Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

Predicting left ventricular contractile function via Gaussian process emulation in aortic-banded rats

Cardiac contraction is the result of integrated cellular, tissue and organ function. Biophysical in silico cardiac models offer a systematic approach for studying these multi-scale interactions. The computational cost of such models is high, due to their multi-parametric and nonlinear nature. This has so far made it difficult to perform model fitting and prevented global sensitivity analysis (GSA) studies. We propose a machine learning approach based on Gaussian process emulation of model simulations using probabilistic surrogate models, which enables model parameter inference via a Bayesian history matching (HM) technique and GSA on whole-organ mechanics. This framework is applied to model healthy and aortic-banded hypertensive rats, a commonly used animal model of heart failure disease. The obtained probabilistic surrogate models accurately predicted the left ventricular pump function (R² = 0.92 for ejection fraction). The HM technique allowed us to fit both the control and diseased virtual bi-ventricular rat heart models to magnetic resonance imaging and literature data, with model outputs from the constrained parameter space falling within 2 SD of the respective experimental values. The GSA identified Troponin C and cross-bridge kinetics as key parameters in determining both systolic and diastolic ventricular function. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Hypokalemia Promotes Arrhythmia by Distinct Mechanisms in Atrial and Ventricular Myocytes

RATIONALE

Hypokalemia occurs in up to 20% of hospitalized patients and is associated with increased incidence of ventricular and atrial fibrillation. It is unclear whether these differing types of arrhythmia result from direct and perhaps distinct effects of hypokalemia on cardiomyocytes.

OBJECTIVE

To investigate proarrhythmic mechanisms of hypokalemia in ventricular and atrial myocytes.

METHODS AND RESULTS

Experiments were performed in isolated rat myocytes exposed to simulated hypokalemia conditions (reduction of extracellular [K⁺] from 5.0 to 2.7 mmol/L) and supported by mathematical modeling studies. Ventricular cells subjected to hypokalemia exhibited Ca²⁺ overload and increased generation of both spontaneous Ca²⁺ waves and delayed afterdepolarizations. However, similar Ca²⁺-dependent spontaneous activity during hypokalemia was only observed in a minority of atrial cells that were observed to contain t-tubules. This effect was attributed to close functional pairing of the Na⁺-K⁺ ATPase and Na⁺-Ca²⁺ exchanger proteins within these structures, as reduction in Na⁺ pump activity locally inhibited Ca²⁺ extrusion. Ventricular myocytes and tubulated atrial myocytes additionally exhibited early afterdepolarizations during hypokalemia, associated with Ca²⁺ overload. However, early afterdepolarizations also occurred in untubulated atrial cells, despite Ca²⁺ quiescence. These phase-3 early afterdepolarizations were rather linked to reactivation of nonequilibrium Na⁺ current, as they were rapidly blocked by tetrodotoxin. Na⁺ current-driven early afterdepolarizations in untubulated atrial cells were enabled by membrane hyperpolarization during hypokalemia and short action potential configurations. Brief action potentials were in turn maintained by ultra-rapid K⁺ current (I_Kur); a current which was found to be absent in tubulated atrial myocytes and ventricular myocytes.

CONCLUSIONS

Distinct mechanisms underlie hypokalemia-induced arrhythmia in the ventricle and atrium but also vary between atrial myocytes depending on subcellular structure and electrophysiology.

Balance of Active, Passive, and Anatomical Cardiac Properties in Doxorubicin-Induced Heart Failure

Late-onset heart failure (HF) is a known side effect of doxorubicin chemotherapy. Typically, patients are diagnosed when already at an irreversible stage of HF, which allows few or no treatment options. Identifying the causes of compromised cardiac function in this patient group may improve early patient diagnosis and support treatment selection. To link doxorubicin-induced changes in cardiac cellular and tissue mechanical properties to overall cardiac function, we apply a multiscale biophysical biomechanics model of the heart to measure the plausibility of changes in model parameters representing the passive, active, or anatomical properties of the left ventricle for reproducing measured patient phenotypes. We create representative models of healthy controls (N = 10) and patients with HF induced by (N = 22) or unrelated to (N = 25) doxorubicin therapy. The model predicts that HF in the absence of doxorubicin is characterized by a 2- to 3-fold stiffness increase, decreased tension (0–20%), and ventricular dilation (of order 10–30%). HF due to doxorubicin was similar but showed stronger bias toward reduced active contraction (10–30%) and less dilation (0–20%). We find that changes in active, passive, and anatomical properties all play a role in doxorubicin-induced cardiotoxicity phenotypes. Differences in parameter changes between patient groups are consistent with doxorubicin cardiotoxicity having a greater dependence on reduced cellular contraction and less anatomical remodeling than HF not caused by doxorubicin.

