Optimization Framework to Identify Constitutive Law Parameters of the Human Heart

Abstract

Over the last decades, computational models have been applied in in-silico simulations of the heart biomechanics. These models depend on input parameters. In particular, four parameters are needed for the constitutive law of Guccione et al., a model describing the stress-strain relation of the heart tissue. In the literature, we could find a wide range of values for these parameters. In this work, we propose an optimization framework which identifies the parameters of a constitutive law. This framework is based on experimental measurements conducted by Klotz et al.. They provide an end-diastolic pressure-volume relationship. We applied the proposed framework on one heart model and identified the following elastic parameters to optimally match the Klotz curve: C=313 Pa, bf=17.8, bt=7.1and bft=12A. In general, this approach allows to identify optimized parameters for a constitutive law, for a patient-specific heart geometry. The use of optimized parameters will lead to physiological simulation results of the heart biomechanics and is therefore an important step towards applying computational models in clinical practice.

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

“…Parameters for the constitutive model are mostly chosen manually [94] by utilizing the empirical end-diastolic pressure-volume relation (EDPVR) described by Klotz et al [95] as a fitting target. In Kovacheva et al [43], the constitutive parameters were determined by solving an optimization problem using a gradient-free method: the distance between the simulated EDPVR and the one proposed by Klotz et al was minimized together with an additional condition imposed on the unloaded volume. The latter volume relation was again proposed by Klotz et al However, values from different sources contradict each other [96].…”

“…In the mechanical model, myocardial tissue in the atria and ventricles was modeled as a transversely isotropic material as defined in Equation ( 4). These parameters were determined using the method proposed by Kovacheva et al [43] to match the empirical EDPVR of Klotz et al [95]. Purely passive tissue was modeled as an isotropic Neo-Hookean solid using different material parameters.…”

“…To make these heart models comparable to each other, universal coordinate systems have been proposed for the atria [40] and the ventricles [41,42]. Furthermore, we can build on already existing pipelines for the personalization of passive mechanical behavior of the heart [43,44], ventricular afterload models [45], and cardiac electrophysiology based on electrocardiograms [46][47][48][49] or electroanatomical mapping [50,51].…”

“…In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart building on previous work in cardiac mechanics [25,31,43,[52][53][54][55] and cardiac electrophysiology [49,[56][57][58][59][60]. We parameterize and use state-of-the-art myofilament models based on human physiology to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles.…”

Causes of Altered Ventricular Mechanics in Hypertrophic Cardiomyopathy—an In-Silico Study

“…We varied the input parameters of the passive force model (described in The Numerical Solver ) which determines the tissue stiffness. To identify the parameters of the passive force model for the control case, we used a method based on the pressure volume relation of LV as described previously [25] and obtained the following parameters for the Guccione model: C = 309 Pa, b f = 17.8, b t = 7.1 and b f t = 12.4. In HCM myocardium, Villemain et al [5] measured a five fold increase of the stiffness compared to controls.…”