The research carried out in the M

Over the past decade, we have laid out the foundations of a multi-scale 3D model of the cardiac mechanical contraction responding to electrical activation. Several collaborations have been crucial in this enterprise, see below references. By integrating this formulation with adapted numerical methods, we are now able to represent the whole organ behavior in interaction with the blood during complete heart beats. This subject was our first achievement to combine a deep understanding of the underlying physics and physiology and our constant concern of proposing well-posed mathematical formulations and adequate numerical discretizations. In fact, we have shown that our model satisfies the essential thermo-mechanical laws, and in particular the energy balance, and proposed compatible numerical schemes that – in consequence – can be rigorously analyzed, see 6. In the same spirit, we have formulated a poromechanical model adapted to the blood perfusion in the heart, hence precisely taking into account the large deformation of the mechanical medium, the fluid inertia and moving domain, and so that the energy balance between fluid and solid is fulfilled from the model construction to its discretization, see 7.

A major challenge in the context of biomechanical modeling – and more generally in modeling for life sciences – lies in using the large amount of data available on the system to circumvent the lack of absolute modeling ground truth, since every system considered is in fact patient-specific, with possibly non-standard conditions associated with a disease. We have already developed original strategies for solving this particular type of inverse problems by adopting the observer stand-point. The idea we proposed consists in incorporating to the classical discretization of the mechanical system an estimator filter that can use the data to improve the quality of the global approximation, and concurrently identify some uncertain parameters possibly related to a diseased state of the patient. Therefore, our strategy leads to a coupled model-data system solved similarly to a usual PDE-based model, with a computational cost directly comparable to classical Galerkin approximations. We have already worked on the formulation, the mathematical and numerical analysis of the resulting system – see 5 – and the demonstration of the capabilities of this approach in the context of identification of constitutive parameters for a heart model with real data, including medical imaging, see 2.

As already emphasized in the team's objectives, we consider experimental studies and clinical applications as crucial, both for motivating our new modeling endeavors, and to validate the global modeling simulation chain, via the numerical simulation and inverse problems (for data-based estimation).

For instance, the translation of the modeling and data assimilation techniques developed in our team into cardiac clinical applications is pursued in two main directions: 1. Cardiac modeling for monitoring purposes in anesthesia and critical care medicine 2. Cardiac modeling in heart diseases. Concerning the clinical applications of lung modeling and data interaction, the team works for a better understanding of pulmonary fibrosis and with recent new research about COVID pulmonary infections. Another example is the clinical relevance of our modeling and characterization of the biomechanical behavior of the cornea.

Beyond medical applications, our general methods have applications in many industrial fields. For instance, our expertise in wave propagation and associated inverse problems have potential applications in non-destructive testing of structure.

Unstable hemodynamics during general anaesthesia increases the risk of cardiac, renal and brain disfunctions during the postoperative period, thus leading to a higher level of morbidity and mortality. To improve the patient's condition, learned societies therefore recommend monitoring the hemodynamics of the patient and having treatment strategies with quantitative objectives based on this monitoring. Currently, medical doctors have at their disposal some physiological signals (ECG, blood pressure) displayed on their monitor, and must rely on established practices and their experience to act in case of a dangerous drift.

The AnaestAssist project proposes to develop an augmented monitoring tool for anaesthesia. The proposed technology will introduce into the monitoring loop a predictive biophysical model, simulated in real time, and fed by the measured physiological signals. The model will be personalised for the patient, thus creating a digital twin of the patient's cardiovascular system. With this digital twin, physiological information that can cannot be measured or that can only be obtained with highly invasive methods will be computed in real time and treatment recommendations will be made. Our system will thus provide a much more complete vision of the patient's cardiovascular state and allow more informed and faster decisions. Eventually, the effects of drugs will be included in the model, which will make it possible to determine (through predictive modeling) adapted action recommendations, or even a real-time automatic drug administration loop. Our technology is expected to allow the medical staff to deliver a better treatment to the patient, to improve the patient's condition through a reduction of the risk related to general anaesthesia and a wiser exposition to drugs, and to reduce the costs for the health care system due to a lower rate of complications and shorter hospital stays.

The AnaestAssist project is intended to lead to a startup creation in the near future.

In response to the ongoing COVID-19 pandemic caused by SARS-CoV-2, governments are taking a wide range of non-pharmaceutical interventions (NPI). These measures include interventions as stringent as strict lockdown but also school, bar and restaurant closures, curfews and barrier gestures, i.e. social distancing. Disentangling the effectiveness of each NPI is crucial to inform response to future outbreaks. To this end, we propose to develop a multi-level estimation of the French COVID-19 epidemic over a period of one year. This work performed with colleagues from project-teams Sistm and Monc among others has been published in 10 for the methodological aspects and in 8 for the applications to the COVID-19 pandemic.