Decreasing Compensatory Ability of Concentric Ventricular Hypertrophy in Aortic-Banded Rat Hearts

The cardiac system compensates for variations in physiological and pathophysiological conditions through a dynamic remodeling at the organ, tissue, and intracellular levels in order to maintain function. However, on longer time scales following the onset of ventricular pressure overload, such remodeling may begin to inhibit physiological function and ultimately lead to heart failure. This progression from compensatory to decompensatory behavior is poorly understood, in particular owing to the absence of a unified perspective of the concomitantly remodeling subsystems. To address this issue, the present study investigates the evolution of compensatory mechanisms, in response to overload, by integrating diffusion-tensor MRI, echocardiography, and intracellular and hemodynamic measurements within consistent computational simulations of aortic-banded rat hearts. This approach allows a comparison of the relative leverage of different cardiac properties (geometry, passive mechanical stiffness, fiber configuration, diastolic and peak calcium concentrations, calcium-binding affinity, and aortic impedance) to affect cardiac contraction. Measurements indicate that, following aortic banding, an ejection fraction (EF) of 75% was maintained, relative to control rats, despite significant remodeling of the left-ventricular wall thickness (increasing by ~90% over 4 weeks). Applying our framework, we identified the left-ventricular wall thickness (concentric hypertrophy) and the intracellular calcium dynamics as playing the dominant roles in preserving EF acutely, whereas the significance of hypertrophy decreased subsequently. This trend suggests an increasing reliance on intracellular mechanisms (average increase ~50%), rather than on anatomical features (average decrease ~60%), to achieve compensation of pump function in the early phase of heart failure.

A phenomenological density-scaling approach to lamellipodial actin dynamics(†)

The integration of protein function studied in vitro in a dynamic system like the cell lamellipodium remains a significant challenge. One reason is the apparent contradictory effect that perturbations of some proteins can have on the overall lamellipodium dynamics, depending on exact conditions. Theoretical modelling offers one approach for understanding the balance between the mechanisms that drive and regulate actin network growth and decay. Most models use a ‘bottom-up’ approach, involving explicitly assembling biochemical components to simulate observable behaviour. Their correctness therefore relies on both the accurate characterization of all the components and the completeness of the relevant processes involved. To avoid potential pitfalls due to this uncertainty, we used an alternative ‘top-down’ approach, in which measurable features of lamellipodium behaviour, here observed in two different cell types (HL60 and B16-F1), directly inform the development of a simple phenomenological model of lamellipodium dynamics. We show that the kinetics of F-actin association and dissociation scales with the local F-actin density, with no explicit location dependence. This justifies the use of a simplified kinetic model of lamellipodium dynamics that yields predictions testable by pharmacological or genetic intervention. A length-scale parameter (the lamellipodium width) emerges from this analysis as an experimentally accessible probe of network regulatory processes.

Hypokalaemia induces Ca²⁺ overload and Ca²⁺ waves in ventricular myocytes by reducing Na⁺,K⁺-ATPase α₂ activity

KEY POINTS

Hypokalaemia is a risk factor for development of ventricular arrhythmias. In rat ventricular myocytes, low extracellular K(+) (corresponding to clinical moderate hypokalaemia) increased Ca(2+) wave probability, Ca(2+) transient amplitude, sarcoplasmic reticulum (SR) Ca(2+) load and induced SR Ca(2+) leak. Low extracellular K(+) reduced Na(+),K(+)-ATPase (NKA) activity and hyperpolarized the resting membrane potential in ventricular myocytes. Both experimental data and modelling indicate that reduced NKA activity and subsequent Na(+) accumulation sensed by the Na(+), Ca(2+) exchanger (NCX) lead to increased Ca(2+) transient amplitude despite concomitant hyperpolarization of the resting membrane potential. Low extracellular K(+) induced Ca(2+) overload by lowering NKA α2 activity. Triggered ventricular arrhythmias in patients with hypokalaemia may therefore be attributed to reduced NCX forward mode activity linked to an effect on the NKA α2 isoform.

