Cardiac resynchronization: insight from experimental and computational models

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Optimization framework for patient-specific modeling under uncertainty

Estimating a patient-specific computational model's parameters relies on data that is often unreliable and ill-suited for a deterministic approach. We develop an optimization-based uncertainty quantification framework for probabilistic model tuning that discovers model inputs distributions that generate target output distributions. Probabilistic sampling is performed using a surrogate model for computational efficiency, and a general distribution parameterization is used to describe each input. The approach is tested on seven patient-specific modeling examples using CircAdapt, a cardiovascular circulatory model. Six examples are synthetic, aiming to match the output distributions generated using known reference input data distributions, while the seventh example uses real-world patient data for the output distributions. Our results demonstrate the accurate reproduction of the target output distributions, with a correct recreation of the reference inputs for the six synthetic examples. Our proposed approach is suitable for determining the parameter distributions of patient-specific models with uncertain data and can be used to gain insights into the sensitivity of the model parameters to the measured data.

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.

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.

The role of regional myocardial topography post-myocardial infarction on infarct extension

Infarct extension involves necrosis of healthy myocardium in the border zone (BZ), progressively enlarging the infarct zone (IZ) and recruiting the remote zone (RZ) into the BZ, eventually leading to heart failure. The mechanisms underlying infarct extension remain unclear, but myocyte stretching has been suggested as the most likely cause. Using human patient-specific left-ventricular (LV) numerical simulations established from cardiac magnetic resonance imaging (MRI) of myocardial infarction (MI) patients, the correlation between infarct extension and regional mechanics abnormality was investigated by analysing the fibre stress-strain loops (FSSLs). FSSL abnormality was characterised using the directional regional external work (DREW) index, which measures FSSL area and loop direction. Sensitivity studies were also performed to investigate the effect of infarct stiffness on regional myocardial mechanics and potential for infarct extension. We found that infarct extension was correlated to severely abnormal FSSL in the form of counter-clockwise loop at the RZ close to the infarct, as indicated by negative DREW values. In regions demonstrating negative DREW values, we observed substantial fibre stretching in the isovolumic relaxation (IVR) phase accompanied by a reduced rate of systolic shortening. Such stretching in IVR phase in part of the RZ was due to its inability to withstand the high LV pressure that was still present and possibly caused by regional myocardial stiffness inhomogeneity. Further analysis revealed that the occurrence of severely abnormal FSSL due to IVR fibre stretching near the RZ-BZ boundary was due to a large amount of surrounding infarcted tissue, or an excessively stiff IZ.

Using cardiac ionic cell models to interpret clinical data

For over 100 years cardiac electrophysiology has been measured in the clinic. The electrical signals that can be measured span from noninvasive ECG and body surface potentials measurements through to detailed invasive measurements of local tissue electrophysiology. These electrophysiological measurements form a crucial component of patient diagnosis and monitoring; however, it remains challenging to quantitatively link changes in clinical electrophysiology measurements to biophysical cellular function. Multi-scale biophysical computational models represent one solution to this problem. These models provide a formal framework for linking cellular function through to emergent whole organ function and routine clinical diagnostic signals. In this review, we describe recent work on the use of computational models to interpret clinical electrophysiology signals. We review the simulation of human cardiac myocyte electrophysiology in the atria and the ventricles and how these models are being used to link organ scale function to patient disease mechanisms and therapy response in patients receiving implanted defibrillators, \cardiac resynchronisation therapy or suffering from atrial fibrillation and ventricular tachycardia. There is a growing use of multi-scale biophysical models to interpret clinical data. This allows cardiologists to link clinical observations with cellular mechanisms to better understand cardiopathophysiology and identify novel treatment strategies. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Patient-specific heart simulation can identify non-responders to cardiac resynchronization therapy

To identify non-responders to cardiac resynchronization therapy (CRT), various biomarkers have been proposed, but these attempts have not been successful to date. We tested the clinical applicability of computer simulation of CRT for the identification of non-responders. We used the multi-scale heart simulator “UT-Heart,” which can reproduce the electrophysiology and mechanics of the heart based on a molecular model of the excitation–contraction mechanism. Patient-specific heart models were created for eight heart failure patients who were treated with CRT, based on the clinical data recorded before treatment. Using these heart models, bi-ventricular pacing simulations were performed at multiple pacing sites adopted in clinical practice. Improvement in pumping function measured by the relative change of maximum positive derivative of left ventricular pressure (%ΔdP/dt_max) was compared with the clinical outcome. The operators of the simulation were blinded to the clinical outcome. In six patients, the relative reduction in end-systolic volume exceeded 15% in the follow-up echocardiogram at 3 months (responders) and the remaining two patients were judged as non-responders. The simulated %ΔdP/dt_max at the best lead position could identify responders and non-responders successfully. With further refinement of the model, patient-specific simulation could be a useful tool for identifying non-responders to CRT.

Optimization Framework for Patient-Specific Cardiac Modeling

PURPOSE

Patient-specific models of the heart can be used to improve the diagnosis of cardiac diseases, but practical application of these models can be impeded by the computational costs and numerical uncertainties of fitting mechanistic models to clinical measurements from individual patients. Reliable and efficient tuning of these models within clinically appropriate error bounds is a requirement for practical deployment in the time-constrained environment of the clinic.

