## Qualitative diagnostic calibration technique

*To the Editor*: The technique known as qualitative diagnostic calibration (QDC), which combines the responses from a pair of Respitrace bands, was first described in your journal (1). QDC has been, and still is, a widely used method of calibration, but in investigating its possible use for a study in my own University I have come to the conclusion that it is not reliable. This conclusion is based on what I think is a problem with the derivation of the method, and not on any experimental evidence, although I include below, by way of illustration, some data collected locally.

The problem addressed by QDC is how to combine the movements in bands placed around the chest and abdomen into a single value that is proportional to change in volume during breathing. The obvious method is to run a calibration trial in which the movements in the bands and the change in volume are measured simultaneously. However, QDC claims to offer an attractive alternative by giving a method of discovering the relative weights that should be given to the bands, without the need for measuring change in volume directly. The idea behind QDC stems from the fact that the relative weight could be found if a set of measurements were made at constant volume. This is not possible if volume is not measured, so QDC takes a set of readings where the sum of the movements in the two bands is constant (or nearly so). The relative weight is then derived as minus the ratio of the SD values of the two restricted sets of readings (see *Eq. 5* in Ref. 1). Because in practice it is not possible to insist on exact equality of the sum, pairs of values within a specified range are taken.

The value given by Sackner et al. (1) in *Eq. 5* is always negative, which is surprising, since intuitively one would expect rib and abdomen often to move in rough unison, implying a positive value. Indeed, it appears from the literature that sometimes the negative sign in *Eq. 5* is ignored.

The problem with QDC stems from the fact that it takes chest and abdomen readings where the sum is constant and then derives its estimate of the relative weight assuming that these pairs of restricted measurements are independent. However, if the chest measurement goes up by a certain amount, to keep the sum constant, the abdomen measurement must come down by the same amount. The measurements will have the same SD and a perfect negative correlation. Even when the restriction of exact equality is relaxed, the correlation will still be high, contradicting the assumption used in deriving the QDC estimate of the relative weight.

If exact equality were possible, it is clear that the SD values of the chest and abdomen measurements would be equal, and so the QDC method would always give a value of −1. If the equality condition were relaxed completely, so that all pairs of readings were included, the value would just be minus the ratio of the SD values of the entire set of measurements. Relaxing the constraint slightly will, therefore, tend to give a value intermediate between these two extremes, which will depend on the extent to which the constraint is relaxed. The result is therefore arbitrary between these two limits.

To check these deductions, I asked my colleagues to let me have a set of Respitrace values from a trial in which volume had also been measured. The set they provided contained 97 pairs of readings, and by using least squares calibration the relative weight, often referred to as *K*, turned out to be +0.35. The value obtained by QDC depends on the extent to which the equality constraint is relaxed, and the values I obtained are shown in Table 1.

In Table 1, the width of the inclusion interval is the number of SDs either side of the mean of the sum. This is only one example used for illustration, but the results are exactly as expected; with a tight constraint, QDC gives a value close to −1. This changes steadily to become minus the ratio of the SDs of all of the data as the constraint is relaxed.

In conclusion, anyone considering using QDC should appreciate that the estimates that it gives for *K* are arbitrary and potentially misleading. Fortunately, the value of *K* is often not critical, since a wide range of values will give very similar correlations with volume. This explains why, in practice, QDC sometimes works reasonably well. However, QDC cannot be relied on to give appropriate values of*K* in all situations.

- Copyright © 1999 the American Physiological Society

## REFERENCES

The following is the abstract of the article discussed in the subsequent letter:

**Sackner, Marvin A., Herman Watson, Anne S. Belsito, Drew Feinerman, Manuel Suarez, Gerardo Gonzalez, Franklin Bizousky, and Bruce Krieger.** Calibration of respiratory inductive plethysmograph during natural breathing. *J. Appl. Physiol.* 66(1): 410–420, 1989.—We describe a single-posture method for deriving the proportionality constant (*K*) between rib cage (RC) and abdominal (AB) amplifiers of the respiratory inductive plethysmograph (RIP). Qualitative diagnostic calibration (QDC) is based on equations of the isovolume maneuver calibration (ISOCAL) and is carried out during a 5-min period of natural breathing without using mouthpiece or mask. In this situation, *K* approximates the ratio of standard deviations (SD) of the uncalibrated changes of AB-to-RC volume deflections. Validity of calibration was evaluated by *1*) analyzing RIP waveforms during an isovolume maneuver and *2*) comparing changes of tidal volume (Vt) amplitude and functional residual capacity (FRC) level measured by spirometry (SP) with RIP values. Comparisons of Vt(RIP) to Vt(SP) were also obtained in a variety of postures during natural (uninstructed) preferential RC and AB breathing and with voluntary changes of Vt amplitude and FRC level. Vt(RIP)-to-Vt(SP) comparisons were equal to or closer than published reports for single posture, ISOCAL, multiple- and linear-regression procedures. QDC of RIP in supine posture with comparisons to SP in that posture and others showed better accuracy in horizontal than upright postures.

