Talk:Body fat excess
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Body fat in the healthy reference population - an alternative route
- 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. 12: 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. 2). Excess body mass, ME, is due to accumulation of an excess fat mass, MFE, accompanied by a gain of excess lean mass, MLE, which . Thus Eq. 12 and 2 combined yield the definition for excess body mass,
Eq. #4: ME ≝ MFE + MLE
- Inserting Eq. #4 into Eq. 12,
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.