Source localization using rational approximation on plane sections

N° RR-7704 http://hal.inria.fr/inria-00613644International audienceIn functional neuroimaging, a crucial problem is to localize active sources within the brain non-invasively, from knowledge of electromagnetic measurements outside the head. Identification of point sources from boundary measurements is an ill-posed inverse problem. In the case of electroencephalography (EEG), measurements are only available at electrode positions, the number of sources is not known in advance and the medium within the head is inhomogeneous. This paper presents a new method for EEG source localization, based on rational approximation techniques in the complex plane. The method is used in the context of a nested sphere head model, in combination with a cortical mapping procedure. Results on simulated data prove the applicability of the method in the context of realistic measurement configurations

Localization of Point Sources for Systems Governed by the Wave Equation

Analytic sensing has recently been proposed for source localization from boundary measurements using a generalization of the finite-rate-of-innovation framework. The method is tailored to the quasi-static electromagnetic approximation, which is commonly used in electroencephalography. In this work, we extend analytic sensing for physical systems that are governed by the wave equation; i.e., the sources emit signals that travel as waves through the volume and that are measured at the boundary over time. This source localization problem is highly ill-posed (i.e., the unicity of the source distribution is not guaranteed) and additional assumptions about the sources are needed. We assume that the sources can be described with finite number of parameters, particularly, we consider point sources that are characterized by their position and strength. This assumption makes the solution unique and turns the problem into parametric estimation. Following the framework of analytic sensing, we propose a two-step method. In the first step, we extend the reciprocity gap functional concept to wave-equation based test functions; i.e., well-chosen test functions can relate the boundary measurements to generalized measure that contain volumetric information about the sources within the domain. In the second step-again due to the choice of the test functions-we can apply the finite-rate-of-innovation principle; i.e., the generalized samples can be annihilated by a known filter, thus turning the non-linear source localization problem into an equivalent root-finding one. We demonstrate the feasibility of our technique for a 3-D spherical geometry. The performance of the reconstruction algorithm is evaluated in the presence of noise and compared with the theoretical limit given by Cramer-Rao lower bounds

Simulated electroencephalography (EEG) source localization using integrated meromorphic approximation

Epilepsy is a chronic brain dysfunction in which neurons and neuronal network malfunction cause symptoms of a seizure. A seizure is an abnormal electrical discharge from the brain appearing at a small area of the brain. The seizure affected zone loses its normal task abilities and might react uncontrollably. Electroencephalography (EEG) is one of the useful instruments in diagnosing many brain disorders like epilepsy. This non-invasive modality is used to localize brain regions involved during the generation of epileptic discharges. At present, many quantitative methods for identifying and localizing the epileptogenic focus from EEG have been invented by scientists around the world. Under quasi-static assumptions, Maxwell’s equations governing the spatial behaviour of the electromagnetic fields lead to Partial Differential Equations (PDE) of elliptic type in domains of R3. This thesis presents a new method based on integrated new EEG source detection, Cortical Brain Scanning (CBS) with meromorphic approximation to identify the sources on the brain scalp, which have highly abnormal activities when a patient is having a seizure attack. Boundary measurements for meromorphic approximation method are considered as isotropic and homogeneous in each layer (brain, skull, and scalp). The proposed method is applied on simulated and published EEG data obtained from epileptic patients. The method can enhance the localizations of sources in comparison to other methods, such as Low Resolution Brain Electromagnetic Tomography (LORETA), Minimum Norm Estimation (MNE), and Weight Minimum Norm Estimate (WMNE), coupled with meromorphic approximation. Standard validation metrics including Root Sum Square (RSS), Mean Square Error (MSE), and Receiver Operating Characteristic Curve (ROC) are used to verify the result. The proposed method produces promising results in enhancing the source of localization accuracy of epileptic foci

Roadmap on signal processing for next generation measurement systems

Signal processing is a fundamental component of almost any sensor-enabled system, with a wide range of applications across different scientific disciplines. Time series data, images, and video sequences comprise representative forms of signals that can be enhanced and analysed for information extraction and quantification. The recent advances in artificial intelligence and machine learning are shifting the research attention towards intelligent, data-driven, signal processing. This roadmap presents a critical overview of the state-of-the-art methods and applications aiming to highlight future challenges and research opportunities towards next generation measurement systems. It covers a broad spectrum of topics ranging from basic to industrial research, organized in concise thematic sections that reflect the trends and the impacts of current and future developments per research field. Furthermore, it offers guidance to researchers and funding agencies in identifying new prospects.AerodynamicsMicrowave Sensing, Signals & System

Identifiability Properties for Inverse Problems in EEG Data Processing and Medical Engineering with Observability and Optimization Issues

International audienceWe consider inverse problems of source identification in electroen-cephalography, modelled by elliptic partial differential equations. Being given boundary data that consist in values of the current flux and of the electric poten-tial on the scalp, the aim is to reconstruct unknown current sources supported within the brain. For spherical layered models of the head, and after a pre-liminary data transmission step, such inverse source problems are tackled using best rational approximation techniques on planar sections. Both theoretical and constructive aspects are described, while numerical illustrations are provided