## REPLY

In his letter, regarding our paper on the QDC procedure for calibrating respiratory inductive plethysmography (1-5), Thompson has not appreciated the fundamental approximation, based on the Konno and Mead (1-4) model, that the respiratory system moves with two degrees of freedom of motion, nor the physiological implications of the isovolume maneuver calibration procedure. Therefore, I feel compelled to address the issues he raises by mainly quoting from the text of our original 1989 paper, “Calibration of respiratory inductive plethysmograph during natural breathing” (1-5). I have left the quoted text in italics.

Thompson states that “the value given by *Eq. 1-5
* is always negative, which is surprising, since intuitively one would expect rib and abdomen to move in rough unison, implying a positive value.” He should reference our *Eq. 1-5
* that is derived from the isovolume maneuver in which tidal volume (Vt) is zero as in *Eq. 4.* The solution of this equation gives a negative proportionality constant (*K*) value that is correct for the isovolume maneuver, i.e., voluntarily shifting volume between rib cage (RC) and abdomen (AB), without changing volume at the airway if electrical polarity of RC and AB traces is set the same. The absolute value of *K*, a constant that sets the proportion for RC and AB, gains for both the isovolume maneuver and QDC calibration procedures. QDC uses an isovolume principle during natural breathing, which is independent of whether the subject has a coordinated or paradoxical thoracoabdominal motion, to compute *K*.

Thompson adds “… if the chest measurement goes up by a certain amount, to keep the sum constant, the abdomen measurement must come down by the same amount.” We stated that the sum of the uncalibrated volumes of the RC and AB (ΔuV_{RC} + ΔuV_{AB}) from one breath does not necessarily equal the sum derived from another breath, even if the amplitudes of both sums are equivalent, since the proportion of unscaled RC and AB excursions to the sum may vary. Rather than argue every statement that Thompson has made, I quote below the pertinent text from our paper he criticized.

*Variations of ΔV _{RC} and ΔV_{AB} during breathing occur from breath to breath even with breaths of equivalent Vt. Furthermore, in preliminary experiments, we found that over a 5- to 10-min period, these variations fit a normal statistical distribution curve. If a subject could breathe with a constant Vt during natural breathing before setting the electrical amplifier gains of RIP {respiratory inductive plethysmograph} according to K, then Eq. 2 {the isovolume equation, ΔV_{ao} ≅ M [K (ΔuV_{RC}) + (ΔuV_{AB}) where ‘u’ signifies uncalibrated} could be transformed utilizing the breath-to-breath SD of ΔuV_{RC} and ΔuV_{AB} signals. In Eq. 2, the SD of a constant Vt is zero, and, therefore, ΔV_{ao} drops out of the equation, and the constant M can be treated as unity gain. Eq. 2 can be rewritten*

*This indicates that the proportionality factor K may be solved from analysis of the uncalibrated RC and AB signals of RIP, which had been present to unity electrical gain, during natural breathing with principles of the ISOCAL {isovolume maneuver calibration method}. However, it is not technically possible for naturally breathing subjects to breathe at a constant Vt. Furthermore, during natural breathing, the sum (ΔuV*

_{RC}+ ΔuV_{AB}) from one breath does not necessarily equal the sum derived from another breath even if the amplitudes of both sums are equivalent, since the proportion of unscaled RC and AB excursions to the sum may vary. Thus one cannot select breaths of equivalent amplitude from the uncalibrated sum waveform and be certain that conditions of the constant Vthave been fulfilled. To circumvent this consideration, we reasoned that collection of a large number of breaths with exclusion of those breaths with large deviations from the mean sum [(ΔuV_{RC}) + (ΔuV_{AB})] might provide an approximation for a constant Vt to solve Eq. 1-5. Therefore, Eq. 1-5 contains two major approximations: 1) the respiratory system is assumed to move solely with two degrees of freedom of motion, and 2) statistical selection of breaths from a calibration period of natural breathing is assumed to provide a constant Vt when in fact Vt is instead a near-constant volume.Without presenting mathematical proof, Thompson states that “if exact equality were possible, it is clear that the SD values would be equal, and so the QDC method would always give a value of −1.” In fact, in his Table 1, giving values from a single trial, he presents varied SD inclusion values, none of which have such a value. He considered that the value of −1.11 with a SD of 0.25 is close to 1, but on the basis of an *n* = 1 I cannot reach such a conclusion! I find it difficult to respond to such fragmentary data without provision of an experimental design. Nonetheless, I could argue that his data are in keeping with our findings, viz., inclusion of SD values between 0.6 and 1.0 of the mean gave the most consistent values of*K*. Thus, inclusion of SD of 0.75 − 1.00 (SD of 0.60 was not listed) gave values that were almost the same, −0.79 and −0.78. In our paper, we addressed the varied values of *K* resulting from different values of SD inclusion. We stated, *in the present investigation, we arbitrarily decided to test 1-, 3-, and 5-min calibration periods and analyze those data for calculation of K, which lay within ±1.0 SD of the mean sum [(ΔuV _{RC} + (ΔuV_{AB})] recognizing that other combinations of collection times and data selection might have provided equivalent or different results than reported in the present study. *As pointed out below, the

*K*value of 0.35 he computed from the least squares method would not fulfill isovolume maneuver criteria most of the time (1-2), whereas a

*K*value of 0.78 based on our experience with QDC (1-5) would satisfy such criteria.

