Active solids are a large class of materials, including both living soft tissues and artificial matter, that share the ability to undergo strain even in absence of external loads. While in engineered materials the actuation is typically designed , in natural materials it is an unknown of the problem. In such a framework, the identification of inactive regions in active materials is of particular interest. An example of paramount relevance is cardiac mechanics and the assessment of regions of the cardiac muscle with impaired contractility. The impossibility to measure the local active forces directly suggests us to develop a novel methodology exploiting kinematic data from clinical images by a variational approach to reconstruct the local contractility of the cardiac muscle. By finding the stationary points of a suitable cost functional we recover the contractility map of the muscle. Numerical experiments, including severe conditions with added noise to model uncertainties, and data knowledge limited to the boundary, demonstrate the effectiveness of our approach. Unlike other methods, we provide a spatially continuous recovery of the contractility map without compromising the computational efficiency.

中文翻译：

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从表观运动学缺陷重建心肌的局部收缩力


活性固体是一大类材料，包括活体软组织和人造物质，即使在没有外部载荷的情况下，它们也具有承受应变的能力。虽然在工程材料中，驱动通常是经过设计的，但在天然材料中，这个问题是未知的。在这样的框架中，活性材料中非活性区域的识别特别令人感兴趣。最重要的一个例子是心脏力学和收缩力受损的心肌区域的评估。由于无法直接测量局部主动力，建议我们开发一种新颖的方法，通过变分方法利用临床图像的运动学数据来重建心肌的局部收缩力。通过找到合适成本函数的驻点，我们恢复了肌肉的收缩力图。数值实验，包括增加模型不确定性噪声的严酷条件，以及仅限于边界的数据知识，证明了我们方法的有效性。与其他方法不同，我们提供了收缩性图的空间连续恢复，而不影响计算效率。