Linear and nonlinear processing of spatial form in primary somatosensory cortex of the monkey

Processing of fine spatial form in primary somatosensory cortex was investigated in the awake behaving monkey. The stimuli consisted of embossed, letters (Helvetica, 8mm high) applied to the distal finger pad while single unit neural responses were recorded from peripheral SAI afferents or cortical neurons in area 3b. The evoked action potential stream from each neuron was converted to an estimate of the mean firing rate using standard histogram techniques. Theoretical derivation of the mean squared error (MSE) between the "true" firing rate estimated by the histogram and the histogram itself produced a formulation of the expected error. The expected error is expressed as the normalized mean square error (NMSE), which is the MSE divided by the mean square value of the "true" rate function. The average NMSE for 114 cortical responses is calculated to be 0.8, which is unacceptably large. An alternative rate estimator (the Adaptive Parzen Window - APW) was derived which produced an average NMSE of 0.24.;The neuronal rate estimates were used to study the cortical processing of spatial form in area 3b using linear and non-linear neural network models. The network models were designed to mimic the functional convergence of activity from the population of SAI afferents on the finger to single cortical neurons. The network input is an array of receptors analogous to the SAI afferents and the output is a single node analogous to a cortical neuron. Networks were trained to minimize the error between their output and the cortical data using a least squares gradient descent technique. Results indicate that the average amount of the cortical response (cortical response variance explained by the model) that is a linear function of the peripheral inputs is approximately 58%, and that an additional 16% of the cortical response variance is explained by non-linear functions of the peripheral inputs. Receptive fields derived from network models of cortical responses that are well-modeled as linear functions of the inputs are composed of simple structured regions of excitation and inhibition, while receptive fields of responses that are primarily non-linear are significantly more complex in structure.