Schulich School of Engineering, University of Calgary, Calgary, Canada.
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, Galway, Republic of Ireland.
J R Soc Interface. 2019 Jul 26;16(156):20190023. doi: 10.1098/rsif.2019.0023. Epub 2019 Jul 24.
The opening angle method is a popular choice in biomechanics to estimate residual stresses in arteries. Experimentally, it means that an artery is cut into rings; then the rings are cut axially or radially allowing them to open into sectors; finally, the corresponding opening angles are measured to give residual stress levels by solving an inverse problem. However, for many tissues, for example in pathological tissues, the ring does not open according to the theory into a neat single circular sector, but rather creates an asymmetric geometry, often with abruptly changing curvature(s). This phenomenon may be due to a number of reasons including variation in thickness, microstructure, mechanical properties, etc. As a result, these samples are often eliminated from studies relying on the opening angle method, which limits progress in understanding and evaluating residual stresses in real arteries. With this work, we propose an effective approach to deal with these non-trivial openings of rings. First, we digitize pictures of opened rings to split them into multiple, connected circular sectors. Then we measure the corresponding opening angles for each sub-sector. Subsequently, we can determine the residual stresses for individual sectors in a closed-ring configuration and, thus, approximate the circumferential residual bending effects.
开口角法是生物力学中估算动脉残余应力的常用方法。从实验的角度来看，它意味着将动脉切成环；然后将环沿轴向或径向切割，使它们张开成扇形；最后，通过求解逆问题来测量相应的开口角度，以给出残余应力水平。然而，对于许多组织，例如在病理组织中，环并不按照理论那样整齐地张开成单个圆形扇形，而是会产生不对称的几何形状，通常具有急剧变化的曲率。这种现象可能是由于多种原因造成的，包括厚度、微观结构、力学性能等方面的变化。因此，这些样本经常会从依赖开口角法的研究中被剔除，这限制了对真实动脉中残余应力的理解和评估的进展。在这项工作中，我们提出了一种有效的方法来处理这些非平凡的环开口。首先，我们对张开的环进行数字化处理，将其分割成多个相连的圆形扇形。然后，我们测量每个子扇形的相应开口角度。随后，我们可以确定在闭环形配置下各个扇形的残余应力，从而近似计算周向残余弯曲效应。
