Fast Simulation of Mechanical Heterogeneity in the Electrically Asynchronous Heart Using the MultiPatch Module

Numerical accuracy of closed-loop steady state in a zero-dimensional cardiovascular model

Closed-loop cardiovascular models are becoming vital tools in clinical settings, making their accuracy and reliability paramount. While these models rely heavily on steady-state simulations, accuracy because of steady-state convergence is often assumed negligible. Using a reduced-order cardiovascular model created with the CircAdapt framework as a case study, we investigated steady-state convergence behaviour across various integration methods and simulation protocols. To minimize the effect of numerical errors, we first quantified the numerical errors originating from integration methods and model assumptions. We subsequently investigate this steady-state convergence error under two distinct conditions: first without, and then with homeostatic pressure-flow control (PFC), providing a comprehensive assessment of the CircAdapt framework's numerical stability and accuracy. Our results demonstrated that achieving a clinically accurate steady state required 7-15 heartbeats in simulations without regulatory mechanisms. When homeostatic control mechanisms were included to regulate mean arterial pressure and blood volume, more than twice the number of heartbeats was needed. By simulating a variable number of heartbeats tailored to each simulation's characteristics, an efficient balance between computational cost and steady-state accuracy can be achieved. Understanding this balance is crucial as cardiovascular models progress towards clinical use.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.

Impact of myocardial phenotype on optimal atrioventricular delay settings during biventricular and left bundle branch pacing at rest and during exercise: insights from a virtual patient study

AIMS

Previous studies have not examined the role of non-electrical myocardial disease substrates in determining the optimal atrio-ventricular delay (AVD) settings. We conducted virtual patient simulations to evaluate whether myocardial disease substrates influence the acute response to AVD optimization at rest and during exercise.

METHODS AND RESULTS

The CircAdapt cardiovascular model was used to simulate various left ventricular (LV) remodelling found in cardiac resynchronization therapy candidates. We simulated electrical dyssynchrony, LV dilatation with preserved and reduced contractility, and increased LV passive stiffness. We simulated cardiac resynchronization following biventricular (BiVP) and non-selective LBB pacing (nsLBBP). The paced-AVD ranged from 220 to 40 ms. Cardiac output and heart rate were increased to simulate different levels of exercise. The optimal AVD was the one leading to the highest stroke volume (SV) and the lowest mean left atrial pressure (mLAP). At rest, in simulations with healthy myocardium the gain in SV by AVD optimization was larger compared to those with reduced contractility and stiff myocardium. However, mLAP was comparably decreased by AVD optimization in both healthy and diseased myocardium. During exercise, the optimal AVD shifted to shorter values, and mLAP was more sensitive to AVD, particularly in the presence of hypo-contractile and stiff myocardium.

CONCLUSION

Simulations show that hypocontractility and stiffness reduce the effect of AVD optimization on SV but enhance its benefit in lowering mLAP. Notably, virtual patients with stiff ventricles experience greater benefits from AVD optimization during exercise compared to resting conditions. Furthermore, nsLBBP provides more favourable improvements in mLAP than BiVP.

The mechanistic interaction between mechanical dyssynchrony and filling pressure in cardiac resynchronisation therapy candidates

AIMS

Both left ventricular (LV) mechanical dyssynchrony and filling pressure have been shown to be associated with outcome in heart failure patient treated with cardiac resynchronisation therapy (CRT). To investigate the mechanistic link between mechanical dyssynchrony and filling pressure and to assess their combined prognostic value in CRT candidates.

METHODS AND RESULTS

Left atrial pressure (LAP) estimation and quantification of mechanical dyssynchrony were retrospectively performed in 219 CRT patients using echocardiography. LAP was elevated (eLAP) in 49% of the population, normal (nLAP) in 40%, and indeterminate in 11%. CRT response was defined as per cent-decrease in LV end-systolic volume after 12 ± 6 months CRT. Clinical endpoint was all-cause mortality during 4.8 years (interquartile range: 2.7-6.0 years). To investigate the mechanistic link between mechanical dyssynchrony and filling pressure, the CircAdapt computer model was used to simulate cardiac mechanics and haemodynamics in virtual hearts with left bundle branch block (LBBB) and various causes of increased filling pressure. Patients with nLAP had more significant mechanical dyssynchrony than those with eLAP. The combined assessment of both parameters before CRT was significantly associated with reverse LV remodelling and post-CRT survival. Simulations revealed that mechanical dyssynchrony is attenuated by increased LV operational chamber stiffness, regardless of whether it is caused by passive or active factors, explaining the link between mechanical dyssynchrony and filling pressure.

CONCLUSION

Our combined clinical-computational data demonstrate that in patients with LBBB, the presence of mechanical dyssynchrony indicates relatively normal LV compliance and low filling pressure, which may explain their strong association with positive outcomes after CRT.

Synergistic biophysics and machine learning modeling to rapidly predict cardiac growth probability

Computational models that can predict growth and remodeling of the heart could have important clinical applications. However, the time it takes to calibrate and run current models while considering data uncertainty and variability makes them impractical for routine clinical use. This study aims to address this need by creating a computational framework to efficiently predict cardiac growth probability. We utilized a biophysics model to rapidly simulate cardiac growth following mitral valve regurgitation (MVR). Here we developed a two-tiered Bayesian History Matching approach augmented with Gaussian process emulators for efficient calibration of model parameters to align with growth outcomes within a 95% confidence interval. We first generated a synthetic data set to assess the accuracy of our framework, and the effect of changes in data uncertainty on growth predictions. We then calibrated our model to match baseline and chronic canine MVR data and used an independent data set to successfully validate the ability of our calibrated model to accurately predict cardiac growth probability. The combined biophysics and machine learning modeling framework we proposed in this study can be easily translated to predict patient-specific cardiac growth.

Accelerated atrial pacing reduces left-heart filling pressure: a combined clinical-computational study

BACKGROUND AND AIMS

Accelerated atrial pacing offers potential benefits for patients with heart failure with preserved ejection fraction (HFpEF) and atrial fibrillation (AF), compared with standard lower-rate pacing. The study investigates the relationship between atrial pacing rate and left-heart filling pressure.

METHODS

Seventy-five consecutive patients undergoing catheter ablation for AF underwent assessment of mean left atrial pressure (mLAP) and atrioventricular (AV) conduction delay (PR interval) in sinus rhythm and accelerated atrial pacing with 10 bpm increments up to Wenckebach block. Computer simulations (CircAdapt) of a virtual HFpEF cohort complemented clinical observations and hypothesized the modulating effects of AV coupling and atrial (dys)function.

RESULTS

In the study cohort, 49(65%) patients had a high HFpEF likelihood (H2FPEF ≥ 5.0), and 28(37%) an elevated mLAP ≥ 15 mmHg at sinus rhythm. Optimal pacing rates of 100 [70-110]bpm (median [IQR]) significantly reduced mLAP from 12.8 [10.0-17.4]mmHg in sinus rhythm (55 [52-61]bpm) to 10.4 [7.8-14.8]mmHg (P < .001). Conversely, higher pacing rates (130 [110-140]bpm) significantly increased mLAP to 14.7 [11.0-17.8]mmHg (P < .05). PR interval and, hence, AV conduction delay prolonged incrementally with increasing pacing rates. Simulations corroborated these clinical findings, showing mLAP reduction at a moderately increased pacing rate and a subsequent increase at higher rates. Moreover, simulations suggested that mLAP reduction is optimized when AV conduction delay shortens with increasing rate.

CONCLUSIONS

Accelerated pacing acutely reduces left-heart filling pressure in patients undergoing AF catheter ablation and computer simulations with HFpEF features, suggesting it as a potential therapeutic strategy to alleviate congestion symptoms. Virtual HFpEF patient cohorts hypothesize that AV sequential pacing may further optimize this therapy's beneficial effects.

