An acute ankle sprain tears capillaries and raises local capillary pressure, so fluid leaks into the tissue faster than the lymphatics can remove it β that's swelling (edema). Net capillary filtration follows the Starling equation:
Jv = Kf Β· [ (Pc β Pi) β ΟΒ·(Οc β Οi) ]
dV/dt = Jv β LclearΒ·V
- Pc β capillary hydrostatic pressure (elevated by injury, inflammation)
- Pi β interstitial hydrostatic pressure (rises with V and with compression)
- Οc, Οi β plasma / interstitial oncotic (protein) pressure, Ο = reflection coefficient
- Kf β capillary filtration coefficient (permeability Γ surface area)
- Lclear β first-order lymphatic clearance rate of the swollen fluid
Each element of RICE changes a term in this system:
- Ice β cold-induced vasoconstriction cuts Kf and lowers Pc, slamming the filtration tap almost shut.
- Compression β external bandage pressure raises Pi directly, opposing further filtration, and the rhythmic tissue pressure boosts lymphatic pumping (Lclear).
- Elevation β raising the limb above heart level lowers the hydrostatic column feeding Pc and improves venous/lymphatic return, adding to Lclear.
- Rest β not modeled numerically here, but avoiding muscle-pump loading prevents re-injury that would reset Pc upward.
The injury grade shown is a simplified clinical proxy from swelling volume: Grade I (mild, <12 mL) is a stretch with minimal fiber tearing; Grade II (moderate, 12β28 mL) is partial ligament tearing with instability; Grade III (severe, >28 mL) is complete rupture. Watch how aggressive Ice + Compression + Elevation flattens the swelling curve compared to no treatment.
This 2D view is drawn as a side-on cross-section of the lateral ankle: the same Starling-forces ODE as the 3D version drives a swelling "cloud" of dots around the joint, plus a live plot of interstitial volume over the last few simulated hours so you can see the filtration/clearance balance shift as you change the treatment.