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Modeling the cortical response elicited by wrist manipulation via a nonlinear delay differential embedding

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Abstract

Regarding motor processes, modeling healthy people’s brains is essential to understand the brain activity in people with motor impairments. However, little research has been undertaken when external forces disturb limbs, having limited information on physiological pathways. Therefore, in this paper, a nonlinear delay differential embedding model is used to estimate the brain response elicited by externally controlled wrist movement in healthy individuals. The aim is to improve the understanding of the relationship between a controlled wrist movement and the generated cortical activity of healthy people, helping to disclose the underlying mechanisms and physiological relationships involved in the motor event. To evaluate the model, a public database from the Delft University of Technology is used, which contains electroencephalographic recordings of ten healthy subjects while wrist movement was externally provoked by a robotic system. In this work, the cortical response related to movement is identified via Independent Component Analysis and estimated based on a nonlinear delay differential embedding model. After a cross-validation analysis, the model performance reaches 90.21% ± 4.46% Variance Accounted For, and Correlation 95.14% ± 2.31%. The proposed methodology allows to select the model degree, to estimate a general predominant operation mode of the cortical response elicited by wrist movement. The obtained results revealed two facts that had not previously been reported: the movement’s acceleration affects the cortical response, and a common delayed activity is shared among subjects. Going forward, identifying biomarkers related to motor tasks could aid in the evaluation of rehabilitation treatments for patients with upper limbs motor impairments.

Graphical abstract

A: General scheme of the methodology to identify the cortical response caused by external disturbances. B. Estimation of the best time delays. C: Sequence of the mathematical model from the perturbation to the cortical response and decomposition of the base matrix through Principal Component Analysis (PCA).

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Data availability

The information utilized in this article is available in [16].

Code availability

The source code used to produce the results and analyses presented in this manuscript are available by sending an email to martin.duranss@udlap.mx.

Notes

  1. EEG: Electroencephalogram.

  2. VAF: Variance Accounted For.

  3. LNS: National Supercomputing Laboratory of Southeast Mexico, https://lns.buap.mx/.

  4. ICA: Independent Component Analysis.

  5. SNR: Signal-to-Noise Ratio.

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Acknowledgements

The authors thankfully acknowledge computer resources, technical advice, and support provided by the Laboratorio Nacional de Supercómputo del Sureste de México (LNS), a member of the Consejo Nacional de Humanidades, Ciencias y Tecnologías (CONAHCYT) national laboratories, with Project No. 202101014C. This work was supported by the CONAHCYT [Grant Number 443962] and the Universidad de las Américas Puebla (UDLAP) [scholar registration number 604161].

Funding

This work was supported by the Laboratorio Nacional de Supercómputo del Sureste de México (LNS), a member of the Consejo Nacional de Ciencia y Tecnología (CONACYT) national laboratories, with project No. 202101014C, the CONACYT [grant number 443962] and the Universidad de las Américas Puebla (UDLAP) [scholar registration number 604161].

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Author notes

  1. R. Salazar-Varas and G. Etcheverry have contributed equally to this work.

Authors and Affiliations

  1. Department of Computing, Electronics and Mechatronics, Universidad de las Americas Puebla (UDLAP), Ex Hacienda Sta. Catarina Mártir S/N, C.P. 72810, San Andrés Cholula, Puebla, Mexico

    Martín Durán-Santos & R. Salazar-Varas

  2. Department of Mathematics, Tiffin University, 155 Miami St, Tiffin, OH, 44883, USA

    Gibran Etcheverry

Authors
  1. Martín Durán-Santos
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  2. R. Salazar-Varas
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  3. Gibran Etcheverry
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Correspondence to Martín Durán-Santos.

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Conflict of interest

The authors declare that they do not have any financial and personal relationships with other people or organizations that could inappropriately influence (bias) their work.

Ethical approval

A public dataset from the Delft University of Technology (the Netherlands) is used in this work. The experimental procedure was approved by the Human Research Ethics Committee of the TU Delft. All participants delivered written informed consent before the performance of experiments.

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Durán-Santos, M., Salazar-Varas, R. & Etcheverry, G. Modeling the cortical response elicited by wrist manipulation via a nonlinear delay differential embedding. Phys Eng Sci Med (2024). https://doi.org/10.1007/s13246-024-01427-8

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