Organ-level validation of a cross-bridge cycling descriptor in a left ventricular finite element model: effects of ventricular loading on myocardial strains

Biventricular finite element modeling of the fetal heart in health and during critical aortic stenosis

Finite Element simulations are a robust way of investigating cardiac biomechanics. To date, it has only been performed with the left ventricle (LV) alone for fetal hearts, even though results are likely different with biventricular (BiV) simulations. In this research, we conduct BiV simulations of the fetal heart based on 4D echocardiography images to show that it can capture the biomechanics of the normal healthy fetal heart, as well as those of fetal aortic stenosis better than the LV alone simulations. We found that performing LV alone simulations resulted in overestimation of LV stresses and pressures, compared to BiV simulations. Interestingly, inserting a compliance between the LV and right ventricle (RV) in the lumped parameter model of the LV only simulation effectively resolved these overestimations, demonstrating that the septum could be considered to play a LV-RV pressure communication role. However, stresses and strains spatial patterns remained altered from BiV simulations after the addition of the compliance. The BiV simulations corroborated previous studies in showing disease effects on the LV, where fetal aortic stenosis (AS) drastically elevated LV pressures and reduced strains and stroke volumes, which were moderated down with the addition of mitral regurgitation (MR). However, BiV simulations enabled an evaluation of the RV as well, where we observed that effects of the AS and MR on pressures and stroke volumes were generally much smaller and less consistent. The BiV simulations also enabled investigations of septal dynamics, which showed a rightward shift with AS, and partial restoration with MR. Interestingly, AS tended to enhance RV stroke volume, but MR moderated that down.

Effects of myocardial sheetlet sliding on left ventricular function

Left ventricle myocardium has a complex micro-architecture, which was revealed to consist of myocyte bundles arranged in a series of laminar sheetlets. Recent imaging studies demonstrated that these sheetlets re-orientated and likely slided over each other during the deformations between systole and diastole, and that sheetlet dynamics were altered during cardiomyopathy. However, the biomechanical effect of sheetlet sliding is not well-understood, which is the focus here. We conducted finite element simulations of the left ventricle (LV) coupled with a windkessel lumped parameter model to study sheetlet sliding, based on cardiac MRI of a healthy human subject, and modifications to account for hypertrophic and dilated geometric changes during cardiomyopathy remodeling. We modeled sheetlet sliding as a reduced shear stiffness in the sheet-normal direction and observed that (1) the diastolic sheetlet orientations must depart from alignment with the LV wall plane in order for sheetlet sliding to have an effect on cardiac function, that (2) sheetlet sliding modestly aided cardiac function of the healthy and dilated hearts, in terms of ejection fraction, stroke volume, and systolic pressure generation, but its effects were amplified during hypertrophic cardiomyopathy and diminished during dilated cardiomyopathy due to both sheetlet angle configuration and geometry, and that (3) where sheetlet sliding aided cardiac function, it increased tissue stresses, particularly in the myofibre direction. We speculate that sheetlet sliding is a tissue architectural adaptation to allow easier deformations of the LV walls so that LV wall stiffness will not hinder function, and to provide a balance between function and tissue stresses. A limitation here is that sheetlet sliding is modeled as a simple reduction in shear stiffness, without consideration of micro-scale sheetlet mechanics and dynamics.

Computational analysis of ventricular mechanics in hypertrophic cardiomyopathy patients

Hypertrophic cardiomyopathy (HCM) is a genetic heart disease that is associated with many pathological features, such as a reduction in global longitudinal strain (GLS), myofiber disarray and hypertrophy. The effects of these features on left ventricle (LV) function are, however, not clear in two phenotypes of HCM, namely, obstructive and non-obstructive. To address this issue, we developed patient-specific computational models of the LV using clinical measurements from 2 female HCM patients and a control subject. Left ventricular mechanics was described using an active stress formulation and myofiber disarray was described using a structural tensor in the constitutive models. Unloaded LV configuration for each subject was first determined from their respective end-diastole LV geometries segmented from the cardiac magnetic resonance images, and an empirical single-beat estimation of the end-diastolic pressure volume relationship. The LV was then connected to a closed-loop circulatory model and calibrated using the clinically measured LV pressure and volume waveforms, peak GLS and blood pressure. Without consideration of myofiber disarray, peak myofiber tension was found to be lowest in the obstructive HCM subject (60 kPa), followed by the non-obstructive subject (242 kPa) and the control subject (375 kPa). With increasing myofiber disarray, we found that peak tension has to increase in the HCM models to match the clinical measurements. In the obstructive HCM patient, however, peak tension was still depressed (cf. normal subject) at the largest degree of myofiber disarray found in the clinic. The computational modeling workflow proposed here can be used in future studies with more HCM patient data.

