## Abstract

Key elements for determining alveolar-capillary membrane conductance (Dm) and pulmonary capillary blood volume (Vc) from the lung diffusing capacity (Dl) for carbon monoxide (Dl_{CO}) or for nitric oxide (Dl_{NO}) are the reaction rate of carbon monoxide with hemoglobin (θ_{CO}) and the Dm_{CO}/Dl_{NO} relationship (α-ratio). Although a range of values have been reported, currently there is no consensus regarding these parameters. The study purpose was to define optimal parameters (θ_{CO}, α-ratio) that would experimentally substantiate calculations of Dm and Vc from the single-inspired O_{2} tension [inspired fraction of O_{2} (Fi_{O2})] method relative to the multiple-Fi_{O2} method. Eight healthy men were studied at rest and during moderate exercise (80-W cycle). Dm and Vc were determined by the multiple-Fi_{O2} and single-Fi_{O2} methods (rebreathe technique) and were tabulated by applying previously reported θ_{CO} equations (both methods) and by varying the α-ratio (single-Fi_{O2} method) from 1.90 to 2.50. Values were then compared between methods throughout the examined α-ratios. Dm and Vc were critically dependent on the applied θ_{CO} equation. For the multiple-Fi_{O2} method, Dm was highly variable between θ_{CO} equations (rest and exercise); the range of Vc was less widespread. For the single-Fi_{O2} method, the θ_{CO} equation by Reeves and Park (1992) combined with an α-ratio between 2.08 and 2.26 gave values for Dm and Vc that most closely matched those from the multiple-Fi_{O2} method and were also physiologically plausible compared with predicted values. We conclude that the parameters used to calculate Dm and Vc values from the single-Fi_{O2} method (using Dl_{CO} and Dl_{NO}) can significantly influence results and should be evaluated within individual laboratories to obtain optimal values.

- carbon monoxide
- nitric oxide
- gas exchange
- gas transfer
- exercise

“lung diffusing capacity” refers to the ability of the lungs to transfer gases between the alveolar and pulmonary capillary compartments and is most frequently quantified by the rate of uptake of carbon monoxide (CO) during breath holding or rebreathing maneuvers (14, 20, 27, 29, 31).

Although the transfer of CO from alveolar space to pulmonary capillary blood in vivo is influenced by a number of factors, the simplified model described by Roughton and Forster is widely accepted as the standard for quantifying lung diffusing capacity (Dl) and more specifically lung diffusing capacity for CO (Dl_{CO}) (4, 16, 17, 21, 25). In this model, the overall conductance of CO from air to blood is represented by two conductance components: *1*) the diffusing capacity of the membrane itself (Dm_{CO}) and *2*) the binding of CO to hemoglobin (Hb) in the blood. These two conductances, arranged in series, are described in *Eq. 1*, where θ_{CO} is the reaction rate between CO and Hb in the blood, and Vc is the pulmonary capillary blood volume.

Since the binding of CO to Hb in blood has been shown to be dependent on O_{2} tensions in the lung (7, 8, 25, 26), the classic method for determining the subcomponents of *Eq. 1* (θ_{CO}, Dm_{CO}, and Vc) involves measurement of Dl_{CO} at multiple alveolar O_{2} tensions (Pa_{O2}). For the “multiple-O_{2} tension” method, Dl_{CO} is measured at two or three levels of Pa_{O2} (typically hypoxic, normoxic, and hyperoxic states). Values for θ_{CO} (as a function of Pa_{O2}) are calculated, a plot of (1/θ_{CO}) vs. (1/Dl_{CO}) is constructed, and a linear relationship is fitted to the data. The slope of this linear relationship is calculated as 1/Vc, and the intercept of the line across the *y*-axis is calculated as 1/Dm. A number of investigators have published equations to describe the mathematical relationship between 1/θ_{CO} and Pa_{O2}; however, these published equations vary greatly depending on the technique and test conditions (i.e., use of plasma vs. tissue vs. whole blood, blood smears vs. unstirred cell layers vs. flowing medium, etc.).

An alternate method was developed in which Dm and Vc values could be determined at a single Pa_{O2} (2, 12). This “single-O_{2} tension” method consists of simultaneously measuring Dl_{CO} with the lung diffusing capacity for nitric oxide (Dl_{NO}) (2, 12). In this method, the Roughton and Forster model of gas transfer across the alveolar capillary membrane is extrapolated to an NO gas species as shown by *Eq. 2*.

