Dynamic finite-strain modelling of the human left ventricle in health and disease using an immersed boundary-finite element method

Abstract

Detailed models of the biomechanics of the heart are important both for developing improved interventions for patients with heart disease and also for patient risk stratification and treatment planning. For instance, stress distributions in the heart affect cardiac remodelling, but such distributions are not presently accessible in patients. Biomechanical models of the heart offer detailed three-dimensional deformation, stress and strain fields that can supplement conventional clinical data. In this work, we introduce dynamic computational models of the human left ventricle (LV) that are derived from clinical imaging data obtained from a healthy subject and from a patient with a myocardial infarction (MI). Both models incorporate a detailed invariant-based orthotropic description of the passive elasticity of the ventricular myocardium along with a detailed biophysical model of active tension generation in the ventricular muscle. These constitutive models are employed within a dynamic simulation framework that accounts for the inertia of the ventricular muscle and the blood that is based on an immersed boundary (IB) method with a finite element description of the structural mechanics. The geometry of the models is based on data obtained non-invasively by cardiac magnetic resonance (CMR). CMR imaging data are also used to estimate the parameters of the passive and active constitutive models, which are determined so that the simulated end-diastolic and end-systolic volumes agree with the corresponding volumes determined from the CMR imaging studies. Using these models, we simulate LV dynamics from enddiastole to end-systole. The results of our simulations are shown to be in good agreement with subject-specific CMR-derived strain measurements and also with earlier clinical studies on human LV strain distributions.

Keywords: excitation–contraction coupling; finite element method; hyperelasticity; immersed boundary method; invariant-based constitutive model; left ventricle; magnetic resonance imaging; myocardial infarction.

Figures

Fig. 1

LV geometry reconstruction for the healthy volunteer: (a) the endocardial (blue online) and epicardial (red online) boundary segmentations and (b) the reconstructed healthy LV model.

Fig. 2

LV geometry reconstruction for the MI patient: (a) endocardial (blue online) and epicardial (red online) boundary segmentations; (b) short-axis LGE MR image slice (the enhanced bright region indicates MI); (c) long-axis LGE MR image slice and (d) reconstructed LV model contoured by the LGE image-based model of MI extent (0: unaffected healthy region; 1: reconstructed infarcted region). A 10-mm thick transition region (border zone) is assumed to lie between the unaffected (blue or right) and infarct (red or left) regions.

Fig. 3

The LV is divided into regions on selected short-axis slices: (a) the positions of the seven short-axis slices; (b) the regions defined on slices 1–5; (c) the regions defined on slices 6 and 7 and (d) the corresponding divisions of the LV wall.

Fig. 4

Illustration of boundary and loading conditions applied to the IB/FE LV models, adapted from Gao et al. (2014b). c: circumferential direction, r: radial direction, z: axial direction. LV cavity pressure loading is applied to the endocardial surface, and displacements of the basal plane are fixed in the c and z directions, therefore permitting only radial expansion. The whole computational domain is represented by the black box with zero pressure and zero tangential slip along ∂Ω, where u is the Eulerian velocity and t is the unit tangential vector.

Fig. 5

Myofibre stress–strain relationship under uni-axial tension along myofibre direction for the healthy volunteer and the MI patient, compared with results from Xi et al. (2011b) and Krishnamurthy et al. (2013).

Fig. 6

Wall deformations of the healthy LV model at end-diastole (a and c) and end-systole (b and d) superimposed on three-chamber long-axis (a and b) and a short-axis (c and d) views of the CMR cine images.

Fig. 7

Wall deformations of the diseased LV model at end-diastole (a and c) and end-systole (b and d) superimposed on three-chamber long-axis (a and b) and short-axis (c and d) views of the CMR cine images.

Fig. 8

Distributions of active tension T at end-systole in the healthy (a) and diseased (b) LV models, regional distributions of T from the base to the apex in the healthy (c) and diseased (d) LV models, and regional distribution of MI extent in the diseased LV model (e). The divisions in (d–f) are defined as in Fig. 3. The rings from outer to inner represent the slices from the base to the apex, and each slice is associated with the volumetric region consisting of the points within 5 mm of that slice plane.

Fig. 9

Distributions of fibre stress at end-systole in the healthy (a) and diseased (b) LV models, regional distributions of fibre stress from the base to the apex in the healthy (c) and diseased (d) LV models. Regional distribution of MI extent in the diseased LV model can be found in Fig. 8(e).

Fig. 10

Distributions of fibre strain at end-systole in the healthy (a) and diseased (b) LV models, regional distributions of fibre stress from the base to the apex in the healthy (c) and diseased (d) LV models. Regional distribution of MI extent in the diseased LV model can be found in Fig. 8(e).

Fig. 11

End-systolic circumferential, radial and longitudinal strain distributions in the healthy (a–c) and diseased (d–f) LV models.

Fig. 12

Average rotations along the seven short-axis slices for the healthy and diseased LV models at end-systole. Note that rotations are constrained in both model on the basal plane. The healthy volunteer is shown in blue/left, and the MI patient is shown in red/right.

Fig. 13

Flow patterns in the healthy (a) and diseased (b) LV models at systole.