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Cardiovascular system and artificial replacements

Pulsatile flow in cardiovascular system

Project description:

Setup for determining the natural frequencies of elastic tubes

Detection of pulse wave velocity in elastic tube with using 3D correlation system Q-450

Detection of pulse wave velocity in elastic tube with using high-speed camera

Mathematical models of elastic tubes are prepared in The Laboratory of Cardiovascular Biomechanics together with the experiments. A mathematical model can verify the obtained constitutive laws for the material of the elastic tubes and decrease therefore the number of experiments with biological materials. The mathematical simulation of elastic tubes is complex, especially for blood vessels.

The first model is based on analogy of fluid flow through an elastic tube and electrical circuit. Electric current is equivalent to volumetric flow, voltage to pressure gradient in the tube. Electric resistance responds to hydraulic friction resistance, electric inductance responds to inertance, caused by inertia of the fluid under acceleration and electric capacitance is equivalent to hydraulic capacity caused by compliance of the elastic vessel wall. We obtain two partial differential equation of the first order for pressure and flow rate from the analogy. We solve the system by method of finite volumes in our own code written in Matlab and Fortran. As boundary conditions, we want to use the values of pressure and flow rate from the experiments.

The aim of the model is to implement and verify the constitutive law obtained from the experiments.

Furthermore, we develop a model describing the water hammer inside the elastic tube that has a clearly defined limiting extensibility. Using mathematical modeling and experiments that have the character of water hammer we develop the construction of a physical model of blood vessel wall with a similar mechanical response under static and dynamic loading as human blood vessel. Mathematical and physical model respect the composite structure of biological material.

Resesrchers:

Cooperation:

Literature:

• Macková, H. - Chlup, H. - Žitný, R.: Numerical model for verification of constitutive laws of blood vessel wall. Journal of Biomechanical Science and Engineering. 2007, vol. 2, no. 2/1, p. s66.
• Macková, H. - Chlup, H. - Žitný, R.: Numerical Model for Verification of Constitutive Laws of Blood Vessel Wall. In Third Asian Pacific Conference on Biomechanics. Tokyo: The University of Tokyo, 2007.
• Chlup, H. - Macková, H. - Vilímek, M. - Kubový, P. - Žitný, R. - et al.: Pulse wave velocity in elastic tube. Modelling, Identification, and Control 2006. vol. 25, no. 25, p. 484-488.
  
• Chlup, H. - Macková, H. - Žitný, R. - Konvičková, S.: Experimental measurement of pulse wave velocity in elastic tube. In Engineering Mechanics 2006. Prague: Institute of Theoretical and Applied Mechanics AS CR, 2006, p. 130-131.