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.

Influence of atrial contraction dynamics on cardiac function.

In recent years, there has been a move from monoventricular or biventricular models of the heart, to more complex models that incorporate the electromechanical function in all 4 chambers. However, the biophysical foundation is still underdeveloped, with most work in atrial cellular models having focused on electrophysiological properties. Here, we present a biophysical model of human atrial contraction at body temperature and use it to study the effects of atrial contraction on whole organ function and a study of the effects of remodelling due to atrial fibrillation on atrial and ventricular function.

A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes.

Experimental data from human cardiac myocytes at body temperature is crucial for a quantitative understanding of clinically relevant cardiac function and development of whole-organ computational models. However, such experimental data is currently very limited. Specifically, important measurements to characterize changes in tension development in human cardiomyocytes that occur with perturbations in cell length are not available. To address this deficiency, in this study we present an experimental data set collected from skinned human cardiac myocytes, including the passive and viscoelastic properties of isolated myocytes, the steady-state force calcium relationship at different sarcomere lengths, and changes in tension following a rapid increase or decrease in length, and after constant velocity shortening. This data set is, to our knowledge, the first characterization of length and velocity-dependence of tension generation in human skinned cardiac myocytes at body temperature. We use this data to develop a computational model of contraction and passive viscoelasticity in human myocytes. Our model includes troponin C kinetics, tropomyosin kinetics, a three-state crossbridge model that accounts for the distortion of crossbridges, and the cellular viscoelastic response. Each component is parametrized using our experimental data collected in human cardiomyocytes at body temperature. Furthermore we are able to confirm that properties of length-dependent activation at 37°C are similar to other species, with a shift in calcium sensitivity and increase in maximum tension. We revise our model of tension generation in the skinned isolated myocyte to replicate reported tension traces generated in intact muscle during isometric tension, to provide a model of human tension generation for multi-scale simulations. This process requires changes to calcium sensitivity, cooperativity, and crossbridge transition rates. We apply this model within multi-scale simulations of biventricular cardiac function and further refine the parametrization within the whole organ context, based on obtaining a healthy ejection fraction. This process reveals that crossbridge cycling rates differ between skinned myocytes and intact myocytes.

A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges.

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca(2+)], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU's unblocking. (4) Myosin affinity for short (1-4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca(2+)] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k(tr) is explained by transient blocking of RU's by a temporary decrease in XB-RU effects.

Towards causally cohesive genotype-phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries.

A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype-phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype-phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.

Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour.

Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

Quantifying inter-species differences in contractile function through biophysical modelling.

Animal models and measurements are frequently used to guide and evaluate clinical interventions. In this context, knowledge of inter-species differences in physiology is crucial for understanding the limitations and relevance of animal experimental assays for informing clinical applications. Extensive effort has been put into studying the structure and function of cardiac contractile proteins and how differences in these translate into the functional properties of muscles. However, integrating this knowledge into a quantitative description, formalising and highlighting inter-species differences both in the kinetics and in the regulation of physiological mechanisms, remains challenging. In this study we propose and apply a novel approach for the quantification of inter-species differences between mouse, rat and human. Assuming conservation of the fundamental physiological mechanisms underpinning contraction, biophysically based computational models are fitted to simulate experimentally recorded phenotypes from multiple species. The phenotypic differences between species are then succinctly quantified as differences in the biophysical model parameter values. This provides the potential of quantitatively establishing the human relevance of both animal-based experimental and computational models for application in a clinical context. Our results indicate that the parameters related to the sensitivity and cooperativity of calcium binding to troponin C and the activation and relaxation rates of tropomyosin/crossbridge binding kinetics differ most significantly between mouse, rat and human, while for example the reference tension, as expected, shows only minor differences between the species. Hence, while confirming expected inter-species differences in calcium sensitivity due to large differences in the observed calcium transients, our results also indicate more unexpected differences in the cooperativity mechanism. Specifically, the decrease in the unbinding rate of calcium to troponin C with increasing active tension was much lower for mouse than for rat and human. Our results also predicted crossbridge binding to be slowest in human and fastest in mouse.

Improving the stability of cardiac mechanical simulations.

