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##### M3DISIM - 2019

New Software and Platforms
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography

## Section: New Results

### Clinical Applications

#### Cardiac displacement tracking with data assimilation combining a biomechanical model and an automatic contour detection

Participants : Radomir Chabiniok, Gautier Bureau, Dominique Chapelle, Philippe Moireau [correspondant] .

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. This work was presented at the Functional Imaging and Modeling of Heart Conference (FIMH2019, Bordeaux, France) and published in [36].

#### Minimally-invasive estimation of patient-specific end-systolic elastance using a biomechanical heart model

Participants : Arthur Le Gall, Fabrice Vallée, Dominique Chapelle, Radomir Chabiniok [correspondant] .

The end-systolic elastance (${E}_{es}$) – 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 ${E}_{es}$ 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 ${E}^{N}\left(t\right)$ 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 ${E}^{N}\left(t\right)$ 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 ${E}^{N}\left(t\right)$. Then, we propose a minimally-invasive method based on a patient-specific biophysical modelling to estimate the whole time-varying elastance curve ${E}^{model}\left(t\right)$. We compare ${E}_{es}^{model}$ with the two single-beat estimation methods, and the normalised varying elastance curve ${E}^{N,model}\left(t\right)$ with ${E}^{N}\left(t\right)$ from published physiological experiments. This work was presented at the Functional Imaging and Modeling of Heart conference (FIMH2019, Bordeaux, France) and published in [38].

#### Model-based indices of early-stage cardiovascular failure and its therapeutic management in Fontan patients

Investigating the causes of failure of Fontan circulation in individual patients remains challenging despite detailed combined invasive 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 – contractility, 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 vascular resistance, aiming at in silico testing of pulmonary vasodilation treatments. This work (in collaboration with Bram Ruijsink and Kuberan Pushparajah from St Thomas Hospital, King's College London) was presented at the Functional Imaging and Modeling of Heart conference (FIMH2019, Bordeaux, France) and published in [40]. It also represents a part of the objectives supported by the Inria-UTSW Associated Team TOFMOD.

#### Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling

Participants : Philippe Moireau, Dominique Chapelle, Radomir Chabiniok [correspondant] .

Understanding (patho)physiological phenomena and mechanisms of failure in patients with Fontan circulation — a surgically established circulation for patients born with a functionally single ventricle — remains challenging due to the complex hemodynamics and high inter-patient variations in anatomy and function. In this work, we present a biomechanical model of the heart and circulation to augment the diagnostic evaluation of Fontan patients with early-stage heart failure. The proposed framework employs a reduced-order model of heart coupled with a simplified circulation including venous return, creating a closed-loop system. We deploy this framework to augment the information from data obtained during combined cardiac catheterization and magnetic resonance exams (XMR), performed at rest and during dobutamine stress in 9 children with Fontan circulation and 2 biventricular controls. We demonstrate that our modeling framework enables patient-specific investigation of myocardial stiffness, contractility at rest, contractile reserve during stress and changes in vascular resistance. Hereby, the model allows to identify key factors underlying the pathophysiological response to stress in these patients. In addition, the rapid personalization of the model to patient data and fast simulation of cardiac cycles makes our framework directly applicable in a clinical workflow. We conclude that the proposed modeling framework is a valuable addition to the current clinical diagnostic XMR exam that helps to explain patient-specific stress hemodynamics and can identify potential mechanisms of failure in patients with Fontan circulation. This work has been submitted for publication in an international journal. This work (in collaboration with Bram Ruijsink and Kuberan Pushparajah from St Thomas Hospital, King's College London and Tarique Hussain, UT Southwestern Medical Center Dallas) also represents a part of the objectives supported by the Inria-UTSW Associated Team TOFMOD.

