Coupling function in the Larter-Breakspear model

[Gianluca Gag]

Dear TVB community,

I am currently using the Larter-Breakspear model and have a question regarding its implementation in TVB. This model utilizes a hyperbolic tangent coupling function, as described in equation 4.14 in [Sanz-Leon, P., Knock, S. A., Spiegler, A., & Jirsa, V. K. (2015). Mathematical framework for large-scale brain network modeling in The Virtual Brain]. According to this equation, multiplying the structural connectivity (SC) weight matrix by a factor (global coupling constant, G) should have no effect on the simulations (given the term 1/∑ukj ). However, my observations do not align with this, as I am obtaining different results when I multiply the weight matrix by G.

Could you kindly clarify how the hyperbolic tangent coupling function is actually implemented in TVB? (maybe the factor 1/∑ukj  in eq. 4.14 might not be used).

Thank you in advance.

Best regards,
Gianluca

[Julie Courtiol]



Dear Gianluca,

In Eq. 4.14, the coupling function does not depend on the SC weights because of the annulation of the weight terms. Therefore, only the summation of the remote nodes’ activity is computed.

For this reason, when varying the coupling strength, you should obtain different simulation results.

Did I answer you question?

Best,

Julie

Best regards,

Dr. Julie Courtiol

Scientific Lab Manager, Brain Simulation Section

Charité - Universitätsmedizin Berlin

Berlin Institut of Health

Brain Simulation

Robert-Kosh-Platz 4

Charitéplatz 1 | 10117 Berlin | Germany

courtio...@gmail.com - www.brainsimulation.org

Twitter: @Courtioljulie

LinkedIn: juliecourtiol

Le 25 juil. 2023 à 11:33, Gianluca Gag <gaglioti...@gmail.com> a écrit :

Dear TVB community,

--
You received this message because you are subscribed to the Google Groups "TVB Users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to tvb-users+...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/tvb-users/a0b41dad-3206-4595-9892-04cff8e6c9c6n%40googlegroups.com.

[Gianluca Gag]

Dear Julie,
Thank you very much for your reply. Unfortunately, perhaps I couldn't understand it fully, and I still have some doubts:

> In Eq. 4.14, the coupling function does not depend on the SC weights because of the annulation of the weight terms.

Ok, according to eq. 4.14 this is what I understand (multiplicative factors cancel out as they are at numerator and denominator)

> Therefore, only the summation of the remote nodes’ activity is computed.

Isn't that in contradiction with your reply? Why should only the remote nodes be relevant here? (What do you mean by summation of remote nodes' activity?)

Thank you again,

Gianluca

To view this discussion on the web visit https://groups.google.com/d/msgid/tvb-users/116AE618-8469-41DE-AE6F-A23620EEDE36%40gmail.com.

[Courtiol, Julie]

Dear Gianluca,

Please see Eq. 4.14 below:

For all node k:

The remaining, right most summation contains the variable Vj, which correspond to the activity of other network node.

Best,

Julie

---

Best regards,

Dr. Julie Courtiol

Scientific Manager, Brain Simulation Section

Charité - Universitätsmedizin Berlin

Berlin Institut of Health

Brain Simulation

Robert-Koch-Platz 4

Charitéplatz 1 | 10117 Berlin | Germany

julie.c...@bih-charite.de - www.brainsimulation.org

Twitter: @Courtioljulie

LinkedIn: juliecourtiol

---

De : tvb-...@googlegroups.com <tvb-...@googlegroups.com> de la part de Gianluca Gag <gaglioti...@gmail.com>
Envoyé : mardi 25 juillet 2023 15:31:28
À : tvb-...@googlegroups.com
Objet : Re: [ext] [TVB] Coupling function in the Larter-Breakspear model

 

To view this discussion on the web visit https://groups.google.com/d/msgid/tvb-users/CAKKOgFBcdEcHzT%2BT50L%3DOr4THrosBzDh2o7BsnNYjw8kXtpjnw%40mail.gmail.com.

[thierry nieus]

Dear Julie,

Thanks for taking care of this issue.

I am working with Gianluca on his project. 

The original 4.14 equation is:

In our work we need to understand how the dynamics of the model change when the coupling coefficients of the connectome are multiplied by a fixed constant (aka Global Coupling coefficient multiplying ukj, e.g. as done in Fig.2 of Deco et al. 2019 ). 

The dynamic of the network indeed changes (also when considering small networks of just 2 or 3 nodes). However when we came back to the literature we found 4.14 which simply tells us that any G multiplying the ujk would have no impact on the gamma(Vk,Vj,ukj) as it would cancel out because it is at the numerator and denominator. 

We are probably missing something there ... Maybe the TVB implementation isn't exactly as in 4.14 ?!

Thanks in advance

Best regards

To view this discussion on the web visit https://groups.google.com/d/msgid/tvb-users/91589cc3d87e47ca910541caf7db9221%40bih-charite.de.

[WOODMAN Michael]

hi,

I read the equation as

    Gamma = afferent_input / in_degree = sum( u Q( ... ) ) / sum(u)

While the summations cannot cancel, a global scaling change, call it K, does cancel:

    Gamma = sum( K u Q(...) ) / sum(K u) = K sum(u Q) / (K * sum(u)) = sum(u Q) / sum(u)

From this standpoint, it's the (weighted) in degree normalization in the model that makes it invariant to global connectome changes.

For modeling purposes it is desirable to scale afferent input and not the connectome, i.e.

    Gamma = K sum(u Q) / sum(u)

which may be what you have done when you mention

> dynamic of the network indeed changes (also when considering small networks of just 2 or 3 nodes).

since that would be the simplest thing to implement in TVB, confirmed by the original observation,

> I am obtaining different results when I multiply the weight matrix by G.

and in fact, in the implementation of the tanh coupling function, no in-degree normalization is performed,

https://github.com/the-virtual-brain/tvb-root/blob/master/tvb_library/tvb/simulator/coupling.py#L264

so the equation 4.14 applies, but without in-degree normalization.

hopefully that helps,

Marmaduke

---

From: tvb-...@googlegroups.com <tvb-...@googlegroups.com> on behalf of thierry nieus <thierry.r...@gmail.com>
Sent: Thursday, July 27, 2023 11:37:11 AM
To: TVB Users
Subject: [RESEAUX SOCIAUX] Fwd: [ext] [TVB] Coupling function in the Larter-Breakspear model

 

To view this discussion on the web visit https://groups.google.com/d/msgid/tvb-users/CANn_Dm%2BQE6LX-yxVuvyUM%3DdjfFixN%2BaLqpxDZz%3DXHgrww4LsWg%40mail.gmail.com.

[thierry nieus]

Hi Marmaduke and Julie,

Thanks to both of you for your prompt reply and extensive replies.

Now it is much clearer!

Best regards

Thierry

To view this discussion on the web visit https://groups.google.com/d/msgid/tvb-users/9fc05fe036df4a6ea125e9d9a5c6f5d9%40univ-amu.fr.