Benoit Perthame – författare

This book presents the state of the art in mathematical research on modelling the mechanics of biological systems – a science at the intersection between biology, mechanics and mathematics known as mechanobiology. The book gathers comprehensive surveys of the most significant areas of mechanobiology: cell motility and locomotion by shape control (Antonio DeSimone); models of cell motion and tissue growth (Benoît Perthame); numerical simulation of cardiac electromechanics (Alfio Quarteroni); and power-stroke-driven muscle contraction (Lev Truskinovsky).

Each section is self-contained in terms of the biomechanical background, and the content is accessible to all readers with a basic understanding of differential equations and numerical analysis. The book disentangles the phenomenological complexity of the biomechanical problems, while at the same time addressing the mathematical complexity with invaluable clarity. The book is intended for a wide audience, in particulargraduate students and applied mathematicians interested in entering this fascinating field.

This book provides an overview of recent mathematical models for dynamics in cellular systems and offers a unique vision of the field by prominent experts.

It covers, among others, the regulatory basis of oscillations in biological systems; ergodic and chaotic properties in biological models with the example of maturity distribution of precursors of blood cells; time-delayed feedbacks; mathematical models of cell division and heterogeneous stem cell regeneration; quantitative mathematical modeling of glucose regulation; data-driven models of chemotherapy-induced neutropenia; and effects of irradiation and antioxidants in Alzheimer’s disease.

This book is directed towards mathematicians interested in learning about modeling in cellular systems and is accessible also to theoreticians in biology and medicine.

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.