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Abstract

Abstract

We consider the deformation of a blood vessel imbedded in soft tissue that is surrounded by a rigid structure. The vessel deforms when the difference between its external and internal pressures exceeds a certain value. To represent the deformation, we use a physical model consisting of two concentric cylinders tethered by numerous nonlinear springs representing the biological tissues surrounding the vessel (see Figure A ); the outer cylinder is taken to be rigid while the inner one is taken to be thin-walled, elastic and free to deform. We formulate the governing equations, and develop suitable numerical techniques for calculating the shape of the cross section of a deformed vessel and the blood flow rate through it (see Figure B ). The dependence of the deformation and the blood flow rate on the elastic parameters is shown (numerically) to be a convex function of the elastic parameters. This allows the formation of a well behaved “Inverse Problem,” where the elasticity of the surrounding soft tissue can be detected from the (measurable) data consisting of: pressure, cross sectional shape and blood flow rate. Since testing the elasticity of human tissue can only be done in vivo, and since such information is important as aid in the diagnosis of some diseases, the present study serves as an advancement in the non-invasive testing of the elasticity of certain soft tissues in the human body.

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/content/papers/10.5339/qfarf.2011.BMP50
2011-11-20
2019-08-18
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