The mechanics of most soft tissues in the human body are determined by the organization of their collagen fibers. Predicting how mechanics will change during growth and remodeling of those tissues requires constitutive laws that account for the density and dispersion of collagen fibers. Post-infarction scar in the heart, a mechanically and structurally complex material, does not yet have a validated fiber-based constitutive model. In this study, we tested four different constitutive laws employing exponential or polynomial strain-energy functions and accounting for either mean fiber orientation alone or the details of the fiber distribution about that mean. We quantified the goodness of fit of each law to mechanical testing data from 6-week-old myocardial scar in the rat using both sum of squared error (SSE) and the Akaike Information Criterion (AIC) to account for differences in the number of material parameters within the constitutive laws. We then compared their ability to prospectively predict the mechanics of independent myocardial scar samples from other time points during healing. Our analysis suggests that a constitutive law with a polynomial form that incorporates detailed information about collagen fiber distribution using a structure tensor provides excellent fits with just two parameters and reasonable predictions of myocardial scar mechanics from measured structure alone in scars containing sufficiently high collagen content.

人体大多数软组织的力学性能是由其胶原纤维的组织决定的。预测这些组织在生长和重塑过程中力学将如何变化需要考虑胶原纤维的密度和分散性的本构定律。心脏梗死后疤痕是一种机械和结构复杂的材料，目前还没有经过验证的基于纤维的本构模型。在这项研究中，我们测试了四种不同的本构定律，采用指数或多项式应变能函数，并单独考虑平均纤维取向或关于该平均值的纤维分布的细节。我们使用误差平方和 (SSE) 和 Akaike 信息准则 (AIC) 来量化每个定律与大鼠 6 周大心肌疤痕机械测试数据的拟合优度，以解释材料数量的差异本构定律内的参数。然后，我们比较了他们前瞻性预测愈合过程中其他时间点的独立心肌疤痕样本力学的能力。我们的分析表明，多项式形式的本构定律使用结构张量结合了有关胶原纤维分布的详细信息，仅用两个参数即可提供出色的拟合，并可根据胶原蛋白含量足够高的疤痕中单独测量的结构对心肌疤痕力学进行合理的预测。