S-hydroxynorketamine, respectively; C50,K, C50,NKandC50,HNKare the steadystate or effect-site concentrations causing 50% of the pharmacodynamic effect; and C100,NK and C100,HNK are the S-norketamine and S-hydroxynorketamine concentrations causing a 100% increase of S-ketamine C50. An effect compartment was postulated to account for the hysteresis between the S-ketamine plasma concentrations (and possibly its metabolites) and its effect. This effect compartment equilibrates with the plasma compartment with plasma-effect-site equilibration half-life (t1/2ke0). The results of the electrical and thermal noxious assays were analyzed using the following inhibitory sigmoid EMAX model: NRS(t)=NRS0 × [1+(CE(t)/C50) γ]−1 where NRS(t) is the NRS in response to the noxious stimulation at time t and NRS0 is the NRS at baseline (pre-drug condition), and γ is a dimensionless shape parameter. For pressure pain, we assume that S-ketamine (and possibly its metabolites) attenuates the response to the applied noxious pressure stimulus by the inhibition of signal propagation and central nociceptive processing. As a consequence, stronger stimuli are needed before the subjects indicate that he or she experiences pain. The attenuation (A) is described by an inhibitory sigmoid EMAX model:12 A= [1+ CE(t)/C50) γ]−1 Since a response of the subjects occurs just above the response threshold, we use the following equation for the pressure pain threshold at time t: P(t)= P0 × 1/A= P0 × [1+ CE(t)/C50) γ] where P0 is the baseline or pre-drug pressure that elicited a pain threshold response. Drug high was modeled using a sigmoid EMAX model: V AS drug high (t)= [Emax × CE(t) γ]/ [C γ 50 + CE(t) γ] where C50 is the S-ketamine concentration that causes a drug high of 50% of EMAX, and EMAX the maximum possible effect on drug high (10 cm). 46
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