Enhanced Extraction of Activation Time and Contractility From Myocardial Strain Data Using Parameter Space Features and Computational Simulations

A computational model enables the extraction of two critical myocardial tissue properties: activation time (AT) and contractility (Con) from recorded cardiac strains. However, interference between these parameters reduces the precision and accuracy of the extraction process. This study investigates whether leveraging features in the parameter space can enhance parameter extraction. We utilized a computational model to simulate sarcomere mechanics, creating a parameter space grid of 41 × 41 AT and Con pairs. Each pair generated a simulated strain pattern, and by scanning the grid, we identified cohorts of similar strain patterns for each simulation. These cohorts were represented as binary images-synthetic fingerprints-where the position and shape of each blob indicated extraction uniqueness. We also generated a measurement fingerprint for a strain pattern from a patient with left bundle branch block and compared it to the synthetic fingerprints to calculate a proximity map based on their similarity. This approach allowed us to extract AT and Con using both the measurement fingerprint and the proximity map, corresponding to simple optimization and enhanced parameter extraction methods, respectively. Each synthetic fingerprint consisted of a single connected blob whose size and shape varied characteristically within the parameter space. The AT values extracted from the measurement fingerprint and the proximity map ranged from -59 to 19 ms and from -16 to 14 ms, respectively, while Con values ranged from 48% to 110% and from 85% to 110%, respectively. This study demonstrates that similarity in simulations leads to an asymmetric distribution of parameter values in the parameter space. By using a proximity map, this distortion is considered, significantly improving the accuracy of parameter extraction.

Electrophysiological effects of stretch-activated ion channels: a systematic computational characterization

Cardiac electrophysiology and mechanics are strongly interconnected. Their interaction is, among others, mediated by mechano-electric feedback through stretch-activated ion channels (SACs). The electrophysiological changes induced by SACs may contribute to arrhythmogenesis, but the precise SAC-induced electrophysiological changes remain incompletely understood. Here, we provide a systematic characterization of stretch effects through three distinguished SACs on cardiac electrophysiology using computational modelling. We implemented potassium-selective, calcium-selective and non-selective SACs in the Tomek-Rodriguez-O'Hara-Rudy model of human ventricular electrophysiology. The model was calibrated to experimental data from isolated cardiomyocytes undergoing stretch, considering inter-species differences, and disease-related remodelling of SACs. SAC-mediated effects on the action potential (AP) were analysed by varying stretch amplitude, application timing and/or duration. Afterdepolarizations of different amplitudes were observed with transient 10-ms stretch stimuli of 15-18% applied during phase 4, while stretch ≥18% during phase 4 elicited triggered APs. Longer stimuli shifted the threshold of AP trigger during phase 4 to lower amplitudes, while shorter stimuli increased it. Continuous stretch provoked electrophysiological remodelling. Furthermore, stretch shortened duration or changed morphology of a subsequent electrically evoked AP, and, if applied during a vulnerable time window with sufficient amplitude, prevented its occurrence because of stretch-induced modulation of sodium and L-type calcium channel gating. These effects were more pronounced with disease-related SAC remodelling due to increased stretch sensitivity of diseased hearts. We showed that SACs may induce afterdepolarizations and triggered activities, and prevent subsequent AP generation or change its morphology. These effects depend on cardiomyocyte stretch characteristics and disease-related SACs remodelling and may contribute to cardiac arrhythmogenesis. KEY POINTS: The interplay between cardiac electrophysiology and mechanics is mediated by mechano-electric feedback through stretch-activated ion channels (SACs). These channels may be pro-arrhythmic, but their precise effect on electrophysiology remains unclear. Here we present a systematic in silico characterization of stretch effects through three SACs by implementing inter-species differences as well as disease-related remodelling of SACs in a novel computational model of human ventricular cardiomyocyte electrophysiology. Our simulations showed that, at the cellular level, SACs may provoke electrophysiological remodelling, afterdepolarizations, triggered activities, change the morphology or shorten subsequent electrically evoked action potentials. The model further suggests that a vulnerable window exists in which stretch prevents the following electrically triggered beat occurrence. The pro-arrhythmic effects of stretch strongly depend on disease-related SAC remodelling as well as on stretch characteristics, such as amplitude, time of application and duration. Our study helps in understanding the role of stretch in cardiac arrhythmogenesis and revealing the underlying cellular mechanisms.

Synergistic Biophysics and Machine Learning Modeling to Rapidly Predict Cardiac Growth Probability

Computational models that can predict growth and remodeling of the heart could have important clinical applications. However, the time it takes to calibrate and run current models while considering data uncertainty and variability makes them impractical for routine clinical use. This study aims to address this need by creating a computational framework to efficiently predict cardiac growth probability. We utilized a biophysics model to rapidly simulate cardiac growth following mitral valve regurgitation (MVR). Here we developed a two-tiered Bayesian History Matching approach augmented with Gaussian process emulators for efficient calibration of model parameters to align with growth outcomes within a 95% confidence interval. We first generated a synthetic data set to assess the accuracy of our framework, and the effect of changes in data uncertainty on growth predictions. We then calibrated our model to match baseline and chronic canine MVR data and used an independent data set to successfully validate the ability of our calibrated model to accurately predict cardiac growth probability. The combined biophysics and machine learning modeling framework we proposed in this study can be easily translated to predict patient-specific cardiac growth.

Parameter subset reduction for imaging-based digital twin generation of patients with left ventricular mechanical discoordination

BACKGROUND

Integration of a patient's non-invasive imaging data in a digital twin (DT) of the heart can provide valuable insight into the myocardial disease substrates underlying left ventricular (LV) mechanical discoordination. However, when generating a DT, model parameters should be identifiable to obtain robust parameter estimations. In this study, we used the CircAdapt model of the human heart and circulation to find a subset of parameters which were identifiable from LV cavity volume and regional strain measurements of patients with different substrates of left bundle branch block (LBBB) and myocardial infarction (MI). To this end, we included seven patients with heart failure with reduced ejection fraction (HFrEF) and LBBB (study ID: 2018-0863, registration date: 2019-10-07), of which four were non-ischemic (LBBB-only) and three had previous MI (LBBB-MI), and six narrow QRS patients with MI (MI-only) (study ID: NL45241.041.13, registration date: 2013-11-12). Morris screening method (MSM) was applied first to find parameters which were important for LV volume, regional strain, and strain rate indices. Second, this parameter subset was iteratively reduced based on parameter identifiability and reproducibility. Parameter identifiability was based on the diaphony calculated from quasi-Monte Carlo simulations and reproducibility was based on the intraclass correlation coefficient ( ICC ) obtained from repeated parameter estimation using dynamic multi-swarm particle swarm optimization. Goodness-of-fit was defined as the mean squared error (χ 2 ) of LV myocardial strain, strain rate, and cavity volume.

RESULTS

A subset of 270 parameters remained after MSM which produced high-quality DTs of all patients (χ 2  < 1.6), but minimum parameter reproducibility was poor (ICC min  = 0.01). Iterative reduction yielded a reproducible (ICC min  = 0.83) subset of 75 parameters, including cardiac output, global LV activation duration, regional mechanical activation delay, and regional LV myocardial constitutive properties. This reduced subset produced patient-resembling DTs (χ 2  < 2.2), while septal-to-lateral wall workload imbalance was higher for the LBBB-only DTs than for the MI-only DTs (p < 0.05).

CONCLUSIONS

By applying sensitivity and identifiability analysis, we successfully determined a parameter subset of the CircAdapt model which can be used to generate imaging-based DTs of patients with LV mechanical discoordination. Parameters were reproducibly estimated using particle swarm optimization, and derived LV myocardial work distribution was representative for the patient's underlying disease substrate. This DT technology enables patient-specific substrate characterization and can potentially be used to support clinical decision making.

