Insights into Nerve Signal Propagation: The Effect of Extracellular Space in Governing Neuronal Signal for healthy and injured Nerve Fiber using Modified Cable Model
Abstract
Nerve injuries are complex medical conditions that may arise from a variety of traumatic events or diseases, altering the intricate structure of neural pathways. During neuronal injury, the potassium and sodium ion concentration that controls signaling endures significant changes such as the ion channels getting blocked or an increase in the intracellular ionic concentration. The Extracellular Space which surrounds a nerve fiber has a significant impact on the neuronal signal and variation in its size can alter neuronal signal transmission. Hence, to fully understand neuronal signal transmission, it is essential to explore the effect that the Extracellular Space exerts on the neuronal signal. The aim of this study is to develop a mathematical model which yields a simplistic yet robust mathematical expression of the nerve membrane potential, incorporating the Extracellular Space dependent parameters for having a holistic approach towards understanding neuronal signal transmission in healthy and injured nerve fiber. The conventional cable model focuses solely on the intrinsic properties of the nerve fiber, but the current work expands this model by incorporating the Extracellular Space dependent parameters into the final membrane potential expression. The results obtained from this study shows that certain combination of the Extracellular Space and fiber diameter could bring about hyperexcitation whereas in some cases it may lead to hypoexcitation to the neuronal signal as it propagates along the nerve fiber. Moreover, prolonged refractory period and delayed refractory period are also observed in certain combination of the Extracellular Space and fiber diameter. The proposed framework manages to show trends associated with certain medical conditions and may also be useful to further understand, and early diagnosis of various neurological conditions under the effect of an Extracellular Space of varied sizes.
Downloads
References
C. Nicholson and S. Hrabětová, “Brain Extracellular Space: The Final Frontier of Neuroscience,” Biophysical Journal, vol. 113, no. 10. Biophysical Society, pp. 2133–2142, Nov. 21, 2017. doi: 10.1016/j.bpj.2017.06.052.
E. Sykova´and, S. Sykova´and, and C. Nicholson, “Diffusion in Brain Extracellular Space,” 2008, doi: 0.1152/physrev.00027.2007.-Diffusion.
Y. Bekku, U. Rauch, Y. Ninomiya, and T. Oohashi, “Brevican distinctively assembles extracellular components at the large diameter nodes of Ranvier in the CNS,” J Neurochem, vol. 108, no. 5, pp. 1266–1276, Mar. 2009, doi: 10.1111/j.1471-4159.2009.05873.x.
S. M. B. Baruah, B. Das, and S. Roy, “Extracellular Conductivity and Nerve Signal Propagation: An Analytical Study,” in Lecture Notes in Electrical Engineering, Springer Science and Business Media Deutschland GmbH, 2021, pp. 399–405. doi: 10.1007/978-981-33-4866-0_49.
A. J. HANSEN and C. E. OLSEN, “Brain extracellular space during spreading depression and ischemia,” Acta Physiol Scand, vol. 108, no. 4, pp. 355–365, 1980, doi: 10.1111/j.1748-1716.1980.tb06544.x.
Bruehlmeier, M., Roelcke, U., Bläuenstein, P., Missimer, J., Schubiger, P. A., Locher, J. T., ... & Ametamey, S. M. (2003). Measurement of the extracellular space in brain tumors using 76Br-bromide and PET. Journal of Nuclear Medicine, 44(8), 1210-1218.
C. Nicholson, P. Kamali-Zare, and L. Tao, “Brain extracellular space as a diffusion barrier,” Comput Vis Sci, vol. 14, no. 7, pp. 309–325, 2011, doi: 10.1007/s00791-012-0185-9.
J. Dimitrova-Shumkovska, L. Krstanoski, and L. Veenman, “Diagnostic and Therapeutic Potential of TSPO Studies Regarding Neurodegenerative Diseases, Psychiatric Disorders, Alcohol Use Disorders, Traumatic Brain Injury, and Stroke: An Update,” Cells, vol. 9, no. 4. NLM (Medline), Apr. 02, 2020. doi: 10.3390/cells9040870.
D. M. Teleanu et al., “An Overview of Oxidative Stress, Neuroinflammation and Neurodegenerative Diseases,” International Journal of Molecular Sciences, vol. 23, no. 11. MDPI, Jun. 01, 2022. doi: 10.3390/ijms23115938.
