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Background Relationships between right ventricular (RV) and left ventricular (LV) shape and function may be useful in determining optimal timing for pulmonary valve replacement in patients with repaired tetralogy of Fallot (rTOF). However, these are multivariate and difficult to quantify. We aimed to quantify variations in biventricular shape associated with pulmonary regurgitant volume (PRV) in rTOF using a biventricular atlas. Methods In this cross-sectional retrospective study, a biventricular shape model was customized to cardiovascular magnetic resonance (CMR) images from 88 rTOF patients (median age 16, inter-quartile range 11.8–24.3 years). Morphometric scores quantifying biventricular shape at end-diastole and end-systole were computed using principal component analysis. Multivariate linear regression was used to quantify biventricular shape associations with PRV, corrected for age, sex, height, and weight. Regional associations were confirmed by univariate correlations with distances and angles computed from the models, as well as global systolic strains computed from changes in arc length from end-diastole to end-systole. Results PRV was significantly associated with 5 biventricular morphometric scores, independent of covariates, and accounted for 12.3% of total shape variation (p Conclusion A biventricular atlas of rTOF patients quantified multivariate relationships between left–right ventricular morphometry and wall motion with pulmonary regurgitation. Regional RV dilation, LV reduction, LV septal-lateral flattening and increased RV strain were all associated with increased pulmonary regurgitant volume. Morphometric scores provide simple metrics linking mechanisms for structural and functional alteration with important clinical indices.

International audience; We proposed a novel method called HARP-I, which enhances the estimation of motion from tagged Magnetic Resonance Imaging (MRI). The harmonic phase of the images is unwrapped and treated as noisy measurements of reference coordinates on a deformed domain, obtaining motion with high accuracy using Radial Basis Functions interpolations. Results were compared against Shortest Path HARP Refinement (SP-HR) and Sine-wave Modeling (SinMod), two harmonic image-based techniques for motion estimation from tagged images. HARP-I showed a favorable similarity with both methods under noise-free conditions, whereas a more robust performance was found in the presence of noise. Cardiac strain was better estimated using HARP-I at almost any motion level, giving strain maps with less artifacts. Additionally, HARP-I showed better temporal consistency as a new method was developed to fix phase jumps between frames. In conclusion, HARP-I showed to be a robust method for the estimation of motion and strain under ideal and non-ideal conditions.

Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient’s pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSMpre, and patient-specific models of the same patients created post-PVR (PSMpost)—both created in our previous published work. Using the PSMpre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSMpost, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSMpost model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.

BACKGROUND: A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health. METHODS: Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. RESULTS: RV contractility before PVR (mean 66 ± kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38–48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Q(eff)—both in line with published data. CONCLUSIONS: This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Qeff) was also compared with expected values.

Ventricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol. Graphic Abstractr

International audience; When combining cardiovascular magnetic resonance imaging (CMR) with pressure catheter measurements, the acquired imageand pressure data need to be synchronized in time. The time offset between the image and pressure data depends on a number of factors,such as the type and settings of the MR sequence, duration and shape of QRS complex or the type of catheter, and cannot be typically estimated beforehand. In the present work we propose using a biophysical heart model to synchronize the left ventricular (LV) pressure and volume (P-V) data. Ten patients, who underwent CMR and LV catheterization, were included. A biophysical model of reduced geometrical complexity with physiologically substantiated timing of each phase of the cardiac cycle was first adjusted to individual patients using basic morphological and functional indicators. The pressure and volume waveforms simulated by the patient-specific models were then used as templates to detect the time offset between the acquired ventricular pressure and volume waveforms. Time-varying ventricular elastance was derived from clinical data both as originally acquired as well as when time-synchronized, and normalized with respect to end-systolic time and maximum elastance value$E^N_\text {orig}(t)$, $E^N_\text {t-syn}(t)$, respectively). $E^N_\text {t-syn}(t)$ was significantly closer to the experimentally obtained $E^N_\text {exp}(t)$ published in the literature (p < 0.05, $L^2$ norm). The work concludes that the model-driven time-synchronization of P-V data obtained by catheter measurement and CMR allows to generate high quality P-V loops, which can then be used for clinical interpretation.

International audience; Purpose:Patients after surgical repair of Tetralogy of Fallot (rTOF) may suffer a decrease in left ventricular (LV) function. The aim of our study is to evaluate a novel method of assessing LV torsion in patients with rTOF, as an early indicator of systolic LV dysfunction. Methods:Motion tracking based on image registration regularized by the equilibrium gap principle, known as equilibrated warping, was employed to assess LV torsion. Seventy-six cases of rTOF and ten normal controls were included. The group of controls was assessed for reproducibility using both equilibrated warping and standard clinical tissue tracking software (CVI42, version 5.10.1, Calgary, Canada). Patients were dichotomized into two groups: normal vs. loss of torsion.Results:Torsion by equilibrated warping was successfully obtained in 68 of 76 (89%) patients and 9 of 10 (90%) controls. For equilibrated warping, the intra- and inter-observer coefficients of variation were 0.095 and 0.117, respectively; compared to 0.260 and 0.831 for tissue tracking by standard clinical software. The intra- and inter-observer intraclass correlation coefficients for equilibrated warping were 0.862 and 0.831, respectively; compared to 0.992 and 0.648 for tissue tracking. Loss of torsion was noted in 32 of the 68 (47%) patients with rTOF. There was no difference in LV or RV volumes or ejection fraction between these groups.Conclusion:The assessment of LV torsion by equilibrated warping is feasible and shows good reliability. Loss of torsion is common in patients with rTOF and its robust assessment might contribute into uncovering heart failure in an earlier stage.

Cardiovascular data of 8 patients with Multisystem Inflammatory Syndrome in Children (MIS-C), caused by an aberrant reaction of immune system to the SARS-CoV-2 coronarovirus, were retrospectively analyzed by using patient-specific biomechanical modeling. The first goal was to increase the understanding of the pathophysiology of the cardiovascular involvement in MIS-C, during the inpatient stay at Intensive Care Unit and after discharge from the hospital. Secondly, hypothetical action of various types of pharmacological therapy was tested in silico using the created patient-specific models, aiming to contribute into the optimal pharmacological management during the acute stage of MIS-C.

Patients after surgical repair of Tetralogy of Fallot (rTOF) may suffer a decrease in left ventricular (LV) function. The aim of our study is to evaluate a novel method of assessing LV torsion in patients with rTOF, as an early indicator of systolic LV dysfunction. Motion tracking based on image registration regularized by the equilibrium gap principle, known as equilibrated warping, was employed to assess LV torsion. Seventy-six cases of rTOF and ten normal controls were included. The group of controls was assessed for reproducibility using both equilibrated warping and standard clinical tissue tracking software (CVI42, version 5.10.1, Calgary, Canada). Patients were dichotomized into two groups: normal vs. loss of torsion. Torsion by equilibrated warping was successfully obtained in 68 of 76 (89%) patients and 9 of 10 (90%) controls. For equilibrated warping, the intra- and interobserver coefficients of variation were 0.095 and 0.117, respectively, compared to 0.260 and 0.831 for tissue tracking by standard clinical software. The intra- and inter-observer intraclass correlation coefficients for equilibrated warping were 0.862 and 0.831, respectively, compared to 0.992 and 0.648 for tissue tracking. Loss of torsion was noted in 32 of the 68 (47%) patients with rTOF. There was no difference in LV or RV volumes or ejection fraction between these groups. The assessment of LV torsion by equilibrated warping is feasible and shows good reliability. Loss of torsion is common in patients with rTOF and its robust assessment might contribute into uncovering heart failure in an earlier stage.

Ventricular volumetric ejection fraction (VV EF) is often normal in patients with single ventricle circulations despite them experiencing symptoms related to circulatory failure. We sought to determine if kinetic energy (KE) could be a better marker of ventricular performance. KE was prospectively quantified using four-dimensional flow MRI in 41 patients with a single ventricle circulation (aged 0.5–28 yr) and compared with 43 healthy volunteers (aged 1.5–62 yr) and 14 patients with left ventricular (LV) dysfunction (aged 28–79 yr). Intraventricular end-diastolic blood was tracked through systole and divided into ejected and residual blood components. Two ejection fraction (EF) metrics were devised based on the KE of the ejected component over the total of both the ejected and residual components using 1) instantaneous peak KE to assess KE EF or 2) summating individual peak particle energy (PE) to assess PE EF. KE EF and PE EF had a smaller range than VV EF in healthy subjects (97.9 ± 0.8 vs. 97.3 ± 0.8 vs. 60.1 ± 5.2%). LV dysfunction caused a fall in KE EF ( P = 0.01) and PE EF ( P = 0.0001). VV EF in healthy LVs and single ventricle hearts was equivalent; however, KE EF and PE EF were lower ( P < 0.001) with a wider range indicating a spectrum of severity. Those reporting the greatest symptomatic impairment (New York Heart Association II) had lower PE EF than asymptomatic subjects ( P = 0.0067). KE metrics are markers of healthy cardiac function. PE EF may be useful in grading dysfunction. NEW & NOTEWORTHY Kinetic energy (KE) represents the useful work of the heart in ejecting blood. This article details the utilization of KE indexes to assess cardiac function in health and a variety of pathophysiological conditions. KE ejection fraction and particle energy ejection fraction (PE EF) showed a narrow range in health and a lower wider range in disease representing a spectrum of severity. PE EF was altered by functional status potentially offering the opportunity to grade dysfunction.

International audience; In this paper we propose a method for locally adjusted optical flow-based registration of multimodal images, which uses the segmentation of the object of interest and its representation by the signed-distance function (OF dist method). We deal with non-rigid registration of the image series acquired by the Modiffied Look-Locker Inversion Recovery (MOLLI) magnetic resonance imaging sequence, which is used for a pixel-wise estimation of T 1 relaxation time. The spatial registration of the images within the series is necessary to compensate the patient's imperfect breath-holding. The evolution of intensities and a large variation of image contrast within the MOLLI image series, together with the myocardium of left ventricle (the object of interest) typically not being the most distinct object in the scene, makes the registration challenging. The paper describes all components of the proposed OF dist method and their implementation. The method is then compared to the performance of a standard mutual information maximization-based registration method, applied either to the original image (MIM) or to the signed-distance function (MIM dist). Several experiments with synthetic and real MOLLI images are carried out. On synthetic image with a single object, MIM performed the best, while OF dist and MIM dist provided better results on synthetic images with more than one object and on real images. When applied to signed-distance function of two objects of interest, MIM dist provided a larger registration error (but more homogeneously distributed) compared to OF dist. For the real MOLLI image series with left ventricle pre-segmented using a level-set method, the proposed OF dist registration performed the best, as is demonstrated visually and by measuring the increase of mutual information in the object of interest and its neighborhood.

International audience; Objective: The accuracy of phase-contrast magnetic resonance imaging (PC-MRI) measurement is investigated using a computational fluid dynamics (CFD) model with the objective to determine the magnitude of the flow underestimation due to turbulence behind a narrowed valve in a phantom experiment. Materials and Methods: An acrylic stationary flow phantom is used with three insertable plates mimicking aortic valvular stenoses of varying degrees. Positive and negative horizontal fluxes are measured at equidistant slices using standard PC-MRI sequences by 1.5T and 3T systems. The CFD model is based on the 3D lattice Boltzmann method (LBM). The experimental and simulated data are compared using the Bland-Altman-derived limits of agreement. Based on the LBM results, the turbulence is quantified and confronted with the level of flow underestimation. Results: LBM gives comparable results to PC-MRI for valves up to moderate stenosis on both field strengths. The flow magnitude through a severely stenotic valve was underestimated due to signal void in the regions of turbulent flow behind the valve, consistently with the level of quantified turbulence intensity.Discussion: Flow measured by PC-MRI is affected by noise and turbulence. LBM can simulate turbulent flow efficiently and accurately, it has therefore the potential to improve clinical interpretation of PC-MRI.

International audience; Data assimilation in computational models represents an essential step in building patient-specific simulations. This work aims at circumventing one major bottleneck in the practical use of data assimilation strategies in cardiac applications, namely, the difficulty of formulating and effectively computing adequate data-fitting term for cardiac imaging such as cine MRI. We here provide a proof-of-concept study of data assimilation based on automatic contour detection. The tissue motion simulated by the data assimilation framework is then assessed with displacements extracted from tagged MRI in six subjects, and the results illustrate the performance of the proposed method, including for circumferential displacements, which are not well extracted from cine MRI alone.

The end-systolic elastance (\(E_{\text {es}}\)) – the slope of the end-systolic pressure-volume relationship (ESPVR) at the end of ejection phase – has become a reliable indicator of myocardial functional state. The estimation of \(E_{\text {es}}\) by the original multiple-beat method is invasive, which limits its routine usage. By contrast, non-invasive single-beat estimation methods, based on the assumption of the linearity of ESPVR and the uniqueness of the normalised time-varying elastance curve \(E^N(t)\) across subjects and physiology states, have been applied in a number of clinical studies. It is however known that these two assumptions have a limited validity, as ESPVR can be approximated by a linear function only locally, and \(E^N(t)\) obtained from a multi-subject experiment includes a confidence interval around the mean function. Using datasets of 3 patients undergoing general anaesthesia (each containing aortic flow and pressure measurements at baseline and after introducing a vasopressor noradrenaline), we first study the sensitivity of two single-beat methods—by Sensaki et al. and by Chen et al.—to the uncertainty of \(E^N(t)\). Then, we propose a minimally-invasive method based on a patient-specific biophysical modelling to estimate the whole time-varying elastance curve \(E^{\text {model}}(t)\). We compare \(E^{\text {model}}_{\text {es}}\) with the two single-beat estimation methods, and the normalised varying elastance curve \(E^{N,\text {model}}(t)\) with \(E^{N}(t)\) from published physiological experiments.

International audience; Investigating the causes of failure of Fontan circulation in individual patients remains challenging despite detailed combined inva-sive cardiac catheterisation and magnetic resonance (XMR) exams at rest and during stress. In this work, we use a biomechanical model of the heart and Fontan circulation with the components of systemic and pulmonary beds to augment the diagnostic assessment of the patients undergoing the XMR stress exam. We apply our model in 3 Fontan patients and one biventricular "control" case. In all subjects, we obtained important biophysical factors of cardiovascular physiology-contractil-ity, contractile reserve and changes in systemic and pulmonary vascular resistance-which contribute to explaining the mechanism of failure in individual patients. Finally, we used the patient-specific model of one Fontan patient to investigate the impact of changes in pulmonary vas-cular resistance, aiming at in silico testing of pulmonary vasodilation treatments.

International audience; We consider flows of an incompressible Navier-Stokes fluid in a tubular domain with Navier's slip boundary condition imposed on the impermeable wall. We focus on several implementational issues associated with this type of boundary conditions within the framework of the standard Taylor-Hood mixed finite element method and present the computational results for flows in a tubular domain of finite length with one inlet and one outlet. In particular, we present the details regarding variants of the Nitsche method concerning the incorporation of the impermeability condition on the wall. We also find that the manner in which the normal to the boundary is numerically implemented influences the nature of the computational results. As a benchmark, we set up steady flows in a tube of finite length and compare the computational results with the analytical solutions. Finally, we identify various quantities of interest, such as the dissipation, wall shear stress, vorticity, pressure drop, and provide their precise mathematical definitions. We document how well these quantities are computationally approximated in the case of the benchmark. Although the geometry of the benchmark is simple, the correct computational results require careful selection of numerical methods and surprisingly non-trivial computational resources. Our goal is to test, using the setting with a known analytical solution, a robust computational tool that would be suitable for computations on real complex geometries that have relevance to problems in engineering and medicine. The model parameters in our computations are chosen based on flows in large arteries.

International audience; Image registration plays an increasingly important role in many fields such as biomedical or mechanical engineering. Generally speaking, it consists in deforming a (moving) source image to match a (fixed) template image. Many approaches have been proposed over the years; if new model-free machine learning-based approaches are now beginning to provide robust and accurate results, extracting motion from images is still most commonly based on combining some statistical analysis of the images intensity and some model of the underlying deformation as initial guess or regularizer. These approaches may be efficient even for complex type of motion; however, any artifact in the source image (e.g., partial voluming, local decrease of signal-to-noise ratio or even local signal void), drastically deteriorates the registration. This paper introduces a novel approach of extracting motion from biomedical image series, based on a model of the imaging modality. It is, to a large extent, independent of the type of model and image data-the prerequisite is to incorporate biomechanical constraints into the motion of the object (organ) of interest and being able to generate data corresponding to the real image, i.e., having an imaging model at hand. We will illustrate the method with examples of synthetically generated 2D tagged magnetic resonance images.

International audience; The human heart is enclosed in the pericardial cavity. The pericardium consists of a layered thin sac and is separated from the myocardium by a thin film of fluid. It provides a fixture in space and friction-less sliding of the myocardium. The influence of the pericardium is essential for predictive mechanical simulations of the heart. However, there is no consensus on physiologically correct and computationally tractable pericardial boundary conditions. Here we propose to model the pericardial influence as a parallel spring and dashpot acting in normal direction to the epicardium. Using a four-chamber geometry, we compare a model with pericardial boundary conditions to a model with fixated apex. The influence of pericardial stiffness is demonstrated in a parametric study. Comparing simu-lation results to measurements from cine magnetic resonance imaging reveals that adding pericardial boundary conditions yields a better approximation with respectto atrioventricular plane displacement, atrial filling, and overall spatial approximation error. We demonstrate that this simple model of pericardial-myocardial interaction can correctly predict the pumping mechanisms ofthe heart as previously assessed in clinical studies. Utilizing a pericardial model can not only provide much more realistic cardiac mechanics simulations but also allows new insights into pericardial-myocardial interaction which cannot be assessed in clinical measurement.

Cardiac electrophysiology simulations are numerically challenging because of the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the hybridizable discontinuous Galerkin method (HDG), which allows an efficient implementation of high-order discretizations into a computational framework. In particular, using the advantage of the discontinuous function space, we present an efficient p-adaptive strategy for accurately tracking the wave front. The HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high-order polynomials. Our results show that for the same number of degrees of freedom, coarse high-order elements provide more accurate results than fine low-order elements. Introducing p-adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high-order elements to resolve the wave front. For a patient-specific simulation of a cardiac cycle, p-adaptivity reduces the average number of degrees of freedom by 95% compared to the nonadaptive model. In addition to reducing computational costs, using coarse meshes with our p-adaptive high-order HDG method also simplifies practical aspects of mesh generation and postprocessing.

International audience; An unresolved issue in patient-specific models of cardiac mechanics is the choice of an appropriate constitutive law, able to accurately capture the passive behavior of the myocardium, while still having uniquely identifiable parameters tunable from available clinical data. In this paper, we aim to facilitate this choice by examining the practical identifiability and model fidelity of constitutive laws often used in cardiac mechanics. Our analysis focuses on the use of novel 3D tagged MRI, providing detailed displacement information in three dimensions. The practical identifiability of each law is examined by generating synthetic 3D tags from in silico simulations, allowing mapping of the objective function landscape over parameter space and comparison of minimizing parameter values with original ground truth values. Model fidelity was tested by comparing these laws with the more complex transversely isotropic Guccione law, by characterizing their passive end-diastolic pressure–volume relation behavior, as well as by considering the in vivo case of a healthy volunteer. These results show that a reduced form of the Holzapfel–Ogden law provides the best balance between identifiability and model fidelity across the tests considered.

In this work we introduce the modeling of atrioventricular valve regurgitation in a spatially reduced order biomechanical heart model. The model can be fast calibrated using non-invasive data of cardiac magnetic resonance imaging and provides an objective measure of contractile properties of the myocardium in the volume overloaded ventricle, for which the real systolic function may be masked by the significant level of the atrioventricular valve regurgitation. After demonstrating such diagnostic capabilities, we show the potential of modeling to address some clinical questions concerning possible therapeutic interventions for specific patients. The fast running of the model allows targeting specific questions of referring clinicians in a clinically acceptable time.

Coronary artery disease, CAD, is associated with both narrowing of the epicardial coronary arteries and microvascular disease, thereby limiting coronary flow and myocardial perfusion. CAD accounts for almost 2 million deaths within the European Union on an annual basis. In this paper, we review the physiological and pathophysiological processes underlying clinical decision making in coronary disease as well as the models for interpretation of the underlying physiological mechanisms. Presently, clinical decision making is based on non-invasive magnetic resonance imaging, MRI, of myocardial perfusion and invasive coronary hemodynamic measurements of coronary pressure and Doppler flow velocity signals obtained during catheterization. Within the euHeart project, several innovations have been developed and applied to improve diagnosis-based understanding of the underlying biophysical processes. Specifically, MRI perfusion data interpretation has been advanced by the gradientogram, a novel graphical representation of the spatiotemporal myocardial perfusion gradient. For hemodynamic data, functional indices of coronary stenosis severity that do not depend on maximal vasodilation are proposed and the Valsalva maneuver for indicating the extravascular resistance component of the coronary circulation has been introduced. Complementary to these advances, model innovation has been directed to the porous elastic model coupled to a one-dimensional model of the epicardial arteries. The importance of model development is related to the integration of information from different modalities, which in isolation often result in conflicting treatment recommendations.

Patient-specific modelling has emerged as a tool for studying heart function, demonstrating the potential to provide non-invasive estimates of tissue passive stiffness. However, reliable use of model-derived stiffness requires sufficient model accuracy and unique estimation of model parameters. In this paper we present personalised models of cardiac mechanics, focusing on improving model accuracy, while ensuring unique parametrisation. The influence of principal model uncertainties on accuracy and parameter identifiability was systematically assessed in a group of patients with dilated cardiomyopathy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=3$$\end{document}n=3) and healthy volunteers (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=5$$\end{document}n=5). For all cases, we examined three circumferentially symmetric fibre distributions and two epicardial boundary conditions. Our results demonstrated the ability of data-derived boundary conditions to improve model accuracy and highlighted the influence of the assumed fibre distribution on both model fidelity and stiffness estimates. The model personalisation pipeline—based strictly on non-invasive data—produced unique parameter estimates and satisfactory model errors for all cases, supporting the selected model assumptions. The thorough analysis performed enabled the comparison of passive parameters between volunteers and dilated cardiomyopathy patients, illustrating elevated stiffness in diseased hearts. Electronic supplementary material The online version of this article (doi:10.1007/s10439-016-1721-4) contains supplementary material, which is available to authorized users.

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, in this study, this approach is further refined through the implementation of a multi-compartment medium where each compartment encapsulates the spatial scales in a certain range by using an effective permeability tensor. Neighbouring compartments then communicate through distributed sources and sinks, acting as volume fluxes. Although elegant from a modelling perspective, the full multi-compartment Darcy system is computationally expensive to solve. We therefore enhance computational efficiency of this model by reducing the N-compartment system of Darcy equations to N pressure equations, and N subsequent projection problems to recover the Darcy velocity. The resulting 'reduced' Darcy formulation leads to a dramatic reduction in algebraic-system size and is therefore computationally cheaper to solve than the full multi-compartment Darcy system. A comparison of the reduced and the full formulation in terms of solution time and memory usage clearly highlights the superior performance of the reduced formulation. Moreover, the implementation of flux and, specifically, impermeable boundary conditions on arbitrarily curved boundaries such as epicardium and endocardium is straightforward in contrast to the full Darcy formulation. Finally, to demonstrate the applicability of our methodology to a personalized model and its solvability in clinically relevant time frames, we simulate perfusion in a subject-specific model of the left ventricle.

