Predicting the Time Course of Ventricular Dilation and Thickening Using a Rapid Compartmental Model

Contributions of mechanical loading and hormonal changes to eccentric hypertrophy during volume overload: a Bayesian analysis using logic-based network models

Primary mitral regurgitation (MR) is a pathology that alters mechanical loading on the left ventricle and induces a distinctive ventricular remodeling response known as eccentric hypertrophy. Drug therapies may alleviate symptoms, but only mitral valve repair can provide significant recovery of cardiac function and dimensions. However, 20% of patients still develop systolic dysfunction post-operatively despite being treated according to the current guidelines. Thus, better understanding of the hypertrophic process in the setting of ventricular volume overload (VO) is needed to improve and better personalize the management of MR. To address this knowledge gap, we employ a Bayesian approach to combine data from 70 studies on experimental volume overload in dogs and rats and use it to calibrate a logic-based network model of hypertrophic signaling in myocytes. The calibrated model suggests that growth in experimental VO is mostly driven by the neurohormonal response, with an initial increase in myocardial tissue stretch being compensated by subsequent remodeling fairly early in the time course of VO. This observation contrasts with a common perception that volume-overload hypertrophy is driven primarily by increased myocyte strain. The model suggests that Endothelin1 receptor activity plays a central role in driving hypertrophic responses and the activation of the fetal gene program. The model reproduces a number of responses to drug therapy not used in its calibration, and predicts that a combination of endothelin receptor antagonist and angiotensin receptor blockers would have the greatest potential to dampen cardiomyocyte hypertrophy and dysfunction in VO.

Multiscale Finite Element Modeling of Left Ventricular Growth in Simulations of Valve Disease

Multiscale models of the cardiovascular system are emerging as effective tools for investigating the mechanisms that drive ventricular growth and remodeling. These models can predict how molecular-level mechanisms impact organ-level structure and function and could provide new insights that help improve patient care. MyoFE is a multiscale computer framework that bridges molecular and organ-level mechanisms in a finite element model of the left ventricle that is coupled with the systemic circulation. In this study, we extend MyoFE to include a growth algorithm, based on volumetric growth theory, to simulate concentric growth (wall thickening/thinning) and eccentric growth (chamber dilation/constriction) in response to valvular diseases. Specifically in our model, concentric growth is controlled by time-averaged total stress along the fiber direction over a cardiac cycle while eccentric growth responds to time-averaged intracellular myofiber passive stress over a cardiac cycle. The new framework correctly predicted different forms of growth in response to two types of valvular diseases, namely aortic stenosis and mitral regurgitation. Furthermore, the model predicted that LV size and function are nearly restored (reversal of growth) when the disease-mimicking perturbation was removed in the simulations for each valvular disorder. In conclusion, the simulations suggest that time-averaged total stress along the fiber direction and time-averaged intracellular myofiber passive stress can be used to drive concentric and eccentric growth in simulations of valve disease.

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.

Computational model captures cardiac growth in hypertensive pregnancies and in the postpartum period

Heart growth in the pregnant patient helps maintain cardiovascular function while supporting the growing fetus. However, in some cases, the cardiovascular demand of pregnancy can trigger life-threatening conditions, including hypertensive disorders of pregnancy and peripartum cardiomyopathy. The mechanisms that control heart growth throughout pregnancy are unclear, and treating these diseases remains elusive. We previously developed a computational model that accounts for hormonal and hemodynamic interactions throughout pregnancy and demonstrated its ability to capture realistic cardiac growth in normal rat pregnancy. In this study, we evaluated whether this model could capture heart growth beyond normal pregnancy. After further validation of our normal pregnancy predictions, we tested our model predictions of three rat studies of hypertensive pregnancies. We next simulated the postpartum period and examined the impact of lactation on cardiac growth in rats. We demonstrate that our multiscale model can capture cardiac growth associated with new-onset hypertension during pregnancy and lactation status in the postpartum period. We conclude by elaborating on the potential clinical utility of our model in the future.NEW & NOTEWORTHY Our multiscale model predicts appropriate heart growth beyond normal pregnancy, including elevated heart weights in rats with induced hypertension during pregnancy and in lactating mice and decreased heart weight in nonlactating mice. Our model captures distinct mechanisms that result in similar organ-level growth, highlighting its potential to distinguish healthy from diseased pregnancy-induced growth.

