Closed-Loop Current Stimulation Feedback Control of a Neural Mass Model Using Reservoir Computing
Round 1
Reviewer 1 Report
Closed-loop current stimulation feedback control of a neural mass model using reservoir computing
The Authorshave been first instantiated a two-column Jansen and Rit model to simulate neuronal dynamics of pyramidal cells and interneurons. An echo-state network (ESN) reservoir computer inverted the dynamics of the model without access to the internal state equations. After inverting the model dynamics, the ESN was used as a closed-loop feedback controller for the neural mass model by predicting the current stimulation input for a desired future output. The ESN was used to predict the endogenous membrane currents of the model from the observable pyramidal membrane potentials and then inject current stimulation to destructively interfere with endogenous membrane currents, thereby reducing the energy of the pyramidal cells. This simulation approach provides a framework for a model-free closed-loop feedback controller in tES experiments.
The single-column JRNMM treats a column of cortex as a combination of intercon- nected excitatory interneurons, pyramidal cells (PC), and inhibitory interneurons [25]. Each subpopulation has a single state parameter that models the membrane potential of a given subpopulation. A sigmoidal function maps the membrane potential of a subpopulation to a mean firing rate, which then serves as an input to another subpopulation through intrinsic connections. Excitatory interneurons receive a mean firing rate input from both a user-defined external signal g and inputs from the PC layer. Inhibitory interneurons receive a mean firing rate input from only the PC layer. The PC layer receives inputs from both the excitatory and inhibitory interneurons.
A Jansen and Rit neural mass model was used to simulate closed-loop current stimulation. An echo-state network, used to invert the dynamics of the stochastic nonlinear neural mass model, successfully predicted current stimulation inputs to modulate the dynamics of the model. The controller implicitly estimated the endogenous membrane currents of the model, and subsequently could be used to successfully modulate output currents. This approach provides a potential framework for delivering closed-loop current stimulation to the brain.
The Authors have been modelled Transcranial electrical stimulation (tES) using a two-column Jansen and Rit model to simulate neuronal dynamics of pyramidal cells and interneurons. An echo-state network (ESN) reservoir computer inverted the dynamics of the model without access to the internal state equations. After inverting the model dynamics, the ESN was used as a closed-loop feedback controller for the neural mass model by predicting the current stimulation input for a desired future output. The ESN was used to predict the endogenous membrane currents of the model from the observable pyramidal membrane potentials and then inject current stimulation to destructively interfere with endogenous membrane currents, thereby reducing the energy of the pyramidal cells. This simulation approach provides a framework for a model-free closed-loop feedback controller in tES experiment.
The stıdy is very interesting and impressed one. My decision is Accept for publication.
Author Response
Dear Reviewer,
Thank you very much for your comments.
Best,
Alex
Reviewer 2 Report
This manuscript applies echo-state network (ESN) reservoir computing to closed-loop control of the Jansen-Rit neural mass model. Simulation results show the effectiveness of the proposed approach.
Overall, the paper is well written and the contribution is clear. The idea of applying reservoir computing to brain stimulation is interesting. I have several minor comments.
1. According to Table 2, the spectral radius of ESN is set to 0.5, which seems to be smaller than usual. Please present and compare the results with larger spectral radius (closer to one).
2. According to Table 2, the number of internal units is set to 10. Please present and compare the results with more internal units.
3. Many figures are presented to show the advantage of the proposed method. To quantify significance, please add p-values to them. For example, Figures 8 and 13 compare several box-plots and I guess t-tests or ANOVA can be used.
4. In the third paragraph of Introduction, the importance of oscillatory phase in brain stimulation is explained. Recently, a method of real-time phase estimation based on a state-space model has been developed [1, 2]. Is it possible to incorporate a similar idea to ESN, which is also based on a special form of a state-space model?
[1] A. Wodeyar, M. Schatza, A. S. Widge, U. T. Eden and M. A. Kramer. A state space modeling approach to real-time phase estimation. eLife 2021.
[2] T. Matsuda and F. Komaki. Time Series Decomposition into Oscillation Components and Phase Estimation, Neural Computation 2017.
Author Response
Dear Reviewer,
Thank you very much for your comments and taking the time to review my paper.
Addressing points 1 and 2, I have rerun the analysis but increased the spectral radius to 0.9, and reran the analysis for 100 internal units. I found that increasing the amount of internal units had a negative impact on the energy suppressing, while changing the spectral radius did not have a large impact. I have included these figures in the Appendix. As a future work, it would be more appropriate to do a grid search of the ESN parameters to find the most optimal parameters that leads to best control of the dynamics.
Regarding point 3, I have added these analyses based on your suggestion. Please see the changes in lines 267 and 288.
Regarding point 4, I have added a brief discussion in the discussion section about how the ESN may be learning information about the representation of phase, similar to the works that you linked. I suggest that in future works it may be beneficial for the ESN to include phase information (wavelet coefficients, or instantaneous phase from the Hilbert transform) to assist it in learning this representation.
Thank you again for everything.
Best,
Alex
Author Response File: 
Author Response.docx
Reviewer 3 Report
I consider the present paper technically sound and providing an interesting piece of information to the field of transient electrical stimulation, which is becoming more and more popular for the treatment of several neurological disorders.
In particular, the implementation of a closed loop based on two parallel JRNMM, to follow up relevant parameters (beyond the neural population resonant frequency), definitely contributes to the refinement of tES and will help broadenign its applications and therapeutic outcome.
Although the findings are not particularly extenstive (only one model is suggested and described) I consider the new implementations (specially the ESN implementation that omits the need for interaction with internal state equations) proposed by the authors quite useful in the field and fully support its publication.
Author Response
Dear Reviewer,
Thank you very much for your comments and suggestions. Inspired by your comment, I hope explore in future works additional neural models, and how the controller performs when the model undergoes small changes in the parameters (perhaps as a function of time throughout the simulation) to mimic realistic biological scenarios and noisy settings. I will make a note of this in the discussion section of the paper.
Best,
Alex
