Modelling, analysis and optimization of biosystems /

Modelling, analysis and optimization of biosystems /

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Bibliographic Details
Author / Creator:Krabs, Werner, 1934-
Imprint:Berlin ; New York : Springer, c2007.
Description:1 online resource (x, 203 p.) : ill., port.
Language:English
Subject:
Biology -- Mathematical models.
Medicine -- Mathematical models.
Evolution -- Mathematical models.
Hemodialysis -- Mathematical models.
Models, Biological.
Mathematics.
Operations Research.
Biology -- Mathematical models.
Evolution -- Mathematical models.
Medicine -- Mathematical models.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8883374
Hidden Bibliographic Details
Other authors / contributors:Pickl, Stefan, 1967-
ISBN:9783540714521 (alk. paper)
3540714529 (alk. paper)
3540714537
9783540714538
6611066365
9786611066369
Notes:Includes bibliographical references and index.
Summary:"Mathematical models in biology and medicine cannot be based on natural laws as it is the case with physics and chemistry. This is due to the fact that biological and medical processes are concerned with living organisms. Mathematical models, however, can be used as a language by which certain aspects of biological or medical processes can be expressed. In general, several mathematical models can be designed in order to describe a biological or medical process and there is no unique criterion which model gives the best description. This book presents several of these models and shows applications of them to different biological and medical problems. The book shows that operations research expertise is necessary in respect to modelling, analysis and optimization of biosystems."--Jacket.
Other form:Print version: Krabs, Werner, 1934- Modelling, analysis and optimization of biosystems. Berlin ; New York : Springer, c2007 9783540714521 3540714529
Table of Contents:
  • Preface
  • 1. Growth Models
  • 1.1. A Growth Model for one Population
  • 1.2. Interacting Growth of two Populations
  • 1.3. Interacting Growth of n [greater than or equal] 2 Populations
  • 1.4. Discretization of the Time-Continuous Model
  • 1.4.1. The n-Population Model
  • 1.4.2. The One-Population Model
  • 1.5. Determination of Model Parameters from Data
  • References
  • 2. A Game-Theoretic Evolution Model
  • 2.1. Evolution-Matrix-Games for one Population
  • 2.1.1. The Game and Evolutionarily Stable Equilibria
  • 2.1.2. Characterization of Evolutionarily Stable Equilibria
  • 2.1.3. Evolutionarily Stable Equilibria for 2x2-Matrices
  • 2.1.4. On the Detection of Evolutionarily Stable Equilibria
  • 2.1.5. A Dynamical Treatment of the Game
  • 2.1.6. Existence and Iterative Calculation of Nash Equilibria
  • 2.1.7. Zero-Sum Evolution Matrix Games
  • 2.2. Evolution-Bi-Matrix-Games for two Populations
  • 2.2.1. The Game and Evolutionarily Stable Equilibria
  • 2.2.2. A Dynamical Treatment of the Game
  • 2.2.3. Existence and Iterative Calculation of Nash Equilibria
  • 2.2.4. A Direct Method for the Calculation of Nash Equilibria
  • References
  • 3. Four Models of Optimal Control in Medicine
  • 3.1. Controlled Growth of Cancer Cells
  • 3.2. Optimal Administration of Drugs
  • 3.2.1. A One-Compartment Model
  • 3.2.2. A Two-Compartment Model
  • 3.3. Optimal Control of Diabetes Mellitus
  • 3.3.1. The Model
  • 3.3.2. On the Approximate Solution of the Model Problem
  • 3.3.3. A Time-Discrete Diabetes Model
  • 3.3.4. An Exact Solution of the Model Problem
  • 3.4. Optimal Control Aspects of the Blood Circulation in the Heart
  • 3.4.1. Blood Circulation in the Heart
  • 3.4.2. A Model of the Left-Ventricular Ejection Dynamics
  • 3.4.3. An Optimal Control Problem
  • 3.4.4. Another Model of the Left-Ventricular Ejection Dynamics
  • References
  • 4. A Mathematical Model of Hemodialysis
  • 4.1. A One-Compartment Model
  • 4.1.1. The Mass Transport in the Dialyzer
  • 4.1.2. The Temporal Development of the Toxin Concentration in the Blood without Ultrafiltration
  • 4.1.3. The Temporal Development of the Toxin Concentration in the Blood with Ultrafiltration
  • 4.2. A Two-Compartment Model
  • 4.2.1. Derivation of the Model Equations
  • 4.2.2. Determination of the Clearance of the Cell Membranes for Urea
  • 4.3. Computation of Periodic Toxin Concentrations
  • 4.3.1. The General Method
  • 4.3.2. The Case of Constant Clearance of the Dialyzer
  • 4.3.3. Discretization of the Model Equations
  • 4.3.4. Numerical Results for Urea
  • 4.3.5. The Influence of the Urea Generation Rate
  • 4.3.6. Determination of the Urea Generation Rate and the Rest Clearance of the Kidneys
  • 4.4. A Three-Compartment Model
  • 4.4.1. Motivation and Derivation of the Model Equations
  • 4.4.2. Determination of the Clearance of the Cell Membranes of the Brain
  • 4.4.3. Computation of Periodic Urea Concentration Curves
  • 4.4.4. Numerical Results
  • References
  • A. Appendix
  • A.1. A Problem of Optimal Control
  • A.1.1. The Problem
  • A.1.2. A Multiplier Rule
  • A.2. Existence of Positive Periodic Solutions in a General Diffusion Model
  • A.2.1. The Model
  • A.2.2. An Existence and Unicity Theorem
  • A.3. Asymptotic Stability of Fixed Points
  • Index

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