Insights into Nerve Signal Propagation: The Effect of Extracellular Space in Governing Neuronal Signal for healthy and injured Nerve Fiber using Modified Cable Model

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.