Computational modeling of neurons: intensity-duration relationship of extracellular electrical stimulation for changes in intracellular calcium

Abstract

In many instances of extensive nerve damage, the injured nerve never adequately heals, leaving lack of nerve function. Electrical stimulation (ES) has been shown to increase the rate and orient the direction of neurite growth, and is a promising therapy. However, the mechanism in which ES affects neuronal growth is not understood, making it difficult to compare existing ES protocols or to design and optimize new protocols. We hypothesize that ES acts by elevating intracellular calcium concentration ([Ca(2+)]i) via opening voltage-dependent Ca(2+) channels (VDCCs). In this work, we have created a computer model to estimate the ES Ca(2+) relationship. Using COMSOL Multiphysics, we modeled a small dorsal root ganglion (DRG) neuron that includes one Na(+) channel, two K(+) channels, and three VDCCs to estimate [Ca(2+)]i in the soma and growth cone. As expected, the results show that an ES that generates action potentials (APs) can efficiently raise the [Ca(2+)]i of neurons. More interestingly, our simulation results show that sub-AP ES can efficiently raise neuronal [Ca(2+)]i and that specific high-voltage ES can preferentially raise [Ca(2+)]i in the growth cone. The intensities and durations of ES on modeled growth cone calcium rise are consistent with directionality and orientation of growth cones experimentally shown by others. Finally, this model provides a basis to design experimental ES pulse parameters, including duration, intensity, pulse-train frequency, and pulse-train duration to efficiently raise [Ca(2+)]i in neuronal somas or growth cones.

Dorsal Root Ganglion Stimulation Used for the Treatment of Chronic Neuropathic Pain in the Groin: A Single-Center Study With Long-Term Prospective Results in 34 Cases

“…The decrease of the pro‐inflammatory effect on microglia has already been shown in a rat injury model during electrical stimulation . Electrical field stimulation induced nerve regeneration with neurite outgrowth, via calcium influx, has also been demonstrated during DRGS . It could finally restore nerve function and thus stabilize the pain neurophysiology.…”

Validation of electrical stimulation models: intracellular calcium measurement in three-dimensional scaffolds

“…However, the mechanism of how ES improves the rate and affects the direction of neurite growth remains poorly understood (Hronik-Tupaj and Kaplan 2012). In a preceding report, we created a computer model relating extracellular ES parameters to elevation in neuronal intracellular calcium concentration ([Ca 2ϩ ] i ) (Adams et al 2016). Others have modeled the relationship of extracellular ES parameters to action potential (AP) generation (Boinagrov et al 2012;Rattay et al 2012), and the relationship of membrane voltage to [Ca 2ϩ ] i (Benison et al 2001).…”

“…Others have modeled the relationship of extracellular ES parameters to action potential (AP) generation (Boinagrov et al 2012;Rattay et al 2012), and the relationship of membrane voltage to [Ca 2ϩ ] i (Benison et al 2001). To the best of our knowledge, the model presented in Adams et al (2016) is the first to compare extracellular ES parameters to elevation in neuronal [Ca 2ϩ ] i . This model was developed before any experimentation was performed to measure [Ca 2ϩ ] i , making it a "naive" model.…”

Gelatin hydrogel membrane containing carbonate hydroxyapatite for nerve regeneration scaffold

“…It was known that neuron responded to Ca 2+ level changes in the environment and neurite elongation proceeded by Ca 2+ supply (Lankford & Letourneau, 1989) because extracellular signal from the environment induces elevation of Ca 2+ level from resting state by promoting Ca 2+ influx from the environment and releasing it from internal storages. Accordingly, cytoplasmic or intracellular Ca 2+ roles to neurite growth and axonal pathfinding were started because of high amplitude Ca 2+ signaling activates Ca 2+ ‐mediated cytoskeleton regulation and leads to neurite attraction and growth (Adams, Willits, & Harkins, 2016; Gomez & Zheng, 2006; Kater & Mills, 1991; Nawrotek, Tylman, Rudnicka, Balcerzak, & Kamiński, 2016; Sutherland, Pujic, & Goodhill, 2014).…”