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/dtmax is 47.5 ± 35 mm Hg s−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.

Biomedical research, combining multi-modal image and geometry data, presents unique challenges for data visualization, processing, and quantitative analysis. Medical imaging provides rich information, from anatomical to deformation, but extracting this to a coherent picture across image modalities with preserved quality is not trivial. Addressing these challenges and integrating visualization with image and quantitative analysis results in Eidolon, a platform which can adapt to rapidly changing research workflows. In this paper we outline Eidolon, a software environment aimed at addressing these challenges, and discuss the novel integration of visualization and analysis components. These capabilities are demonstrated through the example of cardiac strain analysis, showing the Eidolon supports and enhances the workflow.

International audience; Advances in medical imaging and image processing are paving the way for personalised cardiac biomechani-cal modelling. Models provide the capacity to relate kinematics to dynamics and—through patient-specific modelling— derived material parameters to underlying cardiac muscle pathologies. However, for clinical utility to be achieved, model-based analyses mandate robust model selection and parameterisation. In this paper, we introduce a patient-specific biomechanical model for the left ventricle aiming to balance model fidelity with parameter identifiability. Using non-invasive data and common clinical surrogates, we illustrate unique identifiability of passive and active parameters over the full cardiac cycle. Identifiability and accuracy of the estimates in the presence of controlled noise are verified with a number of in silico datasets. Unique parametrisation is then obtained for three datasets acquired in vivo. The model predictions show good agreement with the data extracted from the images providing a pipeline for personalised biomechan-ical analysis.

International audience; We present a patient-specific biomechanical modeling framework and an initial case study for investigating cardiac amyloidosis (CA). Our patient-specific heartbeat simulations are in good agreement with the data, and our model calibration indicates that the major effect of CA in the biophysical behavior lies in a dramatic increase of the passive stiffness. We also conducted a preliminary trial for predicting the effects of pharmacological treatments – which is an important clinical challenge – based on the model combined with a simple venous return representation. This requires further investigation and validation, albeit provides some valuable preliminary insight.

International audience; In this work we aim to advance the translation of model-based myocardial contractility estimation to the clinical problem of quantitative assessment of the dobutamine stress exam. In particular, we address the question of limited spatial resolution of the observations obtained from cine MRI during the stress test, in which typically only a small number of cine MRI slices are acquired. Due to the relative risk during the dobutamine infusion, a safe acquisition protocol with a healthy volunteer under the infusion of a beta-blocker is applied in order to get a better insight into the contractility estimation using such a type of clinical data. The estimator is compared for three types of observations, namely the processed short axis cine stack contiguously covering the ven-tricles, the short axis stack limited to only 3 slices and the combination of 3 short and 3 long axis slices. A decrease of contractilities in AHA regions under the beta-blocker infusion was estimated for each observation. The corrected model (by using the estimated parameters) was then compared with the displacements extracted from 3D tagged MRI.

Cardiac electrophysiology simulations are numerically challenging because of the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the hybridizable discontinuous Galerkin method (HDG), which allows an efficient implementation of high-order discretizations into a computational framework. In particular, using the advantage of the discontinuous function space, we present an efficient p-adaptive strategy for accurately tracking the wave front. The HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high-order polynomials. Our results show that for the same number of degrees of freedom, coarse high-order elements provide more accurate results than fine low-order elements. Introducing p-adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high-order elements to resolve the wave front. For a patient-specific simulation of a cardiac cycle, p-adaptivity reduces the average number of degrees of freedom by 95% compared to the nonadaptive model. In addition to reducing computational costs, using coarse meshes with our p-adaptive high-order HDG method also simplifies practical aspects of mesh generation and postprocessing.

In this work we apply manifold learning to biophysical modeling of cardiac contraction with the aim of estimating material parameters characterizing myocardial stiffness and contractility. The set of cardiac cycle simulations spanning the parameter space of myocardial stiffness and contractility is used to create a manifold structure based on the motion pattern of the left ventricle endocardial surfaces. First, we assess the proposed method by using synthetic data generated by the model specifically to test our approach with the known ground truth parameter values. Then, we apply the method on cardiac magnetic resonance imaging (MRI) data of two healthy volunteers. The post-processed cine MRI for each volunteer were embedded into the manifold together with the simulated samples and the global parameters of contractility and stiffness for the whole myocardium were estimated. Then, we used these parameters as an initialization into an estimator of regional contractilities based on a reduced order unscented Kalman filter. The global values of stiffness and contractility obtained by manifold learning corrected the model in comparison to a standard model calibration by generic parameters, and a significantly more accurate estimation of regional contractilities was reached when using the initialization given by manifold learning.

