Difference between revisions of "Talk:Body fat excess"
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''Work in progress'' | ''Work in progress'' | ||
=== Body fat in the healthy reference population === | === Body fat in the healthy reference population - an alternative route === | ||
:::: [[Lean body mass]] of an individual (object), ''M''<sub>L</sub> [kg/x], is the fat-free body mass, and is thus defined as ''M''<sub>L</sub> <big>≝</big> ''M''-''M''<sub>F</sub>, | :::: [[Lean body mass]] of an individual (object), ''M''<sub>L</sub> [kg/x], is the fat-free body mass, and is thus defined as ''M''<sub>L</sub> <big>≝</big> ''M''-''M''<sub>F</sub>, | ||
<big>'''Eq. | <big>'''Eq. 12''': ''M'' <big>≝</big> ''M''<sub>L</sub> + ''M''<sub>F</sub></big> | ||
:::: In turn, ''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. | :::: In turn, ''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. 2). 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>, which . Thus Eq. 12 and 2 combined yield the definition for excess body mass, | ||
<big>'''Eq. #4''': ''M''<sub>E</sub> <big>≝</big> ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> | <big>'''Eq. #4''': ''M''<sub>E</sub> <big>≝</big> ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> | ||
:::: Inserting Eq. #4 into Eq. | :::: Inserting Eq. #4 into Eq. 12, | ||
<big>'''Eq. #5''': ''M'' = ''M''° + ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> | <big>'''Eq. #5''': ''M'' = ''M''° + ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> |
Revision as of 14:02, 17 January 2020
Work in progress
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.