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A spectral element method with adaptive segmentation for accurately simulating extracellular electrical stimulation of neurons

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Abstract

The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.

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Acknowledgments

The authors would like to thank Dr. Tianruo Gou for his generous assistance in providing the parameters of the ion channel model and the expertise to translate its implementation. We would also like to thank Chih (John) Yang and Dr. Andrew Wooley for providing the detailed anatomical images of RGCs used in this work.

This research was supported by the National Health and Medical Research Council (APP1087224), Australia, and the Australian Research Council through its Special Research Initiative in Bionic Vision Science and Technology granted to Bionic Vision Australia.

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  1. Calvin D. Eiber

    Present address: Save Sight Institute, University of Sydney, 8 Macquarie St, Sydney, NSW, 2000, Australia

Authors and Affiliations

  1. Graduate School of Biomedical Engineering, University of New South Wales, Sydney, NSW, 2052, Australia

    Calvin D. Eiber, Socrates Dokos, Nigel H. Lovell & Gregg J. Suaning

Authors
  1. Calvin D. Eiber
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  2. Socrates Dokos
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  3. Nigel H. Lovell
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Correspondence to Calvin D. Eiber.

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All applicable international, national, and institutional guidelines for the care and use of animals were followed. All procedures performed involving animals were in accordance with the ethical standards of the institution or practice at which the studies were conducted. Surgical and experimental procedures were reviewed and conducted with approval from the UNSW Animal Care and Ethics Committee.

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Eiber, C.D., Dokos, S., Lovell, N.H. et al. A spectral element method with adaptive segmentation for accurately simulating extracellular electrical stimulation of neurons. Med Biol Eng Comput 55, 823–831 (2017). https://doi.org/10.1007/s11517-016-1558-x

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  • DOI: https://doi.org/10.1007/s11517-016-1558-x

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