Difference between revisions of "Talk:Body fat excess"
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=== Body fat in the healthy reference population === | === Body fat in the healthy reference population === | ||
:::: [[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''-'' | :::: [[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. 2''': ''M'' <big>≝</big> ''M''<sub>L</sub> + '' | <big>'''Eq. 2''': ''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''°, | :::: 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''°, | ||
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<big>'''Eq. 3''': ''M'' <big>≝</big> ''M''° + ''M''<sub>E</sub></big> | <big>'''Eq. 3''': ''M'' <big>≝</big> ''M''° + ''M''<sub>E</sub></big> | ||
:::: Excess body mass, ''M''<sub>E</sub>, is due to accumulation of an excess fat mass, '' | :::: 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 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, | ||
<big>'''Eq. 4''': ''M''<sub>E</sub> <big>≝</big> '' | <big>'''Eq. 4''': ''M''<sub>E</sub> <big>≝</big> ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> | ||
:::: Inserting Eq. 4 into Eq. 3, | :::: Inserting Eq. 4 into Eq. 3, | ||
<big>'''Eq. 5''': ''M'' = ''M''° + '' | <big>'''Eq. 5''': ''M'' = ''M''° + ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big> | ||
:::: The fat mass, '' | :::: 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 | ||
<big>'''Eq. 6''': '' | <big>'''Eq. 6''': ''M''<sub>FE</sub> <big>≝</big> ''M''<sub>F</sub> - ''M''°<sub>F</sub></big> | ||
:::: 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''°<sub>L</sub> = ''M''-'' | :::: 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''°<sub>L</sub> = ''M''-''M''°<sub>F</sub>), plus the total body fat mass and the excess lean mass, | ||
<big>'''Eq. 7''': ''M'' = ''M''° - '' | <big>'''Eq. 7''': ''M'' = ''M''° - ''M''°<sub>F</sub> + ''M''<sub>F</sub> + ''M''<sub>LE</sub></big> | ||
:::: Normalization for ''M''° and considering that the [[body mass excess]] is BME=''M''/''M''°-1, | :::: Normalization for ''M''° and considering that the [[body mass excess]] is BME=''M''/''M''°-1, | ||
<big>'''Eq. 8''': BME = '' | <big>'''Eq. 8''': BME = ''M''<sub>F</sub>/''M''° - ''M''°<sub>F</sub>/''M''° + ''M''<sub>LE</sub>/''M''°</big> | ||
:::: The excess lean mass normalized for ''M''° is a function of BME, | :::: The excess lean mass normalized for ''M''° is a function of BME, | ||
<big>'''Eq. 9''': '' | <big>'''Eq. 9''': ''M''<sub>LE</sub>/''M''° = ''f''(BME)</big> | ||
:::: Inserting Eq. 8 and 9 into Eq. 7.2 yields | :::: Inserting Eq. 8 and 9 into Eq. 7.2 yields | ||
<big>'''Eq. 10''': BME = '' | <big>'''Eq. 10''': BME = ''M''<sub>F</sub>/''M''° - ''M''°<sub>F</sub>/''M''° + ''f''(BME)</big> | ||
:::: Solving for the measured variable '' | :::: Solving for the measured variable ''M''<sub>F</sub> normalized for ''M''°, | ||
<big>'''Eq. 11''': '' | <big>'''Eq. 11''': ''M''<sub>F</sub>/''M''° = BME - ''f''(BME) + ''M''°<sub>F</sub>/''M''°</big> | ||
:::: which finally shows the equation derived to plot the normalized body fat mass as a function of BME, | :::: which finally shows the equation derived to plot the normalized body fat mass as a function of BME, | ||
<big>'''Eq. 12''': '' | <big>'''Eq. 12''': ''M''<sub>F</sub>/''M''° = (1-''f'')·BME + ''M''°<sub>F</sub>/''M''°</big> | ||
:::: 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. | :::: 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. |
Revision as of 19:38, 15 January 2020
Work in progress
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.