Parameterizing the Passive Mechanics of the Heart

Published in Biomechanics and Modeling in Mechanobiology (available here).

Patient-specific modelling of cardiac mechanics has evolved into a powerful tool for assessing cardiac function and pathology. Its joint use with novel 3D tagged MRI data which provide non-invasive quantitative information on regional myocardial motion enables quantification of model constitutive parameters. These passive constitutive parameters often describe intrinsic properties of the myocardium and could therefore be used as clinical biomarkers of disease. As a result, there is a strong need for unique and accurate parameter estimates, an increasingly challenging task as the model complexity increases to better describe the tissue’s passive behavior.

Figure 1: Workflow followed for the study of practical identifiability using 3D tags. The in silico testing protocol is presented in blue, while in red is the pipeline followed in the in vivo case.

Figure 2: Extracted myocardial motion applied on an end-diastolic mesh

In this work, we aim to assist the choice of an appropriate cardiac constitutive law, able to accurately capture the tissue behavior while having uniquely identifiable parameters tunable from the available clinical data. Specifically, we compare the practical identifiability of progressively more complex models often used in cardiac mechanics applications, using 3D tagged MRI as the data source. The practical identifiability of each law is examined  using synthetic 3D tags, following the workflow described in figure 1. For each of the laws considered, synthetic 3D tags are generated directly from diastolic filling simulations. The myocardial motion is then extracted (figure 2) and compared with deformation from simulations with varying parameter combinations (parameter sweeps), providing the parameter estimates as well as the landscape of the objective function over the parameter space. Within this controlled in silico environment we are able to quantify the accuracy of the parameter estimates, examine the identifiability of each law and assess the potential of using 3D tagged MRI in patient-specific applications.

Model fidelity for the laws considered is tested  through comparisons with the more complex and widely used Gucccione law, and by comparing their passive end-diastolic pressure-volume response with the empirical Klotz curve (figure 3).

Figure 3: Typical EDPVR curves for the constitutive laws considered and ground truth Klotz curve.

Our study verifies the reported coupling between the parameters of the Guccione law, suggesting the need for a law with better identifiability characteristics. The Neohookean and a fiber-enhanced version of it are both shown to have practically identifiable parameters; however the Neohookean model is unable to reproduce physiological cardiac deformations and both are incapable of generating physiological pressure-volume relations. A two-parameter version of the Holzapfel- Ogden model is shown to combine practical identifiability with adequate representation of heart function and pressure-volume relations. Finally, its application on an in vivo case of a healthy volunteer where good identifiabilty characteristics are maintained, suggests that the reduced Holzapfel-Ogden law provides a sensible choice for patient specific applications with 3D tagged MRI.