Because NO has such a high affinity for Hb (∼300 times faster than CO), the reaction rate of NO with Hb becomes a negligible component in the model in *Eq. 1*, and thus the disappearance of NO in the lung is considered to be directly proportional to the conductance of a gas across the membrane (Dm) only.

In the single-O_{2} tension method, one must make an assumption about the ratio of Dm_{NO} to Dm_{CO} (α-ratio). Theoretically, the α-ratio should be the ratio of the square root of molecular weights corrected by solubilities of NO and CO in tissue, giving a value of 1.93. However, in practice, this value appears to be too low to produce physiologically meaningful values for Dm and Vc, so values up to 2.49 have been used by many laboratories (32, 34).

Because these two parameters are fundamental to the determination of Dm and Vc in the single-Fi_{O2} method, the objective of the study was to define for our laboratory and experimental setup the optimal set of calculation parameters that would substantiate the single-Fi_{O2} method relative to the classic or multiple-Fi_{O2} method. The study is novel because *1*) it directly compares the multiple-Fi_{O2} and single-Fi_{O2} methods, using various θ_{CO} equations available in the published literature, and *2*) systematically investigates the effect of the α-ratio through a range of values. We suggest that such a survey of these measurements needs to be made on a laboratory-specific basis, particularly given the variation in technique as described in the literature.

## METHODS

### Subject and Ethical Information

Eight healthy nonsmoking adult men with no history of cardiopulmonary problems participated in the study. Individuals being treated for cardiovascular or pulmonary disorders were excluded from the study. This study was approved by the Mayo Clinic Institutional Review Board and conducted in accordance with the Declaration of Helsinki; all procedures followed institutional and Health Insurance Portability and Accountability Act (HIPAA) guidelines.

### Protocol

Subjects reported to the laboratory and participated in 1 day of testing. Resting measures of pulmonary function were performed and used to determine the bag volume for subsequent techniques. Rebreathe soluble gas measures for cardiac output (Q̇), lung diffusing capacity for CO (Dl_{CO}), and lung diffusing capacity for NO (Dl_{NO}) were collected under hypoxic, normoxic, and hyperoxic (initial Fi_{O2} of 18%, 35%, 55%, respectively) conditions. Measures at each condition were conducted in random order at rest and during constant-load exercise (80 W, cycle ergometry). Heart rate (HR) and oxygen saturation (%Sa_{O2}), were monitored throughout the study by pulse oximetry. Systolic blood pressure (BP) and diastolic BP were assessed by sphygmomanometer and taken by the same technician throughout the entire study.

### Cardiac Output and Diffusing Capacity Gas Measurements

A 5-liter rebreathe bag was filled with one of three test gas mixtures, in which only O_{2} content was varied (18%, 35%, 55%, respectively) between the three mixtures. Other components of the gas mixtures consisted of 9% helium (He), 0.6% acetylene (C_{2}H_{2}), 0.3% of a stable isotope of carbon monoxide (C^{18}O), 40 parts per million (ppm) NO (diluted immediately before the test into the bag from an 800-ppm NO source), and balance nitrogen (N_{2}). Gases were sampled by mass spectrometer (Perkin-Elmer 1100) and NO analyzer (Sievers Instruments, Boulder, CO); analysis was performed with a custom software package (28, 32). The more common isotope of CO was not used because the molecular mass of C^{18}O is nearly identical to that of N_{2}, making these gases indistinguishable by the mass spectrometer.

For each maneuver, subjects were switched to the rebreathe bag at the end of a normal expiration (end-expiratory lung volume, EELV) and instructed to nearly empty the bag with each breath for 10 consecutive breaths. The respiratory rate during the rebreathe maneuver was controlled with a metronome at a rate of 32 breaths/min. The rebreathe bag was then emptied with a suction device and refilled immediately before the next maneuver. Rebreathe bag volume was set at 75% of each individual's inspiratory capacity, and each maneuver was performed in duplicate. To preequilibrate the alveolar compartment with the proper O_{2} tension, subjects were given 18%, 35%, or 55% O_{2} to breathe for 5 min before each maneuver, as appropriate.