More specifically in this work, we rely on a global extended Susceptible-Infectious-Recovered (SIR) mechanistic model of the infection including a dynamical (over time) transmission rate containing a Wiener process accounting for modeling error. Random effects are integrated following an innovative population approach based on a Kalman-type filter where the log-likelihood functional couples data across French regions. We then fit the estimated time-varying transmission rate using a regression model depending on NPI, while accounting for vaccination coverage, apparition of variants of concern (VoC) and seasonal weather conditions. We show that all NPI considered have an independent significant effect on the transmission rate. We additionally demonstrate a strong effect from weather conditions which decrease transmission during the summer period, and also estimate increased transmissibility of VoCs.

With the french compagny Withings, specialized in health monitoring solutions through connected devices (watch, balance, etc.), we propose to process the collected measurements by our data assimilation approaches based on the modeling of the underlying biophysical processes. These models of the cardiovascular system and the real-time estimation methods developed by the team are ideally suited to the distal data on cardiovascular functioning collected by Withings. New algorithms for estimating the physiology of subjects respecting the constraints of optimal regularization of signals, detection of defects by searching for causality, privacy on shared data will make it possible in the future to detect deterioration in the cardiovascular state of patients.

Philippe Moireau participated to the Programme “The mathematical and statistical foundation of future data-driven engineering” at Isaac Newton Institute for Mathematical Sciences, Cambridge from January to end of june.

Martin Genet has been promoted Associate Professor at Polytechnique.

A former PhD student of the team, Federica Caforio, received this year L’Oréal-UNESCO For Women in Science, partly her work in the team.

As part of Julien Bonnafé's PhD, which began this year, we have carried out a literature review on the different components of the eye, and in particular on their mechanical roles. A specific question is the importance of the muscle and the surrounding tissues. Our aim is to predict the mechanical loadings due to major eye movements, and their possible impact on the optical capacity of the eye. This state of the art consisted of an evaluation of the models present in the literature, an identification of feasible simulation methods, a biometric assessment of anatomical features, as well as the collection of mechanical parameters of the various tissues of the ocular system.

The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) was proposed in 29 for the simulation of nuclear fuel assemblies at the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but with a reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions.

Contractile force in muscle tissue is produced by myosin molecular motors that bind and pull on specific sites located on surrounding actin filaments. The classical framework to model this active system was set by the landmark works of A.F. Huxley and T.L. Hill. This framework is built on the central assumption that the relevant quantity for the model parametrization is the myosin head reference position. In this paper, we present an alternative formulation that allows to take into account the current position of the myosin head as the main model parameter. The actin-myosin system is described as a Markov process combining Langevin drift-diffusion and Poisson jumps dynamics. We show that the corresponding system of Stochastic Differential Equation is well-posed and derive its Partial Differential Equation analog in order to obtain the thermodynamic balance laws. We finally show that by applying standard elimination procedures, a modified version of the original Huxley-Hill framework can be obtained as a reduced version of our model. Theoretical results are supported by numerical simulations where the model outputs are compared to benchmark experimental data. This work was published as 17.

Muscle contraction at the macro level is a physiological process that is ultimately due to the interaction between myosin and actin proteins at the micro level. The actin-myosin interaction involves slow attachment and detachment responses and a rapid temporal change in protein conformation called power-stroke. Jump-diffusion models that combine jump processes between attachment and detachment with a mechanical description of the power-stroke have been proposed in the literature. However, the current formulations of these models are not fully compatible with the principles of thermodynamics. To solve the problem of coupling continuous mechanisms with discrete chemical transitions, we rely on the mathematical formalism of Poisson random measures. First, we design an efficient stochastic formulation for existing muscle contraction PDE models. Then, we write a new jump- diffusion model for actin-myosin interaction. This new model describes both the behavior of muscle contraction on multiple time scales and its compatibility with thermodynamic principles. Finally, following a classical calibration procedure, we demonstrate the ability of the model to reproduce experimental data characterizing muscle behavior on fast and slow time scales. This work was published as 19.

Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-order finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, for example, for pre-calibration of full-order models, fast predictions, real-time applications, and so forth. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of Guccione, McCulloch, & Waldman (1991); Guccione, Waldman, & McCulloch (1993), albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel aswell, with consistent spatial (finite element) and time discretizations. Finally, we analyze the sensitivity of the model response to various numerical and physical parameters, and study its physiological response. This work was published in 22.

Porous materials are ubiquitous in nature – notably living tissues, which often undergo large deformations – and engineering applications. Poromechanics is an established theory to model the response of such materials; however, it is limited in its description of microscale phenomena, and structure-properties relationships. In this paper, we propose a microscopic poromechanical model based on a novel formulation of the micro-poro-mechanics problem, which allows to compute the response of a periodic porous microstructure to any loading involving fluid pressure, macroscopic strain, and/or macroscopic stress. We systematically compare the global response of our micro-model to macro-poromechanics, in both the infinitesimal and finite strain settings, and investigate in particular three mechanisms, namely solid compressibility, strain-pressure coupling and deviatoric-volumetric strain coupling. We notably illustrate how the micro-model can be used to derive macroscopic parameters, and how these parameters depend on microscopic features like pore shape, porosity, material properties, etc. This modeling framework will be the basis for powerful micro-poro-mechanical models of various materials and tissues, where pore-scale phenomena can be incorporated explicitly. This work has just been submitted to the Journal of Mechanics and Physics of Solids.