#### Signed-distance function based non-rigid registration of image sequences with varying image intensity

In this work we deal with non-rigid registration of the image series acquired by the Modified 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 the 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. 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. We describe all the components of the proposed OF${}^{dist}$ method and their implementation. The OF${}^{dist}$ 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 sequence with left ventricle pre-segmented using 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. This collaborative work (Katerina Skardova, Czech Technical University, Institute of Clinical and Experimental Medicine in Prague) has been submitted for publication in an international journal. It also represents a part of the objectives supported by the Inria-UTSW Associated Team TOFMOD.

#### Estimation of left ventricular pressure-volume loop using hemodynamic monitoring augmented by a patient-specific biomechanical model. An observational study

Participants : Arthur Le Gall, Fabrice Vallée, Dominique Chapelle, Radomir Chabiniok [correspondant] .

Background During general anaesthesia, direct analysis of the arterial pressure or aortic flow waveforms may be confusing in complex haemodynamic situations. Patient-specific biomechanical modelling allows to simulate Pressure-Volume (PV) loops and obtain functional indicators of the cardiovascular (CV) system, such as ventricular-arterial coupling (Vva), cardiac efficiency (CE) or myocardial contractility. It therefore augments the information obtained by monitoring and could help in medical decision-making. Methods Patients undergoing GA for neuroradiological procedure were included in this prospective observational study. A biomechanical model of heart and vasculature specific to each patient was built using transthoracic echocardiography and aortic pressure and flow signals. If intraoperative hypotension (IOH) appeared, diluted noradrenaline (NOR) was administered and the model readjusted. Results The model was calibrated for 29 (64%) normotensive and for 16 (36%) hypotensive patients before and after NOR administration. The simulated mean aortic pressure (MAP) and stroke volume (SV) were equivalent to the measurements (Percentage Error: 6% for MAP and 18% for SV) in all 45 datasets at baseline. After NOR administration, the percentage of concordance with 10% exclusion zone between measurement and simulation was > 95% for both MAP and SV. The modelling results showed a decreased Vva (0.64±0.37 vs 0.88±0.43; p=0.039), and an increased CE (0.8±0.1 vs 0.73±0.11; p=0.042) in hypotensive as compared with normotensive patients. After NOR administration, Vva increased by 92±101%, CE decreased by 13±11% (p<0.001 for both) and contractility increased by 14±11% (p=0.002). Conclusions The numerical models built for individual patients were applied to estimate patients' PV loops and functional indicators of CV system during haemodynamic alterations and during restoration by NOR. This study demonstrates the feasibility of patient-specific cardiovascular modelling using clinical data readily available during GA and paves the way for model-augmented haemodynamic monitoring at operating theatres and intensive care units. This work is about to be submitted for publication in an international journal. It also represents a part of the objectives supported by the Inria-UTSW Associated Team TOFMOD.

#### Investigation of phase contrast magnetic resonance imaging underestimation of turbulent flow through the aortic valve phantom: Experimental and computational study by using lattice Boltzmann method

Work in collaboration with Radek Fucik, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague.

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 Matching results of PC-MRI flow were obtained 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. This collaborative work (Czech Technical University, Institute of Clinical and Experimental Medicine in Prague and Inria) has been submitted for publication in an international journal. It also represents a part of the objectives supported by the Inria-UTSW Associated Team TOFMOD.

#### Left ventricular torsion obtained using equilibrated warping in patients with repaired Tetralogy of Fallot

Participants : Martin Genet, Radomir Chabiniok [correspondant] .

Work in collaboration with Katerina Skardova, Department of Mathematics, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague and Tarique Hussain UT Southwestern Medical Center Dallas.

