Selective activation of distant nerve fibers

Abstract

I. ~ T ~ ~ O D I J C ~ O N Electrical stimulation of the nervous system using implanted electrodes is a technique to restore sensory and motor functions to neurologically impaired persons. Using conventional stimuli (10-5OOpec rectangular current pulses) fibcrs lying closer to the electrode are recruited first, and larger amplitude currents are required to activate nerve fibers that lie further from the electrode. The threshold current for myelinated nerve fiber excitation is proportional to the square of the electrode-to-fiber distance at close eIecuode-lo-fiber spacings and proportional to the electrode-to-fiber distance at larger spacings (Fig. 1) [I]. We have developed and tested a multiple contact nerve cuff electrode to activate selectively discrete regions of peripheral nerve trunks for neural prosthetic applications [51. The elcccrode allows selective and graded activation of fascicles located on the periphery of the nerve trunk, but does not yet allow selective activation of centrally located nerve fibers. The goal of this work was rhus to develop a method 10 activate selectively fibers at some distance from the electrode without activaung the fibers close to the electrode. We hypothesized that, by using novel pulse waveforms, we could manipulate the non-linear properries of the nerve membrane to elevate threshold for fibers lying close to the electrode. The diameter of the model nerve fiber was set at either 10Fm or 2 0 p U) span the range of diameters of a-motoneurons. The nerve fiber was assumed to lie i n a homogeneous isotropic medium (p=55 R-cm), and the electrode was modeled as a point source at different distances above the center compartment of the 21 compartment cable. The response of the fiber (i.e., the transmembrane voltage) to an extracellular current stimulus was solved as a function of time using fourth order Runge-Kutta integration. Threshold stk"us current for generation of an action potential with differen; waveforms was calculated (+l% error) for each fiber diameter as a function of the electrode-to-fiber dismce. In. RESULTS A. Current-Distance Reldionrhip for Short-Duraion Pulses In Fig. 1 is shown the threshold current as a function of ihe electrode-to-fiber spacing for lOpm and 2 O p nerve fibcrs when the stimulus was a 500psec rectangular cathodic current pulse (inset). Fibers that were further from the electrode required more current to excite, as expected. Very close to the electrode there was little difference between the thresholds of the lOpm and 20pm nerve fibers. but beyond 0.5" substantially more current was required to excite the 10" fiber than the 2Opn fiber. 11. METHODS A cable model of a mammalian myelinated axon [4] was uscd to study the effects of different waveforms on the excitabilily of axons. The parameters of the model are based on voltage clamp data from rat and rabbit myelinated axons, and the model represents accurately rhe shape and conduction velocity of a mammalian action potential at 37°C. This work was supported by a grant from the Paralyzed Vetaans of &erica Spinal Cord Research Foundation. Fig. 1: Current-distance relationship of 10pm and 20 pm nerve f i b s for a 500psec rectangular current pulse. B . Current-Disrance Relalionship after Depolarizing Pre-Pulse In Fig. 2 is shown Lhe response (LranSmembJane potential as a function of h e ) of two 20p.m newe fibers, with electrodcto-fiber spacings of 0.25mm and OS", to a 500psec stimulus pulse preceded by a sub-threshold 500pec depolarizing pre-pulse. The amplitude of the pre-pulse was equal to 95% of the threshold current for the 2Op.m fiber at 0,25mm, and the stimulus amplitude was equal to threshold 0-78031377-1/93 $3.00 01993 IEEE 1249 for the 2Op-n fiber at 0.5". The pre-pulse elicited a larger depolarization and thus a greater elevation in threshold for the fiber lying at 0.25" as compared to the fiber lying at 0.5". The elevation in threshold resulted from a reduction in the value of the sodium inactivation parameter, h, which reduced the magnitude of the inward sodium current that flowed upon further depolarization [2,3]. Since the threshold was more elevated in the fiber at 0.25mm, the subsequent stimulus purse elicited an action potential in the fiber at OS", but not in the fiber at 0.25". Fig. 2: Transmembrane potential tu a function of time in two 20pm nerve fibers in response lo the pulse waveform. In Fig. 3 is shown the threshold current as a function of electrode-to-fiber spacing for low and 2 0 p nerve fibers when the 500pe.c stimulus pulse was preceded by a subthreshold 500!~sec pre-pulse (inset). As in Fig. 2, the amplitude of the pre-pulse was set equal to 95% of the threshold current for a 2 0 p fiber at 0.25". The fibers located close to the electrode (Xt0.25") had a higher chreshold than the fibers lying at an intermediate distance from the electrode (0.25mm