METHODS

We developed an optimization framework to tune parameters of patient-specific mechanistic models using routinely-acquired non-invasive patient data more efficiently than manual methods. We employ a hybrid particle swarm and pattern search optimization algorithm, but the framework can be readily adapted to use other optimization algorithms.

RESULTS

We apply the proposed framework to tune full-cycle lumped parameter circulatory models using clinical data. We show that our framework can be easily adapted to optimize cross-species models by tuning the parameters of the same circulation model to four canine subjects.

CONCLUSIONS

This work will facilitate the use of biomechanics and circulatory cardiac models in both clinical and research environments by ameliorating the tedious process of manually fitting the parameters.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Computational Modeling for Cardiac Resynchronization Therapy

Cardiac resynchronization therapy (CRT) is an effective treatment for heart failure (HF) patients with an electrical substrate pathology causing ventricular dyssynchrony. However 40-50% of patients do not respond to treatment. Cardiac modeling of the electrophysiology, electromechanics, and hemodynamics of the heart has been used to study mechanisms behind HF pathology and CRT response. Recently, multi-scale dyssynchronous HF models have been used to study optimal device settings and optimal lead locations, investigate the underlying cardiac pathophysiology, as well as investigate emerging technologies proposed to treat cardiac dyssynchrony. However the breadth of patient and experimental data required to create and parameterize these models and the computational resources required currently limits the use of these models to small patient numbers. In the future, once these technical challenges are overcome, biophysically based models of the heart have the potential to become a clinical tool to aid in the diagnosis and treatment of HF.

Modelling the effects of chloroquine on KCNJ2-linked short QT syndrome

A gain-of-function KCNJ2 D172N mutation in KCNJ2-encoded Kir2.1 channels underlies one form of short QT syndrome (SQT3), which is associated with increased susceptibility to arrhythmias and sudden death. Anti-malarial drug chloroquine was reported as an effective inhibitor of Kir2.1 channels. Using biophysically-detailed human ventricle computer models, this study assessed the effects of chloroquine on SQT3. The ten Tusscher et al. model of human ventricular cell action potential was modified to recapitulate functional changes in the inward rectifier K⁺ current (I_K1) due to heterozygous and homozygous forms of the D172N mutation. Mutant formulations were incorporated into multi-scale models. The blocking effects of chloroquine on ionic currents were modelled using IC₅₀ and Hill coefficient values from literatures. Effects of chloroquine on action potential duration (APD), effective refractory period (ERP) and pseudo-ECGs were quantified. It was shown that chloroquine caused a dose-dependent reduction in I_K1, prolonged APD, and decreased the maximum voltage heterogeneity. Chloroquine prolonged QT interval and declined the T-wave amplitude. Although chloroquine reduced tissue’s temporal vulnerability, it increased the minimum substrate size necessary for sustaining re-entry. The actions of chloroquine decreased arrhythmia risk, due to the reduced tissue vulnerability, prolonged ERP and wavelength of re-entrant excitation waves, which in combination prevented and terminated re-entry in the tissue models. In conclusion, the results of this study provide new evidence that the anti-arrhythmic effects of chloroquine on SQT3 and, by extension, to the possibility that chloroquine may be a potential therapeutic agent for SQT3 treatment.

Prediction of optimal cardiac resynchronization by vectors extracted from electrograms in dyssynchronous canine hearts

INTRODUCTION

Proper optimization of atrioventricular (AV) and interventricular (VV) intervals can improve the response to cardiac resynchronization therapy (CRT). It has been demonstrated that the area of the QRS complex (QRSarea) extracted from the vectorcardiogram can be used as a predictor of optimal CRT-device settings. We explored the possibility of extracting vectors from the electrograms (EGMs) obtained from pacing electrodes and of using these EGM-based vectors (EGMVs) to individually optimize acute hemodynamic CRT response.

METHODS AND RESULTS

Biventricular pacing was performed in 13 dogs with left bundle branch block (LBBB) of which five also had myocardial infarction (MI), using 100 randomized AV- and VV-settings. Settings providing an acute increase in LV dP/dt_max ≥ 90% of the highest achieved value were defined as optimal. The prediction capability of QRSarea derived from the EGMV (EGMV-QRSarea) was compared with that of QRS duration. EGMV-QRSarea strongly correlated to the change in LV dP/dt_max (R = -0.73 ± 0.19 [LBBB] and -0.66 ± 0.14 [LBBB + MI]), while QRS duration was more poorly related to LV dP/dt_max changes (R = -0.33 ± 0.25 [LBBB] and -0.47 ± 0.39 [LBBB + MI]). This resulted in a better prediction of optimal CRT-device settings by EGMV-QRSarea than by QRS duration (LBBB: AUC = 0.89 [0.86-0.93] vs. 0.76 [0.69-0.83], P < 0.01; LBBB + MI: AUC = 0.91 [0.84-0.99] vs. 0.82 [0.59-1.00], P = 0.20, respectively).

CONCLUSION

In canine hearts with chronic LBBB with or without MI, the EGMV-QRSarea predicts acute hemodynamic CRT response and identifies optimal AV and VV settings accurately. These data support the potency of EGM-based vectors as a noninvasive, easy and patient-tailored tool to optimize CRT-device settings.

Multi-scale, tailor-made heart simulation can predict the effect of cardiac resynchronization therapy

BACKGROUND

The currently proposed criteria for identifying patients who would benefit from cardiac resynchronization therapy (CRT) still need to be optimized. A multi-scale heart simulation capable of reproducing the electrophysiology and mechanics of a beating heart may help resolve this problem. The objective of this retrospective study was to test the capability of patient-specific simulation models to reproduce the response to CRT by applying the latest multi-scale heart simulation technology.

METHODS AND RESULTS

We created patient-specific heart models with realistic three-dimensional morphology based on the clinical data recorded before treatment in nine patients with heart failure and conduction block treated by biventricular pacing. Each model was tailored to reproduce the surface electrocardiogram and hemodynamics of each patient in formats similar to those used in clinical practice, including electrocardiography (ECG), echocardiography, and hemodynamic measurements. We then performed CRT simulation on each heart model according to the actual pacing protocol and compared the results with the clinical data. CRT simulation improved the ECG index and diminished wall motion dyssynchrony in each patient. These results, however, did not correlate with the actual response. The best correlation was obtained between the maximum value of the time derivative of ventricular pressure (dP/dt_max) and the clinically observed improvement in the ejection fraction (EF) (r=0.94, p<0.01).

CONCLUSIONS

By integrating the complex pathophysiology of the heart, patient-specific, multi-scale heart simulation could successfully reproduce the response to CRT. With further verification, this technique could be a useful tool in clinical decision making.

Mathematical modeling of cardiac growth and remodeling

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

A self-taught artificial agent for multi-physics computational model personalization

Personalization is the process of fitting a model to patient data, a critical step towards application of multi-physics computational models in clinical practice. Designing robust personalization algorithms is often a tedious, time-consuming, model- and data-specific process. We propose to use artificial intelligence concepts to learn this task, inspired by how human experts manually perform it. The problem is reformulated in terms of reinforcement learning. In an off-line phase, Vito, our self-taught artificial agent, learns a representative decision process model through exploration of the computational model: it learns how the model behaves under change of parameters. The agent then automatically learns an optimal strategy for on-line personalization. The algorithm is model-independent; applying it to a new model requires only adjusting few hyper-parameters of the agent and defining the observations to match. The full knowledge of the model itself is not required. Vito was tested in a synthetic scenario, showing that it could learn how to optimize cost functions generically. Then Vito was applied to the inverse problem of cardiac electrophysiology and the personalization of a whole-body circulation model. The obtained results suggested that Vito could achieve equivalent, if not better goodness of fit than standard methods, while being more robust (up to 11% higher success rates) and with faster (up to seven times) convergence rate. Our artificial intelligence approach could thus make personalization algorithms generalizable and self-adaptable to any patient and any model.

Tailor-made heart simulation predicts the effect of cardiac resynchronization therapy in a canine model of heart failure

Despite extensive studies on clinical indices for the selection of patient candidates for cardiac resynchronization therapy (CRT), approximately 30% of selected patients do not respond to this therapy. Herein, we examined whether CRT simulations based on individualized realistic three-dimensional heart models can predict the therapeutic effect of CRT in a canine model of heart failure with left bundle branch block. In four canine models of failing heart with dyssynchrony, individualized three-dimensional heart models reproducing the electromechanical activity of each animal were created based on the computer tomographic images. CRT simulations were performed for 25 patterns of three ventricular pacing lead positions. Lead positions producing the best and the worst therapeutic effects were selected in each model. The validity of predictions was tested in acute experiments in which hearts were paced from the sites identified by simulations. We found significant correlations between the experimentally observed improvement in ejection fraction (EF) and the predicted improvements in ejection fraction (P<0.01) or the maximum value of the derivative of left ventricular pressure (P<0.01). The optimal lead positions produced better outcomes compared with the worst positioning in all dogs studied, although there were significant variations in responses. Variations in ventricular wall thickness among the dogs may have contributed to these responses. Thus CRT simulations using the individualized three-dimensional heart models can predict acute hemodynamic improvement, and help determine the optimal positions of the pacing lead.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

An integrated electromechanical-growth heart model for simulating cardiac therapies

An emerging class of models has been developed in recent years to predict cardiac growth and remodeling (G&R). We recently developed a cardiac G&R constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this G&R model to an existing strongly coupled electromechanical model of the heart. A separation of timescale between growth deformation and elastic deformation was invoked in this integrated electromechanical-growth heart model. To test our model, we applied the G&R scheme to simulate the effects of myocardial infarction in a realistic left ventricular (LV) geometry using the finite element method. We also simulate the effects of a novel therapy that is based on alteration of the infarct mechanical properties. We show that our proposed model is able to predict key features that are consistent with experiments. Specifically, we show that the presence of a non-contractile infarct leads to a dilation of the left ventricle that results in a rightward shift of the pressure volume loop. Our model also predicts that G&R is attenuated by a reduction in LV dilation when the infarct stiffness is increased.

Towards Personalized Cardiology: Multi-Scale Modeling of the Failing Heart

BACKGROUND

Despite modern pharmacotherapy and advanced implantable cardiac devices, overall prognosis and quality of life of HF patients remain poor. This is in part due to insufficient patient stratification and lack of individualized therapy planning, resulting in less effective treatments and a significant number of non-responders.

METHODS AND RESULTS

State-of-the-art clinical phenotyping was acquired, including magnetic resonance imaging (MRI) and biomarker assessment. An individualized, multi-scale model of heart function covering cardiac anatomy, electrophysiology, biomechanics and hemodynamics was estimated using a robust framework. The model was computed on n=46 HF patients, showing for the first time that advanced multi-scale models can be fitted consistently on large cohorts. Novel multi-scale parameters derived from the model of all cases were analyzed and compared against clinical parameters, cardiac imaging, lab tests and survival scores to evaluate the explicative power of the model and its potential for better patient stratification. Model validation was pursued by comparing clinical parameters that were not used in the fitting process against model parameters.

CONCLUSION

This paper illustrates how advanced multi-scale models can complement cardiovascular imaging and how they could be applied in patient care. Based on obtained results, it becomes conceivable that, after thorough validation, such heart failure models could be applied for patient management and therapy planning in the future, as we illustrate in one patient of our cohort who received CRT-D implantation.

Current concepts relating coronary flow, myocardial perfusion and metabolism in left bundle branch block and cardiac resynchronisation therapy

Cardiac resynchronisation therapy (CRT) improves mortality and symptoms in heart failure patients with electromechanically dyssynchronous ventricles. There is a 50% non-response rate and reproducible biomarkers to predict non-response have not been forthcoming. Therefore, there has been increasing interest in the pathophysiological effects of dyssynchrony particularly focusing on coronary flow, myocardial perfusion and metabolism. Studies suggest that dyssynchronous electrical activation effects coronary flow throughout the coronary vasculature from the epicardial arteries to the microvascular bed and that these changes can be corrected by CRT. The effect of both electrical and mechanical dyssynchrony on myocardial perfusion is unclear with some studies suggesting there is a reduction in septal perfusion whilst others propose that there is an increase in lateral perfusion. Better understanding of these effects offers the possibility for better prediction of non-response. CRT appears to improve homogeneity in myocardial perfusion where heterogeneity is described in the initial substrate. Novel approaches to the identification of non-responders via metabolic phenotyping both invasively and non-invasively have been encouraging. There remains a need for further research to clarify the interaction of coronary flow with perfusion and metabolism in patients who undergo CRT.

The direct incorporation of perfusion defect information to define ischemia and infarction in a finite element model of the left ventricle

This paper describes the process in which complex lesion geometries (specified by computer generated perfusion defects) are incorporated in the description of nonlinear finite element (FE) mechanical models used for specifying the motion of the left ventricle (LV) in the 4D extended cardiac torso (XCAT) phantom to simulate gated cardiac image data. An image interrogation process was developed to define the elements in the LV mesh as ischemic or infarcted based upon the values of sampled intensity levels of the perfusion maps. The intensity values were determined for each of the interior integration points of every element of the FE mesh. The average element intensity levels were then determined. The elements with average intensity values below a user-controlled threshold were defined as ischemic or infarcted depending upon the model being defined. For the infarction model cases, the thresholding and interrogation process were repeated in order to define a border zone (BZ) surrounding the infarction. This methodology was evaluated using perfusion maps created by the perfusion cardiac-torso (PCAT) phantom an extension of the 4D XCAT phantom. The PCAT was used to create 3D perfusion maps representing 90% occlusions at four locations (left anterior descending (LAD) segments 6 and 9, left circumflex (LCX) segment 11, right coronary artery (RCA) segment 1) in the coronary tree. The volumes and shapes of the defects defined in the FE mechanical models were compared with perfusion maps produced by the PCAT. The models were incorporated into the XCAT phantom. The ischemia models had reduced stroke volume (SV) by 18-59 ml. and ejection fraction (EF) values by 14-50% points compared to the normal models. The infarction models, had less reductions in SV and EF, 17-54 ml. and 14-45% points, respectively. The volumes of the ischemic/infarcted regions of the models were nearly identical to those volumes obtained from the perfusion images and were highly correlated (R² = 0.99).

Images as drivers of progress in cardiac computational modelling

Computational models have become a fundamental tool in cardiac research. Models are evolving to cover multiple scales and physical mechanisms. They are moving towards mechanistic descriptions of personalised structure and function, including effects of natural variability. These developments are underpinned to a large extent by advances in imaging technologies. This article reviews how novel imaging technologies, or the innovative use and extension of established ones, integrate with computational models and drive novel insights into cardiac biophysics. In terms of structural characterization, we discuss how imaging is allowing a wide range of scales to be considered, from cellular levels to whole organs. We analyse how the evolution from structural to functional imaging is opening new avenues for computational models, and in this respect we review methods for measurement of electrical activity, mechanics and flow. Finally, we consider ways in which combined imaging and modelling research is likely to continue advancing cardiac research, and identify some of the main challenges that remain to be solved.

An automatic service for the personalization of ventricular cardiac meshes

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

Left ventricular finite element model bounded by a systemic circulation model

A series of models were developed in which a circulatory system model was coupled to an existing series of finite element (FE) models of the left ventricle (LV). The circulatory models were used to provide realistic boundary conditions for the LV models. This was developed for the JSim analysis package and was composed of a systemic arterial, capillary, and venous system in a closed loop with a varying elastance LV and left atria to provide the driving pressures and flows matching those of the FE model. Three coupled models were developed, a normal LV under normotensive aortic loading (116/80 mm Hg), a mild hypertension (137/89 mm Hg) model, and a moderate hypertension model (165/100 mm Hg). The initial step in the modeling analysis was that the circulation was optimized to the end-diastolic pressure and volume values of the LV model. The cardiac FE models were then optimized to the systolic pressure/volume characteristics of the steady-state JSim circulatory model solution. Comparison of the stress predictions for the three models indicated that the mild hypertensive case produced a 21% increase in the average fiber stress levels, and the moderate hypertension case had a 36% increase in average stress. The circulatory work increased by 18% and 43% over that of the control for the mild and moderate hypertensive cases, respectively.

In silico study of the haemodynamic effects induced by mechanical ventilation and biventricular pacemaker

In silico modeling of the cardiovascular system (CVS) can help both in understanding pharmacological or pathophysiological process and in providing information which could not be obtained by means of traditional clinical research methods due to practical or ethical reasons. In this work the numerical CVS was used to study the effect of interaction between mechanical ventilation and biventricular pacemaker by haemodynamic and energetic point of view. Starting from literature data on patients with intra and/or inter-ventricular activation time delay and treated using biventricular pacemaker, we used in silico simulator to analyse the effects induced by mechanical ventilatory assistance (MVA). After reproducing baseline and CRT conditions, the MVA was simulated changing the mean intrathoracic pressure value. Results show that simultaneous application of CRT and MVA yields a reduction of cardiac output, left ventricular end-diastolic and end-systolic volume when positive mean intrathoracic pressure is applied. In the same conditions, when MVA is applied, left ventricular ejection fraction, mean left (right) atrial and pulmonary arterial pressure increase.

Computational cardiology: how computer simulations could be used to develop new therapies and advance existing ones

This article reviews the latest developments in computational cardiology. It focuses on the contribution of cardiac modelling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modelling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

Mechanical discoordination increases continuously after the onset of left bundle branch block despite constant electrical dyssynchrony in a computational model of cardiac electromechanics and growth

AIMS

To test whether a functional growth law leads to asymmetric hypertrophy and associated changes in global and regional cardiac function when integrated with a computational model of left bundle branch block (LBBB).

METHODS AND RESULTS

In recent studies, we proposed that cardiac myocytes grow longer when a threshold of maximum fibre strain is exceeded and grow thicker when the smallest maximum principal strain in the cellular cross-sectional plane exceeds a threshold. A non-linear cardiovascular model of the beating canine ventricles was combined with the cellular growth law. After inducing LBBB, the ventricles were allowed to adapt in shape over time in response to mechanical stimuli. When subjected to electrical dyssynchrony, the combined model of ventricular electromechanics, haemodynamics, and growth led to asymmetric hypertrophy with a faster increase of wall mass in the left ventricular (LV) free wall (FW) than the septum, increased LV end-diastolic and end-systolic volumes, and decreased LV ejection fraction. Systolic LV pressure decreased during the acute phase of LBBB and increased at later stages. The relative changes of these parameters were similar to those obtained experimentally. Most of the dilation was due to radial and axial fibre growth, and hence altered shape of the LVFW.

CONCLUSION

Our previously proposed growth law reproduced measured dyssynchronously induced asymmetric hypertrophy and the associated functional changes, when combined with a computational model of the LBBB heart. The onset of LBBB leads to a step increase in LV mechanical discoordination that continues to increase as the heart remodels despite the constant electrical dyssynchrony.

Assessment of hemodynamic load components affecting optimization of cardiac resynchronization therapy by lumped parameter mode

Timing of biventricular pacing devices employed in cardiac resynchronization therapy (CRT) is a critical determinant of efficacy of the procedure. Optimization is done by maximizing function in terms of arterial pressure (BP) or cardiac output (CO). However, BP and CO are also determined by the hemodynamic load of the pulmonary and systemic vasculature. This study aims to use a lumped parameter circulatory model to assess the influence of the arterial load on the atrio-ventricular (AV) and inter-ventricular (VV) delay for optimal CRT performance.

Computational cardiology: the heart of the matter

This paper reviews the newest developments in computational cardiology. It focuses on the contribution of cardiac modeling to the development of new therapies as well as the advancement of existing ones for cardiac arrhythmias and pump dysfunction. Reviewed are cardiac modeling efforts aimed at advancing and optimizing existent therapies for cardiac disease (defibrillation, ablation of ventricular tachycardia, and cardiac resynchronization therapy) and at suggesting novel treatments, including novel molecular targets, as well as efforts to use cardiac models in stratification of patients likely to benefit from a given therapy, and the use of models in diagnostic procedures.

A framework for personalization of computational models of the human atria

A framework for step-by-step personalization of a computational model of human atria is presented. Beginning with anatomical modeling based on CT or MRI data, next fiber structure is superimposed using a rule-based method. If available, late-enhancement-MRI images can be considered in order to mark fibrotic tissue. A first estimate of individual electrophysiology is gained from BSPM data solving the inverse problem of ECG. A final adjustment of electrophysiology is realized using intracardiac measurements. The framework is applied using several patient data. First clinical application will be computer assisted planning of RF-ablation for treatment of atrial flutter and atrial fibrillation.

Mechanistic Evaluation of Echocardiographic Dyssynchrony Indices

Background—

The power of echocardiographic dyssynchrony indices to predict response to cardiac resynchronization therapy (CRT) appears to vary between indices and between studies. We investigated whether the variability of predictive power between the dyssynchrony indices can be explained by differences in their operational definitions.

Methods and Results—

In 132 CRT-candidates (left ventricular [LV] ejection fraction, 19 ± 6%; QRS width, 170 ± 22 ms), 4 mechanical dyssynchrony indices (septal systolic rebound stretch [SRSsept], interventricular mechanical dyssynchrony [IVMD], septal-to-lateral peak shortening delay [Strain-SL], and septal-to-posterior wall motion delay [SPWMD]) were quantified at baseline. CRT response was quantified as 6-month percent change of LV end-systolic volume. Multiscale computer simulations of cardiac mechanics and hemodynamics were used to assess the relationships between dyssynchrony indices and CRT response within wide ranges of dyssynchrony of LV activation and reduced contractility. In patients, SRSsept showed best correlation with CRT response followed by IVMD, Strain-SL, and SPWMD ( R =−0.56, −0.50, −0.48, and −0.39, respectively; all P <0.01). In patients and simulations, SRSsept and IVMD showed a continuous linear relationship with CRT response, whereas Strain-SL and SPWMD showed discontinuous relationships characterized by data clusters. Model simulations revealed that this data clustering originated from the complex multipeak pattern of septal strain and motion. In patients and simulations with (simulated) LV scar, SRSsept and IVMD retained their linear relationship with CRT response, whereas Strain-SL and SPWMD did not.

Conclusions—

The power to predict CRT response differs between indices of mechanical dyssynchrony. SRSsept and IVMD better represent LV dyssynchrony amenable to CRT and better predict CRT response than the indices assessing time-to-peak deformation or motion.

Patient-specific finite element-based analysis of ventricular myofiber stress after Coapsys: importance of residual stress

BACKGROUND

We sought to determine regional myofiber stress after Coapsys device (Myocor, Inc, Maple Grove, MN) implantation using a finite element model of the left ventricle (LV). Chronic ischemic mitral regurgitation is caused by LV remodeling after posterolateral myocardial infarction. The Coapsys device consists of a single trans-LV chord placed below the mitral valve such that when tensioned it alters LV shape and decreases chronic ischemic mitral regurgitation.

METHODS

Finite element models of the LV were based on magnetic resonance images obtained before (preoperatively) and after (postoperatively) coronary artery bypass grafting with Coapsys implantation in a single patient. To determine the effect of Coapsys and LV before stress, virtual Coapsys was performed on the preoperative model. Diastolic and systolic material variables in the preoperative, postoperative, and virtual Coapsys models were adjusted so that model LV volume agreed with magnetic resonance imaging data. Chronic ischemic mitral regurgitation was abolished in the postoperative models. In each case, myofiber stress and pump function were calculated.

RESULTS

Both postoperative and virtual Coapsys models shifted end-systolic and end-diastolic pressure-volume relationships to the left. As a consequence and because chronic ischemic mitral regurgitation was reduced after Coapsys, pump function was unchanged. Coapsys decreased myofiber stress at end-diastole and end-systole in both the remote and infarct regions of the myocardium. However, knowledge of Coapsys and LV prestress was necessary for accurate calculation of LV myofiber stress, especially in the remote zone.

CONCLUSIONS

Coapsys decreases myofiber stress at end-diastole and end-systole. The improvement in myofiber stress may contribute to the long-term effect of Coapsys on LV remodeling.

Modeling cardiac electromechanics and mechanoelectrical coupling in dyssynchronous and failing hearts: insight from adaptive computer models

Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are created that describe heart function at different length and time scales. In this review, we describe basic modules that can be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling, excitation-contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation, ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy.

Mathematical modeling and simulation of ventricular activation sequences: implications for cardiac resynchronization therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy.

Septal Deformation Patterns Delineate Mechanical Dyssynchrony and Regional Differences in Contractility

Background—

Response to cardiac resynchronization therapy depends both on dyssynchrony and (regional) contractility. We hypothesized that septal deformation can be used to infer integrated information on dyssynchrony and regional contractility, and thereby predict cardiac resynchronization therapy response.

