Identify the Problem
Air Displacement Plethysmography (ADP) is a simple, formula-based approach used to determine one’s body composition. Body composition is used to determine physiological health risks of individuals that may be related to weight. It is very important that all results presented by ADP are accurate, in order to ensure that the patient and clinician are receiving correct information regarding the patient’s health.
Raw body volume can easily be determined by measuring the amount of air displaced from the chamber, but there are other factors that can affect body volume measurements that must be accounted for. It’s incredibly important that all potential sources of error are minimized to ensure for the most accurate calculations of body composition. Sources of isothermal air within the measurement chamber can lead to an underestimation of body volume because isothermal air is more compressible than air in adiabatic conditions. This underestimation in volume can lead to an overestimation in body density and an overestimation of percent fat.  One source of isothermal air is air that is on or near skin and clothing, which is represented by Surface Area Artifact (SAA). This accounts for a small constant, k, as well as the body surface area of the individual. Another source of isothermal air is thoracic gas volume (VTG), which is measured at mid-exhalation through pulmonary plethysmography or it is estimated by ADP. Research has shown that 40% of VTG has an impact on body volume.  Here is the formula for the corrected body volume determined through ADP:
VBcorrected = VBraw – SAA + .4*TVG
Another design aspect of the device that has speculated to alter calculations is patient positioning. The current testing procedure requires subjects to sit up straight in the measurement chamber, but what if they were bent over? How would the change in position change body composition calculations? The aspect of patient positioning could affect VTG because individuals in the bent over position may show different breathing patterns, which would impact VTG. A study that analyzed the effects of body positioning on ADP measurements found that there was a slight difference in VTG between individuals sitting in the straight up and bent over positions, so we will be using some of their data in this problem. 
Here is the engineering problem I propose: Using the densitometric principles of ADP, hand calculate the % body fat of an individual sitting straight up, and then calculate the % body fat of the same individual in the bent over position. Does the position of the patient have a significant impact on % body fat calculations?
We want to assume mostly adiabatic conditions within the measurement chamber. This means Poisson’s Law should be used to determine the volume of air within the chamber. The formula below, initial conditions of the chamber, and the given values below should be used to calculate the volume of air in the chamber. Initial conditions are those of an empty chamber, and then an individual sits in the chamber, which changes the pressure and volume in the chamber. 450L is the volume of air in an empty chamber and the change in pressure is caused the presence of a body in the chamber and the pressure values remain in the acceptable range for ADP.  Y represents the specific heat capacity of the air within the chamber at the designated temperature.  All pressure and volume values were estimated based on typical characteristics and conditions of ADP. [3,4]
(P1V1)^Y = (P2V2)^Y
P1 = 75 kPa, P2 = 88.4 kPa, V1 = 450 L, V2 = ?, Y= 1.401 @ 25°C
For the sake of this problem, let’s assume that surface area artifact can be ignored. The formula for SAA is SAA= k x BSA, where k is a constant derived by a manufacturer and BSA is body surface area. A typical value used for k is -4.7 x 10-5. Since this value is very small, it will result in a surface area artifact that is also very small. [1,2] Therefore, the new formula for corrected body volume is:
VBcorrected = VBraw + .4*TVG
We also want to assume for the presence of some isothermal air within the chamber that is caused by thoracic gas volume in each scenario. An ADP related study looked at the difference in VTG between a person sitting straight up and a person bent over in a chamber.  We can use their average determined values here in our problem.
VTGstraight = 4.517 L, VTGbent = 4.445 L
Here is some more information and assumptions needed to solve the problem:
- The mass of the individual is 74kg and the same individual is tested in both cases
- Assume the subject has consistent breathing rates during testing
- Assume the temperature within ADP remains at 25°C 
- Assume the change in positioning does not impact body volume
- Body Density = Body Mass / Body Volume 
- Use Siri’s Equation (below) to determine body fat % in both cases 
- % fat mass= [(4.95/Density)-4.5]*100
- Assume the patient is in the positions according to the figure below. “A” represents the subject bent over and “B” represents the patient sitting straight up. 
Solve the Problem
- Determine the volume of air within the measurement chamber when a subject enters the chamber using Poisson’s Law.
(P1V1)^Y = (P2V2)^Y
P1 = 75 kPa, P2 = 88.4 kPa, V1 = 450 L , V2 = ?= 1.401 @ 25°C
(75*450)^1.401 = (88.4*V2)^1.401
33750 = 88.4V2
V2 = 381.88 L
Find the air displaced from the measurement chamber and equate it to raw body volume.
V1 – V2 = Vdisplaced = VBraw
450 L – 381.88 L = 68.2 L = Vdisplaced = VBraw
- Find the corrected body volume of the individual in each position.
Bent: VBcorrected = VBraw + .4*TVG = 68.2 L + (.4*4.445 L) = 69.978 L
Straight: VBcorrected = VBraw + .4*TVG = 68.2 L + (.4*4.517 L) = 70.007 L
- Find the body density of the individual in each position.
Bent: BD=BM/BV= 74 kg / 69.978L = 1.0574 kg/L
Straight: BD=BM/BV= 74 kg / 70.007 = 1.0570 kg/L
- Use Siri’s Equation to find the % fat mass of the individual in each position.
Bent: % fat mass= [(4.95/Density)-4.5]*100 = [(4.95/1.0574)-4.5]*100 = 18.13 % fat mass
Straight: % fat mass= [(4.95/Density)-4.5]*100 = [(4.95/1.057)-4.5]*100 = 18.31 % fat mass
The percent body mass for the individual in the bent position is 18.13% and the percent body mass for the individual in the straight position in 18.31%. There is a small difference between the two positions, which does support the findings of the study that the values were based off of. However, it is still important that the sitting position of the individual is standardized across all testing procedures to decrease variability in testing results. Limitations of the results include not accounting for surface area artifact and estimations of VTG using ADP technology.
- David A Fields, Michael I Goran, Megan A McCrory, Body-composition assessment via air-displacement plethysmography in adults and children: a review, The American Journal of Clinical Nutrition, Volume 75, Issue 3, March 2002, Pages 453–467, https://doi.org/10.1093/ajcn/75.3.453
- Peeters M. W. (2012). Subject positioning in the BOD POD® only marginally affects measurement of body volume and estimation of percent body fat in young adult men. PloS one, 7(3), e32722. https://doi.org/10.1371/journal.pone.0032722
- COSMED. The World’s Gold Standard for Fast, Accurate and Safe Body Composition Assessment. COSMED USA Inc., 2019. https://www.cosmed.com/hires/Bod_Pod_Brochure_EN_C03837-02-93_A4_print.pdf
- Engineering ToolBox, (2003). Specific Heat Ratio of Air. Available at: https://www.engineeringtoolbox.com/specific-heat-ratio-d_602.html