Epidural electrical stimulation (EES) of the lumbosacral spinal cord can re-enable stepping below a spinal cord injury by exciting the intrinsic locomotor circuitry when descending drive from the brain is lost. Two mechanisms combine here:
Recruitment (Henneman's size principle):
I_pool(x) = A · exp(-(x - x_electrode)² / 2σ²), σ ≈ 0.5 + 0.05·A
unit i fires once I_pool exceeds its threshold Tᵢ (small, low-threshold units recruited first)
Current amplitude A and electrode position x set how much depolarizing current reaches the flexor pool (rostral, ≈L2–L4) versus the extensor pool (caudal, ≈L5–S1) — this is the same rostrocaudal recruitment mapping used clinically to steer which muscle groups activate.
Half-center CPG (Matsuoka oscillator), one pair {flexor, extensor}:
τ·ẋᵢ = -xᵢ - β·vᵢ - w·yⱼ + uᵢ
τ'·v̇ᵢ = -vᵢ + yᵢ
yᵢ = max(0, xᵢ) (i,j = flexor,extensor; j is the other neuron)
Each side's tonic drive uᵢ is the sum of a small residual descending drive (set by Injury completeness — 100% = no spared supraspinal input) and the stimulation-evoked drive from recruitment above. Reciprocal inhibition (the −w·yⱼ term) and self-adaptation (vᵢ) make the pair burst in antiphase — the classic half-center explanation (Brown, 1911) for alternating flexor/extensor rhythm, still the working model behind CPG-based locomotor rehabilitation.
- Amplitude / position — control how much of each motor pool is recruited (size principle) and where along the cord the current is centered.
- Frequency — below ≈15 Hz the CPG drive is delivered as discrete pulses (choppy stepping); the 20–50 Hz band used in real EES protocols drives smooth, well-fused alternation; above ≈60 Hz reciprocal inhibition breaks down and both pools co-contract instead of stepping.
- Injury completeness — near 100% (motor-complete injury) the legs stay still without stimulation; lower values leave enough spared drive for some rhythm even at zero amplitude.
This mirrors the mechanism behind published human locomotor-EES trials (Harkema et al. 2011; Angeli et al. 2018; Wagner et al. 2018): the spinal circuitry below the lesion still contains a working step-generator — stimulation supplies the missing excitability to switch it on.