Predicted effects of pulse width programming in spinal cord stimulation: a mathematical modeling study

Abstract

To understand the theoretical effects of pulse width (PW) programming in spinal cord stimulation (SCS), we implemented a mathematical model of electrical fields and neural activation in SCS to gain insight into the effects of PW programming. The computational model was composed of a finite element model for structure and electrical properties, coupled with a nonlinear double-cable axon model to predict nerve excitation for different myelinated fiber sizes. Mathematical modeling suggested that mediolateral lead position may affect chronaxie and rheobase values, as well as predict greater activation of medial dorsal column fibers with increased PW. These modeling results were validated by a companion clinical study. Thus, variable PW programming in SCS appears to have theoretical value, demonstrated by the ability to increase and even 'steer' spatial selectivity of dorsal column fiber recruitment. It is concluded that the computational SCS model is a valuable tool to understand basic mechanisms of nerve fiber excitation modulated by stimulation parameters such as PW and electric fields.

Figures

Fig. 1

Depiction of the mesh of the FEM for the spinal cord and multicontact lead. a Components and structure of model. b Model mesh—only the high density part (middle block) is shown. The mesh was segmented into sections of variable node density: near the contacts (≤300 μm); insulator, dura, and spinal cord (≤750 μm); epidural space (≤3000 μm); and vertebral bone (≤5000 μm)

Fig. 2

Structure of spinal cord model. a Transverse view of spinal cord and location of dorsal column fibers. b Dorsal roots are composed of a mother fiber and bifurcated daughter fibers. The trajectory of the mother fiber was digitized from Struijk 1993. c Three-dimensional view of spinal cord and DR fibers

Fig. 3

a Cross section of spinal cord with grid overlay to quantify the fiber diameter distribution b as a function of distance from midline, parameterized by fiber size [20]

Fig. 4

Analysis method to compute the number of stimulated fiber from lateral versus medial regions. For all fibers recruited by stimulation, medial fibers (MedF) were defined as stimulated fibers located within 600 μm of the spinal cord midline, and lateral fibers (LatF) as stimulated fibers located greater than 600 μm from the midline [32]. Using these definitions, the location of the focus of paresthesia for each PW was estimated by computing the total number of stimulated fibers from the medial (MedF) and lateral (LatF) regions and their ratio (LatF/MedF). Legend shows fiber diameter and corresponding colors. Percentage represents population of the corresponding size fibers out of total population in dorsal column fibers [20]

Fig. 5

Strength-duration curve of DC (11.5 and 8.7 μm diameter) and DR (12.8 and 15.0 μm diameter) fibers. Depending on electrode placement, nerve fibers stimulated at perception threshold might be different and might have different values of chronaxie and rheobase. Fiber sizes were selected to show that the strength-duration curve with different PWs can depend upon fiber diameter

Fig. 6

Stimulated DC fibers segmented by fiber diameter for varied PW and two pulse amplitude intensities (1.4 * Pth, DRth). Along the top of the figure is a graphic reflecting the width and amplitude of the applied stimulation pulse. Below this are the model-generated recruitment contours shown in a transverse slice of the spinal cord. The model contours in each spinal cord slice are segmented by fiber diameter, as shown in the Legend. Below each spinal cord slice is the mediolateral histogram of total number of fibers stimulated for each stimulation pulse

Fig. 7

Effect of PW on paresthesia coverage. a Normalized total paresthesia coverage from 19 patients as a function of pulse width [5]. b Cross-sectional recruited area for each fiber type with different PW. Results are averages of the two stimulation conditions (1.4Pth and DRth)

Fig. 8

Fiber ratio (LatF/MedF) from FEM model was compared to regression line from 6 patient ‘responders’ [5, 34]. Increasing PW in the model resulted in more medial than lateral fiber recruitment, which might be related to the clinical observation of increasing caudal dermatome coverage with larger PW (via lower-lumbar and sacral fiber recruitment located in medial portions of DC)