© 2013

Mathematical Modeling and Validation in Physiology

Applications to the Cardiovascular and Respiratory Systems

  • Jerry J. Batzel
  • Mostafa Bachar
  • Franz Kappel


  • 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 Lecture Notes in Mathematics book series (LNM, volume 2064)

Also part of the Mathematical Biosciences Subseries book sub series (LNMBIOS, volume 2064)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Theory

    1. Front Matter
      Pages 1-1
    2. Jerry J. Batzel, Mostafa Bachar, John M. Karemaker, Franz Kappel
      Pages 3-19
    3. Thomas Heldt, George C. Verghese, Roger G. Mark
      Pages 21-41
    4. H. T. Banks, Ariel Cintrón-Arias, Franz Kappel
      Pages 43-73
    5. Adam Attarian, Jerry J. Batzel, Brett Matzuka, Hien Tran
      Pages 75-88
  3. Practice

    1. Front Matter
      Pages 119-119
    2. Eugene N. Bruce
      Pages 121-132
    3. Clive M. Brown
      Pages 163-176
    4. Karl Thomaseth, Jerry J. Batzel, Mostafa Bachar, Raffaello Furlan
      Pages 215-246
  4. Back Matter
    Pages 247-254

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.


34-XX, 92-XX, 92C30, 92C42, 92C50, 93A30 experimental design interdisciplinary research model development and parameter identification sensitivity analysis

Editors and affiliations

  • Jerry J. Batzel
    • 1
  • Mostafa Bachar
    • 2
  • Franz Kappel
    • 3
  1. 1.Mathematics and Scientific ComputingUniversity of GrazGrazAustria
  2. 2.College of Sciences, Department of MathematicsKing Saud UniversityRiyadhSaudi Arabia
  3. 3.Institute for Mathematics, and Scientific ComputingUniversity of GrazGrazAustria

Bibliographic information