Modeling the Impact of the Variation in Peripheral Nerve Anatomy on Stimulation

Lakshmi Narayan Mishra 1 , Gaurav Kulkarni2, Mandar Gadgil 2

1 Nalu Medical Inc., Carlsbad, CA, USA; 2 Oneirix Engineering Laboratories Pvt. Ltd., Pune, MH, India

Correspondence: Lakshmi Narayan Mishra, Nalu Medical Inc., 2320 Faraday Avenue, Suite 100, Carlsbad, CA, 92008, USA, Tel +1 760-448-2360, Email mishra@nalumed.com

Introduction: The peripheral nervous system has a complex anatomical structure. Stimulation of nerve fibers in the peripheral nervous system depends on the fiber diameter and myelination as well as its location within the nerve, packing fraction, and fascicle distribution within the nerve bundle. This paper analyzes the impact of the variation in peripheral nervous system anatomy and the distance of the stimulating electrodes on the probability of generating an action potential.

Methods: A mathematical model for effective fascicle conductivity has been developed to capture the variation in the packing fraction and fiber diameter. A linear activating function is utilized to analyze the impact of this effective conductivity and fascicle distribution as an indicator of generating an action potential.

Results: Finite element simulations are performed for the nerve-electrode configuration to evaluate the electric field. The simulation results are used to analyze the activating function for different packing fractions and types of nerve fibers. The effect of electrode distance on the activating function and the total current through a nerve bundle has also been studied.

Discussion: The simulation results indicate that the peripheral nerve anatomy and electrode distance have a significant effect on action potential generation.

Keywords: peripheral nerve stimulation, packing fraction, computational modeling, fascicle distribution, activating function

Introduction

The therapeutic application of peripheral nervous system stimulation has been a field of growing interest throughout the last few years, particularly as an effective tool for the treatment of chronic pain. According to the gate control theory of pain, non-painful input closes the nerve gates to painful inputs. Painful nociceptive stimuli are carried by Aδ and C nerve fibers, while Aα, Aβ nerve fibers carry non-nociceptive stimuli for proprioception and touch. The gate control theory implies that the effectiveness of pain relief depends on the selective activation of Aα, Aβ nerve fibers within a nerve bundle. Stimulation of nerve fibers leads to depolarization, which beyond a threshold, leads to the generation of an action potential. Hence, selective activation of the Aα and Aβ nerve fibers within a nerve bundle will require preferential stimulation.

Methods

Nerve fiber diameters range from 1 [μm] to 10 [μm], whereas fascicle diameters are in the range of 0.075 [mm] to 1 [mm] and nerve bundle diameters are of the order of 5 [mm] to 15 [mm]. Modeling a geometry comprising parts ranging from 1 [μm] to 15 [mm] in a single simulation model is difficult. Hence, in peripheral nervous system models, nerve fibers are not considered explicitly, but their contribution is considered in computing the effective conductivity of a fascicle.

Effective Axial Conductivity

In computing an effective conductivity estimate for a fascicle, it can be assumed that nerve fibers travel parallel to each other. A fascicle primarily consists of three types of biological materials – endoneurium, axon and myelin. If a fascicle is placed between two conducting plates and a potential difference is applied, then the total current flowing through the fascicle will depend on the effective conductance of the fascicle.

Effective Radial Conductivity

The total current flowing through the box is measured using FEA simulations. More details about the FEA simulations are provided in the section Stimulation of a peripheral nerve. The cross-sectional area of fibers was computed using the mean diameter values listed in Table 1.

Discussion

Anatomical studies have shown that the packing fraction varies in a wide range. These results clearly indicate that Q(X) values change as the packing fraction changes even for fascicles with the same type of fibers. Therefore, fascicles with the same fiber type but different packing fractions could require different magnitudes of stimulation to generate an action potential. Observing the Q(X) values for Aδ with respect to Q(X) values for Aα with different packing fractions reinforces the complexity in using a single threshold for electrical stimulation.

Conclusion

Simulation results indicate that the anatomy of the peripheral nerve – in terms of packing fraction and fascicle distribution has a significant effect on the stimulation. Results further indicate that a single electrode cannot selectively stimulate all non-nociceptive fibers while avoiding stimulation of other neural targets. A system with more electrodes that are placed close to the target nerve will have better spatial control to selectively depolarize the non-nociceptive fibers while consuming less power.