Simulating Waves of Activity across Grids of Neurons

BACKGROUND:

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When building mathematical models of brain tissue, there are a few choices we have to make.  How many neurons do we want to consider, and in how much detail do we want to consider each neuron?  Do we want to consider individual neurons at all, or do we want to take averages across many? And how do we connect them together?

 

My research focuses on modelling large grids of individual neurons to observe behaviour that only appears at larger scales, but nonetheless requires the individual dynamics often left out of population models.  The simplest of these are travelling waves of firing events — which are more like the Mexican wave of a football stand than a light or sound wave.  A neuron can’t fire twice as hard, and a fan can’t stand up twice as tall, so rather than overlapping with additive interference we see other effects where waves can bounce off, block, or obliterate each other.

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RESULTS:

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Coming from a pure maths background, I’ve found it interesting to not only learn the biological facts of the field, but also the applied techniques, and the use of simulations to guide analysis and explore new behaviour.  There are far too many possible configurations to study everything, so I have to build a sense of what is representative, what is tractable, and what is interesting.

 

Alas, while I can simulate many pretty patterns, at this moment I can only explain the boring ones.  Lots of straight lines and linear relations. I was actually surprised by how readily some of these long-winded equations spit out a straight line.

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FUTURE WORK:

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Of course, the “boring” cases act at the foundation for studying more varied behaviours.  I hope I’ll soon be able to demonstrate the underlying behaviours for some more elegant patterns soon.  I’ve also got some work to do on documenting and publishing my code, given its importance for review and replication.

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FUNDED BY:

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CONTACT:

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