Epidural electrical stimulation of posterior structures of the human lumbosacral cord: 2. quantitative analysis by computer modeling

Objectives: Analysis of the computed recruitment order of an ensemble of ventral and dorsal root fibers should enlighten the relation between the position of a bipolar electrode and the observed order of muscle twitches. Material and methods: Thresholds of selected spinal root fibers are investigated in a two step procedure. First the electric field generated by the electrodes is computed with the Finite Element Method. In the second step the calculated voltage profile along each target neuron is used as input data for a cable model. For every electrode position the electrical excitability is analyzed for 12 large diameter ventral and dorsal root fibers of the second and fourth lumbar and first sacral segment. The predictions of the neural responses of any target fiber are based on the activating function concept and on the more accurate computer simulations of the electrical behavior of all nodes and internodes in the vicinity of the electrode. Results: For epidural dorsal lumbosacral spinal cord stimulation we found the following rules. (i) The recruitment order of the spinal roots is highly related to the cathode level. (ii) Dorsal root fibers have the lowest threshold values, ventral root fibers are more difficult to excite and dorsal columns are not excitable within the clinical range of 10 V. (iii) For a cathode close to the level of the spinal cord entry of a target fiber thresholds are lowest and spike initiation is expected at the border between cerebrospinal fluid and white matter; excitation of L4 roots is not possible with 210 mu s/10 V pulses when cathode is more than 2.2 cm cranial to their entry level (1.5 cm for S1 roots; standard data). (iv) Cathodes positioned (essentially) below the entry level cause spike initiation close to the cathode, in a region where the fibers follow the descending course within the cerebospinal fluid. (v) At rather low stimulation voltage twitches are expected in all investigated lower limb muscles for cathodes below L5 spinal cord level. Conclusions: Our simulations demonstrate a strong relation between electrode position and the order of muscle twitches which is based on the segmental arrangement of innervation of lower limb muscles. The proposed strategy allows the identification of the position of the electrode relative to spinal cord segments.