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The study of blood flow in the vicinity of cerebral vascular pathologies is important both from an applied and from a scientific point of view. The main characteristics of blood flow are the dependence of velocity and pressure on time. Currently, the dependence of velocity on time can be measured by various methods (for example, ultrasound). But, currently non-invasive pressure measurement is impossible.
In my talk I will present a mathematical model of blood flow, which allows for a particular patient to restore the dependence of pressure on time by the dependence of velocity on time. To build the model under study, clinical data on the pressure and velocity of blood flow in the vessels of the brain in the vicinity of the pathology obtained during neurosurgical operations are used. The model is a nonlinear ordinary differential equation, the coefficients of which are determined by clinical data. We study equation's properties as well as a correlation of equation properties and pathologies properties.