Analysis of passive cardiac constitutive laws for parameter estimation using 3D tagged MRI

Abstract

An unresolved issue in patient-specific models of cardiac mechanics is the choice of an appropriate constitutive law, able to accurately capture the passive behavior of the myocardium, while still having uniquely identifiable parameters tunable from available clinical data. In this paper, we aim to facilitate this choice by examining the practical identifiability and model fidelity of constitutive laws often used in cardiac mechanics. Our analysis focuses on the use of novel 3D tagged MRI, providing detailed displacement information in three dimensions. The practical identifiability of each law is examined by generating synthetic 3D tags from in silico simulations, allowing mapping of the objective function landscape over parameter space and comparison of minimizing parameter values with original ground truth values. Model fidelity was tested by comparing these laws with the more complex transversely isotropic Guccione law, by characterizing their passive end-diastolic pressure–volume relation behavior, as well as by considering the in vivo case of a healthy volunteer. These results show that a reduced form of the Holzapfel–Ogden law provides the best balance between identifiability and model fidelity across the tests considered.

Non-invasive Model-Based Assessment of Passive Left-Ventricular Myocardial Stiffness in Healthy Subjects and in Patients with Non-ischemic Dilated Cardiomyopathy

“…The personalised models are built using comprehensive state-of-the-art clinical data [cine and 3D tagged MRI (TMRI)] which were non-invasively acquired. A reduced version of the Holzapfel–Ogden16 law is employed, in accordance with our previous works2,14 whereby it was identified as a suitable choice for parameter estimation applications based on TMRI. Important model uncertainties are systematically examined, with the objective of improving model accuracy while ensuring stiffness identifiability.…”

“…The transition from bulk measures to more comprehensive data, such as tissue displacements and strains, has enabled more elaborate approaches for estimating a larger number of parameters12,35 and heterogeneous parameter distributions 25,38. As recent advances in medical imaging offer increasingly more detail on the heart anatomy and regional kinematics, rich datasets for model personalisation and characterisation of passive parameters are becoming more accessible 2,14,39…”

“…A fundamental prerequisite is the reliable quantification of myocardial stiffness, an issue tightly coupled to the unique and accurate estimation of model parameters which was analysed in our previous study 14. Briefly, while extracting an error-minimising set of parameters is generally attainable, demonstrating that the obtained estimates are meaningful—and thus potentially clinically useful—requires ensuring parameter uniqueness.…”

“…Briefly, while extracting an error-minimising set of parameters is generally attainable, demonstrating that the obtained estimates are meaningful—and thus potentially clinically useful—requires ensuring parameter uniqueness. While previous studies have proposed a variety of techniques for obtaining unique parameter estimates,13,38 reliable parametrisation also depends on the model’s ability to accurately represent individual hearts ( model fidelity ), raising the core challenge of dealing with model uncertainties 14. Important modelling aspects such as the unstressed reference domain, the material law or appropriate boundary conditions remain relatively unknown, despite the wide range of experimental and modelling studies.…”

Special Issue: Spotlight on the Future of Cardiovascular Engineering:Frontiers and Challenges in Cardiovascular Biomechanics

“…Some of these are already under active discussion. For example, simulation run times are frequently reported, although concerns about whether long run times are practical for clinical application are frequently dismissed with a cursory assertion that computers will [27,28]. The cardiovascular fluid biomechanics community has also organized an intriguing series of computational challenges that highlight the challenges of standardizing the construction and application of PSMs [29][30][31].…”