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

INTRODUCTION: Although 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 METHODS: Sixty 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%). RESULTS: We 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. CONCLUSION: Our findings provide information on the intracranial and brain biomechanics and should help further developments on intracerebral electrode design and surgical issues.

Ising distribution as a latent variable model.

During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary ("spin") variables with observed means and covariances. However, numerically speaking, the Ising distribution is unpractical, so alternative models are often preferred to handle correlated binary data. One popular alternative, especially in life sciences, is the Cox distribution (or the closely related dichotomized Gaussian distribution and log-normal Cox point process), where the spins are generated independently conditioned on the drawing of a latent variable with a multivariate normal distribution. This article explores the conditions for a principled replacement of the Ising distribution by a Cox distribution. It shows that the Ising distribution itself can be treated as a latent variable model, and it explores when this latent variable has a quasi-normal distribution. A variational approach to this question reveals a formal link with classic mean-field methods, especially Opper and Winther's adaptive TAP approximation. This link is confirmed by weak coupling (Plefka) expansions of the different approximations and then by numerical tests. Overall, this study suggests that an Ising distribution can be replaced by a Cox distribution in practical applications, precisely when its parameters lie in the "mean-field domain."

On the number of neurons and time scale of integration underlying the formation of percepts in the brain.

All of our perceptual experiences arise from the activity of neural populations. Here we study the formation of such percepts under the assumption that they emerge from a linear readout, i.e., a weighted sum of the neurons' firing rates. We show that this assumption constrains the trial-to-trial covariance structure of neural activities and animal behavior. The predicted covariance structure depends on the readout parameters, and in particular on the temporal integration window w and typical number of neurons K used in the formation of the percept. Using these predictions, we show how to infer the readout parameters from joint measurements of a subject's behavior and neural activities. We consider three such scenarios: (1) recordings from the complete neural population, (2) recordings of neuronal sub-ensembles whose size exceeds K, and (3) recordings of neuronal sub-ensembles that are smaller than K. Using theoretical arguments and artificially generated data, we show that the first two scenarios allow us to recover the typical spatial and temporal scales of the readout. In the third scenario, we show that the readout parameters can only be recovered by making additional assumptions about the structure of the full population activity. Our work provides the first thorough interpretation of (feed-forward) percept formation from a population of sensory neurons. We discuss applications to experimental recordings in classic sensory decision-making tasks, which will hopefully provide new insights into the nature of perceptual integration.

Population-wide distributions of neural activity during perceptual decision-making.

Cortical activity involves large populations of neurons, even when it is limited to functionally coherent areas. Electrophysiological recordings, on the other hand, involve comparatively small neural ensembles, even when modern-day techniques are used. Here we review results which have started to fill the gap between these two scales of inquiry, by shedding light on the statistical distributions of activity in large populations of cells. We put our main focus on data recorded in awake animals that perform simple decision-making tasks and consider statistical distributions of activity throughout cortex, across sensory, associative, and motor areas. We transversally review the complexity of these distributions, from distributions of firing rates and metrics of spike-train structure, through distributions of tuning to stimuli or actions and of choice signals, and finally the dynamical evolution of neural population activity and the distributions of (pairwise) neural interactions. This approach reveals shared patterns of statistical organization across cortex, including: (i) long-tailed distributions of activity, where quasi-silence seems to be the rule for a majority of neurons; that are barely distinguishable between spontaneous and active states; (ii) distributions of tuning parameters for sensory (and motor) variables, which show an extensive extrapolation and fragmentation of their representations in the periphery; and (iii) population-wide dynamics that reveal rotations of internal representations over time, whose traces can be found both in stimulus-driven and internally generated activity. We discuss how these insights are leading us away from the notion of discrete classes of cells, and are acting as powerful constraints on theories and models of cortical organization and population coding.

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

We propose a new retina simulation software, called Virtual Retina, which transforms a video into spike trains. Our goal is twofold: Allow large scale simulations (up to 100,000 neurons) in reasonable processing times and keep a strong biological plausibility, taking into account implementation constraints. The underlying model includes a linear model of filtering in the Outer Plexiform Layer, a shunting feedback at the level of bipolar cells accounting for rapid contrast gain control, and a spike generation process modeling ganglion cells. We prove the pertinence of our software by reproducing several experimental measurements from single ganglion cells such as cat X and Y cells. This software will be an evolutionary tool for neuroscientists that need realistic large-scale input spike trains in subsequent treatments, and for educational purposes.

Formal modeling with multistate neurones and multidimensional synapses.

Multistate neurones, a generalization of the popular McCulloch-Pitts binary neurones, are described; they are intended to model the fact that neurones may be in several different states of activity, while McCulloch-Pitts neurones model two states only: active or inactive. We show that as a consequence, multidimensional synapses are necessary to describe the dynamics of the model. As an illustration, we show how to derive the parameters of formal multistate neurones and their associated multidimensional synapses from simulations involving Hodgkin-Huxley neurones. Our approach opens the way to solve in a more biologically plausible way, two problems that were addressed previously: (1) the resolution of 'inverse problems', i.e. the construction of formal networks, whose dynamics follows a pre-defined spatio-temporal binary sequence, (2) the generation of spatio-temporal patterns that reproduce exactly the 'code' extracted from experimental recordings (olfactory codes at the glomerular level).