An integrated model for the interaction of muscle relaxants with their antagonists

The impact of arteriovenous concentration differences on pharmacodynamic parameter estimates

In many pharmacodynamic investigations venous drug concentrations are measured and linked to effect-site concentrations by means of a traditional first-order effect-compartment model to estimate pharmacodynamic (PD) parameters. This analysis ignores the underlying physiology that arterial blood supplies both the venous sampling site and effect site. Recently, an extended effect-compartment model has been proposed that reflects physiology by postulating a first-order rate constant of equilibrium between arterial and effect-site concentrations (ke0) as well as first-order rate constant between arterial and venous concentrations (kv0). In the current paper, we evaluate the bias in PD parameter estimates if venous drug concentrations are measured and linked to effect-site concentrations by a traditional effect compartment as a function ke0, kv0, and the drug's elimination half-life (T1/2); we present an analytical solution to the differential equations characterizing the extended effect-compartment model; and we evaluate the performance of the extended effect-compartment model to estimate pharmacodynamic parameters on the basis of venous drug concentrations. Time profiles of venous drug concentrations and drug effect were simulated for a wide range of different values of the half-life of ke0 (T1/2,e0), the half-life of kv0 (T1/2,v0), and T1/2. The simulations showed that a significant bias (up to 90%) in PD parameter estimates occurred for certain values of T1/2,e0, T1/2,v0, and T1/2 if venous drug concentrations are linked to effect-site concentrations by a traditional effect-compartment model. This model misspecification is not apparent from the results of the fitting procedure. The extended effect-compartment model provided unbiased but imprecise PD parameter estimates. The extended effect-compartment model was also able to analyze instances in which the venous concentrations equilibrate slower with the arterial concentrations than the effect-site concentrations, and proteresis is observed in the concentration--effect relationship. It is concluded that if the apparent T1/2 of the drug in the time period in which the decline in pharmacological effect is most pronounced is greater than 5 times T1/2,e0 and T1/2,e0 is greater than T1/2,v0 there is no need to model the underlying arteriovenous equilibrium delay. Under these conditions a traditional first-order link between venous and effect-site concentrations will yield accurate and reliable (less than 10% bias) estimates of the PD parameters such as Emax, EC50 and N. If T1/2 is less than 5 times T1/2,e0 or if T1/2,v0 is greater than T1/2,e0, the underlying arteriovenous equilibration delay needs to be taken into account in the model to obtain unbiased estimates of the PD parameters. This applies for almost all values of T1/2.v0. Arteriovenous equilibration delay can be best taken into account by measuring arterial blood concentrations. If this is not possible, the extended effect-compartment link model can be used. However, a large number of effect measurements needs to be obtained to estimate the model parameters accurately.

Reversal of neuromuscular blockade in humans by neostigmine and edrophonium: a mathematical model

Generalizations of the integrated model describing the interaction of nondepolarizing neuromuscular blocking drugs with reversible anticholinesterase drugs described in Unadkat et al. (1) are reported. The models can deal with possible incomplete reversal (irreversible block) and/or noninstantaneous anticholinesterase kinetics. Experimental data were obtained from 22 human volunteers. Different levels of steady-state vecuronium block were induced in each volunteer (in the range of 50% to 95%), and reversed by short infusions of edrophonium (10 volunteers) or neostigmine (12 volunteers). Edrophonium or neostigmine concentrations and twitch tension (measured as the force of thumb adduction) were measured. The generalized integrated models fit the data well. In the case of neostigmine we find a nondistributional delay in its action. We relate this delay to the slow decarbamylation rate of the (neostigmine-induced) carbamylated anticholinesterase observed in vitro, and are able to model such noninstantaneous anticholinesterase kinetic processes. For both edrophonium and neostigmine we detect an inverse relationship between the (induced) level of initial block and maximal percentage recovery.