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Talk:Body fat excess

From Bioblast
Revision as of 08:41, 15 January 2020 by Gnaiger Erich (talk | contribs)
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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 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.