Talk:Body fat excess

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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, M_E ≝ M-M°(Eq. 3). Excess body mass, M_E, is due to accumulation of an excess fat mass, M_FE, accompanied by a gain of excess lean mass, M_LE, which . Thus Eq. 13 and 2 combined yield the definition for excess body mass, M_E ≝ M_FE + M_LE (Eq. 4).

Inserting Eq. 4 into Eq. 3,

Eq. 13:  M = M° + MFE + MLE

The fat mass, M_F, is defined as the sum of the reference fat mass and excess fat mass, M_F ≝ M°_F+M_{FE, 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 = (M_F-M°_F)/M° (Eq. 5b), and BLE = M_LE/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 f_FE = BFE/BME (Eq. 9) and f_LE = BLE/BME (Eq. 10),

Eq. 17:  1 = fFE + fLE

where f_FE = 0.57 is the slope in Fig. 5b.

To derive the M_LE/M_FE 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/f_FE (Eq. 9).