Contribution of Ventricular Motion and Sampling Location to Discrepancies in Two-Dimensional Versus Three-Dimensional Fetal Ventricular Strain Measures

BACKGROUND

Echocardiographic quantification of fetal cardiac strain is important to evaluate function and the need for intervention, with both two-dimensional (2D) and three-dimensional (3D) strain measurements currently feasible. However, discrepancies between 2D and 3D measurements have been reported, the etiologies of which are unclear. This study sought to determine the etiologies of the differences between 2D and 3D strain measurements.

METHODS

A validated cardiac motion-tracking algorithm was used on 3D cine ultrasound images acquired in 26 healthy fetuses. Both 2D and 3D myocardial strain quantifications were performed on each image set for controlled comparisons. Finite element modeling of 2 left ventricle (LV) models with minor geometrical differences were performed with various helix angle configurations for validating image processing results.

RESULTS

Three-dimensional longitudinal strain (LS) was significantly lower than 2D LS for the LV free wall and septum but not for the right ventricular (RV) free wall, while 3D circumferential strain (CS) was significantly higher than 2D CS for the LV, RV, and septum. The LS discrepancy was due to 2D long-axis imaging not capturing the out-of-plane motions associated with LV twist, while the CS discrepancy was due to the systolic motion of the heart toward the apex that caused out-of-plane motions in 2D short-axis imaging. A timing mismatch between the occurrences of peak longitudinal and circumferential dimensions caused a deviation in zero-strain referencing between 2D and 3D strain measurements, contributing to further discrepancies between the 2.

CONCLUSIONS

Mechanisms for discrepancies between 2D and 3D strain measurements in fetal echocardiography were identified, and inaccuracies associated with 2D strains were highlighted. Understanding of this mechanism is useful and important for future standardization of fetal cardiac strain measurements, which we propose to be important in view of large discrepancies in measured values in the literature.

The dependency of fetal left ventricular biomechanics function on myocardium helix angle configuration

The helix angle configuration of the myocardium is understood to contribute to the heart function, as finite element (FE) modeling of postnatal hearts showed that altered configurations affected cardiac function and biomechanics. However, similar investigations have not been done on the fetal heart. To address this, we performed image-based FE simulations of fetal left ventricles (LV) over a range of helix angle configurations, assuming a linear variation of helix angles from epicardium to endocardium. Results showed that helix angles have substantial influence on peak myofiber stress, cardiac stroke work, myocardial deformational burden, and spatial variability of myocardial strain. A good match between LV myocardial strains from FE simulations to those measured from 4D fetal echo images could only be obtained if the transmural variation of helix angle was generally between 110 and 130°, suggesting that this was the physiological range. Experimentally discovered helix angle configurations from the literature were found to produce high peak myofiber stress, high cardiac stroke work, and a low myocardial deformational burden, but did not coincide with configurations that would optimize these characteristics. This may suggest that the fetal development of myocyte orientations depends concurrently on several factors rather than a single factor. We further found that the shape, rather than the size of the LV, determined the manner at which helix angles influenced these characteristics, as this influence changed significantly when the LV shape was varied, but not when a heart was scaled from fetal to adult size while retaining the same shape. This may suggest that biomechanical optimality would be affected during diseases that altered the geometric shape of the LV.

Mechanism of exercise intolerance in heart diseases predicted by a computer model of myocardial demand-supply feedback system

BACKGROUND AND OBJECTIVE

The myocardial demand-supply feedback system plays an important role in augmenting blood supply in response to exercise-induced increased myocardial demand. During this feedback process, the myocardium and coronary blood flow interact bidirectionally at many different levels.

METHODS

To investigate these interactions, a novel computational framework that considers the closed myocardial demand-supply feedback system was developed. In the framework coupling the systemic circulation of the left ventricle and coronary perfusion with regulation, myocardial work affects coronary perfusion via flow regulation mechanisms (e.g., metabolic regulation) and myocardial-vessel interactions, whereas coronary perfusion affects myocardial contractility in a closed feedback system. The framework was calibrated based on the measurements from healthy subjects under graded exercise conditions, and then was applied to simulate the effects of graded exercise on myocardial demand-supply under different physiological and pathological conditions.

