Introduction to Modeling in Physiology and Medicine

Introduction to Modeling in Physiology and Medicine

2nd Edition - August 1, 2019

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  • Authors: Claudio Cobelli, Ewart Carson
  • eBook ISBN: 9780128158050
  • Paperback ISBN: 9780128157565

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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.

Key Features

  • 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


Professionals, researchers, and graduate students in biomedical engineering, biomedical research, and health informatics

Table of Contents

  • Chapter 1 – Introduction

      1. Introduction
      2. The book in context
      3. The major ingredients
      4. Readership
      5. 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


    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

    1. Chapter 9 – Non-parametric Models - Signal Estimation

    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


    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



Product details

  • No. of pages: 384
  • Language: English
  • Copyright: © Academic Press 2019
  • Published: August 1, 2019
  • Imprint: Academic Press
  • eBook ISBN: 9780128158050
  • Paperback ISBN: 9780128157565

About the Authors

Claudio Cobelli

Claudio Cobelli received a Doctoral degree (Laurea) in Electrical Engineering in 1970 from the University of Padova, Padova, Italy. From 1970 to 1980, he was a Research Fellow of the Institute of System Science and Biomedical Engineering, National Research Council, Padova, Italy. From 1973 to 1975 and 1975 to 1981, he was Associate Professor of Biological Systems at the University of Florence and Associate Professor of Biomedical Engineering at the University of Padova, respectively. In 1981, he becomes Full Professor of Biomedical Engineering at University of Padova. From 2000 to 2009, he has been Chairman of the Graduate Program in Biomedical Engineering. From 2000 to 2011, he has been Chairman of the Ph.D. Program in Bioengineering at the University of Padova. His main research activity is in the field of modeling and identification of physiological systems, especially metabolic systems. His research is currently supported by NIH, JDRF and European Comunity. He has published 450 papers in internationally refereed journals, co-author of 8 books and holds 11 patents. He is currently Associate Editor of IEEE Transaction on Biomedical Engineering and Journal of Diabetes Science & Technology. He is on the Editorial Board of Diabetes and Diabetes Technology &Therapeutics. Dr.Cobelli has been Chairman (1999-2004) of the Italian Biomedical Engineering Group, Chairman (1990-1993 & 1993-1996) of IFAC TC on Modeling and Control of Biomedical Systems and member of the IEEE EMBS AdCom Member (2008-2009). He has been a member of the Gruppo di Esperti della Valutazione (GEV), Area 09, of the Agenzia Nazionale per la Valutazione del Sistema Universitario e della Ricerca (ANVUR) for the period 2011-2013. He is President of the Organo di Indirizzo of the Azienda Ospedaliera Universita' di Trieste In 2010 he received the Diabetes Technology Artificial Pancreas Research Award. He is Fellow of IEEE, BMES and EAMBES.

Affiliations and Expertise

Department of Information Engineering, Universita di Padova, Italy

Ewart Carson

Ewart Carson is Emeritus Professor of Systems Science in the School of Mathematics, Computer Science and Engineering at City, University of London. Educated at the University of St Andrews in Scotland and City University London, he holds a PhD in Systems Science and a DSc in Measurement and Information in Medicine. He holds Honorary Membership of the Royal College of Physicians (London) , a Life Fellowship of the IEEE, Fellowships of the International Academy of Medical and Biological Engineering and the American Institute of Medical and Biological Engineers, and is a Foundation Fellow of the European Alliance for Medical and Biological Engineering and Science Publications include 13 authored and edited books and more than 300 journal papers and chapters. Areas of research interest and expertise include: modelling in physiology and medicine; modelling methodology for health resource management; clinical decision support systems; evaluation methodologies with particular application in telemedicine; and integrated policy modelling for ICT enhanced public healthcare. As a systems scientist, all this research is undertaken within a clear systemic framework.

Affiliations and Expertise

Emeritus Professor of Systems Science in the School of Mathematics, Computer Science and Engineering at City University of London, UK

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