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

本研究涉及通过现代成像和扫描技术（例如MRI， CT等）自动确定可变形固体材料特性的优化技术的开发，特别关注大变形，高应变率和通常塑性的超弹性材料。这些材料是生物软组织（如肌肉、脂肪、皮肤等）的特征，它们的测定对于创建这些解剖结构功能的准确、受试者特定模拟至关重要。使用现代计算技术的模拟是回答生物医学工程中从基本功能到复杂解剖区域的术后反应等许多问题的越来越可靠的工具。然而，只有当模拟材料的准确本构描述可用时，才有可能得到可靠的结果。尽管已经做了很多工作来开发和确定生物软组织的本构模型，但大多数材料参数都是从尸体标本或一小群个体中估计出来的。这是一个不可接受的暗示，因为材料在不同对象之间的行为存在广泛的差异，并且材料的变化来自于室内标本的固有变化。本研究将建立近乎自动确定受试者特定行为的技术，以继续软组织生物医学模拟的相关性和可靠性。虽然受到生物医学模拟的启发，但本研究中开发的技术超越了生物力学的界限，并将为确定工程应用中的材料特性提供更通用的框架。PI和合作者将利用他们的非本构建模、软组织有限元模拟、网格生成、优化和医学成像的综合经验，制定和开发从成像行为确定本构参数的方法。该任务是将本构模型拟合到观察到的材料运动（包括成像，分割和去噪）的反问题。PI和合作者将利用他们之前的经验，利用类似的技术来估计肌肉激活参数和肌肉材料的变形特性。要解决的关键问题包括用成像技术精确跟踪材料颗粒轨迹，以及在给定的本构模型中近似未知材料参数下软组织弹性平衡构型的雅可比矩阵。有了这个功能，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（两者都是由前面提到的顶点问题的成功解决方案产生的）。

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).