Mechanisms of coronary sinus reducer for treatment of myocardial ischemia: in silico study

The coronary sinus reducer (CSR) is an emerging medical device for treating patients with refractory angina, often associated with myocardial ischemia. Patients implanted with CSR have shown positive outcomes, but the underlying mechanisms are unclear. This study sought to understand the mechanisms of CSR by investigating its effects on coronary microcirculation hemodynamics that may help explain the therapy's efficacy. We applied a validated computer model of the coronary microcirculation to investigate how CSR affects hemodynamics under different degrees of coronary artery stenosis. With moderate coronary stenosis, an increase in capillary transit time (CTT) [up to 69% with near-complete coronary sinus (CS) occlusion] is the key change associated with CSR. Because capillaries in the microcirculation can still receive oxygenated blood from the upstream artery with moderate stenosis, the increase in CTT allows more time for the exchange of gases and nutrients, aiding tissue oxygenation. With severe coronary stenosis; however, the redistribution of blood draining from the nonischemic region to the ischemic region (up to 96% with near-complete CS occlusion) and the reduction in capillary flow heterogeneity are the key changes associated with CSR. Because blood draining from the nonischemic region is not completely devoid of O2, the redistribution of blood to the capillaries in the ischemic region by CSR is beneficial especially when little or no oxygenated blood reaches these capillaries. This simulation study provides insights into the mechanisms of CSR in improving clinical symptoms. The mechanisms differ with the severity of the upstream stenosis.NEW & NOTEWORTHY Emerging coronary venous retroperfusion treatments, particularly coronary sinus reducer (CSR) for refractory angina linked to myocardial ischemia, show promise; however, their mechanisms of action are not well understood. We find that CSR's effectiveness varies with the severity of coronary stenosis. In moderate stenosis, CSR improves tissue oxygenation by increasing capillary transit time, whereas in severe stenosis, it redistributes blood from nonischemic to ischemic regions and reduces capillary flow heterogeneity.

Simulation of coronary capillary transit time based on full vascular model of the heart

Capillary transit time (CTT) is a fundamental determinant of gas exchange between blood and tissues in the heart and other organs. Despite advances in experimental techniques, it remains difficult to measure coronary CTT in vivo. Here, we developed a novel computational framework that couples coronary microcirculation with cardiac mechanics in a closed-loop system that enables prediction of hemodynamics in the entire coronary network, including arteries, veins, and capillaries. We also developed a novel "particle-tracking" approach for computing CTT where "virtual tracers" are individually tracked as they traverse the capillary network. Model predictions compare well with blood pressure and flow rate distributions in the arterial network reported in previous studies. Model predictions of transit times in the capillaries (1.21 ± 1.5 s) and entire coronary network (11.8 ± 1.8 s) also agree with measurements. We show that, with increasing coronary artery stenosis (as quantified by fractional flow reserve, FFR), intravascular pressure and flow rate downstream are reduced but remain non-stationary even at 100 % stenosis because some flow (∼3 %) is redistributed from the non-occluded to the occluded territories. Importantly, the model predicts that occlusion of a large artery results in higher CTT. For moderate stenosis (FFR > 0.6), the increase in CTT (from 1.21 s without stenosis to 2.23 s at FFR=0.6) is caused by a decrease in capillary flow rate. In severe stenosis (FFR = 0.1), the increase in CTT to 14.2 s is due to both a decrease in flow rate and an increase in path length taken by "virtual tracers" in the capillary network.

