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Which root does a contact reach? Epidural stimulation of the cervical cord, simulated

A stimulation lead acts through the nerve roots it reaches, and each root drives its own muscles. This model computes which root each contact combination recruits first, and at what current.

Service: Simulation-derived visualization and modelling studies

The fifth cervical vertebra cut across, seen from above and behind, with labels. In the spinal canal the cut shows fat, dura, fluid and cord, coloured by the electric potential, brightest under one contact of a see-through paddle. Behind the cut the canal curves away between cut-open vertebrae, and the rootlets of three nerve roots are coloured by the current at which they respond. Axes, a scale bar, two colour scales and a front view of the paddle with the active contact are drawn in.
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Overview

Epidural stimulation of the cervical cord is being studied as a way to improve arm and hand movement after spinal cord injury or stroke. It is thought to act through the nerve roots: a contact excites the sensory fibres of a root, these drive the motoneurons of that segment, and each segment serves its own, overlapping muscles. So the question for a lead is which root a contact reaches first, and how far the current can rise before the neighbour answers.

This sample computes that. Its anatomy comes from published measurements: a cord that widens through the cervical enlargement, a canal that follows the curve of the neck, vertebrae, and the rootlets of C5 to C8. A finite-element model gives the field of a 16-contact paddle, and nerve-fibre models turn it into the current each fibre needs.

The result is a map from contact combinations to roots. Under Results it stands beside what surgeons measured: the muscles that respond when each root is stimulated. That is what such a model is for: comparing leads, positions and contact combinations for a target movement before anything is built.

The model stops at the fibres. It does not predict a movement, and its numbers describe this generic anatomy, not a patient. Another lead, level or target is a rerun, not a redraw.

Results

The spinal cord seen from behind, four times side by side, each with the paddle’s 16 contacts and four pairs of nerve roots. In each, a different contact of the left column is ringed as cathode, and the rootlets on the left are coloured by the current at which they respond. The brightest rootlets lie next to the ringed contact and move down from the first picture to the fourth.
Rootlet by rootlet: the current at which the first fibre of each rootlet fires (0.3 to 7.9 mA; brighter fires earlier, and everything from 2.5 mA up has the darkest colour), for four single cathodes down the left column of the paddle. The response follows the cathode from root to root. Only the left side was simulated. Open the picture at full size
A table in two parts that share four columns, the roots C5 to C8. In the upper part, one row per root shows which contacts are used and, as coloured discs with numbers, the current at which half of each root’s fibres respond. In the lower part, one row per muscle shows discs whose size is the share of responses when that root was stimulated in surgery, with the muscle’s action beside it.
Two layers that share the roots as their columns. Top, computed: for each root the contact combination, of twelve tried, that reaches it with the widest margin, and the current at which half of each root’s afferent fibres respond. A single cathode reaches C5 alone: half of its afferents respond at 0.46 mA, the next root at 2.6 times that current. For C6 and C7 no single cathode gives more than 1.5 times; a bipole, with the anode on the next contact down, gives 2.2 and 2.0 times. C8 stays the hard one: at best 1.3 times, so here C7 follows closely. Bottom, measured by others: the relative response of each muscle when the root itself was stimulated during surgery (Schirmer et al. 2011, Table 3). The step from a recruited root to these muscles is the published account of how the stimulation acts (Greiner et al. 2021); the model does not compute it. Open the picture at full size

Mesh and render

The model as a finite-element mesh. On the cut, the cells of each tissue, small in the canal and under the paddle, larger in the vertebra, whose edge runs through them; cord and paddle are drawn as wireframes.

Mesh

The same view with the result. In the canal the cut is coloured by the computed potential, the rootlets by the current at which their first fibre fires.

Result

Both pictures are drawn from the simulation files; the cut passes through the active contact and the fifth cervical vertebra. Dura and vertebrae are cut away on the viewer’s side, and the paddle is drawn see-through so its 16 contacts show.

Method note

Computed, not illustrated.

Modelled
  • Cervical cord C5 to C8 with each segment’s published diameters, grey matter, cerebrospinal fluid, dura and epidural fat, in a canal bent to the natural curve of the neck
  • Vertebrae C3 to T2 as bone. Their shape is typical, set by eye, not measured
  • Rootlets and roots after published cadaver measurements; their courses are designed
  • A generic 16-contact paddle of my own design, not a model of any product
  • Published tissue conductivities; 150 nerve fibres on the left side, with assumed diameters
Computed
  • The electric field of the paddle’s contacts, by the finite element method (1.32 million tetrahedra)
  • The current at which each fibre fires, for twelve contact combinations, with nerve-fibre models in NEURON run through a modified PyNS
  • For each root, the combination that reaches it with the widest margin before a neighbour follows
Artistic choices
  • Cuts and cut-aways, the see-through paddle, cut bone in one flat colour
  • How rootlets join their root, and the ganglion’s swelling: drawn, not modelled
  • Colour scales, camera and lighting
Checked
  • Solver verified against an analytical benchmark (layered sphere, also with bone represented as the vertebrae are): resistance within 0.3 %.
  • Anisotropic conductivity verified with a manufactured solution: convergence order 2.99, where 3 is expected.
  • Mesh convergence confirmed for this model on three meshes: impedance within 0.04 %, fibre thresholds within 0.3 %. Currents through cathode and anode balance to one part in a billion.
Tools
Python, gmsh, DOLFINx, NEURON, PyNS (modified), Blender
References

Available for this kind of work.

Typical timeline
8–12 weeks, scoped individually
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