In the field of cardiac modeling, the mechanical action of the heart is often simulated using finite element methods. These simulations are becoming increasingly challenging as the computational domain is customized to a patient's anatomy, within which large heterogeneous tension gradients are generated via biophysical cell models which drive simulations of the cardiac pump cycle. The convergence of nonlinear solvers in simulations of large deformation mechanics depends on many factors. When extreme stress or irregular deformations are modeled, commonly used numerical methods can often fail to find a solution, which can prevent investigation of interesting parameter variations or use of models in a clinical context with high standards for robustness. This paper outlines a novel numerical method that is straightforward to implement and which significantly improves the stability of these simulations. The method involves adding a compressibility penalty to the standard incompressible formulation of large deformation mechanics. We compare the method's performance when used with both a direct discretization of the equations for incompressible solid mechanics, as well as the formulation based on an isochoric/deviatoric split of the deformation gradient. The addition of this penalty decreases the tendency for solutions to deviate from the incompressibility constraint, and significantly improves the ability of the Newton solver to find a solution. Additionally, our method maintains the expected order of convergence under mesh refinement, has nearly identical solutions for the pressure-volume relations, and stabilizes the solver to allow challenging simulations of both diastolic and systolic function on personalized patient geometries.

Computational modeling of Takotsubo cardiomyopathy: effect of spatially varying ß-adrenergic stimulation in the rat left ventricle.

In Takotsubo cardiomyopathy, the left ventricle shows apical ballooning combined with basal hypercontractility. Both clinical observations in humans and recent experimental work on isolated rat ventricular myocytes suggest the dominant mechanisms of this syndrome are related to acute catecholamine overload. However, relating observed differences in single cells to the capacity of such alterations to result in the extreme changes in ventricular shape seen in Takotsubo syndrome is difficult. By using a computational model of the rat left ventricle, we investigate which mechanisms can give rise to the typical shape of the ventricle observed in this syndrome. Three potential dominant mechanisms related to effects of ß-adrenergic stimulation were considered: apical-basal variation of calcium transients due to differences in L-type and sarco(endo)plasmic reticulum Ca(2+)-ATPase activation, apical-basal variation of calcium sensitivity due to differences in troponin I phosphorylation, and apical-basal variation in maximal active tension due to, e.g., the negative inotropic effects of p38 MAPK. Furthermore, we investigated the interaction of these spatial variations in the presence of a failing Frank-Starling mechanism. We conclude that a large portion of the apex needs to be affected by severe changes in calcium regulation or contractile function to result in apical ballooning, and smooth linear variation from apex to base is unlikely to result in the typical ventricular shape observed in this syndrome. A failing Frank-Starling mechanism significantly increases apical ballooning at end systole and may be an important additional factor underpinning Takotsubo syndrome.

A computational pipeline for quantification of mouse myocardial stiffness parameters.

The mouse is an important model for theoretical-experimental cardiac research, and biophysically based whole organ models of the mouse heart are now within reach. However, the passive material properties of mouse myocardium have not been much studied. We present an experimental setup and associated computational pipeline to quantify these stiffness properties. A mouse heart was excised and the left ventricle experimentally inflated from 0 to 1.44kPa in eleven steps, and the resulting deformation was estimated by echocardiography and speckle tracking. An in silico counterpart to this experiment was built using finite element methods and data on ventricular tissue microstructure from diffusion tensor MRI. This model assumed a hyperelastic, transversely isotropic material law to describe the force-deformation relationship, and was simulated for many parameter scenarios, covering the relevant range of parameter space. To identify well-fitting parameter scenarios, we compared experimental and simulated outcomes across the whole range of pressures, based partly on gross phenotypes (volume, elastic energy, and short- and long-axis diameter), and partly on node positions in the geometrical mesh. This identified a narrow region of experimentally compatible values of the material parameters. Estimation turned out to be more precise when based on changes in gross phenotypes, compared to the prevailing practice of using displacements of the material points. We conclude that the presented experimental setup and computational pipeline is a viable method that deserves wider application.

Insight into model mechanisms through automatic parameter fitting: a new methodological framework for model development.

