After a stroke, the hand's cortical representation in primary motor cortex (M1) shrinks. Because the unaffected hand is easier to use, patients default to it — a spiral called learned non-use that starves the affected map of activity. Constraint-Induced Movement Therapy (CIMT) breaks the spiral by restraining the unaffected arm in a mitt and forcing hours of intensive practice with the affected one, driving competitive, use-dependent cortical reorganization (Nudo et al.).
dA/dt = k·Ua·(1 − A) − d·Uu·A
Ua = C · H/8 (forced-use time fraction)
Uu = (1 − C) · (8 − H)/8 (unaffected-hand time fraction)
F = 100 · A^0.7 (saturating function-vs-territory map)
- A — affected-hand territory in M1, normalized to pre-stroke baseline (1.0 = fully restored).
- Mitt constraint C — fraction of the day the unaffected arm is restrained; raising it removes the competing "easy" pathway and reallocates use-time toward the affected limb.
- Forced-use hours H — daily structured practice dose; standard CIMT protocols run ≈ 6 h/day for 10–15 consecutive days.
- Shaping — breaking tasks into small, just-beyond-reach steps with immediate feedback (vs. plain repetition) raises the learning-rate constant k by 40%, matching the outcome gap reported for shaping vs. non-shaping CIMT trials.
- Stroke severity — new in this 2D companion: sets the starting cortical territory A₀ (mild 0.35 / moderate 0.20 / severe 0.08) and the non-use decay constant d, so a more severe infarct both starts lower and erodes faster under continued reliance on the unaffected arm — the same ODE above, just parameterized by initial injury.
- The grid below is a schematic top-down patch of M1 hand cortex: cell color = local synaptic weight, radiating outward from a seed point as A grows.