Simulation of the Kinetics of Neuromuscular Block

Abstract

The onset time for paralysis varies 3-fold among nondepolarizing muscle relaxants. Possible explanations include: (a) pharmacokinetic differences among drugs and (b) buffering of drug molecules by acetylcholine receptors as they diffuse into the neuromuscular junction. Although some pharmacokinetic models consider buffered diffusion, these models do not account for either the high density of receptors or synapse geometry. Here, I used computer simulations to calculate the kinetics of buffered diffusion. The goal was to determine the conditions under which buffered diffusion could account for differences in onset time among nondepolarizing muscle relaxants. Monte Carlo simulation was used along with a realistic 3-dimensional model of the rat neuromuscular junction. Simulations determined the time dependence of the number of drug-bound receptors. A 1000-fold range of drug potency was examined. In some simulations, the drug concentration outside the junction was changed instantaneously. In other simulations, the concentration changed according to predictions of pharmacokinetic models assuming time-dependent changes in plasma drug concentration. The rate constant for equilibration of drug between plasma and muscle, keo, was varied between 0.15 and 0.6 min(-1). Twitch amplitude was calculated from receptor occupancy assuming a high safety margin for neuromuscular transmission. Some simulations used a synaptic model with an increased nerve-muscle contact width. Simulations with instantaneous changes in drug concentration at the synapse, indicated that the time to 50% twitch depression (onset time) was 0.1 to 30 seconds and was proportional to drug potency. This corresponds to iontophoretic application of drug to isolated neuromuscular junctions, but is too fast to explain onset times in humans. When pharmacokinetic models were used to calculate the drug concentration outside the synapse, buffered diffusion increased onset times of potent drugs (drugs for which the effective concentration at 50% twitch height is <600 nM). Simulations using keo = 0.6 min(-1) and a model with a 2- to 3-fold wider nerve-muscle contact width indicated that buffered diffusion could account for the differences in clinical onset times among the nondepolarizing muscle relaxants. Monte Carlo simulation provides a biophysically appropriate way to incorporate buffered diffusion into pharmacokinetic modeling. The simulations indicated that buffered diffusion could account for differences in onset time among drugs. However, a better understanding of the geometry of the human neuromuscular junction is needed before the magnitude of the effect of buffered diffusion can be quantified.