Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics

Abstract

Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

Quantitative mapping of force–pCa curves to whole‐heart contraction and relaxation

“…The multiscale modelling approach allowed them to characterize LV function sensitivities one at a time to both cellular and haemodynamic properties, highlighting the potential of this type of model to quantify the impact of possible therapeutic interventions. In other LV models, either full (Campos et al., 2020) or only passive (Cai et al., 2021; Lazarus et al., 2022) contraction mechanics were developed to study the impact of geometry, fibre orientation, passive material properties and active stress cellular properties on LV systolic and diastolic function. Different surrogate modelling approaches, including polynomial chaos expansion, K‐nearest neighbour, gradient boost decision tree, multilayer perceptron and Gaussian process regression, were used to speed up forward model evaluations for uncertainty quantification, sensitivity analysis and parameter inference in these cardiac simulation studies (Cai et al., 2021; Campos et al., 2020; Lazarus et al., 2022).…”

“…In other LV models, either full (Campos et al, 2020) or only passive (Cai et al, 2021;Lazarus et al, 2022) contraction mechanics were developed to study the impact of geometry, fibre orientation, passive material properties and active stress cellular properties on LV systolic and diastolic function. Different surrogate modelling approaches, including polynomial chaos expansion, K-nearest neighbour, gradient boost decision tree, multilayer perceptron and Gaussian process regression, were used to speed up forward model evaluations for uncertainty quantification, sensitivity analysis and parameter inference in these cardiac simulation studies (Cai et al, 2021;Campos et al, 2020;Lazarus et al, 2022). When studying myofilament calcium sensitivity using F-pCa curves, simply considering the Ca 2+ sensitivity as a stand-alone measurement is not sufficient for translation into dynamic contraction and relaxation.…”

Image-based estimation of the left ventricular cavity volume using deep learning and Gaussian process with cardio-mechanical applications

“…where 𝑎, 𝑏, 𝑎 f , 𝑏 f , 𝑎 s , 𝑏 s , 𝑎 fs , and 𝑏 fs are material constants describing the stiffness of the myocardium. In this equation, the two most significant parameters are 𝑎 and 𝑏, which are related to the isotropic response of the myocardium, while 𝑎 f and 𝑏 f as the second set of significant parameters describe the reinforced stiffness along myofibres (Lazarus et al, 2022a). The LV passive filling is mathematically formulated as a quasi-static pressure-loaded boundary-value problem, which can be solved numerically using finite element packages, e.g.…”

“…The remaining parameters in Eq. ( 4) have been kept fixed at nominal values, based on our previous global sensitivity analysis study (Lazarus et al, 2022a). The output of our emulator is the enddiastolic LV volume (in mL), which feeds into the objective function Eq.…”

Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

“…These choices are motivated by the fact that both EF and dP=dt max are commonly used mechanical biomarkers, and are usually included among the outputs of interests in SA studies in cardiac mechanics and electromechanics simulations. 23,31,88,89 Nonetheless, since Deep-HyROMnet computes the whole displacement at each time instance, any additional output, such as, for example, the wall thickening, the end-systolic pressure or the longitudinal fractional shortening, 23,88 as well as other field quantities such as the axial stresses along different directions, can be considered online without the need to rebuild the ROM, see, for example, Figure 18. This is a distinguishing feature of the proposed reduction technique, compared to recent frameworks addressing NN-based or GPE-based approximations of quantities of interest, without taking into account the approximation of the field variables involved in the output evaluations.…”