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Substrate oxidation equations

Source: R/utils.R
substrate_oxidation.Rd

Calculate fat and carbohydrate oxidation from VO2 and VCO2 using different stoichiometric equations.

Usage

substrate_oxidation(
  VO2,
  VCO2,
  author,
  VO2max = NULL,
  phase = c("exercise", "rest"),
  energy_equivalents = c("classic", "source")
)

Arguments

VO2

oxygen consumption in ml/min (scalar or vector)

VCO2

carbon dioxide production in ml/min (same length as VO2)

author

equation set: "Frayn", "Jeukendrup", or "Peronnet"

VO2max

maximum oxygen uptake in ml/min (required for Jeukendrup during exercise)

phase

"exercise" (default) or "rest". Only changes "Jeukendrup".

energy_equivalents

kcal per g of CHO and FAT used for `Kcal`: "classic" (default, 4 and 9) or "source" (values of the equation's source, see Details).

Value

Named list with CHO (g/min), FAT (g/min), Kcal (kcal/min)

Details

Rule: a coefficient printed in the source is used as printed; a derived coefficient is used only where the source prints no equation (SPEC 19).

**Frayn (1983)** (J Appl Physiol 55: 628-634, eqs. 5 and 6, n = 0), as printed: CHO = 4.55 VCO2 - 3.21 VO2, FAT = 1.67 VO2 - 1.67 VCO2. Deriving them from his Table 1 constants (glucose 0.746/0.746, fat 2.03/1.43 L/g) gives 4.535/3.195 and 1.667/1.667; this is only a cross-check in the tests.

**Peronnet & Massicotte (1991)** (Can J Sport Sci 16: 23-29) print no equations. The package derives them from the O2/CO2 constants of their Table 1 (glucose 0.7455/0.7426, fatty acid 2.0092/1.4136 L/g) by solving VO2 = 0.7455 CHO + 2.0092 FAT and VCO2 = 0.7426 CHO + 1.4136 FAT for CHO and FAT: CHO = 4.58519 VCO2 - 3.22597 VO2, FAT = 1.69469 VO2 - 1.70130 VCO2. Up to v0.2.0 the rounded 4.585 / 3.2255 / 1.6946 / 1.7012 were used (SPEC 19, finding 6).

**Jeukendrup & Wallis (2005)** (Int J Sports Med 26 Suppl 1: S28-S37), with the coefficients printed in their Table 5:

  • below 50 % VO2max (40-50 % set): CHO = 4.344 VCO2 - 3.061 VO2;

  • at or above 50 % VO2max (50-75 % set): CHO = 4.210 VCO2 - 2.962 VO2;

  • FAT = 1.695 VO2 - 1.701 VCO2 in both.

With `phase = "rest"` there is no printed equation: Jeukendrup & Wallis propose none. As a package decision (pure glucose, no glycogen use at rest), the pair is derived from the O2/CO2 constants of their Table 4 (glucose 0.7455/0.7426, fatty acid 2.0092/1.4136 L/g) by solving the 2x2 system: CHO = 4.58519 VCO2 - 3.22597 VO2, FAT = 1.69469 VO2 - 1.70130 VCO2. The same derivation with 50/50 and 20/80 glucose/glycogen reproduces the Table 5 coefficients within 0.005 and is kept as a cross-check in the tests.

The Table 5 sets are defined for 40-75 % VO2max only. Below 40 % the 40-50 % set and above 75 % the 50-75 % set are extrapolated; [calculate_vars()] warns when an exercise step falls outside the range (SPEC 3, 9.5). Resting values (`phase = "rest"`) never trigger that warning.

**Energy equivalents** (`Kcal = CHO * e_cho + FAT * e_fat`, SPEC 19, finding 1):

  • "classic": 4 kcal/g CHO and 9 kcal/g FAT for every equation (v0.2.0). Default in 0.2.x; the default will change to "source" in 0.3.0.

  • "source", `author = "Peronnet"`: glucose 3.8683 and fat 9.7460 kcal/g (Peronnet & Massicotte 1991, Table 1).

  • "source", `author = "Frayn"`: Frayn (1983, p. 632) gives no energy equivalents; as a package decision the Peronnet & Massicotte values are used.

  • "source", `author = "Jeukendrup"`: Jeukendrup & Wallis (2005, Table 5), CHO 3.95 kcal/g below 50 % VO2max (40-50 % set) and 4.07 kcal/g at or above 50 % (50-75 % set), fat 9.75 kcal/g. At rest (`phase = "rest"`, pure glucose pair, package decision) the Peronnet & Massicotte glucose and fat values are used, because they are the constants of that pair. `Kcal` jumps at 50 % VO2max with the CHO value.