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The first SC model presented by Rowland et al. is a single-neuron model in which sensory and cortical input is simply summed and passed through a sigmoid squashing function.

The sigmoid squashing function used in Rowland et al.'s first model leads to inverse effectiveness: The sum of weak inputs generally falls into the supra-linear part of the sigmoid and thus produces a superadditive response.

The temporal time course of neural integration in the SC reveals considerable non-linearity: early on, neurons seem to be super-additive before later settling into an additive or sub-additive mode of computation.

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.

The model due to Rowland and Stein manages to reproduce the nonlinear time course of neural responses to, and enhancement in magnitude and inverse effectiveness in multisensory integration in the SC.

Since the model does not include spatial properties, it does not reproduce the spatial principle (ie. no depression).

Rowland et al. derive a model of cortico-collicular multi-sensory integration from findings concerning the influence of deactivation or ablesion of cortical regions anterior ectosylvian cortex (AES) and rostral lateral suprasylvian cortex.

It is a single-neuron model.