Methods and Results—

In 132 cardiac resynchronization therapy candidates with left bundle branch block (LBBB)-like electrocardiogram morphology (left ventricular ejection fraction 19±6%; QRS width 170±23 ms), longitudinal septal strain was assessed by speckle tracking echocardiography. To investigate the effects of dyssynchronous activation and differences in septal and left ventricular free wall contractility on septal deformation pattern, we used the CircAdapt computer model of the human heart and circulation. In the patients, 3 characteristic septal deformation patterns were identified: LBBB-1=double-peaked systolic shortening (n=28); LBBB-2=early systolic shortening followed by prominent systolic stretching (n=34); and LBBB-3=pseudonormal shortening with less pronounced late systolic stretch (n=70). LBBB-3 revealed more scar (2 [2–5] segments) compared with LBBB-1 and LBBB-2 (both 0 [0–1], P <0.05). In the model, imposing a time difference of activation between septum and left ventricular free wall resulted in pattern LBBB-1. This transformed into pattern LBBB-2 by additionally simulating septal hypocontractility, and into pattern LBBB-3 by imposing additional left ventricular free wall or global left ventricular hypocontractility. Improvement of left ventricular ejection fraction and reduction of left ventricular volumes after cardiac resynchronization therapy were most pronounced in LBBB-1 and worst in LBBB-3 patients.

Conclusions—

A double-peaked systolic septal deformation pattern is characteristic for LBBB and results from intraventricular dyssynchrony. Abnormal contractility modifies this pattern. A computer model can be helpful in understanding septal deformation and predicting cardiac resynchronization therapy response.

Patient-specific electromechanical models of the heart for the prediction of pacing acute effects in CRT: a preliminary clinical validation

Cardiac resynchronisation therapy (CRT) is an effective treatment for patients with congestive heart failure and a wide QRS complex. However, up to 30% of patients are non-responders to therapy in terms of exercise capacity or left ventricular reverse remodelling. A number of controversies still remain surrounding patient selection, targeted lead implantation and optimisation of this important treatment. The development of biophysical models to predict the response to CRT represents a potential strategy to address these issues. In this article, we present how the personalisation of an electromechanical model of the myocardium can predict the acute haemodynamic changes associated with CRT. In order to introduce such an approach as a clinical application, we needed to design models that can be individualised from images and electrophysiological mapping of the left ventricle. In this paper the personalisation of the anatomy, the electrophysiology, the kinematics and the mechanics are described. The acute effects of pacing on pressure development were predicted with the in silico model for several pacing conditions on two patients, achieving good agreement with invasive haemodynamic measurements: the mean error on dP/dt(max) is 47.5±35mmHgs(-1), less than 5% error. These promising results demonstrate the potential of physiological models personalised from images and electrophysiology signals to improve patient selection and plan CRT.

Incorporation of a left ventricle finite element model defining infarction into the XCAT imaging phantom

The 4D extended cardiac-torso (XCAT) phantom was developed to provide a realistic and flexible model of the human anatomy and cardiac and respiratory motions for use in medical imaging research. A prior limitation to the phantom was that it did not accurately simulate altered functions of the heart that result from cardiac pathologies such as coronary artery disease (CAD). We overcame this limitation in a previous study by combining the phantom with a finite-element (FE) mechanical model of the left ventricle (LV) capable of more realistically simulating regional defects caused by ischemia. In the present work, we extend this model giving it the ability to accurately simulate motion abnormalities caused by myocardial infarction (MI), a far more complex situation in terms of altered mechanics compared with the modeling of acute ischemia. The FE model geometry is based on high resolution CT images of a normal male subject. An anterior region was defined as infarcted and the material properties and fiber distribution were altered, according to the bio-physiological properties of two types of infarction, i.e., fibrous and remodeled infarction (30% thinner wall than fibrous case). Compared with the original, surface-based 4D beating heart model of the XCAT, where regional abnormalities are modeled by simply scaling down the motion in those regions, the FE model was found to provide a more accurate representation of the abnormal motion of the LV due to the effects of fibrous infarction as well as depicting the motion of remodeled infarction. In particular, the FE models allow for the accurate depiction of dyskinetic motion. The average circumferential strain results were found to be consistent with measured dyskinetic experimental results. Combined with the 4D XCAT phantom, the FE model can be used to produce realistic multimodality sets of imaging data from a variety of patients in which the normal or abnormal cardiac function is accurately represented.

Anisotropy of wave propagation in the heart can be modeled by a Riemannian electrophysiological metric

It is well established that wave propagation in the heart is anisotropic and that the ratio of velocities in the three principal directions may be as large as v(f)v(s)v(n) approximately 4(fibers)2(sheets)1(normal). We develop an alternative view of the heart based on this fact by considering it as a non-Euclidean manifold with an electrophysiological(el-) metric based on wave velocity. This metric is more natural than the Euclidean metric for some applications, because el-distances directly encode wave propagation. We develop a model of wave propagation based on this metric; this model ignores higher-order effects like the curvature of wavefronts and the effect of the boundary, but still gives good predictions of local activation times and replicates many of the observed features of isochrones. We characterize this model for the important case of the rotational orthotropic anisotropy seen in cardiac tissue and perform numerical simulations for a slab of cardiac tissue with rotational orthotropic anisotropy and for a model of the ventricles based on diffusion tensor MRI scans of the canine heart. Even though the metric has many slow directions, we show that the rotation of the fibers leads to fast global activation. In the diffusion tensor MRI-based model, with principal velocities 0.25051 m/s, we find examples of wavefronts that eventually reach speeds up to 0.9 m/s and average velocities of 0.7 m/s. We believe that development of this non-Euclidean approach to cardiac anatomy and electrophysiology could become an important tool for the characterization of the normal and abnormal electrophysiological activity of the heart.

