By Luca Formaggia, Alfio Quarteroni, Allesandro Veneziani
Mathematical types and numerical simulations can reduction the understanding of physiological and pathological procedures. This booklet bargains a mathematically sound and updated beginning to the learning of researchers and serves as an invaluable reference for the improvement of mathematical types and numerical simulation codes.
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Additional resources for Cardiovascular Mathematics: Modeling and simulation of the circulatory system (MS&A)
The lymphocytes, 25–35 % of all leukocytes, diameter 8–15 μm, also play an important role in the immune response by providing antigenspeciﬁc acquired immunity (immunological memory). The monocytes, 3–9 % of all leukocytes, diameter 15–25 μm, give rise to mature macrophages that reside in the tissues and defend the body against viruses and bacteria. The platelets, diameter 2–4 μm, are non-nucleated cells with an average life span of 10 days that are involved in coagulation. Platelets are dense in granules which contain serotonin, granulophysin, P-selectin, growth factors, clotting molecules and chemotactic compounds.
Replacement, or end-to-end anastomosis, involves removing the diseased artery and replacing it with another vessel sutured end-to-end with the remaining arteries. Bypass, or side-to-side anastomosis, provides an alternative route for blood to bypass the stenoses which are left in place. Vascular grafts can be divided into three types: (i) grafts using arteries or veins from the patient (autologous) or a donor (homologous), (ii) xenografts using vessels from other species (usually bovine or porcine) and (iii) artiﬁcial grafts (usually either woven or knitted dacron or expanded polytetraﬂuoroethylene PTFE).
During this period, the myocardium continues to relax and the pressure in the LV to fall. When the LV pressure decreases below the pressure in the LA, the mitral valve opens, beginning the phase of ventricular ﬁlling when the mitral valve is open and the aortic valve closed. Filling initially occurs passively, the Ewave of mitral ﬂow driven by the pressure in the atrium. There is considerable debate about the role of the ventricle during the passive ﬁlling, some cardiologists believing that the ventricle generates suction during this period due to the over-contraction of the ventricle past its equilibrium conﬁguration.
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