A multiscale finite element model of left ventricular mechanics incorporating baroreflex regulation

Cardiovascular function is regulated by a short-term hemodynamic baroreflex loop, which tries to maintain arterial pressure at a normal level. In this study, we present a new multiscale model of the cardiovascular system named MyoFE. This framework integrates a mechanistic model of contraction at the myosin level into a finite-element-based model of the left ventricle pumping blood through the systemic circulation. The model is coupled with a closed-loop feedback control of arterial pressure inspired by a baroreflex algorithm previously published by our team. The reflex loop mimics the afferent neuron pathway via a normalized signal derived from arterial pressure. The efferent pathway is represented by a kinetic model that simulates the net result of neural processing in the medulla and cell-level responses to autonomic drive. The baroreflex control algorithm modulates parameters such as heart rate and vascular tone of vessels in the lumped-parameter model of systemic circulation. In addition, it spatially modulates intracellular Ca2+ dynamics and molecular-level function of both the thick and the thin myofilaments in the left ventricle. Our study demonstrates that the baroreflex algorithm can maintain arterial pressure in the presence of perturbations such as acute cases of altered aortic resistance, mitral regurgitation, and myocardial infarction. The capabilities of this new multiscale model will be utilized in future research related to computational investigations of growth and remodeling.

Understanding heterogeneous mechanisms of heart failure with preserved ejection fraction through cardiorenal mathematical modeling

In contrast to heart failure (HF) with reduced ejection fraction (HFrEF), effective interventions for HF with preserved ejection fraction (HFpEF) have proven elusive, in part because it is a heterogeneous syndrome with incompletely understood pathophysiology. This study utilized mathematical modeling to evaluate mechanisms distinguishing HFpEF and HFrEF. HF was defined as a state of chronically elevated left ventricle end diastolic pressure (LVEDP > 20mmHg). First, using a previously developed cardiorenal model, sensitivities of LVEDP to potential contributing mechanisms of HFpEF, including increased myocardial, arterial, or venous stiffness, slowed ventricular relaxation, reduced LV contractility, hypertension, or reduced venous capacitance, were evaluated. Elevated LV stiffness was identified as the most sensitive factor. Large LV stiffness increases alone, or milder increases combined with either decreased LV contractility, increased arterial stiffness, or hypertension, could increase LVEDP into the HF range without reducing EF. We then evaluated effects of these mechanisms on mechanical signals of cardiac outward remodeling, and tested the ability to maintain stable EF (as opposed to progressive EF decline) under two remodeling assumptions: LV passive stress-driven vs. strain-driven remodeling. While elevated LV stiffness increased LVEDP and LV wall stress, it mitigated wall strain rise for a given LVEDP. This suggests that if LV strain drives outward remodeling, a stiffer myocardium will experience less strain and less outward dilatation when additional factors such as impaired contractility, hypertension, or arterial stiffening exacerbate LVEDP, allowing EF to remain normal even at high filling pressures. Thus, HFpEF heterogeneity may result from a range of different pathologic mechanisms occurring in an already stiffened myocardium. Together, these simulations further support LV stiffening as a critical mechanism contributing to elevated cardiac filling pressures; support LV passive strain as the outward dilatation signal; offer an explanation for HFpEF heterogeneity; and provide a mechanistic explanation distinguishing between HFpEF and HFrEF.

The impact of thickness heterogeneity on soft tissue biomechanics: a novel measurement technique and a demonstration on heart valve tissue

The mechanical properties of soft tissues are driven by their complex, heterogeneous composition and structure. Interestingly, studies of soft tissue biomechanics often ignore spatial heterogeneity. In our work, we are therefore interested in exploring the impact of tissue heterogeneity on the mechanical properties of soft tissues. Therein, we specifically focus on soft tissue heterogeneity arising from spatially varying thickness. To this end, our first goal is to develop a non-destructive measurement technique that has a high spatial resolution, provides continuous thickness maps, and is fast. Our secondary goal is to demonstrate that including spatial variation in thickness is important to the accuracy of biomechanical analyses. To this end, we use mitral valve leaflet tissue as our model system. To attain our first goal, we identify a soft tissue-specific contrast protocol that enables thickness measurements using a Keyence profilometer. We also show that this protocol does not affect our tissues' mechanical properties. To attain our second goal, we conduct virtual biaxial, bending, and buckling tests on our model tissue both ignoring and considering spatial variation in thickness. Thereby, we show that the assumption of average, homogeneous thickness distributions significantly alters the results of biomechanical analyses when compared to including true, spatially varying thickness distributions. In conclusion, our work provides a novel measurement technique that can capture continuous thickness maps non-invasively, at high resolution, and in a short time. Our work also demonstrates the importance of including heterogeneous thickness in biomechanical analyses of soft tissues.

