» Research » Biomechanics of the Cardiovascular System

Biomechanics of the Cardiovascular System

Main research domains

  • mathematical modelling of the nonstationary (pulsatile) flow of a Newtonian and non-Newtonian fluid (blood) in tubes with axially symmetric and axially non-symmetric restrictions
  • physical (hydrodynamical) and mathematical investigation of pulsatile velocity and shear stress field in rigid and elastic tubes with singularities
  • mathematical modelling of the circulation in the whole cardiovascular system for main pathological changes and for the practical use for clinical and study purposes

Most important results

  • research of hydrodynamical characteristics of the artificial heart valve (type Björk-Shiley), measurement of the pressure and velocity fields behind the valve, calculation of the turbulent characteristics and energetic spectra leads to the conclusion, that values of turbulent shear stresses in their peaks approach to their critical magnitude, significant for the danger of damage of erythrocytes. New device with the synchronized acquisition of data was proposed and realized for the purpose of this measurement.
  • realization of the mathematical model of blood circulation in the whole cardiovascular system, numerical investigation of the influence of defect of valves, contractility of the heart muscle, increased frequency and the other factors on the circulation. Time course of pressure and flow rate well corresponds with the data given in the physiological literature. The program is suitable also for tuition purposes, especially for students of medicine.
  • hydrodynamical research of flow in the tube singularity (sudden expansion and contraction). Velocity profiles for two sets of parameters of flow were measured and the turbulent characteristics and energetic spectra derived. The expanding jet was detected in the expanded part of the tube and back flow was observed near the wall. The highest values of the Reynold stress were found in the domain of separation. New device with the vertical arrangement of the tube and with the synchronized acquisition of data was proposed for this measurement
  • mathematical description of stress changes in the location of surgical joint of the natural and artificial blood vessels. Mechanical properties of the joint exhibit little dependence on the type of connection and the so-called boundary imperfection is located only in the neighbourhood of the connections.
  • development of two numerical methods (MAC and Finite Element Methods) for the solution of the mathematical models of stationary, periodic and pulsatile flows in two-dimensional channels and axisymmetric tubes with single and periodic singularities. Using the methods, partial results were obtained concerning
    • dependence of frequency, amplitude and other flow parameters on the geometry of the singularity in periodic flows
    • the critical Reynolds number for the appearance of periodic flows and its dependence on the geometry
    • two branches of the mathematical solutions in pulsatile flows for increasing Reynolds and Womersley numbers
    Non-symmetric periodic flows in the double-cell geometry for two-dimensional corrugated channels were discovered and are currently studied.