Model Development for Soft Tissue Biomechanics by Full-Field Characterization and Variational System Identification

每年有数十万人遭受软组织损伤，需要手术重建。前十字韧带(ACL)损伤/断裂是运动员最常见的损伤。值得注意的是，与男性相比，相对风险系数为4-6的女性的伤害率更高，而在军事训练中，这一比例上升到10。为了在几年内使替代或工程化组织的移植有效且不会对患者造成伤害，能够准确地表征其机械性能以及开发其机械性能的计算模型是重要的。这个项目将通过新的实验技术解决表征方面的挑战，这些技术可以绘制出膝关节韧带和肌腱标本每一点的变形情况。开发准确模型的问题将通过进一步发展机器学习的最新进展来解决，机器学习可以使用三维数据来识别最合适的模型。该项目将提供基本知识，使修复和替换膝关节和其他关节的韧带和肌腱的整形外科手术取得进展。本项目中使用的实验和机器学习方法将被转化为针对高中生的教育模块，并旨在吸引这些学生学习工程和计算。本项目研究了一种新的、全三维的软材料表征和本构建模方法。实验方法包括在磁场中进行原位机械加载，在整个试件体积中产生有限变形张量场。这与我们最近在反向建模方面的计算进展相结合，以从一系列可接受的候选模型中推断出最能代表全场变形数据的软组织力学本构模型，具有简洁的表示、准确的系数和不确定性量化。这种新颖的方法组合克服了传统实验中识别软组织材料属性的挑战，传统实验依赖于规则形状的测试样本上均匀的、主要是一维的变形假设。在这项工作中，由于可用的全三维有限应变张量场，可以用更少的形变状态来表征不规则形状和边界。推理技术从运算符的库中组装最优本构表示，不受限制地仅确定预先选择的模型的系数。全场方法使得能够表征膝关节的软组织，并通过置信限和不确定性量化来推断其机械响应的物理上最合适和简明的数学模型。这些模型被合并到膝关节的计算模型中，该模型可以准确地模拟损伤导致的负荷，并在损伤导致的变形过程中这些组织中的完整应变和应力场。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Each year hundreds of thousands of people suffer soft tissue injuries that require surgical reconstruction. Anterior Cruciate Ligament (ACL) damage/rupture is the most common injury in athletic individuals. Notably, injury rates are higher in women with a relative risk factor of 4-6 compared to men, and this rises to 10 for women in military training. For grafts of replacement or engineered tissue to be effective and not harmful to the patient in a few years, it is important to be able to precisely characterize their mechanical properties, as well as to develop computational models of their mechanical performance. This project will address the challenge of characterization via novel experimental techniques that can map out the deformation at every point in specimens of ligaments and tendons of the knee. The problem of developing accurate models will be addressed by furthering recent advances in machine learning that can use the three-dimensional data to identify the most appropriate model. This project will provide fundamental knowledge that will enable advances in orthopedic surgery for repair and replacement of ligaments and tendons of the knee and other joints. Experimental and machine learning methods used in this project will be translated into educational modules aimed at high school students and designed to attract these students to study engineering and computation. A new, fully three-dimensional approach to soft material characterization and constitutive modeling is studied in this project. The experimental approach involves in situ mechanical loading in a magnetic field, yielding the finite deformation tensor field throughout the volume of the specimen. This has been coupled with our recent computational advances in inverse modeling to infer the soft tissue mechanics constitutive model that best represents full-field deformation data, from a spectrum of admissible candidate models, with parsimonious representation, accurate coefficients, and uncertainty quantification. This novel combination of approaches overcomes the challenges of identifying material properties of soft tissue in traditional experiments that rely on the assumption of uniform, largely one-dimensional, deformation over regularly shaped test specimens. In this work, characterization of irregular shapes and boundaries is possible with a reduced number of deformation states due to the available full, three-dimensional, finite strain tensor field. Inference techniques assemble the optimal constitutive representation from a library of operators without restriction to only determining the coefficients of a pre-selected model. The full-field approach makes it possible to characterize soft tissues of the knee and infer the physically best-suited and parsimonious mathematical models of their mechanical responses with confidence bounds and uncertainty quantification. Those models are incorporated into computational models of the knee that can simulate injury-inducing loading accurately and with the full strain and stress fields in these tissues during injury-inducing deformations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.