BACKGROUND: Striking a balance between the degree of model complexity and parameter identifiability, while still producing biologically feasible simulations using modelling is a major challenge in computational biology. While these two elements of model development are closely coupled, parameter fitting from measured data and analysis of model mechanisms have traditionally been performed separately and sequentially. This process produces potential mismatches between model and data complexities that can compromise the ability of computational frameworks to reveal mechanistic insights or predict new behaviour. In this study we address this issue by presenting a generic framework for combined model parameterisation, comparison of model alternatives and analysis of model mechanisms. RESULTS: The presented methodology is based on a combination of multivariate metamodelling (statistical approximation of the input-output relationships of deterministic models) and a systematic zooming into biologically feasible regions of the parameter space by iterative generation of new experimental designs and look-up of simulations in the proximity of the measured data. The parameter fitting pipeline includes an implicit sensitivity analysis and analysis of parameter identifiability, making it suitable for testing hypotheses for model reduction. Using this approach, under-constrained model parameters, as well as the coupling between parameters within the model are identified. The methodology is demonstrated by refitting the parameters of a published model of cardiac cellular mechanics using a combination of measured data and synthetic data from an alternative model of the same system. Using this approach, reduced models with simplified expressions for the tropomyosin/crossbridge kinetics were found by identification of model components that can be omitted without affecting the fit to the parameterising data. Our analysis revealed that model parameters could be constrained to a standard deviation of on average 15% of the mean values over the succeeding parameter sets. CONCLUSIONS: Our results indicate that the presented approach is effective for comparing model alternatives and reducing models to the minimum complexity replicating measured data. We therefore believe that this approach has significant potential for reparameterising existing frameworks, for identification of redundant model components of large biophysical models and to increase their predictive capacity.

An automatic service for the personalization of ventricular cardiac meshes.

Computational cardiac physiology has great potential to improve the management of cardiovascular diseases. One of the main bottlenecks in this field is the customization of the computational model to the anatomical and physiological status of the patient. We present a fully automatic service for the geometrical personalization of cardiac ventricular meshes with high-order interpolation from segmented images. The method is versatile (able to work with different species and disease conditions) and robust (fully automatic results fulfilling accuracy and quality requirements in 87% of 255 cases). Results also illustrate the capability to minimize the impact of segmentation errors, to overcome the sparse resolution of dynamic studies and to remove the sometimes unnecessary anatomical detail of papillary and trabecular structures. The smooth meshes produced can be used to simulate cardiac function, and in particular mechanics, or can be used as diagnostic descriptors of anatomical shape by cardiologists. This fully automatic service is deployed in a cloud infrastructure, and has been made available and accessible to the scientific community.

Beta-adrenergic stimulation maintains cardiac function in Serca2 knockout mice.

Previous studies on Serca2 knockout (KO) mice showed that cardiac function is sustained in vivo for several weeks after knockout, whereas SERCA protein levels decrease and calcium dynamics are significantly impaired. In this study, we reconcile observed cellular and organ level contractile function using a cardiac multiscale model. We identified and quantified the changes in cellular function that are both consistent with observations and able to compensate for the decrease in SERCA. Calcium transients were used as input for multiscale computational simulations to predict whole-organ response. Although this response matched experimental pressure-volume (PV) measurements in healthy mice, the reduced magnitude calcium transients observed in KO cells were insufficient to trigger ventricular ejection. To replicate the effects of elevated catecholamine levels observed in vivo, cells were treated with isoproterenol. Incorporation of the resulting measured ß-adrenergically stimulated calcium transients into the model resulted in a close match with experimental PV loops. Changes in myofilament properties, when considered in isolation, were not able to increase tension development to levels consistent with measurements, further confirming the necessity of a high ß-adrenergic state. Modeling additionally indicated that increased venous return observed in the KO mice helps maintain a high ejection fraction via the Frank-Starling effect. Our study shows that increased ß-adrenergic stimulation is a potentially highly significant compensatory mechanism by which cardiac function is maintained in Serca2 KO mice, producing the increases in both systolic and diastolic calcium, consistent with the observed contractile function observed in experimental PV measurements.

Quality metrics for high order meshes: analysis of the mechanical simulation of the heart beat.