Backpressure corrections for the gases CO and C_{2}H_{2} were applied to the raw data from each rebreathe maneuver. Briefly, alveolar concentrations of CO and C_{2}H_{2} were monitored in the air exhaled from the subject directly preceding each rebreathing maneuver. Residual CO or C_{2}H_{2} was used in the calculation of Dl_{CO} and cardiac output as follows in *Eq. 4*:
_{gas,lung} is the end-tidal fractional concentration of soluble gas in the breath immediately preceding the rebreathe maneuver, F_{gas,i} is the end-tidal fractional concentration of soluble gas in *breath i*, and F_{gas,0} is the fractional concentration of soluble gas at *time 0* (*t*_{0}) as described by Sackner et al. (27). The slope of ln[F_{gas(corrected)i}] vs. time was used to calculate Dl_{CO} and cardiac output as described by Sackner et al. (27) and Triebwasser et al. (33), respectively.

Also, because each maneuver was performed with <30 s of rebreathing, the recirculation of acetylene, CO, and NO are considered to be negligible (22, 23). To confirm that the maneuver time was less than the recirculation time, the change in the breath-to-breath end-tidal concentration of C_{2}H_{2} was noted during the analysis of each maneuver. A decrease in the rate of decline in breath-to-breath end-tidal C_{2}H_{2} would indicate recirculation of the inhaled soluble gases (22, 23). In the present study, such a recirculation was not detected; linear regression of the natural logarithmic decay of C_{2}H_{2} was always linear with high *R*^{2} value of the linear fit line, thus providing evidence of a negligible recirculation effect.

### Mathematical Model for Diffusing Capacity and Its Subcomponents

The Roughton and Forester model for CO transport across the alveolar-capillary membrane was used as the basis for all calculations of Dm and Vc (25) described by *Eq. 1*.

The θ_{CO} term describes the reaction rate of CO with Hb in the blood and is expressed in units of milliliters per minute per millimeter of mercury. Numerous authors have published equations on the relationship between 1/θ_{CO} and inspired O_{2} concentration (6, 13, 24, 25, 30). The exact equations used in the present analyses are based on the general relationship shown in *Eq. 5*, in which the parameters *a* and *b* are varied according to previously published relationships as outlined in Table 1.

### Calculation of Dm and Vc Using Multiple Fi_{O2}: Classical Method

Three-point measures of Dm and Vc were calculated with data collected from 18%, 35%, and 55% Fi_{O2} trials. Measured Dl_{CO} values as well as the averaged end-tidal O_{2} (Pet_{O2}, a surrogate for alveolar O_{2}) were collected from each maneuver and used to calculate values for 1/θ_{CO} and 1/Dl_{CO} at each of the three Fi_{O2} levels. Plots of the relationship between 1/θ_{CO} (*x*-axis) and 1/Dl_{CO} (*y*-axis) were constructed, and linear fit lines were applied for measures obtained from each individual. The *y*-axis intercept of the linear fit line was defined as the inverse of the membrane diffusion resistance (1/Dm), and the slope of the linear fit line was defined as the inverse of the pulmonary capillary blood volume (1/Vc).

### Calculations of Dm and Vc Using a Single Fi_{O2}: Contemporary Method

Values for Dl_{CO} and Dl_{NO} collected at 35% Fi_{O2} were used to calculate values for Dm and Vc at a single O_{2} gas tension as originally derived by Guenard et al. (12) and executed as described by Borland and Higenbottam (2). Briefly, Dm_{CO} is estimated from the Dl_{NO} measurement and the ratio of the solubility of NO and CO gases into blood defined by the Bunsen solubility coefficient (α_{Bi}) in tissue and the molecular weight (MW) of each gas species. This relationship is described by *Eq. 6*. Solving for Dm_{CO} yields the relationship shown in *Eq. 7*.

To calculate values for Vc, the 1/Vc term shown in *Eq. 1* is isolated and the derived relationship for Dm_{CO} is incorporated to yield *Eq. 8*.

[adapted from Guenard et. al. (12)].

Using Bunsen solubility coefficients as published by Meyer et al. (20) yields a theoretical α-ratio value of 1.93; the additional incorporation of the heavy isotope of carbon monoxide (C^{18}O) yields a theoretical α-ratio value of 1.99. However, the optimal α-ratio used for determining Dm and Vc with this method is debatable. Published or utilized values for this factor range from 1.93 to 2.49 (1, 12, 32, 34) and it is recognized that it is unlikely this ratio would fall below 1.93.

A program was constructed (MATLAB, version 7.6, R2008a) to evaluate data over a range of α-ratios from 1.90 to 2.50. Values for Dm and Vc were calculated for each α-ratio and for each of the listed 1/θ_{CO} equations.

