Mathematical modelling in the early visual system: Why and how?

An overview over the different approaches to mathematical modelling in neuroscience in general, with special emphasis on the early visual system, is presented. Questions such as``Why do we make mathematical models at all?'', ``What makes a mathematical model good?'', ``What types of mathematical models exist?'', and``What is the right level of detail in a model?'' are addressed. Results from a project on constructing mechanistic models of the spatial receptive-field organization of cells in the dorsal lateral geniculate nucleus (dLGN) are also presented. In contrast to the traditional descriptive modelling based on the difference-of-Gaussians model, our model takes the known physiological couplings between retina and dLGN and within dLGN into account. The advantage of this modelling approach is that in addition to providing mathematical descriptions of the receptive fields of dLGN neurons, it also make explicit the contributions from the geniculate circuit. Moreover, the model parameters have direct physiological relevance and can be manipulated and measured experimentally. The model is applied to experimental data on neural responses to spots of varying sizes for X dLGN cells and for their retinal input (S-potentials). The model is able to account for these results. Moreover, model predictions regarding receptive-field center sizes of interneurons, distances between neighboring retinal ganglion cells providing input to interneurons, and the amount of center-surround antagonism for interneurons compared to relay cells, are all compatible with data available in the literature.