Mathematical modelling of aortic dissection

[摘要] An aortic dissection is a tear of the intima of the aortic wall that spreads into the mediaor between the media and adventitia. In addition to the original lumen for blood flow,the dissection creates a new flow channel, the `false' lumen that may cause the artery tonarrow or even close over entirely. Aortic dissection is a medical emergency and can quicklylead to death.The mechanical property of the aorta has been described by the strain energy functiongiven by Holzapfel et al. [2000]. The aorta is idealized as an elastic axisymmetric thickwalledtube with 3 layers. We focus on the dissection in media, which is considered asa composite reinforced by two families of fibres. We assume the dissection in the mediais axisymmetric. The mathematical model for the dissection is presented. The 2D planecrack problem in linear elastic infinity plane and 2D strip, the axisymmetric crack problemin linear elastic compressible and incompressible tube, the axisymmetric crack problem inan incompressible axisymmetric aorta are applied to obtain solutions to three differentproblems. And the fluid flow inside the crack has been studied.The 2D plane crack problem in linear elastic infinity plane has been solved analytically.The 2D plane crack problem in linear elastic compressible and incompressible strip is modelled respectively and solved numerically.The models for axisymmetric crack problem in linear elastic compressible and incompressible tube are presented respectively. The numerical solutions for the crack problems are expressed, and the results are analyzed.The mathematical model of the incompressible aorta axisymmetric dissection is given,and the solutions are found numerically. The results change along with the different parameters in the strain energy function, which are analyzed and compared.The fluid flow inside the tear is assumed very thin which is expressed as the lubricationtheory. We use the implicit method to model the Stokes equation numerically, andtest the crack opening change along with time.

[发布机构] University:University of Glasgow;Department:School of Mathematics and Statistics

[关键词] QA Mathematics