Jean-Frédéric Gerbeau

A methodological paradigm for patient-specific multi-scale CFD simulations: from clinical measurements to parameter estimates for individual analysis

A new framework for estimation of lumped (for instance, Windkessel) model parameters from uncertain clinical measurements is presented. The ultimate aim is to perform patient-specific haemodynamic analysis. This framework is based on sensitivity analysis tools and the sequential estimation approach of the unscented Kalman filter. Sensitivity analysis and parameter estimation are performed in lumped parameter models, which act as reduced order surrogates of the 3D domain for haemodynamic analysis. While the goal of sensitivity analysis is to assess potential identifiability problems, the unscented Kalman filter estimation leads to parameter estimates based on clinical measurements and modelling assumptions. An application of such analysis and parameter estimation methodology is demonstrated for synthetic and real data. Equality constraints on various physiological parameters are enforced. Since the accuracy of the Windkessel parameter estimates depends on the lumped parameter representativeness, the latter is iteratively improved by running few 3D simulations while simultaneously improving the former. Such a method is applied on a patient-specific aortic coarctation case. Less than 3% and 9% errors between the clinically measured quantities and 3D simulation results for rest and stress are obtained, respectively. Knowledge on how these Windkessel parameters change from rest to stress can thus be learned by such an approach. Lastly, it is demonstrated that the proposed approach is capable of dealing with a wide variety of measurements and cases where the pressure and flow clinical measurements are not taken simultaneously.

SPURIOUS VELOCITIES IN THE STEADY FLOW OF AN INCOMPRESSIBLE FLUID SUBJECTED TO EXTERNAL FORCES

SUMMARY We show that a non-physical velocity may appear in the numerical computation of the flow of an incompressible fluid subjected to external forces. A distorted mesh and the use of a numerical method which does not rigorously ensure the incompressibility condition turn out to be responsible for this phenomenon. We illustrate it with numerical examples and we propose a projection method which improves the results. # 1997 John Wiley & Sons, Ltd.

Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the definition of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed, we aggregate a Luenberger observer for the mechanical state and a Reduced-Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the advantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart.

Identification of artery wall stiffness: in vitro validation and in vivo results of a data assimilation procedure applied to a 3D fluid-structure interaction model

We consider the problem of estimating the stiffness of an artery wall using a data assimilation method applied to a 3D fluid-structure interaction (FSI) model. Recalling previous works, we briefly present the FSI model, the data assimilation procedure and the segmentation algorithm. We present then two examples of the procedure using real data. First, we estimate the stiffness distribution of a silicon rubber tube from image data. Second, we present the estimation of aortic wall stiffness from real clinical data.

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

3D computational fluid dynamics (CFD) in patient-specific geometries provides complementary insights to clinical imaging, to better understand how heart disease, and the side effects of treating heart disease, affect and are affected by hemodynamics. This information can be useful in treatment planning for designing artificial devices that are subject to stress and pressure from blood flow. Yet, these simulations remain relatively costly within a clinical context. The aim of this work is to reduce the complexity of patient-specific simulations by combining image analysis, computational fluid dynamics and model order reduction techniques. The proposed method makes use of a reference geometry estimated as an average of the population, within an efficient statistical framework based on the currents representation of shapes. Snapshots of blood flow simulations performed in the reference geometry are used to build a POD (Proper Orthogonal Decomposition) basis, which can then be mapped on new patients to perform reduced order blood flow simulations with patient specific boundary conditions. This approach is applied to a data-set of 17 tetralogy of Fallot patients to simulate blood flow through the pulmonary artery under normal (healthy or synthetic valves with almost no backflow) and pathological (leaky or absent valve with backflow) conditions to better understand the impact of regurgitated blood on pressure and velocity at the outflow tracts. The model reduction approach is further tested by performing patient simulations under exercise and varying degrees of pathophysiological conditions based on reduction of reference solutions (rest and medium backflow conditions respectively).

