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BME 314 Lecture 12 2009

# BME 314 Lecture 12 2009 - Krish Roy Ph.D Associate...

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Cardiovascular Mechanics II Krish Roy, Ph.D. Associate Professor Dept. of Biomedical Engineering

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Learning Objectives Fundamental equations and concepts in fluid mechanics Blood Flow Reynold’s number: Laminar vs. turbulent flow Hagen-Poiseulle’s Equation Solid mechanics of blood vessels Why is the stress-strain curve of blood vessels highly non-linear Relevance in aneurysms
Poiseuille flow model The simplest model for blood flow through a vessel would be to treat the same as steady, fully developed flow of a Newtonian fluid through a straight portion of a cylindrical tube of circular cross- section In this relationship, Q is the flow rate, p is the drop in pressure in a tube of length L and diameter D. K was a constant that was found to be independent of the other variables. L pD K Q 4 =

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Hagenbach-Poiseuille law Hagenbach independently arrived at the theoretical solution for the above problem that introduced fluid viscosity as follows: where μ is the coefficient of viscosity and a is the tube radius . From these two Equations, it can be observed that L p p a Q μ π 8 ) ( 2 1 4 - = μ π 128 = K
Assumptions used Newtonian fluid Laminar flow No slip at the vascular wall Steady flow Cylindrical shape Rigid wall Fully developed flow

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Vascular resistance The vascular resistance is given by the relationship This is analogous to the electrical resistance given by where I is the current and V the voltage across a segment of a circuit. If the pressure drop is measured in terms of mmHg and the flow rate in terms of cc/s, then the resistance is expressed as a peripheral resistance unit (PRU) and it is used in physiological literature.
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