Translating myosin-binding protein C and titin abnormalities to whole-heart function using a novel calcium-contraction coupling model

Mutations in cardiac myosin-binding protein C (cMyBP-C) or titin may respectively lead to hypertrophic (HCM) or dilated (DCM) cardiomyopathies. The mechanisms leading to these phenotypes remain unclear because of the challenge of translating cellular abnormalities to whole-heart and system function. We developed and validated a novel computer model of calcium-contraction coupling incorporating the role of cMyBP-C and titin based on the key assumptions: 1) tension in the thick filament promotes cross-bridge attachment mechanochemically, 2) with increasing titin tension, more myosin heads are unlocked for attachment, and 3) cMyBP-C suppresses cross-bridge attachment. Simulated stationary calcium-tension curves, isotonic and isometric contractions, and quick release agreed with experimental data. The model predicted that a loss of cMyBP-C function decreases the steepness of the calcium-tension curve, and that more compliant titin decreases the level of passive and active tension and its dependency on sarcomere length. Integrating this cellular model in the CircAdapt model of the human heart and circulation showed that a loss of cMyBP-C function resulted in HCM-like hemodynamics with higher left ventricular end-diastolic pressures and smaller volumes. More compliant titin led to higher diastolic pressures and ventricular dilation, suggesting DCM-like hemodynamics. The novel model of calcium-contraction coupling incorporates the role of cMyBP-C and titin. Its coupling to whole-heart mechanics translates changes in cellular calcium-contraction coupling to changes in cardiac pump and circulatory function and identifies potential mechanisms by which cMyBP-C and titin abnormalities may develop into HCM and DCM phenotypes. This modeling platform may help identify distinct mechanisms underlying clinical phenotypes in cardiac diseases.

How to assess and treat right ventricular electromechanical dyssynchrony in post-repair tetralogy of Fallot: insights from imaging, invasive studies, and computational modelling

BACKGROUND AND AIMS

Right bundle branch block (RBBB) and resulting right ventricular (RV) electromechanical discoordination are thought to play a role in the disease process of subpulmonary RV dysfunction that frequently occur post-repair tetralogy of Fallot (ToF). We sought to describe this disease entity, the role of pulmonary re-valvulation, and the potential added value of RV cardiac resynchronization therapy (RV-CRT).

METHODS

Two patients with repaired ToF, complete RBBB, pulmonary regurgitation, and significantly decreased RV function underwent echocardiography, cardiac magnetic resonance, and an invasive study to evaluate the potential for RV-CRT as part of the management strategy. The data were used to personalize the CircAdapt model of the human heart and circulation. Resulting Digital Twins were analysed to quantify the relative effects of RV pressure and volume overload and to predict the effect of RV-CRT.

RESULTS

Echocardiography showed components of a classic RV dyssynchrony pattern which could be reversed by RV-CRT during invasive study and resulted in acute improvement in RV systolic function. The Digital Twins confirmed a contribution of electromechanical RV dyssynchrony to RV dysfunction and suggested improvement of RV contraction efficiency after RV-CRT. The one patient who underwent successful permanent RV-CRT as part of the pulmonary re-valvulation procedure carried improvements that were in line with the predictions based on his Digital Twin.

CONCLUSION

An integrative diagnostic approach to RV dysfunction, including the construction of Digital Twins may help to identify candidates for RV-CRT as part of the lifetime management of ToF and similar congenital heart lesions.

Left Atrial Function in Patients with Titin Cardiomyopathy

BACKGROUND

Truncating variants in titin (TTNtv) are the most prevalent genetic etiology of dilated cardiomyopathy (DCM). Although TTNtv has been associated with atrial fibrillation, it remains unknown whether and how left atrial (LA) function differs between patients with DCM with and without TTNtv. We aimed to determine and compare LA function in patients with DCM with and without TTNtv and to evaluate whether and how left ventricular (LV) function affects the LA using computational modeling.

METHODS AND RESULTS

Patients with DCM from the Maastricht DCM registry that underwent genetic testing and cardiovascular magnetic resonance (CMR) were included in the current study. Subsequent computational modeling (CircAdapt model) was performed to identify potential LV and LA myocardial hemodynamic substrates. In total, 377 patients with DCM (n = 42 with TTNtv, n = 335 without a genetic variant) were included (median age 55 years, interquartile range [IQR] 46-62 years, 62% men). Patients with TTNtv had a larger LA volume and decreased LA strain compared with patients without a genetic variant (LA volume index 60 mLm-2 [IQR 49-83] vs 51 mLm-2 [IQR 42-64]; LA reservoir strain 24% [IQR 10-29] vs 28% [IQR 20-34]; LA booster strain 9% [IQR 4-14] vs 14% [IQR 10-17], respectively; all P < .01). Computational modeling suggests that while the observed LV dysfunction partially explains the observed LA dysfunction in the patients with TTNtv, both intrinsic LV and LA dysfunction are present in patients with and without a TTNtv.

CONCLUSIONS

Patients with DCM with TTNtv have more severe LA dysfunction compared with patients without a genetic variant. Insights from computational modeling suggest that both intrinsic LV and LA dysfunction are present in patients with DCM with and without TTNtv.

Increased Chamber Resting Tone Is a Key Determinant of Left Ventricular Diastolic Dysfunction

BACKGROUND

Twitch-independent tension has been demonstrated in cardiomyocytes, but its role in heart failure (HF) is unclear. We aimed to address twitch-independent tension as a source of diastolic dysfunction by isolating the effects of chamber resting tone (RT) from impaired relaxation and stiffness.

METHODS

We invasively monitored pressure-volume data during cardiopulmonary exercise in 20 patients with hypertrophic cardiomyopathy, 17 control subjects, and 35 patients with HF with preserved ejection fraction. To measure RT, we developed a new method to fit continuous pressure-volume measurements, and first validated it in a computational model of loss of cMyBP-C (myosin binding protein-C).

RESULTS

In hypertrophic cardiomyopathy, RT (estimated marginal mean [95% CI]) was 3.4 (0.4-6.4) mm Hg, increasing to 18.5 (15.5-21.5) mm Hg with exercise (P<0.001). At peak exercise, RT was responsible for 64% (53%-76%) of end-diastolic pressure, whereas incomplete relaxation and stiffness accounted for the rest. RT correlated with the levels of NT-proBNP (N-terminal pro-B-type natriuretic peptide; R=0.57; P=0.02) and with pulmonary wedge pressure but following different slopes at rest and during exercise (R2=0.49; P<0.001). In controls, RT was 0.0 mm Hg and 1.2 (0.3-2.8) mm Hg in HF with preserved ejection fraction patients and was also exacerbated by exercise. In silico, RT increased in parallel to the loss of cMyBP-C function and correlated with twitch-independent myofilament tension (R=0.997).

CONCLUSIONS

Augmented RT is the major cause of LV diastolic chamber dysfunction in hypertrophic cardiomyopathy and HF with preserved ejection fraction. RT transients determine diastolic pressures, pulmonary pressures, and functional capacity to a greater extent than relaxation and stiffness abnormalities. These findings support antimyosin agents for treating HF.

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

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

Biventricular Interaction During Acute Left Ventricular Ischemia in Mice: A Combined In-Vivo and In-Silico Approach

Computational models provide an efficient paradigm for integrating and linking multiple spatial and temporal scales. However, these models are difficult to parameterize and match to experimental data. Recent advances in both data collection and model analyses have helped overcome this limitation. Here, we combine a multiscale, biventricular interaction model with mouse data before and after left ventricular (LV) ischemia. Sensitivity analyses are used to identify the most influential parameters on pressure and volume predictions. The subset of influential model parameters are calibrated to biventricular pressure-volume loop data (n = 3) at baseline. Each mouse underwent left anterior descending coronary artery ligation, during which changes in fractional shortening and RV pressure-volume dynamics were recorded. Using the calibrated model, we simulate acute LV ischemia and contrast outputs at baseline and in simulated ischemia. Our baseline simulations align with the LV and RV data, and our predictions during ischemia complement recorded RV data and prior studies on LV function during myocardial infarction. We show that a model with both biventricular mechanical interaction and systems-level cardiovascular dynamics can quantitatively reproduce in-vivo data and qualitatively match prior findings from animal studies on LV ischemia.

