Strength–Duration Relationship for Extracellular Neural Stimulation: Numerical and Analytical Models

Abstract

Boinagrov D, Loudin J, Palanker D. Strength-duration relationship for extracellular neural stimulation: numerical and analytical models. J Neurophysiol 104: 2236 -2248, 2010. First published August 11, 2010 doi:10.1152/jn.00343.2010. The strength-duration relationship for extracellular stimulation is often assumed to be similar to the classical intracellular stimulation model, with a slope asymptotically approaching 1/ at pulse durations shorter than chronaxy. We modeled extracellular neural stimulation numerically and analytically for several cell shapes and types of active membrane properties. The strength-duration relationship was found to differ significantly from classical intracellular models. At pulse durations between 4 s and 5 ms stimulation is dominated by sodium channels, with a slope of Ϫ0.72 in log-log coordinates for the Hodgkin-Huxley ion channel model. At shorter durations potassium channels dominate and slope decreases to Ϫ0.13. Therefore the charge per phase is decreasing with decreasing stimulus duration. With pulses shorter than cell polarization time (ϳ0.1-1 s), stimulation is dominated by polarization dynamics with a classical Ϫ1 slope and the charge per phase becomes constant. It is demonstrated that extracellular stimulation can have not only lower but also upper thresholds and may be impossible below certain pulse durations. In some regimes the extracellular current can hyperpolarize cells, suppressing rather than stimulating spiking behavior. Thresholds for burst stimuli can be either higher or lower than that of a single pulse, depending on pulse duration. The modeled thresholds were found to be comparable to published experimental data. Electroporation thresholds, which limit the range of safe stimulation, were found to exceed stimulation thresholds by about two orders of magnitude. These results provide a biophysical basis for understanding stimulation dynamics and guidance for optimizing the neural stimulation efficacy and safety.

Upper threshold of extracellular neural stimulation

“…A previously described (Boinagrov et al 2010) computational model of extracellular stimulation in RGCs, based on five-ion channel approximation (Fohlmeister and Miller 1997), was used with the minor modifications explained below.…”

“…A computational model of extracellular stimulation in RGCs, based on a five (plus leakage)-ion channel model (Fohlmeister and Miller 1997), was recently described (Boinagrov et al 2010). One of the features predicted by that model was the existence of the upper stimulation threshold, caused by the reversal of sodium ion current.…”

“…In all of these applications, the characteristics of the stimulation waveform (principally the amplitude, polarity, and pulse width) play an important role in the design of a particular prosthetic device, making it critical to understand the relationship between stimulation threshold and pulse duration. Electrical stimulation of the retinal ganglion cells (RGC), used in epiretinal prostheses, was extensively studied by several research groups (Fried et al 2006;Jensen et al 2003Jensen et al , 2005Sekirnjak et al 2006Sekirnjak et al , 2008Stett et al 2000Stett et al , 2007Tsai et al 2009), and the strengthduration relationship has been experimentally measured (Jensen et al 2003(Jensen et al , 2005Sekirnjak et al 2006;Tsai et al 2009) and modeled computationally (Boinagrov et al 2010;Greenberg et al 1999). The strength-duration relationship defines for a given pulse duration the minimum stimulus strength, or stimulation threshold, above which an action potential (AP) is generated.…”

“…Recent computational studies (Boinagrov et al 2010), based on the ion channel model for RGCs, predicted the existence of a stimulation upper threshold, above which no spiking could be elicited. Experimental evidence of this phenomenon in RGCs has not been reported.…”

Electrical stimulation of retinal neurons in epiretinal and subretinal configuration using a multicapacitor array

“…3, B and C). This type of stimulation has been analyzed recently for the epiretinal configuration (Boinagrov et al 2010;Fried et al 2009;Sekirnjak et al 2008). We conclude that a single cathodal epiretinal stimulus (500 ϫ 500 m 2 ) excites all three excitatory retinal cell classes.…”