Micro-pharmacokinetics of lidocaine and bupivacaine transfer across a myelinated nerve fiber.

Background: The aim of the present study was to predict the time to onset and duration of action of two local anesthetics (lidocaine and bupivacaine) based on experimental dimensions of a typical nerve and experimental octanol/water partition coefficients.
Methods: We began our compilation of experimental data with a numerical solution of the Smoluchowski equation for the transfer of lidocaine and bupivacaine across the axon membrane in the region of the node of Ranvier (axolemma) and across the Schwann cell. The difference between the aqueous and lipid environments of the neuron was simulated by including the coordinate-dependent chemical potential. In the second step, the permeation rates calculated using the diffusion equation were used to solve a system of four ordinary differential equations. This approach allowed us to simulate the cellular environment for a longer time and to compare our model with pharmacokinetic properties (time to onset and duration of action) of local anesthetics from the literature. The behavior of local anesthetics under physiological conditions and in case of local acidosis was also simulated.
Results: We demonstrated that local anesthetics cross the axolemma in a time span of less than 1 μs. The time to onset of action, controlled by diffusion from the epineurium to an axon with a typical distance of 500 μm, was 167 s and 186 s for lidocaine and bupivacaine, respectively. The calculated half-life, which is a measure of the duration of action, was 41 min and 328 min for lidocaine and bupivacaine, respectively.
Conclusions: Duration of action is controlled by the storage capacity of lipophilic compartments around the axon, which is higher for bupivacaine but lower in local acidosis. For the latter case, the literature, including textbooks, provides a misinterpretation, namely that protonated species cannot penetrate the membrane.
Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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