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.

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.

Computational modelling of multi-temporal ventricular-vascular interactions during the progression of pulmonary arterial hypertension

A computational framework is developed to consider the concurrent growth and remodelling (G&R) processes occurring in the large pulmonary artery (PA) and right ventricle (RV), as well as ventricular-vascular interactions during the progression of pulmonary arterial hypertension (PAH). This computational framework couples the RV and the proximal PA in a closed-loop circulatory system that operates in a short timescale of a cardiac cycle, and evolves over a long timescale due to G&R processes in the PA and RV. The framework predicts changes in haemodynamics (e.g. 68.2% increase in mean PA pressure), RV geometry (e.g. 38% increase in RV end-diastolic volume) and PA tissue microstructure (e.g. 90% increase in collagen mass) that are consistent with clinical and experimental measurements of PAH. The framework also predicts that a reduction in RV contractility is associated with long-term RV chamber dilation, a common biomarker observed in the late-stage PAH. Sensitivity analyses on the G&R rate constants show that large PA stiffening (both short and long term) is affected by RV remodelling more than the reverse. This framework can serve as a foundation for the future development of a more predictive and comprehensive cardiovascular G&R model with realistic heart and vascular geometries.

Multiscale model of heart growth during pregnancy: integrating mechanical and hormonal signaling

Pregnancy stands at the interface of mechanics and biology. The growing fetus continuously loads the maternal organs as circulating hormone levels surge, leading to significant changes in mechanical and hormonal cues during pregnancy. In response, maternal soft tissues undergo remarkable growth and remodeling to support the mother and baby for a healthy pregnancy. We focus on the maternal left ventricle, which increases its cardiac output and mass during pregnancy. This study develops a multiscale cardiac growth model for pregnancy to understand how mechanical and hormonal cues interact to drive this growth process. We coupled a cell signaling network model that predicts cell-level hypertrophy in response to hormones and stretch to a compartmental model of the rat heart and circulation that predicts organ-level growth in response to hemodynamic changes. We calibrated this multiscale model to data from experimental volume overload and hormonal infusions of angiotensin 2 (AngII), estrogen (E2), and progesterone (P4). We then validated the model's ability to capture interactions between inputs by comparing model predictions against published observations for the combinations of VO + E2 and AngII + E2. Finally, we simulated pregnancy-induced changes in hormones and hemodynamics to predict heart growth during pregnancy. Our model produced growth consistent with experimental data. Overall, our analysis suggests that the rise in P4 during the first half of gestation is an important contributor to heart growth during pregnancy. We conclude with suggestions for future experimental studies that will provide a better understanding of how hormonal and mechanical cues interact to drive pregnancy-induced heart growth.

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.

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.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

Predictive Modeling of Secondary Pulmonary Hypertension in Left Ventricular Diastolic Dysfunction

Diastolic dysfunction is a common pathology occurring in about one third of patients affected by heart failure. This condition may not be associated with a marked decrease in cardiac output or systemic pressure and therefore is more difficult to diagnose than its systolic counterpart. Compromised relaxation or increased stiffness of the left ventricle induces an increase in the upstream pulmonary pressures, and is classified as secondary or group II pulmonary hypertension (2018 Nice classification). This may result in an increase in the right ventricular afterload leading to right ventricular failure. Elevated pulmonary pressures are therefore an important clinical indicator of diastolic heart failure (sometimes referred to as heart failure with preserved ejection fraction, HFpEF), showing significant correlation with associated mortality. However, accurate measurements of this quantity are typically obtained through invasive catheterization and after the onset of symptoms. In this study, we use the hemodynamic consistency of a differential-algebraic circulation model to predict pulmonary pressures in adult patients from other, possibly non-invasive, clinical data. We investigate several aspects of the problem, including the ability of model outputs to represent a sufficiently wide pathologic spectrum, the identifiability of the model's parameters, and the accuracy of the predicted pulmonary pressures. We also find that a classifier using the assimilated model parameters as features is free from the problem of missing data and is able to detect pulmonary hypertension with sufficiently high accuracy. For a cohort of 82 patients suffering from various degrees of heart failure severity, we show that systolic, diastolic, and wedge pulmonary pressures can be estimated on average within 8, 6, and 6 mmHg, respectively. We also show that, in general, increased data availability leads to improved predictions.