### Statistical Comparison Between Classic and Contemporary Methods

Calculated values for Dm and Vc were compared between the methods (multiple-Fi_{O2} vs. single-Fi_{O2} method). Lin's concordance correlation coefficient (CCC) was used to quantify subject-by-subject measurement agreement between the two methods (19). Paired *t*-tests were used to detect differences between the two methods. The threshold for significance for all statistical testing was set at *P* < 0.05.

#### Concordance correlation coefficient.

The CCC, as defined by *Eq. 9*, was used to determine the agreement of paired measures between the two methods across all subjects. In *Eq. 9*, *X̄ _{i}* is the mean of

*group i*,

*s*

_{Xi}

^{2}is the variance of

*group i*, and

*s*is the covariance between

_{xixj}*group i*and

*group j*, where

*group 1*and

*group 2 in*

*Eq. 9*refer to the multiple-Fi

_{O2}versus single-Fi

_{O2}methods, respectively.

For the CCC, a value of 0.20–0.40 indicates a fair agreement, 0.41–0.60 indicates a moderate agreement, 0.61–0.80 indicates a strong agreement, and 0.81–1.00 indicates an outstanding agreement between the compared methods. A negative CCC indicates a negative relationship between the methods. The optimal α-ratio each for Dm or Vc was determined as the α-ratio in which the CCC was at a maximum.

#### t-Statistic.

The *t*-statistic, as defined by *Eq. 10*, was used to determine the magnitude and direction of differences between the measurements obtained from the different calculation methods across the given range of α-values. In *Eq. 10*, *X̄ _{i}* is the mean of

*group i*,

*s*is the standard deviation of

_{Xi}*group i*, and

*n*is the sample size.

*Group 1*reflects values obtained with the multiple-Fi

_{O2}method, and

*group 2*reflects values obtained with the single-Fi

_{O2}method.

*t*-Statistics between −2 and +2 are not considered to be statistically different between the two techniques; where *t* = 0 there is no statistical difference between the two methods. *t*-Statistic values greater than +2 or less than −2 indicate that the calculated values are statistically different between the two techniques (*P* < 0.05). For this data set, a positive *t*-statistic indicates that the single-Fi_{O2} method underestimated values compared with the values obtained by the multiple-Fi_{O2} method; a negative *t*-statistic indicates that the single-Fi_{O2} method overestimated values compared with the values obtained by the multiple-Fi_{O2} method. With the values obtained from the multiple-Fi_{O2} method as the standard, the optimal α-ratio for each value (Dm or Vc) was determined as the α-ratio in which the absolute value of the *t*-statistic (i.e., |*t*-statistic|) was at a minimum or equal to zero. The optimal α-ratio using the *t*-statistic for each equation was then determined as the α-ratio in which the *t*-statistic was closest to zero for both the Dm and Vc values.

## RESULTS

Subject characteristics and the cardiovascular and metabolic measurements at rest and during exercise are shown in Tables 2 and 3, respectively. As expected, there were significant increases in cardiovascular (HR, Q̇, stroke volume) and metabolic [O_{2} consumption (V̇o_{2}), minute ventilation (V̇e)] variables with exercise. Measures of Dl_{CO} and Dl_{NO} also increased with exercise.

### Multiple-Fi_{O2} Method

With the multiple-Fi_{O2} method, Dm and Vc values were tabulated using the seven equations for θ_{CO} for each individual for each test condition. Data obtained with the RP θ_{CO} equation are shown in Fig. 1.

#### Resting condition.

For use as a general physiological reference, predicted values for Dm and Vc at rest with rebreathing techniques were calculated from equations previously published by Crapo et al. (5). [It should be noted that experiments to determine predicted values of Dm and Vc were obtained using the RF2.5 θ_{CO} equation (5).] With the multiple-Fi_{O2} method, calculated values along with percent predicted values for Dm and Vc at rest are shown in Table 4. Briefly, there was considerable variation in the calculated Dm values depending on the applied θ_{CO} equation. For resting Dm calculations, equations RFinf and Stam yielded values that were within two standard deviations of the predicted value; equation RP yielded a Dm value within four standard deviations of the predicted value. The remainder of the equations yielded Dm values that were beyond four standard deviations of the predicted value, with one equation (RF7.4) generating negative Dm values that are not considered to be physiologically plausible. For Vc calculations at rest, equation RP yielded values within two standard deviations of the predicted value and equation Hol yielded values within three standard deviations of the predicted value. All other equations yielded Vc values beyond four standard deviations of the predicted values. Also notable, Vc values obtained by equations RF1.5, RF2.5, and RFinf were equivalent. This result was expected, given that the calculation of 1/Vc is dependent only on the slope of the 1/Dl_{CO} vs. 1/θ_{CO} curve, a factor defined as variable *a* in *Eq. 5* that is constant across these three equations.

