S4: Smoothed Solvers for Soft Tissue Simulation

在这个项目中，将建立一个新的解决方案框架和模拟工具包，用于模拟时间紧迫的生物医学应用中的软组织变形，目的是使计算生物力学更接近临床。本文将提出一种基于光滑有限元法（SFEM）的方法。这项工作将涵盖数值解决框架和基于图形处理单元（gpu）的高性能计算方案的开发。由此产生的软件库将以开源的形式发布给生物医学界，以促进传播和进一步发展。计算生物力学为生物医学应用中的软组织建模提供了强有力的基础。在这个项目中，固体生物力学问题是感兴趣的：分析和模拟可变形固体组织的运动和机械响应。在这里，连续介质力学的形式为分析提供了数学基础，通常被表述为一组偏微分方程，而有限元（FE）方法很容易成为主要的求解方法。利用这种框架，原则上可以计算任意复杂结构在任意复杂荷载作用下产生的变形和应力。这种能力在生物力学中是至关重要的。它也是虚拟生理人（www.vph-noe.eu）和生理组项目（http://physiomeproject.org）等项目的关键支持技术，这些项目的最终目标是实现基于个性化计算建模的计算机医学愿景。这些模拟技术也是开发用于指导和规划高度本地化和微创治疗的系统以及交互式模拟器（例如用于无风险外科医生培训）的重要工具。该项目的动机是抑制将基于有限元的模型整合到临床应用中的三个关键困难：(i)模型构建：有限元方法需要将所涉及的结构离散成高质量的“形状良好”元素网格，这一过程对于复杂的生物结构来说仍然是劳动密集型和耗时的，当需要特定患者的模型时，这是特别有害的；（ii）处理大变形：即使在精心构造的高质量网格已经生产出来之后，软组织可能经历的大变形可能会扭曲网格，以至于解决方案失败；（iii）计算时间：有限元方法是计算密集型的，使得它们不适合时间紧迫的应用，如手术指导和交互式模拟器，或者限制骨微结构模型等大规模模拟的分辨率。sfem是本项目发展的重点，是计算力学中的一项最新创新，它源于有限元网格子域上空间梯度场（例如应变）的“平滑”。在其他有利的特性中，已知现有配方可以大大降低网格灵敏度。在这个项目中，这个特征将成为一个算法的起点，该算法首先更容易构建网格，随后对大变形不敏感。该方法还将明确制定，以最大限度地提高其在并行硬件上的执行效率，从而允许使用廉价高效的gpu进行大幅加速。通过这些方法，提出的模拟框架可能会改善上述所有三个困难，从而促进计算生物力学与临床相关应用的整合。

In this project a new solution framework and simulation toolkit for modelling soft tissue deformations in time-critical biomedical applications will be established, with the aim of bringing computational biomechanics closer to the clinic. An approach based on the smoothed finite element method (SFEM) will be formulated. The work will cover development of both the numerical solution framework and a high performance computation scheme based on graphics processing units (GPUs). The resulting software library will be released to the biomedical community as open source, to promote dissemination and further development.Computational biomechanics provides a powerful basis for modelling soft tissues in biomedical applications. In this project, solid biomechanics problems are of interest: analysis and simulation of the motion and mechanical response of deformable solid tissues. Herein, continuum mechanics formalism provides the mathematical basis for analysis, generally formulated as a set of partial differential equations, and the finite element (FE) method is easily the predominant solution approach. With such a framework, one can, in principle, compute the deformations and stresses produced in arbitrarily complicated structures, under the influence of arbitrarily complicated loads. This capability is of central importance in biomechanics. It is also a key enabling technology for initiatives like the Virtual Physiological Human (www.vph-noe.eu) and the Physiome Project (http://physiomeproject.org), which aim, ultimately, to realise the vision of in silico medicine based on personalised computational modelling. These simulation technologies are also essential tools in development of systems for guidance and planning of highly localised and minimally invasive therapies, and in interactive simulators, for example for risk-free surgeon training.This project is motivated by three key difficulties that inhibit integration of FE-based models of this kind into clinical applications: (i) model construction: FE methods require discretisation of the involved structures into a high quality mesh of "well shaped" elements, which process remains labour intensive and time consuming for complicated biological structures, and which is particularly detrimental when patient-specific models are required; (ii) handling of large deformations: even after a carefully constructed, high quality mesh has been produced, the large deformations that soft tissues may undergo can distort the mesh so much that the solution fails nonetheless; and (iii) computation time: FE methods are computationally intensive, rendering them unsuitable for time-critical applications like surgical guidance and interactive simulators, or limiting the resolution of large scale simulations like bone microstructural models. SFEMs, the focus of developments in this project, are a recent innovation in computational mechanics, which arise from "smoothing" of spatial gradient fields (e.g. strains) over subdomains of the FE mesh. Among other favourable properties, existing formulations are known to reduce mesh sensitivity substantially. In this project, this feature will form the starting point for an algorithm for which meshes are easier to construct in the first place, and which is insensitive to large deformations, subsequently. The approach will also be explicitly formulated to maximise its efficiency in execution on parallel hardware, thus allowing substantial acceleration using cheap and efficient GPUs. By these means, the proposed simulation framework potentially will ameliorate all three of the mentioned difficulties, thus promoting integration of computational biomechanics into clinically-relevant applications.