The 3D companion computes each macrophage's local paracrine factor as a direct sum of static Gaussian falloffs from every MSC — a mean-field shortcut, not real diffusion — over a fixed population that never gains or loses cells. This 2D version solves an actual diffusion–decay PDE for the secreted factor across a wound-bed cross-section, and adds continuous fresh-monocyte recruitment from the wound margins, which the 3D model has no equivalent for at all:
∂C/∂t = D∇²C + S·Σ_j source_j − k_deg·C
dP_i/dt = α·C_i·(1 − P_i) − β·(1 + P_i)
recruit rate ∝ inflammation severity (fresh M1 monocytes enter from margin vessels)
C_i is now the field sampled at each macrophage's own grid cell, not a formula evaluated at its coordinates — it lags behind MSC placement the way a real diffusing factor does, and a low diffusivity D visibly leaves cells far from the MSC cluster under-signaled even at high dose. Meanwhile ongoing inflammation keeps recruiting brand-new, fully M1 monocytes from the tissue margins at a rate set by severity — a real feature of active wounds (chemokine-driven monocyte influx) that a fixed-population model cannot represent. The therapy only wins the wound if MSC dose and potency can repolarize incoming cells faster than severity replaces them.
- MSC dose and secretion potency S — how many stem cells are engrafted and how much factor each releases into the field.
- Factor diffusivity D — how fast the secreted factor actually spreads through tissue (real diffusion, not a fixed radius); low D starves macrophages far from the MSC cluster.
- Inflammation severity — drives the rate at which fresh, fully pro-inflammatory (P = −1) monocytes are recruited in from margin vessels — the ongoing challenge the 3D snapshot never has to contend with.
- Baseline reversion β — how fast an unsignaled macrophage already in the wound drifts back toward M1.
- Tissue repair progress integrates the M1/M2 balance over time into a single healing-trajectory number — rising while M2 dominates, stalling or reversing while M1 does — something a single instantaneous phenotype count cannot show.
Real-world relevance: this is why MSC dosing trials track sustained cytokine/phenotype shifts over days, not a single time point — a therapy that wins the local signaling contest only briefly will lose ground again once the diffusible factor decays and severity keeps recruiting new inflammatory cells.