#### Exercise condition.

Calculated values for Dm and Vc with the multiple-Fi_{O2} method during exercise are also shown in Table 4. Comparing the matching θ_{CO} equation values to the resting condition, the range in values for Dm and for Vc observed during exercise were similar to those obtained at rest. The only exception was the values obtained with equation RF7.4, where Dm increases from an unphysiologically large negative value to a positive value. Similar to that seen at rest, considerable variation in the Dm values was observed during exercise depending on the θ_{CO} equation applied. Overall, Dm increased with exercise in all but one θ_{CO} equation. The exception was equation RF1.5, where a decrease in Dm of 18% was observed (Table 4). Calculations for Vc during exercise increased relative to baseline for all θ_{CO} equations. The observed increase in Vc during exercise was ∼6.5% of the resting Vc value, and, surprisingly, the magnitude of the increase was consistent across all θ_{CO} equations.

### Single-Fi_{O2} Method

Calculated values for Dm were only dependent on measured Dl_{NO} and the α-ratio and not dependent on the applied θ_{CO} equation. With the single-Fi_{O2} method, we obtained Dm values for each α-ratio and Vc values for each applied α-ratio and for each θ_{CO} equation for all individuals under both test conditions.

#### Resting and exercise conditions.

As shown in Fig. 2, Dm decreases in a curvilinear fashion with an increasing α-ratio. At rest, Dm varies from a maximum of 55.3 ± 9.2 ml·min^{−1}·mmHg^{−1} at α = 1.90 to a minimum of 42.0 ± 7.0 ml·min^{−1}·mmHg^{−1} at α = 2.50. Calculated Dm values during exercise vary from a maximum of 64.0 ± 7.8 ml·min^{−1}·mmHg^{−1} at α = 1.90 to a minimum of 48.7 ± 5.9 ml·min^{−1}·mmHg^{−1} at α = 2.50. [Recall that for the single-Fi_{O2} method, determination of Dm is only dependent on measured Dl_{NO} and the assumed α-ratio (*Eqs. 6* and *7*). Thus the observed Dm values from the single-Fi_{O2} method are independent of the applied θ_{CO} equation.]

The Vc values for the single-Fi_{O2} method are dependent on two factors, the applied θ_{CO} equation and the applied α-ratio. As shown in Fig. 3, for all equations, minimum Vc values occurred at the smallest applied α-ratio (i.e., α = 1.90) and increased in an accelerated fashion with increasing α-ratio such that maximum Vc values occurred at the largest applied α-ratio (i.e., α = 2.50). Also, the standard deviation and standard error of group increased with increasing α-ratio.

### Comparison Between Multiple-Fi_{O2} and Single-Fi_{O2} Methods

Shown in Table 5 is the observed Dl_{NO}-to-Dm_{CO} ratio that is representative of the α-ratio that is necessarily approximated when using the single-Fi_{O2} method. For this ratio, Dm_{CO} was obtained from the multiple-Fi_{O2} method and Dl_{NO} was directly measured. Also summarized in Table 5 are the numeric values for comparisons between calculated Dm and Vc values using the *t*-statistic and the CCC. Briefly, when comparing the multiple-Fi_{O2} and single-Fi_{O2} methods the most favorable α-ratios for all but one applied θ_{CO} equation occurred at the extremes of the α-range examined here. It is only with equation RP that the calculated Dm and Vc values are comparable between the methods at an intermediate α-value (see Table 5). Figure 4 shows how the *t*-statistic varies with α-ratio for each θ_{CO} equation. Similarly, Fig. 5 illustrates the variability in the CCC comparison for each θ_{CO} equation.

For both Dm and Vc, the RP θ_{CO} equation produced the best overall agreement at rest and during exercise with the greatest agreement as shwon by the *t*-statistic, occurring at α-ratios between 2.08 and 2.26. In this range of α-ratios, the CCC confirmed this agreement with a reasonable demonstration of concordance between the multiple-Fi_{O2} and single-Fi_{O2} methods (Fig. 5).

