Identify, Formula, Solve: Patient Positioning and ADP

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. [1] 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. [1] 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. [2]

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?

Formulate Problem 

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. [3] Y represents the specific heat capacity of the air within the chamber at the designated temperature. [4] 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. [2] 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 [3]
  • Assume the change in positioning does not impact body volume 
  • Body Density = Body Mass / Body Volume [1]
  • Use Siri’s Equation (below) to determine body fat % in both cases [1]
    • % 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. [2]

Solve the Problem 

  1.   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

  2. 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

  3.  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

  4. 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

  5. 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. 


  1. 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,
  2. 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.
  3. COSMED. The World’s Gold Standard for Fast, Accurate and Safe Body Composition Assessment. COSMED USA Inc., 2019.
  4. Engineering ToolBox, (2003). Specific Heat Ratio of Air. Available at: 

A Look into Air Displacement Plethysmography

All information about this Air Displacement Plethysmography Chamber was retrieved from this patent: Air Circulation Apparatus and Methods for Plethysmographic Measurement Chambers 

Air Displacement Plethysmography

This air displacement plethysmography chamber is used to assess the body composition of patients. The measurements of fat and fat-free mass allow physicians to record important physical information about patients. Excess body fat and low levels of free-fat mass are indicators of various different diseases and developmental problems.  The major claim of the device is that air displacement plethysmography determines the volume of a patient by measuring the amount of air displaced when the patient sits in an enclosed chamber. This invention specifically includes an apparatus and plethysmographic measurements chamber that use air that has circulated through the chamber and replaced with air from outside the chamber in order to record its measurements. [1]

Who uses it?

Physicians primarily use air displacement plethysmography within the populations of infants and obese individuals. For low birth weight infants, variations in body composition can dictate infant energy needs and can indicate the health progression and future physical development of the infant. Air displacement measurements for infants must be more accurate than other body composition determining techniques because of an infant’s metabolic rate and longer measurement periods required due to their larger breathing artifacts. Excess body fat within obese individuals can be indicators of diseases such as cardiovascular disease, diabetes, hyper tension, hyperlipidemia, kidney disease, and musculoskeletal disorders. Athletes can also use this technology to determine their body composition to ensure that they are at peak physical shape for their required sport. [1]

How it works: A little bit of engineering for you

In air displacement plethysmography, the volume of air in the chamber is calculated through Boyle’s Law and/or Poisson’s Law. In most technologies, volume perturbations of a fixed frequency of oscillation are induced with the chamber and the perturbations lead to pressure fluctuations. The amplitude of the pressure fluctuations is determined and is used to determine the amount of air in the chamber through Boyle’s Law (isothermal conditions) or Poisson’s Law (using adiabatic conditions). [1]

Boyle’s Law: For gases at room temperature, there is an inversely proportional relationship between pressure and volume of that gas. [2]

P1V1 = P2V2


  • P1 is the initial pressure of the gas
  • V1 is the initial volume of the gas 
  • P2 is the final pressure of the gas 
  • V2 is the final volume of the gas

Poisson’s Law: In an adiabatic process, no heat transfer takes place between the surroundings and the system, or within the system. [3]

(P1V1)^Y= (P2V2)^Y


  • P1 is the initial pressure exerted by the gas
  • V1 is the initial volume occupied by the gas
  • P2 is the final pressure exerted by the gas
  • V2 is the final volume occupied by the gas
  • Υ is the ratio of specific heats, CP/ CV

By subtracting the volume of air remaining in the chamber (when the subject is in the container) from the volume of air in an empty chamber, body volume can be calculated indirectly.

Once the volume of the subject is known, body composition can be found with the volume, the weight, and the surface area of the subject. Body composition can be found by using the relationship between density and percent fat mass. The following two equations can be used to determine percent fat mass: 

Siri’s Equation: Percent Fat Mass=(4.95/Density)-4.5)*100) 

Brozek’s Equation: Percent Fat mass=((4.57/Density)-4.142)* 100)


