An Optimization Framework to Personalize Passive Cardiac Mechanics

TL;DR

This work presents a nested inverse finite element analysis (iFEA) framework to personalize passive cardiac mechanics from time-resolved CT data, estimating both material parameters and the stress-free configuration via outer optimization and inner Sellier iterations, respectively. It employs stabilized variational multiscale FE formulations with orthotropic Holzapfel-Ogden and Guccione-McCulloch constitutive laws to simulate biventricle and left atrial mechanics under physiologic loading. The framework is validated on a healthy subject and three HOCM patients, showing strong agreement with image-derived cavity volumes and displacements, while revealing sensitivity to fiber orientation and the choice of optimization method (GA/BO robust vs LM sensitive). This approach enables patient-specific assessment of myocardial mechanics and holds potential for personalized diagnosis, prognosis, and treatment planning, with future work extending to active contraction and larger subject cohorts.

Abstract

Personalized cardiac mechanics modeling is a powerful tool for understanding the biomechanics of cardiac function in health and disease and assisting in treatment planning. However, current models are limited to using medical images acquired at a single cardiac phase, often limiting their applicability for processing dynamic image acquisitions. This study introduces an inverse finite element analysis (iFEA) framework to estimate the passive mechanical properties of cardiac tissue using time-dependent medical image data. The iFEA framework relies on a novel nested optimization scheme, in which the outer iterations utilize a traditional optimization method to best approximate material parameters that fit image data, while the inner iterations employ an augmented Sellier's algorithm to estimate the stress-free reference configuration. With a focus on characterizing the passive mechanical behavior, the framework employs structurally based anisotropic hyperelastic constitutive models and physiologically relevant boundary conditions to simulate myocardial mechanics. We use a stabilized variational multiscale formulation for solving the governing nonlinear elastodynamics equations, verified for cardiac mechanics applications. The framework is tested in myocardium models of biventricle and left atrium derived from cardiac phase-resolved computed tomographic (CT) images of a healthy subject and three patients with hypertrophic obstructive cardiomyopathy (HOCM). The impact of the choice of optimization methods and other numerical settings, including fiber direction parameters, mesh size, initial parameters for optimization, and perturbations to optimal material parameters, is assessed using a rigorous sensitivity analysis. The performance of the current iFEA is compared against an assumed power-law-based pressure-volume relation, typically used for single-phase image acquisition.

Figures (17)

• Figure 1: Workflow for patient-specific modeling of myocardial mechanics. Time-dependent 3D-CT images are used as the starting point. The myocardium is segmented at different phases of the cardiac cycle, either manually using SimVascular and Meshixer (Autodesk Inc.),vedula2017methodbaumler2020fluid or using a machine learning approach based on deep neural networks (DNN).kong2023learning An optimization framework is then applied to estimate the stress-free configuration and the passive material parameters specific to the patient's model. (iFEA: inverse finite element analysis; EDV: end-diastolic volume; ESV: end-systolic volume;)
• Figure 2: Time-varying representative hemodynamic pressure (top) and cavity volumes (center) for the control subject. The pressure profiles are adapted from M.E. Klingensmith et al.klingensmith2008washington The cavity volumes for each chamber are obtained by applying HeartDeformNet, a DNN-based automatic cardiac segmentation toolkit.kong2023learning The manually segmented myocardium of the biventricle and left atrium (LA) is highlighted in the time interval of interest to simulate passive mechanics (bottom).
• Figure 3: Patient-specific myocardium models and fiber orientations of the (a) biventricle and (b) left atrium (LA) from a healthy subject, along with the boundary conditions used for the finite element simulations. For the biventricular model (a), hemodynamic pressure is applied on the left and right endocardial surfaces. Robin boundary conditions are applied on the basal plane and the epicardial surface to account for the effect of pericardium.pfaller2019importance For the LA model (b), pressure is applied on the endocardial surface as a Neumann boundary condition, while Robin boundary conditions are applied on the pulmonary venous sections and the epicardial surface.
• Figure 4: Inverse FEA using a nested optimization scheme to estimate the stress-free configuration (inner loop) using augmented Sellier's method and the best-fit material parameters (outer loop).
• Figure 5: (a) Selected landmarks on the biventricle geometry, among which three are selected from the left ventricle and three from the right ventricle. (b) Sellier’s method to determine the stress-free reference configuration by iteratively subtracting the difference in nodal displacements between the FEA-predicted deformed configuration and the image-based myocardium model at its relaxed state from the reference configuration. The deformed configuration is obtained by loading the myocardium with the pressure at the relaxed state using a forward FEA simulation. A relaxed state is defined, for convenience, as the diastasis phase ($\sim$70% R-R) for the biventricle or the mid-systolic phase ($\sim$20% R-R) for LA.

Theorems & Definitions (3)

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