RESULTS

We found that the framework can recapitulate key features found during exercise in clinical and animal studies. We showed that myocardial blood flow is increased but maximum hyperemia is reduced during exercise, which led to a reduction in coronary flow reserve. For coronary stenosis and myocardial inefficiency, the model predicts that an increase in heart rate is necessary to maintain the baseline cardiac output. Correspondingly, the resting coronary flow reserve is exhausted and the range of heart rate before exhaustion of coronary flow reserve is reduced. In the presence of metabolic regulation dysfunction, the model predicts that the metabolic vasodilator signal is higher at rest, saturates faster during exercise, and as a result, causes quicker exhaustion of coronary flow reserve.

CONCLUSIONS

Model predictions showed that the coronary flow reserve deteriorates faster during graded exercise, which in turn, suggests a decrease in exercise tolerance for patients with stenosis, myocardial inefficiency and metabolic flow regulation dysfunction. The findings in this study may have clinical implications in diagnosing cardiovascular diseases.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Fluid structure computational model of simulating mitral valve motion in a contracting left ventricle

BACKGROUND

Fluid structure interaction simulations h hold promise in studying normal and abnormal cardiac function, including the effect of fluid dynamics on mitral valve (MV) leaflet motion. The goal of this study was to develop a 3D fluid structure interaction computational model to simulate bileaflet MV when interacting with blood motion in left ventricle (LV).

METHODS

The model consists of ideal geometric-shaped MV leaflets and the LV, with MV dimensions based on human anatomical measurements. An experimentally-based hyperelastic isotropic material was used to model the mechanical behaviour of the MV leaflets, with chordae tendineae and papillary muscle tips also incorporated. LV myocardial tissue was prescribed using a transverse isotropic hyperelastic formulation. Incompressible Navier-Stokes fluid formulations were used to govern the blood motion, and the Arbitrary Lagrangian Eulerian (ALE) method was employed to determine the mesh deformation of the fluid and solid domains due to trans-valvular pressure on MV boundaries and the resulting leaflet movement.

RESULTS

The LV-MV generic model was able to reproduce physiological MV leaflet opening and closing profiles resulting from the time-varying atrial and ventricular pressures, as well as simulating normal and prolapsed MV states. Additionally, the model was able to simulate blood flow patterns after insertion of a prosthetic MV with and without left ventricular outflow tract flow obstruction. In the MV-LV normal model, the regurgitant blood flow fraction was 10.1 %, with no abnormality in cardiac function according to the mitral regurgitation severity grades reported by the American Society of Echocardiography.

CONCLUSION

Our simulation approach provides insights into intraventricular fluid dynamics in a contracting LV with normal and prolapsed MV function, as well as aiding in the understanding of possible complications after transcatheter MV implantation prior to clinical trials.

Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

Myocardial supply changes to accommodate the variation of myocardial demand across the heart wall to maintain normal cardiac function. A computational framework that couples the systemic circulation of a left ventricular (LV) finite element model and coronary perfusion in a closed loop is developed to investigate the transmural distribution of the myocardial demand (work density) and supply (perfusion) ratio. Calibrated and validated against measurements of LV mechanics and coronary perfusion, the model is applied to investigate changes in the transmural distribution of passive coronary perfusion, myocardial work density, and their ratio in response to changes in LV contractility, preload, afterload, wall thickness, and cavity volume. The model predicts the following: (1) Total passive coronary flow varies from a minimum value at the endocardium to a maximum value at the epicardium transmurally that is consistent with the transmural distribution of IMP; (2) Total passive coronary flow at different transmural locations is increased with an increase in either contractility, afterload, or preload of the LV, whereas is reduced with an increase in wall thickness or cavity volume; (3) Myocardial work density at different transmural locations is increased transmurally with an increase in either contractility, afterload, preload or cavity volume of the LV, but is reduced with an increase in wall thickness; (4) Myocardial work density-perfusion mismatch ratio at different transmural locations is increased with an increase in contractility, preload, wall thickness or cavity volume of the LV, and the ratio is higher at the endocardium than the epicardium. These results suggest that an increase in either contractility, preload, wall thickness, or cavity volume of the LV can increase the vulnerability of the subendocardial region to ischemia.

