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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.

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 --- 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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal