Continuum Model of Retinal Waves in Starburst Amacrine Cells
Benjamin Lansdell (Department of Applied Mathematics, University of Washington), J. Nathan Kutz (Department of Applied Mathematics, University of Washington)
We develop a continuous spatial and temporal model of these waves in order to understand how their structure depends on underlying parameters. We use a Fitzhugh-Nagumo model of neuron dynamics and, following the study by Ford et al. , include spatial coupling via the diffusion of neurotransmitter – here acetylcholine (Figure a). Our simplified model allows us to study retinal waves as a reaction-diffusion type system whose role in pattern formation in biological systems is well documented. Preliminary results show that our model is able to produce qualitatively the key features of recorded waves. Similar to  our model suggests that cell to cell variability is a necessary component of the system needed to generate realistic localised wave structures (Figure b).
Future work includes determining how the speed and size of waves depend on the model parameters -- afforded by the use of a reaction-diffusion type model -- and investigating the role noise plays in the wave structures formed. Retinal waves are one, well-studied, example of patterned spontaneous activity in the developing central nervous system therefore our efforts represent a novel approach to studying the self-organization of neural activity more generally.
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 Kevin J Ford, Aude L Felix, and Marla B Feller. Cellular mechanisms underlying spatio-temporal features of cholinergic retinal waves. Journal of neuroscience, 32(3):850–63, 2012. http://dx.doi.org/10.1523/JNEUROSCI.5309-12.2012