A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.

Computational Modeling Studies of the Roles of Left Ventricular Geometry, Afterload, and Muscle Contractility on Myocardial Strains in Heart Failure with Preserved Ejection Fraction

Global longitudinal strain and circumferential strain are found to be reduced in HFpEF, which some have interpreted that the global left ventricular (LV) contractility is impaired. This finding is, however, contradicted by a preserved ejection fraction (EF) and confounded by changes in LV geometry and afterload resistance that may also affect the global strains. To reconcile these issues, we used a validated computational framework consisting of a finite element LV model to isolate the effects of HFpEF features in affecting systolic function metrics. Simulations were performed to quantify the effects on myocardial strains due to changes in LV geometry, active tension developed by the tissue, and afterload. We found that only a reduction in myocardial contractility and an increase in afterload can simultaneously reproduce the blood pressures, EF and strains measured in HFpEF patients. This finding suggests that it is likely that the myocardial contractility is reduced in HFpEF patients. Graphical abstract.

Effects of Left Ventricular Hypertrophy and Myocardial Stiffness on Myocardial Strain Under Preserved Ejection Fraction

Despite numerous experimental observations regarding heart failure with preserved ejection fraction (HFpEF), which is characterized mainly by left ventricular hypertrophy and a left ventricular ejection fraction over 50%, myocardial dynamics under HFpEF have not yet been fully clarified, particularly regarding the relationship between myocardial strain distribution and myocardial work. To address this issue, we numerically investigated radial distribution of myocardial strain during a cardiac cycle with fixed internal volume at the end of the systolic and diastolic phases under different mechanical conditions, such as those involving myocardial thickness and elasticity of myocardial fibers. The myocardium was a modeled as a visco-hyperelastic continuous material. This model was taken into account that active contractile stress along the myocardial fiber direction depends on membrane potential change. Our numerical results showed that both radial and circumferential strains decreased as wall thickness increased, which reflected cardiac hypertrophy, but that myocardial work became larger than that observed with thin ventricular walls. Further, the change in left ventricular diastolic internal pressure caused circumferential strain, while fiber stiffness contributed to radial strain. Since peak circumferential strain was well estimated by the maximum difference between total internal and myocardial volumes, measuring the epicardial contraction rate should be helpful in understanding patients with HFpEF.

Biomechanics of Human Fetal Hearts with Critical Aortic Stenosis

Critical aortic stenosis (AS) of the fetal heart causes a drastic change in the cardiac biomechanical environment. Consequently, a substantial proportion of such cases will lead to a single-ventricular birth outcome. However, the biomechanics of the disease is not well understood. To address this, we performed Finite Element (FE) modelling of the healthy fetal left ventricle (LV) based on patient-specific 4D ultrasound imaging, and simulated various disease features observed in clinical fetal AS to understand their biomechanical impact. These features included aortic stenosis, mitral regurgitation (MR) and LV hypertrophy, reduced contractility, and increased myocardial stiffness. AS was found to elevate LV pressures and myocardial stresses, and depending on severity, can drastically decrease stroke volume and myocardial strains. These effects are moderated by MR. AS alone did not lead to MR velocities above 3 m/s unless LV hypertrophy was included, suggesting that hypertrophy may be involved in clinical cases with high MR velocities. LV hypertrophy substantially elevated LV pressure, valve flow velocities and stroke volume, while reducing LV contractility resulted in diminished LV pressure, stroke volume and wall strains. Typical extent of hypertrophy during fetal AS in the clinic, however, led to excessive LV pressure and valve velocity in the FE model, suggesting that reduced contractility is typically associated with hypertrophy. Increased LV passive stiffness, which might represent fibroelastosis, was found to have minimal impact on LV pressures, stroke volume, and wall strain. This suggested that fibroelastosis could be a by-product of the disease progression and does not significantly impede cardiac function. Our study demonstrates that FE modelling is a valuable tool for elucidating the biomechanics of congenital heart disease and can calculate parameters which are difficult to measure, such as intraventricular pressure and myocardial stresses.