To elucidate the mechanisms governing coronary blood flow in health and disease requires an understanding of the structure—function relationship of the coronary system, which exhibits distinct characteristics over multiple scales. Given the complexities arising from the multiscale and distributed nature of the coronary system and myocardial mechanical coupling, computational modelling provides an indispensable tool for advancing our understanding. In this work, we describe our strategy for an integrative whole-organ perfusion model, and illustrate a series of examples which apply the framework within both basic science and clinical translation settings. In particular, the one-dimensional reduced approach common in vascular modelling is combined with a new poromechanical formulation of the myocardium that is capable of reproducing the full contractile cycle, to enable simulation of the dynamic coronary and myocardial blood flow. In addition, a methodology for estimating continuum porous medium parameters from discrete network geometry is presented. The benefit of this framework is first demonstrated via an application to coronary wave intensity analysis, a technique developed to study time-dependent aspects of pulse waves invasively measured in the vessels. It is shown that, given experimentally-acquired boundary conditions the 1D model is capable of reproducing a wave behaviour broadly consistent with that observed in vivo, however, its utility is limited to a phenomenological level. The integrated 1D-poromechanical model on the other hand enables a mechanistic investigation of wave generation thus allowing the influence of contractile function and distal hemodynamic states on coronary flow to be described. In addition, when coupled with the advection-diffusion-reaction equation, the integrated model can be used to study the transport of tracers through the vascular network, thus allowing the dependence of noninvasive imaging signal intensities on the diffusive properties of the contrast agent to be quantified. A systematic investigation of the commonly used clinical indices and whole-organ modelling results are illustrated. Taken together, the proposed model provides a comprehensive framework with which to apply quantitative analysis in whole organ coronary artery disease diagnosis using noninvasive perfusion imaging modalities. The added value of the model in clinical practice lies in its ability to combine comprehensive patient-specific information into therapy. In this regard, we close the chapter with a discussion on potential model-aided strategies of disease management.

International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced-dimen\-sional models, in ''0D'' --~typically, to represent a cardiac cavity, or several coupled cavities --~and in ''1D'' --~to model elongated structures such as muscle samples or myocytes. We apply this approach with an earlier-proposed 3D cardiac model designed to capture length-dependence effects in contraction, which we here complement by an additional modeling component devised to represent length-dependent relaxation. We then pre\-sent experimental data produced with rat papillary muscles samples when varying preload and afterload conditions, and we achieve some detailed validations of the 1D model with these data, including for the length-dependence effects that are accurately captured. Finally, when running simulations of the 0D model pre-calibrated with the 1D model parameters, we obtain pressure-volume indicators of the left ventricle in good agreement with some important features of cardiac physiology, including the so-called Frank-Starling mechanism, the End-Systolic Pres\-sure-Volume Relationship (ESPVR), as well as varying elastance properties. This integrated multi-dimensional modeling approach thus sheds new light on the relations between the phenomena observed at different scales and at the local vs. organ levels.

A method to extract myocardial coronary permeabilities appropriate to parameterise a continuum porous perfusion model using the underlying anatomical vascular network is developed. Canine and porcine whole-heart discrete arterial models were extracted from high-resolution cryomicrotome vessel image stacks. Five parameterisation methods were considered that are primarily distinguished by the level of anatomical data used in the definition of the permeability and pressure-coupling fields. Continuum multi-compartment porous perfusion model pressure results derived using these parameterisation methods were compared quantitatively via a root-mean-square metric to the Poiseuille pressure solved on the discrete arterial vasculature. The use of anatomical detail to parameterise the porous medium significantly improved the continuum pressure results. The majority of this improvement was attributed to the use of anatomically-derived pressure-coupling fields. It was found that the best results were most reliably obtained by using porosity-scaled isotropic permeabilities and anatomically-derived pressure-coupling fields. This paper presents the first continuum perfusion model where all parameters were derived from the underlying anatomical vascular network.

To be published as proceedings in: Functional Imaging and Modeling of the Heart 7th International Conference, FIMH 2013, London, UK, Lecture Notes in Computer Science 7945; International audience; Complex 3D beating heart models are now available, but their complexity makes calibration and validation very difficult tasks. We thus propose a systematic approach of deriving simplified reduced- dimensional models, in "0D" - typically, to represent a cardiac cavity, or several coupled cavities - and in "1D" - to model elongated structures such as fibers or myocytes. As illustrations of our approach, we demon- strate model validation based on experiments performed with papillary muscles, and calibration using patient-specific pressure-volume loops.