A Computational Model of Ventricular Dimensions and Hemodynamics in Growing Infants

Previous computer models have successfully predicted cardiac growth and remodeling in adults with pathologies. However, applying these models to infants is complicated by the fact that they also undergo normal, somatic cardiac growth and remodeling. Therefore, we designed a computational model to predict ventricular dimensions and hemodynamics in healthy, growing infants by modifying an adult canine left ventricular growth model. The heart chambers were modeled as time-varying elastances coupled to a circuit model of the circulation. Circulation parameters were allometrically scaled and adjusted for maturation to simulate birth through 3 yrs of age. Ventricular growth was driven by perturbations in myocyte strain. The model successfully matched clinical measurements of pressures, ventricular and atrial volumes, and ventricular thicknesses within two standard deviations of multiple infant studies. To test the model, we input 10th and 90th percentile infant weights. Predicted volumes and thicknesses decreased and increased within normal ranges and pressures were unchanged. When we simulated coarctation of the aorta, systemic blood pressure, left ventricular thickness, and left ventricular volume all increased, following trends in clinical data. Our model enables a greater understanding of somatic and pathological growth in infants with congenital heart defects. Its flexibility and computational efficiency when compared to models employing more complex geometries allow for rapid analysis of pathological mechanisms affecting cardiac growth and hemodynamics.

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.

Myocardial perfusion and flow reserve in the asynchronous heart: mechanistic insight from a computational model

The tight coupling between myocardial oxygen demand and supply has been recognized for decades, but it remains controversial whether this coupling persists under asynchronous activation, such as during left bundle branch block (LBBB). Furthermore, it is unclear whether the amount of local cardiac wall growth, following longer-lasting asynchronous activation, can explain differences in myocardial perfusion distribution between subjects. For a better understanding of these matters, we built upon our existing modeling framework for cardiac mechanics-to-perfusion coupling by incorporating coronary autoregulation. Regional coronary flow was regulated with a vasodilator signal based on regional demand, as estimated from regional fiber stress-strain area. Volume of left ventricular wall segments was adapted with chronic asynchronous activation toward a homogeneous distribution of myocardial oxygen demand per tissue weight. Modeling results show that 1) both myocardial oxygen demand and supply are decreased in early activated regions and increased in late-activated regions; 2) but that regional hyperemic flow remains unaffected; while 3) regional myocardial flow reserve (the ratio of hyperemic to resting myocardial flow) decreases with increases in absolute regional myocardial oxygen demand as well as with decreases in wall thickness. These findings suggest that septal hypoperfusion in LBBB represents an autoregulatory response to reduced myocardial oxygen demand. Furthermore, oxygen demand-driven remodeling of wall mass can explain asymmetric hypertrophy and the related homogenization of myocardial perfusion and flow reserve. Finally, the inconsistent observations of myocardial perfusion distribution can primarily be explained by the degree of dyssynchrony, the degree of asymmetric hypertrophy, and the imaging modality used.NEW & NOTEWORTHY This versatile modeling framework couples myocardial oxygen demand to oxygen supply and myocardial growth, enabling simulation of resting and hyperemic myocardial flow during acute and chronic asynchronous ventricular activation. Model-based findings suggest that reported inconsistencies in myocardial perfusion and flow reserve responses with asynchronous ventricular activation between patients can primarily be explained by the degree of dyssynchrony and wall mass remodeling, which together determine the heterogeneity in regional oxygen demand and, hence, supply with autoregulation.

Monitoring of Myocardial Involvement in Early Arrhythmogenic Right Ventricular Cardiomyopathy Across the Age Spectrum

BACKGROUND

Arrhythmogenic right ventricular cardiomyopathy (ARVC) is characterized by fibrofatty replacement of primarily the right ventricular myocardium, a substrate for life-threatening ventricular arrhythmias (VAs). Repeated cardiac imaging of at-risk relatives is important for early disease detection. However, it is not known whether screening should be age-tailored.

OBJECTIVES

The goal of this study was to assess the need for age-tailoring of follow-up protocols in early ARVC by evaluating myocardial disease progression in different age groups.

METHODS

We divided patients with early-stage ARVC and genotype-positive relatives without overt structural disease and VA at first evaluation into 3 groups: age <30 years, 30 to 50 years, and ≥50 years. Longitudinal biventricular deformation characteristics were used to monitor disease progression. To link deformation abnormalities to underlying myocardial disease substrates, Digital Twins were created using an imaging-based computational modeling framework.

RESULTS

We included 313 echocardiographic assessments from 82 subjects (57% female, age 39 ± 17 years, 10% probands) during 6.7 ± 3.3 years of follow-up. Left ventricular global longitudinal strain slightly deteriorated similarly in all age groups (0.1%-point per year [95% CI: 0.05-0.15]). Disease progression in all age groups was more pronounced in the right ventricular lateral wall, expressed by worsening in longitudinal strain (0.6%-point per year [95% CI: 0.46-0.70]) and local differences in myocardial contractility, compliance, and activation delay in the Digital Twin. Six patients experienced VA during follow-up.

CONCLUSIONS

Disease progression was similar in all age groups, and sustained VA also occurred in patients aged >50 years without overt ARVC phenotype at first evaluation. Unlike recommended by current guidelines, our study suggests that follow-up of ARVC patients and relatives should not stop at older age.

Cell to whole organ global sensitivity analysis on a four-chamber heart electromechanics model using Gaussian processes emulators

Cardiac pump function arises from a series of highly orchestrated events across multiple scales. Computational electromechanics can encode these events in physics-constrained models. However, the large number of parameters in these models has made the systematic study of the link between cellular, tissue, and organ scale parameters to whole heart physiology challenging. A patient-specific anatomical heart model, or digital twin, was created. Cellular ionic dynamics and contraction were simulated with the Courtemanche-Land and the ToR-ORd-Land models for the atria and the ventricles, respectively. Whole heart contraction was coupled with the circulatory system, simulated with CircAdapt, while accounting for the effect of the pericardium on cardiac motion. The four-chamber electromechanics framework resulted in 117 parameters of interest. The model was broken into five hierarchical sub-models: tissue electrophysiology, ToR-ORd-Land model, Courtemanche-Land model, passive mechanics and CircAdapt. For each sub-model, we trained Gaussian processes emulators (GPEs) that were then used to perform a global sensitivity analysis (GSA) to retain parameters explaining 90% of the total sensitivity for subsequent analysis. We identified 45 out of 117 parameters that were important for whole heart function. We performed a GSA over these 45 parameters and identified the systemic and pulmonary peripheral resistance as being critical parameters for a wide range of volumetric and hemodynamic cardiac indexes across all four chambers. We have shown that GPEs provide a robust method for mapping between cellular properties and clinical measurements. This could be applied to identify parameters that can be calibrated in patient-specific models or digital twins, and to link cellular function to clinical indexes.

Comparison of novel ventricular pacing strategies using an electro-mechanical simulation platform

AIMS

Focus of pacemaker therapy is shifting from right ventricular (RV) apex pacing (RVAP) and biventricular pacing (BiVP) to conduction system pacing. Direct comparison between the different pacing modalities and their consequences to cardiac pump function is difficult, due to the practical implications and confounding variables. Computational modelling and simulation provide the opportunity to compare electrical, mechanical, and haemodynamic consequences in the same virtual heart.

METHODS AND RESULTS

Using the same single cardiac geometry, electrical activation maps following the different pacing strategies were calculated using an Eikonal model on a three-dimensional geometry, which were then used as input for a lumped mechanical and haemodynamic model (CircAdapt). We then compared simulated strain, regional myocardial work, and haemodynamic function for each pacing strategy. Selective His-bundle pacing (HBP) best replicated physiological electrical activation and led to the most homogeneous mechanical behaviour. Selective left bundle branch (LBB) pacing led to good left ventricular (LV) function but significantly increased RV load. RV activation times were reduced in non-selective LBB pacing (nsLBBP), reducing RV load but increasing heterogeneity in LV contraction. LV septal pacing led to a slower LV and more heterogeneous LV activation than nsLBBP, while RV activation was similar. BiVP led to a synchronous LV-RV, but resulted in a heterogeneous contraction. RVAP led to the slowest and most heterogeneous contraction. Haemodynamic differences were small compared to differences in local wall behaviour.