Building And Validating Next-Generation Neurodevices Using Novel Materials, Fabrication, And Analytic Strategies

Technologies that enable scientists to record and modulate neural activity across spatial scales are advancing the way that neurological disorders are diagnosed and treated, and fueling breakthroughs in our fundamental understanding of brain function. Despite the rapid pace of technology development, significant challenges remain in realizing safe, stable, and functional interfaces between manmade electronics and soft biological tissues. Additionally, technologies that employ multimodal methods to interrogate brain function across temporal and spatial scales, from single cells to large networks, offer insights beyond what is possible with electrical monitoring alone. However, the tools and methodologies to enable these studies are still in their infancy. Recently, carbon nanomaterials have shown great promise to improve performance and multimodal capabilities of bioelectronic interfaces through their unique optical and electronic properties, flexibility, biocompatibility, and nanoscale topology. Unfortunately, their translation beyond the lab has lagged due to a lack of scalable assembly methods for incorporating such nanomaterials into functional devices. In this thesis, I leverage carbon nanomaterials to address several key limitations in the field of bioelectronic interfaces and establish scalable fabrication methods to enable their translation beyond the lab. First, I demonstrate the value of transparent, flexible electronics by analyzing simultaneous optical and electrical recordings of brain activity at the microscale using custom-fabricated graphene electronics. Second, I leverage a recently discovered 2D nanomaterial, Ti3C2 MXene, to improve the capabilities and performance of neural microelectronic devices. Third, I fabricate and validate human-scale Ti3C2 MXene epidermal electrode arrays in clinical applications. Leveraging the unique solution-processability of Ti3C2 MXene, I establish novel fabrication methods for both high-resolution microelectrode arrays and macroscale epidermal electrode arrays that are scalable and sufficiently cost-effective to allow translation of MXene bioelectronics beyond the lab and into clinical use. Thetechnologies and methodologies developed in this thesis advance bioelectronic technology for both research and clinical applications, with the goal of improving patient quality of life and illuminating complex brain dynamics across spatial scales

Construction of boundary element models in bioelectromagnetism

Multisensor electro- and magnetoencephalographic (EEG and MEG) as well as electro- and magnetocardiographic (ECG and MCG) recordings have been proved useful in noninvasively extracting information on bioelectric excitation. The anatomy of the patient needs to be taken into account, when excitation sites are localized by solving the inverse problem. In this work, a methodology has been developed to construct patient specific boundary element models for bioelectromagnetic inverse problems from magnetic resonance (MR) data volumes as well as from two orthogonal X-ray projections. The process consists of three main steps: reconstruction of 3-D geometry, triangulation of reconstructed geometry, and registration of the model with a bioelectromagnetic measurement system. The 3-D geometry is reconstructed from MR data by matching a 3-D deformable boundary element template to images. The deformation is accomplished as an energy minimization process consisting of image and model based terms. The robustness of the matching is improved by multi-resolution and global-to-local approaches as well as using oriented distance maps. A boundary element template is also used when 3-D geometry is reconstructed from X-ray projections. The deformation is first accomplished in 2-D for the contours of simulated, built from the template, and real X-ray projections. The produced 2-D vector field is back-projected and interpolated on the 3-D template surface. A marching cube triangulation is computed for the reconstructed 3-D geometry. Thereafter, a non-iterative mesh-simplification method is applied. The method is based on the Voronoi-Delaunay duality on a 3-D surface with discrete distance measures. Finally, the triangulated surfaces are registered with a bioelectromagnetic measurement utilizing markers. More than fifty boundary element models have been successfully constructed from MR images using the methods developed in this work. A simulation demonstrated the feasibility of X-ray reconstruction; some practical problems of X-ray imaging need to be solved to begin tests with real data.reviewe

Clinical applications of magnetic resonance imaging based functional and structural connectivity

Advances in computational neuroimaging techniques have expanded the armamentarium of imaging tools available for clinical applications in clinical neuroscience. Non-invasive, in vivo brain MRI structural and functional network mapping has been used to identify therapeutic targets, define eloquent brain regions to preserve, and gain insight into pathological processes and treatments as well as prognostic biomarkers. These tools have the real potential to inform patient-specific treatment strategies. Nevertheless, a realistic appraisal of clinical utility is needed that balances the growing excitement and interest in the field with important limitations associated with these techniques. Quality of the raw data, minutiae of the processing methodology, and the statistical models applied can all impact on the results and their interpretation. A lack of standardization in data acquisition and processing has also resulted in issues with reproducibility. This limitation has had a direct impact on the reliability of these tools and ultimately, confidence in their clinical use. Advances in MRI technology and computational power as well as automation and standardization of processing methods, including machine learning approaches, may help address some of these issues and make these tools more reliable in clinical use. In this review, we will highlight the current clinical uses of MRI connectomics in the diagnosis and treatment of neurological disorders; balancing emerging applications and technologies with limitations of connectivity analytic approaches to present an encompassing and appropriate perspective