K. Facecchia, L. A. Fochesato, S. D. Ray, S. J. Stohs, and S. Pandey, “Oxidative toxicity in neurodegenerative diseases: Role of mitochondrial dysfunction and therapeutic strategies,” J Toxicol, vol. 2011, 2011, doi: 10.1155/2011/683728.
M. Cruz-Haces, J. Tang, G. Acosta, J. Fernandez, and R. Shi, “Pathological correlations between traumatic brain injury and chronic neurodegenerative diseases,” Translational Neurodegeneration, vol. 6, no. 1. BioMed Central Ltd., Jul. 11, 2017. doi: 10.1186/s40035-017-0088-2.
N. Hübel, R. D. Andrew, and G. Ullah, “Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na+/K + pumps–dependent manner,” J Comput Neurosci, vol. 40, no. 2, pp. 177–192, Apr. 2016, doi: 10.1007/s10827-016-0591-y.
X. Zhang, J. R. Roppolo, W. C. De Groat, and C. Tai, “Mechanism of nerve conduction block induced by high-frequency biphasic electrical currents,” IEEE Trans Biomed Eng, vol. 53, no. 12, pp. 2445–2454, Dec. 2006, doi: 10.1109/TBME.2006.884640.
W. A. Catterall, “Voltage-gated sodium channels at 60: Structure, function and pathophysiology,” Journal of Physiology, vol. 590, no. 11. pp. 2577–2589, Jun. 2012. doi: 10.1113/jphysiol.2011.224204.
Q. Ding and Y. Jia, “Effects of temperature and ion channel blocks on propagation of action potential in myelinated axons,” Chaos, vol. 31, no. 5, May 2021, doi: 10.1063/5.0044874.
G. Yi and W. M. Grill, “Kilohertz waveforms optimized to produce closed-state Na+ channel inactivation eliminate onset response in nerve conduction block,” PLoS Comput Biol, vol. 16, no. 6, Jun. 2020, doi: 10.1371/journal.pcbi.1007766.
M. H. P. Kole, S. U. Ilschner, B. M. Kampa, S. R. Williams, P. C. Ruben, and G. J. Stuart, “Action potential generation requires a high sodium channel density in the axon initial segment,” Nat Neurosci, vol. 11, no. 2, pp. 178–186, Feb. 2008, doi: 10.1038/nn2040.
W. M. Liu, J. Y. Wu, F. C. Li, and Q. X. Chen, “Ion channel blockers and spinal cord injury,” Journal of Neuroscience Research, vol. 89, no. 6. pp. 791–801, Jun. 2011. doi: 10.1002/jnr.22602.
K. Mori, M. Miyazaki, H. Iwase, and M. Maeda, “Temporal Profile of Changes in Brain Tissue Extracellular Space and Extracellular Ion (Na 1 , K 1 ) Concentrations after Cerebral Ischemia and the Effects of Mild Cerebral Hypothermia,” 2002.
Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology, 117(4), 500.
H. Meffin, B. Tahayori, D. B. Grayden, and A. N. Burkitt, “Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations,” in Journal of Neural Engineering, Dec. 2012. doi: 10.1088/1741-2560/9/6/065005.
Nó, R. L. D., & Condouris, G. A. (1959). Decremental conduction in peripheral nerve. Integration of stimuli in the neuron. Proceedings of the National Academy of Sciences, 45(4), 592-617.
Bishop, G. H. (1956). Natural history of the nerve impulse. Physiological Reviews, 36(3), 376-399.
B. Das, S. Malla Bujar Baruah, and S. Roy, “Modeling and Simulation of Successful Signal Transmission Without Information Loss in Axon,” in Lecture Notes in Electrical Engineering, Springer Science and Business Media Deutschland GmbH, 2024, pp. 397–409. doi: 10.1007/978-981-99-4362-3_36.
S. Ferré, D. García-Borreguero, R. P. Allen, and C. J. Earley, “New Insights into the Neurobiology of Restless Legs Syndrome,” Neuroscientist, vol. 25, no. 2. SAGE Publications Inc., pp. 113–125, Apr. 01, 2019. doi: 10.1177/1073858418791763.
E. Antelmi et al., “Restless Legs Syndrome: Known Knowns and Known Unknowns,” Brain Sci, vol. 12, no. 1, Jan. 2022, doi: 10.3390/brainsci12010118.