CONCLUSION

Using a computational modelling framework, we investigated the mechanical and haemodynamic outcome of the prevailing pacing strategies in hearts with normal electrical and mechanical function. For this class of patients, nsLBBP was the best compromise between LV and RV function if HBP is not possible.

Modelling cardiac mechanics in doxorubicin-induced cardiotoxicity following childhood acute lymphoblastic leukemia using a combination of cardiac magnetic resonance imaging, cardiopulmonary exercise testing and the CircAdapt model

Children with acute lymphoblastic leukemia (ALL) are treated with doxorubicin-based chemotherapy that can lead to cardiotoxicity which is a well-known cause of mortality. This study aims to characterize myocardial subtle changes induced by doxorubicin-related cardiotoxicity. We used the combination of cardiac magnetic resonance (CMR) imaging, cardiopulmonary exercise testing and the CircAdapt model to explore hemodynamics and intraventricular mechanisms at rest and during exercise in 53 childhood ALL survivors. A sensitivity analysis of the CircAdapt model identified the most influencing parameters on the left ventricle volume. ANOVA were performed to explore significant differences between left ventricle stiffness, contractility, and arteriovenous pressure drop, as well as survivors' prognostic risk groups. No significant differences were observed between prognostic risk groups. The left ventricle stiffness and left ventricle contractility were non-significantly higher in survivors receiving cardioprotective agents (94.3 %), compared to those at standard and high prognostic risk (77 % and 86 %, respectively). In both left ventricle stiffness and left ventricle contractility, we observed that survivors receiving cardioprotective agents were close to the nominal value of CircAdapt (healthy reference group value is 100 %). This study allowed to improve our knowledge of potential subtle myocardial changes induced by doxorubicin-related cardiotoxicity in childhood ALL survivors. This study confirms that survivors exposed to a high cumulative dose of doxorubicin during treatments are at potential risk of myocardial changes many years after the end of their cancer, while cardio-protective agents may prevent changes in cardiac mechanical properties.

Mechanoelectric effects in healthy cardiac function and under Left Bundle Branch Block pathology

Mechanoelectric feedback (MEF) in the heart operates through several mechanisms which serve to regulate cardiac function. Stretch activated channels (SACs) in the myocyte membrane open in response to cell lengthening, while tension generation depends on stretch, shortening velocity, and calcium concentration. How all of these mechanisms interact and their effect on cardiac output is still not fully understood. We sought to gauge the acute importance of the different MEF mechanisms on heart function. An electromechanical computer model of a dog heart was constructed, using a biventricular geometry of 500K tetrahedral elements. To describe cellular behavior, we used a detailed ionic model to which a SAC model and an active tension model, dependent on stretch and shortening velocity and with calcium sensitivity, were added. Ventricular inflow and outflow were connected to the CircAdapt model of cardiovascular circulation. Pressure-volume loops and activation times were used for model validation. Simulations showed that SACs did not affect acute mechanical response, although if their trigger level was decreased sufficiently, they could cause premature excitations. The stretch dependence of tension had a modest effect in reducing the maximum stretch, and stroke volume, while shortening velocity had a much bigger effect on both. MEF served to reduce the heterogeneity in stretch while increasing tension heterogeneity. In the context of left bundle branch block, a decreased SAC trigger level could restore cardiac output by reducing the maximal stretch when compared to cardiac resynchronization therapy. MEF is an important aspect of cardiac function and could potentially mitigate activation problems.

Biventricular interaction during acute left ventricular ischemia in mice: a combined in-vivo and in-silico approach

Computational models provide an efficient paradigm for integrating and linking multiple spatial and temporal scales. However, these models are difficult to parameterize and match to experimental data. Recent advances in both data collection and model analyses have helped overcome this limitation. Here, we combine a multiscale, biventricular interaction model with mouse data before and after left ventricular (LV) ischemia. Sensitivity analyses are used to identify the most influential parameters on pressure and volume predictions. The subset of influential model parameters are calibrated to biventricular pressure-volume loop data (n=3) at baseline. Each mouse underwent left anterior descending coronary artery ligation, during which changes in fractional shortening and RV pressure-volume dynamics were recorded. Using the calibrated model, we simulate acute LV ischemia and contrast outputs at baseline and in simulated ischemia. Our baseline simulations align with the LV and RV data, and our predictions during ischemia complement recorded RV data and prior studies on LV function during myocardial infarction. We show that a model with both biventricular mechanical interaction and systems level cardiovascular dynamics can quantitatively reproduce in-vivo data and qualitatively match prior findings from animal studies on LV ischemia.

Hemodynamics-driven mathematical model of third heart sound generation

The proto-diastolic third heart sound (S3) is observed in various hemodynamic conditions in both normal and diseased hearts. We propose a novel, one-degree of freedom mathematical model of mechanical vibrations of heart and blood that generates the third heart sound, implemented in a real-time model of the cardiovascular system (CircAdapt). To examine model functionality, S3 simulations were performed for conditions mimicking the normal heart as well as heart failure with preserved ejection fraction (HFpEF), atrioventricular valve regurgitation (AVR), atrioventricular valve stenosis (AVS) and septal shunts (SS). Simulated S3 showed both qualitative and quantitative agreements with measured S3 in terms of morphology, frequency, and timing. It was shown that ventricular mass, ventricular viscoelastic properties as well as inflow momentum play a key role in the generation of S3. The model indicated that irrespective of cardiac conditions, S3 vibrations are always generated, in both the left and right sides of the heart, albeit at different levels of audibility. S3 intensities increased in HFpEF, AVR and SS, but the changes of acoustic S3 features in AVS were not significant, as compared with the reference simulation. S3 loudness in all simulated conditions was proportional to the level of cardiac output and severity of cardiac conditions. In conclusion, our hemodynamics-driven mathematical model provides a fast and realistic simulation of S3 under various conditions which may be helpful to find new indicators for diagnosis and prognosis of cardiac diseases.

An in-silico analysis of experimental designs to study ventricular function: A focus on the right ventricle

In-vivo studies of pulmonary vascular disease and pulmonary hypertension (PH) have provided key insight into the progression of right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are practically identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct a practical identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for practical identifiability using profile likelihood-based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from practical identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure-volume data reveals that at least some quantitative data from both ventricles should be included for future experimental studies.

Computational models of ventricular mechanics and adaptation in response to right-ventricular pressure overload

Pulmonary arterial hypertension (PAH) is associated with substantial remodeling of the right ventricle (RV), which may at first be compensatory but at a later stage becomes detrimental to RV function and patient survival. Unlike the left ventricle (LV), the RV remains understudied, and with its thin-walled crescent shape, it is often modeled simply as an appendage of the LV. Furthermore, PAH diagnosis is challenging because it often leaves the LV and systemic circulation largely unaffected. Several treatment strategies such as atrial septostomy, right ventricular assist devices (RVADs) or RV resynchronization therapy have been shown to improve RV function and the quality of life in patients with PAH. However, evidence of their long-term efficacy is limited and lung transplantation is still the most effective and curative treatment option. As such, the clinical need for improved diagnosis and treatment of PAH drives a strong need for increased understanding of drivers and mechanisms of RV growth and remodeling (G&R), and more generally for targeted research into RV mechanics pathology. Computational models stand out as a valuable supplement to experimental research, offering detailed analysis of the drivers and consequences of G&R, as well as a virtual test bench for exploring and refining hypotheses of growth mechanisms. In this review we summarize the current efforts towards understanding RV G&R processes using computational approaches such as reduced-order models, three dimensional (3D) finite element (FE) models, and G&R models. In addition to an overview of the relevant literature of RV computational models, we discuss how the models have contributed to increased scientific understanding and to potential clinical treatment of PAH patients.