Effects of Mechanical Dyssynchrony on Coronary Flow: Insights From a Computational Model of Coupled Coronary Perfusion With Systemic Circulation

Mechanical dyssynchrony affects left ventricular (LV) mechanics and coronary perfusion. Due to the confounding effects of their bi-directional interactions, the mechanisms behind these changes are difficult to isolate from experimental and clinical studies alone. Here, we develop and calibrate a closed-loop computational model that couples the systemic circulation, LV mechanics, and coronary perfusion. The model is applied to simulate the impact of mechanical dyssynchrony on coronary flow in the left anterior descending artery (LAD) and left circumflex artery (LCX) territories caused by regional alterations in perfusion pressure and intramyocardial pressure (IMP). We also investigate the effects of regional coronary flow alterations on regional LV contractility in mechanical dyssynchrony based on prescribed contractility-flow relationships without considering autoregulation. The model predicts that LCX and LAD flows are reduced by 7.2%, and increased by 17.1%, respectively, in mechanical dyssynchrony with a systolic dyssynchrony index of 10% when the LAD's IMP is synchronous with the arterial pressure. The LAD flow is reduced by 11.6% only when its IMP is delayed with respect to the arterial pressure by 0.07 s. When contractility is sensitive to coronary flow, mechanical dyssynchrony can affect global LV mechanics, IMPs and contractility that in turn, further affect the coronary flow in a feedback loop that results in a substantial reduction of dP_LV/dt, indicative of ischemia. Taken together, these findings imply that regional IMPs play a significant role in affecting regional coronary flows in mechanical dyssynchrony and the changes in regional coronary flow may produce ischemia when contractility is sensitive to the changes in coronary flow.

Uncertainty quantification and sensitivity analysis of left ventricular function during the full cardiac cycle

Patient-specific computer simulations can be a powerful tool in clinical applications, helping in diagnostics and the development of new treatments. However, its practical use depends on the reliability of the models. The construction of cardiac simulations involves several steps with inherent uncertainties, including model parameters, the generation of personalized geometry and fibre orientation assignment, which are semi-manual processes subject to errors. Thus, it is important to quantify how these uncertainties impact model predictions. The present work performs uncertainty quantification and sensitivity analyses to assess the variability in important quantities of interest (QoI). Clinical quantities are analysed in terms of overall variability and to identify which parameters are the major contributors. The analyses are performed for simulations of the left ventricle function during the entire cardiac cycle. Uncertainties are incorporated in several model parameters, including regional wall thickness, fibre orientation, passive material parameters, active stress and the circulatory model. The results show that the QoI are very sensitive to active stress, wall thickness and fibre direction, where ejection fraction and ventricular torsion are the most impacted outputs. Thus, to improve the precision of models of cardiac mechanics, new methods should be considered to decrease uncertainties associated with geometrical reconstruction, estimation of active stress and of fibre orientation. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Force-dependent recruitment from myosin OFF-state increases end-systolic pressure-volume relationship in left ventricle

Finite element (FE) modeling is becoming increasingly prevalent in the world of cardiac mechanics; however, many existing FE models are phenomenological and thus do not capture cellular-level mechanics. This work implements a cellular-level contraction scheme into an existing nonlinear FE code to model ventricular contraction. Specifically, this contraction model incorporates three myosin states: OFF-, ON-, and an attached force-generating state. It has been speculated that force-dependent transitions from the OFF- to ON-state may contribute to length-dependent activation at the cellular level. The current work investigates the contribution of force-dependent recruitment out of the OFF-state to ventricular-level function, specifically the Frank-Starling relationship, as seen through the end-systolic pressure-volume relationship (ESPVR). Five FE models were constructed using geometries of rat left ventricles obtained via cardiac magnetic resonance imaging. FE simulations were conducted to optimize parameters for the cellular contraction model such that the differences between FE predicted ventricular pressures for the models and experimentally measured pressures were minimized. The models were further validated by comparing FE predicted end-systolic strain to experimentally measured strain. Simulations mimicking vena cava occlusion generated descending pressure volume loops from which ESPVRs were calculated. In simulations with the inclusion of the OFF-state, using a force-dependent transition to the ON-state, the ESPVR calculated was steeper than in simulations excluding the OFF-state. Furthermore, the ESPVR was also steeper when compared to models that included the OFF-state without a force-dependent transition. This suggests that the force-dependent recruitment of thick filament heads from the OFF-state at the cellular level contributes to the Frank-Starling relationship observed at the organ level.

