Modelling Methodology for Physiology and Medicine

Modelling Methodology for Physiology and Medicine, Second Edition, offers a unique approach and an unprecedented range of coverage of the state-of-the-art, advanced modeling methodology that is widely applicable to physiology and medicine. The second edition, which is completely updated and expanded, opens with a clear and integrated treatment of advanced methodology for developing mathematical models of physiology and medical systems. Readers are then shown how to apply this methodology beneficially to real-world problems in physiology and medicine, such as circulation and respiration.

The focus of Modelling Methodology for Physiology and Medicine, Second Edition, is the methodology that underpins good modeling practice. It builds upon the idea of an integrated methodology for the development and testing of mathematical models. It covers many specific areas of methodology in which important advances have taken place over recent years and illustrates the application of good methodological practice in key areas of physiology and medicine. It builds on work that the editors have carried out over the past 30 years, working in cooperation with leading practitioners in the field.

• Builds upon and enhances the reader's existing knowledge of modeling methodology and practice
• Editors are internationally renowned leaders in their respective fields
• Provides an understanding of modeling methodologies that can address real problems in physiology and medicine and achieve results that are beneficial either in advancing research or in providing solutions to clinical problems

Practitioners, researchers, and students in the field of modelling with specialties in physiology and medicine (drawn from the related fields of engineering, informatics, computing, medicine, and physiology).

