Precision medicine in human heart modeling : Perspectives, challenges, and opportunities.

Precision medicine is a new frontier in healthcare that uses scientific methods to customize medical treatment to the individual genes, anatomy, physiology, and lifestyle of each person. In cardiovascular health, precision medicine has emerged as a promising paradigm to enable cost-effective solutions that improve quality of life and reduce mortality rates. However, the exact role in precision medicine for human heart modeling has not yet been fully explored. Here, we discuss the challenges and opportunities for personalized human heart simulations, from diagnosis to device design, treatment planning, and prognosis. With a view toward personalization, we map out the history of anatomic, physical, and constitutive human heart models throughout the past three decades. We illustrate recent human heart modeling in electrophysiology, cardiac mechanics, and fluid dynamics and highlight clinically relevant applications of these models for drug development, pacing lead failure, heart failure, ventricular assist devices, edge-to-edge repair, and annuloplasty. With a view toward translational medicine, we provide a clinical perspective on virtual imaging trials and a regulatory perspective on medical device innovation. We show that precision medicine in human heart modeling does not necessarily require a fully personalized, high-resolution whole heart model with an entire personalized medical history. Instead, we advocate for creating personalized models out of population-based libraries with geometric, biological, physical, and clinical information by morphing between clinical data and medical histories from cohorts of patients using machine learning. We anticipate that this perspective will shape the path toward introducing human heart simulations into precision medicine with the ultimate goals to facilitate clinical decision making, guide treatment planning, and accelerate device design.

Using machine learning to characterize heart failure across the scales.

Heart failure is a progressive chronic condition in which the heart undergoes detrimental changes in structure and function across multiple scales in time and space. Multiscale models of cardiac growth can provide a patient-specific window into the progression of heart failure and guide personalized treatment planning. Yet, the predictive potential of cardiac growth models remains poorly understood. Here, we quantify predictive power of a stretch-driven growth model using a chronic porcine heart failure model, subject-specific multiscale simulation, and machine learning techniques. We combine hierarchical modeling, Bayesian inference, and Gaussian process regression to quantify the uncertainty of our experimental measurements during an 8-week long study of volume overload in six pigs. We then propagate the experimental uncertainties from the organ scale through our computational growth model and quantify the agreement between experimentally measured and computationally predicted alterations on the cellular scale. Our study suggests that stretch is the major stimulus for myocyte lengthening and demonstrates that a stretch-driven growth model alone can explain [Formula: see text] of the observed changes in myocyte morphology. We anticipate that our approach will allow us to design, calibrate, and validate a new generation of multiscale cardiac growth models to explore the interplay of various subcellular-, cellular-, and organ-level contributors to heart failure. Using machine learning in heart failure research has the potential to combine information from different sources, subjects, and scales to provide a more holistic picture of the failing heart and point toward new treatment strategies.

Multiscale characterization of heart failure.

Dilated cardiomyopathy is a progressive irreversible disease associated with contractile dysfunction and heart failure. During dilated cardiomyopathy, elevated diastolic wall strains trigger mechanotransduction pathways that initiate the addition of sarcomeres in series and an overall increase in myocyte length. At the whole organ level, this results in a chronic dilation of the ventricles, an increase in end diastolic and end systolic volumes, and a decrease in ejection fraction. However, how exactly changes in sarcomere number translate into changes in myocyte morphology, and how these cellular changes translate into ventricular dilation remains incompletely understood. Here we combined a chronic animal study, continuum growth modeling, and machine learning to quantify correlations between sarcomere dynamics, myocyte morphology, and ventricular dilation. In an eight-week long volume overload study of six pigs, we found that the average sarcomere number increased by +3.8%/week, from 47 to 62, resulting in a myocyte lengthening of +3.3%/week, from 85 to 108 µm, while the sarcomere length and myocyte width remained unchanged. At the same time, the average end diastolic volume increased by +6.0%/week. Using continuum growth modeling and Bayesian inference, we correlated alterations on the subcellular, cellular, and organ scales and found that the serial sarcomere number explained 88% of myocyte lengthening, which, in turn, explained 54% of cardiac dilation. Our results demonstrate that sarcomere number and myocyte length are closely correlated and constitute the major determinants of dilated heart failure. We anticipate our study to be a starting point for more sophisticated multiscale models of heart failure. Our study suggests that altering sarcomere turnover-and with it myocyte morphology and ventricular dimensions-could be a potential therapeutic target to attenuate or reverse the progression of heart failure. STATEMENT OF SIGNIFICANCE: Heart failure is a significant global health problem that affects more than 25 million people worldwide and increases in prevalence as the population ages. Heart failure has been studied excessively at various scales; yet, there is no compelling concept to connect knowledge from the subcellular, cellular, and organ level across the scales. Here we combined a chronic animal study, continuum growth modeling, and machine learning to quantify correlations between sarcomere dynamics, myocyte morphology, and ventricular dilation. We found that the serial sarcomere number explained 88% of myocyte lengthening, which, in turn, explained 54% of cardiac dilation. Our results show that sarcomere number and myocyte length are closely correlated and constitute the major determinants of dilated heart failure. This suggests that altering the sarcomere turnover-and with it myocyte morphology and ventricular dimensions-could be a potential therapeutic target to attenuate or reverse heart failure.

