2.4. Data Analysis

The stimulation threshold (H50) is defined as the radiant exposure at which 50% of the laser pulses evoked CMAP responses, and this definition is used to compare all data. To determine the stimulation threshold, recordings from each trial were used to determine the number of INS-evoked CMAPs. It is important to note that CMAP amplitude increases with the magnitude of radiant exposure.^20,62 For the purposes of this study, the presence of a CMAP regardless of its amplitude is used as the physiological end point to indicate successful INS, and thus the probability of evoking a CMAP is unaffected. Responses with a peak magnitude greater than two standard deviations above the baseline were considered evoked CMAPs. The number of evoked CMAPs was then divided by the total number of delivered pulses to determine the activation probability for every radiant exposure. A cumulative distribution function (CDF) of the standard normal distribution

where x is the radiant exposure with mean μ and variance σ2, was then fit to the data to determine the radiant exposure corresponding to μ or the 50% probability of evoking a CMAP (H50).⁶³ While the H50 is of little use for practical applications, this method is a common means to determine and compare dosimetric thresholds for radiation bioeffects.^63–68 INS parameters with a lower H50 are considered more efficacious as they require less energy and produce smaller temperature rises.

Another measure of stimulation efficacy is the transition rate to 100% activation probability. The transition rate to 100% activation probability is defined as the peak slope of the fitted CDF (mpeak)

where F′ denotes the first derivative of F. This calculation represents the determinacy of the stimulation threshold. A larger mpeak (i.e., a sharper transition rate) translates to a more reliable and predictable stimulation. This characteristic is more desirable since a smaller range of radiant exposures exists where one may experience ambiguity as to whether a given pulse evokes an action potential or not. Graphical representations of H50 and mpeak calculations can be found in Fig. S2 in the Supplemental Materials.