## DISCUSSION

Although the resistive model first described by Roughton and Forster is widely used as the underlying mathematical basis for soluble gas transport across the lung, the specifics of the mathematical equations used to obtain values for Dm and Vc are not standardized and can vary greatly between laboratories. In this study, we directly compared two common methods for obtaining Dm and Vc, the classic multiple-Fi_{O2} method and the newer single-Fi_{O2} method. In eight normal subjects at rest and during low-level exercise we found the best agreement between the two methods by using the θ_{CO} equation published by Reeves and Park (24) to determine the reaction rate of CO with Hb (θ_{CO}) in blood and an α-ratio defining the Dm_{NO}-to-Dm_{CO} ratio of 2.26. With this study, we contend that investigators should consider carefully what θ_{CO} equation and α-ratio to apply when calculating Dm and Vc values from measures of Dl_{CO} or Dl_{NO}.

### Major Findings

The present data set demonstrates that there is substantial variability in calculated values for Dm and Vc specifically related to the θ_{CO} equation and, when using the single-Fi_{O2} method, also related to the α-ratio. When the Crapo et al. predicted values (5) are used as a broad predictor of expected values for Dm and Vc, it is clear that not all of the θ_{CO} equations used in these analyses yield data within reasonable range of the predicted estimates (± 4 SD). Indeed, with the multiple-Fi_{O2} method the Dm values at rest obtained from equations RF1.5 and Hol are greatly exaggerated compared with the predicted values and the Dm values obtained from equation RF7.4 are negative. The Vc calculations by all θ_{CO} equations are in closer proximity to the predicted values at rest and demonstrate increases during exercise. The increases in Vc and in Dl_{CO} with exercise, however, are lower than would have been expected for an exercise load of 80 W. The blunted increase is thought to be due to the fact that bag volume was set at 75% of inspiratory capacity for all rebreathing maneuvers. This required subjects to breathe at an augmented tidal volume at rest; during exercise tidal volume and rebreathe bag volume were more closely matched. Because both Dl_{CO} and Dl_{NO} (and consequently Dm and Vc) increase with increasing alveolar volume (10), it is likely that these variables were somewhat overestimated in the resting condition and the increases observed when going from rest to exercise would subsequently be underestimated (10) It is also recognized that the Dl_{NO}-to-Dl_{CO} ratio observed in the present study is on the low end of that reported by other investigators (10). At this time, we do not have a definitive explanation for this difference.

For the present data set, when comparing Dm and Vc values between methods and calculated over the given range of α-ratios, we noted how the optimal ratio for Dm compared with the optimal α-ratios for Vc for a given equation. Also noted was how the optimal α-ratios at rest compared with those during exercise. In determining the optimal combination of θ_{CO} equation and α-ratio, equations that yielded statistically different values between the two methods for either Dm or Vc in the resting condition or during exercise were eliminated. Equations in which the optimal α-ratios for Dm and Vc in the same condition occurred at diametrically opposite ends of the α-ratio range were also eliminated. The θ_{CO} equation that remained was that published by Reeves and Park (equation RP). Additionally, for equation RP the optimal α-ratios with a minimum *t*-statistic and with a maximum CCC are similar and are comparable to the calculated Dl_{NO}-to-Dm_{CO} ratio. The α-ratios that yielded Dm and Vc results most similar between the two methods were between 2.15 and 2.26 at rest and between 2.08 and 2.26 during exercise. Thus we conclude that, for the data collection system used and for the conditions in which the data were collected, the RP θ_{CO} equation coupled with the associated optimal α-ratios provides Dm and Vc values from the single-Fi_{O2} method most closely related to those obtained with the multiple-Fi_{O2} method. Using α-ratios below these ranges may result in underestimated Dm and overestimated Vc values. Conversely, using α-ratios above these ranges may result in overestimated Dm and underestimated Vc values.

### Variation in the θ_{CO} Equation: Roughton and Forster, 1957

Because it applies to both the multiple-Fi_{O2} method and the single-Fi_{O2} method, selection of the θ_{CO} equation is critically important to the resultant calculation of Dm and Vc values. Thus this parameter needs to be carefully considered when using soluble gas measures to determine Dm and Vc. Sources of θ_{CO} equation variability arise from the use of diverse techniques with which to quantify the rate of CO binding to Hb and specifically Hb in blood.

