• Chad R Johnson, Roger C Barr, and Stephen M Klein.
• Department of Anesthesiology, Duke University, Durham, North Carolina 27110, USA.
• Anesthesiology. 2007 Feb 1; 106 (2): 323-30.

BackgroundNerve stimulation for regional anesthesia can be modeled mathematically. The authors present a mathematical framework to model the underlying electrophysiology, the development of software to implement that framework, and examples of simulation results.MethodsThe mathematical framework includes descriptions of the needle, the resulting potential field, and the active nerve fiber. The latter requires a model of the individual membrane ionic currents. The model geometry is defined by a three-dimensional coordinate system that allows the needle to be manipulated as it is clinically and tracked in relation to the nerve fiber. The skin plane is included as an electrical boundary to current flow. The mathematical framework was implemented in the Matlab (The MathWorks, Natick, MA) computing environment and organized around a graphical user interface. Simulations were performed using an insulated needle or an uninsulated needle inserted perpendicular to the skin with the nerve fiber at a depth of 2 cm. For each needle design, data were obtained with the needle as cathode or anode. Data are presented as current-distance maps that highlight combinations of current amplitude and tip-to-nerve distance that evoked a propagated response.ResultsWith the needle tip positioned 2 mm proximal to the depth of the nerve, an insulated needle required a current greater than 0.457 mA for impulse propagation when attached to the cathode; when attached to the anode, the minimal current was 2.354 mA. In the same position, an uninsulated needle attached to the cathode required a current greater than 2.395 mA to generate a response. However, when an uninsulated needle was attached to the anode, currents up to 7 mA were inadequate to produce a propagated response. Of particular interest were combinations of current amplitude and needle position that activated the fiber but blocked impulse propagation for cathodal stimulation.ConclusionsMathematical modeling of nerve stimulation for regional anesthesia is possible and could be used to investigate new equipment or needle designs, test nerve localization protocols, enhance clinical and experimental data, and ultimately generate new hypotheses.

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