Computational protocol: A Neural Field Model of the Somatosensory Cortex: Formation, Maintenance and Reorganization of Ordered Topographic Maps

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Protocol publication

[…] The set of stimuli that is used during training is initially generated by equation (4) over a subset of the skin patch . Stimuli locations are set on a regular grid (see ) in order to ensure proper coverage of the patch. During training, a stimulus is uniformly drawn from within this training set. Unless stated otherwise, the same stimuli set is used for all simulations. The neural field has been discretized into spatial elements and the integration of equation (2) is performed using the forward Euler’s method (time step is given in ). Feed-forward weights are randomly initialized in the range . During all simulations we used epochs. In each epoch, the stimulus is presented to the model and the field is integrated over a fixed time window while the learning rule is applied to the feed-forward weights. Spatial convolution in equations (2) and (7) is calculated using a fast Fourier transform (FFT) in order to accelerate this operation. Then the activity of the field is reset to zero. This represents the removal of pressure from the skin patch (we could wait for the field to go back to the steady state but it is numerically faster to reset it). The feed-forward weights average evolution of a neuron was measured by using the following equation:(8)where represents the expected value (i.e. the mean value of the array) and represents the absolute value. Lesions of type I, II and III (skin or cortex) have been implemented using three masks displayed in . For skin lesion, input was nullified at lesion sites before being transmitted to the neural field while for cortical lesions, lesioned units were nullified at each time step.The receptive field of each neuron has been computed from a set of ( in this work) regularly distributed stimulus over the subset that have been presented sequentially to the model. Each individual neuron activity has been recorded and aggregated into a matrix of activities. The size of the receptive field has been identified with the normalized sum of non null values while the center has been computed as the center of mass of the receptive field given by the following equation:(9)where denotes the respective position of stimuli used to compute RF and is the activity at position . Using self-organization information from the intact model, we translated those centers into the skin reference such that topographical information corresponds, this eases the lecture of the figure without changing the results.Simulations were performed on a HP Z800 Workstation. The source code of all simulations is written in Python (Numpy, Scipy and Matplotlib) and it is available on-line at http://www.loria.fr/~rougier/coding/software/DNF-SOM.tgz. During a simulation of training epochs (sweeps), simulation program consumes ∼190 MB of physical memory and requires ∼13 minutes of CPU time until reaching final epoch. […]

Pipeline specifications

Software tools Numpy, SciPy, matplotlib
Applications Miscellaneous, WGS analysis
Diseases Brain Diseases, Kidney Failure, Chronic, Skin Diseases