Effects of myocardial function and systemic circulation on regional coronary perfusion

Cardiac-coronary interaction and the effects of its pathophysiological variations on spatial heterogeneity of coronary perfusion and myocardial work are still poorly understood. This hypothesis-generating study predicts spatial heterogeneities in both regional cardiac work and perfusion that offer a new paradigm on the vulnerability of the subendocardium to ischemia, particularly at the apex. We propose a mathematical and computational modeling framework to simulate the interaction of left ventricular mechanics, systemic circulation, and coronary microcirculation. The computational simulations revealed that the relaxation rate of the myocardium has a significant effect whereas the contractility has a marginal effect on both the magnitude and transmural distribution of coronary perfusion. The ratio of subendocardial to subepicardial perfusion density (Q_endo/Q_epi) changed by -12 to +6% from a baseline value of 1.16 when myocardial contractility was varied by +25 and -10%, respectively; Q_endo/Q_epi changed by 37% when sarcomere relaxation rate, b, was faster and increased by 10% from the baseline value. The model predicts axial differences in regional myocardial work and perfusion density across the wall thickness. Regional myofiber work done at the apex is 30-50% lower than at the center region, whereas perfusion density in the apex is lower by only 18% compared with the center. There are large axial differences in coronary flow and myocardial work at the subendocardial locations, with the highest differences located at the apex region. A mismatch exists between perfusion density and regional work done at the subendocardium. This mismatch is speculated to be compensated by coronary autoregulation.NEW & NOTEWORTHY We present a model of left ventricle perfusion based on an anatomically realistic coronary tree structure that includes its interaction with the systemic circulation. Left ventricular relaxation rate has a significant effect on the regional distribution of coronary flow and myocardial work.

Multiscale Modeling Framework of Ventricular-Arterial Bi-directional Interactions in the Cardiopulmonary Circulation

Ventricular-arterial coupling plays a key role in the physiologic function of the cardiovascular system. We have previously described a hybrid lumped-finite element (FE) modeling framework of the systemic circulation that couples idealized FE models of the aorta and the left ventricle (LV). Here, we describe an extension of the lumped-FE modeling framework that couples patient-specific FE models of the left and right ventricles, aorta and the large pulmonary arteries in both the systemic and pulmonary circulations. Geometries of the FE models were reconstructed from magnetic resonance (MR) images acquired in a pediatric patient diagnosed with pulmonary arterial hypertension (PAH). The modeling framework was calibrated with pressure waveforms acquired in the heart and arteries by catheterization as well as ventricular volume and arterial diameter waveforms measured from MR images. The calibrated model hemodynamic results match well with the clinically-measured waveforms (volume and pressure) in the LV and right ventricle (RV) as well as with the clinically-measured waveforms (pressure and diameter) in the aorta and main pulmonary artery. The calibrated framework was then used to simulate three cases, namely, (1) an increase in collagen in the large pulmonary arteries, (2) a decrease in RV contractility, and (3) an increase in the total pulmonary arterial resistance, all characteristics of progressive PAH. The key finding from these simulations is that hemodynamics of the pulmonary vasculature and RV wall stress are more sensitive to vasoconstriction with a 10% of reduction in the lumen diameter of the distal vessels than a 67% increase in the proximal vessel's collagen mass.

Multisite pacing and myocardial scars: a computational study

Cardiac resynchronization therapy (CRT) is a frequently effective treatment modality for dyssynchronous heart failure, however, 30% of patients do not respond, usually due to suboptimal activation of the left ventricle (LV). Multisite pacing (MSP) may increase the response rate, but its effect in the presence of myocardial scars is not fully understood. We use a computational model to study the outcome of MSP in an LV with scars in two different locations and of two different sizes. The LV was stimulated from anterior, posterior and lateral locations individually and in pairs, while a septal stimulation site represented right ventricular (RV) pacing. Intraventricular pressures were measured, and outcomes evaluated in terms of maximum LV pressure gradient (dP/dt_max)- change compared to isolated RV pacing. The best result obtained using various LV pacing locations included a combination of sites remote from scars and the septum. The highest dP/dt_max increase was achieved, regardless of scar size, using MSP with one pacing site located on the LV free wall opposite to the scar and one site opposite to the septum. These in silico modelling results suggest that making placement of pacing electrodes dependent on location of scarring, may alter acute haemodynamics and that such modelling may contribute to future CRT optimization.

