# Difference between revisions of "Talk:Body fat excess"

```Work in progress
```

### Body fat in the healthy reference population

Lean body mass of an individual (object), ML [kg/x], 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.