Difference between revisions of "Body fat excess"
From Bioblast
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:::: 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> | <big>''M''<sub>E</sub> <big>≝</big> ''m''<sub>FE</sub> + ''m''<sub>LE</sub> (Eq. 4)</big> | ||
:::: Inserting Eq. 4 into Eq. 3, | :::: Inserting Eq. 4 into Eq. 3, | ||
<big>''M'' = ''M''° + ''m''<sub> | <big>''M'' = ''M''° + ''m''<sub>FE</sub> + ''m''<sub>LE</sub> (Eq. 5)</big> | ||
:::: The fat mass, ''m''<sub>F</sub>, is defined as the sum of the reference fat mass and excess 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>''m''<sub> | <big>''m''<sub>FE</sub> <big>≝</big> ''m''<sub>F</sub> - ''m''°<sub>F</sub> (Eq. 6)</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, | |||
::: | |||
<big>''M'' = ''M''° - ''m''°<sub>F</sub> + ''m''<sub>F</sub> + ''m''<sub>LE</sub> (Eq. 7)</big> | |||
:::: Normalization for ''M''° yields, | |||
<big>''M'' | <big>BME = ''M''/''M''° = 1 + ''m''<sub>F</sub>/''M''° - ''m''°<sub>F</sub>/''M''° + ''m''<sub>LE</sub>/''M''° (Eq. 8)</big> | ||
:::: | :::: which is related to the [[body mass excess]], BME=''M''/''M''°. | ||
[[File:BF-BME.png|right|400px]] | |||
:::::::: '''Figure 1''': Body fat mass, ''m''<sub>F</sub>, normalized for reference body mass, ''M''°, as a function of body mass excess, BME. Assuming a linear relationship of ''f''(BME-1) (dashed lines), ''R''<big>2</big> is 0.969 and 0.985 for women and men, respectively. A logarithmic model (full lines) improves the fit slightly for both women and men (''R''<sup>2</sup> = 0.979 and 0.988, respectively). The intercept at BME=1 is the relative body fat mass of the healthy reference population. For the two models, this is 0.24 to 0.27 for women and 0.13 to 0.15 for men. The linear slopes are not significantly different in women and men, at 0.59 and 0.54, respectively. The linear model, therefore, implies that an average fraction of 0.44 of the excess body mass is due to a gain of lean body mass, and a fraction of 0.66 is due to a gain of fat mass. Data were calculated from tabulated values in the original references, including European white populations, African Americans, Japanese and Asien Indian populations as indicated. The purported differences between Asian and non-Asien populations is based on BMI, ignoring the effect of height on BMI. In contrast, BME provides a unifying concept for ethnic groups of different evolutionary backgroud, with differences in body height as a key to normalize for appropriate reference body mass, ''M''°. Althoug ''M''° at any given height is identical in women and men, a well defined difference exists in the reference body fat fraction between women and men, independent of height and evolutionary background of the populations covered in the original publications. | |||
:::: The excess lean mass normalized for ''M''° is a function of BME (or BME-1), | :::: The excess lean mass normalized for ''M''° is a function of BME (or BME-1), | ||
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:::: Inserting Eq. 8 and 9 into Eq. 7.2 yields | :::: Inserting Eq. 8 and 9 into Eq. 7.2 yields | ||
<big>BME | <big>BME = 1 + ''m''<sub>F</sub>/''M''° - ''m''°<sub>F</sub>/''M''° + ''f''(BME-1) (Eq. 10)</big> | ||
:::: Solving for the measured variable ''m''F normalized for ''M''°, | :::: Solving for the measured variable ''m''<sub>F</sub> normalized for ''M''°, | ||
<big>''m''<sub>F</sub>/''M''° = (BME-1) - ''f''(BME-1) + ''m''°<sub>F</sub>/''M''° (Eq. 11)</big> | <big>''m''<sub>F</sub>/''M''° = (BME-1) - ''f''(BME-1) + ''m''°<sub>F</sub>/''M''° (Eq. 11)</big> | ||
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Revision as of 01:36, 4 January 2020
Description
Body fat is conventionally expressed as BF%, which is the percentage of body fat mass relative to the total body mass. In the healthy reference population (HRP), there is no excess body fat, and the fraction of body fat in the HRP is expressed - by definition - relative to the reference body mass, M°, at any given height. Although M° is identical in females and males at any given height, the fraction of body fat is higher in females than males in the HRP.
