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

该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发展。特别关注在大变形、高应变率和塑性条件下的超弹性材料。 这些材料是生物软组织（例如肌肉、脂肪、皮肤等）的特征。并且它们的确定对于创建这些解剖结构的功能的准确的、对象特定的模拟是关键的。 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，可靠的结果是可能的，只有当准确的本构描述的模拟材料是可用的。 虽然已经做了大量的工作来开发和确定生物软组织的本构模型，大多数材料参数已经估计从尸体标本或从一小群人。 这是一个不可接受的简化，因为在不同的学科和从材料变化固有的尸体标本中广泛建立的材料行为的变化。 本研究将建立耳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和合作者将利用他们在本构建模，软组织有限元模拟，网格生成，优化和医学成像，制定和发展的方法，从imagedbehaviors的本构参数的确定。该任务被公式化为将本构模型拟合到观察到的材料运动的逆问题（涉及成像、分割和去噪）。 PI和合作者将利用他们先前的经验，通过材料变形估计肌肉激活参数和肌肉材料特性。 要解决的顶点问题包括利用成像技术精确跟踪材料颗粒的运动轨迹，以及在给定的本构模型中近似软组织弹性平衡构型相对于未知材料参数的雅可比矩阵。 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（两者都是通过成功解决前面提到的顶点问题而产生的）。

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).