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A modular inverse elastostatics approach to resolve the pressure-induced stress state for in vivo imaging based cardiovascular modeling

机译:模块化反弹静止方法来解决基于体内成像的心血管造型的压力诱导应力状态

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Patient-specific biomechanical modeling of the cardiovascular system is complicated by the presence of a physiological pressure load given that the imaged tissue is in a pre-stressed and -strained state. Neglect of this prestressed state into solid tissue mechanics models leads to erroneous metrics (e.g. wall deformation, peak stress, wall shear stress) which in their turn are used for device design choices, risk assessment (e.g. procedure, rupture) and surgery planning. It is thus of utmost importance to incorporate this deformed and loaded tissue state into the computational models, which implies solving an inverse problem (calculating an undeformed geometry given the load and the deformed geometry). Methodologies to solve this inverse problem can be categorized into iterative and direct methodologies, both having their inherent advantages and disadvantages. Direct methodologies are typically based on the inverse elastostatics (IE) approach and offer a computationally efficient single shot methodology to compute the in vivo stress state. However, cumbersome and problem-specific derivations of the formulations and non-trivial access to the finite element analysis (FEA) code, especially for commercial products, refrain a broad implementation of these methodologies. For that reason, we developed a novel, modular IE approach and implemented this methodology in a commercial FEA solver with minor user subroutine interventions. The accuracy of this methodology was demonstrated in an arterial tube and porcine biventricular myocardium model. The computational power and efficiency of the methodology was shown by computing the in vivo stress and strain state, and the corresponding unloaded geometry, for two models containing multiple interacting incompressible, anisotropic (fiber-embedded) and hyperelastic material behaviors: a patient-specific abdominal aortic aneurysm and a full 4-chamber heart model.
机译:鉴于成像组织处于预应力和训练状态,心血管系统的特异性生物力学建模是通过存在的生理压力负荷的复杂性。将该预应力的状态忽略到固体组织力学模型中导致错误的指标(例如墙壁变形,峰值应力,壁剪应力),其转弯用于器件设计选择,风险评估(例如程序,破裂)和手术规划。因此,最重要的是将这种变形和加载的组织状态结合到计算模型中,这意味着解决逆问题(计算给定负载和变形几何形状的未变形几何形状)。解决这个逆问题的方法可以分类为迭代和直接方法,都具有其固有的优缺点。直接方法通常基于逆弹性效果(IE)方法,并提供计算有效的单次射击方法来计算体内应力状态。然而,对有限元分析(FEA)代码(特别是商业产品)的制剂的繁琐和特定于有限元分析(FEA)代码的特定推导,避免了这些方法的广泛实现。因此,我们开发了一种新颖的,模块化的IE方法,并在商业FEA求解器中实现了该方法,其中具有次要用户子程序干预。该方法的准确性在动脉管和猪生物心肌模型中证明。通过计算体内应力和应变状态和相应的卸载几何形状来显示方法的计算能力和效率,适用于含有多个相互作用的不可压缩,各向异性(纤维嵌入)和超弹性材料行为的两种模型:患者特异性腹部主动脉动脉瘤和全4室心脏模型。

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