Lactase (a brush-border disaccharidase) hydrolyses lactose into absorbable glucose + galactose following saturable Michaelis–Menten kinetics:
dC/dt = -Vmax · C / (Km + C)
Vmax = Vmax₀ · (lactase activity / 100)
The concentration curve C(t) is stepped numerically (Euler integration) across the chosen transit time to get the fraction still undigested when the meal reaches the ileocecal valve. Whatever is left is osmotically active — it pulls water into the colon lumen — and is fermented by anaerobic bacteria:
Lactose + gut bacteria → SCFAs + H₂ + CO₂ (± CH₄)
gas volume ≈ undigested grams × yield(fermentation activity)
- Lactase activity — the genetically-determined, and population-variable, brush-border enzyme level: this single number is the biophysical reason milk tolerance differs so sharply between individuals and ethnic groups.
- Dose & transit time — more substrate or less contact time both push more lactose past the point of saturation and into the colon undigested.
- Fermentation activity — how vigorously the resident colonic microbiota converts the leftover sugar into gas, which (together with osmotic water) produces the classic bloating/cramping/diarrhea of lactose intolerance.
- Particles travelling the tube are colour-coded live from this same model: yellow = intact lactose, green = hydrolysed monosaccharides absorbed in the small intestine, amber → bubbles = undigested sugar fermenting in the colon.