Applied Mathematical Models in Human Physiology
This book introduces mathematicians to real applications from physiology. Using mathematics to analyze physiological systems, the authors discuss models reflecting current research in cardiovascular and pulmonary physiology. In particular, they present models describing blood flow in the heart and the cardiovascular system, as well as the transport of oxygen and carbon dioxide through the respiratory system and a model for baroreceptor regulation. This is the only book available that analyzes up-to-date models of the physiological system at several levels of detail; both simple 'real-time' models that can be directly used in larger systems, and more detailed 'reference' models that show the underlying physiological mechanisms and provide parameters for and validation of simpler models. The book also covers two-dimensional modeling of the fluid dynamics in the heart and its ability to pump, and includes a discussion of modeling wave-propagation throughout the systemic arteries.
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alveoli anesthesia aorta aortic outflow aortic valve approximately arterial pressure arterioles atrium baroreceptor mechanism baroreceptor model blood flow boundary condition capillaries carbon dioxide cardiac cycle cardiac output cardiovascular model cardiovascular system carotid sinus pressure chapter compartment compliance component computed results concentration constant contractility cross-sectional area curve Danielsen described diastole diffusion dissociation functions ejection effect elastic end-diastolic volume firing rates flow and pressure fluid gases heart model heart rate hemoglobin hyperactivation impedance increase inflow large arteries left ventricle linear mathematical models measured metabolism mitral annulus mitral valve mmHg muscle Noordergraaf normal obtained Ottesen outflow condition outflow tract oxygen parameter values partial pressures peripheral resistance Peskin physiological pressure pv pulmonary radius rate H respiratory shown in Figure Siggaard-Andersen simulation small arteries solid line structured tree model systemic arteries systole tension tissue unstressed volume vector velocity profiles venous ventricular pressure viscosity vortex Windkessel model