Effects of left ventricle wall thickness uncertainties on cardiac mechanics

Computational models of the heart have reached a level of maturity that enables sophisticated patient-specific simulations and hold potential for important applications in diagnosis and therapy planning. However, such clinical use puts strict demands on the reliability and accuracy of the models and requires the sensitivity of the model predictions due to errors and uncertainty in the model inputs to be quantified. The models typically contain a large number of parameters, which are difficult to measure and therefore associated with considerable uncertainty. Additionally, patient-specific geometries are usually constructed by semi-manual processing of medical images and must be assumed to be a potential source of model uncertainty. In this paper, we assess the model accuracy by considering the impact of geometrical uncertainties, which typically occur in image-based computational geometries. An approach based on 17 AHA segments diagram is used to consider uncertainties in wall thickness and also in the material properties and fiber orientation, and we perform a comprehensive uncertainty quantification and sensitivity analysis based on polynomial chaos expansions. The quantities considered include stress, strain and global deformation parameters of the left ventricle. The results indicate that important quantities of interest may be more affected by wall thickness, and highlight the need for accurate geometry reconstructions in patient-specific cardiac mechanics models.

In-silico assessment of the effects of right ventricular assist device on pulmonary arterial hypertension using an image based biventricular modeling framework

Pulmonary arterial hypertension (PAH) is a heart disease that is characterized by an abnormally high pressure in the pulmonary artery (PA). While right ventricular assist device (RVAD) has been considered recently as a treatment option for the end-stage PAH patients, its effects on biventricular mechanics are, however, largely unknown. To address this issue, we developed an image-based modeling framework consisting of a biventricular finite element (FE) model that is coupled to a lumped model describing the pulmonary and systemic circulations in a closed-loop system. The biventricular geometry was reconstructed from the magnetic resonance images of two PAH patients showing different degree of RV remodeling and a normal subject. The framework was calibrated to match patient-specific measurements of the left ventricular (LV) and RV volume and pressure waveforms. An RVAD model was incorporated into the calibrated framework and simulations were performed with different pump speeds. Results showed that RVAD unloads the RV, improves cardiac output and increases septum curvature, which are more pronounced in the PAH patient with severe RV remodeling. These improvements, however, are also accompanied by an adverse increase in the PA pressure. These results suggest that the RVAD implantation may need to be optimized depending on disease progression.

Relationship of Transmural Variations in Myofiber Contractility to Left Ventricular Ejection Fraction: Implications for Modeling Heart Failure Phenotype With Preserved Ejection Fraction

The pathophysiological mechanisms underlying preserved left ventricular (LV) ejection fraction (EF) in patients with heart failure and preserved ejection fraction (HFpEF) remain incompletely understood. We hypothesized that transmural variations in myofiber contractility with existence of subendocardial dysfunction and compensatory increased subepicardial contractility may underlie preservation of LVEF in patients with HFpEF. We quantified alterations in myocardial function in a mathematical model of the human LV that is based on the finite element method. The fiber-reinforced material formulation of the myocardium included passive and active properties. The passive material properties were determined such that the diastolic pressure-volume behavior of the LV was similar to that shown in published clinical studies of pressure-volume curves. To examine changes in active properties, we considered six scenarios: (1) normal properties throughout the LV wall; (2) decreased myocardial contractility in the subendocardium; (3) increased myocardial contractility in the subepicardium; (4) myocardial contractility decreased equally in all layers, (5) myocardial contractility decreased in the midmyocardium and subepicardium, (6) myocardial contractility decreased in the subepicardium. Our results indicate that decreased subendocardial contractility reduced LVEF from 53.2 to 40.5%. Increased contractility in the subepicardium recovered LVEF from 40.5 to 53.2%. Decreased contractility transmurally reduced LVEF and could not be recovered if subepicardial and midmyocardial contractility remained depressed. The computational results simulating the effects of transmural alterations in the ventricular tissue replicate the phenotypic patterns of LV dysfunction observed in clinical practice. In particular, data for LVEF, strain and displacement are consistent with previous clinical observations in patients with HFpEF, and substantiate the hypothesis that increased subepicardial contractility may compensate for subendocardial dysfunction and play a vital role in maintaining LVEF.

