Figure 1.

Parameter estimation for Process S in a representative recording from a C57BL/6 mouse. The variable S was assumed to increase toward an upper asymptote UA during 10-s epochs of wakefulness and rapid eye movement sleep and decrease toward a lower asymptote LA during 10-s epochs of slow-wave sleep (SWS) according to Equations 1 and 2. (A) UA and LA were constructed using the relative frequency histogram of delta power for 10-s epochs scored as R or SWS during the recording. The 99% level of the SWS histogram was chosen as the upper asymptote (UA) and the intersection of the histogram curves for SWS and R was chosen as the lower asymptote (LA). (B) The data used to choose the optimal values of τ_i and τ_d were the median values of delta power reached during 5-min segments in which at least 90% of the epochs were scored as SWS. (C) To determine the optimal values for the parameters τ_i and τ_d in brute force fashion we performed an exhaustive search over a reasonable range of values for these two parameters and computed the sum of squares error for each combination. (D) Best fit of the model to the data from (B) using the optimal parameters found from exhaustive search (τ_i = 2.39 and τ_d = 3.18). (E) Successive guesses for the optimal choices of τ_i and τ_d using the Nelder-Mead method. The iterative method converges to (τ_i = 2.39 and τ_d = 3.18) in just 45 calculations. (F) Best fit of the model to the data from (B) using the optimal parameters found from Nelder-Mead. Black horizontal bars on the tops of (B,D,F) indicate the 12 h dark periods and the gray horizontal bar indicates when sleep deprivation occurred.