Actual values for inspiratory and expiratory duration measured at (A) analgesic and (B) apneic remifentanil concentrations before and after local naloxone injections for the data presented in fig. 3A (analgesic) and fig. 4A (apneic) and their corresponding input values; naloxone injection into the parabrachial nucleus/Kölliker–Fuse decreased expiratory duration after apneic remifentanil bolus from 10.3 to 3 s, which reflected an increase in inputs to expiratory duration from 100.01 to 107% (a 7% increase) of the apneic threshold (purple arrow). σ is a step input pattern with onset at t = 0, and LI(σ) is the output step response of the leaky integrator. In contrast, naloxone injection into the parabrachial nucleus/Kölliker–Fuse decreased expiratory duration during analgesic remifentanil concentrations from 2.2 to 1.3 s, reflecting an increase in inputs to expiratory duration from 114 to 143% of apneic threshold (red arrow). This illustrates that at high input levels (short respiratory phase durations), the same change in the sum of inputs results in a much smaller change in phase duration than at low input levels, for which small changes in the sum of inputs can change phase duration by several seconds. Calculating the inputs to phase duration allows comparison of opioid effects, as determined by the amount of naloxone reversal, from multiple injections without bias resulting from the respiratory rate at the time of injection. NAL, naloxone; PBN/KF, parabrachial nucleus/Kölliker–Fuse complex; preBotC, pre-Bötzinger complex.