Perotti Luigi E, Ponnaluri Aditya V S, Krishnamoorthi Shankarjee, Balzani Daniel, Ennis Daniel B, Klug William S
Department of Radiological Sciences and Department of Bioengineering, University of California, Los Angeles, USA.
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, USA.
Int J Numer Method Biomed Eng. 2017 Nov;33(11). doi: 10.1002/cnm.2866. Epub 2017 May 30.
Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.
对生物组织的材料特性（如刚度）进行定量测量有望成为一种强大的诊断工具。目前文献中有几种估计材料刚度的方法，我们通过构建一个能唯一确定材料特性的框架来拓展这项工作。我们设计了一种处理全场位移数据的方法，即假设由于外力产生的位移场在感兴趣物体的边界和内部都是已知的，并寻找能在模型中使内力和外力平衡的刚度参数。对于体内应用，位移数据可通过磁共振成像在临床上获取，而力可从压力测量中计算得出，例如通过导管插入术。我们概述了一组条件，在这些条件下最小二乘力误差目标函数是凸的，从而能唯一确定材料特性。我们框架的一个重要组成部分是一种新的数值策略，用于制定在材料特性方面呈线性的多凸材料能量定律，并提供对现有实验数据的一种最优描述。我们方法的一个成果是对所确定材料特性的可靠性进行分析，即使对于那些不允许唯一特性识别的材料定律也是如此。最后，我们在材料点使用被动心肌实验数据评估我们的方法，并通过模拟左心室被动充盈的计算机实验展示其在识别心肌刚度方面的应用。