The quality of a computational mesh is an important characteristic for stable and accurate simulations. Quality depends on the regularity of the initial mesh, and in mechanical simulations it evolves in time, with deformations causing changes in volume and distortion of mesh elements. Mesh quality metrics are therefore relevant for both mesh personalization and the monitoring of the simulation process. This work evaluates the significance, in meshes with high order interpolation, of four quality metrics described in the literature, applying them to analyse the stability of the simulation of the heart beat. It also investigates how image registration and mesh warping parameters affect the quality and stability of meshes. Jacobian-based metrics outperformed or matched the results of coarse geometrical metrics of aspect ratio or orthogonality, although they are more expensive computationally. The stability of simulations of a complete heart cycle was best predicted with a specificity of 61%, sensitivity of 85%, and only nominal differences were found changing the intra-element and per-element combination of quality values. A compromise between fitting accuracy and mesh stability and quality was found. Generic geometrical quality metrics have a limited success predicting stability, and an analysis of the simulation problem may be required for an optimal definition of quality.

The estimation of patient-specific cardiac diastolic functions from clinical measurements.

An unresolved issue in patients with diastolic dysfunction is that the estimation of myocardial stiffness cannot be decoupled from diastolic residual active tension (AT) because of the impaired ventricular relaxation during diastole. To address this problem, this paper presents a method for estimating diastolic mechanical parameters of the left ventricle (LV) from cine and tagged MRI measurements and LV cavity pressure recordings, separating the passive myocardial constitutive properties and diastolic residual AT. Dynamic C1-continuous meshes are automatically built from the anatomy and deformation captured from dynamic MRI sequences. Diastolic deformation is simulated using a mechanical model that combines passive and active material properties. The problem of non-uniqueness of constitutive parameter estimation using the well known Guccione law is characterized by reformulation of this law. Using this reformulated form, and by constraining the constitutive parameters to be constant across time points during diastole, we separate the effects of passive constitutive properties and the residual AT during diastolic relaxation. Finally, the method is applied to two clinical cases and one control, demonstrating that increased residual AT during diastole provides a potential novel index for delineating healthy and pathological cases.

Integrating multi-scale data to create a virtual physiological mouse heart.

While the virtual physiological human (VPH) project has made great advances in human modelling, many of the tools and insights developed as part of this initiative are also applicable for facilitating mechanistic understanding of the physiology of a range of other species. This process, in turn, has the potential to provide human relevant insights via a different scientific path. Specifically, the increasing use of mice in experimental research, not yet fully complemented by a similar increase in computational modelling, is currently missing an important opportunity for using and interpreting this growing body of experimental data to improve our understanding of cardiac function. This overview describes our work to address this issue by creating a virtual physiological mouse model of the heart. We describe the similarities between human- and mouse-focused modelling, including the reuse of VPH tools, and the development of methods for investigating parameter sensitivity that are applicable across species. We show how previous results using this approach have already provided important biological insights, and how these can also be used to advance VPH heart models. Finally, we show an example application of this approach to test competing multi-scale hypotheses by investigating variations in length-dependent properties of cardiac muscle.

An analysis of deformation-dependent electromechanical coupling in the mouse heart.

To investigate the effects of the coupling between excitation and contraction on whole-organ function, we have developed a novel biophysically based multiscale electromechanical model of the murine heart. Through comparison with a comprehensive in vivo experimental data set, we show good agreement with pressure and volume measurements at both physiological temperatures and physiological pacing frequencies. This whole-organ model was used to investigate the effects of material and haemodynamic properties introduced at the tissue level, as well as emergent function of our novel cell contraction model. Through a comprehensive sensitivity analysis at both the cellular and whole organ level, we demonstrate the sensitivity of the model's results to its parameters and the constraining effect of experimental data. These results demonstrate the fundamental importance of length- and velocity-dependent feedback to the cellular scale for whole-organ function, and we show that a strong velocity dependence of tension is essential for explaining the differences between measured single cell tension and whole-organ pressure transients.

Efficient computational methods for strongly coupled cardiac electromechanics.

Strongly coupled cardiac electromechanical models can further our understanding of the relative importance of feedback mechanisms in the heart, but computational challenges currently remain a major obstacle, which limit their widespread use. To address this issue, we present a set of efficient computational methods including an efficient adaptive cell model integration scheme and a solution method for the monodomain equations that maintains high conduction velocity for time steps greater than 0.1 ms. We also present a novel method for increasing the efficiency of simulating electromechanical coupling, which shows a significant reduction in computational cost of the mechanical component on a personalized left ventricular geometry with an active contraction cell model reparametrized for human cells.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark.

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.