Difference between revisions of "Talk:Body fat excess"
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:::: [[Lean body mass]], ''M''<sub>L</sub> [kg], 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]], ''M''<sub>L</sub> [kg], is the fat-free body mass, and is thus defined as ''M''<sub>L</sub> <big>≝</big> ''M''-''m''<sub>F</sub>, | ||
<big>''M'' <big>≝</big> ''M''<sub>L</sub> + ''m''<sub>F</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''°, | ||
<big>''M'' <big>≝</big> ''M''° + ''M''<sub>E</sub> | <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, ''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, | :::: 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>''M''<sub>E</sub> <big>≝</big> ''m''<sub>FE</sub> + ''m''<sub>LE</sub> | <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>''M'' = ''M''° + ''m''<sub>FE</sub> + ''m''<sub>LE</sub> | <big>'''Eq. 5''': ''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, hence | ||
<big>''m''<sub>FE</sub> <big>≝</big> ''m''<sub>F</sub> - ''m''°<sub>F</sub> | <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''-''m''°<sub>F</sub>), plus the total body fat mass and the excess lean mass, | :::: 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>''M'' = ''M''° - ''m''°<sub>F</sub> + ''m''<sub>F</sub> + ''m''<sub>LE</sub> | <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>BME = ''m''<sub>F</sub>/''M''° - ''m''°<sub>F</sub>/''M''° + ''m''<sub>LE</sub>/''M''° | <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>''m''<sub>LE</sub>/''M''° = ''f''(BME | <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>BME = ''m''<sub>F</sub>/''M''° - ''m''°<sub>F</sub>/''M''° + ''f''(BME | <big>'''Eq. 10''': BME = ''m''<sub>F</sub>/''M''° - ''m''°<sub>F</sub>/''M''° + ''f''(BME)</big> | ||
:::: Solving for the measured variable ''m''<sub>F</sub> normalized for ''M''°, | :::: Solving for the measured variable ''m''<sub>F</sub> normalized for ''M''°, | ||
<big>''m''<sub>F</sub>/''M''° = BME - ''f''(BME) + ''m''°<sub>F</sub>/''M''° | <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>''m''<sub>F</sub>/''M''° = (1-''f'')·BME + ''m''°<sub>F</sub>/''M''° | <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 10:42, 10 January 2020
Work in progress
Body fat in the healthy reference population
- Lean body mass, ML [kg], 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.
