The body box made simple.
How in the world does the box do that? When we look at textbooks to find the answer, we see equations like this:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
What does it all really mean? I will explain the theory of lung volume measurements in its simplest terms and then go on to explain it in slightly greater detail. I will only briefly refer to the derivations that produce the collection of obtuse equations we have all seen and dreaded.
The operating principle of the body plethysmograph is simply based on Boyle's gas law. The law states that a volume of confined gas, at constant temperature, varies inversely to the pressure applied to it. If we let the temperature remain constant, during the small volume changes when the lung is being compressed and expanded, the following equation would apply:
P1V1 = P2V2
(The subscripts indicate conditions 1 and 2, compressed and expanded respectively)
Before we go further, I think the very simplest way of visualizing the process is to assign:
* P1 to equal the pressure in the lung which is the same at the mouthpiece with glottis open
* V1 to equal the volume at the end of a normal breath or VTG
* P2 to equal the pressure in the box
* V2 to equal the volume in the box.
Algebraically we can solve for V1 which would be:
[V.sub.1] = [[P.sub.2][V.sub.2]/[P.sub.1]]
Inside the body plethysmograph with the door closed, the patient breathes normally on the mouthpiece. At the end of a normal breath or functional residual capacity (FRC), the mouth shutter distal to a pressure transducer is closed. As the patient takes the next breath in, the pressures are simultaneously measured in the lung (P1) and in the body box (P2).
In this scenario the volume of the box (V2) is known and does not change. With the box pressure known, and the two pressures measured simultaneously, the unknown lung volume is calculated with the above equation. The V1 is approximately equal to the FRC and is called the thoracic lung volume, or VTG. This is the very simplest description of the process and allows us to visualize the principles involved. The next step in understanding how the body plethysmograph works is to further develop Boyle's equation.
In reality, the body box does not measure the absolute values for P2 and V2. Instead, the amount of changes both in pressure ([DELTA]P) and volume ([DELTA]V) during the maneuver are measured and used in the equation. Algebraic manipulation, involving all the tricks we learned in high school, is used to modify Boyle's law into its practical form:
[V.sub.1] = [[P.sub.1]/[P/V]]
During the procedure, the shutter is occluded suddenly at the end of a normal breath or at end-expiration just prior to inspiration and without warning. Light panting is performed at approximately 2 cycles per second for several breaths against the closed shutter. If the panting is too fast or too slow, the increased airway resistance can change measured pressures.
Because the patient is panting, the airway is continually patent or unobstructed, with glottis and epiglottis open from the mouth all the way to the furthest alveoli. Therefore, according to the laws of physics, which roughly states that pressures within a connected closed tubular system are basically equal, airway pressure changes in the mouth are equal to alveolar pressure changes ([DELTA]PA).
The thoracic-pulmonary volume changes ([DELTA]VA) during the panting maneuver, produce air pressure changes inside the closed box which can be extrapolated to volume changes within the box. Decreases in cabinet volume are in equal inverse response to thoracic volume increases. Changes in the subject's mouth pressure are measured, and the box volume is either less accurately estimated from the patients entered height and weight or much more accurately measured directly through box pressure changes as described above.
Measurement of V[logical not]TG is measured while the patient is at FRC, making FRC the V1 in the equation above. Alveolar pressure P1 just prior to the inspiratory effort may be assumed to be equal to atmospheric pressure PATM. The PATM used must have BTPS water vapor pressure (47 mmHg) subtracted. With the pressure ([DELTA]PA) and volume ([DELTA]VA) changes recorded during plethysmographic maneuver, the equation used for determining VTG becomes:
[V.sub.TG] = [[P.sub.ATM]/[[P.sub.A]/[V.sub.A]]]
The computer creates a real-time graph representation of the pressure and volume changes during panting. Generally, the results are shown with [DELTA]PA on the vertical axis and [DELTA]WA on the horizontal axis. The angle is measured, and the value of the angle's tangent, which is the slope, provides an average value for [DELTA]PA/[DELTA]VA over the length of the tracing. Using this information, the basic equation for determining VTG can then be simplified to:
[V.sub.TG] = [[P.sub.ATM]/tangent]
Two important adjustments are required for the calculation of VTG to accurately reflect the patient's actual FRC volume. The first is a [DELTA]P/[DELTA]W calibration factor (FCal) for the box. This calibration factor is obtained when we measure the graphic deflections when pushing into the box known volumes and producing proper pressures and resultant flows, as well as ascertaining the graphic relationship between volume and pressure within the closed box.
The second is the adjustment for box volume loss due to the presence of the subject in the box. This is based upon the box volume when empty (VCab) and the patient's volume. Because all the measurements are made under BTPS conditions, the VTG does not have to be corrected to BTPS.
The entire thoracic gas volume is measured regardless of the degree of airway obstruction or distribution of ventilation. Body plethysmograph measurements for VTG or FRC are always slightly higher than normal becasue esophageal volume is included in the measurement. Of course, the main advantage of using the body plethysmograph for measuring lung volumes is that all thoracic gas is measured, whether it communicates with the mouth or not. The results are completely independent upon the degree of airway obstruction.
Airway resistance (Raw) in the pulmonary airways is the result of the molecular friction as the air travels in and out of the airway. It is actually the drive pressure required to create the flow of air in out of the lungs. Thus, the units for Raw are cmH2O/L/second.
The respiratory tree consists of tubes having many different diameters, from the smallest respiratory bronchial to the trachea. The Raw depends on the size of the tube lumen, and it also depends upon the lung volume at which the measurement is being measured. Raw is less at large lung volumes and greater when measured at small lung volumes. This is partly due to the fact that at smaller lung volumes the airways are not as patent or open, especially in patients with any degree of obstruction.
Airway conductance (Gaw) is the reciprocal of Raw. It looks at the same phenomena but with the opposite viewpoint. Instead of looking at resistance to flow, we are looking at the conductance of flow. This reciprocal relationship is demonstrated in the following equation:
[G.sub.aw] = [1/[R.sub.aw]]
It is the measure of flow that is generated from the available drive pressure and its units are:
Because the accurate measurement of Raw is dependent on the lung volume, the standard technique is to make the measurements at FRC. It is evident that patients with large lungs will have higher Gaw than patients with smaller lungs, and so to make a fair comparison to standard, the Gaw is divided by the VTG to produce specific airway conductance (SGaw), which is simply Gaw corrected for lung volume at FRC.
The equation derivation for Raw is very complicated, and I'll save that for another paper. The body plethysmograph is not a simple instrument, and we can take pride in its complexity.
by Jim Harvey MS, RPFT, RCP
Jim Harvey MS, RPFT, RCP works in the Pulmonary Function Laboratory at Stanford Hospital and Clinics in Palo Alto, and teaches Pulmonary Function at Skyline College in San Bruno, California.