Organ-level validation of a cross-bridge cycling descriptor in a left ventricular finite element model: effects of ventricular loading on myocardial strains

Although detailed cell‐based descriptors of cross‐bridge cycling have been applied in finite element (FE) heart models to describe ventricular mechanics, these multiscale models have never been tested rigorously to determine if these descriptors, when scaled up to the organ‐level, are able to reproduce well‐established organ‐level physiological behaviors. To address this void, we here validate a left ventricular (LV) FE model that is driven by a cell‐based cross‐bridge cycling descriptor against key organ‐level heart physiology. The LV FE model was coupled to a closed‐loop lumped parameter circulatory model to simulate different ventricular loading conditions (preload and afterload) and contractilities. We show that our model is able to reproduce a linear end‐systolic pressure volume relationship, a curvilinear end‐diastolic pressure volume relationship and a linear relationship between myocardial oxygen consumption and pressure–volume area. We also show that the validated model can predict realistic LV strain‐time profiles in the longitudinal, circumferential, and radial directions. The predicted strain‐time profiles display key features that are consistent with those measured in humans, such as having similar peak strains, time‐to‐peak‐strain, and a rapid change in strain during atrial contraction at late‐diastole. Our model shows that the myocardial strains are sensitive to not only LV contractility, but also to the LV loading conditions, especially to a change in afterload. This result suggests that caution must be exercised when associating changes in myocardial strain with changes in LV contractility. The methodically validated multiscale model will be used in future studies to understand human heart diseases.

High Spatial Resolution Multi-Organ Finite Element Modeling of Ventricular-Arterial Coupling

While it has long been recognized that bi-directional interaction between the heart and the vasculature plays a critical role in the proper functioning of the cardiovascular system, a comprehensive study of this interaction has largely been hampered by a lack of modeling framework capable of simultaneously accommodating high-resolution models of the heart and vasculature. Here, we address this issue and present a computational modeling framework that couples finite element (FE) models of the left ventricle (LV) and aorta to elucidate ventricular-arterial coupling in the systemic circulation. We show in a baseline simulation that the framework predictions of (1) LV pressure-volume loop, (2) aorta pressure-diameter relationship, (3) pressure-waveforms of the aorta, LV, and left atrium (LA) over the cardiac cycle are consistent with the physiological measurements found in healthy human. To develop insights of ventricular-arterial interactions, the framework was then used to simulate how alterations in the geometrical or, material parameter(s) of the aorta affect the LV and vice versa. We show that changing the geometry and microstructure of the aorta model in the framework led to changes in the functional behaviors of both LV and aorta that are consistent with experimental observations. On the other hand, changing contractility and passive stiffness of the LV model in the framework also produced changes in both the LV and aorta functional behaviors that are consistent with physiology principles.

Cardiophysiology Illustrated by Comparing Ventricular Volumes in Healthy Adult Males and Females

Recent advances in cardiac imaging techniques have substantially contributed to a growing interest in the analysis of global cardiac chamber dimensions and regional myocardial deformation. During the cardiac cycle, ventricular luminal volume varies due to the contraction process, which also confers a shape change including substantial alteration of long axis length, as well as rotation of the base compared to the apex. Local deformation can be assessed by strain (rate) analysis. Reviewing the present literature, it must be concluded that there is no single metric available to comprehensively characterize ventricular function. Every candidate advanced thus far has been found to incompletely reflect ventricular performance. This observation is not surprising in view of the complexity of the cardiac pump system. Additionally, sex-specific modifiers may play a role. More than three decades ago, it was shown that on average the ventricular volume is smaller in healthy women compared to matched males. Therefore, the present contribution concerns the interpretation of data derived from the healthy heart in both men and women. Starting from the classical Starling concept, we apply a simple mathematical transformation which permits an insightful representation of ventricular mechanics. Relating end-systolic volume (ESV) to end-diastolic volume creates the ventricular volume regulation graph which features the pertinent working point of an individual heart. This fundamental approach illustrates why certain proposed performance indexes cannot individually reveal the essence of ventricular systolic function. We demonstrate that particular metrics are highly interconnected and just tell us the same story in a different disguise. It is imperative to understand which associations exist and if they expectedly are (nearly) linear or frankly nonlinear. Notably, ejection fraction (EF) is primarily determined by ESV, while in turn EF is not much different from ventriculo-arterial coupling (VAC). Insight into cardiac function is promoted by identification of the paramount/essential components involved. The smaller ESV (p < 0.0001) implies that EF is higher in women and may also have consequences for VAC.