Can the human lumbar posterior columns be stimulated by transcutaneous spinal cord stimulation? A modeling study

Abstract

Stimulation of different spinal cord segments in humans is a widely developed clinical practice for modification of pain, altered sensation, and movement. The human lumbar cord has become a target for modification of motor control by epidural and, more recently, by transcutaneous spinal cord stimulation. Posterior columns of the lumbar spinal cord represent a vertical system of axons and when activated can add other inputs to the motor control of the spinal cord than stimulated posterior roots. We used a detailed three-dimensional volume conductor model of the torso and the McIntyre-Richard-Grill axon model to calculate the thresholds of axons within the posterior columns in response to transcutaneous lumbar spinal cord stimulation. Superficially located large-diameter posterior column fibers with multiple collaterals have a threshold of 45.4 V, three times higher than posterior root fibers (14.1 V). With the stimulation strength needed to activate posterior column axons, posterior root fibers of large and small diameters as well as anterior root fibers are coactivated. The reported results inform on these threshold differences, when stimulation is applied to the posterior structures of the lumbar cord at intensities above the threshold of large-diameter posterior root fibers.

Figure 1

Information on the volume conductor model and positions of simulated fibers. (a) Sketch of posterior roots (1) and anterior roots (2) joining to form the spinal nerves (3), and of the posterior columns (4) in relation to the spinal cord and the vertebrae. (b) Transverse section of the model with compartments of different electrical conductivities as well as surface electrodes. (c) Entry (and exit) levels of simulated posterior and anterior root fibers, respectively, marked by arrows. Reference center of the inferior-to-superior axis is given by the center of the stimulation electrode. (d) Section of the spinal cord consisting of white and grey matter with some of the positions of simulated posterior column fibers indicated.

Figure 2

Dependence of the excitation threshold of posterior column fibers on the fiber position. Anteroposterior depths within the midsagittal plane studied were 50, 150, 300, 500, 1000, 1500 and 2000 μm and mediolateral positions were 0, 1000 and 2000 μm at 50 μm depth within the white matter, cf. figure 1(d). The posterior column fibers were modeled as straight fibers of 11.5 μm diameter.

Figure 3

Stimulation effect evaluated along sensory structures and motor fibers. (a) Extracellular potential V^e along selected target fibers generated by transcutaneous spinal cord stimulation at −1 V. Posterior root (PR) and anterior root (AR) fibers enter and exit the spinal cord at the central level of the stimulation electrode, respectively. The posterior column (Pcol) fiber is located medially and superficially in the white matter. The abscissa is the distance along the fiber trajectories from the level of the center of the stimulation electrode. The dashed arrow shows the site of action potential initiation of the AR fiber. Anatomical relations of the PR and AR fiber are illustrated below the abscissa. (b) Activating functions corresponding to cases in (a). (c) Enlarged view of the box in (a). Arrows indicate the lowest threshold sites of the PR and Pcol fiber, respectively. (d) Top view of the trajectories of the AR and PR fibers and of the simulated Pcol fiber location (x).