Preface

Preface to the Second Edition

List of Contributors

1. An Introduction to Modelling Methodology

Abstract

1.1 Introduction

1.2 The Need for Models

1.3 Approaches to Modelling

1.4 Simulation

1.5 Model Identification

1.6 Model Validation

Reference

2. Control in Physiology and Medicine

2.1 Introduction

2.2 Modelling for Control System Design and Analysis

2.3 Block Diagram Analysis

2.4 Proportional-Integral-Derivative Control

2.5 Model Predictive Control

2.6 Other Control Algorithms

2.7 Application Examples

2.8 Summary

References

3. Deconvolution

3.1 Problem Statement

3.2 Difficulty of the Deconvolution Problem

3.3 The Regularization Method

3.4 Other Deconvolution Methods

3.5 Conclusions

References

4. Structural Identifiability of Biological and Physiological Systems

4.1 Introduction

4.2 Background and Definitions

4.3 Identifiability and Differential Algebra

4.4 The Question of Initial Conditions

4.5 Identifiability of Some Nonpolynomial Models

4.6 A Case Study

4.7 Conclusion

References

5. Parameter Estimation

5.1 Problem Statement

5.2 Fisherian Parameter Estimation Approaches

5.3 Bayesian Parameter Estimation Approaches

5.4 Conclusions

References

6. New Trends in Nonparametric Linear System Identification

6.1 Introduction

6.2 System Identification Problem

6.3 The Classical Approach to System Identification

6.4 Limitations of the Classical Approach to System Identification: Assessment of Cerebral Hemodynamics Using MRI

6.5 The Nonparametric Gaussian Regression Approach to System Identification

6.6 Assessment of Cerebral Hemodynamics Using the Stable Spline Estimator

6.7 Conclusions

References

7. Population Modelling

7.1 Introduction

7.2 Naïve Data Approaches: Naïve Average and Naïve Pooled Data

7.3 Two-Stage Approaches: Standard, Global, and Iterative Two-Stage

7.4 Nonlinear Mixed-Effects Modelling

7.5 Covariate Models in Nonlinear Mixed-Effects Models

References

8. Systems Biology

8.1 Introduction

8.2 Modelling the System: ODE Models

8.3 Modelling the Data: Statistical Models

8.4 Applications

8.5 Conclusions

Acknowledgments

References

9. Reverse Engineering of High-Throughput Genomic and Genetic Data

Abstract

9.1 Introduction

9.2 Reverse Engineering Transcriptional Data

9.3 Reverse Engineering Genetic Genomics Data

9.4 Conclusion

References

10. Tracer Experiment Design for Metabolic Fluxes Estimation in Steady and Nonsteady State

Abstract

10.1 Introduction

10.2 Fundamentals

10.3 Accessible Pool and System Fluxes

10.4 The Tracer Probe

10.5 Estimation of Tracee Fluxes in Steady State

10.6 Estimation of Nonsteady-State Fluxes

10.7 Conclusion

References

11. Stochastic Models of Physiology

Abstract

11.1 Introduction

11.2 Randomness and Probability

11.3 Probability Distributions and Stochastic Processes

11.4 The Law of Large Numbers and Limit Theorems

11.5 Analysis of Stochastic Associations: Correlation and Regression

11.6 Distances, Mean Comparisons, Clustering, and Principal Components

11.7 Markov Chains

11.8 State Estimation for Discrete-Time Linear Systems: Kalman Filtering

11.9 Conclusion

References

12. Probabilistic Modelling with Bayesian Networks

Abstract

12.1 Introduction

12.2 Theoretical Foundations

12.3 Algorithms

12.4 Examples

12.5 Conclusions and Future Perspectives

References

13. Mathematical Modelling of Pulmonary Gas Exchange

13.1 Standard Equations Used to Describe Gas Transport in the Lungs

13.2 Models of Diffusion Limitation

13.3 Models of Ventilation–Perfusion Mismatch

13.4 Application of Mathematical Models of Ventilation, Perfusion, and Diffusion

References

Appendix A—Glossary

Appendix B—Calculations Necessary to Convert Inspired Gas at ATPD to BTPS

14. Mathematical Models for Computational Neuroscience

14.1 Introduction

14.2 Models of Individual Neural Units

14.3 Networks of Neurons

14.4 Conclusions

References

15. Insulin Modelling

15.1 Dynamics of Insulin Secretion

15.2 Cellular Modelling of Beta-Cell Function

15.3 Whole-Body Modelling of Beta-Cell Function

15.4 Multiscale Modelling of Insulin Secretion

15.5 Conclusion

References

16. Glucose Modelling

16.1 Introduction

16.2 Oral Glucose Minimal Models

16.3 Oral Glucose Maximal Models

16.4 Conclusion

References

17. Blood–Tissue Exchange Modelling

17.1 Introduction

17.2 Theory and Experimental Approaches

17.3 Models of Blood–Tissue Exchange

17.4 Identification of Blood–Tissue Exchange Models

17.5 Applications

17.6 Conclusions

References

18. Physiological Modelling of Positron Emission Tomography Images

18.1 Introduction

18.2 Modelling Strategies

18.3 PET Measurement Error

18.4 Models of Regional Glucose Metabolism

18.5 Models of [15O]H2O Kinetics to Assess Blood Flow

18.6 Models of the Ligand–Receptor System

18.7 The Way Forward

18.8 Conclusion

References

19. Tumor Growth Modelling for Drug Development

19.1 Introduction

19.2 R&D Cycle Time: From Discovery to Launch

19.3 Preclinical Development in Oncology

19.4 A Preclinical Tumor Growth Inhibition Model

19.5 Mathematical Analysis of the TGI Model

19.6 Model Identification and its Applications

19.7 Combined Administration of Drugs

19.8 Model-Based Clinical Dose Prediction

19.9 Conclusions

References

20. Computational Modelling of Cardiac Biomechanics

20.1 Introduction

20.2 Modelling of Ventricular Biomechanics

20.3 Models Assessing Ventricular Global Function

20.4 Image-Based Assessment of Ventricular Biomechanics

20.5 Multiphysics Patient-Specific Models of the Left Ventricle

20.6 3D Patient-Specific Heart Valve Modelling: Early Approaches

20.7 3D Patient-Specific Heart Valve Modelling: Recent Advances

20.8 Conclusion

References

21. Downstream from the Heart Left Ventricle: Aortic Impedance Interpretation by Lumped and Tube-Load Models

21.1 Introduction

21.2 Lumped-Parameter Models

21.3 Tube-Load Models

21.4 Conclusion

References

22. Finite Element Modelling in Musculoskeletal Biomechanics

22.1 Introduction

22.2 Background

22.3 Finite Element Modelling in Biomechanics

22.4 The Modelling Process

22.5 Postprocessing

22.6 Validation

22.7 Case Study: FEA Foot Biomechanics

22.8 Conclusion

Acknowledgment

References

23. Modelling for Synthetic Biology

23.1 Background

23.2 Models of Genetic Circuits

23.3 Experimental Measurements for Parameter Identification

23.4 Conclusion

References