Electrocutaneous stimulus setting for identification of the ascending nociceptive pathway

We model this pathway as a cascaded two leaky integrate-and-fire models followed by a nonlinear binary detector at the supraspinal level (Figure 1B). A white noise source presents at the output of neuronal activity. The model has five unknown parameters: two time constants (τ₁, τ₂ [msec]), two compound gain-threshold parameters (α₁, α₂) and standard deviation of the neuronal noise (σ_ε). The multiple combinations of stimulus settings depend on two variables IPI_t and PW_t [msec] (Table 1). Using each setting to generate an artificial dataset, we estimate the parameters by maximizing the likelihood function of these parameters and the stimulus-response dataset. Varying IPI_t and PW_t, we look for an optimal setting of the stimulus.

For each setting, we present estimation errors in a cumulative distribution with particular values of the parameters, θ= (τ₁ = 0.2, τ₂ = 20, α₁ = 0.1, α₂ = 0.04, σ_ε = 0.005). The chance with an estimation error below 17% is a half when IPI_t is 10 and PW_t is 0.2. Furthermore, we show the median of the estimation error in a 2D plot with varying IPI_t and PW_t.

To identify the ascending nociceptive pathway, we have proposed an estimation approach using stimulus-response measurements. Optimal temporal settings of stimulus are found for a reliable estimation within the region of IPI_t 10-25 [msec] and PW_t 0.15-0.4 [msec].