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Modelling of population of neurons 
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#1
Jun314, 08:12 PM

P: 6

I am a bit confused between single neuron models and population of neuron models. If we have single neuron models (Integrate and fire model etc) then why we want to develop models for population of neurons? Although single neuron models are ordinary differential equations (easy to analyze) and population models are complex partial differential equations difficult to analyze. What are the advantages of population of neuron models over single neuron models?



#2
Jun514, 07:55 AM

PF Gold
P: 4,287

Interactions that emerge from neuron networks are distinct from the dynamics of a single neuron. Determining brain function has a lot do with how the neurons are coupled together. Concepts like feedback and entrainment, the "bump" in bump attractor networks.



#3
Jun1214, 10:29 PM

P: 580

FROM SINGLE NEURONS TO BRAIN CHAOS You can find it on this website: http://sulcus.berkeley.edu/ Unfortunately, I can't provide a direct link, but the whole article is there, just scroll down and look for it. Once you click on the article, scroll down to figure 10. That will answer your question. The main difference between the single neuron model and the population model is that the population model posits a nonlinear gain function to drive information flow which takes the shape of a sigmoid curve, while the single neuron "integrate and fire" model is more linear. It's basically a summation of dendritic pulses that add at the axon hillock, or as Freeman calls it the trigger zone. It's all there in the article, though. Happy searching. 


#4
Jun1714, 12:40 AM

P: 6

Modelling of population of neurons
if you look at this article they modeled the population of neurons by developing a pde model:
A principled dimensionreduction method for the population density approach to modeling networks of neurons with synaptic dynamics. (http://www.ncbi.nlm.nih.gov/pubmed/23777517) and all the references in this article also modeled using pde. 


#5
Jun1714, 02:59 AM

P: 580

First of all, thanks for the thanks, uetmathematics. I'm trying to catch up to WannabeNewton, but have a ways to go.
Plus, you have several nested layers of gradiently distributed feedback from progressively removed cortical regions. These regions disrupt the periodic oscillations in the target cortex which lead to aperiodicity, more specifically they show up as chaotic attractors on phase portraits which themselves oscillate between more chaotic forms and near limit cycle attractors. Interestingly, it kind of works like a Carnot cycle. Check out this article: http://www.ncbi.nlm.nih.gov/pubmed/?term=freeman+carnot Getting back to your original question, though, it doesn't add anything to try to model these networks as PDE's. It's enough of a pain that the equations are nonlinear, but thankfully we have Matlab and RungeKutta to help us out with that. You might also want to check out this article:http://www.ncbi.nlm.nih.gov/pubmed/19395236 


#6
Jun1714, 06:44 AM

Sci Advisor
P: 8,658

uetmathematics is correct that some model networks of neurons have collective behaviours that can be described by partial diferential equations. Here are some examples in addition to the reference he provided.
http://www.math.pitt.edu/~bard/pubs/nnetrev.pdf Neural networks as spatiotemporal patternforming systems Reports on Progress in Physics, 61:353430, 1998 Ermentrout B http://galton.uchicago.edu/~nbrunel/...unel00JCNS.pdf http://www.ncbi.nlm.nih.gov/pubmed/10809012 J Comput Neurosci. 2000 MayJun;8(3):183208. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Brunel N. http://www.ploscompbiol.org/article/...l.pcbi.1002872 http://www.ncbi.nlm.nih.gov/pubmed/23359258 PLoS Comput Biol. 2013;9(1):e1002872. doi: 10.1371/journal.pcbi.1002872. Epub 2013 Jan 24. Dynamic finite size effects in spiking neural networks. Buice MA, Chow CC 


#7
Jun1714, 02:55 PM

P: 580




#8
Jun1714, 03:02 PM

Sci Advisor
P: 8,658




#9
Jun1714, 04:33 PM

P: 580

In that spirit, I will give you something specific to read and comment on. Not only that, there's some source code you can play around with. Scroll down to section 3.2., entitled "ODE based approach to neural populations." http://www.sciencedirect.com/science...93608009000434 This model is also a DARPA funded project designed to work towards the creation of autonomous rovers:http://wwwrobotics.jpl.nasa.gov/pub...kAdvRob2.pdf If you want to challenge that model, then do so. Otherwise, I don't know what your point is? 


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