Finite elastic wrinkling deformations of incompressible fiber-reinforced plates.

A two-dimensional plate theory, valid for finite elastic deformations with small strains, is derived for incompressible, fiber-reinforced materials. Single-layer plates and two-layer laminates are considered. Numerical simulations illustrate the substantial effect that fiber reinforcement has on wrinkling patterns in the sheet.

Effect of intra-myocardial Algisyl-LVR™ injectates on fibre structure in porcine heart failure.

Recent preclinical trials have shown that alginate injections are a promising treatment for ischemic heart disease. Although improvements in heart function and global structure have been reported following alginate implants, the underlying structure is poorly understood. Using high resolution ex vivo MRI and DT-MRI of the hearts of normal control swine (n = 8), swine with induced heart failure (n = 5), and swine with heart failure and alginate injection treatment (n = 6), we visualized and quantified the fibre distribution and implant material geometry. Our findings show that the alginate injectates form solid ellipsoids with a retention rate of 68.7% ±â€¯21.3% (mean ±â€¯SD) and a sphericity index of 0.37 ±â€¯0.03. These ellipsoidal shapes solidified predominantly at the mid-wall position with an inclination of -4.9°â€¯±â€¯31.4° relative to the local circumferential direction. Overall, the change to left ventricular wall thickness and myofiber orientation was minor and was associated with heart failure and not the presence of injectates. These results show that alginate injectates conform to the pre-existing tissue structure, likely expanding along directions of least resistance as mass is added to the injection sites. The alginate displaces the myocardial tissue predominantly in the longitudinal direction, causing minimal disruption to the surrounding myofiber orientations.

Mathematical modeling of cardiac growth and remodeling.

This review provides an overview of the current state of mathematical models of cardiac growth and remodeling (G&R). We concisely describe the experimental observations associated with cardiac G&R and discuss existing mathematical models that describe this process. To facilitate the discussion, we have organized the G&R models in terms of (1) the physical focus (biochemical vs mechanical) and (2) the process that they describe (myocyte hypertrophy vs extracellular matrix remodeling). The review concludes with a discussion of some possible directions that can advance the existing state of cardiac G&R mathematical modeling. WIREs Syst Biol Med 2016, 8:211-226. doi: 10.1002/wsbm.1330 For further resources related to this article, please visit the WIREs website.

Modeling Pathologies of Diastolic and Systolic Heart Failure.

Chronic heart failure is a medical condition that involves structural and functional changes of the heart and a progressive reduction in cardiac output. Heart failure is classified into two categories: diastolic heart failure, a thickening of the ventricular wall associated with impaired filling; and systolic heart failure, a dilation of the ventricles associated with reduced pump function. In theory, the pathophysiology of heart failure is well understood. In practice, however, heart failure is highly sensitive to cardiac microstructure, geometry, and loading. This makes it virtually impossible to predict the time line of heart failure for a diseased individual. Here we show that computational modeling allows us to integrate knowledge from different scales to create an individualized model for cardiac growth and remodeling during chronic heart failure. Our model naturally connects molecular events of parallel and serial sarcomere deposition with cellular phenomena of myofibrillogenesis and sarcomerogenesis to whole organ function. Our simulations predict chronic alterations in wall thickness, chamber size, and cardiac geometry, which agree favorably with the clinical observations in patients with diastolic and systolic heart failure. In contrast to existing single- or bi-ventricular models, our new four-chamber model can also predict characteristic secondary effects including papillary muscle dislocation, annular dilation, regurgitant flow, and outflow obstruction. Our prototype study suggests that computational modeling provides a patient-specific window into the progression of heart failure with a view towards personalized treatment planning.

Heterogeneous growth-induced prestrain in the heart.

Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung׳s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6±13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

A computational model that predicts reverse growth in response to mechanical unloading.

Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure-volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.

Residual stress produced by ventricular volume reduction surgery has little effect on ventricular function and mechanics: a finite element model study.