A multiscale model of cardiac concentric hypertrophy incorporating both mechanical and hormonal drivers of growth

Growth and remodeling in the heart is driven by a combination of mechanical and hormonal signals that produce different patterns of growth in response to exercise, pregnancy, and various pathologies. In particular, increases in afterload lead to concentric hypertrophy, a thickening of the walls that increases the contractile ability of the heart while reducing wall stress. In the current study, we constructed a multiscale model of cardiac hypertrophy that connects a finite-element model representing the mechanics of the growing left ventricle to a cell-level network model of hypertrophic signaling pathways that accounts for changes in both mechanics and hormones. We first tuned our model to capture published in vivo growth trends for isoproterenol infusion, which stimulates β-adrenergic signaling pathways without altering mechanics, and for transverse aortic constriction (TAC), which involves both elevated mechanics and altered hormone levels. We then predicted the attenuation of TAC-induced hypertrophy by two distinct genetic interventions (transgenic Gq-coupled receptor inhibitor overexpression and norepinephrine knock-out) and by two pharmacologic interventions (angiotensin receptor blocker losartan and β-blocker propranolol) and compared our predictions to published in vivo data for each intervention. Our multiscale model captured the experimental data trends reasonably well for all conditions simulated. We also found that when prescribing realistic changes in mechanics and hormones associated with TAC, the hormonal inputs were responsible for the majority of the growth predicted by the multiscale model and were necessary in order to capture the effect of the interventions for TAC.

Computational models of cardiac hypertrophy

Cardiac hypertrophy, defined as an increase in mass of the heart, is a complex process driven by simultaneous changes in hemodynamics, mechanical stimuli, and hormonal inputs. It occurs not only during pre- and post-natal development but also in adults in response to exercise, pregnancy, and a range of cardiovascular diseases. One of the most exciting recent developments in the field of cardiac biomechanics is the advent of computational models that are able to accurately predict patterns of heart growth in many of these settings, particularly in cases where changes in mechanical loading of the heart play an import role. These emerging models may soon be capable of making patient-specific growth predictions that can be used to guide clinical interventions. Here, we review the history and current state of cardiac growth models and highlight three main limitations of current approaches with regard to future clinical application: their inability to predict the regression of heart growth after removal of a mechanical overload, inability to account for evolving hemodynamics, and inability to incorporate known growth effects of drugs and hormones on heart growth. Next, we outline growth mechanics approaches used in other fields of biomechanics and highlight some potential lessons for cardiac growth modeling. Finally, we propose a multiscale modeling approach for future studies that blends tissue-level growth models with cell-level signaling models to incorporate the effects of hormones in the context of pregnancy-induced heart growth.

Biomechanics of infarcted left ventricle: a review of modelling

Mathematical modelling in biomechanics of infarcted left ventricle (LV) serves as an indispensable tool for remodelling mechanism exploration, LV biomechanical property estimation and therapy assessment after myocardial infarction (MI). However, a review of mathematical modelling after MI has not been seen in the literature so far. In the paper, a systematic review of mathematical models in biomechanics of infarcted LV was established. The models include comprehensive cardiovascular system model, essential LV pressure-volume and stress-stretch models, constitutive laws for passive myocardium and scars, tension models for active myocardium, collagen fibre orientation optimization models, fibroblast and collagen fibre growth/degradation models and integrated growth-electro-mechanical model after MI. The primary idea, unique characteristics and key equations of each model were identified and extracted. Discussions on the models were provided and followed research issues on them were addressed. Considerable improvements in the cardiovascular system model, LV aneurysm model, coupled agent-based models and integrated electro-mechanical-growth LV model are encouraged. Substantial attention should be paid to new constitutive laws with respect to stress-stretch curve and strain energy function for infarcted passive myocardium, collagen fibre orientation optimization in scar, cardiac rupture and tissue damage and viscoelastic effect post-MI in the future.