Left atrial remodeling in mitral regurgitation: A combined experimental-computational study

Aims

Progressive changes to left atrial (LA) structure and function following mitral regurgitation (MR) remain incompletely understood. This study aimed to demonstrate potential underlying mechanisms using experimental canine models and computer simulations.

Methods

A canine model of MR was created by cauterization of mitral chordae followed by radiofrequency ablation-induced left bundle-branch block (LBBB) after 4 weeks (MR-LBBB group). Animals with LBBB alone served as control. Echocardiography was performed at baseline, acutely after MR induction, and at 4 and 20 weeks, and correlated with histology and computer simulations.

Results

Acute MR augmented LA reservoir and contractile strain (40±4 to 53±6% and -11±5 to -22±9% respectively, p<0.05). LA fractional area change increased significantly (47±4 to 56±4%, p<0.05) while LA end-systolic area remained unchanged (7.2±1.1 versus 7.9±1.1 cm2 respectively, p = 0.08). LA strain ‘pseudonormalized’ after 4 weeks and decompensated at 20 weeks with both strains decreasing to 25±6% and -3±2% respectively (p<0.05) together with a progressive increase in LA end-systolic area (7.2±1.1 to 14.0±6.3 cm2, p<0.05). In the LBBB-group, LA remodeling was less pronounced. Histology showed a trend towards increased interstitial fibrosis in the LA of the MR-LBBB group. Computer simulations indicated that the progressive changes in LA structure and function are a combination of progressive eccentric remodeling and fibrosis.

Conclusion

MR augmented LA strain acutely to supranormal values without significant LA dilation. However, over time, LA strain gradually decreases (pseudornormal and decompensated) with LA dilation. Histology and computer simulations indicated a correlation to a varying degree of LA eccentric remodeling and fibrosis.

A Lumped Two-Compartment Model for Simulation of Ventricular Pump and Tissue Mechanics in Ischemic Heart Disease

Introduction: Computational modeling of cardiac mechanics and hemodynamics in ischemic heart disease (IHD) is important for a better understanding of the complex relations between ischemia-induced heterogeneity of myocardial tissue properties, regional tissue mechanics, and hemodynamic pump function. We validated and applied a lumped two-compartment modeling approach for IHD integrated into the CircAdapt model of the human heart and circulation.

Methods: Ischemic contractile dysfunction was simulated by subdividing a left ventricular (LV) wall segment into a hypothetical contractile and noncontractile compartment, and dysfunction severity was determined by the noncontractile volume fraction (NCVF). Myocardial stiffness was determined by the zero-passive stress length (Ls0,pas) and nonlinearity (kECM) of the passive stress-sarcomere length relation of the noncontractile compartment. Simulated end-systolic pressure volume relations (ESPVRs) for 20% acute ischemia were qualitatively compared between a two- and one-compartment simulation, and parameters of the two-compartment model were tuned to previously published canine data of regional myocardial deformation during acute and prolonged ischemia and reperfusion. In six patients with myocardial infarction (MI), the NCVF was automatically estimated using the echocardiographic LV strain and volume measurements obtained acutely and 6 months after MI. Estimated segmental NCVF values at the baseline and 6-month follow-up were compared with percentage late gadolinium enhancement (LGE) at 6-month follow-up.

Results: Simulation of 20% of NCVF shifted the ESPVR rightward while moderately reducing the slope, while a one-compartment simulation caused a leftward shift with severe reduction in the slope. Through tuning of the NCVF, Ls0,pas, and kECM, it was found that manipulation of the NCVF alone reproduced the deformation during acute ischemia and reperfusion, while additional manipulations of Ls0,pas and kECM were required to reproduce deformation during prolonged ischemia and reperfusion. Out of all segments with LGE>25% at the follow-up, the majority (68%) had higher estimated NCVF at the baseline than at the follow-up. Furthermore, the baseline NCVF correlated better with percentage LGE than NCVF did at the follow-up.

Conclusion: We successfully used a two-compartment model for simulation of the ventricular pump and tissue mechanics in IHD. Patient-specific optimizations using regional myocardial deformation estimated the NCVF in a small cohort of MI patients in the acute and chronic phase after MI, while estimated NCVF values closely approximated the extent of the myocardial scar at the follow-up. In future studies, this approach can facilitate deformation imaging–based estimation of myocardial tissue properties in patients with cardiovascular diseases.

An accurate, robust, and efficient finite element framework with applications to anisotropic, nearly and fully incompressible elasticity

Fiber-reinforced soft biological tissues are typically modeled as hyperelastic, anisotropic, and nearly incompressible materials. To enforce incompressibility a multiplicative split of the deformation gradient into a volumetric and an isochoric part is a very common approach. However, the finite element analysis of such problems often suffers from severe volumetric locking effects and numerical instabilities. In this paper, we present novel methods to overcome volumetric locking phenomena for using stabilized P1-P1 elements. We introduce different stabilization techniques and demonstrate the high robustness and computational efficiency of the chosen methods. In two benchmark problems from the literature as well as an advanced application to cardiac electromechanics, we compare the approach to standard linear elements and show the accuracy and versatility of the methods to simulate anisotropic, nearly and fully incompressible materials. We demonstrate the potential of this numerical framework to accelerate accurate simulations of biological tissues to the extent of enabling patient-specific parameterization studies, where numerous forward simulations are required.

A Closed-Loop Modeling Framework for Cardiac-to-Coronary Coupling

The mechanisms by which cardiac mechanics effect coronary perfusion (cardiac-to-coronary coupling) remain incompletely understood. Several coronary models have been proposed to deepen our understanding of coronary hemodynamics, but possibilities for in-depth studies on cardiac-to-coronary coupling are limited as mechanical properties like myocardial stress and strain are most often neglected. To overcome this limitation, a mathematical model of coronary mechanics and hemodynamics was implemented in the previously published multi-scale CircAdapt model of the closed-loop cardiovascular system. The coronary model consisted of a relatively simple one-dimensional network of the major conduit arteries and veins as well as a lumped parameter model with three transmural layers for the microcirculation. Intramyocardial pressure was assumed to arise from transmission of ventricular cavity pressure into the myocardial wall as well as myocardial stiffness, based on global pump mechanics and local myofiber mechanics. Model-predicted waveforms of global epicardial flow velocity, as well as of intramyocardial flow and diameter were qualitatively and quantitatively compared with reported data. Versatility of the model was demonstrated in a case study of aortic valve stenosis. The reference simulation correctly described the phasic pattern of coronary flow velocity, arterial flow impediment, and intramyocardial differences in coronary flow and diameter. Predicted retrograde flow during early systole in aortic valve stenosis was in agreement with measurements obtained in patients. In conclusion, we presented a powerful multi-scale modeling framework that enables realistic simulation of coronary mechanics and hemodynamics. This modeling framework can be used as a research platform for in-depth studies of cardiac-to-coronary coupling, enabling study of the effect of abnormal myocardial tissue properties on coronary hemodynamics.

Individual variability in animal-specific hemodynamic compensation following myocardial infarction

Ventricular enlargement and heart failure are common in patients who survive a myocardial infarction (MI). There is striking variability in the degree of post-infarction ventricular remodeling, however, and no one factor or set of factors have been identified that predicts heart failure risk well. Sympathetic activation directly and indirectly modulates hypertrophic stimuli by altering both neurohormonal milieu and ventricular loading. In a recent study, we developed a method to identify the balance of reflex compensatory mechanisms employed by individual animals following MI based on measured hemodynamics. Here, we conducted prospective studies of acute myocardial infarction in rats to test the degree of variability in reflex compensation as well as whether responses to pharmacologic agents targeted at those reflex mechanisms could be anticipated in individual animals. We found that individual animals use very different mixtures of reflex compensation in response to experimental coronary ligation. Some of these mechanisms were related - animals that compensated strongly with venoconstriction tended to exhibit a decrease in the contractility of the surviving myocardium and those that increased contractility tended to exhibit venodilation. Furthermore, some compensatory mechanisms - such as venoconstriction - increased the extent of predicted ventricular enlargement. Unfortunately, initial reflex responses to infarction were a poor predictor of subsequent responses to pharmacologic agents, suggesting that customizing pharmacologic therapy to individuals based on an initial response will be challenging.

