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The model due to Anastasio and Patton reproduces multi-sensory enhancement.

Deactivating modulatory, cortical input also deactivates multi-sensory enhancement.

Pavlou and Casey model the SC.

They use Hebbian, competitive learning to learn and topographic mapping between modalities.

They also simulate cortical input.

The leaky-integrate-and-fire model due to Rowland and Stein models a single multisensory SC neuron receiving input from a number of sensory, cortical, and sub-cortical sources.

Each of the sources is modeled as a single input to the SC neuron.

Local inhibitory interaction between neurons in multi-sensory trials is modeled by a single time-variant subtractive term which sets in shortly after the actual sensory input, thus not influencing the first phase of the response after stimulus onset.

Without an intact association cortex (or LIP), SC neurons cannot develop or maintain cross-modal integration.

(Neither multi-sensory enhancement nor depression.)