In microgravity, unloaded bone loses mineral through osteoclast-driven resorption — astronauts lose roughly 1–1.5% of hip/spine bone mass per month. That released calcium is filtered by the kidneys, so urinary calcium excretion rises quickly and plateaus within about two weeks:
B(t) = 1 − exp(−k·(1−0.65E)·t/30) bone Ca loss fraction
Ca_u(t)= Ca0 + ΔCa·(1−0.6E)·(1−exp(−t/14)) urinary Ca, mg/day
V = 0.62·F urine volume, L/day (F = fluid intake)
RSR = ([Ca_u/V]·[Ox_u/V]) / (Ksp·c) relative supersaturation, calcium oxalate
E is resistive-exercise adherence (0–1) — the ARED-style loaded exercise used on ISS — which blunts both the resorption rate and the calcium spike. F is daily fluid intake: more urine volume dilutes both calcium and oxalate, cutting the supersaturation product. Potassium citrate (c = 1.9 when on) chelates urinary calcium and raises urine pH, pushing the effective solubility product up and RSR down — a countermeasure studied for exactly this risk.
- RSR < 1 — undersaturated, crystals dissolve faster than they form (low risk).
- 1 ≤ RSR ≤ 2 — metastable supersaturation, slow crystal growth (moderate risk).
- RSR > 2 — spontaneous nucleation and rapid growth (high risk).
Whenever RSR exceeds 1, crystal mass accumulates over the elapsed mission time (dM/dt ∝ max(0, RSR−1)); its volume, and hence the drawn stone's radius, follows from a whewellite density of ≈1.9 mg/mm³. This 2D redraw keeps the same closed-form physiology as the 3D version but renders it as four flat panels instead of a camera-orbited scene: a thinning trabecular-bone grid, a flowing renal-tubule schematic with a growing crystal cluster at the outlet, a risk-zone gauge, and a scrubbable RSR-vs-time timeline.