Cortical Remapping Diffusion Lab (2D)

Infarct

Infarct radius 2.2 mm

Rehabilitation

Training intensity Moderate

Plasticity rate η 0.60

Lateral spread D 0.030 mm²/day

Recovery

Map recovered

100%

Dead tissue

Centroid shift

0.0 mm

Rehab day

How it works

This is the 2D sibling of the 3D cortical remapping model, and it solves recruitment differently on purpose. The 3D version assigns each peri-infarct neuron a recruitment rate from an assumed exponential falloff with distance to the infarct border, exp(−r/λ). Real cortex doesn't know its own distance to a lesion — recruitment signal actually has to propagate through the lateral cortico-cortical connections that link neighbouring cortical columns. So here the falloff is not assumed: it emerges from solving a genuine 2D reaction-diffusion PDE for the synaptic weight field w(x,y,t) across a 2D grid of the cortical patch, by explicit finite differences (FTCS) every frame:

∂w/∂t = D·∇²w  +  η·I·a(x,y)·(1 − w)  −  δ·w

D    = lateral diffusion coefficient (cortico-cortical spread)
a(x,y) = local baseline hand-relevance (Gaussian bump)
I    = training intensity (reps/day), η = plasticity rate
δ    = passive synaptic decay
Dead cells: zero-flux boundary — no diffusion in or out

The (1 − w) term makes each cell saturate smoothly toward a self-consistent steady state w* = ηIa/(ηIa + δ) instead of being hard-clamped, and the ∇²w term lets strongly-recruited peri-infarct cells actively pull their still-weak neighbours upward — exactly the lateral-spread mechanism thought to underlie the expanding "penumbra" of use-dependent reorganization seen on serial fMRI/TMS mapping after stroke. Dead (infarcted) cells act as insulating boundaries: no signal diffuses through the lesion core itself, only around it.

Infarct radius / Trigger infarct — sets and detonates the ischemic core; dead cells are a diffusion barrier and never recover.
Training intensity / Plasticity rate η — scale the local reaction (recruitment) source term, same roles as the 3D model.
Lateral spread D — new here: how far a recruitment signal diffuses per day through surviving tissue. D = 0 collapses to purely local (no-neighbour) recruitment; higher D lets a well-trained patch "recruit outward" into cortex that isn't itself receiving much direct drive.
Map recovered / Centroid shift — same read-outs as the 3D sibling, computed from this independently-solved 2D field.

Day 0 · pre-stroke baseline

Strong hand representation Low / unrecruited activity Dead (infarcted) tissue