In silico models of the lungs have been widely developed in recent years, to improve the care of patients with pulmonary diseases, for example. A wide range of models, with different levels of complexity, can be found in the literature. In particular, the loading considered usually consists solely in the implementation of the pleural pressure —a negative pressure keeping the lungs inflated—. Gravity, usually considered to be small in relation to the pleural pressure, has often been neglected. Beyond its supposedly limited impact, gravity has also been neglected due to the complexity of formulating physiological boundary conditions to counterbalance it.
Gravity is however known to have many effects on pulmonary functions, e.g. on ventilation. We therefore chose to implement gravity in our model to verify that it is not negligible and therefore improve the accuracy of our model should it be the case. In this article, we propose a formulation of a counterbalancing pressure as boundary condition to implement gravity.
We then study the effect of gravity on global and local behavior of our model, such as the pressure-volume response or the porosity. This study shows that, although small, gravity does have an impact on lung response. In particular, implementing gravity in our model induces the appearance of heterogeneities in the deformation and stress distribution, which could be valuable information to predict the evolution of certain pulmonary diseases, by correlating areas subjected to higher deformation and stresses with the evolution patterns of a given disease, for example.
This work is about to be submitted to the Biomechanics and Modeling in Mechanobiology journal.

Ultrasonic testing techniques such as guided wave-based structural health monitoring aim to evaluate the integrity of a material with sensors and actuators that operate in situ, i.e. while the material is in use. Since ultrasonic wave propagation is sensitive to environmental conditions such as pre-deformation of the structure, the design and performance evaluation of monitoring systems in this context is a complicated task that requires quantitative data and the associated modeling effort. In this work, we propose a set of numerical tools to solve the problem of mechanical wave propagation in materials subjected to pre-deformation. This type of configuration is usually treated in the domain of acoustoelasticity. A relevant modeling approach is to consider two different problems: a quasi-static nonlinear problem for the large displacement field of the structure and a linearized time-domain wave propagation problem. After carefully reviewing the modeling ingredients to represent the configurations of interest, we propose an original combination of numerical tools that leads to a computationally efficient algorithm. More specifically, we use 3D shell elements for the quasi-static nonlinear problem and the time-domain spectral finite element method to numerically solve the wave propagation problem. Our approach can represent any type of material constitutive law, geometry or mechanical solicitation. We present realistic numerical results on 3D cases related to the monitoring of both isotropic and anisotropic materials, illustrating the genericity and efficiency of our method. We also validate our approach by comparing it to experimental data from the literature.

Dynamic elastography is a fundamental technique to study the local mechanical property of biological tissues, such as the cornea. It is based on in-vivo tracking of shear waves propagation as a result of a transient stimulation. Due to high water content, the cornea is a nearly incompressible tissue where the shear waves are 150 times slower than the compressional waves. The incompressibility and the double-scale of the phenomena make the finite element (FE) approximation difficult. The objective of this study is to propose an efficient scheme to obtain a reliable modelling of transient elastography measurements applied to the cornea and to improve tissue characterization techniques.

In order to model the resulting shear-wave propagation phenomenon, we propose a FE approximation with high-order spectral elements together with Mass Lumping approach. This allows to avoid the inversion of mass matrix at each time-step by computing an approximated value of the mass integrals with a numerical integration formula (Gauss-Lobatto rule).

Incompressibility is a well-known problem in FE approximation with pure displacement method, due to locking, ill-conditioning of the stiffness matrix and incorrect pressures approximations. To overcome these limitations, we use a mixed formulation with the introduction of the pressure as a local variable defined on each element. The approximation of the displacement and the pressure field are performed with

For the time discretization, the explicit leapfrog (LF) scheme shows high efficiency and second order accuracy. However, the time-step is strongly decreased by the velocity of the compressional wave. In this study, we propose a strategy inspired by local time-stepping method. The contribution of pressure wave is computed explicitly in an inner loop. While maintaining stability and accuracy, we obtain a fully explicit algorithm that is more efficient in terms of CPU time compared to the standard LF scheme.

We have performed simulations of elastic wave propagation on a homogeneous isotropic cornea with a CPU time of 75 minutes. In preliminary simulations we achieve a computational time three times lower, with a

The objective of this work is first to analyze the numerical method for the shear wave propagation in tissues developped in a previous work and second to extend the method to other types of finite elements strategy. In particular we use enriched finite element space on tetrahedrals in order to construct provably inf-sup stable finite elements of order 2 and 3 that allow using a mass lumping strategy.

