An Optimization Framework for the Estimation of Material Properties of Deformable Materials from Volumetric Deformation Measurements

这项研究涉及通过现代成像和扫描技术(如MRI、CT等)自动确定可变形固体的材料特性的优化技术的开发。特别关注大变形、高应变率和经常具有塑性的超弹性材料。这种材料是生物软组织(如肌肉、脂肪、皮肤等)的特征。而它们的确定对于创建准确的、特定于对象的对这些解剖结构功能的模拟至关重要。使用现代计算技术的模拟是一种越来越可靠的工具，用于回答生物医学工程中的许多问题，从基本功能到解剖结构复杂区域的手术后反应。然而，只有当模拟材料的准确本构描述可用时，可靠的结果才是可能的。虽然已经做了很多工作来建立和确定生物软组织的本构模型，但大多数材料参数都是从身体标本或一小部分人身上估计出来的。这是一种不可接受的简化，因为不同受试者的材料行为存在广泛的差异，而且来自凹凸体标本固有的材料变化。这项研究将建立近乎自动确定受试者特定行为的技术，这是继续软组织生物医学模拟的相关性和可靠性所必需的。虽然这项研究的动机是生物医学模拟，但这些技术超越了生物力学的界限，将为工程应用提供一个更通用的确定材料特性的框架。PI和合作者将结合他们在本构建模、软组织有限元模拟、网格生成、优化和医学成像方面的经验，制定和开发从成像行为确定本构参数的方法。这项任务被描述为一个将本构模型与观测到的材料运动(包括成像、分割和去噪)相匹配的反问题。PI和合作者将利用他们以前的经验，利用类似的技术从材料变形中估计肌肉激活参数和肌肉材料属性。需要解决的顶峰问题包括用成像技术精确跟踪材料颗粒的轨迹，以及在给定的本构模型中近似软组织相对于未知材料参数的弹性平衡构型的雅可比。有了这一功能，PI和合作者将确定已建立的优化技术的适用性，并开发新的方法(这两种方法都是由前面提到的顶峰问题的成功解决产生的)。

This research involves the development of optimization techniques forthe automatic determination of the material properties of deformablesolids via modern imaging and scanning technologies (e.g. MRI, CT,etc.) with particular focus on hyper-elastic materials under largedeformation, high strain rates and often plasticity. Such materialsare characteristic of biological soft tissues (e.g. muscle, fat, skinetc.) and their determination is critical to creating accurate,subject specific simulations of the function of these anatomicalstructures. Simulation using modern computational techniques is anincreasingly reliable tool for answering many questions in biomedicalengineering ranging from basic functionality to post-surgical responseof complex regions of the anatomy. However, reliable results are onlypossible when accurate constitutive descriptions of the simulatedmaterials are available. Although much work has been done to developand determine constitutive models for biological soft tissues, mostmaterial parameters have been estimated from cadaveric specimens orfrom a small group of individuals. This is an unacceptablesimplification given the widely established variation in materialbehavior across subjects and from the material changes inherent incadaveric specimens. This research will establish techniques for thenear-automatic determination of subject specific behavior necessary tocontinue the relevance and reliability of biomedical simulation ofsoft tissues. Though motivated by biomedical simulation, thetechniques developed in this research transcend the boundaries ofbiomechanics and will provide a more general framework for determiningmaterial properties for engineering applications.The PI and collaborators will use their combined experience inconstitutive modeling, finite element simulation of soft tissues, meshgeneration, optimization and medical imaging to formulate and developmethods for the determination of constitutive parameters from imagedbehaviors. This task is formulated as an inverse problem of fitting aconstitutive model to observed material motion (involving imaging,segmentation and denoising). The PI and collaborators will draw upontheir prior experience with similar techniques for estimating musclesactivation parameters and muscle material properties from materialdeformation. The capstone problems to be solved involve accuratelytracking material particle trajectories with imaging technologies andapproximating the Jacobian of elastic equilibrium configurations ofsoft tissues with respect to unknown material parameters in a givenconstitutive model. With this functionality, the PI and collaboratorswill determine the suitability of established optimization techniquesand develop novel approaches (both engendered by the successfulsolution of previously mentioned capstone problems).