**Identify**

** **It is common for people worry about their Body Mass Index (BMI) values after visiting the doctor’s office. What many people don’t know is that these BMI values do not take into account what body weight comes from muscle and what comes from fat. This can be hard for individuals who contain high amounts of muscle, which weighs more than fat, and get a BMI value back saying that they are overweight.

One way to differentiate between an individual’s fat free mass (FFM) and their fat mass (

FM) is by using a bioelectrical impedance analyzer. These analyzers work by sending a low electrical current through the body from one electrode to another. This electrical current will pass quickly through hydrated tissues such as muscle and slowly through low hydrated tissues like fat.

There are many different factors to be taken into consideration when programming a bioelectrical impedance analyzer as shown above. Many estimated values for these analyzers come from average values and standard deviations of measurements from more accurate body composition tests such as hydrostatic weighing or Dual-energy X-ray absorptiometry (DXA). Specific equations based off of these values must be input into the system that will be able to give back estimates of an individual’s specific body composition given an input of the individuals weight, height, and gender. The problem with these analyzers is that the estimated values don’t accurately or even closely relate to each individual.

** ****Formulate**

For a bioelectrical impedance analyzer, the impedance value is mathematically found from the equation Z^2 = R^2 + Xc^2. Within this equation Z is the impedance, R is the resistance, and Xc is the reactance. The resistance is the opposition of a conductor to the alternating current and the reactance is the additional opposition to the current from the storage effects of the cell membranes and tissue interfaces.

As an engineer it is important to find the right programming equations for the technology being made. These equations will vary in accuracy depending on the sex and ethnicity of its user. After the impedance has been calculated from the electrical current, it will need to be plugged into an equation, along with height, weight, and gender to find fat mass. When using segmental analyzers each different segment being measured will use its own specific equations for FM and the segments will then be summed for a total body FM. A typical FM equation for a non-segmental analyzer for ages 16-80 may be set up as:

FM(kg) = C1 + C2 Age + W + C3 (H(m)^2 / Z) – C4 H(m)

Where H(m) is height in meters, W is weight kg, Age is age in years, Z is from the previous equation depending of the testing frequency and each C variable is a different constant. The constant values will be determined using linear regression models of data taken on a group of individuals using a different form of body composition analysis.

The following assumptions can be made when programming the equations:

- The electrical current follows the path of least resistance within the body
- Both the body and its specified segments follow a cylindrical ‘typical’ shape

If these two assumptions hold true and the following equations are programmed correctly an FM estimate can accurately be made.

**Solve**

** **The following measurements and calculations will then be made for fat mass:

Z^2 = R^2 + Xc^2

FM(kg) = C1 + C2 Age + W + C3 (H(m)^2 / Z) – C4 H(m)

Using the standard deviations as C values from data taken from a previous body composition study in Japanese women [1],the following equation can be determined:

FM(kg) = 37.91 + 18 Age + W + 0.6144 (H(m)^2 / Z) – 6.7 H(m)

Using these calculations along with a weight measurement from a scale an individual can then accurately assess their body composition health and fat free mass rather than using the BMI percentile chart.

Weight = FFM + FM

FFM = Weight – FM

It is important to understand that this developed equation will be limited only to Japanese females. If a scale programmed to find fat mass using this equation was used by a male, even a Japanese male, they would get an inaccurate reading. These reading will be inaccurate mainly due to the differences in how each sex and different ethnicities hold water within their body. This equation found for a BIA scale would be reasonable for female Japanese users only. In order for the scale to be reasonable for other individuals the programmed equation will need to be changed based of previous body composition findings of other groups based on ethnicity and sex.

**Further Readings:**

** **https://www.sciencedirect.com/science/article/pii/S0261561408000666?via%3Dihub

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4608267/#CR18

**References:**

** **https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5551247/

** ****Image Sources**

** **https://www.valhallawellness.com/weight-loss-services/bioelectrical-impedance-analysis/