Mathematical study of a neural gain control mechanism

This report presents a dynamical mechanism of gain control, inspired by a simple membranar model for neurons. Mathematical results are enounced for the system under sinusoidal stimulation. We thus prove that the system induces under-linearity with input ampitude, and time advance for high input amplitudes, which are the dual mark of contrast gain control in retinal neurons

The vertebrate retina: a functional review

In this report, we summarize the major properties of retinal filtering and organization, as understood by numerous experiments and models over the last decades. For this review, we take a functional approach, trying to answer this apparently simple question: What are the main characteristics of the retinal output in terms of signal processing, which should be retained in a functional model

Modèle et simulateur à grande échelle d'une rétine biologique, avec contrôle de gain

The retina is a complex neural structure. The characteristics of retinal processing are reviewed extensively in Part I of this work: It is a very ordered structure, which proceeds to band-pass spatio-temporal enhancements of the incoming light, along different parallel output pathways with distinct spatio-temporal properties. The spike trains emitted by the retina have a complex statistical structure, such that precise spike timings may play a role in the code conveyed by the retina. Several mechanisms of gain control provide a constant adaptation of the retina to luminosity and contrast. The retina model that we have defined and implemented in Part II can account for a good part of this complexity. It can model spatio-temporal band-pass behavior with adjustable filtering scales, with the inclusion of plausible mechanisms of contrast gain control and spike generation. The gain control mechanism proposed in the model provides a good fit to experimental data, and it can induce interesting effects of local renormalization in the output retinal image. Furthermore, a mathematical analysis confirms that the gain control behaves well under simple sinusoidal stimulation. Finally, the simulator /Virtual Retina/ implements the model on a large-scale, so that it can emulate up to around 100,000 cells with a processing speed of about 1/100 real time. It is ready for use in various applications, while including a number of advanced retinal functionalities which are too often overlooked.La rétine est une structure neuronale complexe, qui non seulement capte la lumière incidente au fond de l'oeil, mais procède également à des transformations importantes du signal lumineux. Dans la Partie I de ce travail, nous résumons en détail les caractéristiques fonctionnelles de la rétine des vertébrés: Il s'agit d'une structure très ordonnée, qui réalise un filtrage passe-bande du stimulus visuel, selon différents canaux parallèles d'information aux propriétés spatio-temporelles distinctes. Les trains de potentiels d'action émis par la rétine ont également une structure statistique complexe, susceptible de véhiculer une information importante. De nombreux mécanismes de contrôle de gain permettent une adaptation constante à la luminosité et au contraste. Le modèle de rétine défini et implémenté dans la Partie II de ce travail prend en compte une part importante de cette complexité. Il reproduit le comportement passe-bande, à l'aide de filtres linéaires spatio-temporels appropriés. Des mécanismes non-linéaires d'adaptation au contraste et de génération de potentiels d'action sont également inclus. Le mécanisme de contrôle du gain au contraste proposé permet une bonne reproduction des données expérimentales, et peut également véhiculer d'importants effets d'égalisation spatiale des contrastes en sortie de rétine. De plus, une analyse mathématique confirme que notre mécanisme a le comportement escompté en réponse à une stimulation sinusoïdale. Enfin, le simulateur /Virtual Retina/ implémente le modèle à grande échelle, permettant la simulation d'environ 100 000 cellules en un temps raisonnable (100 fois le temps réel)

Virtual Retina : a biological retina model and simulator, with contrast gain control

A detailed retina model is proposed, that transforms a video sequence into a set of spike trains, as those emitted by retinal ganglion cells. It includes a linear model of filtering in the Outer Plexiform Layer (OPL), a contrast gain control mechanism modeling the non-linear feedback of some amacrine cells on bipolar cells, and a spike generation process modeling ganglion cells. A strength of the model is that each of its features can be associated to a precise physiological signification and location. The resulting retina model can simulate physiological recordings on mammalian retinas, including such non-linearities as cat Y cells, or contrast gain control. Furthermore, the model has been implemented on a large-scale simulator that can emulate the spikes of up to 100,000 neurons