Thus, we stated that *the validity of applying Eq. 1-5 to calibration of RIP can be tested by ascertaining whether the isovolume maneuver leads to expected results, viz. the calibrated ΔV _{RC} and ΔV_{AB}signals have equal amplitudes in opposite directions such that their sum approaches zero. We performed a number of preliminary experiments to ascertain how many breaths were needed for collection during the calibration procedure and how many outliers from the mean uncalibrated sum [ΔuV_{RC}) + ΔuV_{AB})] were necessary to discard to obtain RC and AB electrical amplifier gains of RIP for satisfactory recordings of ΔV_{RC} and ΔV_{AB}during the isovolume maneuver. We considered both the inspiratory and expiratory limbs of the breaths for data selection over collection periods of 1-, 3-, 5-, and 10-min periods in six naturally breathing normal subjects whose respiratory rate ranged from 14 to 22 breaths/min. In addition, we utilized a range of multipliers of the SD of the mean sum [(ΔuV_{RC}) + (ΔuV_{AB})] to discard outliers and to calculate K from Eq. 1-5 while also testing the validity of K with isovolume maneuvers. A 3- to 10-min calibration period and elimination of data from analysis with Eq. 1-5 between 0.6 and 1.0 SD outside the mean uncalibrated sum [(ΔuV_{RC}) + (ΔuV_{AB})] gave the most consistent expected breath waveforms during the isovolume maneuvers.* This comparison explicitly demonstrated that the error in assuming approximation of a constant tidal volume in the QDC equations must have been inconsequential, since the values of

*K*from the isovolume maneuver calibration and the QDC procedures showed close correspondence.

The *K* value from a least squares calibration cannot be used as a standard for assessing volume-motion coefficients of the respiratory system if one accepts the Konno-Mead (1-4) hypothesis. This point was borne out by comparisons of volume validations and isovolume maneuver displays on a cathode ray oscilloscope made by Chadha et al. (1-2) among least squares and isovolume maneuver calibration procedures. We cited the results of this study in our 1989 paper (1-5) as printed below.

*… the QDC is a two-step procedure, viz, first the RC and AB electrical gains of the RIP amplifiers are correctly proportioned, and then the subject breathes to an external volumetric device such as a SP or integrated PNT system to attain equivalency. If the procedure is halted at the first step, then relative changes of Vt can be tracked. Completion of the second step allows calibration of RIP to absolute volume values. QDC differs from other calibration methods for RIP which incorporate breathing to an external volumetric device in one or two body postures as a one-step process. It follows that the QDC procedure itself can be tested for accurate proportioning of the RC and AB waveforms of RIP when the isovolume maneuver is performed after calibration. In this instance, deflections from the RC and AB excursions should be nearly equal and opposite in sign such that the sum of the two is zero or nearly zero. Confirmation of the validity of K in the supine posture was found in all normal trained subjects who were tested with the isovolume maneuver. This contrasts with the two-posture least-squares calibration procedure previously utilized, in which 55% of isovolume maneuvers in the supine and standing posture gave isovolume angles that significantly deviated from a 45° angle expected for the RC vs. AB (Konno-Mead) plot* (1-2).

Thompson concludes “anyone using QDC should appreciate that the estimates that it gives for *K* are arbitrary and potentially misleading.” I take issue with this statement, since the study by Chadha et al. (1-2) indicated that the value of *K* obtained from a calibration procedure must be tested with an isovolume maneuver in order to establish its validity. QDC was designed to provide a*K* value equivalent to the isovolume maneuver. The data presented in our paper indicate that the QDC procedure meets this test (1-5). Thompson mentions “fortunately the value of *K* is often not critical, since a wide range of values will give similar correlations with volume.” This may be true when breathing is associated with coordinated thoracoabdominal motion but not when there is significant discoordinated or paradoxical thoracoabdominal motion, as in severe inspiratory resistive loading, active sleep in newborns, and obstructive apneas and hypopneas. Thus Adams et al. (1-1) showed that the QDC procedure provided satisfactory validations for RIP against integrated pneumotachography in babies for both active and quiet sleep. On the other hand, using a single-position, simultaneous equation method for calibrating RIP in babies, Dolfin et al. (1-3) found that volume validation against integrated pneumotachography was satisfactory during quiet sleep (coordinated thoracoabdominal motion) but not during active sleep (paradoxical thoracoabdominal motion). The failure of Dolfin et al. to validate RIP during active sleep was most likely due to the inaccurate *K* value that would be expected from simultaneous equations or least squares calibration procedures (1-2).

- Copyright © 1999 the American Physiological Society