Talk:Body fat excess
From Bioblast
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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 β M-MF,
Eq. 2: M β ML + MF
- In turn, M is the sum of the reference mass at a given height and excess body mass, ME β M-MΒ°,
Eq. 3: M β MΒ° + 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 β MFE + MLE
- Inserting Eq. 4 into Eq. 3,
Eq. 5: M = MΒ° + MFE + MLE
- The fat mass, MF, is defined as the sum of the reference fat mass and excess fat mass, MF β MΒ°F+MFE, hence
Eq. 6: MFE β MF - MΒ°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, MΒ°L = M-MΒ°F), plus the total body fat mass and the excess lean mass,
Eq. 7: M = MΒ° - MΒ°F + MF + MLE
- Normalization for MΒ° and considering that the body mass excess is BME=M/MΒ°-1,
Eq. 8: BME = MF/MΒ° - MΒ°F/MΒ° + MLE/MΒ°
- The excess lean mass normalized for MΒ° is a function of BME,
Eq. 9: MLE/MΒ° = f(BME)
- Inserting Eq. 8 and 9 into Eq. 7.2 yields
Eq. 10: BME = MF/MΒ° - MΒ°F/MΒ° + f(BME)
- Solving for the measured variable MF normalized for MΒ°,
Eq. 11: MF/MΒ° = BME - f(BME) + MΒ°F/MΒ°
- which finally shows the equation derived to plot the normalized body fat mass as a function of BME,
Eq. 12: MF/MΒ° = (1-f)Β·BME + MΒ°F/MΒ°
- 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.