A Multiscale Filtering-Based Parameter Estimation Method for Patient-Specific Coarctation Simulations in Rest and Exercise

The 2nd CFD Challenge Predicting Patient-Specific Hemodynamics at Rest and Stress through an Aortic Coarctation provides patient-specific flow and pressure data. In this work, a multiscale 0D-3D strategy is tested to match the given data. The 3D outlet boundary conditions for the supra-aortic vessels are represented by three-element Windkessel models. In order to estimate the Windkessel parameters at these outlets, a 0D lumped parameter model for the full aorta is considered. The parameters in such a 0D model are estimated by a sequential estimation method, the unscented Kalman filter. The filtering approach estimates the parameters such that the results of the 0D model closely match the measured data: flow waveforms in the ascending and diaphragmatic aorta, mean flow rates in the supra-aortic vessels, and the pressure waveform in the ascending aorta. Information from the 3D model is taken into account in the full 0D model. This process is repeated for the two separate cases of rest and stress conditions to estimate separate sets of parameters for the two physiological states. Results such as the pressure gradient across the coarctation, comparison with target values and more detailed time or spatial variations are presented. Modelling choices and assumptions about how the data are interpreted are then discussed.

Surface-based electrophysiology modeling and assessment of physiological simulations in atria

The objective of this paper is to assess a previously-proposed surface-based electrophysiology model with detailed atrial simulations. This model --- derived and substantiated by mathematical arguments --- is specifically designed to address thin structures such as atria, and to take into account strong anisotropy effects related to fiber directions with possibly rapid variations across the wall thickness. The simulation results are in excellent adequacy with previous studies, and confirm the importance of anisotropy effects and variations thereof. Furthermore, this surface-based model provides dramatic computational benefits over 3D models with preserved accuracy.

Reduced order model in cardiac electrophysiology with approximated Lax pairs

A reduced-order method based on Approximated Lax Pairs (ALP) is applied to the integration of electrophysiology models. These are often high-dimensional parametric equation systems, challenging from a model reduction standpoint. The method is tested on two and three dimensional test-cases, of increasing complexity. The solutions are compared to the ones obtained by a finite element. The reduced-order simulation of pseudo-electrocardiograms based on ALP is proposed in the last part.

Modelling variability in cardiac electrophysiology: a moment-matching approach.

The variability observed in action potential (AP) cardiomyocyte measurements is the consequence of many different sources of randomness. Often ignored, this variability may be studied to gain insight into the cell ionic properties. In this paper, we focus on the study of ionic channel conductances and describe a methodology to estimate their probability density function (PDF) from AP recordings. The method relies on the matching of observable statistical moments and on the maximum entropy principle. We present four case studies using synthetic and sets of experimental AP measurements from human and canine cardiomyocytes. In each case, the proposed methodology is applied to infer the PDF of key conductances from the exhibited variability. The estimated PDFs are discussed and, when possible, compared to the true distributions. We conclude that it is possible to extract relevant information from the variability in AP measurements and discuss the limitations and possible implications of the proposed approach.

Composite biomarkers derived from Micro-Electrode Array measurements and computer simulations improve the classification of drug-induced channel block

The Micro-Electrode Array (MEA) device enables high-throughput electrophysiology measurements that are less labor-intensive than patch-clamp based techniques. Combined with human-induced pluripotent stem cells cardiomyocytes (hiPSC-CM), it represents a new and promising paradigm for automated and accurate in vitro drug safety evaluation. In this article, the following question is addressed: which features of the MEA signals should be measured to better classify the effects of drugs? A framework for the classification of drugs using MEA measurements is proposed. The classification is based on the ion channels blockades induced by the drugs. It relies on an in silico electrophysiology model of the MEA, a feature selection algorithm and automatic classification tools. An in silico model of the MEA is developed and is used to generate synthetic measurements. An algorithm that extracts MEA measurements features designed to perform well in a classification context is described. These features are called composite biomarkers. A state-of-the-art machine learning program is used to carry out the classification of drugs using experimental MEA measurements. The experiments are carried out using five different drugs: mexiletine, flecainide, diltiazem, moxifloxacin, and dofetilide. We show that the composite biomarkers outperform the classical ones in different classification scenarios. We show that using both synthetic and experimental MEA measurements improves the robustness of the composite biomarkers and that the classification scores are increased.