🧠 Microglia Activation: Dose-Response & Cytokine Field

A Continuous Dose-Response Model of Microglial Activation

The 3D version of this simulation walks through five discrete narrative stages of microglial activation with individually animated cells. This 2D companion instead treats activation as a continuous dynamical system: an injury/pathogen signal drives a Hill-function dose-response curve, activated microglia split into pro-inflammatory (M1) and repair-oriented (M2) fractions, M1 output diffuses across tissue as a cytokine concentration field, and that field damages or spares a grid of neurons in real time — with an anti-inflammatory drug dose acting directly on the M1/M2 balance and cytokine clearance rate.

Dose-response activation, not a switch

Activation A(t) does not jump between three fixed levels. It relaxes toward a Hill-function target set by the current injury signal S: A_target = S^n / (S^n + K^n), with A itself evolving smoothly via dA/dt = k·(A_target − A). This produces realistic behaviors a stepped model cannot: partial activation at moderate signal, hysteresis-like lag when the signal changes quickly, and a graded rather than binary neurotoxicity risk.

M1/M2 polarization balance

Of the activated microglial population, a fraction p is pro-inflammatory (M1) and the rest is repair-oriented (M2). The injury signal pushes p toward M1; the anti-inflammatory drug dose pulls p toward M2 and additionally raises the cytokine clearance rate. The M1:M2 ratio shown live is the same balance clinically targeted by anti-inflammatory and immunomodulatory therapies aimed at this cascade.

Cytokine diffusion field driving real tissue damage

Rather than individual cytokine particles drifting past individual neurons, this model solves a 2D reaction-diffusion equation on a tissue grid: cytokine is produced in proportion to local M1 output, diffuses to neighboring cells, and decays. Neuron health at each grid point falls when local cytokine concentration exceeds a damage threshold, and recovers in proportion to local M2 activity — so chronic, unresolved M1-dominant activation visibly spreads tissue damage outward, while a shift toward M2 lets the field heal.