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.

Stimulus-effect relations for left ventricular growth obtained with a simple multi-scale model: the influence of hemodynamic feedback

Cardiac growth is an important mechanism for the human body to respond to changes in blood flow demand. Being able to predict the development of chronic growth is clinically relevant, but so far models to predict growth have not reached consensus on the stimulus–effect relation. In a previously published study, we modeled cardiac and hemodynamic function through a lumped parameter approach. We evaluated cardiac growth in response to valve disease using various stimulus–effect relations and observed an unphysiological decline pump function. Here we extend that model with a model of hemodynamic feedback that maintains mean arterial pressure and cardiac output through adaptation of peripheral resistance and circulatory unstressed volume. With the combined model, we obtain stable growth and restoration of pump function for most growth laws. We conclude that a mixed combination of stress and strain stimuli to drive cardiac growth is most promising since it (1) reproduces clinical observations on cardiac growth well, (2) requires only a small, clinically realistic adaptation of the properties of the circulatory system and (3) is robust in the sense that results were fairly insensitive to the exact choice of the chosen mechanics loading measure. This finding may be used to guide the choice of growth laws in more complex finite element models of cardiac growth, suitable for predicting the response to spatially varying changes in tissue load. Eventually, the current model may form a basis for a tool to predict patient-specific growth in response to spatially homogeneous changes in tissue load, since it is computationally inexpensive.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression

A key feature of living tissues is their capacity to remodel and grow in response to environmental cues. Within continuum mechanics, this process can be captured with the multiplicative split of the deformation gradient into growth and elastic contributions. The mechanical and biological response during tissue adaptation is characterized by inherent variability. Accounting for this uncertainty is critical to better understand tissue mechanobiology, and, moreover, it is of practical importance if we aim to develop predictive models for clinical use. However, the current gold standard in computational models of growth and remodeling remains the use of deterministic finite element (FE) simulations. Here we focus on tissue expansion, a popular technique in which skin is stretched by a balloon-like device inducing its growth. We construct FE models of tissue expansion with various levels of detail, and show that a sufficiently broad set of FE simulations from these models can be used to train an accurate and efficient multi-fidelity Gaussian process (GP) surrogate. The approach is not limited to simulation data, rather, it can fuse different kinds of data, including from experiments. The main appeal of the framework relies on the common experience that highly detailed models (or experiments) are more accurate but also more costly, while simpler models (or experiments) can be easily evaluated but are bound to have some error. In these situations, doing uncertainty analysis tasks with the high fidelity models alone is not feasible and, conversely, relying solely on low fidelity approximations is also undesirable. We show that a multi-fidelity GP outperforms the high fidelity GP and low fidelity GP when tested against the most detailed FE model. In turn, having trained the multi-fidelity GP model, we showcase the propagation of uncertainty from the mechanical and biological response parameters to the spatio-temporal growth outcomes. We expect that the methods and applications in this paper will enable future research in parameter calibration under uncertainty and uncertainty propagation in real clinical scenarios involving tissue growth and remodeling.

