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models.glycogen

models.glycogen

Fast water compartments: glycogen-bound and sodium-associated water.

These two states exist to explain the difference between what you weigh and what you are. Both respond within days to dietary inputs, both move the scale by kilograms, and neither has anything to do with fat.

Glycogen. Stored carbohydrate is held with roughly three grams of water per gram of glycogen. Total stores range over ~300-600 g, so a swing between carbohydrate restriction and repletion moves 200 g of glycogen plus 600 g of water: nearly a kilogram of scale weight with zero change in tissue. This single mechanism explains the notorious first-week “success” of low-carbohydrate diets and the equally notorious overnight “relapse” after one high-carbohydrate meal.

Sodium. Extracellular fluid volume tracks sodium load on a one-to-two day timescale. Frequently a larger source of scale noise than carbohydrate, and almost never logged, which is why an unlogged salty meal is the single most common explanation for an inexplicable overnight gain.

Both are modeled as first-order lags toward an input-proportional steady state. Deviations are measured from the subject’s habitual (pre-diet) intake, the episode’s carb_ref_g/sodium_ref_mg (see ~wdm.io.Episode), so a diet that starts from ordinary eating starts both states at zero, and the drain of glycogen water as carbohydrate drops is predicted rather than absorbed.

Functions

Name	Description
glycogen_rate	Time derivative of the glycogen-water compartment, kg/day.
glycogen_steady_state	Equilibrium glycogen-complex deviation for today’s carbohydrate, kg.
sodium_rate	Time derivative of the sodium-water compartment, kg/day.
sodium_steady_state	Equilibrium sodium-associated water deviation, kg.

glycogen_rate

models.glycogen.glycogen_rate(x, u, p)

Time derivative of the glycogen-water compartment, kg/day.

glycogen_steady_state

models.glycogen.glycogen_steady_state(u, p)

Equilibrium glycogen-complex deviation for today’s carbohydrate, kg.

sodium_rate

models.glycogen.sodium_rate(x, u, p)

Time derivative of the sodium-water compartment, kg/day.

sodium_steady_state

models.glycogen.sodium_steady_state(u, p)

Equilibrium sodium-associated water deviation, kg.

Identically zero when no sodium column is supplied, since sodium_dev_mg is then zero for every day and the state decays to and stays at zero. The compartment costs nothing when unused, which is why it is always present in the state vector rather than switched in and out.