ABSTRACT

Hypokalaemia is a risk factor for development of ventricular arrhythmias. The aim of this study was to determine the cellular mechanisms leading to triggering of arrhythmias in ventricular myocytes exposed to low Ko. Low Ko, corresponding to moderate hypokalaemia, increased Ca(2+) transient amplitude, sarcoplasmic reticulum (SR) Ca(2+) load, SR Ca(2+) leak and Ca(2+) wave probability in field stimulated rat ventricular myocytes. The mechanisms leading to Ca(2+) overload were examined. Low Ko reduced Na(+),K(+)-ATPase (NKA) currents, increased cytosolic Na(+) concentration and increased the Na(+) level sensed by the Na(+), Ca(2+) exchanger (NCX). Low Ko also hyperpolarized the resting membrane potential (RMP) without significant alterations in action potential duration. Experiments in voltage clamped and field stimulated ventricular myocytes, along with mathematical modelling, suggested that low Ko increases the Ca(2+) transient amplitude by reducing NKA activity despite hyperpolarization of the RMP. Selective inhibition of the NKA α2 isoform by low dose ouabain abolished the ability of low Ko to reduce NKA currents, to increase Na(+) levels sensed by NCX and to increase the Ca(2+) transient amplitude. We conclude that low Ko, within the range of moderate hypokalaemia, increases Ca(2+) levels in ventricular myocytes by reducing the pumping rate of the NKA α2 isoform with subsequent Na(+) accumulation sensed by the NCX. These data highlight reduced NKA α2 -mediated control of NCX activity as a possible mechanism underlying triggered ventricular arrhythmias in patients with hypokalaemia.

Species-dependent adaptation of the cardiac Na+/K+ pump kinetics to the intracellular Na+ concentration

The Na(+)/K(+) ATPase (NKA) plays a critical role in maintaining ionic homeostasis and dynamic function in cardiac myocytes, within both the in vivo cell and in silico models. Physiological conditions differ significantly between mammalian species. However, most existing formulations of NKA used to simulate cardiac function in computational models are derived from a broad range of experimental sources spanning many animal species. The resultant inability of these models to discern species-specific features is a significant obstacle to achieving a detailed quantitative and comparative understanding of physiological behaviour in different biological contexts. Here we present a framework for characterising the steady-state NKA current using a biophysical mechanistic model specifically designed to provide a mechanistic explanation of the NKA flux supported by self-consistent species-specific data. We thus compared NKA kinetics specific to guinea- pig and rat ventricular myocytes. We observe that the apparent binding affinity for sodium in the rat is significantly lower, whereas the overall pump cycle rate is doubled, in comparison to the guinea pig. This sensitivity of NKA to its regulatory substrates compensates for the differences in Na(+) concentrations between the cell types. NKA is thereby maintained within its dynamic range over a wide range of pacing frequencies in these two species, despite significant disparities in sodium concentration. Hence, by replacing a conventional generic NKA model with our rat-specific NKA formula into a whole-cell simulation, we have, for the first time, been able to accurately reproduce the action potential duration and the steady-state sodium concentration as functions of pacing frequency.

Mechanisms of leading edge protrusion in interstitial migration

While the molecular and biophysical mechanisms underlying cell protrusion on two-dimensional substrates are well understood, our knowledge of the actin structures driving protrusion in three-dimensional environments is poor, despite relevance to inflammation, development and cancer. Here we report that, during chemotactic migration through microchannels with 5 μm × 5 μm cross-sections, HL60 neutrophil-like cells assemble an actin-rich slab filling the whole channel cross-section at their front. This leading edge comprises two distinct F-actin networks: an adherent network that polymerizes perpendicular to cell-wall interfaces and a ‘free’ network that grows from the free membrane at the cell front. Each network is polymerized by a distinct nucleator and, due to their geometrical arrangement, the networks interact mechanically. On the basis of our experimental data, we propose that, during interstitial migration, medial growth of the adherent network compresses the free network preventing its retrograde movement and enabling new polymerization to be converted into forward protrusion.

