Schematic Data Demonstrating Path-Dependent and Path-Independent State Transitions.

(A) Hysteresis defines path-dependent processes. The solid black curve represents a population of individuals entering the state of unconsciousness as a function of anesthetic dose. The dashed black curve represents the same population returning to a state of wakefulness as a function of anesthetic dose. (B) In the absence of hysteresis, the forward and reverse paths are superimposed (thick gray curve). Modeling studies of anesthetic-induced unconsciousness often collapse the hysteresis into a single curve to create path-independence. Experimental determination of arousal state at the steady-state anesthetic dose(s) half way between the top and bottom asymptotes, the EC50, can easily distinguish path-dependent from path-independent processes. In the former, the EC50 for induction and emergence differ significantly, whereas in the latter they are statistically indistinguishable.