In this work we propose a new implicit-explicit scheme to address the challenge of modeling wave propagation within thin structures using the time-domain finite element method. Compared to standard explicit schemes, our approach renders a time marching algorithm with a time step independent of the plate thickness and its associated discretization parameters (mesh step and order of approximation). Relying on the standard three dimensional elastodynamics equations, our strategy can be applied to any type of material, either isotropic or anisotropic, with or without discontinuities in the thickness direction. Upon the assumption of an extruded mesh of the plate-like geometry, we show that the linear system to be solved at each time step is partially lumped thus efficiently treated. We provide numerical evidence of an adequate convergence behavior, similar to a reference solution obtained using the well-known leapfrog scheme. Further numerical investigations show significant speed up factors compared to the same reference scheme, proving the efficiency of our approach for the configurations of interest. This work is published in 30

The objective of this work is to propose and analyze numerical schemes for solving boundary control problems or data assimilation problems by observers for wave propagation problems. The efficiency of the considered control or data assimilation strategy relies on the exponentially stable character of the underlying system. Therefore, the aim of our work is to propose a discretization process that allows preserving the exponential stability at the discrete level when using high-order spectral finite element approximation. The main idea is to add a stabilizing term to the wave equation that dampens the spurious oscillatory components of the solutions. This term is based on a discrete multiplier analysis that gives us the exponential stability of the semi-discrete problem at any order without affecting the approximation properties. This work is submitted and the preprint is available at 47.

Classically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition on the constraint. In this work, we propose an alternative framework to study such problems by using the T-coercivity approach to derive a global inf-sup condition. Generally speaking, this is a constructive approach that, in addition, drives the design of suitable approximations. As a matter of fact, the derivation of the uniform discrete inf-sup condition for the approximate problems follows easily from the study of the original problem. To support our view, we solve a series of classical mixed problems with the T-coercivity approach. Among others, the celebrated Fortin Lemma appears naturally in the numerical analysis of the approximate problems.

This work is devoted to the numerical analysis of the full discretization of a generalized poromechanical model resulting from the linearization of an initial model fitted to soft tissue perfusion. Our strategy here is based on the use of energy-based estimates and T-coercivity methods, so that the numerical analysis benefits from the essential tools used in the existence analysis of the continuous-time and continuous-space formulation. In particular, our T-coercivity strategy allows us to obtain the necessary inf-sup condition for the global system from the inf-sup condition restricted to a subsystem having the same structure as the Stokes problem. This allows us to prove that any finite element pair adapted to the Stokes problem is also suitable for this global poromechanical model regardless of porosity and permeability, generalizing previous results from the literature studying this model. This work is now published in 16.

We address the problem of deterministic sequential estimation for a nonsmooth dynamics governed by a variational inequality. An example of such dynamics is the Skorokhod problem with a reflective boundary condition. For smooth dynamics, Mortensen introduced in 1968 a nonlinear estimator based on likelihood maximisation. Then, starting with Hijab in 1980, several authors established a connection between Mortensen?s approach and the vanishing noise limit of the robust form of the so-called Zakai equation. In this paper, we investigate to what extent these methods can be developed for dynamics governed by a variational inequality. On the one hand, we address this problem by relaxing the inequality constraint by penalization: this yields an approximate Mortensen estimator relying on an approximating smooth dynamics. We verify that the equivalence between the deterministic and stochastic approaches holds through a vanishing noise limit. On the other hand, inspired by the smooth dynamics approach, we study the vanishing viscosity limit of the Hamilton-Jacobi equation satisfied by the Hopf-Cole transform of the solution of the robust Zakai equation. In contrast to the case of smooth dynamics, the zero-noise limit of the robust form of the Zakai equation cannot be understood in our case from the Bellman equation on the value function arising in Mortensen?s procedure. This unveils a violation of equivalence for dynamics governed by a variational inequality between the Mortensen approach and the low noise stochastic approach for nonsmooth dynamics. This work was published as 18.

The objective of this work is to propose a method using observers to estimate a source term of a wave equation from internal measurements in a subdomain. The first part of the work consists in proving an identifiability result from classical observability conditions for wave equations. We show that the source reconstruction is an ill-posed inverse problem of degree 1 or 2 depending on the measurements type. This inverse problem is solved using observers – a sequential strategy – that is proven to be equivalent to a minimization of a cost functional with Tikhonov regularization.

The goal of this work is to derive a reliable stable and accurate inverse problem strategy for reconstructing cardiac output blood flow entering the ascending aorta from pressure measurements at a distal site of the arterial tree, assumed here to be the descending aorta. We assume that a reduced one-dimensional model of the aorta can be linearized around its steady state, resulting in a wave system with absorbing boundary condition at the outlet. Using this model, we attempt to reconstruct the inlet flow from a pressure measurement at the distal outlet. First, we investigate the observability of the problem and prove that the inversion of the input-output operator for the flow and pressure in the space of time-periodic solutions is ill-posed of degree one. We then develop a variational approach where we minimize the discrepancy between measurements and a simulated state and penalize the error with respect to a periodic state. It is shown that the penalty strategy is convergent and provides an efficient solution for the minimization. Numerical results illustrate the robustness of our approach to noise and the potential of our method to reconstruct inlet flow from real pressure recordings during anesthesia. This work is publised in 27.