Density= subject mass/subject volume


Better Than the Rest

There are other methods out there used to determine body composition, but they contain flaws compared to air displacement plethysmography. One method is skin folding, which uses calipers that compress the skin at certain points on the body. This technique is inaccurate in accounting for variations in fat patterning and requires perfect application of the calipers by a technician. Biometric impedance analysis (BIA) is also used to determine body composition. This technique requires the passing an electric current through a patient’s body, measuring its impedance value and comparing it to the known impedance value of muscle tissue thus to determine body composition. This method is not effective because impedance can be affected by the patient’s state of hydration, internal and external temperature, and BIA has not been used on infants. Lastly, the most common technique used to measure body composition is hydrostatic weighing. This process includes weighing the patient on land and repeatedly underwater to estimate the amount of air present in their lungs. This technique is incredibly invasive and unpleasant, especially for the populations of infants, the elderly, and individuals with disabilities. Air plethysmography is used because it is a less invasive technique for the populations of interest and it provides more accurate readings of body composition. [1]

There are a few components of the invention in the patent that differentiate it from other air displacement plethysmography devices. This plethysmographic measurement chamber prevents the accumulation of water vapor and carbon dioxide in the chamber, it addresses variations in chamber temperature due to body heat produced by the subject, and it maintains a safe and comfortable air composition for infants. All of these measures are due to internal systems and methods of circulating and renewing air within the chamber, while also maintaining the acoustic properties of the chamber at the perturbation frequency used to conduct the volume measurements. [1] 

Patent Information

The information from this post was retrieved from the following patent:

Patent Title: Air circulation apparatus and methods for plethysmography measurement chambers

Patent Number: US 2004/0193074 A1

Patent Filing Date: March 26, 2003

Patent Issue Date: September 30, 2004

How long it took for this patent to be issued: About 1.5 years 

Inventors: Philip T. Dempster, Michael V. Homer, Mark Lowe 

Assignee: Fish & Neave 

U.S. Classification: 600/587; 73/149

Amount of Claims: 57


Detailed Drawing

Figure 1: Labeled drawing of an air plethysmography displacement system with the following labeled components: 50. Entire plethysmographic system,  52. Plethysmographic measurement chamber, 54. Chamber door, 56. Plethysmographic measurement components, 58. Volume perturbation element, 60. Air circulation chamber, 62. Plethysmographic measurement components, 64. Computer, 66. Software for controlling operation of measurement components, 68. Inlet tube, 70. Exhaust tube [1]


  1. Dempster et al. (2004). Air Circulation Apparatus and Methods for Plethysmographic Measurement Chambers.  US 2004/0193074 A1. U.S. Patent and Trademark Office 
  2. (2019) Boyle’s Law – Statement, Detailed Explanation, and Examples. Retrieved from
  3. (n.d.) Adiabatic Process. Retrieved from

Enough (N)SAID about Ibuprofen & Soreness

If I’m being honest here, it’s been a while since I’ve had a solid gym routine. But this semester I’ve been going pretty regularly, and let me tell you, I’ve felt the burn. My muscles have felt pretty sore in the 2-3 days following my workouts, so I’ve had to turn to ibuprofen a few times to relieve the pain. But even after taking ibuprofen in the morning, I’ve felt sore again by the end of the day. This got me thinking: how effective is ibuprofen at reducing muscle soreness?

Non-steroidal anti-inflammatory drugs (NSAIDs) are commonly served over-the-counter at pharmacies. Some common forms you may recognize include aspirin and ibuprofen (Motrin, Advil). NSAIDs are taken for many reasons; they reduce pain and inflammation, lower fevers, and reduce clotting action.[1,2] The typical dosage for adults who are looking to reduce mild-moderate pain is 400 mg every 4-6 hours. For adults who have pain caused by osteoarthritis, the typical prescribed dose is 1200 mg.[3] However, despite their pain reducing use, NSAIDs could yield negative side effects such as increased risk in developing nausea, stomach pains, or an ulcer.[1]

The mechanism of NSAIDs when it comes to reducing pain and inflammation is known and understood. After intense workouts, prostaglandins are produced by muscle cells. They aid in the healing process of muscle, but this often leads to inflammation, pain, and fever. Enzymes called cyclooxygenases (COX-1, COX-2) produce the prostaglandins that promote inflammation, pain, and fever. The goal of NSAIDs is to inhibit COX-1 and COX-2 from producing prostaglandins, thus decreasing the pain. However, the COX-1 enzyme is responsible for creating prostaglandins that protect the stomach lining and support platelet aggregation, so the inhibition of the enzyme is what could lead to stomach ulcers and the promotion of bleeding.[1,2,4] The science behind NSAIDs seems promising, but clinical research may prove otherwise.

