Difference between revisions of "Talk:Body fat excess"
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=== Body fat in the healthy reference population - a complementary route === | === Body fat in the healthy reference population - a complementary route === | ||
:::: | :::: ''M'' is the sum of the reference mass at a given height and excess body mass, ''M''<sub>E</sub> <big>≝</big> ''M''-''M''°(Eq. 3). Excess body mass, ''M''<sub>E</sub>, is due to accumulation of an excess fat mass, ''M''<sub>FE</sub>, accompanied by a gain of excess lean mass, ''M''<sub>LE</sub>. Inserting ''M''<sub>E</sub> <big>≝</big> ''M''<sub>FE</sub> + ''M''<sub>LE</sub> (Eq. 4) into Eq. 3 and rearranging, | ||
<big>'''Eq. 13''': ''M'' = ''M''° + ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> | <big>'''Eq. 13''': ''M'' = ''M''° + ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> | ||
:::: The fat mass, ''M''<sub>F</sub>, is defined as the sum of the reference fat mass and excess fat mass, ''M''<sub>F</sub> <big>≝</big> ''M''°<sub>F</sub>+''M''<sub>FE, hence | :::: The fat mass, ''M''<sub>F</sub>, is defined as the sum of the reference fat mass and excess fat mass, ''M''<sub>F</sub> <big>≝</big> ''M''°<sub>F</sub>+''M''<sub>FE</sub> (Eq. 5b), hence | ||
<big>'''Eq. 14''': ''M''<sub>FE</sub> <big>≝</big> ''M''<sub>F</sub> - ''M''°<sub>F</sub></big> | <big>'''Eq. 14''': ''M''<sub>FE</sub> <big>≝</big> ''M''<sub>F</sub> - ''M''°<sub>F</sub></big> | ||
:::: Inserting Eq. 14 into Eq. 13 yields body mass as the sum of the reference mass minus reference fat mass (which is the reference lean mass, ''M''°<sub>L</sub> = ''M''-''M''°<sub>F</sub>), plus | :::: Inserting Eq. 14 into Eq. 13 yields body mass as the sum of the reference mass plus the total body fat mass minus the reference fat mass (which is the reference lean mass, ''M''°<sub>L</sub> = ''M''-''M''°<sub>F</sub>; Eq. 5c), plus the excess lean mass, | ||
<big>'''Eq. 15''': ''M'' = ''M''° + ''M''<sub>F</sub> - ''M''°<sub>F</sub> + ''M''<sub>LE</sub></big> | <big>'''Eq. 15''': ''M'' = ''M''° + ''M''<sub>F</sub> - ''M''°<sub>F</sub> + ''M''<sub>LE</sub></big> | ||
:::: Normalization of Eq. 15 for ''M''° and considering that the [[body mass excess]] is BME=''M''/''M''°-1 (Eq. 5a), BFE = (''M''<sub>F</sub>-''M''°<sub>F</sub>)/''M''° (Eq. 5b), and BLE = ''M''<sub>LE</sub | :::: Normalization of Eq. 15 for ''M''° and considering that the [[body mass excess]] is BME=''M''/''M''°-1 (Eq. 5a), BFE = (''M''<sub>F</sub>-''M''°<sub>F</sub>)/''M''° (Eq. 5b), and BLE = ''M''<sub>LE</sub>/''M''° (Eq. 5c), yields Eq. 7 in the form of, | ||
<big>'''Eq. 16''': BME = BFE + BLE</big> | <big>'''Eq. 16''': BME = BFE + BLE</big> | ||
Revision as of 18:51, 17 January 2020
Body fat in the healthy reference population - a complementary route
- M is the sum of the reference mass at a given height and excess body mass, ME ≝ M-M°(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. Inserting ME ≝ MFE + MLE (Eq. 4) into Eq. 3 and rearranging,
Eq. 13: 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 (Eq. 5b), hence
Eq. 14: MFE ≝ MF - M°F
- Inserting Eq. 14 into Eq. 13 yields body mass as the sum of the reference mass plus the total body fat mass minus the reference fat mass (which is the reference lean mass, M°L = M-M°F; Eq. 5c), plus the excess lean mass,
Eq. 15: M = M° + MF - M°F + MLE
- Normalization of Eq. 15 for M° and considering that the body mass excess is BME=M/M°-1 (Eq. 5a), BFE = (MF-M°F)/M° (Eq. 5b), and BLE = MLE/M° (Eq. 5c), yields Eq. 7 in the form of,
Eq. 16: BME = BFE + BLE
- By further normalization of Eq. 16 for BME, we obtain the summation of fFE = BFE/BME (Eq. 9) and fLE = BLE/BME (Eq. 10),
Eq. 17: 1 = fFE + fLE
- where fFE = 0.57 is the slope in Fig. 5b.
- To derive the MLE/MFE ratio (Eq. 12), which is equal to BLE/BFE (Eq. 5b and 5c), Eq. 16 is divided by BFE and rearranged,
Eq. 18: BLE/BFE = BME/BFE - 1
- Eq. 18 is equivalent to Eq. 12, since BME/BFE = 1/fFE (Eq. 9).
