform 73
4 5 The solution of linear differential
equations using Laplace transforms 80
4 6 Relation between time and frequency
domain representations 88
4 7 Frequency response of systems 91
5 Graphical Representation of Dynamic Systems 107
5 1 Introduction 107
5 2 Graphical representation of physical
interactions 107
5 3 Graphical representation of mathematical
models 109
5 4 Other forms of graphical representation 115
6 Non-linear Dynamic Systems 117
6 1 Introduction 117
6 2 An example of a non-linear system 118
6 3 The behaviour of a first-order
non-linear dynamic system 119
6 4 The principal forms of non-linearity 121
6 5 State variable representation 123
6 6 Linearisation 125
6 7 Separable non-linearities 131
6 8 Behaviour of non-linear systems 131
7 Feedback 135
7 1 Introduction 135
7 2 The behaviour of negative feedback
control systems 139
7 3 General negative feedback systems 154
7 4 Stability 159
7 5 Inherent feedback 160
7 6 Positive feedback 161
8 Formulation of Mathematical Models 163
i
8 1 Introduction 163
8 2 The modelling process 164
8 3 Purposes of modelling 165
8 4 The basis of model formulation 166
8 5 Correspondence between model and system 167
8 6 Aggregation, abstraction and idealisa-
tion 168
8 7 Description of model formulation
process 169
8 8 Classification of mathematical models 170
8 9 Examples of modelling the unit chemical
and material transfer processes of
physiology 170
8 10 Examples of transport processes 177
8 11 Compartmental, control system and
non-compartmental models 180
8 12 Examples of mathematical models of
metabolic processes 185
8 13 Examples of mathematical models of
physiological systems 202
9 Introduction to the Identification and Vali-
dation of Mathematical Models of Dynamic
systems 221
9 1 Introduction 221
9 2 Identification 221
9 3 Model to be identified 223
9 4 Test signals 226
9 5 Theoretical identifiability 234
9 6 The sources of error 237
9 7 Identification procedure 237
9 8 Identification of model structure 242
9 9 Identification case study - albumin
metabolism 243
t
9 10 Validation 258
9 11 Some examples of problems and
approaches relating to model validity 263
10 Time-Discrete Systems 277
10 1 Basic concepts 277
10 2 Fundamentals of the time domain
approach 280
10 3 Properties of linear difference
equations 288
10 4 z transform 291
10 5 Effect of sampling frequency - the
sampling theorem 295
10 6 Data hold techniques 296
10 7 Discrete system models 297
11 Computer Implementation 299
11 1 Introduction 299
11 2 Continuous and discrete systems 300
11 3 Simulation by digital computer 302
11 4 Identification and parameter estimation 305
11 5 Example: simulation of the cardio-
vascular system 306
11 6 Example: modelling of hormonal
dynamics in the management of thyroid 309
disease
11 7 Suggestions for further reading 317
Appendix I - Mathematical concepts 319
Appendix II - Differential equations -
general definitions 329
Appendix III - Table of Laplace transforms 333
Appendix IV - Matrix definitions and operations 337
References 343
Index 351
|
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| discipline | Biologie |
| edition | 2. ed., repr. |
| format | Book |
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| indexdate | 2024-07-09T21:59:38Z |
| institution | BVB |
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| physical | XII, 355 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Reserach Studies Pr. <<[u.a.]>> |
| record_format | marc |
| series | Medical computing series |
| series2 | Medical computing series |
| spelling | Finkelstein, Ludwik Verfasser aut Mathematical modelling of dynamic biological systems Ludwik Finkelstein and Ewart R. Carson 2. ed., repr. Letchworth Reserach Studies Pr. <<[u.a.]>> 1986 XII, 355 S. txt rdacontent n rdamedia nc rdacarrier Medical computing series 3 Carson, Ewart R. Sonstige oth Medical computing series 3 (DE-604)BV008920770 3 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018416684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Finkelstein, Ludwik Mathematical modelling of dynamic biological systems Medical computing series |
| title | Mathematical modelling of dynamic biological systems |
| title_auth | Mathematical modelling of dynamic biological systems |
| title_exact_search | Mathematical modelling of dynamic biological systems |
| title_full | Mathematical modelling of dynamic biological systems Ludwik Finkelstein and Ewart R. Carson |
| title_fullStr | Mathematical modelling of dynamic biological systems Ludwik Finkelstein and Ewart R. Carson |
| title_full_unstemmed | Mathematical modelling of dynamic biological systems Ludwik Finkelstein and Ewart R. Carson |
| title_short | Mathematical modelling of dynamic biological systems |
| title_sort | mathematical modelling of dynamic biological systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018416684&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008920770 |
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