Androgen Deprivation Therapy 2D: Castration-Resistance Model

Hormone Therapy

Suppression dose 80%

Initial resistant clone 1.0%

Sim speed 1.0×

Live Readouts

Testosterone

500 ng/dL

PSA (proxy)

100%

Time on trial

0 wk

Resistant fraction

1.0%

Androgen-dependent cell (AR-driven) Castration-resistant clone

How it works

Androgen deprivation therapy (ADT) removes the testosterone that drives androgen-receptor (AR) signalling in prostate-cancer cells. AR activation saturates with a Michaelis–Menten term:

A(T) = T / (T + Km),  Km ≈ 250 ng/dL

Androgen-dependent (AD) cells need AR signalling above half-maximal to keep growing; below it they regress:

dN_AD/dt = r_max · (2A - 1) · N_AD · (1 - N/K)

A rare androgen-independent (castration-resistant, CR) subclone — expanded AR gene copies, AR splice variants, or a bypass pathway — keeps a slow constant growth rate regardless of testosterone:

dN_CR/dt = r_CR · N_CR · (1 - N/K)

GnRH Agonist (leuprolide-style) first over-stimulates the pituitary, producing a 1–2 week testosterone flare before receptor downregulation suppresses it.
GnRH Antagonist (degarelix-style) blocks the receptor directly — testosterone falls immediately, no flare.
Suppression dose sets how far testosterone is pushed toward the castrate floor (~15 ng/dL).
Continuous vs Intermittent — intermittent ADT lets testosterone recover during scheduled "off" windows once PSA falls, which is thought to slow — not stop — selection for the resistant clone.
PSA here is a live proxy for total AR-driven output: k·(N_AD·A + N_CR·A_CR), where CR cells keep producing a low, T-independent baseline via AR amplification. Watch it fall with therapy, then climb again once the resistant clone dominates — the hallmark of clinical progression to castration-resistant prostate cancer (CRPC).

Note on this 2D adaptation: the original 3D engine's math was re-derived and checked numerically (Node script, not shipped) against the growth-rate sign flip at A=0.5 (T = Km = 250 ng/dL) and the PSA-proxy normalisation at t=0; both were internally consistent, so the equations above are carried over unchanged — this rebuild only replaces the InstancedMesh sphere cluster with a 2D packed-disk cross-section plus a live strip chart of T / PSA / resistant-fraction.

Drag to pan · scroll to zoom the tumor view
Blue = AR-driven cells · Orange = resistant clone

Androgen Deprivation Therapy & Castration Resistance (2D)