Towards a Mathematical Theory of Complex Biological Systems Series in Mathematical Biology and Medicine 1st Edition by C Bianca, N Bellomo ISBN 978-9814340533 9814340537

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Product details: 

ISBN 10:  9814340537

ISBN 13: 978-9814340533

Author:  C Bianca, N Bellomo

This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy.The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others.Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

Table of contents: 

1. Looking for a Mathematical Theory of Biological Systems
   1.1 Introduction
   1.2 On the Concept of Mathematical Theory
   1.3 Plan of the Monograph

2. On the Complexity of Biological Systems
   2.1 Ten Common Features of Living Systems
   2.2 Some Introductory Concepts of Systems Biology
   2.3 Reducing Complexity

   1. Immune System, Wound Healing Process, and Systems Biology

3. The Immune System: A Phenomenological Overview
   3.1 Introduction
   3.2 Bacteria and Viruses
   3.3 The Immune System Components
   3.3.1 The Lymphatic System
   3.3.2 The White Blood Cells
   3.4 The Immune Response
   3.4.1 Innate Immunity
   3.4.2 Adaptive Immunity
   3.5 Immune System Diseases
   3.6 Critical Analysis

4. Wound Healing Process and Organ Repair
   4.1 Introduction
   4.2 Genes and Mutations
   4.3 The Phases of Wound Healing
   4.3.1 Hemostasis Phase
   4.3.2 Inflammation Phase
   4.3.3 Proliferation Phase
   4.3.4 Maturation or Remodeling Phase
   4.4 The Fibrosis Disease
   4.5 Critical Analysis

5. From Levels of Biological Organization to Systems Biology
   5.1 Introduction
   5.2 From Scaling to Mathematical Structures
   5.3 Guidelines to the Modeling Approach

6. Mathematical Tools and Structures
   6.1 Introduction
   6.2 Mathematical Frameworks of the Kinetic Theory of Active Particles
   6.3 Guidelines Towards Modeling at the Molecular and Cellular Scales
   6.4 Additional Analysis Looking at the Immune Competition
   6.5 Critical Analysis

7. Multiscale Modeling: Linking Molecular, Cellular, and Tissue Scales
   7.1 Introduction
   7.2 On the Phenomenological Derivation of Macroscopic Tissue Models
   7.3 Cellular-Tissue Scale Modeling of Closed Systems
   7.3.1 Asymptotic Methods for a Single Subsystem
   7.3.2 Asymptotic Methods for Binary Mixtures of Subsystems
   7.4 Cellular-Tissue Scale Modeling of Open Systems
   7.5 On the Molecular-Cellular Scale Modeling
   7.6 Critical Analysis

8. Applications and Research Perspectives
   8.1 A Model for Malignant Keloid Formation and Immune System Competition
   8.2 The Mathematical Model
   8.3 Simulations and Emerging Behaviors
   8.3.1 Sensitivity Analysis of the Progression Rate
   8.3.2 Sensitivity Analysis of the Proliferation Rate
   8.3.3 Sensitivity Analysis of the Initial Distributions
   8.4 Critical Analysis and Perspectives

9. Macroscopic Models of Chemotaxis by KTAP Asymptotic Methods
   9.1 Introduction
   9.2 Linear Turning Kernels: Relaxation Models
   9.2.1 The Case of a Single Subsystem
   9.2.2 The Case of a Binary Mixture of Subsystems
   9.3 Cellular-Tissue Scale Models of Chemotaxis
   9.3.1 Classical Keller-Segel Type Models
   9.3.2 Optimal Drift Following the Chemoattractant
   9.3.3 Nonlinear Flux-Limited Model by the Mixed Scalings
   9.4 Critical Analysis

10. Looking Ahead
    10.1 Introduction
    10.2 Some Challenges for Applied Mathematicians and Biologists
    10.3 How Far Is the Mathematical Theory for Biological Systems?
    10.4 Closure

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Tags: C Bianca, N Bellomo, Towards a Mathematical, Theory of Complex, Series in Mathematical