A Simulation Model of the Electrical Characteristics of Human Myelinated Sensory Nerve Fibers

A new nerve fiber model has been developed, incorporating electrical characteristics of human myelinated sensory nerve fibers. It will be used to determine the response of myelinated somatosensory nerve fibers in the spinal cord to electrical stimulation with an epidurally placed electrode. Index terms Spinal cord stimulation, human sensory nerve fiber, simulated action potential, chronaxie diameter. Schalow er al. [6] showed that the ratio between the conduction velocity and the diameter of human touch stimulated afferents approximates 4* lo6, which is considerably less than previously assumed for human (and mammals in general), i.e. 6*106. These morphometric data, and the dynamics of the human nodal membrane conductance were incorporated in a new nerve fiber model, which will be used to determine the response of sensory nerve fibers in the dorsal columns to epidural electrical stimulation of the spinal cord. Introduction Methods Spinal cord stimulation (SCS) for the management of chronic pain implies electrical stimulation of large myelinated somatosensory dorsal column (DC) fibers to block pain pathways to the brain. At the University of Twente, a computer model has been developed, which simulates the direct effects of SCS [I]. This model consists of a volume conductor model and a nerve fiber model, representing the spinal cord and surrounding anatomical structures, and the electrical behavior of the myelinated nerve fibers in the spinal cord, respectively. After calculation of the potential field in the inhomogeneous volume conductor model resulting from electrical stimulation, the response of myelinated nerve fibers in the spinal cord is determined with an electrical equivalent cable model, as presented by McNeal [2]. Until now, the characteristics of the nerve fiber model were based on experimental data from rabbit nerve fibers [3], and adapted for use at 37°C. In the current study, a new model is presented, merely based on properties of human nerve fibers. Schwarz et al. [4] have presented results from experiments on single human myelinated sensory nerve fibers. They recorded sodium and potassium currents under currentand voltage clamp conditions at room temperature. Morphometric data concerning the myelin sheath thickness and internodal distance of human myelinated sensory nerve fibers were presented by Behse [5], who has shown that the ratios of fiber diameter, axon diameter and internodal length are not constant, as previously assumed, but vary with the fiber From their recordings of action potentials (AP) and membrane currents in human myelinated nerve fiber, Schwarz et al. [4] constructed a mathematical model describing the electrical characteristics of the human node of Ranvier. After we applied temperature correction to these data with Q l O values estimated by Schwarz et al. [4], action potentials could be simulated at 37°C at one node of Ranvier. For application in the SCS computer model, it is necessary to have a McNeal type [2] cable model with compartments for each node of Ranvier. In the Appendix, the complete model is listed. The sodium equilibrium potential was taken from [7], and used to calculate the intracellular sodium concentration. All parameters were taken from literature, except for the intra axonal resistance and the leakage conductance. Both parameters were adjusted toobtain a correct conduction velocity and AP amplitude. The results presented here were calculated with a simple configuration. A point source was modeled in an infinite, homogeneous medium (resistance 3.0 am) , containing a single, straight, myelinated nerve fiber at 3 mm distance, whose presence did not disturb the potential distribution. The nerve fiber model had 51 nodes of Ranvier, all of them made excitable. The nodal membrane current has a capacitive, a leakage, a sodium, and a (fast) potassium component. The sodium and potassium channels are voltage dependent. The myelin sheath is supposed to be a perfect insulator, periodically interrupted at the nodes of Ranvier. (0-7803-4262-3/97/$10.00 (G) 1997 IEEE) 2029 Proceedings 19th International Conference IEEE/EMBS Oct. 30 Nov. 2, 1997 Chicago, IL. USA