OBJECTIVES: Residual stress is the stress (force per unit area) that remains when all external loads (eg, left ventricular chamber and pericardial pressures) are removed. It has been suggested that ventricular volume reduction surgery can reconstitute the residual stress-strain state of the left ventricle. To determine the extent to which residual stress is involved, we used a mathematical (finite element) model to simulate the effect of volume reduction operations on left ventricular stroke volume/end-diastolic pressure (Starling) relationships, as well as on regional distributions of stress in the local muscle fiber direction (fiber stress). METHODS: The nonlinear stress-strain relationship for the diastolic myocardium was anisotropic with respect to the local muscle fiber direction. An elastance model for active fiber stress was incorporated in an axisymmetric geometric model of the dilated, poorly contractile left ventricular wall. RESULTS: When residual stress is implemented in the model simulation of volume reduction operations, the additional decrease in stroke volume at fixed left ventricular end-diastolic pressure is small (10% volume reduction: 2.0% at 1 mm Hg and 2.0% at 20 mm Hg; 20% volume reduction: 2.2% at 1 mm Hg and 3.1% at 20 mm Hg). Furthermore, there is little change in the mean fiber stress throughout the left ventricular wall (10% volume reduction: +1.0% at end-diastole and -0.3% at end-systole; 20% volume reduction: +2.1% at end-diastole and -1.0% at end-systole). CONCLUSIONS: These results suggest that residual stress produced by volume reduction operations has little effect on left ventricular function and the mean fiber stresses at end-diastole and end-systole.

Mechanism underlying mechanical dysfunction in the border zone of left ventricular aneurysm: a finite element model study.

BACKGROUND: The global left ventricular dysfunction characteristic of left ventricular aneurysm is associated with muscle fiber stretching in the adjacent noninfarcted (border zone) region during isovolumic systole. The mechanism of this regional dysfunction is poorly understood. METHODS: An anteroapical transmural myocardial infarct was created by coronary arterial ligation in an adult Dorset sheep and was allowed to mature into left ventricular aneurysm for 10 weeks. The animal was imaged subsequently using magnetic resonance imaging with simultaneous recording of intraventricular pressures. A realistic mathematical model of the three-dimensional ovine left ventricle with an anteroapical aneurysm was constructed from multiple short-axis and long-axis magnetic resonance imaging slices at the beginning of diastolic filling. RESULTS: Three model simulations are presented: (1) normal border zone contractility and normal aneurysmal material properties; (2) greatly reduced border zone contractility (by 50%) and normal aneurysmal material properties; and (3) greatly reduced border zone contractility (by 50%) and stiffened aneurysmal material properties (by 1000%). Only the latter two simulations were able to reproduce experimentally observed stretching of border zone fibers during isovolumic systole. CONCLUSIONS: The mechanism underlying mechanical dysfunction in the border zone region of left ventricular aneurysm is primarily the result of myocardial contractile dysfunction rather than increased wall stress in this region.

Epicardial suction: a new approach to mechanical testing of the passive ventricular wall.

The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics.

The effects of cross-fiber deformation on axial fiber stress in myocardium.

We incorporated a three-dimensional generalization of the Huxley cross-bridge theory in a finite element model of ventricular mechanics to examine the effect of nonaxial deformations on active stress in myocardium. According to this new theory, which assumes that macroscopic tissue deformations are transmitted to the myofilament lattice, lateral myofilament spacing affects the axial fiber stress. We calculated stresses and deformations at end-systole under the assumption of strictly isometric conditions. Our results suggest that at the end of ejection, nonaxial deformations may significantly reduce active axial fiber stress in the inner half of the wall of the normal left ventricle (18-35 percent at endocardium, depending on location with respect to apex and base). Moreover, this effect is greater in the case of a compliant ischemic region produced by occlusion of the left anterior descending or circumflex coronary artery (26-54 percent at endocardium). On the other hand, stiffening of the remote and ischemic regions (in the case of a two-week-old infarct) lessens the effect of nonaxial deformation on active stress at all locations (9-32 percent endocardial reductions). These calculated effects are sufficiently large to suggest that the influence of nonaxial deformation on active fiber stress may be important, and should be considered in future studies of cardiac mechanics.

A distribution-moment model of deactivation in cardiac muscle.

The Distribution Moment (DM) model has simulated experimental data on skeletal muscle, but it has not been used previously to study the mechanics of active contraction in cardiac muscle. In contrast to previous models of striated muscle contraction, all parameters have physical meaning and assumptions concerning biophysical events within the cell are consistent with available data. In order to simulate cardiac muscle deactivation using the DM model it was necessary to make the cross-bridge detachment rates large for large displacements from the neutral equilibrium position of a cross-bridge. To examine the effect of cooperativity on cardiac muscle contraction, we used the DM model's tight coupling scheme with binding of one or two calcium sites regulating contraction. As observed experimentally, our model predicted a reduction of isometric tension development following rapid shortening lengthening transients when contraction is regulated by either one or two calcium binding sites. The predicted deactivating effect increased if the transient was applied late in the twitch when contraction is regulated by two calcium binding sites, but not when it is regulated by one site. This is the first study in which deactivation has been simulated without making any provisions for length-dependent calcium trononin dissociation.