Z. H. Li, D. Cui, C. J. Qiu, and X. J. Song, “Cyclic nucleotide signaling in sensory neuron hyperexcitability and chronic pain after nerve injury,” Neurobiology of Pain, vol. 6. Elsevier B.V., Aug. 01, 2019. doi: 10.1016/j.ynpai.2019.100028.
Z. H. Li, D. Cui, C. J. Qiu, and X. J. Song, “Cyclic nucleotide signaling in sensory neuron hyperexcitability and chronic pain after nerve injury,” Neurobiology of Pain, vol. 6. Elsevier B.V., Aug. 01, 2019. doi: 10.1016/j.ynpai.2019.100028.
K. T. Sumadewi, S. Harkitasari, and D. C. Tjandra, “Biomolecular mechanisms of epileptic seizures and epilepsy: a review,” Acta Epileptologica, vol. 5, no. 1. BioMed Central Ltd, Dec. 01, 2023. doi: 10.1186/s42494-023-00137-0.
Holmes, G. L., & Ben-Ari, Y. (2001). The neurobiology and consequences of epilepsy in the developing brain. Pediatric research, 49(3), 320-325.
Scharfman, H. E. (2007). The neurobiology of epilepsy. Current neurology and neuroscience reports, 7(4), 348-354.
M. M. Dimachkie and R. J. Barohn, “Guillain-Barré syndrome and variants,” Neurologic Clinics, vol. 31, no. 2. pp. 491–510, May 2013. doi: 10.1016/j.ncl.2013.01.005.
S. H. Nam and B.-O. Choi, “Clinical and genetic aspects of Charcot-Marie-Tooth disease subtypes,” Precision and Future Medicine, vol. 3, no. 2, pp. 43–68, Jun. 2019, doi: 10.23838/pfm.2018.00163.
L. C. L. S. Barreto et al., “Epidemiologic Study of Charcot-Marie-Tooth Disease: A Systematic Review,” Neuroepidemiology, vol. 46, no. 3. S. Karger AG, pp. 157–165, Apr. 01, 2016. doi: 10.1159/000443706.
B. A. Brouwer, I. S. J. Merkies, M. M. Gerrits, S. G. Waxman, J. G. J. Hoeijmakers, and C. G. Faber, “Painful neuropathies: the emerging role of sodium channelopathies,” 2014. doi: 10.1111/jns.12071.
A. Lampert, A. O. O’Reilly, P. Reeh, and A. Leffler, “Sodium channelopathies and pain,” Pflugers Archiv European Journal of Physiology, vol. 460, no. 2. pp. 249–263, Jul. 2010. doi: 10.1007/s00424-009-0779-3.
M. H. Meisler, S. F. Hill, and W. Yu, “Sodium channelopathies in neurodevelopmental disorders,” Nature Reviews Neuroscience, vol. 22, no. 3. Nature Research, pp. 152–166, Mar. 01, 2021. doi: 10.1038/s41583-020-00418-4.
Weber, F. R. A. N. K., Brinkmeier, H., Aulkemeyer, P., Wollinsky, K. H., & Rüdel, R. (1999). A small sodium channel blocking factor in the cerebrospinal fluid is preferentially found in Guillain-Barré syndrome: a combined cell physiological and HPLC study. Journal of neurology, 246, 955-960.
H. Brinkmeier et al., “Brinkmeier, H., Wollinsky, K. H., Hülser, P. J., Seewald, M. J., Mehrkens, H. H., Kornhuber, H. H., & Rüdel, R. (1992). The acute paralysis in Guillain-Barré syndrome is related to a Na+ channel blocking factor in the cerebrospinal fluid. Pflügers Archiv, 421, 552-557..
Sanguinetti, M. C., & Spector, P. S. (1997). Potassium channelopathies. Neuropharmacology, 36(6), 755-762.
Arimura, K., Sonoda, Y., Watanabe, O., Nagado, T., Kurono, A., Tomimitsu, H., ... & Osame, M. (2002). Isaacs' syndrome as a potassium channelopathy of the nerve. Muscle & Nerve: Official Journal of the American Association of Electrodiagnostic Medicine, 25(S11), S55-S58.
Benatar, M. (2000). Neurological potassium channelopathies. Qjm, 93(12), 787-797.

Copyright (c) 2024 Biswajit Das, Satyabrat Malla Bujar Baruah, Sneha Singh, Soumik Roy

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-ShareAlikel 4.0 International (CC BY-SA 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).