A nonlinear, anisotropic and axisymmetric model for balloon angioplasty

Abstract

A nonlinear elastic, anisotropic and axisymmetric balloon angioplasty model, consisting of the balloon, the atherosclerotic plaque and the artery wall, has been developed and analysed in this paper. The deformation of the angioplasty compound, i.e. the balloon, the plaque and the artery, for slowly increasing dilation pressure within the balloon, is investigated. The plaque has been considered as a circular cylindrical tube extending all around the artery circumference. Normal radial stress and radial displacement boundary conditions have been imposed along the balloon–plaque and the plaque–artery interfaces. Large elastic deformations have been accommodated in the model. The balloon material has been considered as isotropic, the plaque material as transversely isotropic and the artery wall material as orthotropic. A strain energy density function, that satisfies existing incomplete experimental data, has been constructed for the plaque material. For a given dilation pressure within the balloon, the deformation of the angioplasty compound is determined via the numerical solution of a system of four nonlinear equations. For a medium hard balloon and a medium stiff plaque, a dilation pressure 7.5 times bigger than the blood pressure is required for an almost full reopening of the narrowed lumen. The percentage increase in length of the inner radius of the plaque is twice bigger than that of the radius of the artery. Results also indicate that the process of full reopening may be achievable, without stressing the artery wall dramatically.