The equilibrium gap principle offers a good trade-off between robustness and accuracy for regularizing motion tracking, as it simply enforces that the tracked motion corresponds to a body deforming under arbitrary loadings. This paper introduces an extension of the equilibrium gap principle in the large deformation setting, a novel regularization term to control surface tractions, both in the context of finite element motion tracking, and an inverse problem consistent reformulation of the tracking problem. Tracking performance of the proposed method, with displacement resolution down to the pixel size, is demonstrated on synthetic images representing various motions with various signal-to-noise ratios. This work has been accepted for publication in the Comptes Rendus Mécanique de l'Académie des Sciences journal 23.

Ultrasonic guided wave-based Structural Health Monitoring (SHM) of structures can be perturbed by Environmental and Operations Conditions (EOCs) that alter wave propagation. In this work, we present an estimation procedure to reconstruct an EOC-free baseline of the structure suitable for SHM from the only available Ultrasonic guided wave measurements. Our approach is model-based, i.e. we use a precise modeling of the wave propagation altered by structure loading conditions. This model is coupled with the acquired data through a data assimilation procedure to estimate the deformation caused by the unknown loading conditions. From a methodological point of view, our approach is original since we have proposed an iterated Reduced-Order Unscented Kalman strategy, which we justify as an alternative to a Levenberg-Marquardt strategy for minimizing the non quadratic least-squares estimation criteria. Therefore, from a data assimilation perspective, we provide a quasi-sequential strategy that can valuably replace more classical variational approaches. Indeed, our resulting algorithm proves to be computationally very effective, allowing us to successfully apply our strategy to realistic 3D industrial SHM configurations.

This work is motivated by data assimilation for wildfire propagation, where the state and the observations of the system are naturally modeled in the manifold of contours. Typically, one can use an estimate-then-project method to address this problem. However, this is purely empirical and, in addition, an embedding in the Euclidean space need to be accessed, which is clearly artificial in the case of contours. Writing and solving the filtering problem directly on the manifold (without using the embedding in the ambient space) is a novel promising research direction, as some recent results in optimization and optimal control suggest. In this talk, using the example of a first-order dynamics on the two-sphere Riemannian manifold, we propose to develop a framework for computing optimal filters in a general manifold from the solution of a Hamilton-Jacobi-Bellman equation in the state space. We then reduce the cost of the resulting algorithm by using a quadratic approximation of the value function solution of the Hamilton-Jacobi-Bellman equation.

Parameter identification in Finite Element models is a key issue in many mechanical problems, when direct testing is not possible, e.g. in biomechanics to identify in vivo tissue properties. Many identification methods based on full-field displacement measurements have been developed, such as the Finite Element Model Updating (FEMU) method, the Equilibrium Gap Method (EGM) or the Virtual Fields Method (VFM). If the accuracy and efficiency of each method have already been investigated in the literature, there is no quantitative study to our knowledge relative to the impact of the noise and/or model errors on the efficiency of these methods. Studies available in the literature also focus on simple elastic problems, which does not allow a comprehensive understanding of the accuracy of the estimation of the different methods for more complex problems.
This article proposes a quantitative study of the impact of the noise and of model errors on the estimation of a parameter of a hyperelastic law when using the FEMU method, the EGM and the VFM. In particular, we compare here the accuracy of each method and their robustness to noise and model errors. The study is based on the creation synthetic images, from which a displacement field is extracted, and then used for the estimation. The estimated parameter is then compared to its ground truth value, which is here known. The method to introduce noise on the displacement field is also discussed: (i) by introducing noise directly on the displacement field and (ii) by introducing noise on the images. This article aims at providing information on the accuracy of each method for complex problems and help choose the best compromise between computational efficiency and accuracy for inverse problems.

A computer-implemented method of determining parameters includes a soft tissue stiffness field and a loading parameter applied to the soft tissue, in particular a pressure field, in which the values are determined from at least two images of this soft tissue oriented in at least two different respective positions relative to the vertical direction, making it possible to minimize a difference between the deformations of at least part of the soft tissue observed from the images and the corresponding deformations determined by a model of the soft tissue which depends on said parameters. This patent was submitted in June 2023.

In this work, we have studied the alterations of the mice skin mechanical properties linked to the role of PCPE-2. More precisely, BMP-1/tolloid-like proteinases (BTPs) are major players in tissue morphogen- esis, growth and repair. They act by promoting the deposition of structural extracellular matrix proteins and by controlling the activity of matricellular proteins and TGF-β superfamily growth factors. They have also been implicated in several pathological conditions such as fibrosis, cancer, metabolic disorders and bone diseases. Despite this broad range of pathophysiological functions, the putative existence of a specific endogenous inhibitor capable of controlling their activities could never be confirmed. Our study shows that procollagen C-proteinase enhancer-2 (PCPE-2), a protein previously reported to bind fibrillar collagens and to promote their BTP-dependent maturation, is primarily a potent and specific inhibitor of BTPs which can counteract their proteolytic activities through direct binding. PCPE-2 therefore differs from the cognate PCPE-1 protein and extends the possibilities to fine-tune BTP activities, both in physiological conditions and in therapeutic settings. This work has been published in 32.