Accelerated methods for acquiring phase contrast (PC) MRI allow the acquisition of 4D flow data of the whole heart in clinically acceptable times. These datasets are becoming interesting both for clinicians --- to better stratify diagnosis --- and in the modeling community --- to constrain patient-specific models. One of the difficulties related to PC data is a limited accuracy in the regions of low flow such as close to the myocardial wall, where the velocity field may even produce observed blood motion across the endocardial surface. To address this issue we propose to constrain the motion of blood in cavity during the analysis by using cine MRI and replacing the PC velocity in the peri-myocardial zone by neighboring tissue velocity obtained by analysis of 3D tagged MRI. We demonstrate the effect of these corrections on 2 healthy volunteer datasets and on one patient with a hypoplastic left ventricle.

Experimental data and advanced imaging techniques are increasingly enabling the extraction of detailed vascular anatomy from biological tissues. Incorporation of anatomical data within perfusion models is non-trivial, due to heterogeneous vessel density and disparate radii scales. Furthermore, previous idealised networks have assumed a spatially repeating motif or periodic canonical cell, thereby allowing for a flow solution via homogenisation. However, such periodicity is not observed throughout anatomical networks. In this study, we apply various spatial averaging methods to discrete vascular geometries in order to parameterise a continuum model of perfusion. Specifically, a multi-compartment Darcy model was used to provide vascular scale separation for the fluid flow. Permeability tensor fields were derived from both synthetic and anatomically realistic networks using (1) porosity-scaled isotropic, (2) Huyghe and Van Campen, and (3) projected-PCA methods. The Darcy pressure fields were compared via a root-mean-square error metric to an averaged Poiseuille pressure solution over the same domain. The method of Huyghe and Van Campen performed better than the other two methods in all simulations, even for relatively coarse networks. Furthermore, inter-compartment volumetric flux fields, determined using the spatially averaged discrete flux per unit pressure difference, were shown to be accurate across a range of pressure boundary conditions. This work justifies the application of continuum flow models to characterise perfusion resulting from flow in an underlying vascular network.

The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory. (C) 2011 Elsevier Ltd. All rights reserved

International audience; The objective of this paper is to propose and assess an estimation procedure - based on data assimilation principles - well-suited to obtain some regional values of key biophysical parameters in a beating heart model, using actual Cine-MR images. The motivation is twofold: (1) to provide an automatic tool for personalizing the characteristics of a cardiac model in order to achieve predictivity in patient-specific modeling, and (2) to obtain some useful information for diagnosis purposes in the estimated quantities themselves. In order to assess the global methodology we specifically devised an animal experiment in which a controlled infarct was produced and data acquired before and after infarction, with an estimation of regional tissue contractility - a key parameter directly affected by the pathology - performed for every measured stage. After performing a preliminary assessment of our proposed methodology using synthetic data, we then demonstrate a full-scale application by first estimating contractility values associated with 6 regions based on the AHA subdivision, before running a more detailed estimation using the actual AHA segments. The estimation results are assessed by comparison with the medical knowledge of the specific infarct, and with late enhancement MR images. We discuss their accuracy at the various subdivision levels, in the light of the inherent modeling limitations and of the intrinsic information contents featured in the data.

We propose a methodology for performing the estimation of a key constitutive parameter in a biomechanical heart model - namely, the tissue contractility - using tagged-MRI data. We adopt a sequential data assimilation strategy, and the image data is assumed to be processed in the form of deforming tag planes, which we employ to obtain a discrepancy between the model and the data by computing distances to these surfaces. We assess our procedure using synthetic measurements produced with a model representing an infarcted heart as observed in an animal experiment, and the estimation results are found to be of superior accuracy compared to assimilation based on segmented endo- and epicardium surfaces.

International audience; In this paper we apply specific data assimilation methods in order to estimate regional contractility parameters in a biomechanical heart model, using as measurements real Cine MR images obtained in an animal experiment. We assess the effectiveness of this estimation based on independent knowledge of the controlled infarcted condition, and on late enhancement images. Moreover, we show that the estimated contractility values can improve the model behavior in itself, and that they can serve as an indicator of the local heart function, namely, to assist medical diagnosis for the post-infarct detection of hypokinetic or akinetic regions in the myocardial tissue

International audience; To regularize cardiac motion recovery from medical images, electromechanical models are increasingly popular for providing a priori physiological motion information. Although these models are macroscopic, there are still many parameters to be specified for accurate and robust recovery. In this paper, we provide a sensitivity analysis of a pro-active electromechanical model-based cardiac motion tracking framework by studying the impacts of its model parameters. Our sensitivity analysis differs from other works by evaluating the motion recovery through a synthetic image sequence with known displacement field as well as cine and tagged MRI sequences. This analysis helps to identify which parameters should be estimated from patient-specific data and which ones can have their values set from the literature.