Talk:Body fat excess
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Body fat in the healthy reference population
- Lean body mass, ML [kg], is the fat-free body mass, and is thus defined as ML β M-mF,
M β ML + mF (Eq. 2)
- In turn, M is the sum of the reference mass at a given height and excess body mass, ME β M-MΒ°,
M β MΒ° + ME (Eq. 3)
- 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,
ME β mFE + mLE (Eq. 4)
- Inserting Eq. 4 into Eq. 3,
M = MΒ° + mFE + mLE (Eq. 5)
- The fat mass, mF, is defined as the sum of the reference fat mass and excess fat mass, mF β mΒ°F+mFE, hence
mFE β mF - mΒ°F (Eq. 6)
- 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,
M = MΒ° - mΒ°F + mF + mLE (Eq. 7)
- Normalization for MΒ° and considering that the body mass excess is BME=M/MΒ°-1,
BME = mF/MΒ° - mΒ°F/MΒ° + mLE/MΒ° (Eq. 8)
- The excess lean mass normalized for MΒ° is a function of BME,
mLE/MΒ° = f(BME) (Eq. 9)
- Inserting Eq. 8 and 9 into Eq. 7.2 yields
BME = mF/MΒ° - mΒ°F/MΒ° + f(BME) (Eq. 10)
- Solving for the measured variable mF normalized for MΒ°,
mF/MΒ° = BME - f(BME) + mΒ°F/MΒ° (Eq. 11)
- which finally shows the equation derived to plot the normalized body fat mass as a function of BME,
mF/MΒ° = (1-f)Β·BME + mΒ°F/MΒ° (Eq. 12)
- 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.