Body Composition Forecast Methodology

A research-backed thermodynamic model for predicting changes in weight, body fat percentage, and lean body mass.

Overview

Protokl uses a weekly time-series simulation to forecast how your body composition will change over 6 to 12 months based on your selected goal (Muscle Gain, Body Recomposition, or Fat Loss), pace (Slow, Moderate, or Aggressive), and training experience level (Beginner, Intermediate, or Advanced).

The model produces two forecast lines on the body composition charts:

• Continuing Trend — A linear regression on the most recent 14 days of observed data, extrapolated 14 days forward.
• Plan Forecast — The full thermodynamic simulation showing where the plan takes you if followed consistently. Includes a 90% confidence band.

Muscle Gain Rate Model

The maximum rate of muscle gain is governed by training experience. Protokl uses the Alan Aragon model:

The model uses a continuous negative exponential bounded by the genetic ceiling (FFMI = 25 for natural males, 22 for females):

Where L_max is calculated from height using the FFMI ceiling, and k is calibrated to match the Aragon cap for the user's training level.

Calorie Surplus Sizing

The calorie surplus for muscle gain is derived from actual muscle-building capacity, not a blanket percentage of TDEE.

1. Calculate weekly muscle gain from the continuous Aragon/FFMI curve
2. Multiply by 2,500 kcal (energy cost to synthesize 1 lb of muscle tissue)
3. Apply a buffer for metabolic inefficiency (Slow: 10%, Moderate: 30%, Aggressive: 50%)
4. Subtract the synthesis cost from the total surplus — only the remainder can become fat
5. Apply 85% thermodynamic efficiency to the remainder

Fat Loss Rate Model

Alpert Limit

The maximum rate at which the body can mobilize energy from fat stores is approximately 22 kcal per pound of fat mass per day (Alpert, 2005).

Pace selects the fraction of the Alpert maximum: Slow = 50%, Moderate = 70%, Aggressive = 90%.

Forbes P-Ratio and Lean Mass Preservation

The Forbes P-ratio determines what fraction of weight lost comes from lean mass versus fat mass:

Protokl shifts the rate constant c based on training status:

Body Recomposition Model

Body recomposition involves simultaneously gaining muscle and losing fat while keeping total weight approximately stable. Building 1 lb of muscle requires approximately 2,500 kcal, while mobilizing 1 lb of fat yields approximately 3,500 kcal. The rate of recomposition is capped at 50% of the surplus growth rate.

TDEE Adaptation

Obligate Adaptation (Tissue Mass)

Each pound of lean mass costs approximately 14 kcal/day to maintain. Each pound of fat mass costs approximately 2 kcal/day.

Facultative Adaptation (Adaptive Thermogenesis)

TEF Elasticity (Thermic Effect of Food)

Glycogen and Water Transient

The body stores approximately 400g of glycogen, and each gram binds approximately 3g of water, creating acute scale weight swings of 2–5 lbs in the first 1–2 weeks. The model tracks glycogen and water as a separate compartment.

Confidence Band

Thermodynamic Efficiency of Fat Spillage

• Dietary fat to adipose: ~96% efficiency
• Surplus carbohydrates to adipose (de novo lipogenesis): ~75–80% efficiency
• Surplus protein to adipose: ~75% efficiency

For a mixed-macro surplus, the blended efficiency is approximately 85%.

References

1. Aragon, A. — Muscle Gain Rates by Training Status
2. McDonald, L. — What's My Genetic Muscular Potential? (FFMI model)
3. Iraki et al. (2019). Nutrition Recommendations for Bodybuilders in the Off-Season. JISSN, 16(1), 38.
4. Helms et al. (2023). Effect of Small and Large Energy Surpluses. IJSNEM.
5. Alpert, S.S. (2005). A Limit on the Energy Transfer Rate from the Human Fat Store. J. Theoretical Biology, 233(1), 1-14.
6. Hall, K.D. (2007). Body Fat and Fat-Free Mass Inter-Relationships. British J. Nutrition, 97(6), 1059-1063.
7. Helms et al. (2014). Evidence-Based Recommendations for Natural Bodybuilding. JISSN, 11(1), 20.
8. Review of Strategies for Achieving Simultaneous Muscle Mass Gain During Fat Reduction (2024). JEHS.
9. Aragon et al. (2017). ISSN Position Stand: Diets and Body Composition. JISSN, 14, 16.
10. Garthe et al. (2011). Effect of Two Different Weight-Loss Rates. IJSNEM, 21(2), 97-104.
11. Precision Nutrition — Realistic Rates of Fat Loss and Muscle Gain
12. Heymsfield et al. (2014). Weight Loss Composition is One-Fourth Fat-Free Mass. Obesity Reviews, 15(4), 310-321.

This methodology is implemented in Protokl's body composition forecasting engine. The model is deterministic given the input parameters and runs entirely on-device. All projections are estimates based on population-level research and individual results will vary.

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