Computer modeling in mechanics of circulation
Abstract
Some cardiovascular pathology connected with variations in geometry, wall properties and microcirculatory disorders can be studied by computer simulations. The mathematical model that allows to calculate the parameters of blood circulation – velocities of blood and pressure, displacements of the artery walls - for a complex vascular tree in real time is proposed.The geometrical model is based on the detailed postmortem measurements on the systemic arterial trees (more than 1000 arterial segments). The aortic model consists of 32 aortic segments and 59 side branches of the aorta including the larger and medium vessels. Mathematical model of blood flow in the system is described by Womersley model of the pulsatile viscous flow in the viscoelastic tube using the pressure and volumetric rate continuity conditions at the bifurcations of arteries. The Windkessel and structured tree outflow boundary conditions at the outlets of the branches have been used. The solution has been found as superposition of the forward and backward running waves. Based on the model, blood circulation parameters were calculated in the aortic model (91 tubes). The calculation results correspond to in vivo measurements. It was shown most of the branches have zero wave reflection coefficients but the large branches like celiac, renal and iliac arteries could produce noticeable wave reflections. The smaller branches possess negative wave reflection coefficient and, thus, contribute to the blood suction effect and lower aortic resistance to the blood flow. It is shown, the individual geometry plays an essential role in the location of the positive and negative wave reflection sites along the aorta and, thus, in the pressure and flow patterns and blood distribution into the branches. The influence of occlusion of the iliac arteries, low/high wall rigidity, and total length of aorta are studied on different individual geometries. The model can be used for determination of the individual parameters for patient-specific cardiovascular models and further modeling of the outcomes of the surgical and therapeutic procedures.
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