Talk:Body fat excess
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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.