Optimization of cardiac resynchronization therapy based on a cardiac electromechanics-perfusion computational model

Cardiac resynchronization therapy (CRT) is an established treatment for left bundle branch block (LBBB) resulting in mechanical dyssynchrony. Approximately 1/3 of patients with CRT, however, are non-responders. To understand factors affecting CRT response, an electromechanics-perfusion computational model based on animal-specific left ventricular (LV) geometry and coronary vascular networks located in the septum and LV free wall is developed. The model considers contractility-flow and preload-activation time relationships, and is calibrated to simultaneously match the experimental measurements in terms of the LV pressure, volume waveforms and total coronary flow in the left anterior descending and left circumflex territories from 2 swine models under right atrium and right ventricular pacing. The model is then applied to investigate the responses of CRT indexed by peak LV pressure and (dP/dt)max at multiple pacing sites with different degrees of perfusion in the LV free wall. Without the presence of ischemia, the model predicts that basal-lateral endocardial region is the optimal pacing site that can best improve (dP/dt)max by 20%, and is associated with the shortest activation time. In the presence of ischemia, a non-ischemic region becomes the optimal pacing site when coronary flow in the ischemic region fell below 30% of its original value. Pacing at the ischemic region produces little response at that perfusion level. The optimal pacing site is associated with one that optimizes the LV activation time. These findings suggest that CRT response is affected by both pacing site and coronary perfusion, which may have clinical implication in improving CRT responder rates.

A rapid electromechanical model to predict reverse remodeling following cardiac resynchronization therapy

Cardiac resynchronization therapy (CRT) is an effective therapy for patients who suffer from heart failure and ventricular dyssynchrony such as left bundle branch block (LBBB). When it works, it reverses adverse left ventricular (LV) remodeling and the progression of heart failure. However, CRT response rate is currently as low as 50-65%. In theory, CRT outcome could be improved by allowing clinicians to tailor the therapy through patient-specific lead locations, timing, and/or pacing protocol. However, this also presents a dilemma: there are far too many possible strategies to test during the implantation surgery. Computational models could address this dilemma by predicting remodeling outcomes for each patient before the surgery takes place. Therefore, the goal of this study was to develop a rapid computational model to predict reverse LV remodeling following CRT. We adapted our recently developed computational model of LV remodeling to simulate the mechanics of ventricular dyssynchrony and added a rapid electrical model to predict electrical activation timing. The model was calibrated to quantitatively match changes in hemodynamics and global and local LV wall mass from a canine study of LBBB and CRT. The calibrated model was used to investigate the influence of LV lead location and ischemia on CRT remodeling outcome. Our model results suggest that remodeling outcome varies with both lead location and ischemia location, and does not always correlate with short-term improvement in QRS duration. The results and time frame required to customize and run this model suggest promise for this approach in a clinical setting.

A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D-0D model to a limit cycle under baseline conditions, the model's ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible.

A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D-0D model to a limit cycle under baseline conditions, the model's ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible.

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.

Uncertainty Quantification of Regional Cardiac Tissue Properties in Arrhythmogenic Cardiomyopathy Using Adaptive Multiple Importance Sampling

Introduction: Computational models of the cardiovascular system are widely used to simulate cardiac (dys)function. Personalization of such models for patient-specific simulation of cardiac function remains challenging. Measurement uncertainty affects accuracy of parameter estimations. In this study, we present a methodology for patient-specific estimation and uncertainty quantification of parameters in the closed-loop CircAdapt model of the human heart and circulation using echocardiographic deformation imaging. Based on patient-specific estimated parameters we aim to reveal the mechanical substrate underlying deformation abnormalities in patients with arrhythmogenic cardiomyopathy (AC). Methods: We used adaptive multiple importance sampling to estimate the posterior distribution of regional myocardial tissue properties. This methodology is implemented in the CircAdapt cardiovascular modeling platform and applied to estimate active and passive tissue properties underlying regional deformation patterns, left ventricular volumes, and right ventricular diameter. First, we tested the accuracy of this method and its inter- and intraobserver variability using nine datasets obtained in AC patients. Second, we tested the trueness of the estimation using nine in silico generated virtual patient datasets representative for various stages of AC. Finally, we applied this method to two longitudinal series of echocardiograms of two pathogenic mutation carriers without established myocardial disease at baseline. Results: Tissue characteristics of virtual patients were accurately estimated with a highest density interval containing the true parameter value of 9% (95% CI [0-79]). Variances of estimated posterior distributions in patient data and virtual data were comparable, supporting the reliability of the patient estimations. Estimations were highly reproducible with an overlap in posterior distributions of 89.9% (95% CI [60.1-95.9]). Clinically measured deformation, ejection fraction, and end-diastolic volume were accurately simulated. In presence of worsening of deformation over time, estimated tissue properties also revealed functional deterioration. Conclusion: This method facilitates patient-specific simulation-based estimation of regional ventricular tissue properties from non-invasive imaging data, taking into account both measurement and model uncertainties. Two proof-of-principle case studies suggested that this cardiac digital twin technology enables quantitative monitoring of AC disease progression in early stages of disease.

Hemodynamics-driven mathematical model of first and second heart sound generation

We propose a novel, two-degree of freedom mathematical model of mechanical vibrations of the heart that generates heart sounds in CircAdapt, a complete real-time model of the cardiovascular system. Heart sounds during rest, exercise, biventricular (BiVHF), left ventricular (LVHF) and right ventricular heart failure (RVHF) were simulated to examine model functionality in various conditions. Simulated and experimental heart sound components showed both qualitative and quantitative agreements in terms of heart sound morphology, frequency, and timing. Rate of left ventricular pressure (LV dp/dt_max) and first heart sound (S1) amplitude were proportional with exercise level. The relation of the second heart sound (S2) amplitude with exercise level was less significant. BiVHF resulted in amplitude reduction of S1. LVHF resulted in reverse splitting of S2 and an amplitude reduction of only the left-sided heart sound components, whereas RVHF resulted in a prolonged splitting of S2 and only a mild amplitude reduction of the right-sided heart sound components. In conclusion, our hemodynamics-driven mathematical model provides fast and realistic simulations of heart sounds under various conditions and may be helpful to find new indicators for diagnosis and prognosis of cardiac diseases.

Among various vital signals used for diagnosis and prognosis of cardiac diseases, heart sounds are not employed precisely because physicians subjectively assess their auscultatory findings. On the other hand, recorded heart sounds are also difficult to quantitatively relate to different cardiac conditions given the complex nature of their generation. We therefore employed cardiovascular modeling and developed a novel hemodynamics-driven mathematical model for heart sound generation to unravel the relationships between heart sounds and other vital signals. Simulated and experimental heart sound components showed qualitative and quantitative agreements in terms of heart sound morphology, frequency, and timing, not only during normal conditions, but also during simulated exercise and heart failure. Our model can be used to understand generation of heart sounds in more details and may be helpful to find new diagnostic indicators and treatment methods of cardiac disorders.

Both beat-to-beat changes in RR-interval and left ventricular filling time determine ventricular function during atrial fibrillation

Aims

The irregular atrial electrical activity during atrial fibrillation (AF) is associated with a variable left ventricular (LV) systolic function. The mechanisms determining LV function during AF remain incompletely understood. We aimed at elucidating how changes in RR-interval and LV preload affect LV function during AF.