In addition to serving as the mathematical basis and setting the standard for experimental methodology when determining Dm and Vc from measures of Dl_{CO}, the seminal publication by Roughton and Forster (25) also set the standard for θ_{CO} equation parameters (23). However, no equation for θ_{CO} is explicitly given by the authors, thus leaving the variables *a* and *b* of *Eq. 5* up for interpretation. The figure likely used to extract a precise θ_{CO} equation shows three different curves for a relationship between 1/θ_{CO} and Po_{2}. The three variants reflect differences in the assumed permeability of the red cell membrane, where low (λ = 1.5), moderate (λ = 2.5), and high (λ = ∞) permeability are considered (producing equations RF1.5, RF2.5, and RFinf, respectively). The slope of the 1/θ_{CO} vs. Po_{2} curve remains constant with these variants, but there is a negative offset with increasing red cell permeability. Factors that contribute to the variation in Dm and Vc determination are also likely again because no explicit equation parameters are stated in the original article, and because there are three variants of the original θ_{CO} equation. Authors who cite the 1957 article likely interpret the given figures slightly differently. This gives rise to multiple versions of the 1/θ_{CO}-Po_{2} relationship although the same source may be cited. At present, equation RF2.5 (assuming moderate red cell permeability) is cited most frequently, but the other variants are also utilized.

### Variation in the θ_{CO} Equation: Corrections for pH

It has since been recognized that experiments described in the classic Roughton and Forster manuscripts were carried out at a pH of ∼8.0 (6–8, 25, 26). Forster (6) comments on this oversight and provides a correction θ_{CO} equation (at pH = 7.4, θ_{CO} equation RF7.4); however, the corrected equation is not often cited. In the present study, equation RF7.4 yielded highly unlikely values for Dm (negative group average at rest, exceedingly high group average during exercise). Similar negative Dm values from equation RF7.4 were also noted by Stam et al. (30). To address the issue, Stam and colleagues estimated a pH correction based on equation RFinf and an abstract by Kraweic et al. (18). This correction provided an additional version of the θ_{CO} equation in the absence of direct experimentation. This also accounts for the close similarity between equations Stam and RFinf in the results of the present study.

### Variation in the θ_{CO} equation: Distinct Technique and Unstirred Cell Layers

Specific details of the techniques can be found in the original articles or in an eloquent review by Hughes and Bates (17). Briefly, many previous experiments incorporated continuous-flow (7, 8, 17, 26) and stopped-flow (13, 17) techniques on red cell suspensions. However, for both the continuous- and stop-flow techniques the unstirred plasma layer directly surrounding red blood cells serves to increase CO diffusion resistance and thus affects the overall rate of interaction between CO and Hb in blood. To minimize the resistance of the unstirred layer, Reeves and Park later used a thin film technique (24).

To determine the mechanisms behind why there are such different descriptions of the same θ_{CO} relationship, Chakraborty et al. (3) examined analytically the uptake of O_{2}, CO, CO_{2}, and NO by red blood cells in blood considering an assortment of physiological variations, including that of Po_{2}. Outputs of their mathematical model were then compared with θ_{CO} equations RF2.5, RF7.4, Hol, and RP (3). With this mathematical model, Chakraborty et al. demonstrated that the uptake of reactive gases (specifically O_{2}, CO, and NO) is highly sensitive to the thickness of the unstirred layers surrounding red blood cells. Greater 1/θ_{CO} values occur with thicker unstirred layers prevalent in both continuous- and stop-flow techniques. In the present study the Dm and Vc values obtained with the RP θ_{CO} equation yield data within a reasonable range of predicted values (±4 SD) for an α-ratio similar to the observed Dl_{NO}-to-Dm_{CO} ratio. Taken together with the findings by Chakraborty et al, the present data suggest that, in vivo, there is minimal thickness to the unstirred layer surrounding red blood cells and strengthens the argument for use of equation RP.

### Comparison Between Multiple- and Single-Fi_{O2} Methods

Also important to the determination of Dm and Vc from soluble gas measures is the method by which the data are collected. Although the classic multiple-Fi_{O2} technique is still widely used, the single-Fi_{O2} method has also been adopted by several investigators. Thus there is additional variation in published Dm and Vc values associated with data collected under separate methodologies and without a clearly defined set of standards.

Similar to the present study, Tamhane et al. (32) previously examined the differences between the multiple- and single-Fi_{O2} methods in human subjects, but these investigators considered only a single θ_{CO} equation (RF2.5) and α-ratio (1.93). In this study, the investigators showed a strong relationship of the calculated Vc values between the two methods for the given θ_{CO} equation and α-ratio. Similar results with the RF2.5 equation were not observed here. Tamhane et al. also reported calculated Dl_{NO}-to-Dm_{CO} ratios of 2.42, 2.49, 2.52, and 2.54 at rest and during 25%, 50%, and 80% V̇o_{2max} exercise, respectively. In the present study, comparable values for the Dl_{NO}-to-Dm_{CO} ratio were observed with the Reeves and Park θ_{CO} equation (rest 2.25, exercise 2.26), but not with any of the other θ_{CO} equations examined.

