Mathematical Modelling in Biomedicine

• Other Authors: Volpert, Vitaly (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021
• Subjects: Research & information: general; Mathematics & science; virus density distribution; genotype; virus infection; immune response; resistance to treatment; nonlocal interaction; quasi-species diversification; mathematical oncology; spatially distributed modeling; reaction-diffusion-convection equations; computer experiment; spiral wave; heterogeneity; heart modeling; myocardium; left ventricle; neural field model; integro-differential equation; waves; brain stimulation; mathematical modeling; cardiac mechanics; multiscale simulation; cardiomyopathies; left ventricle remodeling; spatially-distributed modeling; gradient descent; 1D haemodynamics; systole variations; coronary circulation; cardiac pacing; tachycardia; bradycardia; interventricular asynchrony; long QT syndrome; premature ventricular contraction; rotary blood pump; lumped heart model; cardiac fibrosis; excitable media; wave break; elongated obstacle; lymph flow; mathematical modelling; lymphatic vessels; lymph nodes; parameter estimation; constrained optimization; derivative free optimization; multiscale models; differential equations; viral hepatitis
• Online Access: DOAB: download the publication; DOAB: description of the publication

Mathematical modelling in biomedicine is a rapidly developing scientific discipline at the intersection of medicine, biology, mathematics, physics, and computer science. Its progress is stimulated by fundamental scientific questions and by the applications to public health. This book represents a collection of papers devoted to mathematical modelling of various physiological problems in normal and pathological conditions. It covers a broad range of topics including cardiovascular system and diseases, heart and brain modelling, tumor growth, viral infections, and immune response. Computational models of blood circulation are used to study the influence of heart arrhythmias on coronary blood flow and on operating modes for left-ventricle-assisted devices. Wave propagation in the cardiac tissue is investigated in order to show the influence of tissue heterogeneity and fibrosis. The models of tumor growth are used to determine optimal protocols of antiangiogenic and radiotherapy. The models of viral hepatitis kinetics are considered for the parameter identification, and the evolution of viral quasi-species is investigated. The book presents the state-of-the-art in mathematical modelling in biomedicine and opens new perspectives in this passionate field of research.