Predictions of hypertrophy and its regression in response to pressure overload

Mechanics-based cardiac growth models can now predict changes in mass, chamber size, and wall thickness in response to perturbations such as pressure overload (PO), volume overload, and myocardial infarction with a single set of growth parameters. As these models move toward clinical applications, many of the most interesting applications involve predictions of whether or how a patient's heart will reverse its growth after an intervention. In the case of PO, significant regression in wall thickness is observed both experimentally and clinically following relief of overload, for example following replacement of a stenotic aortic valve. Therefore, the objective of this work was to evaluate the ability of a published cardiac growth model that captures forward growth in multiple situations to predict growth reversal following relief of PO. Using a finite element model of a beating canine heart coupled to a circuit model of the circulation, we quantitatively matched hemodynamic data from a canine study of aortic banding followed by unbanding. Surprisingly, although the growth model correctly predicted the time course of PO-induced hypertrophy, it predicted only limited growth reversal given the measured unbanding hemodynamics, contradicting experimental and clinical observations. We were able to resolve this discrepancy only by incorporating an evolving homeostatic setpoint for the governing growth equations. Furthermore, our analysis suggests that many strain- and stress-based growth laws using the traditional volumetric growth framework will have similar difficulties capturing regression following the relief of PO unless growth setpoints are allowed to evolve.

Evaluation of stimulus-effect relations in left ventricular growth using a simple multiscale model

Cardiac growth is the natural capability of the heart to change size in response to changes in blood flow demand of the growing body. Cardiac diseases can trigger the same process leading to an abnormal type of growth. Prediction of cardiac growth would be clinically valuable, but so far published models on cardiac growth differ with respect to the stimulus-effect relation and constraints used for maximum growth. In this study, we use a zero-dimensional, multiscale model of the left ventricle to evaluate cardiac growth in response to three valve diseases, aortic and mitral regurgitation along with aortic stenosis. We investigate how different combinations of stress- and strain-based stimuli affect growth in terms of cavity volume and wall volume and hemodynamic performance. All of our simulations are able to reach a converged state without any growth constraint, with the most promising results obtained while considering at least one stress-based stimulus. With this study, we demonstrate how a simple model of left ventricular mechanics can be used to have a first evaluation on a designed growth law.

The Impact of Hemodynamic Reflex Compensation Following Myocardial Infarction on Subsequent Ventricular Remodeling

Patients who survive a myocardial infarction (MI) are at risk for ventricular dilation and heart failure. While infarct size is an important determinant of post-MI remodeling, different patients with the same size infarct often display different levels of left ventricular (LV) dilation. The acute physiologic response to MI involves reflex compensation, whereby increases in heart rate, arterial resistance, venoconstriction, and contractility of the surviving myocardium act to maintain mean arterial pressure. We hypothesized that variability in compensation might underlie some of the reported variability in post-MI remodeling, a hypothesis that is difficult to test using experimental data alone because some responses are difficult or impossible to measure directly. We therefore employed a computational model to estimate the balance of compensatory mechanisms from experimentally reported hemodynamic data. We found a strikingly wide range of compensatory reflex profiles in response to MI in dogs and verified that pharmacologic blockade of sympathetic and parasympathetic reflexes nearly abolished this variability. Then, using a previously published model of post-infarction remodeling, we showed that observed variability in compensation translated to variability in predicted LV dilation consistent with published data. Treatment with a vasodilator shifted the compensatory response away from arterial and venous vasoconstriction and towards increased heart rate and myocardial contractility. Importantly, this shift reduced predicted dilation, a prediction that matched prior experimental studies. Thus, post-infarction reflex compensation could represent both a source of individual variability in the extent of LV remodeling and a target for therapies aimed at reducing that remodeling.

Clinical Applications of Patient-Specific Models: The Case for a Simple Approach

Over the past several decades, increasingly sophisticated models of the heart have provided important insights into cardiac physiology and are increasingly used to predict the impact of diseases and therapies on the heart. In an era of personalized medicine, many envision patient-specific computational models as a powerful tool for personalizing therapy. Yet the complexity of current models poses important challenges, including identifying model parameters and completing calculations quickly enough for routine clinical use. We propose that early clinical successes are likely to arise from an alternative approach: relatively simple, fast, phenomenologic models with a small number of parameters that can be easily (and automatically) customized. We discuss examples of simple yet foundational models that have already made a tremendous impact on clinical education and practice, and make the case that reducing rather than increasing model complexity may be the key to realizing the promise of patient-specific modeling for clinical applications.