Tissue engineering is a promising alternative to current full thickness circumferential esophageal replacement methods. The aim of our study was to develop a clinical grade Decellularized Human Esophagus (DHE) for future clinical applications. After decontamination, human esophagi from deceased donors were placed in a bioreactor and decellularized with sodium dodecyl sulfate (SDS) and ethylendiaminetetraacetic acid (EDTA) for 3 days. The esophagi were then rinsed in sterile water and SDS was eliminated by filtration on an activated charcoal cartridge for 3 days. DNA was removed by a 3-hour incubation with DNase. A cryopreservation protocol was evaluated at the end of the process to create a DHE cryobank. The decellularization was efficient as no cells and nuclei were observed in the DHE. Sterility of the esophagi was obtained at the end of the process. The general structure of the DHE was preserved according to immunohistochemical and scanning electron microscopy images. SDS was efficiently removed, confirmed by a colorimetric dosage, lack of cytotoxicity on Balb/3T3 cells and mesenchymal stromal cell long term culture. Furthermore, DHE did not induce lymphocyte proliferation in‑vitro. The cryopreservation protocol was safe and did not affect the tissue, preserving the biomechanical properties of the DHE. Our decellularization protocol allowed to develop the first clinical grade human decellularized and cryopreserved esophagus. This work has been published in 25.

Hypercoagulability is a pathology that remains difficult to explain today in most cases. It is likely due to a modification of the conditions of polymerization of the fibrin, the main clot component. Using passive microrheology, we measured the mechanical properties of clots and correlated them under the same conditions with structural information obtained with confocal microscopy. We tested our approach with known alterations: an excess of fibrinogen and of coagulation Factor VIII. We observed simultaneously a rigidification and densification of the fibrin network, showing the potential of microrheology for hypercoagulability diagnosis. This first work has been published in 33. It is now continued by Lionel Lartigue (post-doc), and Simon Kouba (PhD student).

Cornea is the outermost layer of the eye. Healthy human cornea is spherical-shaped. However, in patients with keratoconus, the cornea becomes thinner and gradually swells outward into an irregular cone shape. Stroma is the thickest layer of the cornea. It is formed of stacked lamellae made of collagen fibrils. The stroma is responsible for corneal biomechanical stability. Weakened biomechanical properties are believed to cause steepening and thinning in keratoconus eyes. We have recently published a review on the mechanical properties of the cornea 24, as well as a book chapter on the structure, the mechanics and the possible biomaterials associated with the cornea 39. Qian Wu (Ph.D) is now continuing this work, focussing on both the control of osmotic flows in the cornea, and on the role of Vogt's striae in the cornea mechanics. Benjmain Memmi (M.D) is working on the link between the errors in laser surgery and patient-specific mechanical properties.

Interstitial lung diseases, such as idiopathic pulmonary fibrosis (IPF) or post-COVID-19 pulmonary fibrosis, are progressive and severe diseases characterized by an irreversible scarring of interstitial tissues that affects lung function. Despite many efforts, these diseases remain poorly understood and poorly treated. In this paper, we propose an automated method for the estimation of personalized regional lung compliances based on a poromechanical model of the lung. The model is personalized by integrating routine clinical imaging data – namely, computed tomography images taken at two breathing levels in order to reproduce the breathing kinematic – notably through an inverse problem with fully personalized boundary conditions that is solved to estimate patient-specific regional lung compliances. A new parametrization of the inverse problem is introduced in this paper, based on the combined estimation of a personalized breathing pressure in addition to material parameters, improving the robustness and consistency of estimation results. The method is applied to three IPF patients and one post-COVID-19 patient. This personalized model could help better understand the role of mechanics in pulmonary remodeling due to fibrosis; moreover, patient-specific regional lung compliances could be used as an objective and quantitative biomarker for improved diagnosis and treatment follow up for various interstitial lung diseases. This work was published in 28.

A simple power law has been proposed in the pioneering work of Klotz et al. (Am J Physiol Heart Circ Physiol 291(1):H403-H412, 2006) to approximate the end-diastolic pressure-volume relationship of the left cardiac ventricle, with limited inter-individual variability provided the volume is adequately normalized. Nevertheless, we use here a biomechanical model to investigate the sources of the remaining data dispersion observed in the normalized space, and we show that variations of the parameters of the biomechanical model realistically account for a substantial part of this dispersion. We therefore propose an alternative law based on the biomechanical model that embeds some intrinsic physical parameters, which directly enables personalization capabilities, and paves the way for related estimation approaches. This work was published in 20.

