Improved identifiability of myocardial material parameters by an energy-based cost function

Abstract

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were and (, , ) for the HF cases and and (, , ) for the healthy case.

Solution to the Unknown Boundary Tractions in Myocardial Material Parameter Estimations

“…In this study we focus on C 1 -α estimation (as they represent the main direction of coupling in the Guccione model [12]) and assume the anisotropy parameters are fixed to the ground truth values (see Section 2.2), following a common approach (see more in [9]). This assumption is revisited in the sensitivity analysis (Section 2.6).…”

“…Parameter estimation in this work is based on previous research [9], where unique parameter estimation was achieved with the use of an energy-based cost function (CF), f EC , that allowed determination of the α parameter. This CF used the principle of energy conservation (EC), dictating that the work of internal stresses inside the tissue (W int ) stored as elastic energy and the external work of external forces (W ext ) are equal, where assumptions of quasi-static loading and absence of residual active tension in the diastolic window of relevance apply.…”

“…Expressing the principle of virtual work over 2 diastolic frames DF 1 and DF 2 , the modified energy-based CF f V W can then be expressed as in Eq. (9).…”

“…Arguably, the expression of energy conservation can provide a richer metric in terms of information than the point by point comparison of a distance or strain based metric, especially in the context of material parameter estimation. And it has been shown to solve the lack of identifiability of material parameters of the myocardium [9,8], thus having the potential of rendering a more accurate parameter estimation pipeline for diagnostic and prognostic purposes. One of the limitations of this approach is that it requires the estimation of the work at the myocardial boundaries and the strain energy stored, tasks that are challenging when external loads are unknown, especially at the base which deforms extensively within the cardiac cycle.…”

Model order reduction for left ventricular mechanics via congruency training

“…Alternative strategies have proposed training purely statistical models (e.g., Gaussian Process regressions [25]) on a relatively limited number of high-resolution runs (e.g., see [26, 27] for applications in diastolic filling). Once fitted to a sampled training set, statistical models can be used as efficient surrogates for the computationally expensive simulations.…”