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# Introduction to Modeling in Physiology and Medicine

- 2nd Edition - August 1, 2019
- Authors: Claudio Cobelli, Ewart Carson
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 5 7 5 6 - 5
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 5 8 0 5 - 0

Introduction to Modeling in Physiology and Medicine, Second Edition, develops a clear understanding of the fundamental principles of good modeling methodology. Sections show how… Read more

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Request a sales quote*Introduction to Modeling in Physiology and Medicine, Second Edition,* develops a clear understanding of the fundamental principles of good modeling methodology. Sections show how to create valid mathematical models that are fit for a range of purposes. These models are supported by detailed explanation, extensive case studies, examples and applications. This updated edition includes clearer guidance on the mathematical prerequisites needed to achieve the maximum benefit from the material, a greater detail regarding basic approaches to modeling, and discussions on non-linear and stochastic modeling. The range of case study material has been substantially extended, with examples drawn from recent research experience.

Key examples include a cellular model of insulin secretion and its extension to the whole-body level, a model of insulin action during a meal/oral glucose tolerance test, a large-scale simulation model of type 1 diabetes and its use in *in silico *clinical trials and drug trials.

- Covers the underlying principles of good quantitative modeling methodology, with applied biomedical engineering and bioscience examples to ensure relevance to students, current research and clinical practice
- Includes modeling data, modeling systems, linear and non-linear systems, model identification, parametric and non-parametric models, and model validation
- Presents clear, step-by-step working plus examples and extensive case studies that relate concepts to real world applications
- Provides end-of-chapter exercises and assignments to reinforce learning

**Chapter 1 – Introduction**

- Introduction
- The book in context
- The major ingredients
- Readership
- Organization of the book

