phi_n_scaling = (jrm.a * jrm.A * (jrm.p_max-jrm.p_min) * 0.5 )**2 / 2. sigma = numpy.zeros(6) sigma[3] = phi_n_scaling
Hi
From the perspective of a neural mass model (especially early papers such as Jansen-Rit), network afferents, noise and stimulus casn often be written as a single “input” term, yet in a modeling project it is interesting to distinguish different mechanisms
The TVB software reflects this set of theoretical distinctions, even if you can in practice ignore them for some purposes.
Scaling noise by sqrt(dt) is a basic element of SDE theory, please see for example the attached intro.
Cheers,
Marmaduke Woodman IR AMU INS U1106 +33 7 67 77 84 72
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hi
I deliberately did not respond in the hopes that someone more knowledgable in Jansen-Rit model would reply...
I can speculate that while a stimulation on those pair of variables may be harder to observe, the stimulation would certainly create a perturbation in state space and therefore exert some influence. If you aren't currently observing any effect of the stimulus, it may be worth plotting phase planes of the JR state variables to see what's happening (and refer to the original equations to check magnitidues etc).
cheers,
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hi
There are several results in that paper, which are you trying to reproduce?
cheers,
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Hi
Reading through the paper, the TVB implementation of the single column model is correct, but implementing the two-column case is not easy, because they have added a PSP blocks for the connections between the columns. In other words, while a single column required 6 ODEs, the two columsn require 2*6 + 2*2 = 16 ODEs. The straightforward adaptation to TVB would add 2 ODEs per node for the afferent PSP, no longer requiring a difference in the coupling function, and a stochastic integartor should be usable for the noise.
This appears to be done in the contributed Jansen-Rit implementation for the David 2005 paper,
but it should be checked again for correctness as it uses another naming scheme so code isn't comparable.
cheers,
Marmaduke
hi
I've put together the following script,
https://gist.github.com/maedoc/d6780270b47f956c541eef5ed85e8194
which runs a two column simulation with equations as in the paper, by adding an PSP to each node and using its output as the coupling variable. This is scaled by the connectivity (K1 and K2 here) and then used as input to the JR equation 6. Furthermore
the noise is factored out of the y4 equation by replacing with a mean (mu=0.22) and adding small white noise.
The single column results Fig 3 can be reproduced by changed J (what JR calls C) in the script on line 15, whereas k1 and k2 are below that. I suspect there's a scaling issue since using k1 & k2 values from the paper don't allow for reproducing all the
results shown, but it could be a useful starting point.
cheers,
Marmaduke
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Hi
It was just a quick guess that the noise could be pulled out of the RHS of the ODE and applied as a more standard SDE. After some experimenting, I don't think it works quite well, and I also just did what JR describe by setting all nsig to 0.0 and putting
In any case, I'd be happy to see any corrections about the noise term.
cheers,
Hi Rachel
(1) Indeed the papers use p(t) as the input, and this is accomodated in TVB. What TVB doesn't work so well for is noise terms which are embedded in the RHS equations of the model. For JR it's
y4' = A a (p(t) + ....)
and the A*a*p(t) can perhaps be factored out and used to scale the noise (with a Gaussian approximation of the uniformly distributed noise) for a proper SDE integration scheme such as HeunStochastic. This is what is happening in the tutorial, though I think it should be assigned to sigma[4] not sigma[3], since the JR paper counts from y0, not y1.
> What is the idea behind scaling noise with sqrt(dt)?
The noise scales with sqrt(dt) because the equivalent Brownian process' variances increases with the sqrt of time. Since we are increasing time by dt at each step, the variance is scaled by sqrt(dt).
> How is that related to the noise input p(t)?
we prefer to formulate the JR equations as SDE since that is what TVB expects, which is why we are trying to find appropriate scaling factors to translate p(t) noise to a normal SDE
> 2. If I use stimulus as p(t) and use deterministic integrator. With a much larger variance, I can get similar behavior as point 1.
Because the stimulus is expressed along side the RHS of the ODEs for the neural mass, the integrator scales it by dt as well. This means that if you just trying to inject noise, you need to increase the noise amplitude by dt to achieve the same effect as
using stochastic integrator.
Cheers,
Marmaduke
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hi
The sigmoidal is part of the PSP block, so it makes sense
I didn't implement that component and not aware of any particular paper to be honest. Still, it would be useful if you wanted an instantaneous coupling instead of through 2 ODEs. I think the JR paper is a challenge to implement with TVB additionally because the connectivity weights K1 and K2 are applied after the PSP blocks, so generalizing to larger networks leaves several choices to the modeler.
cheers,
Marmaduke
hi Rachel
Thanks this is a helpful way of explaining the difference between what the paper does and what TVB does by default. I think the original set up can be replicated in TVB but requires a uniform noise source & factoring the noise out of the ODEs, which I didn't have time to do before. In any case this should all be enough for someone else to pick it up if desired.
cheers,
Marmaduke Woodman,
TVB Engineer, INS AMU; +33 7 67 77 84 72