Retinal filtering and image reconstruction

In previous work, we have proposed a bio-plausible model of retinal processing, based on the physiological literature. A strong characteristic of this model was to reproduce the temporal delay of the surround component of filtering, as observed in real retinas. In this report, we study the possibilities of image reconstruction based on the response of such a model to the sudden appearance of a static image. In this report, we mostly focus on the first stage of the model, which performs \emph{linear spatio-temporal filtering} on the input image. We view this stage as a linear application from a 2D space (the image) to a 2D+T space (the temporal response of the retina), which bears an optimal inverse transformation in terms of robustness to noise: the pseudo-inverse of Moore-Penrose. We study the particular structure of this pseudo-inverse, due to the structure of retinal filtering with a delayed surround component. As a result, the pseudo-inverse-based image reconstruction reconstructs low spatial frequencies before high spatial frequencies. This property could have psychophysical correlates, for example during perception of very short image presentations

Retinal filtering and image reconstruction

In previous work, we have proposed a bio-plausible model of retinal processing, based on the physiological literature. A strong characteristic of this model was to reproduce the temporal delay of the surround component of filtering, as observed in real retinas. In this report, we study the possibilities of image reconstruction based on the response of such a model to the sudden appearance of a static image. In this report, we mostly focus on the first stage of the model, which performs \emph{linear spatio-temporal filtering} on the input image. We view this stage as a linear application from a 2D space (the image) to a 2D+T space (the temporal response of the retina), which bears an optimal inverse transformation in terms of robustness to noise: the pseudo-inverse of Moore-Penrose. We study the particular structure of this pseudo-inverse, due to the structure of retinal filtering with a delayed surround component. As a result, the pseudo-inverse-based image reconstruction reconstructs low spatial frequencies before high spatial frequencies. This property could have psychophysical correlates, for example during perception of very short image presentations

A Biologically-Inspired Model for a Spiking Retina

The purpose of this research is to provide potential neuroscientists and computer scientists with an artificial retina model, delivering spikes to higher-level visual tasks simulations. The architecture of our retina model is based on recent physiological studies, so that each feature is related to real retina characteristics. The model includes a linear filtering process, followed by a static non-linearity, and then a spike generation process. It thus simulates the output of the Parvocellular pathway of primate retinas, possibly for large-scale simulations. Two series of tests were performed: firstly on single cells for which ground truth is available, secondly on realistic visual scenes. The report sets the basis for further modeling. This includes nonlinear effects that could occur due to the conductance-based nature of synaptic interactions. Another future extension is modeling of the Magnocellular pathway of primate retinas. It is our conviction that building such a bio-inspired model will help in better understanding how the retina performs and also in relating observations to biological mechanisms

Early Deformation of Deep Brain Stimulation Electrodes Following Surgical Implantation: Intracranial, Brain, and Electrode Mechanics

IntroductionAlthough deep brain stimulation is nowadays performed worldwide, the biomechanical aspects of electrode implantation received little attention, mainly as physicians focused on the medical aspects, such as the optimal indication of the surgical procedure, the positive and adverse effects, and the long-term follow-up. We aimed to describe electrode deformations and brain shift immediately after implantation, as it may highlight our comprehension of intracranial and intracerebral mechanics.Materials and MethodsSixty electrodes of 30 patients suffering from severe symptoms of Parkinson’s disease and essential tremor were studied. They consisted of 30 non-directional electrodes and 30 directional electrodes, implanted 42 times in the subthalamus and 18 times in the ventrolateral thalamus. We computed the x (transversal), y (anteroposterior), z (depth), torsion, and curvature deformations, along the electrodes from the entrance point in the braincase. The electrodes were modelized from the immediate postoperative CT scan using automatic voxel thresholding segmentation, manual subtraction of artifacts, and automatic skeletonization. The deformation parameters were computed from the curve of electrodes using a third-order polynomial regression. We studied these deformations according to the type of electrodes, the clinical parameters, the surgical-related accuracy, the brain shift, the hemisphere and three tissue layers, the gyration layer, the white matter stem layer, and the deep brain layer (type I error set at 5%).ResultsWe found that the implanted first hemisphere coupled to the brain shift and the stiffness of the type of electrode impacted on the electrode deformations. The deformations were also different according to the tissue layers, to the electrode type, and to the first-hemisphere-brain-shift effect.ConclusionOur findings provide information on the intracranial and brain biomechanics and should help further developments on intracerebral electrode design and surgical issues