Method for the unique identification of hyperelastic material properties using full‐field measures. Application to the passive myocardium material response

Abstract

Summary Quantitative measurement of the material properties (e.g., 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 — i.e., 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, e.g., 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.

Microstructurally Anchored Cardiac Kinematics by Combining In Vivo DENSE MRI and cDTI

“…In vivo averaged I 1 (≈ 3.6) is consistent with the analytic values computed from the CDP ( $I_1^{\mathit{an}}\approx 3.5$ – Table 3). In this study, we focused on comparing I 1 and I 4 because these deformation invariants are commonly used to formulate material energy laws describing passive cardiac mechanics, e.g., [7,10]. …”

The Elastic Share of Inelastic Stress–Strain Paths of Woven Fabrics

“…The are internal parameters controlling the nonlinearity of each deformation mode. They are identified and fixed for each group of fabrics; i.e., PES-PVC and glass-PTFE, following [ 8 ] which is based on the proposed method in [ 25 ]. Thus, the final form of the nonlinear model becomes linear in the material parameters while staying nonlinear in the deformations and is obtained in the following form …”

“…As demonstrated in [ 15 ], the 4 model parameters can be initially identified as a part of the model and kept fixed for each group of fabric material, i.e., either glass-PTFE or PES-PVC, also independent from their types, see Table 1 . The main idea behind the identification of the model parameters is to minimize the deviation from the average value of the material parameters , which can be identified and computed for each individual stress–strain point [ 25 ]. Once this variation becomes minimized, the model parameters are identified and fixed for all types of a membrane material.…”

“…(c) As it will be demonstrated, the identified model parameters can be used for all types of a fabric material at different stress–strain states, despite the fact that the material response is significantly changing from an initial load cycle (LC) to the latest one at LC 1000. (d) Following the method in [ 25 ], a unique identification of material parameters may become feasible as the remaining parameters appear only linearly in the formulation and thereby, the least-square error functional in terms of the stress deviation becomes convex in the material properties , see [ 8 ]. Moreover, since the material parameters mainly act as scaling factors of each deformation mode, a quite small sensitivity on the material behavior is automatically included.…”

Real-time 3T MRI-guided cardiovascular catheterization in a porcine model using a glass-fiber epoxy-based guidewire

“…The experiments described in this MRI-guided catheterization study were part of a larger overall study aimed at identifying the material properties of the passive myocardium [20]. In the overall study, intraventricular pressure was measured to provide the LV loading condition, which is critical to compute the myocardial material properties together with displacement [21] and microstructure [22] data.…”