Talk:Body fat excess
From Bioblast
Revision as of 20:38, 15 January 2020 by Gnaiger Erich (talk | contribs)
Work in progress
Body fat in the healthy reference population
- Lean body mass of an individual (object), ML [kg/x], is the fat-free body mass, and is thus defined as ML ≝ M-MF,
Eq. 2: M ≝ ML + MF
- In turn, M is the sum of the reference mass at a given height and excess body mass, ME ≝ M-M°,
Eq. 3: M ≝ M° + ME
- Excess body mass, ME, is due to accumulation of an excess fat mass, MFE, accompanied by a gain of excess lean mass, MLE, which includes increased bone mineral density, added bone mass and muscle mass due to the mechanical 'weight-lifting effect' (Iwaniec 2016 J Endocrinol). Thus Eq. 2 and 3 combined yield the definition for excess body mass,
Eq. 4: ME ≝ MFE + MLE
- Inserting Eq. 4 into Eq. 3,
Eq. 5: M = M° + MFE + MLE
- The fat mass, MF, is defined as the sum of the reference fat mass and excess fat mass, MF ≝ M°F+MFE, hence
Eq. 6: MFE ≝ MF - M°F
- Inserting Eq. 6 into Eq. 5 yields body mass as the sum of the reference mass minus reference fat mass (which is the reference lean mass, M°L = M-M°F), plus the total body fat mass and the excess lean mass,
Eq. 7: M = M° - M°F + MF + MLE
- Normalization for M° and considering that the body mass excess is BME=M/M°-1,
Eq. 8: BME = MF/M° - M°F/M° + MLE/M°
- The excess lean mass normalized for M° is a function of BME,
Eq. 9: MLE/M° = f(BME)
- Inserting Eq. 8 and 9 into Eq. 7.2 yields
Eq. 10: BME = MF/M° - M°F/M° + f(BME)
- Solving for the measured variable MF normalized for M°,
Eq. 11: MF/M° = BME - f(BME) + M°F/M°
- which finally shows the equation derived to plot the normalized body fat mass as a function of BME,
Eq. 12: MF/M° = (1-f)·BME + M°F/M°
- In this plot (Fig. 1), the slope equals (1-f), and the intercept is the fat mass normalized for the reference mass at a given height in the HRP.