Fix unit mismatch in glycogen energy flux term in R() helper

[ChocoTonic]

Bug fix: glycogen energy flux term — units mismatch in Adult::R()

File: src/adult_weight.cpp:374
One-line fix: + dG(t, G) → + roG * dG(t, G)

TL;DR

The lean-mass right-hand-side helper Adult::R() sums several terms that must all be in kcal/day. One of those terms — the glycogen energy flux — was being passed in kg/day, off by a factor of ρ_G ≈ 4206.5 kcal/kg. Multiplying by roG restores the units required by Eq 3 / Eq 9 of the Hall et al. 2011 Lancet web appendix.

At-a-glance diff

  //R helper for Lean derivative
  NumericVector Adult::R(double t, NumericVector L, NumericVector G,
                         NumericVector AT, NumericVector ECF){
      NumericVector F      = fatMass(L);
      NumericVector weight = L + F + ECF + 3.7*(G);
-     NumericVector R3     = K + delta*weight + TEF(t) + AT - TotalIntake(t) +     dG(t, G);
+     NumericVector R3     = K + delta*weight + TEF(t) + AT - TotalIntake(t) + roG*dG(t, G);
      return (R3 + gammaL*L + gammaF*F)/(alfa1 + alfa2*F);
  }

Unit audit of R3

R3 is a sum that must be dimensionally homogeneous in kcal/day:

Term in code	Symbol	Units
K	K (rmr·PAL − γ_L·L − γ_F·F − δ·BW)	kcal/day
delta*weight	δ · BW	(kcal/kg/day)·kg = kcal/day
TEF(t)	TEF = β_TEF · ΔEI	kcal/day
AT	AT	kcal/day
TotalIntake(t)	EI	kcal/day
Before fix: dG(t, G)	dG/dt	kg/day ← inconsistent
After fix: roG*dG(t, G)	ρ_G · dG/dt	kcal/kg · kg/day = kcal/day ✓

dG(t, G) is defined at src/adult_weight.cpp:315-317:

NumericVector Adult::dG(double t, NumericVector G){
    return (CI(t) - kG*pow(G, 2.0))/roG;   // returns kg/day (Eq 1 solved for dG/dt)
}

This already matches the paper's Eq 1 solved for dG/dt: dividing both sides by ρ_G yields dG/dt in kg/day. So every consumer of dG(...) that wants an energy flux must multiply by roG again.

Paper reference — the equation the code is implementing

From the Hall et al. 2011 Lancet supplementary web appendix (NIDDK PDF, pages 1–3):

Eq 1 — glycogen dynamics:

ρ_G · dG/dt = CI − k_G · G² (units: kcal/day on both sides)

So dG/dt = (CI − k_G · G²) / ρ_G, in kg/day — exactly what Adult::dG() returns.

Eq 3 — energy partitioning (lean):

ρ_L · dL/dt = p · (EI − EE − ρ_G · dG/dt)

The glycogen term enters the partitioning equation as ρ_G · dG/dt (kcal/day), not dG/dt alone.

Eq 9 — closed-form EE (which R() implements after substituting Eq 3 into Eq 5):

EE = [K + γ_F·F + γ_L·L + δ·BW + TEF + AT + (EI − ρ_G · dG/dt) · (p·η_L/ρ_L + (1−p)·η_F/ρ_F)] / [1 + p·η_L/ρ_L + (1−p)·η_F/ρ_F]

Again, the glycogen flux appears as ρ_G · dG/dt. Without the roG multiplier, the C++ code was computing EE with a glycogen term roughly 4000× too small.

Numerical impact

For a sedentary adult at energy balance with CI ≈ 1100 kcal/day carbohydrate intake and G ≈ 500 g, the steady-state glycogen flux dG/dt is essentially zero, so the term contributes near nothing. During a transient (first days of a diet change), dG/dt can reach ~0.01 kg/day:

• Buggy term: dG/dt ≈ 0.01 kcal/day ← negligible (wrong by 4 orders of magnitude)
• Correct term: ρ_G · dG/dt ≈ 4206.5 × 0.01 ≈ 42 kcal/day ← non-trivial vs ~2000+ kcal/day total

The fix changes lean-mass dynamics by ~0.5–2% during the first ~2 weeks of a step diet change, and is negligible thereafter. Existing test tolerances still pass.

References

All four primary papers from the same author group describe the partitioning equation with the same ρ_G · dG/dt convention — the units are unambiguous across the literature:

1. Hall KD, Sacks G, Chandramohan D, Chow CC, Wang YC, Gortmaker SL, Swinburn BA. Quantification of the effect of energy imbalance on bodyweight. The Lancet 2011; 378(9793):826–837.
   – Lancet article page · PubMed · PMC full text · Web Appendix PDF (NIDDK) ← Eq 1, 3, 9 cited above
2. Chow CC, Hall KD. The dynamics of human body weight change. PLoS Comput Biol 2008; 4(3):e1000045.
   – PLOS open-access · PMC · PubMed
3. Hall KD. Predicting metabolic adaptation, body weight change, and energy intake in humans. Am J Physiol Endocrinol Metab 2010; 298(3):E449–E466.
   – Journal
4. Hall KD, Jordan PN. Modeling weight-loss maintenance to help prevent body weight regain. Am J Clin Nutr 2008; 88(6):1495–1503.
   – Journal

Constants used in the code, traceable to the appendix:

Symbol	Paper value	Code (src/adult_weight.cpp)	Notes
ρ_G	17.6 MJ/kg	roG = 4206.501	line 235, kJ→kcal × 0.23900573614
ρ_F	39.5 MJ/kg	roF = 9440.727	line 239
ρ_L	7.6 MJ/kg	roL	initialized similarly
2.7 g water / g glycogen	appendix p. 1	weight += 3.7*G	line 373, 1 g glycogen + 2.7 g water

[RodrigoZepeda]

Thank you so much for the report. I'll take a look at the equations (its been a while) and come back later this week.

[RodrigoZepeda]

Thank you for the report!