Abbreviation: BF
Reference: BME
Body fat in the healthy reference population
- If body fat is expressed as BF% = 100*mF/M (Gallagher et al 2000; Deurenberg et al 2001; Romero-Corral et al 2008; Bosy-Westphal et al 2009), then the body fat mass, mF [kg], is calculated from total body mass, M [kg],
mF = (BF%/100)*M (Eq. 1)
- Lean body mass, ML [kg], is the fat-free body mass, and is thus defined as ML ≝ M-mF,
M ≝ ML + mF (Eq. 2)
- In turn, M is the sum of the reference mass at a given height and excess body mass, ME ≝ M-M°,
M ≝ M° + ME (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, 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,
ME ≝ mFE + mLE (Eq. 4)
- Inserting Eq. 4 into Eq. 3,
M = M° + mFE + mLE (Eq. 5)
- The fat mass, mF, is defined as the sum of the reference fat mass and excess fat mass, mF ≝ m°F+mFE, hence
mFE ≝ mF - m°F (Eq. 6)
- 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,
M = M° - m°F + mF + mLE (Eq. 7)
- Normalization for M° yields,
BME = M/M° = 1 + mF/M° - m°F/M° + mLE/M° (Eq. 8)
- which is related to the body mass excess, BME=M/M°.
- Figure 1: Body fat mass, mF, normalized for reference body mass, M°, as a function of body mass excess, BME. Assuming a linear relationship of f(BME-1) (dashed lines), R2 is 0.969 and 0.985 for women and men, respectively. A logarithmic model (full lines) improves the fit slightly for both women and men (R2 = 0.979 and 0.988, respectively). The intercept at BME=1 is the relative body fat mass of the healthy reference population. For the two models, this is 0.24 to 0.27 for women and 0.13 to 0.15 for men. The linear slopes are not significantly different in women and men, at 0.59 and 0.54, respectively. The linear model, therefore, implies that an average fraction of 0.44 of the excess body mass is due to a gain of lean body mass, and a fraction of 0.66 is due to a gain of fat mass. Data were calculated from tabulated values in the original references, including European white populations, African Americans, Japanese and Asien Indian populations as indicated. The purported differences between Asian and non-Asien populations is based on BMI, ignoring the effect of height on BMI. In contrast, BME provides a unifying concept for ethnic groups of different evolutionary backgroud, with differences in body height as a key to normalize for appropriate reference body mass, M°. Althoug M° at any given height is identical in women and men, a well defined difference exists in the reference body fat fraction between women and men, independent of height and evolutionary background of the populations covered in the original publications.
- The excess lean mass normalized for M° is a function of BME (or BME-1),
mLE/M° = f(BME-1) (Eq. 9)
- Inserting Eq. 8 and 9 into Eq. 7.2 yields
BME = 1 + mF/M° - m°F/M° + f(BME-1) (Eq. 10)
- Solving for the measured variable mF normalized for M°,
mF/M° = (BME-1) - f(BME-1) + m°F/M° (Eq. 11)
- which finally shows the equation derived to plot the normalized body fat mass as a function of BME (or BME-1),
mF/M° = (1-f)·(BME-1) + m°F/M° (Eq. 12)
- 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.
MitoPedia: BME
References
- Bosy-Westphal A, Plachta-Danielzik S, Dörhöfer RP, Müller MJ (2009) Short stature and obesity: positive association in adults but inverse association in children and adolescents. Br J Nutr 102:453-61. - »Bioblast link«
- Deurenberg P, Andreoli A, Borg P, Kukkonen-Harjula K, de Lorenzo A, van Marken Lichtenbelt WD, Testolin G, Vigano R, Vollaard N (2001) The validity of predicted body fat percentage from body mass index and from impedance in samples of five European populations. Eur J Clin Nutr 55:973-9. - »Bioblast link«
- Gallagher D, Heymsfield SB, Heo M, Jebb SA, Murgatroyd PR, Sakamoto Y (2000) Healthy percentage body fat ranges: an approach for developing guidelines based on body mass index. Am J Clin Nutr 72:694-701. - »Bioblast link«
- Iwaniec UT, Turner RT (2016) Influence of body weight on bone mass, architecture and turnover. J Endocrinol 230: R115-30. - »Bioblast link«
- Misra P, Singh AK, Archana S, Lohiya A, Kant S (2019) Relationship between body mass index and percentage of body fat, estimated by bio-electrical impedance among adult females in a rural community of North India: A cross-sectional study. J Postgrad Med 65:134-40. - »Bioblast link«
- Romero-Corral A, Somers VK, Sierra-Johnson J, Thomas RJ, Collazo-Clavell ML, Korinek J, Allison TG, Batsis JA, Sert-Kuniyoshi FH, Lopez-Jimenez F (2008) Accuracy of body mass index in diagnosing obesity in the adult general population. Int J Obes (Lond) 32:959-66. - »Bioblast link«
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