A neural network model of multisensory integration also accounts for unisensory integration in superior colliculus

Abstract

Sensory integration is a characteristic feature of superior colliculus (SC) neurons. A recent neural network model of single-neuron integration derived a set of basic biological constraints sufficient to replicate a number of physiological findings pertaining to multisensory responses. The present study examined the accuracy of this model in predicting the responses of SC neurons to pairs of visual stimuli placed within their receptive fields. The accuracy of this model was compared to that of three other computational models (additive, averaging and maximum operator) previously used to fit these data. Each neuron's behavior was assessed by examining its mean responses to the component stimuli individually and together, and each model's performance was assessed to determine how close its prediction came to the actual mean response of each neuron and the magnitude of its predicted residual error. Predictions from the additive model significantly overshot the actual responses of SC neurons and predictions from the averaging model significantly undershot them. Only the predictions of the maximum operator and neural network model were not significantly different from the actual responses. However, the neural network model outperformed even the maximum operator model in predicting the responses of these neurons. The neural network model is derived from a larger model that also has substantial predictive power in multisensory integration, and provides a single computational vehicle for assessing the responses of SC neurons to different combinations of cross-modal and within-modal stimuli of different efficacies.

Figure 1. An illustration of the essential architecture of the neural network model

Stimulus information is conveyed to the SC through ascending and cortically-derived descending afferents. The inputs independently stimulated by two visual stimuli are depicted as separate channels. These inputs contact principal SC neurons (as illustrated in the schematic) and an interneuron population (I) which projects inhibitory (GABAergic) connections to the principal neuron. Inputs belonging to the same sensory channel do not preferentially cluster together on the principal neuron, thus establishing a balance of excitation and inhibition that predicts responses to two stimuli that are no greater than the response to a single stimulus.

Figure 2. Within-modal test: multisensory neuron

The visual (dark ovoid) receptive fields and the positions of the visual stimuli within the receptive fields are shown in the schematics of visual space (each circle = 10E) at the top of the figure. The visual stimuli were moving bars of light (arrow) as indicated by the electronic traces shown as ramps. Below the receptive fields and electronic stimulus traces, are shown the neuronal responses to these stimuli. These are displayed in rasters, histograms and summary bar graphs at three ascending levels of visual stimulus effectiveness. The within-modal tests in a multisensory neuron produced responses that were no different from that to the best unisensory component stimulus and the computational operation utilized was subadditive at all levels of stimulus effectiveness.

Figure 3. Within-modal test: unisensory neuron

Here are shown the results of within-modal tests in a unisensory visual neuron. The results are similar to those obtained in multisensory neurons. Essentially no response enhancement resulted from the addition of the second visual stimulus and responses to the stimulus combination were subadditive at all levels of stimulus effectiveness. Conventions are the same as in Figure 2.

Figure 4. Predicted responses according to the different models

The histograms show the predicted responses for each one of the model evaluated. In the neural network model (A) the predicted combined response will fall along a continuum determined by Equation 2. This equation predicts that the responses approximate those predicted by a maximum operator (described in D, below) when the effectiveness of the two visual stimuli is very far apart as illustrated in the plot on the left. However, it also predicts a mix of averaging (as shown in the plot on the right, and described in C, below) and maximum operator responses when the effectiveness of the two visual stimuli is closer together. In the additive model (B) the predicted combined response is similar to the sum of the responses evoked by the stimuli individually. In the averaging model (C) the predicted combined response is similar to the mean of the responses evoked by the stimuli individually. In the maximum operator model (D) the predicted combined response is similar to the strongest response evoked by either stimulus individually

Figure 5. Mean impulses of the actual and predicted responses

Shown here are population data consisting of the mean impulses number of the actual unisensory responses and those predicted by the 4 models evaluated. There were significant differences between the actual responses and those predicted by the additive and averaging models. The additive model overestimated the responses, the averaging model underestimated the responses, but no significant differences were found between the actual and predicted responses of the maximum operator and the neural network models. ** p < 0.01; * p < 0.05.

Figure 6. Unisensory responses are predicted better by the maximum operator and neural network models

The graphs show each neuron’s mean response to the stimulus combination plotted against the mean of its predicted responses by the additive (A), averaging (B), maximum operator (C) and neural network (D) models. In the additive model (A), the majority of the responses to the within-modal tests fell below the line of unity, reveal response overestimation. Conversely, in the averaging model (B), most of the combined unisensory responses fell above the line of unity, revealing response underestimation. In the maximum operator (C) and neural network (D) models, the predicted unisensory responses were clustered around the line of unity, revealing better prediction by these two models than the additive and averaging models. Insets: a blow-up of the first ten values of each plot.

Figure 7. Contrast index reveals the predictive accuracy of the neural network model

The graphs illustrate the distributions contrast index values for additive (A), averaging (B), maximum operator (C) and neural network (D) models. A: In the additive model the majority of the predicted responses yielded positive contrast values, indicating response overestimation. Although, values for average (B), maximum operator (C) and neural network (D) models yielded predications much closer to the actual combined responses, the neural network (D) model was the most accurate having a mean nearest to zero. The relative performance of the 4 models is compared directly in (E) by plotting the cumulative density functions for each model’s distribution on the same axes.