Continuum-Mechanical modeling of aneurysm formation

动脉瘤是动脉（通常是主动脉）壁上的凸起（扩张）。动脉瘤长大并变得足够大时可能破裂，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艰难的决定，即一旦动脉瘤被诊断出来，该采取何种行动（是进行手术，开适当的药物来降低动脉瘤破裂的风险，还是简单地观察病人）。以前的研究主要是通过假设动脉发生了严重的不均匀弱化，来对动脉瘤的演变进行数值模拟。我们的目标是从不同的角度来模拟动脉瘤的形成：我们认为动脉瘤的起始是一个分叉问题；即使沿着动脉的材料性质是均匀的，也可能发生这种情况。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形成，一旦进行了切除或修复动脉瘤的手术，就可以评估手术部分的完整性。这将涉及以下两项任务：(i)为健康和病理动脉推导适当的本构模型，以及（ii）给定特定的材料模型，精确描述动脉瘤是否可以形成以及它将如何形成（例如，它是轴对称生长还是从侧面生长）。

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).