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Author Bianca, C. (Carlo)
Title Towards a mathematical theory of complex biological systems / C. Bianca, N. Bellomo.
Imprint Singapore ; Hackensack, NJ : World Scientific, ©2011.

Author Bianca, C. (Carlo)
Series Series in mathematical biology and medicine ; v. 11
Series in mathematical biology and medicine ; v. 11.
Subject Biomathematics.
Biological systems -- Mathematical models.
Immune System -- physiology.
Wound Healing -- physiology.
Models, Theoretical.
Computational Biology.
Alt Name Bellomo, N.
Description 1 online resource (xvii, 208 pages) : illustrations
Bibliography Note Includes bibliographical references and index.
Note Print version record.
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 -- 3. The immune system : A phenomenological overview. 3.1. Introduction. 3.2. Bacteria and viruses. 3.3. The immune system components. 3.4. The immune response. 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. 4.4. The fibrosis disease. 4.5. Critical analysis -- 5. From levels of biological organization to system 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 tissues scales. 7.1. Introduction. 7.2. On the phenomenological derivation of macroscopic tissue models. 7.3. Cellular-tissue scale modeling of closed systems. 7.4. Cellular-tissue scale modeling of open systems. 7.5. On the molecular-cellular scale modeling. 7.6. Critical analysis -- 8. A model for Malign Keloid Formation and immune system competition. 8.1. Introduction. 8.2. The mathematical model. 8.3. Simulations and emerging behaviors. 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. 9.3. Cellular-tissue scale models of chemotaxis. 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.
Summary 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.
ISBN 9789814340540 (electronic bk.)
9814340545 (electronic bk.)
ISBN/ISSN 3609947
OCLC # 733048104
Additional Format Print version: Bianca, Concetta. Towards a mathematical theory of complex biological systems. Singapore ; Hackensack, NJ : World Scientific, ©2011 9789814340533 (DLC) 2010043493 (OCoLC)678534348

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