BME 314 Lecture 12 2009

BME 314 Lecture 12 2009 - CardiovascularMechanicsII Krish...

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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
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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 - = 128 = K
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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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This note was uploaded on 11/29/2010 for the course BME 314 taught by Professor Frey during the Fall '08 term at University of Texas at Austin.

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BME 314 Lecture 12 2009 - CardiovascularMechanicsII Krish...

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