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| === Body fat in the healthy reference population - a complementary route ===
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| :::: ''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. 3). 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>. Inserting ''M''<sub>E</sub> <big>≝</big> ''M''<sub>FE</sub> + ''M''<sub>LE</sub> (Eq. 4) into Eq. 3 and rearranging,
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| <big>'''Eq. 13''': ''M'' = ''M''° + ''M''<sub>FE</sub> + ''M''<sub>LE</sub></big>
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| :::: 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</sub> (Eq. 5b), hence
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| <big>'''Eq. 14''': ''M''<sub>FE</sub> <big>≝</big> ''M''<sub>F</sub> - ''M''°<sub>F</sub></big>
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| :::: Inserting Eq. 14 into Eq. 13 yields body mass as the sum of the reference mass plus the total body fat mass minus the reference fat mass (which is the reference lean mass, ''M''°<sub>L</sub> = ''M''-''M''°<sub>F</sub>; Eq. 5c), plus the excess lean mass,
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| <big>'''Eq. 15''': ''M'' = ''M''° + ''M''<sub>F</sub> - ''M''°<sub>F</sub> + ''M''<sub>LE</sub></big>
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| :::: Normalization of Eq. 15 for ''M''° and considering that the [[body mass excess]] is BME=''M''/''M''°-1 (Eq. 5a), BFE = (''M''<sub>F</sub>-''M''°<sub>F</sub>)/''M''° (Eq. 5b), and BLE = ''M''<sub>LE</sub>/''M''° (Eq. 5c), yields Eq. 7 in the form of,
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| <big>'''Eq. 16''': BME = BFE + BLE</big>
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| :::: By further normalization of Eq. 16 for BME, we obtain the summation of ''f''<sub>FE</sub> = BFE/BME (Eq. 9) and ''f''<sub>LE</sub> = BLE/BME (Eq. 10),
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| <big>'''Eq. 17''': 1 = ''f''<sub>FE</sub> + ''f''<sub>LE</sub>
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| :::: where ''f''<sub>FE</sub> = 0.57 is the slope in Fig. 5b.
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| :::: To derive the ''M''<sub>LE</sub>/''M''<sub>FE</sub> ratio (Eq. 12), which is equal to BLE/BFE (Eq. 5b and 5c), Eq. 16 is divided by BFE and rearranged,
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| <big>'''Eq. 18''': BLE/BFE = BME/BFE - 1</big>
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| :::: Eq. 18 is equivalent to Eq. 12, since BME/BFE = 1/''f''<sub>FE</sub> (Eq. 9).
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