Myocardial infarction does not preclude electrical and hemodynamic benefits of cardiac resynchronization therapy in dyssynchronous canine hearts

BACKGROUND

Several studies suggest that patients with ischemic cardiomyopathy benefit less from cardiac resynchronization therapy. In a novel animal model of dyssynchronous ischemic cardiomyopathy, we investigated the extent to which the presence of infarction influences the short-term efficacy of cardiac resynchronization therapy.

METHODS AND RESULTS

Experiments were performed in canine hearts with left bundle branch block (LBBB, n=19) and chronic myocardial infarction, created by embolization of the left anterior descending or left circumflex arteries followed by LBBB (LBBB+left anterior descending infarction [LADi; n=11] and LBBB+left circumflex infarction [LCXi; n=7], respectively). Pacing leads were positioned in the right atrium and right ventricle and at 8 sites on the left ventricular (LV) free wall. LV pump function was measured using the conductance catheter technique, and synchrony of electrical activation was measured using epicardial mapping and ECG. Average and maximal improvement in electric resynchronization and LV pump function by right ventricular+LV pacing was similar in the 3 groups; however, the site of optimal electrical and mechanical benefit was LV apical in LBBB hearts, LV midlateral in LBBB+LCXi hearts and LV basal-lateral in LBBB+LADi hearts. The best site of pacing was not the site of latest electrical activation but that providing the largest shortening of the QRS complex. During single-site LV pacing the range of atrioventricular delays yielding > or =70% of maximal hemodynamic effect was approximately 50% smaller in infarcted than noninfarcted LBBB hearts (P<0.05).

CONCLUSIONS

Cardiac resynchronization therapy can improve resynchronization and LV pump function to a similar degree in infarcted and noninfarcted hearts. Optimal lead positioning and timing of LV stimulation, however, require more attention in the infarcted hearts.

Right ventricular free wall pacing improves cardiac pump function in severe pulmonary arterial hypertension: a computer simulation analysis

In pulmonary arterial hypertension (PAH), duration of myofiber shortening is prolonged in the right ventricular (RV) free wall (RVfw) compared with that in the interventricular septum and left ventricular free wall. This interventricular mechanical asynchrony eventually leads to right heart failure. We investigated by computer simulation whether, in PAH, early RVfw pacing may improve interventricular mechanical synchrony and, hence, cardiac pump function. A mathematical model of the human heart and circulation was used to simulate left ventricular and RV pump mechanics and myofiber mechanics. First, we simulated cardiovascular mechanics of a healthy adult at rest. Size and mass of heart and blood vessels were adapted so that mechanical tissue load was normalized. Second, compensated PAH was simulated by increasing mean pulmonary artery pressure to 32 mmHg while applying load adaptation. Third, decompensated PAH was simulated by increasing mean pulmonary artery pressure further to 79 mmHg without further adaptation. Finally, early RVfw pacing was simulated in severely decompensated PAH. Time courses of circumferential strain in the ventricular walls as simulated were similar to the ones measured in healthy subjects (uniform strain patterns) and in PAH patients (prolonged RVfw shortening). When simulating pacing in decompensated PAH, RV pump function was best upon 40-ms RVfw preexcitation, as evidenced by maximal decrease of RV end-diastolic volume, reduced RVfw myofiber work, and most homogeneous distribution of workload over the ventricular walls. Thus our simulations indicate that, in decompensated PAH, RVfw pacing may improve RV pump function and may homogenize workload over the ventricular walls.

Three-wall segment (TriSeg) model describing mechanics and hemodynamics of ventricular interaction

A mathematical model (TriSeg model) of ventricular mechanics incorporating mechanical interaction of the left and right ventricular free walls and the interventricular septum is presented. Global left and right ventricular pump mechanics were related to representative myofiber mechanics in the three ventricular walls, satisfying the principle of conservation of energy. The walls were mechanically coupled satisfying tensile force equilibrium in the junction. Wall sizes and masses were rendered by adaptation to normalize mechanical myofiber load to physiological standard levels. The TriSeg model was implemented in the previously published lumped closed-loop CircAdapt model of heart and circulation. Simulation results of cardiac mechanics and hemodynamics during normal ventricular loading, acute pulmonary hypertension, and chronic pulmonary hypertension (including load adaptation) agreed with clinical data as obtained in healthy volunteers and pulmonary hypertension patients. In chronic pulmonary hypertension, the model predicted right ventricular free wall hypertrophy, increased systolic pulmonary flow acceleration, and increased right ventricular isovolumic contraction and relaxation times. Furthermore, septal curvature decreased linearly with its transmural pressure difference. In conclusion, the TriSeg model enables realistic simulation of ventricular mechanics including interaction between left and right ventricular pump mechanics, dynamics of septal geometry, and myofiber mechanics in the three ventricular walls.