Unstable hemodynamics during general anesthesia increases the risk of cardiac, renal and brain disfunctions during the postoperative period, thus leading to a higher level of morbidity and mortality. To improve the patient's condition, learned societies therefore recommend monitoring the hemodynamics of the patient and having treatment strategies with quantitative objectives based on this monitoring. Currently, medical doctors have at their disposal some physiological signals (ECG, blood pressure) displayed on their monitor, and must rely on established practices and their experience to act in case of a dangerous drift.

The AnaestAssist project proposes to develop an augmented monitoring tool for anesthesia. The proposed technology will introduce into the monitoring loop a predictive biophysical model, simulated in real time, and fed by the routinely measured physiological signals. The model will be personalized for the patient creating a digital twin of the patient's cardiovascular system. With this digital twin, physiological information that can cannot be measured or that can only be obtained with highly invasive methods will be computed in real time and treatment recommendations will be made. Our system will thus provide a much more complete vision of the patient's cardiovascular state and allow more informed and faster decisions. Eventually, the effects of drugs will be included in the model, which will make possible to determine (through predictive modelling) adapted action recommendations, or even a real-time automatic drug administration loop. Our technology is expected to allow the medical staff to deliver a better treatment to the patient, to improve the patient condition through a reduction of the risk related to general anesthesia and a wiser exposition to drugs, and to reduce the costs for the health care system due to a lower rate of complications and shorter stays of the patients at the hospital.

The AnaestAssist project is intended to lead to a startup creation.

The AnaestAssist team presented project for the national innovation competition iLab organised by Bpifrance. The project was selected for the oral hearings but did not win the competition.

The AnaestAssist contributed to set up the Diip-Heart projet led by the Inserm U942 MASCOT team in response to the call for proposal PEPR Santé numérique. The Diip-Heart project aims to set up elements of augmented monitoring in the perioperative period allowing to anticipate all serious cardiovascular events. The Diip-Heart proposal has been award a PEPR Santé numérique grant.

The AnaestAssist team also presented the MAJOR project in response to a call of AP-HP research and innovation department along with the anesthesia department of Lariboisière Hospital (AP-HP) and the Inria team COMMEDIA. The projet MAJOR aims to extend to AnaestAssist augmented monitoring tools to intensive care, which requires to incorporate the pulmonary system into the models. The evaluation phase of this call is ongoing.

The H

Lung function is a central concern in the fight against covid-19. Beyond the pandemic heavy losses and long-term health implications, respiratory diseases represent a major threat for the World Health Organisation. It is one of the leading causes of death worldwide, associated with our way of living and impacting all of society. In V|LF-Spiro3D, reference datasets are being acquired at standard MRI field to produce large sets of normative and training data covering six major respiratory diseases: asthma, chronic obstructive pulmonary diseases, bronchopulmonary dysplasia, cystic fibrosis, and bronchiolitis obliterans syndrome in transplant recipients. V|LF-Spiro3D will then redesign the current MRI architecture to perform 3D MR spirometry at low and very low field by highly-processed MRI throughout the lung while the patient is freely breathing, either lying, sitting, or standing in a light V|LF-MRI system. By prioritizing both technology transfer and innovation, V|LF-Spiro3D aims to build up a one-stop-shop imaging standard for the unrestricted assessment of lung pathophysiology.

Structural Health Monitoring (SHM) consists of integrating sensors into a high-stakes structure (aircraft, nuclear power plant, wind turbine, etc.) to monitor its state of health in real time and thus anticipate maintenance operations. The project entitled "SACHEMS" ("SAClay High-end Equipment for the Monitoring of Structures"), as it was funded in 2019 under the SESAME system of the Ile-de-France region, aims to create a federative platform for research and innovation for the SHM, allowing the development of complete SHM systems and to deploy them on the application cases provided by industrial end users. This platform brings together both academic teams and industrial end-users. It offers to the public laboratories involved the possibility of carrying out research in close collaboration with industrial partners.

ANR JCJC LungManyScale (383 k€)

The lungs’ architecture and function are well characterized; however, many fundamental questions remain (e.g., there is no quantitative link between tissue- and organ-level material responses), which represent real health challenges (e.g., Idiopathic Pulmonary Fibrosis is a poorly understood disease, for which a mechanical vicious cycle has been hypothesized, but not demonstrated). The general objective of this project is twofold: (i) scientifically, to better understand pulmonary mechanics, from the alveola to the organ in health and disease; (ii) clinically, to improve diagnosis and prognosis of patients through personalized computational modeling. More precisely, This project aims at developing a many-scale model of the pulmonary biomechanics, linked by computational nonlinear homogenization. The model will integrate the experimental and clinical data produced by partners, through an estimation pipeline that will represent augmented diagnosis and prognosis tools for the clinicians.

ANR ODISSE, (154 k€)

Motivated by some recent developments from two different fields of research, that is, observer design for finite-dimensional systems and inverse problems analysis for some PDE systems, the ODISSE project aims at developing rigorous methodological tools for the design of estimation algorithms for infinite-dimensional systems arising from hyperbolic PDE systems.

