Multiscale simulations of left ventricular growth and remodeling

Abstract

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

Keywords: Cardiac growth; Cardiomyopathy; Machine learning; Multiscale modeling; Myofiber remodeling; Sarcomeres.

Fig. 1.

Highlights on computational modeling of cardiac growth, based on volumetric growth theory and fiber remodeling, throughout the last three decades.

Fig. 2.

Schematic showing how F_e, F_g, F_e^*, and F map between configurations in volumetric growth theory. Ultimately F maps from the reference configuration β⁰ to the loaded, grown, and deformed configuration β. F_g maps from β⁰ to β^∗ representing the stress-free removal or addition of material. This configuration is not necessarily compatible, as shown via discontinuities and overlaps here. Compatibility is restored via F_e^* to a new unloaded geometry. Finally, F_e maps from the incompatible grown configuration β^∗ to the final loaded configuration β.

Fig. 3.

Schematic showing finite deformation of a soft tissue according to constrained mixture model. Each constituent α = 1, 2, …, n deposits within the current mixture with a preferred deposition stretch G^α(λ) at G&R time of λ ∈ [0, s] from its stress-free configuration of ${\kappa }_n^{\alpha }\left(\lambda \right)$. However, the constituent α may have a different deformation because all constituents are constrained to deform within a single continuum from the configuration at time of λ, κ(λ), to current configuration at time s, κ(s). Constituent-specific deformation gradient associated with constituent-specific stored energy function then can be formulated as $F_n^{\alpha \left(\lambda \right)}\left(s\right)=F\left(s\right)F{\left(\lambda \right)}^{-1}{G}^{\alpha }\left(\lambda \right)$.

Fig. 4.

Schematic showing remodeling of myofiber orientation based on the remodeling law proposed by Kroon et al. (2009b). Transition (A) describes the deformation of tissue under contractile loading. Transition (B) shows how the contractile deformation results in local loss of matrix integrity. Transition (C) depicts the restoration of matrix that remodels the orientation of myofibers in the new passive state towards the orientation of myofibers in the active state. This figure is adopted from Bovendeerd with permission (Bovendeerd 2012).

Fig. 5.

Kinetic scheme. Sites on the thin filament switch between states that are available (N_on) and unavailable (N_off) for cross-bridges to bind to. Myosin heads transition between a super-relaxed detached state (M_SRX), a disordered-relaxed detached state (M_DRX), and a single attached force-generating state (M_FG). J terms indicate fluxes between different states.

Fig. 6.

Multiscale patient-specific modeling scheme for hypertrophic cardiomyopathy (HCM). A patient’s genetic data drives the model properties of the sarcomere mechanics and determines the HCM mutations. Cardiac magnetic resonance images (MRI) form the patient-specific geometry of the heart for computational modeling. A multiscale model of HCM then predicts the progression of cardiac growth and remodeling (G&R) in response to specific mutations associated with HCM. The bi-ventricular scheme of the heart for “model of cardiac mechanics and growth” subfigure is adopted from Sack et al. with permission (Sack et al. 2018). The schematic subfigure for “model of myofiber remodeling” is adopted from Washio et al. with permission (Washio et al. 2016).