Questions on Reduced Wong Wang Model

[John Kochalka]

I am interested in the recent work by Deco et al (J Neuro 2013) and other related work (Nakagawa et al NeuroImage 2013) which use this model. Can anyone comment on the model as implemented in TVB in terms of the parameters w, J_11 (local excitatory recurrence and synaptic coupling) and G (global coupling) in the equation for x_i? Specifically, it appears that w and J_11 are left out of the TVB version entirely, and that the term G*J_N is represented by the value of 'a' in the TVB coupling function. Is this correct? Thanks for your help!

Cheers,

John

[Paula Sanz Leon]

Dear John

Apologies for the late reply. The model implemented in TVB was a

simple reduction of the original Wong and Wang model. This model has

recently been updated to match the equations as presented in Deco et

al., 2013 and will be included in the next release.  In this new

version 'w' and 'J_N' are included in the model and 'G' maps to the

value 'a' (for a linear long range coupling function)

In the following weeks we'll probably get an implementation written

by the authors, so we can verify that ours is indeed correct

Please notice that in TVB time delays are always included; in this

work they consider inter-regional connections as instantaneous (page

11249); additionally, their connectome represents 66 cortical regions and the

weights range between 0 and 1. So, with the default TVB connectivity matrix 

and the parameters values from the article you might not get the exact same results.

best

Paula

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[john.kochalka]

Hi Paula,

Thanks for the reply. In terms of implementation, is it as simple as adding w and J_N variables in models.py and updating the equations appropriately? Do we also need to take explicit steps to bound S on [0,1]? Are there other changes needed to accommodate the global coupling as well? I ask because I am fairly comfortable working with the python source and would like to move forward as quickly as I can. Thanks for your help.

Cheers,

John

[Michael WOODMAN]

"john.kochalka" <jkoc...@gmail.com> wrote:

Hi Paula,

Thanks for the reply. In terms of implementation, is it as simple as adding w and J_N variables in models.py and updating the equations appropriately? Do we also need to take explicit steps to bound S on [0,1]? Are there other changes needed to accommodate the global coupling as well? I ask because I am fairly comfortable working with the python source and would like to move forward as quickly as I can. Thanks for your help.

Not knowing this model in detail, I can't say in detail, but
 if you want to look for yourself about coupling, you can find
the main loop in simulator's __call__ method, where the
coupling is computed on past history, and passed through
the coupling function & integration scheme to the model's
dfun.

If this mechanism requires adjustment to encompass your
case, let us know :)

[Paula Sanz Leon]

Hi John,

Indeed, both 'w' and 'J_N' parameters should be included in the equations. The global coupling parameter 'G' , with the updated equations, should directly map to the parameter 'a' for a linear global coupling function and it's not included in the model's equations. Also, there's a parameter in this model: 'sigma_noise' which was included to document the default noise amplitude value used in (Deco, PonceAlvarez et al., 2013). It corresponds to the 'nsigma'  parameter when performing a simulation with a stochastic integration method. 

Comments & more feedback are most welcome.

best,

Paula

 

[john.kochalka]

Hi Paula,

Thanks for clarifying. One last thing I'm having trouble sorting out is the parameter gamma. From what I see, H(x) is in kHz (a quick dimensional analysis of the numerator a*x - b gives (pC)^-1*nA - kHz --> 10^12 (A*s)^-1 * 10-9 A - kHz --> 10^3 s^-1 - kHz --> kHz, and the denominator is dimensionless). Given that tau_s is in ms, all the terms in the dS/dt equation are already in units of (fraction of synapses)/ms, so we shouldn't need the factor of 1000^-1 that Deco, PonceAlvarez et al. 2013 use to express things in ms (their H(x) is in Hz). At any rate, I can't see where we would get 0.0641/1000 but perhaps I have gone astray somewhere. Please let me know what you think when you get a chance. 

Thanks,

John

[Paula Sanz Leon]

Hi John,

I'm finally back. 

0.0641 is a mistake. In both the original paper and the most recent one this value is 0.641

Thank you for pointing this out. 

In (Deco, PonceAlvarez et al, 2013) they actually use gamma=0.641 while expressing the temporal parameters in [s] and [Hz] and then they rescale the H(x) term of the equation by a factor of /1000 to express this in kHz. So, indeed this factor shouldn't be included since all the temporal parameters in the equation are already in [ms] and [kHz].

Also a = 270[nC]^-1 although in (Wong&Wong, 2006) you can find a=270 [V*nC]^-1, but it's a mistake because the numerator a*x - b couldn't be expressed in Hz or kHz. In Deco, PonceAlvarez et al, 2013) a = [n/C] but I guess that is a typo and the value is actually in [nC] or equivalently 0.270 [pC]^-1. 

best,

Paula

[Paula Sanz Leon]

In Deco, PonceAlvarez et al, 2013) a = [n/C] but I guess that is a typo and the value is actually in [nC] or equivalently 0.270 [pC]^-1. 

