Complexities of modeling the nervous system: limitations of current mathematical and computational approaches

Authors

Keywords:

mathematical models, computational models, neural complexity, nervous system, simulations

Abstract

This paper presents an analysis of the limitations of modern mathematical and computational approaches to modeling the nervous system. Although these methods provide meaningful data and form a basis for quantitative description of neurophysiological processes, they often fail to adequately reproduce the complexity of the structural and functional organization of the nervous system. Simplification of neural dynamics and interactions required to implement computational algorithms imposes limitations on the accuracy of models, their predictive ability, and scalability. In addition, the use of complex mathematical models is associated with high computational costs, which hinders their application in real time or for processing large amounts of data. The article considers in detail the main challenges associated with increasing the reliability and biological validity of models and discusses promising directions for the development of computational approaches aimed at integrating more realistic characteristics of the nervous system in the context of modern research.

Author Biographies

  • Yusif A. Abdulkareem, Far Eastern Federal University

    2nd year Student of the General Medicine program, School of Medicine and Life Sciences

  • Bogdan O. Shcheglov, Far Eastern Federal University

    Assistant of the Department of Fundamental Medicine, School of Medicine and Life Sciences

  • Galina V. Reva, Far Eastern Federal University

    MD, Professor, Professor of the Department of Fundamental Medicine, School of Medicine and Life Sciences

References

1. Hall J.E., Hall M.E. Guyton and Hall textbook of medical physiology: 14th edition. Elsevier Health Sciences, 2020.

2. Fang X., Duan S., Wang L. Memristive Hodgkin-Huxley spiking neuron model for reproducing neuron behaviors. Frontiers in Neuroscience, 2021, vol. 15, art. 730566. DOI: https://doi.org/10.3389/fnins.2021.730566

3. Zhen B., Song Z. The study for synchronization between two coupled FitzHugh – Nagumo neurons based on the laplace transform and the adomian decomposition method. Neural Plasticity, 2021, vol. 2021, no. 1, art. 6657835. DOI: https://doi.org/10.1155/2021/6657835

4. Gonçalves P.J., Lueckmann J.-M., Deistler M., Nonnenmacher M., Öcal K., Bassetto G., Chintaluri C., Podlaski W.F., Haddad S.A., Vogels T.P., Greenberg D.S., Macke J.H. Training deep neural density estimators to identify mechanistic models of neural dynamics. Elife, 2020, vol. 9, art. e56261. DOI: https://doi.org/10.7554/eLife.56261

5. Fu E. Dynamics of the FitzHugh – Nagumo equation with numerical methods. Theoretical and Natural Science, 2023, vol. 10, pp. 179–185. DOI: https://doi.org/10.54254/2753-8818/10/20230339

6. Schmidpeter P.A.M., Nimigean C.M. Correlating ion channel structure and function. Methods in Enzymology, 2021, vol. 652, pp. 3–30. DOI: https://doi.org/10.1016/bs.mie.2021.02.016

7. Keener J.P. Invariant manifold reductions for Markovian ion channel dynamics. Journal of Mathematical Biology, 2009, vol. 58, pp. 447–457. DOI: https://doi.org/10.1007/s00285-008-0199-6

8. Bartolo R., Averbeck B.B. Prefrontal cortex predicts state switches during reversal learning. Neuron, 2020, vol. 106, no. 6, pp. 1044–1054. DOI: https://doi.org/10.1016/j.neuron.2020.03.024

9. Petousakis K.E., Apostolopoulou A.A., Poirazi P. The impact of Hodgkin – Huxley models on dendritic research. The Journal of Physiology, 2023, vol. 601, no. 15, pp. 3091–3102. DOI: https://doi.org/10.1113/jp282756

10. Marasco A., Spera E., De Falco V., Iuorio A., Lupascu C. A., Solinas S., Migliore M. An adaptive generalized leaky integrate-and-fire model for hippocampal CA1 pyramidal neurons and interneurons. Bulletin of Mathematical Biology, 2023, vol. 85, art. 109. DOI: https://doi.org/10.1007/s11538-023-01206-8

11. Fang X., Duan S., Wang L. Memristive izhikevich spiking neuron model and its application in oscillatory associative memory. Frontiers in Neuroscience, 2022, vol. 16, art. 885322. DOI: https://doi.org/10.3389/fnins.2022.885322

12. Uda K. Ergodicity and spike rate for stochastic FitzHugh – Nagumo neural model with periodic forcing. Chaos, Solitons & Fractals, 2019, vol. 123, pp. 383–399. DOI: https://doi.org/10.1016/j.chaos.2019.04.014

13. Yamakou M.E., Tran T.D., Duc L.H., Jost J. The stochastic Fitzhugh – Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model. Journal of Mathematical Biology, 2019, vol. 79, pp. 509–532. DOI: https://doi.org/10.1007/s00285-019-01366-z

14. Che Y.Q., Wang J., Wei X.L., Deng B., Dong F., Li H.Y. Bifurcations in Morris – Lecar model exposed to DC electric field. 31st Annual international conference of the IEEE engineering in medicine and biology society: engineering the future of biomedicine, EMBC, 2009, pp. 3433–3436. DOI: https://doi.org/10.1109/IEMBS.2009.5332510

15. Kameneva T., Abramian M., Zarelli D., Nĕsić D., Burkitt A.N., Meffin H., Grayden D.B. Spike history neural response model. Journal of Computational Neuroscience, 2015, vol. 38, pp. 463–481. DOI: https://doi.org/10.1007/s10827-015-0549-5

16. Saponati M., Vinck M. Sequence anticipation and spike-timing-dependent plasticity emerge from a predictive learning rule. Nature Communications, 2023, vol. 14, no. 1, art. 4985. DOI: https://doi.org/10.1038/s41467-023-40651-w

17. Uddin L.Q. Bring the noise: reconceptualizing spontaneous neural activity. Trends in Cognitive Sciences, 2020, vol. 24, no. 9, pp. 734–746. DOI: https://doi.org/10.1016/j.tics.2020.06.003

18. Carnevale N.T., Hines M.L. The NEURON book. Cambridge University Press, 2006, 457 p. DOI: https://doi.org/10.1017/CBO9780511541612

19. Щеглов Б.О. Разработка алгоритма математического моделирования активности флуоресцентного сигнала на примере кальциевой проводимости нейронов в культуре // Инновации и технологии в биомедицине: сборник материалов, Владивосток, 10–13 июня 2019 года. Владивосток: Дальневосточный федеральный университет, 2019. С. 87–91.

20. Щеглов Б.О., Щеглова С.Н. Российская Федерация. Программа для математического моделирования динамических процессов, происходящих в биологических системах: № 2020617496. заявл. 21.07.2020: опубл. 30.07.2020 / свидетельство о государственной регистрации программы для ЭВМ № 2020618525; заявитель ДВФУ.

Downloads

Published

2025-06-11

Issue

Section

CELL BIOLOGY

How to Cite

Complexities of modeling the nervous system: limitations of current mathematical and computational approaches. (2025). Clinical and Fundamental Medicine, 1(2), 44-51. https://journals.dvfu.ru/clinfundmed/article/view/1516

Most read articles by the same author(s)