Chapter 2 – Physiological Complexity and the Need for Models

2.1 Introduction

2.2 Complexity

2.3 System dynamics

2.3.1 First-order linear time-invariant systems

2.3.2 The dynamic behavior of first-order linear time-invariant systems – solution by

integration

2.3.3 The classical solution for a first-order system

2.3.4 General case of a first-order linear system

2.4 Feedback

2.4.1 Negative feedback

2.4.2 Positive feedback

2.4.3 Inherent feedback

2.4.4 Combining negative and positive feedback

2.4.5 Derivative and integral feedback

2.4.6 Effects of feedback on the complexity of system dynamics

2.5 Control in physiological systems

2.5.1 General features

2.5.2 Enzymes

2.5.3 Hormones

2.6 Hierarchy

2.7 Redundancy

2.8 Function and behavior and their measurement

2.9 Challenges to understanding

2.10 Exercises and assignment questions

Chapter 3 – Models and the Modeling Process

3.1 Introduction

3.2 What is a model?

3.3 Why model? – the purpose of modeling

3.4 How do we model? – the modeling process

3.5 Model formulation

3.6 Model identification

3.7 Model validation

3.8 Model simulation

3.9 Summary

3.10 Exercises and assignment questions

Chapter 4 – Modeling the Data

4.1 Introduction

4.2 The basis of data modeling

4.3 The why and when of data models

4.4 Approaches to data modeling

4.5 Modeling a single variable occurring spontaneously

4.5.1 Temperature

4.5.2 Urine potassium

4.5.3 Gastro-intestinal rhythms

4.5.4 Hormonal time series

4.6 Modeling a single variable in response to a perturbation

4.6.1 Glucose home monitoring data

4.6.2 Response to drug therapy – prediction of bronchodilator response

4.7 Two variables causally related

4.7.1 Hormone/hormone and substrate/hormone series

4.7.2 Urine sodium response to water loading

4.8 Input/output modeling for control

4.8.1 Pupil control

4.8.2 Control of blood glucose by insulin

4.8.3 Control of blood pressure by sodium nitroprusside

4.9 Input/output modeling: impulse response and deconvolution

4.9.1 Impulse response estimation

4.9.2 The convolution integral

4.9.3 Reconstructing the input

4.10 Summary

4.11 Exercises and assignment questions

Chapter 5 – Modeling the System

5.1 Introduction

5.2 Static models

5.3 Linear modeling

5.3.1 The windkessel circulatory model

5.3.2 Elimination from a single compartment

5.3.3 Gas exchange

5.3.4 The dynamics of a swinging limb

5.3.5 A model of glucose regulation

5.4 Distributed modeling

5.4.1 Blood-tissue exchange

5.4.2 Hepatic removal of materials

5.4.3 Renal medulla

5.5 Nonlinear modeling

5.5.1 The action potential model

5.5.2 Enzyme dynamics

5.5.3 Baroreceptors

5.5.4 Central nervous control of heart rate

5.5.5 Compartmental modeling

5.5.6 Insulin receptor regulation

5.5.7 Insulin action modeling

5.5.8 Thyroid hormone regulation

5.5.9 Modeling the chemical control of breathing

5.6 Time-varying modeling

5.6.1 An example in cardiac modeling

5.7 Stochastic modeling

5.7.1 Cellular modeling

5.7.2 Insulin secretion

5.7.3 Markov model

5.8 Summary

5.9 Exercises and assignment questions

Chapter 6 – Model Identification

6.1 Introduction

6.2 Data for identification

6.2.1 Selection of test signals

6.2.2 Transient test signals

6.2.3 Harmonic test signals

6.2.4 Random signal testing

6.3 Errors

6.4 The way forward

6.4.1 Parameter estimation

6.4.2 Signal estimation

6.5 Summary

6.6 Exercises and assignment questions

Chapter 7 – Parametric Models – The Identifiability Problem

7.1 Introduction

7.2 Some examples

7.3 Definitions

7.4 Linear models – the transfer function method

7.5 Nonlinear models – the Taylor series expansion method

7.6 Qualitative experimental design

7.6.1 Fundamentals

7.6.2 An amino acid model

7.7 Summary

7.8 Exercises and assignment questions

Chapter 8 – Parametric Models – The Estimation Problem

8.1 Introduction

8.2 Linear and nonlinear parameters

8.3 Regression – basic concepts

8.3.1 The residual

8.3.2 The residual sum of squares

8.3.3 The weighted residual sum of squares

8.3.4 Weights and error in the data

8.4 Linear regression

8.4.1 The problem

8.4.2 Test on residuals

8.4.3 An example

8.4.4 Extension to the vector case

8.5 Nonlinear regression

8.5.1 The scalar case

8.5.2 Extension to the vector case

8.5.3 Algorithms

8.5.4 An example

8.6 Tests for model order

8.7 Maximum likelihood estimation

8.8 Bayesian estimation

8.9 Optimal experimental design

8.10 Summary

8.11 Exercises and assignment questions

9.1 Introduction

9.2 Why is deconvolution important?

9.3 The problem

9.4 Difficulty of the deconvolution problem

9.5 The regularization method

9.5.1 Fundamentals

9.5.2 Choice of the regularization parameter

9.5.3 The virtual grid

9.6 Summary

9.7 Exercises and assignment questions

Chapter 10 - Model Validation

10.1 Introduction

10.2 Model validation and the domain of validity

10.2.1 Validation during model formulation

10.2.2 Validation of the completed model

10.3 Validation strategies

10.3.1 Validation of a single model – basic approach

10.3.2 Validation of a single model – additional quantitative tools for numerically identified

models

10.3.3 Validation of competing models

10.4 Good practice in good modeling

10.5 Summary

10.6 Exercises and assignment questions

Chapter 11 - Case Studies

11.1 Case study 1: A sum of exponentials tracer disappearance model

11.2 Case study 2: Blood flow modeling

11.3 Case study 3: Cerebral glucose modeling

11.4 Case study 4: Models of the ligand-receptor system

11.5 Case study 5: A model of insulin secretion: from a stochastic cellular model to a whole-body model

11.5.1 The stochastic cellular model

11.5.2 The whole-body model

11.6 Case study 6: A model of insulin control during an intravenous and oral glucose tolerance test

11.7 Case study 7: A simulation model of the glucose-insulin system

11.7.1 Model formulations

11.7.2 Results

11.8 Case study 8: The UVA/Padova type 1 diabetes simulator: *in silico* clinical and drug trials

11.9 Case study 9: Illustrations of Bayesian estimation

11.10 Postscript

References

Index

- No. of pages: 384
- Language: English
- Edition: 2
- Published: August 1, 2019
- Imprint: Academic Press
- Paperback ISBN: 9780128157565
- eBook ISBN: 9780128158050

CC

### Claudio Cobelli

EC

### Ewart Carson

*Introduction to Modeling in Physiology and Medicine*on ScienceDirect