* I meant a = [n/C]-^1 --> therefore a is expressed in [nC]^-1

[Shruti Naik]

Hi Paula,
I am Master's student in computer science interested in bifurcation diagram generated by Deco et al.,2013. I am new to TVB as well as neural modeling. I am exploring latest version of TVB. I have a few questions:

1. To implement instantaneous connectivity as in the mentioned paper, can I ignore delays using connectivity.Connectivity.from_file("connectivity_998.zip").delays=zeros((998,998))  ??

2. I want to deal with mean firing rates. For that I am using monitors.Raw()  (which has direct access to variable S I suppose) and monitors.TemporalAverage().  Both are giving me same results. Should I simply take arithmetic mean of all the values to get firing rate for each area? 

3. Can you suggest a good material to clear my  doubts regarding different monitors (Specially, monitors.Raw(), monitors.TemporalAverage(),  monitors.SubSample() and monitors.SpatialAverage() ) implemented in TVB?

Thanks in advance,
Shruti

[Shruti Naik]

Also, regarding the noise parameter :
Can I access sigma_noise directly from the model as follows:

rww = models.ReducedWongWang(w=1.0, I_o=0.32, sigma_noise=0.006) ?

What effects will  nsig variable (corresponding to network noise) have on the firing rate? Is there anyway to remove this noise if I am already adding sigma_noise=X term in my model specification?

 ( nsig variable as in :
    integrator=integrators.HeunStochastic(dt=dt, noise=noise.Additive(nsig=array([D]))),  )

Thanks again,
Shruti

[marmaduke woodman]

On 7/11/2016 8:46 AM, Shruti Naik wrote:
> 1. To implement instantaneous connectivity as in the mentioned paper,

First create the object

conn = connectivity.Connectivity.from_file("connectivity_998.zip")

Then set its speed to infinity to force zero delays:

conn.speed = numpy.inf

Once your simulation is configured, you can check that all delays are
zeros,

assert (conn.delays == 0.0).all()

> 2. I want to deal with mean firing rates. For that I am using
> monitors.Raw() (which has direct access to variable S I suppose) and
> monitors.TemporalAverage(). Both are giving me same results. Should I
> simply take arithmetic mean of all the values to get firing rate for
> each area?

Both monitors result in an array of shape (n_time, 1, n_node, 1), which
you can reduce to a matrix to have time series of S(t) per region.

Note, though, that S(t) is the synaptic activation. The firing rate for
this model corresponds to the 'x' variable, so you need to apply the
transfer function as described in the paper.

[marmaduke woodman]

On 7/11/2016 9:01 AM, Shruti Naik wrote:
> Also, regarding the noise parameter :
> Can I access sigma_noise directly from the model as follows:
>
> rww = models.ReducedWongWang(w=1.0, I_o=0.32, sigma_noise=0.006) ?
>
> What effects will nsig variable (corresponding to network noise) have
> on the firing rate? Is there anyway to remove this noise if I am already
> adding sigma_noise=X term in my model specification?

The sigma_noise attribute on this model was an implementation bug on our
part and has no effect.

Please use only the nsig attribute of the network noise (properly, the
integrator's noise scheme).

[Shruti Naik]

Thanks so much Marmaduke,
Pretty much solves all doubts for me. I will try those things and get back in case of doubts.

[Shruti Naik]

Hello Marmaduke,
I was able to generate bistable behavior of the rWW model for my connectivity matrix with a few changes.
However, I am only simulating activity for  5000ms. Although for most initial values(coupling strengths), S seems to stabilize within 5000ms(conduction speed is inf) , in some cases, it converges very slowly to the fixed point (Figures attached). Can you comment on what should be the ideal length of simulation over which I can assess system behavior?

Thanks,
Shruti

On Monday, July 11, 2016 at 2:31:29 PM UTC+5:30, marmaduke.woodman wrote:

[WOODMAN Michael]

hi

5 s should be sufficient for this system. If you don't see fast convergence, it simply means some eigenvalues have a small real part. How you handle that is up to you.

You may want to determine when you stop the simulation by some criterion on the time series, instead of a fixed stopping time. You could for example, set simulation_length to very large number and during the integration loop measure the change in mean in subsequent windows and test whether it's changed.

Hope this helps,

Marmaduke

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From: tvb-...@googlegroups.com <tvb-...@googlegroups.com> on behalf of Shruti Naik <shrutin...@gmail.com>
Sent: Thursday, July 14, 2016 22:44
To: TVB Users
Subject: Re: [TVB] Re: Questions on Reduced Wong Wang Model

 

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[Shruti Naik]

Thank you Marmaduke,
It helped a lot. I can say I am now fairly comfortable with the TVB distribution package and would like to contribute to the project. What is the fastest way to start?

Thanks
Shruti

[Marmaduke Woodman]

Hi

Depends on what your interests are: what's your background and area of interest in contributing?

Cheers

Marmaduke 

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