Background Patients after surgical repair of Tetralogy of Fallot (rTOF) have right ventricular (RV) dysfunction and may subsequently suffer a decrease in left ventricular (LV) function. Previous studies evaluating the assessment of LV torsion have shown poor reproducibility using cardiovascular magnetic resonance imaging (CMR). The aim of our study is to evaluate a novel finite element method of image registration to assess LV torsion in patients with rTOF and explore the relationship between LV torsion and cardiac parameters routinely obtained with CMR. Methods The assessment of torsion is based on the finite element method for image registration, and the equilibrium gap principle for problem regularization, known as equilibrated warping developed by M. Genet (Inria Saclay). It has been shown to be able to predict global torsion in regular cine images as well in 3D tagged images, despite low contrast. Seventy-six cases of rTOF and ten controls were included. The group of control patients were assessed for reproducibility using equilibrated warping and standard tissue tracking software (cvi42, version 5.10.1, Calgary, Canada). RV end-systolic volume (RVESV), RV end-diastolic volume (RVEDV), RV ejection fraction (RVEF), LVESV, LVEDV, LVEF, LV peak systolic torsion and peak systolic torsion gradient (normalized by mesh length) were obtained for each patient with rTOF. Patients were dichotomized into two groups: those with normal torsion (systolic basal clockwise rotation and apical counterclockwise rotation, representative example is shown in Image 1) and those with loss of torsion, defined as a reversal of normal systolic basal clockwise rotation (representative example is shown in Image 2). Results Torsion by equilibrated warping was successfully obtained in 68 of 76 (89%) patients with rTOF and 9 of 10 (90%) normal controls. For equilibrated warping, the intra- and inter-observer coefficients of variation were 0.095 and 0.117, respectively; compared to 0.668 and 0.418 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 0.250 and 0.621 for tissue tracking. Loss of torsion was noted in 32 of the 68 (47%) patients with rTOF and there was a significant difference in peak systolic torsion gradient between patients with normal torsion and loss of torsion. There was no difference in LV or RV volumes or function between these groups. Conclusion The equilibrated warping method of image registration to assess LV torsion is feasible in patients with rTOF and shows good reliability. Loss of torsion is common in patients with rTOF. In our study, there was no significant association between loss of torsion and other ventricular parameters indicative of a worsening cardiac condition. Future studies committed to the long- term follow-up of this population are needed to assess the role of torsion in predicting ventricular dysfunction and death. This work was accepted for presentation at SCMR conference 2020 (Society for Cardiovascular Magnetic Resonance). It also represents a part of the objectives supported by the Inria-UTSW Associated Team TOFMOD.

#### Volume administration protocol to assess ventricular mechanics during interventional cardiac magnetic resonance procedures

Work in collaboration with Joshua Greer and Tarique Hussain UT Southwestern Medical Center Dallas.

Pulmonary arterial hypertension (PAH) causes an increase in the mechanical loading imposed on the right ventricle (RV) that results in progressive changes to its mechanics and function. Here, we quantify the mechanical changes associated with PAH by assimilating clinical data consisting of reconstructed three-dimensional geometry, pressure, and volume waveforms, as well as regional strains measured in patients with PAH ($n=12$) and controls ($n=6$) within a computational modeling framework of the ventricles. Modeling parameters reflecting regional passive stiffness and load-independent contractility as indexed by the tissue active tension were optimized so that simulation results matched the measurements. The optimized parameters were compared with clinical metrics to find usable indicators associated with the underlying mechanical changes. Peak contractility of the RV free wall (RVFW) ${\gamma }_{RVFW,max}$ was found to be strongly correlated and had an inverse relationship with the RV and left ventricle (LV) end-diastolic volume ratio (i.e., RVEDV/LVEDV) (RVEDV/LVEDV)+0.44, ${R}^{2}=0.77$). Correlation with RV ejection fraction (${R}^{2}=0.50$) and end-diastolic volume index (${R}^{2}=0.40$) were comparatively weaker. Patients with $RVEDV/LVEDV>1.5$ had $25%$ lower ${\gamma }_{RVFW,max}$ ($P<0.05$) than that of the control. On average, RVFW passive stiffness progressively increased with the degree of remodeling as indexed by RVEDV/LVEDV. These results suggest a mechanical basis of using RVEDV/LVEDV as a clinical index for delineating disease severity and estimating RVFW contractility in patients with PAH. See [25] for more detail.