Excitation of dorsal root fibers in spinal cord stimulation: a theoretical study

Abstract

In epidural spinal cord stimulation it is likely that not only dorsal column fibers are activated, but that dorsal root fibers will be involved as well. In this investigation a volume conductor model of the spinal cord was used and dorsal root fibers were modeled by an electrical network including fiber excitation. The effects of varying some geometrical fiber characteristics, as well as the influence of the dorsal cerebrospinal fluid layer and the electrode configuration on the threshold stimulus for their excitation, were assessed. The threshold values were compared with those of dorsal column fibers. The results of this modeling study predict that, besides the well known influence of fiber diameter, the curvature of the dorsal root fibers and the angle between these fibers and the spinal cord axis were of major influence on their threshold values. Because of these effects, threshold stimuli of dorsal root fibers were relatively low as compared to dorsal column fibers. Excitation of the dorsal root fibers occurred near the entry point of the fibers.

Computer modelling of spinal cord stimulation and its contribution to therapeutic efficacy

“…Struijk et al 14,18 developed 3D models with a similar transverse composition as the 2D model by Rusinko et al 12 Thè surrounding' layer of their models represents all anatomical structures peripheral to the spinal canal, such as vertebral bone, dorsal muscles, thorax, fat and skin. Spinal roots are not included in their models, whereas vertebral bone and a dura mater at the dorsal side are only incorporated in later model versions, 15,19 as shown in Figure 2A.…”

“…Each element is de®ned by its conductivity and thus represents (part of) an anatomical structure. All 3D models are composed of layers along the spinal axis and each layer consists of wedges 14 or bricks 15,18,19 with a node on each corner (Figure 2A). Various shapes, including curved elements needing more nodes for their de®nition, can be implemented when a ®nite element approach is used 11,12,16,17 (Figure 1).…”

“…Coburn and Sin 11,16,17 represented each cathode or anode by a constant current source (+1 mA) con®ned to a single node of the mesh. Struijk et al 14,15,18,19 used electrode contacts with a rectangular shape and a realistic size, de®ned as constant voltage sources (1 Volt between anode and cathode). A point source is not a good electrode model, because the potential distribution in the DCs is in¯uenced by the size of the electrode contact, especially when the distance between the contact and the spinal cord is small.…”

“…Calculation of the potential ®eld Numerical methods applied to calculate the potentials at all nodes of a mesh are steady-state solutions, ie the boundary conditions such as voltage and current are kept constant. In both the ®nite element method 11,12,17 and the ®nite di erence method 15,18,19 direct discretizations of the Laplace equation are used, resulting in second-order di erences to be solved. Although these methods are basically identical, there are di erences of practical interest.…”

“…As opposed to 3D models, 2D models are inappropriate for a quantitative analysis of current densities and potentials. 11,14,16 When stimulating electrode contacts are modelled as voltage sources, 15,18,19 it should be considered that the boundary of the model is generally a voltage source as well (0 V). In unipolar stimulation this boundary is used as the anode.…”