Figure 1.
Finite element model of the spine and spinal cord.
Sagittal (left), transverse (middle-top), and 3D (right) views of the modeled spine, which consists of 12 vertebrae spaced by disks and a dural sac and spinal cord that traversed the spinal canal. The transverse section of the modeled spine is overlaid with a transverse magnetic resonance image of the spine of Patient 2 (middle-bottom).
Table 1.
Electrical conductivity of tissues represented in the volume conductor model of spinal cord stimulation.
Figure 2.
Placement of model dorsal column (DC) fibers, model dorsal root (DR) fibers, and the stimulation electrode.
(a) The modeled percutaneous array was placed in (b) nine different locations: three extradural locations and six intradural locations. (c) Transverse view of the spinal cord showing the locations of the modeled DC fibers and DR fibers within the dorsomedial white matter. (d) Planar dorsal and lateral views (left) and 3D view (right) illustrating modeled DC fibers and DR fibers.
Table 2.
Spinal cord geometry from individual patientsa.
Figure 3.
Five SCS electrode designs evaluated with the computational model.
(a) Medtronic Models 3776/3876 (left) and 3777/3877 (right) in longitudinal tripolar configurations. (b) St. Jude Medical Penta in two transverse tripolar configurations. (c) A transverse view of a novel percutaneous lead with an azimuthal array of electrodes in a tripolar configuration. Inactive contacts were not represented.
Figure 4.
Reported locations of paresthesias in Patients 1–5.
Paresthesias in each patient (P) were charted based on their oral descriptions at the sensory threshold (IS) and increasing amplitudes until the discomfort threshold (ID) was reached. Dermatome maps were adapted from a free resource on http://www.change-pain.co.uk/.
Figure 5.
Predicting the diameter of dorsal column (DC) fibers activated based on clinical thresholds.
The percentage of MRG model DC fibers (denoted by circles and squares) activated at the sensory (top) and discomfort (bottom) thresholds compared to the percent activation expected (denoted by solid and dashed lines) based on the number of dermatomes reported at the corresponding clinical thresholds (see Methods). The filled shapes indicate the fiber diameters that yielded the smallest percent difference between the former and latter cases.
Figure 6.
Comparing model predictions of stimulation thresholds between MRG and SW models of dorsal column (DC) fibers.
Plotted are distributions of the stimulation threshold currents of DC fibers when the AD-TECH was placed 1 mm above the spinal cord and 1 mm above the dura in the intradural and extradural cases, respectively. The therapeutic range is defined as the stimulation amplitudes between the measured sensory and discomfort thresholds.
Figure 7.
Power efficiency of extradural SCS versus intradural SCS. Average power required to stimulate the dorsal column (DC) fibers in the SCS model of Patient 2.
The shaded black and grey areas encompass the range of stimulation powers calculated over the three extradural electrode locations and six intradural electrode locations, respectively.
Figure 8.
The selectivity of extradural SCS versus intradural SCS in model of Patient 5.
The maximum percentage of dorsal column (DC) fibers activated with no activation of dorsal root (DR) fibers (DC0) when the array was placed in the extradural (top row) and intradural (bottom row) spaces at lateral deviations of 0° (left column), −10° (middle column), and −20° (right column). For comparison, the range of DC0 across all patients is shown below each panel. (b) Curves of the proportion of DC fibers activated versus proportion of DR fibers activated for three different electrode locations along the midline.
Figure 9.
Selective activation of dorsal column (DC) fibers in the low back (L2–L5) dermatomes of Patient 1.
(a) Stimulation threshold current of each of the model DC fibers, split by dermatome (see inset), when the AD-TECH array was placed in the intradural space and laterally displaced 0° (left) and −20° (right) from the midline. The shaded area in the inset illustrates where the Aβ collaterals of the DR fibers were located with respect to DC dermatomes at T8. (b) The same as (a), except for the angular tripole electrode geometry. The locations of the paresthesias at the sensory and discomfort thresholds are denoted by the open black rectangles and filled grey rectangles, respectively.
Figure 10.
Selectivity of five tripolar electrode designs in model of Patient 2.
(a) The percent of dorsal column (DC) fibers activated with no dorsal root (DR) fiber activation (i.e., DC0) when the electrode was placed along the midline, 1 mm above (top) and below (bottom) the spinal cord. DC0 is shown above the spinal cord. For comparison, the range of DC0 across all patients is shown below each panel. (b) Proportion of DC fibers activated versus proportions of the DR fibers activated (i.e., DCX) for three electrode designs in the extradural (left) and intradural (right) cases. The inset shows a close-up of the curves. LT = longitudinal tripolar, TT = transverse tripolar, AT = angular tripolar, and the number after the hyphen indicates the interelectrode spacing in mm.
Figure 11.
The source driving membrane polarization with three different electrode designs.
(a) Examples of the centered second difference of the potentials (Δ2Φ) along two dorsal column (DC) fibers and two dorsal root (DR) fibers. The grey boxes indicate regions where changes in tissue conductivity caused abrupt changes in Δ2Φ. (b) The range of maximum Δ2Φ across across all modeled DC fibers and DR fibers for three electrode configurations. LT = longitudinal tripolar, TT = transverse tripolar, AT = angular tripolar, and the number after the hyphen indicates the interelectrode spacing in mm.