Amy Cypher, J Mohamed B. Elgindi, Hatem Kouriachi, David Peschman, Reba Shotwell

Abstract: In this paper, we present the mathematical equations that govern the deformation of an imbedded blood vessel under external uniform pressure taking into consideration the nonliner behavior of the soft tissue surrounding the vessel. We present a bifurcation analysis and give explicit formulas for the bifurcation points and the corresponding first order approximations for the\emph{non-trivial} solutions. We then show the results of a MATLAB program that integrates the equilibrium equations and calculates the blood flow rate through a deformed cross section for given values of the elasticity parameters and pressure. Finally, we provide (numerical) verification that the flow rate as a function of the elasticity parameters of the soft tissue surrounding the blood vessel is convex, and therefore validate the invertibility of our model.

Keywords: Blood Vessel, Deformation of Elastic Tube

Cite this paper: nullA. Cypher, J. Elgindi, H. Kouriachi, D. Peschman and R. Shotwell, "Flow Rate through a Blood Vessel Deformed Due To a Uniform Pressure," Journal of Biomaterials and Nanobiotechnology, Vol. 2 No. 4, 2011, pp. 369-377. doi: 10.4236/jbnb.2011.24046.

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