Much of our understanding of the role of actin in cell migration is based on studies of cells moving across two-dimensional surfaces. Wilson et al. show that cells crawling in three dimensions through a narrow channel form two functionally distinct actin networks at the leading edge.

Analysis of turnover dynamics of the submembranous actin cortex

Two filament subpopulations with very different turnover rates make up the actin cortex in living cells: one with fast turnover dynamics and polymerization resulting from addition of monomers to free barbed ends, and one with slow turnover dynamics with polymerization resulting from formin-mediated filament growth.

The cell cortex is a thin network of actin, myosin motors, and associated proteins that underlies the plasma membrane in most eukaryotic cells. It enables cells to resist extracellular stresses, perform mechanical work, and change shape. Cortical structural and mechanical properties depend strongly on the relative turnover rates of its constituents, but quantitative data on these rates remain elusive. Using photobleaching experiments, we analyzed the dynamics of three classes of proteins within the cortex of living cells: a scaffold protein (actin), a cross-linker (α-actinin), and a motor (myosin). We found that two filament subpopulations with very different turnover rates composed the actin cortex: one with fast turnover dynamics and polymerization resulting from addition of monomers to free barbed ends, and one with slow turnover dynamics with polymerization resulting from formin-mediated filament growth. Our data suggest that filaments in the second subpopulation are on average longer than those in the first and that cofilin-mediated severing of formin-capped filaments contributes to replenishing the filament subpopulation with free barbed ends. Furthermore, α-actinin and myosin minifilaments turned over significantly faster than F-actin. Surprisingly, only one-fourth of α-actinin dimers were bound to two actin filaments. Taken together, our results provide a quantitative characterization of essential mechanisms under­lying actin cortex homeostasis.

Axisymmetric Optical-Trap Measurement of Red Blood Cell Membrane Elasticity

The elastic properties of the cell membrane play a crucial role in determining the equilibrium shape of the cell, as well as its response to the external forces it experiences in its physiological environment. Red blood cells are a favored system for studying membrane properties because of their simple structure: a lipid bilayer coupled to a membrane cytoskeleton and no cytoplasmic cytoskeleton. An optical trap is used to stretch a red blood cell, fixed to a glass surface, along its symmetry axis by pulling on a micron-sized latex bead that is bound at the center of the exposed cell dimple. The system, at equilibrium, shows Hookean behavior with a spring constant of 1.5×10−6 N/m over a 1–2 μm range of extension. This choice of simple experimental geometry preserves the axial symmetry of the native cell throughout the stretch, probes membrane deformations in the small-extension regime, and facilitates theoretical analysis. The axisymmetry makes the experiment amenable to simulation using a simple model that makes no a priori assumption on the relative importance of shear and bending in membrane deformations. We use an iterative relaxation algorithm to solve for the geometrical configuration of the membrane at mechanical equilibrium for a range of applied forces. We obtain estimates for the out-of-plane membrane bending modulus B≈1×10−19 Nm and an upper limit to the in-plane shear modulus H<2×10−6 N/m. The partial agreement of these results with other published values may serve to highlight the dependence of the cell’s resistance to deformation on the scale and geometry of the deformation.

Reconciling the working strokes of a single head of skeletal muscle myosin estimated from laser-trap experiments and crystal structures

Myosin generates force by a rotation of its lever arm. Crystal structures of myosin II indicate an unloaded working stroke of 10-12 nm, a range confirmed by recent x-ray interference experiments. However, when an actin filament, held between two weakly, optically trapped beads is made to interact with a single head of skeletal myosin, the bead displacements have often been reported as having a mean value of 5-6 nm, a value that is commonly interpreted as the working stroke. In general, the observed displacement is not expected to be equal to the working stroke because the kinetics of the stroke is necessarily strain-dependent: this effect biases the frequency of binding events to different actin sites so that displacements smaller than the working stroke are preferentially selected. Our analysis is tailored to current trap experiments, in which the time resolution is insufficient to detect pre-rigor states. If the preceding transitions are in equilibrium, the mean displacement is zero, contrary to observations in the presence of ATP. However, under ATP-cycling conditions, we find that the mean displacement is deflated to 0.3-0.7 of the true working stroke, depending on the equilibrium constant of the stroke and the rate at which the first myosin product state can detach from actin. The primary working stroke of processive myosin motors as measured by optical trapping is similarly uncertain.