Difference between revisions of "Talk:Body fat excess"
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<big>'''Eq. 18''': BLE/BFE = BME/BFE - 1</big> | <big>'''Eq. 18''': BLE/BFE = BME/BFE - 1</big> | ||
:::: Eq. 18 is equivalent to Eq. 12, since BME/BFE = ''f''<sub>FE</sub> (Eq. 9). | :::: Eq. 18 is equivalent to Eq. 12, since BME/BFE = 1/''f''<sub>FE</sub> (Eq. 9). |
Revision as of 18:28, 17 January 2020
Work in progress
Body fat in the healthy reference population - a complementary route
- In turn, 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, which . Thus Eq. 13 and 2 combined yield the definition for excess body mass, ME ≝ MFE + MLE (Eq. 4).
- Inserting Eq. 4 into Eq. 3,
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, hence
Eq. 14: MFE ≝ MF - M°F
- 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°L = M-M°F), plus the total body fat mass and 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).