ANR SIMR (97 k€)

SIMR is a multi-disciplinary project seeking a better understanding of the biophysical mechanisms involved in mitral valve (MV) regurgitation diseases, to improve decision-making in patients by helping to determine the optimal timing for surgery. This project aims at facing this major issue with the following main two objectives: (1) Evaluate the biophysical consequences of MV repair and (2) Design numerical tools for cardiac hemodynamics, fluid-structure interaction and myocardium biomechanics to provide an in silico counterpart of the in vivo data obtained by tension measurement and imaging.

ANR AAP RA-COVID-19 SILICOVILUNG (55k€)
It is currently impossible to predict the evolution of severe COVID19-induced lung pathologies, in particular towards pulmonary fibrosis. A patient-specific model of lungs at 2-3 months after the acute stage will be used to seek mechanical indicators that may be valuable to predict the lung state after one year.

ANR Elastoheart (212k€)
The objective of this project is to develop a comprehensive mathematical and numerical modeling (direct and inverse) of 3D Shear-Wave (SW) propagation in cardiac realistic physiological models, and to demonstrate in vivo that shear velocity can assess important cardiac function and characteristics in experimental pathological models and in patients.

ANR CorMecha (191k€),

This project aims at: (i) setting up an atlas of cornea 3D structure from the sub-micrometer scale (intra-lamellar organization of collagen fibrils) to the millimeter-centimeter scale, (ii) accurately measuring the biomechanical properties linked to this structure in physiological conditions and in various pathological conditions, and (iii) building a model of corneal biomechanics based on these microstructural and macroscopic data in order to provide insight into the role of specific stromal structures. It relies on the highly original combination of well-controlled inflation device and state-of-the-art imaging setups, mainly polarization-resolved second harmonic generation microscope. Specific bioimage informatics tools and pipelines will be developed to process the very large data sets (Gb to Tb) generated by this new device and quantify clinically-relevant parameters of interest. Advanced statistical analysis of the series of clinical, structural and mechanical data obtained on the same cornea will then be performed for normal, keratoconic and photo-ablated corneas. The ultimate goals are twofold: (i) to translate the structural features observed with advanced research microscopes into easily-detectable features using commonly used techniques in clinical ophthalmology, in order to enable the diagnosis of structural defects related to defective mechanical properties; (ii) to develop a patient-specific simplified model to serve as a predictive tool by clinicians, mainly to improve refractive surgery procedures.

ANR MLQ-CT (140k€),

High-Resolution Computed Tomography (HRCT) scans have a pivotal role in revolutionizing pulmonary medicine, particularly in the classification of Interstitial Lung Diseases (ILDs). However, predicting the prognosis of fibrosing ILDs, such as Idiopathic Pulmonary Fibrosis (IPF), remains a challenge despite advancements in HRCT analysis. The project aims to develop qualitative and quantitative biomarkers from routine HRCT scans for fibrosing ILDs, focusing on those with a Progressive Pulmonary Fibrosis (PPF) phenotype. Two anti-fibrotic drugs, Pirfenidone and Nintedanib, show promise, but there is a lack of specific data on patient selection and timing of prescription. The research hypothesizes that real-time analysis of HRCT scans can yield significant candidate biomarkers for fibrosis progression. The objective is to advance existing software tools to a Technology Readiness Level 6, creating an implantable prototype for hospital use and testing it on ILDs patient data to identify potential biomarkers for PPF characterization.

ANR KAYO (200k€),

KAYO project aims to determine which hyper coagulability conditions can be detected through microrheoglogy measurements, and at which selectivity and sensitivity. The main underlying hypothesis is that hypercoagulability is associated with a change of the fibrin network, as it modifies the coagulation factors. Thus, the project will explore the impact of different known hypercoagulability conditions on the structure of the fibrin network (through confocal or SEM images) and on its microscopic rheological properties. Once the effects of known conditions will be determine, it will be tested on real blood samples.

AMIES Project WithCardiacModels, in partnership with Withings company (98k€)

Connected objects are now emerging as an effective tool for non-invasive monitoring of the general state of health day and night. In order to process the generated data streams, many signal processing and learning algorithms are required to reconstruct actionable outputs about the user's health. Many objects providing interesting cardiovascular information for the general public already exist on the market, such as the Withings Scanwatch, which measures an ECG and detects atrial fibrillation.

In this project, we propose to process the measurements collected by data assimilation approaches based on the modeling of the underlying biophysical processes. These models of the cardiovascular system and the real-time estimation methods developed by the M3DISIM team are ideally suited to the distal data on cardiovascular functioning collected by Withings. New algorithms for estimating the physiology of subjects respecting the constraints of optimal regularization of signals, detection of defects by searching for causality, privacy on shared data will make it possible tomorrow to detect deterioration in the cardiovascular health of heart failure patients, for example.

RheCa Labex (70k€),

RheCa project focusses on the multi-scale study of venous blood clots for the diagnosis of thrombosis. It aims at building an original device for the microrheological of blood clot, usable for clinical studies.