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Документ Mathematical modeling of the bioactive arterial wall(V. N. Karazin Kharkiv National University, 2018) Kizilova, N. N.; Solovyova (Philippova), Е. N.Документ Modeling of pulse wave propagation and reflection along human aorta(University of Zielona Góra, Poland, 2018) Kizilova, N. N.; Solovyova (Philippova), H. N.; Mizerski, J. K.Документ Pulse wave propagation along human aorta: a model study(2020) Kizilova, N. N.; Mizerski, J. K.; Solovyova (Philippova), H. N.In the study, wave propagation along aorta is studied for different normal and pathological conditions in distal arteries. The mathematical model is based on the axisymmetric incompressible Navier-Stokes equations for blood and momentum equations for an incompressible viscoelastic arterial wall. The solution has been found as a superposition of forward and backward running waves. The blood pressure and flow curves measured by ultrasound in larger systemic arteries of ten healthy volunteers have been used for identification of the model parameters. It is shown that individual geometry plays an essential role in the location of positive and negative wave reflection sites along the aorta and, thus, in the pressure and flow patterns as well as blood distribution into the side branches. The model is validated by comparative study with the same dependencies computed previously on a 55-tube model as well as on the measurement data. The model can be used for determination of the individual parameters for patient-specific cardiovascular models and further in silico modeling of the outcomes of surgical and therapeutic procedures.Документ Mathematical modeling of bioactive arterial wall(Харківський національний університет імені В. Н. Каразіна, 2018) Solovyova (Philippova), H. N.; Kizilova, N. N.Biological tissues and their artificial substitutes are composed by different fibers and possess complex viscoelastic properties. Here the most popular 3-element and 5-element rheological models of human soft tissues as viscoelastic bodies are considered accounting for the time delay between the load and mechanical respond of the material.The obtained data compared to the experimental curves got on the vessel wall and heart tissues.Документ A system for monitoring the state of human cardiovascular system based on the most complete mathematical model of vascular bed(Харківський національний університет імені В. Н. Каразіна, 2019) Solovyova (Philippova), Е. N.; Kizilova, N. N.The structure of a new system for monitoring the state of the human cardiovascular system based on geometric and biomechanical models of the vascular bed as a branching tree of arteries is presented. The tree geometry has been obtained by averaging the data of postmortem measurements from five bodies, a statistical analysis of the patterns of the structure of vascular trees, and a new technique for generating an individual tree for a particular patient by performing several in vivo measurements. The developed biomechanical model allows for numerical calculations of pressures and blood flow velocities in each artery, storing information in a database, analyzing the distribution of blood volumes, calculating important diagnostic indices, identifying pathologies and planning surgical operations in silico.