Large deformation modelling of the human heart via the Material Point Method

随着更复杂的人造器官被设计出来并植入病人体内，模拟生物力学结构的能力变得越来越重要。在被创建准备使用之前，它们必须被设计和测试。这就是需要计算模型的地方。材料点法（MPM）是Sulsky埃塔尔提出的一种用于处理历史相关材料的质点法。1994年MPM将结构离散为粒子，粒子通过背景网格移动，意味着在整个分析过程中不会发生元素失真。这意味着避免了大网格扭曲的问题，允许问题包括大变形力学，这意味着可以运行更真实的模拟。由于是粒子定义了结构的响应，因此不需要重新划分网格，这可以提高计算时间。然而，MPM在某些应用中也存在一些缺陷，例如，由于物理边界和网格的不匹配性，当分析的物体/结构由粒子表示时，由于没有定义边界条件，因此很难应用边界条件。令人惊讶的是，使用MPM建模生物材料的研究很少。2015年，Guilkey等人使用MPM来模拟多细胞构建体。这涉及扫描胶原凝胶内的微血管碎片的血管化支架，用大量的材料点将其离散化，并使用MPM来确定施加单轴拉伸时的应力响应。Lui等人也使用MPM模拟啄木鸟的头部，以确定啄木鸟大脑上存在的巨大力量的影响。据作者所知，这些案例是使用MPM建模生物力学问题的唯一研究，本研究的目的是发展一种使用MPM建模生物力学结构的方法，特别是针对心脏。心脏是一个非常重要的器官，在我们的一生中，由于其每个腔室中的巨大流体压力，心脏一直处于巨大的压力之下。通过模拟心壁在承受各种压力时的情况，我们可以更好地了解如何更有效地构建现在使用得更频繁的人工对应物。该项目将从研究目前用于生物力学建模的技术以及如何使用MPM作为这些技术的改进开始。将开展一项研究，探讨使用无网格方法（如MPM）的好处和挑战。MPM在分析心脏方面的一个潜在好处是简化了从体素化心脏扫描到数值分析的过渡，因为不需要网格。试图解决的问题，应用边界条件内的MPM将被探讨。将开发一个MPM代码，该代码将模拟心脏对施加的压力和表面流量的反应。模拟将运行，以确定改变心脏的结构特性和改变外部条件的影响。

The ability to model biomechanical structures is becoming more important now that morecomplex artificial organs are being designed and fitted into patients. Before being created ready for use, theymust be designed and tested. This is where computational modelling is needed. The standard modelling techniques discretise the structure into very small elements which are distorted in response to external forces.The Material Point Method (MPM) is a particle method for history-dependent materials developed by Sulsky etal. in 1994 . The MPM discretises a structure into particles which move through a background grid meaningno element distortion takes place throughout the analysis. This means that the problem of large mesh distortionis avoided allowing for problems to include large deformation mechanics, meaning more realistic simulationscan be run. As it is the particles that define the response of the structure, there is no need for remeshingwhich can improve computational time. The MPM does however have some drawbacks for certain applications.For example, due to the non-matching nature of the physical boundaries and the mesh, it is difficult to applyboundary conditions as no edges are defined when analysed body/structure is represented by particles.Surprisingly, there has been very little research into using the MPM to model biological materials. In 2015,Guilkey et al. used the MPM to model multicellular constructs. This involved scanning a vascularisedscaffold of microvascular fragments within a collagen gel, discretising it with a large amount of material pointsand using the MPM to determine the stress response when uniaxial tension was applied. Lui et al. also usedthe MPM to model a woodpeckers head as it pecks to determine the effect of the large forces present on thebirds brain. To the author's knowledge, these cases are the only studies into using the MPM to modelbiomechanical problems.The aim of this research is to develop a method of using the MPM to model biomechanical structures with spe-cific focus on the heart. The heart is a very important organ which is under a great amount of stress constantlythroughout our lives due to the large fluid pressures within each of its chambers. By modelling the heart wallswhen they are subject to the various stresses that are imposed on them, we can gain a greater understandingof how to more efficiently construct the artificial counterparts which are being used more frequently now. Theproject will start with research into what techniques are currently being used for biomechanical modelling andhow the MPM can be used as an improvement on these techniques. A study into the benefits and challengesof using a meshless method such as the MPM will be undertaken.One potential benfit of the MPM in analysing the heart is simplifying the transition from voxelised heart scansinto numerical analysis as meshing is not required. Attempts to solve the issue of applying boundary conditionswithin the MPM will be explored. An MPM code will be developed which will model theresponse of the heart to an applied pressure and flow over the surface. Simulations will be run to determine toeffect of changing the heart's structural properties and varying the external conditions.