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Neuroinformatics
Published in: Neuroinformatics 4/2022

18-03-2022 | Original Article

Estimating the Parameters of the Epileptor Model for Epileptic Seizure Suppression

Authors: João Angelo Ferres Brogin, Jean Faber, Douglas D. Bueno

Published in: Neuroinformatics | Issue 4/2022

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Abstract

Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Given the partially successful existing treatments for epileptiform activity suppression, dynamic mathematical models have been proposed with the purpose of better understanding the factors that might trigger an epileptic seizure and how to mitigate it, among which Epileptor stands out, due to its relative simplicity and consistency with experimental observations. Recent studies using this model have provided evidence that establishing a feedback-based control approach is possible. However, for this strategy to work properly, Epileptor’s parameters, which describe the dynamic characteristics of a seizure, must be known beforehand. Therefore, this work proposes a methodology for estimating such parameters based on a successive optimization technique. The results show that it is feasible to approximate their values as they converge to reference values based on different initial conditions, which are modeled by an uncertainty factor or noise addition. Also, interictal (healthy) and ictal (ongoing seizure) conditions, as well as time resolution, must be taken into account for an appropriate estimation. At last, integrating such a parameter estimation approach with observers and controllers for purposes of seizure suppression is carried out, which might provide an interesting alternative for seizure suppression in practice in the future.
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Appendix
Available only for authorised users
Footnotes
1
See, for instance, references Hodgkin and Huxley (1952); FitzHugh (1961); Morris and Lecar (1981); Hindmarsh and Rose (1984); Izhikevich (2003); Grimbert and Faugeras (2006); Jirsa et al. (2014); Chizhov et al. (2018).
 
2
In the context of system identification, this process is known as parameter estimation, which implies finding the parameters of a model that best describe the existing data Ljung (1998); Van den Bos (2007).
 
3
An interesting investigation on this topic is provided by Luersen and Le Riche (2004).
 
4
As stated by Ref. Luersen and Le Riche (2004), the number of analyses (in this case, optimizations) in real situations is usually restricted. Naturally, we take this fact into account by using a limited number of iterations and threshold, since computational applications are sometimes time-consuming and require a high processing. However, as seen in the next sections, our approach provides a good strategy for estimating the parameters of the system with a strong practical appeal.
 
5
This formulation, although applied to the notation developed in this work, is consistent with Gao and Han (2012).
 
6
A detailed formulation on how to obtain such an equivalence can be found in Tanaka and Wang (2004); Brogin et al. (2020, 2021) and Appendix A.
 
7
In practice, once the model and nonlinear functions are available, they are measured for a specific time interval of interest, so the model is exactly reconstructed for this period of time. Further details can be found in Brogin et al. (2020).
 
8
Further details about how to obtain these MFs can be found in Appendix A.
 
9
All the steps and derivatives for this formulation have been addressed elsewhere. For a detailed analysis, refer to Brogin et al. (2021).
 
10
Although II is considered as the best region for \(I_{\text{rest2}}\), note that there is not a clear visual distinction between II and IC, in terms of estimation.
 
11
The effect of progressive degradation caused by noise is commonly found in applications envolving brain signals, in which the source can be from eye movements, muscle artifacts or the environment, for example Agarwal et al. (2017); Hussein et al. (2018).
 
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Metadata
Title
Estimating the Parameters of the Epileptor Model for Epileptic Seizure Suppression
Authors
João Angelo Ferres Brogin
Jean Faber
Douglas D. Bueno
Publication date
18-03-2022
Publisher
Springer US
Published in
Neuroinformatics / Issue 4/2022
Print ISSN: 1539-2791
Electronic ISSN: 1559-0089
DOI
https://doi.org/10.1007/s12021-022-09583-6

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