Hypothetical model of inputs determining (A) inspiratory and (B) expiratory phase duration. Intrinsic activity (I_intrinsic) is modified by opioid-sensitive inputs from the preBötzinger complex (F_preBötC), the tachypneic area of the parabrachial nucleus (FtPBN), and additional brainstem sites (F_additional). Systemic opioids reduce these inputs by the factor “r.” F_preBötC increases (+) inspiratory duration (T_I), while FtPBN and F_additional decrease (–) T_I. Systemic opioids reduce these inputs, resulting in a net increase in T_I. All of the opioid-sensitive inputs decrease T_E. Systemic opioids reduce these inputs, resulting in a large increase in T_E.