By Luca Formaggia, Alfio Quarteroni, Allesandro Veneziani
Mathematical types and numerical simulations can relief the understanding of physiological and pathological tactics. This ebook deals a mathematically sound and up to date origin to the educational of researchers and serves as an invaluable reference for the advance of mathematical types and numerical simulation codes.
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Additional info for Cardiovascular Mathematics: Modeling and simulation of the circulatory system (MS&A)
Hormonal mechanisms, including (i) the renin-angiotensin system, (ii) ANP and (iii) the antidiuretic hormone, regulate blood volume and indirectly the blood pressure. Cardiovascular sensors Mechano- and chemoreceptors are widely distributed throughout the cardiovascular system: in the heart, the coronary arteries, the carotid sinuses, the large intrathoracic blood vessels (particularly along the inner aortic arch and at the bases of both venae cavae) and the cervical vessels. These receptors continuously monitor the state of the circulation and feed their signals to the corresponding aﬀerent neurons.
In normal conditions, the endothelium prevents clotting (thrombin inactivation and proﬁbrinolytic activity). Endothelial cells have cell-surface substances, such as thrombomodulin, protein C, lipoprotein-associated coagulation inhibitor, tissue factor pathway inhibitor, protease-nexin and heparan sulphate. They inhibit platelet aggregation, releasing inhibitors like prostacyclins and NO. They activate ﬁbrinolysis by binding the plasminogen activator inhibitor, which inhibits the ﬁbrinolytic system.
These receptors continuously monitor the state of the circulation and feed their signals to the corresponding aﬀerent neurons. The chemoreceptors transduce reduced O2 concentration and increased CO2 and H+ concentrations into an action potential. The impulses are transmitted via the vagus into the vasomotor centres, as well as the respiratory centres. The baroreceptors are sensitive to both mean pressure and the rate of change of pressure. An increase in mean pressure or pulse pressure increases the ﬁring rate of the baroreceptor nerves, which not only inhibits sympathetic tonic activity to the heart and blood vessels, but also increases vagal tone to the heart.