Methods and results

Beat-to-beat speckle-tracking echocardiography was performed in 10 persistent AF patients. We evaluated the relation between longitudinal LV peak strain and preceding RR-interval during AF. We used the CircAdapt computational model to evaluate beat-to-beat preload and peak strain during AF for each patient by imposing the patient-specific RR-interval sequences and a non-contractile atrial myocardium. Generic simulations with artificial RR-interval sequences quantified the haemodynamic changes induced by sudden irregular beats. Clinical data and simulations both showed a larger sensitivity of peak strain to changes in preceding RR-interval at slow heart rate (HR) (cycle length, CL <750 ms) than at faster HR. Simulations explained this by a difference in preload of the current beat. Generic simulations confirmed a larger sensitivity of peak strain to preceding RR-interval at fast HR (CL = 600 ms: Δ peak strain = 3.7% vs. 900 ms: Δ peak strain = 0.3%) as in the patients. They suggested that longer LV activation with respect to preceding RR-interval is determinant for this sensitivity.

Conclusions

During AF, longitudinal LV peak strain is highly variable, particularly at fast HR. Beat-to-beat changes in preload explain the differences in LV systolic function. Simulations revealed that a reduced diastolic LV filling time can explain the increased variability at fast HR.

Electromechanical substrate characterization in arrhythmogenic cardiomyopathy using imaging-based patient-specific computer simulations

AIMS

Arrhythmogenic cardiomyopathy (AC) is an inherited cardiac disease, characterized by life-threatening ventricular arrhythmias and progressive cardiac dysfunction. The aim of this study is to use computer simulations to non-invasively estimate the individual patient's myocardial tissue substrates underlying regional right ventricular (RV) deformation abnormalities in a cohort of AC mutation carriers.

METHODS AND RESULTS

In 68 AC mutation carriers and 20 control subjects, regional longitudinal deformation patterns of the RV free wall (RVfw), interventricular septum (IVS), and left ventricular free wall (LVfw) were obtained using speckle-tracking echocardiography. We developed and used a patient-specific parameter estimation protocol based on the multi-scale CircAdapt cardiovascular system model to create virtual AC subjects. Using the individual's deformation data as model input, this protocol automatically estimated regional RVfw and global IVS and LVfw tissue properties. The computational model was able to reproduce clinically measured regional deformation patterns for all subjects, with highly reproducible parameter estimations. Simulations revealed that regional RVfw heterogeneity of both contractile function and compliance were increased in subjects with clinically advanced disease compared to mutation carriers without clinically established disease (17 ± 13% vs. 8 ± 4%, P = 0.01 and 18 ± 11% vs. 10 ± 7%, P < 0.01, respectively). No significant difference in activation delay was found.

CONCLUSION

Regional RV deformation abnormalities in AC mutation carriers were related to reduced regional contractile function and tissue compliance. In clinically advanced disease stages, a characteristic apex-to-base heterogeneity of tissue abnormalities was present in the majority of the subjects, with most pronounced disease in the basal region of the RVfw.

Increased myocardial stiffness more than impaired relaxation function limits cardiac performance during exercise in heart failure with preserved ejection fraction: a virtual patient study

Aims

The relative impact of left ventricular (LV) diastolic dysfunction (LVDD) and impaired left atrial (LA) function on cardiovascular haemodynamics in heart failure with preserved ejection fraction (HFpEF) is largely unknown. We performed virtual patient simulations to elucidate the relative effects of these factors on haemodynamics at rest and during exercise.

Methods and results

The CircAdapt cardiovascular system model was used to simulate cardiac haemodynamics in wide ranges of impaired LV relaxation function, increased LV passive stiffness, and impaired LA function. Simulations showed that LV ejection fraction (LVEF) was preserved (>50%), despite these changes in LV and LA function. Impairment of LV relaxation function decreased E/A ratio and mildly increased LV filling pressure at rest. Increased LV passive stiffness resulted in increased E/A ratio, LA dilation and markedly elevated LV filling pressure. Impairment of LA function increased E/A ratio and LV filling pressure, explaining inconsistent grading of LVDD using echocardiographic indices. Exercise simulations showed that increased LV passive stiffness exerts a stronger exercise-limiting effect than impaired LV relaxation function does, especially with impaired LA function.

Conclusion

The CircAdapt model enabled realistic simulation of virtual HFpEF patients, covering a wide spectrum of LVDD and related limitations of cardiac exercise performance, all with preserved resting LVEF. Simulations suggest that increased LV passive stiffness, more than impaired relaxation function, reduces exercise tolerance, especially when LA function is impaired. In future studies, the CircAdapt model can serve as a valuable platform for patient-specific simulations to identify the disease substrate(s) underlying the individual HFpEF patient's cardiovascular phenotype.

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.

Parameter subset reduction for patient-specific modelling of arrhythmogenic cardiomyopathy-related mutation carriers in the CircAdapt model

Arrhythmogenic cardiomyopathy (AC) is an inherited cardiac disease, clinically characterized by life-threatening ventricular arrhythmias and progressive cardiac dysfunction. Patient-specific computational models could help understand the disease progression and may help in clinical decision-making. We propose an inverse modelling approach using the CircAdapt model to estimate patient-specific regional abnormalities in tissue properties in AC subjects. However, the number of parameters (n = 110) and their complex interactions make personalized parameter estimation challenging. The goal of this study is to develop a framework for parameter reduction and estimation combining Morris screening, quasi-Monte Carlo (qMC) simulations and particle swarm optimization (PSO). This framework identifies the best subset of tissue properties based on clinical measurements allowing patient-specific identification of right ventricular tissue abnormalities. We applied this framework on 15 AC genotype-positive subjects with varying degrees of myocardial disease. Cohort studies have shown that atypical regional right ventricular (RV) deformation patterns reveal an early-stage AC disease. The CircAdapt model of cardiovascular mechanics and haemodynamics has already demonstrated its ability to capture typical deformation patterns of AC subjects. We, therefore, use clinically measured cardiac deformation patterns to estimate model parameters describing myocardial disease substrates underlying these AC-related RV deformation abnormalities. Morris screening reduced the subset to 48 parameters. qMC and PSO further reduced the subset to a final selection of 16 parameters, including regional tissue contractility, passive stiffness, activation delay and wall reference area. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Software for Post-Processing Analysis of Strain Curves: The D-Station

Fundamento

O emprego de Speckle Tracking para estudo da função cardíaca tem grande aplicabilidade em diversos cenários. A expansão do uso deste método requer ferramentas que permitam a extração de dados relevantes das curvas de deformação cardíaca e que sejam adicionais aos parâmetros habitualmente utilizados.

Objetivos

O presente trabalho visa apresentar e validar um software de uso livre, denominado D-station, para análise das curvas de deformação cardíaca.

Métodos

A partir de arquivos raw data, o D-Station realiza a separação das fases do ciclo cardíaco, exibe simultaneamente curvas de Strain e Strain Rate de diferentes câmaras cardíacas. Para validação do software utilizamos o parâmetro Global Longitudinal Strain (GLS) avaliando-o: 1) Graficamente, a partir da comparação das Medidas emparelhadas de GLS no EchoPAC e D-Station frente à linha de igualdade; 2) pelo Coeficiente de Correlação dessas medidas; 3) pelo Teste de Hipóteses (p > 0,05); e 4) pelo Método Gráfico de Bland-Altman.

Resultados

O Coeficiente rho de Spearman apontou forte correlação entre as medidas, o Teste de Hipóteses retornou um p-value = 0.6798 >> 0,05, que também indicou a equivalência entre elas; o Método gráfico de Bland-Altman mostrou um viés ≤ 1% e dispersão ≤ 2% entre as medidas. Os testes mostraram que para valores de GLS inferiores à 10% há a tendência de aumento das diferenças percentuais, mas seus valores absolutos ainda são baixos.

Conclusão

O D-Station foi validado como uma aplicação suplementar ao EchoPAC que utiliza o raw data das curvas de Strain e Strain Rate obtidos por software proprietário. (Arq Bras Cardiol. 2020; 114(3):496-506)