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

Abstract

Patient-specific modelling has emerged as a tool for studying heart function, demonstrating the potential to provide non-invasive estimates of tissue passive stiffness. However, reliable use of model-derived stiffness requires sufficient model accuracy and unique estimation of model parameters. In this paper we present personalised models of cardiac mechanics, focusing on improving model accuracy, while ensuring unique parametrisation. The influence of principal model uncertainties on accuracy and parameter identifiability was systematically assessed in a group of patients with dilated cardiomyopathy ([Formula: see text]) and healthy volunteers ([Formula: see text]). For all cases, we examined three circumferentially symmetric fibre distributions and two epicardial boundary conditions. Our results demonstrated the ability of data-derived boundary conditions to improve model accuracy and highlighted the influence of the assumed fibre distribution on both model fidelity and stiffness estimates. The model personalisation pipeline-based strictly on non-invasive data-produced unique parameter estimates and satisfactory model errors for all cases, supporting the selected model assumptions. The thorough analysis performed enabled the comparison of passive parameters between volunteers and dilated cardiomyopathy patients, illustrating elevated stiffness in diseased hearts.

Keywords: Model uncertainties; Myocardium; Parameter uniqueness; Patient-specific modelling; Stiffness.

Figure 1

Workflow followed for the development and analysis of personalised diastolic heart models. Following spatial registration of images, segmentations of end-diastolic cine images were used to create an LV mesh, on which motion extracted from TMRI was propagated through the cardiac cycle. Personalised models were driven by extracted cavity volumes, while data-derived boundary conditions were applied on the basal and epicardial boundaries. Finally, parameter estimates were obtained through minimisation.

Figure 2

$\mathcal{J}$ over the parameter ratio $\mathit{\gamma }$ for V5, for $\mathit{\theta }=\{{50}^{\circ },{60}^{\circ },{70}^{\circ }\}$ and NT BC / RV BC. Also presented are data-derived (mesh lines) and simulated (surface) end-diastolic states, with colour showing the error magnitude in metres.

Figure 3

Model error (minimum value of the objective function) ${\mathcal{J}}_{\min }$ across fibre angle $\mathit{\theta }$, using NT BC and RV BC, for all the volunteers (in black) and DCM patients (in grey).

Figure 4

Effect of fibre distribution on (left) model error and (right) parameter ratio estimates, when the RV BC is employed. Here, normalised magnitudes are used for the objective function and parameter ratio estimates ($\widehat{f}=\frac{f(\mathit{\theta })-minf(\mathit{\theta })}{maxf(\mathit{\theta })-minf(\mathit{\theta })}$) and bars show average values over the volunteer and patient groups.

Figure 5

Objective function $\mathcal{J}$ over the parameter ratio $\mathit{\gamma }$, with three different data frames (end-systolic (ES), the second and fourth after ES) assumed as the reference, for (left) V1 and (right) P1. Bisected meshes present ES (grey) and ES+4 (red) geometries.

Figure 6

Comparison of data-derived metrics between the volunteer and patient groups. Red lines show the median, the boxes’ edges denote 25th and 75th percentiles, while black lines show extreme data points.

Figure 7

(a) Parameter estimates ($\mathit{\gamma }$, a and $a_{\mathrm{f}}$) for the volunteers and patients, along with the simulated end-diastolic pressure, ${\mathit{\lambda }}_{\ell }^{\mathrm{ED}}$. (b) Comparison of (top) isotropic parameter a and (bottom) fibre parameter $a_{\mathrm{f}}$ between the volunteer and patient groups.