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Mathematical Modeling and Validation in Physiology

Applications to the Cardiovascular and Respiratory Systems

  • Book
  • © 2013

Overview

Editors:
  1. Jerry J. Batzel

    1. Mathematics and Scientific Computing, University of Graz, Graz, Austria

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  2. Mostafa Bachar

    1. College of Sciences, Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

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    You can also search for this editor in PubMed   Google Scholar

  3. Franz Kappel

    1. Institute for Mathematics, and Scientific Computing, University of Graz, Graz, Austria

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  • Focused study of modeling from model design to model identifiability and validation
  • Written by current leading experts in the field and including topics of current research interest in state of the art questions and methods
  • Focus on interdisciplinary (physiological and mathematical) collaboration and applications of modeling with clinical relevance
  • Presentation of key theoretical ideas and current areas of research interest through clear and motivated examples of application and implementation

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2064)

Part of the book sub series: Mathematical Biosciences Subseries (LNMBIOS)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xx
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  2. Theory

    1. Front Matter

      Pages 1-1
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    2. Merging Mathematical and Physiological Knowledge: Dimensions and Challenges

      • Jerry J. Batzel, Mostafa Bachar, John M. Karemaker, Franz Kappel
      Pages 3-19

    3. Mathematical Modeling of Physiological Systems

      • Thomas Heldt, George C. Verghese, Roger G. Mark
      Pages 21-41

    4. Parameter Selection Methods in Inverse Problem Formulation

      • H. T. Banks, Ariel Cintrón-Arias, Franz Kappel
      Pages 43-73

    5. Application of the Unscented Kalman Filtering to Parameter Estimation

      • Adam Attarian, Jerry J. Batzel, Brett Matzuka, Hien Tran
      Pages 75-88

    6. Integrative and Reductionist Approaches to Modeling of Control of Breathing

      • Chung Tin, Chi-Sang Poon
      Pages 89-103

    7. Parameter Identification in a Respiratory Control System Model with Delay

      • Ferenc Hartung, Janos Turi
      Pages 105-118

  3. Practice

    1. Front Matter

      Pages 119-119
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    2. Experimental Studies of Respiration and Apnea

      • Eugene N. Bruce
      Pages 121-132

    3. Model Validation and Control Issues in the Respiratory System

      • James Duffin
      Pages 133-162

    4. Experimental Studies of the Baroreflex

      • Clive M. Brown
      Pages 163-176

    5. Development of Patient Specific Cardiovascular Models Predicting Dynamics in Response to Orthostatic Stress Challenges

      • Johnny T. Ottesen, Vera Novak, Mette S. Olufsen
      Pages 177-213

    6. Parameter Estimation of a Model for Baroreflex Control of Unstressed Volume

      • Karl Thomaseth, Jerry J. Batzel, Mostafa Bachar, Raffaello Furlan
      Pages 215-246

  4. Back Matter

    Pages 247-254
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Keywords

About this book

This volume synthesizes theoretical and practical aspects of both the mathematical and life science viewpoints needed for modeling of the cardiovascular-respiratory system specifically and physiological systems generally. Theoretical points include model design, model complexity and validation in the light of available data, as well as control theory approaches to feedback delay and Kalman filter applications to parameter identification. State of the art approaches using parameter sensitivity are discussed for enhancing model identifiability through joint analysis of model structure and data. Practical examples illustrate model development at various levels of complexity based on given physiological information. The sensitivity-based approaches for examining model identifiability are illustrated by means of specific modeling examples. The themes presented address the current problem of patient-specific model adaptation in the clinical setting, where data is typically limited.

Editors and Affiliations

  • Mathematics and Scientific Computing, University of Graz, Graz, Austria

    Jerry J. Batzel

  • College of Sciences, Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mostafa Bachar

  • Institute for Mathematics, and Scientific Computing, University of Graz, Graz, Austria

    Franz Kappel

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