Measurements of active myocardial tension under a wide range of physiological loading conditions.

Active tension developed while cardiac muscle shortens has been studied extensively under afterloaded isotonic or isovelocity conditions. However, these are not true in vivo loading conditions. To obtain more physiological loading, we controlled sarcomere length to follow the time courses that we observed previously in a beating canine left ventricle. Sarcomere length was measured by laser diffraction in 12 rat cardiac trabeculae, superfused with Krebs-Henseleit solution (25 degrees C; [Ca] = 1.5 mM). Force was measured by a silicon strain gauge. Sarcomere length time courses were scaled slightly in time to account for temperature and species differences. We examined the relationships between active tension and sarcomere length under loading observed over a wide range of left ventricular preloads and afterloads, and at two sites. Under all loading conditions, active tension was not isotonic but declined steadily throughout the ejection period. While there were major differences in peak tension dependent on loading conditions and the incidence of 'pre-ejection' sarcomere shortening, these factors did not influence the relationship between sarcomere length and peak active tension. This study provides excellent illustrations of the potential differences in stress (1) within a ventricular wall, and (2) under different operating conditions. Moreover, it provides data for developing models of fiber contraction to be synthesized into a whole heart for predicting potential differences in stress at all sites and under all loading conditions.

Anterior and posterior left ventricular sarcomere lengths behave similarly during ejection.

Previous studies of regional differences in myocardial deformation between the anterior and posterior walls of the canine left ventricle were based on strain, which is not an absolute measure of deformation. We thus compared sarcomere lengths at anterior and posterior sites during ejection in isolated dog hearts. Cineradiographic imaging of regional deformation with radiopaque markers implanted near the midwall in five hearts and just below the epicardium in six hearts, combined with postmortem histology, allowed sarcomere length reconstruction throughout the cardiac cycle. The amount of sarcomere shortening accompanying left ventricular ejection was similar in both walls of the left ventricle for sarcomeres located at epicardial and midwall sites. The mean sarcomere length (taken at the middle of the ejecting range) was also similar between the anterior and posterior sites when averaged over all hearts. The similarity of sarcomere function held not only at end systole but throughout ejection and over wide ranges of ventricular pre- and afterloads. Hence functional measurements of relative myocardial shortening may not be indicative of regional sarcomere length heterogeneity.

A three-dimensional finite element method for large elastic deformations of ventricular myocardium: I--Cylindrical and spherical polar coordinates.

A three-dimensional Galerkin finite element method was developed for large deformations of ventricular myocardium and other incompressible, nonlinear elastic, anisotropic materials. Cylindrical and spherical elements were used to solve axisymmetric problems with r.m.s. errors typically less than 2 percent. Isochoric interpolation and pressure boundary constraint equations enhanced low-order curvilinear elements under special circumstances (69 percent savings in degrees of freedom, 78 percent savings in solution time for inflation of a thick-walled cylinder). Generalized tensor products of linear Lagrange and cubic Hermite polynomials permitted custom elements with improved performance, including 52 percent savings in degrees of freedom and 66 percent savings in solution time for compression of a circular disk. Such computational efficiencies become significant for large scale problems such as modeling the heart.

A three-dimensional finite element method for large elastic deformations of ventricular myocardium: II--Prolate spheroidal coordinates.

A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.

Finite element stress analysis of left ventricular mechanics in the beating dog heart.

A three-dimensional finite element model was used to explore whether or not transmural distributions of end-diastolic and end-systolic fiber stress are uniform from the apex to the base of the canine left ventricular wall. An elastance model for active fiber stress was incorporated in an axisymmetric model that accurately represented the geometry and fiber angle distribution of the anterior free wall. The nonlinear constitutive equation for the resting myocardium was transversely isotropic with respect to the local fiber axis. Transmural distributions of end-diastolic fiber stress became increasingly nonuniform from midventricle toward the apex or the base. At a typical diastolic left ventricular pressure (1 kPa), the differences between largest and smallest fiber stresses were only 0.5 kPa near midventricle, compared with 4.6 kPa at the apex, and 3.3 kPa at the base. Transmural fiber stress differences at end-systole (14 kPa) were relatively small in regions from the base to the midventricle (13-22 kPa), but were larger between midventricle and the apex (30-43 kPa). All six three-dimensional end-diastolic strain components were within or very close to one standard deviation of published measurements through the midanterior left ventricular free wall of the passive canine heart [Omens et al., Am. J. Physiol. 261, H918-H928 (1991)]. End-systolic in-plane normal and shear strains also agreed closely with published experimental measurements in the beating dog heart [Waldman et al., Circ. Res. 63, 550-562 (1988)]. The results indicate that, unlike in the midventricle region that has been studied most fully, there may be significant regional nonhomogeneity of fiber stress in the normal left ventricle associated with regional variations in shape and fiber angle.