Athletes commonly take NSAIDs after performing physical activity because they claim the drugs reduce pain and decrease recovery time. But here is the issue: only very few studies have been able to support this claim. Some studies have reported results that do indicate a beneficial effect, by stating NSAIDs used prophylactically mitigate exercise-induced inflammation, circulating creatine kinase levels, and muscle soreness.[5] On the other hand, these claims made by athletes lack scientific support. NSAIDs are known to treat inflammation, but many histological studies have proven that most overuse injuries are caused by tissue degeneration and not inflammation. Also, NSAIDs temporarily “mask” the pain caused by tissue degeneration or soreness. This does not ensure that muscles or tissues are actively getting healthier; it only hides the pain from the athlete. [5] Clearly, there are many different opinions about the use of NSAIDs, specifically ibuprofen, in the sports medicine field. Let’s take a look at what the “research says” about it. 

A study at the University of Saskatchewan was conducted to determine the effects of ibuprofen on muscle hypertrophy, strength, and soreness during resistance training. Participants (12 males, 6 females) trained their left and right biceps for six weeks, alternating arms on each day. The training program called for concentric curls at 70% of RM and eccentric curls at 100% of 1 RM. Every day after their training, they either received a 400 mg dose of ibuprofen or a placebo. On training days, each participant was asked to rate their soreness on a scale from 0-9. For both the placebo and ibuprofen, the participants reported soreness during the first week and that soreness decreased throughout the program to the point where participants felt no soreness in either arm during the final week. The researchers concluded that ibuprofen was not effective in reducing perceived soreness during the training. However, the researchers do not reflect on the limitations of their own study.  They had a small and uneven sample size when it came to gender and there could have been discrepancies and residual effects that came along with taking ibuprofen inconsistently. Additionally, they seemed pretty convinced by their findings, but maybe the dose they chose was not strong enough to show any reduction in soreness in a long term study.[6]

On the other hand, another study drew opposite conclusions. Researchers in Greece conducted a study to determine the effects of ibuprofen on delayed onset muscle soreness (DOMS) and muscular performance. Participants (14 men, 5 women) who have not done strength training in the last 6 months performed eccentric leg curls at 100% RM. Nine (9) subjects were given a 400 mg dose of ibuprofen every 8 hours for 48 hours after exercise, while the remaining 10 subjects received a placebo. The subjects rated their amount of soreness on a scale of 1-10 prior to exercising, 24 hours after exercising and 48 hours after exercising.  The results showed that muscle soreness was significantly lower for the ibuprofen group at both 24 hours and 48 hours after exercising. Similar to the previous study, the researchers did not evaluate the limitations of their study. The number of participants and number of each gender were low and uneven, respectively. Also, the soreness results were not discussed much in the conclusion of the paper. The researchers did not support why the soreness decreased with scientific evidence, which is what they did for the other the parameters they were testing for.[7]

Clearly, both studies came to different conclusions. However, both studies were conducted for different amounts of time, contained different exercises, and with subjects of different athletic abilities. There have been plenty of studies conducted to determine how effective ibuprofen is at reducing soreness, but each study contradicts the next. 

Overall, many studies show that ibuprofen is a short term solution to hiding muscle soreness, but it may not be effective long term. Though, I’m still going to keep on using it to treat my soreness.

Questions to consider:

  • Do you take NSAIDs to reduce your soreness after working out? How effective do you find them to be?
  • Do you think there’s a better way to measure soreness and how ibuprofen affects our muscles?
  • Do you think the length of the study has any correlation with the effectiveness of ibuprofen?


  1. (n.d.) Nonsteroidal Anti-inflammatory Drugs (NSAIDs). Retrieved from
  2. Tscholl, M., et al (2016). A sensible approach to the use of NSAIDs in sports medicine . Swiss Sports & Exercise Medicine , 65(2), 15–20.
  3. (n.d.) Ibuprofen (Oral Route). Retrieved from 
  4. (n.d.) What Are NSAIDs? Retrieve from
  5. Stuart J. Warden (2010) Prophylactic Use of NSAIDs by Athletes: A Risk/Benefit Assessment, The Physician and Sportsmedicine, 38:1, 132-138, DOI: 10.3810/ psm.2010.04.1770
  6. Krentz , J. (2008). The effects of ibuprofen on muscle hypertrophy, strength, and soreness during resistance training. Applied Physiology Nutrition and Metabolism , 33(3), 470–475. doi: 10.1139/H08-019