The path of least impedance

Identify 

I am sure most of you are familiar with the term Body Mass Index (BMI), and some of you may have even received one. Also, I am sure most of you are familiar with the controversy regarding the accuracy of BMIs. Unfortunately, BMI results do not accurately reflect the body fat percentage of certain populations, such as athletes and the elderly, because muscle mass is not taken into account [1]. For example, an athlete with significant muscle mass would report as overweight and an older individual lacking muscle mass would report as underweight [1]. In hopes of correcting the inaccuracies stemming from BMI calculations, bioelectrical impedance analysis (BIA) became a popular method for measuring body fat mass and body fat percentage.

With BIA, a small, alternating current is sent throughout the body and the impedance of electrical current to fat, water, and muscle content is recorded [2]. Fattier tissues will reduce the speed of electrical current whereas hydrated and muscular tissues will not [3]. Assuming that the body exists as a conductive cylinder uniform in material and density, allows for these impedance measurements to be easily converted into body composition measurements [4]. However, due to these assumptions, inaccuracies persist and an advantage of BIA over BMI remains unclear. BIA has the potential of providing more accurate and reliable results, but that must start with correcting the issues that result from its assumptions, more specifically its assumption that the body exists as a conductive cylinder.

Preliminary bioelectrical impedance analyzers made use of a one-cylinder model to make body composition measurements [5]. Unfortunately this method led to the underestimation of total body water, thus, leading to inaccurate results of body fat mass and lean body mass (Figure 1) [5]. To improve upon this issue, the 5-cylinder model was developed which makes cylinders out of the arms, legs, and trunk (Figure 1) [5]. In addition, the 5-cylinder model was able to expand upon its predecessor by providing detailed reports of each body part’s composition and whole-body composition [5].

Figure 1. Schematic of a one-cylinder model versus a 5-cylinder model [5].

In Calculus we learned that when approximating the area under the curve our estimation yields better results when we add more rectangles with smaller widths. Analogous to the previous scenario, our body composition measurements would prove to be more accurate by increasing the number of cylinders our body could model. Instead of using one cylinder, it may be more beneficial to have 5 cylinders.

Formulate

To measure impedance among 5 cylinders requires more electrodes than the four that come with conventional BIA (Figure 2) [6]. Moreover, for the 5-cylinder model, all alternating current is supplied between the right ankle and right wrist [6]. To measure the potential difference of the upper limbs, lower limbs, and trunk, the electrodes are placed between the right and left wrist, right and left ankle, and left ankle and wrist, respectively [6]. All electrodes pairs are then attached to a four-channel, battery operated impedance instrument that reports the resistance, reactance, phase angle, and impedance [6].

Figure 2. 5-cylinder model electrode placement schematic [6].

In order to calculate impedance, the resistance, R, reactance, Xc, and phase angle must be known (Equation 1) [7]. Resistance is reflective of electrolyte-containing total body water in which lean muscles tend to have low resistance and fattier tissues tend to have a high resistance [7]. Reactance is reflective of body cell mass in which a higher proportion of cells gives rise to low reactance and a lower proportion of cells gives rise to a high reactance [7]. The phase angle readout is a component of the impedance instrument that allows for differentiation between resistance and reactance [7].

Z^2 = R^2 + Xc^2                        Equation 1

Now that we know how to calculate impedance, we must now relate impedance to total body water (TBW) shown in Equation 2 [6].

TBW = L^2/Z                            Equation 2

L: length of cylinder

Z: impedance of cylinder

To make use of these equations while maintaining full transparency, we must clarify the assumptions. Therefore, we assume:

  1. The supplied current follows the path of least resistance.
  2. The body is made up of segmental conductive cylinders [6].
  3. The total body water occupies a cylinder of length, L, and is uniform in resistivity (Equation 2) [6].

By assuming the path of least resistance we can exclude extraneous and complex equations that would otherwise be needed to solve for resistance. Secondly, by assuming segmental conductive cylinders, we can analyze a body part’s contribution to whole body impedance. Lastly, by assuming what is shown in Equation 2 we can again exclude extraneous and complex equations that would otherwise be needed to solve for TBW.

Solve

With this segmented approach, we can better estimate lean body mass (LBM) and fat mass (FM) by recording the individual lengths and resistivities of upper limb, lower limb, and trunk cylinders (Equation 3). Whereas for a one-cylinder model, the entire body was assumed to have one resistivity, which is inherently untrue considering the trunk and limbs distribute lean muscle and fat differently [6]. Unfortunately, even through a segmented approach of solving for TBW, reliability of Equation 2 is questionable which continues into Equation 3 [6]. Studies have shown that impedance, Z, contributes little to solving for lean body mass (LBM). Moreover, changes in impedance showed little to no change in LBM [6].

TBW = Lᵤₗ^2/Zᵤₗ + Lₗₗ^2/Zₗₗ + Lₜ^2/Zₜ                Equation 3

ul: upper limb

ll: lower limb

t: trunk

Despite its reliability being under question, we continue to make use of assumptions to simplify equations while maintaining some degree of accuracy. Moreover, now that we know TBW, we can solve for LBM and fat mass (FM) through the empirical estimations shown in Equation 5 and Equation 4 [7]. These empirical estimations are based on observations of human biological phenomena where on average a human’s lean body mass contains 73% of their total body water [7]. Because we are not all the same, deviations from Equation 4 do exist, which is a limitation of using empirical calculations.

LBM = TBW/0.73                        Equation 4

FM = Body Mass – LBM                    Equation 5

Although the segmental approach improves accuracy in comparison to the one-cylinder model, discrepancies still exist through the use of assumptions and empirical estimations. To further improve upon BIA, it is important that we rid of all empirical estimations and analyze impedance solely on the person. Fortunately, companies like InBody have made strides in improving this technology by minimizing the use of empirical estimations [5].

References

  1. Assessing Your Weight and Health Risk. NIH. Website. https://www.nhlbi.nih.gov/health/educational/lose_wt/risk.htm. Accessed May 1, 2020.
  2. Grossi, M., Ricco, B. Electrical impedance spectroscopy (EIS) for biological analysis and food characterization: a review. J Sens Sens Syst. 2017; 6: 303-325. https://doi.org/10.5194/jsss-6-303-2017.
  3. Bioelectrical Impedance Analysis (BIA). Science for Sport. Website. https://www.scienceforsport.com/bioelectrical-impedance-analysis-bia/. Published May 20, 2018. Accessed February 27, 2020.
  4. Dehghan, M., Merchant A.T. Is bioelectrical impedance accurate for use in large epidemiological studies? Nutr J. 2008; 7: 36. doi: 10.1186/1475-2891-7-26
  5. Revolutionizing BIA Technology with InBody. InBody. Website. https://inbodyusa.com/general/technology/. Accessed May 12, 2020.
  6. Organ LW, Bradham GB, Gore DT, Lozier SL. Segmental bioelectrical impedance analysis: theory and application of a new technique. Journal of Applied Physiology. 1994 Jul; 77(1): 98-112.
  7. Bioelectrical Impedance Analysis (BIA) and Body Composition Analyse. DANTEST Media Inc. Website. http://www.dantest.com/dtr_bioscan_bia.htm. Accessed May 12, 2020.

 

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

Where,

  • 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

Where,

  • 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)

Where,

Density= subject mass/subject volume

[1]

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

[1]

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]

References

  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 https://byjus.com/chemistry/boyles-law/
  3. (n.d.) Adiabatic Process. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html

How it Works: Air Displacement Plethysmography

How it Works: BIA and EIM