Purpose

Residual stress tensor has an essential influence on the mechanical behaviour of soft tissues and can be particularly useful in evaluating growth and remodelling of the heart and arteries. It is currently unclear if one single radial cut using the opening angle method can accurately estimate the residual stress. In many previous models, it has been assumed that a single radial cut can release the residual stress in a ring of the artery or left ventricle. However, experiments by Omens et al. (Biomech Model Mechanobiol 1:267–277, 2003) on mouse hearts, have shown that this is not the case. The aim of this paper is to answer this question using a multiple-cut mathematical model.

Methods

In this work, we have developed models of multiple cuts to estimate the residual stress in the left ventricle and compared with the one-cut model. Both two and four-cut models are considered. Given that the collagen fibres are normally coiled in the absence of loading, we use the isotropic part of the Holzapfel-Ogden strain energy function to model the unloaded myocardium.

Results

The estimated residual hoop stress from our multiple-cut model is around 8 to 9 times greater than that of a single-cut model. Although in principle infinite cuts are required to release the residual stress, we find four cuts seem to be sufficient as the model agrees well with experimental measurements of the myocardial thickness. Indeed, even the two-cut model already gives a reasonable estimate of the maximum residual hoop stress. We show that the results are not significantly different using homogeneous or heterogeneous material models. Finally, we explain that the multiple cuts approach also applies to arteries.

Conclusion

We conclude that both radial and circumferential cuts are required to release the residual stress in the left ventricle; using multiple radial cuts alone is not sufficient. A multiple-cut model gives a marked increase of residual stress in a left ventricle ring compared to that of the commonly used single-cut model.

中文翻译：

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从左心室的多个切开角度估计残余应力。

目的

残余应力张量对软组织的机械行为具有重要影响，并且在评估心脏和动脉的生长和重塑时​​特别有用。目前尚不清楚使用开角法进行的单个径向切割是否可以准确估计残余应力。在许多以前的模型中，已经假定单个径向切口可以释放动脉环或左心室中的残余应力。然而，由Omens等人进行的实验。（Biomech Model Mechanobiol 1：267–277，2003）在小鼠心脏上的研究表明并非如此。本文的目的是使用多重切割数学模型来回答这个问题。

方法

在这项工作中，我们开发了多个切口的模型来估计左心室的残余应力，并将其与一切口模型进行比较。同时考虑了两个切割模型和四个切割模型。假设胶原纤维通常在没有负载的情况下盘绕，我们使用Holzapfel-Ogden应变能函数的各向同性部分对卸载的心肌进行建模。

结果

我们的多次切割模型估计的残余环向应力约为单次切割模型的8至9倍。尽管原则上需要无限次切割以释放残余应力，但我们发现四个切割似乎已足够，因为该模型与心肌厚度的实验测量值非常吻合。实际上，即使是两次切割模型也已经给出了最大残余环向应力的合理估计。我们显示，使用同质或异质材料模型的结果没有显着差异。最后，我们解释了多次切开方法也适用于动脉。

结论

我们得出结论，需要进行径向和周向切开以释放左心室中的残余应力。仅使用多个径向切口是不够的。与常用的单切口模型相比，多切口模型在左心室环中的残余应力显着增加。