Fast and Efficient Formulations for Electroencephalography-Based Neuroimaging Strategies

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A Generic Coq Proof of Typical Worst-Case Analysis

International audienceThis paper presents a generic proof of Typical Worst-Case Analysis (TWCA), an analysis technique for weakly-hard real-time uniprocessor systems. TWCA was originally introduced for systems with fixed priority preemptive (FPP) schedulers and has since been extended to fixed-priority nonpreemptive (FPNP) and earliest-deadline-first (EDF) schedulers. Our generic analysis is based on an abstract model that characterizes the exact properties needed to make TWCA applicable to any system model. Our results are formalized and checked using the Coq proof assistant along with the Prosa schedulability analysis library. Our experience with formalizing real-time systems analyses shows that this is not only a way to increase confidence in our claimed results: The discipline required to obtain machine checked proofs helps understanding the exact assumptions required by a given analysis, its key intermediate steps and how this analysis can be generalized

A Hybrid Integral Equation Approach to Solve the Anisotropic Forward Problem in Electroencephalography

International audienceThe boundary element method provides a computa-tionally efficient solution to the Electroencephalography (EEG) forward problem on piece-wise homogeneous head models by using surface integral equations. However, realistic modeling of the head medium requires a proper account of the anisotropic electric nature of the human skull, which cannot be handled by standard surface integral equations. This work addresses this issue by presenting a new formulation which perturbs the standard Lippmann-Schwinger approach with volume elements within the skull. The resulting surface/volume integral equation can handle computations of fully realistic modeling for both skull and white matter. Numerical results will confirm the validity of the approach as well as its applicability to real case scenarios

Diffusion MRI Consistent Wire Models for Efficient Solutions of the Anisotropic Forward Problem in Electroencephalography

The surface Boundary Element Method (BEM) is one of the most commonly employed formulations to solve the forward problem in electroencephalography, but the applicability of its classical incarnations is lamentably limited to piece-wise homogeneous media. Several head tissues, however, are strongly anisotropic due to their complex underlying micro-structure. This implies that standard boundary integral formulations oversimplify the electrical properties of the head and produce unrealistic solutions, something that drastically limits the suitability and impact of BEM technologies to brain imaging. This contribution addresses this issue by observing that the brain anisotropy in the white matter is due to the presence of neuronal wire-like structures. We then extend the well known wire integral equations used for high frequency problems to the imperfectly conducting quasi-static case and we propose a new hybrid wire/surface/volume integral equation. When applied on multimodal magnetic resonance images combined with tractography, this new approach can flexibly and realistically handle the conductivity anisotropy in any head compartment providing high level of accuracy and efficiency. The beneficial properties of the new formulation together with its impact on brain imaging is demonstrated via numerical results on both canonical and realistic case scenarios

A Generic Coq Proof of Typical Worst-Case Analysis

International audienceThis paper presents a generic proof of Typical Worst-Case Analysis (TWCA), an analysis technique for weakly-hard real-time uniprocessor systems. TWCA was originally introduced for systems with fixed priority preemptive (FPP) schedulers and has since been extended to fixed-priority nonpreemptive (FPNP) and earliest-deadline-first (EDF) schedulers. Our generic analysis is based on an abstract model that characterizes the exact properties needed to make TWCA applicable to any system model. Our results are formalized and checked using the Coq proof assistant along with the Prosa schedulability analysis library. Our experience with formalizing real-time systems analyses shows that this is not only a way to increase confidence in our claimed results: The discipline required to obtain machine checked proofs helps understanding the exact assumptions required by a given analysis, its key intermediate steps and how this analysis can be generalized

A Hybrid Volume-Surface-Wire Integral Equation for the Anisotropic Forward Problem in Electroencephalography

International audienceSolving the electroencephalography (EEG) forward problem is a fundamental step in a wide range of applications including biomedical imaging techniques based on inverse source localization. State-of-the-art electromagnetic solvers resort to a computationally expensive volumetric discretization of the full head to account for its complex and heterogeneous electric profile. The more efficient, popular in biomedical imaging circles, but unfortunately oversimplifying Boundary Element Method (BEM) relies instead on a piecewise-uniform approximation that severely curbs its application in high resolution EEGs. This contribution lifts the standard BEM contraints by treating the local anisotropies with adequate wire and thin volume integral equations that are tailored to specific structures of the fibrous white matter and the inhomogeneous skull. The proposed hybrid integral equation formulation thereby avoids the full volumetric discretization of the head medium and allows for a realistic and efficient BEM-like solution of the anisotropic EEG forward problem. The accuracy and flexibility of the proposed formulation is demonstrated through numerical experiments involving both canonical and realistic MRI-based head models

Après la projection - Discussion autour du film "Incandescence des hyènes", de Nicolas Matos Ichaso: Cinéma du réel à la BULAC - édition 2021

Discussion avec le réalisateur Nicolas Matos Ichaso, Maxime Ruscio, chargé de l'audiovisuel et du multimédia à la BULAC, Alice Monin et Camille Salimon, étudiantes en master Cinéma et audiovisuel à l'université Sorbonne Nouvelle.Synopsis : En Éthiopie, les forgerons de Harar ont la réputation de se transformer en hyènes, pour rôder dans la vieille ville. Une plongée dans le travail des ferronniers éthiopiens, déclassés socialement, avec en toile de fond la beauté nocturne de Harar et sa passion pour le khât. La nuit, derrière la modification des corps au travail et la possible métamorphose des forgerons en hyènes, naît un basculement du réel.Nicolas Matos Ichaso est né en 1982. Il vit et travaille à Saint-Étienne. Après de nombreux voyages en Asie du Sud-Est et en Afrique, il s’oriente vers l’anthropologie visuelle en axant son travail notamment sur les forgerons en Éthiopie. En parallèle, il se forme aux métiers de la ferronnerie. Il intègre en 2016 l’École du Documentaire Ardèche Image à Lussas. Incandescence des hyènes est son premier film documentaire

On a Fast Solution Strategy for a Surface-Wire Integral Formulation of the Anisotropic Forward Problem in Electroencephalography

This work focuses on a quasi-linear-in-complexity strategy for a hybrid surface-wire integral equation solver for the electroencephalography forward problem. The scheme exploits a block diagonally dominant structure of the wire self block -- that models the neuronal fibers self interactions -- and of the surface self block -- modeling interface potentials. This structure leads to two Neumann iteration schemes further accelerated with adaptive integral methods. The resulting algorithm is linear up to logarithmic factors. Numerical results confirm the performance of the method in biomedically relevant scenarios