Continuum-Mechanical modeling of aneurysm formation

动脉瘤是动脉壁的隆起（扩张），通常是主动脉。动脉瘤生长并变得足够大时会破裂，导致危险的，通常是致命的体内出血。来自动脉瘤形成的数学模型的信息可以帮助医生做出关于一旦诊断出动脉瘤就采取何种行动的艰难决定（是否进行手术，开适当的药物以降低动脉瘤破裂的风险，或者只是将患者置于观察之下）。以前的研究主要集中在假设动脉的严重不均匀弱化已经发生，对动脉瘤的演变进行数值建模。我们的目标是从不同的角度对动脉瘤形成进行建模：我们将动脉瘤的形成视为分叉问题;即使材料特性沿动脉沿着均匀，也可能发生动脉瘤。我们希望建立一个理论框架，在这个框架下，可以预测动脉瘤的发生，一旦进行了动脉瘤切除或修复手术，就可以评估手术部分的完整性。这将涉及以下两项任务：（i）推导健康和病理动脉的适当本构模型，以及（ii）给定特定材料模型，精确描述动脉瘤是否可以形成以及如何形成（例如，它是否会轴对称地生长或从侧面生长）。

An aneurysm is a bulge (dilation) in the wall of an artery, usually the aorta. An aneurysm that grows and becomes large enough can burst, causing dangerous, often fatal, bleeding inside thebody. Information from mathematical modeling of aneurysm formation can help doctors make the difficult decision about which course of action to take once an aneurysm has been diagnosed (whether to carry out a surgery, to prescribe appropriate drugs to reduce the risk of aneurysm bursting or to simply put the patient under observation). Previous studies have focused on modeling the evolution of aneurysms numerically by assuming that a seriously enough inhomogeneous weakening of the artery has taken place. We aim to model aneurysm formation from a different perspective: we view the initiation of an aneurysm as a bifurcation problem; it can occur even if the material properties are homogeneous along the artery. We hope to establish a theoretical framework under which the initiation of an aneurysm can be predicted, and once an operation to remove or repair an aneurysm has been carried out the integrity of the operated section can be assessed. This will involve the following two tasks: (i) derivation of appropriate constitutive models for healthy and pathological arteries, and (ii) given a particular material model, describing precisely whether an aneurysm can form or not and how it will form (e.g. whether it will grow axi-symmetrically or from the side).