Notably, both the Tamhane study and the present study yielded ratios that were considerably greater than the theoretical values of 1.93 (Tamhane et al.) or 1.99 (present study), indicating a greater disappearance of NO than theoretically expected. Possible contributors to the discrepancy between the theoretical and empirical values for the α-ratio include *1*) the uptake of NO by blood passing through the bronchial mucosal circulation in the non-gas-exchanging airways, *2*) the rapid conversion of NO to N_{2} and O_{2} with exposure to O_{2}, or *3*) the fact that the existing values for the Bunsen solubility coefficients for NO and CO are for solubility of these gas species in saline, plasma, or a nondescript substance labeled “tissue.” Thus the Bunsen solubilities which provide the basis for the theoretical α-ratio may not necessarily reflect nonheterogeneic diffusion pathways in the tissue or the authentic solubility of each gas in a colloidal substance.

### Hypoxic, Normoxic, and Hyperoxic Testing

A physiological consideration that should be acknowledged is the use of a hypoxic gas mixture in the multiple-Fi_{O2} method. In the mathematical model presented by Chakraborty et al., at Po_{2} < 300 mmHg there is considerable variability in the calculated θ_{CO} value dependent on boundary conditions and initial values applied to the analyses. Interestingly, the curves defined by the empirically obtained data (i.e., θ_{CO} equations RF2.5, RF7.4, Hol, and RP) tended to be bound within the analytical solutions provided by the model based on an initial rate of diffusion and the model based on a 10-s time-averaged rate of diffusion. At first glance, this mathematical model appears to support the argument that only normoxic and hyperoxic measures be considered if using the multiple-Fi_{O2} method. Indeed, it is well documented and widely accepted that when Pa_{O2} levels are maintained above 100 mmHg, the diffusing capacity of CO is based on an “oxyhemoglobin replacement reaction” and the uptake of CO in this situation is entirely reaction rate limited (24). At Pa_{O2} levels below 100 mmHg, it is thought that CO begins binding to unliganded heme sites (i.e., to the available sites of partially deoxygenated hemoglobin); thus the uptake of CO transitions from reaction rate limitation to a transport limitation (specifically a diffusion rate limitation). While the technique should typically use inspired O_{2} concentrations that keep Pa_{O2} above 100 mmHg, we did not observe a significant difference between data obtained from a 2-point linear fit (norm- and hyperoxic, where Pa_{O2} > 100 mmHg; data not shown) and a 3-point linear fit (hypo-, norm-, and hyperoxic, where the hypoxic Pa_{O2} < 100 mmHg). Paired *t*-tests between Dm and Vc results obtained with the 2-point versus the 3-point linear fit methods show that the measures obtained by each of these calculation approaches is not different (*P* = 0.74 at rest, *P* = 0.25 during exercise); however, this does not directly infer that the measures are alike. To evaluate the agreement between the two approaches, we used the CCC. The two methods for Vc values showed strong agreement for all the θ_{CO} equations used (CCC > 0.7 for each θ_{CO} equation at rest, CCC > 0.6 for each θ_{CO} equation during exercise). Agreement between the two methods for Dm values varied for each θ_{CO} equation used. At rest, fair to moderate Dm agreement was seen with equations RF2.5, RFinf, RP, and Stam. During exercise, fair Dm agreement was seen with equations RFinf, RP, and Stam. While the inclusion of a hypoxic data point may increase θ_{CO} and decrease 1/Dl_{CO}, causing a steepening of the slope of 1/Vc, this was not observed in the present study.

In the context of the mathematical model put forth by Chakraborty et al. (3), this in vivo finding may suggest that despite the fact that the gas reaction in the hypoxic condition was one of low O_{2} levels, the overall transport of CO across the alveolar-capillary space does not appear to have been significantly altered (Fig. 1). It is possible that at the hypoxic exposure level the increased rate of reaction associated with CO binding to deoxyhemoglobin (compared with the rate of the oxyhemoglobin replacement reaction) may be offset by an increased CO transport limitation associated with a lower driving pressure gradient across the alveolar-capillary spaces. However, validation of this theory would need to be done in additional in vitro and in vivo studies.

### Study Limitations

#### Influence of repeated Dl_{CO} measures.

It is well documented that repeated inhalations of CO will cause *1*) a rise in plasma CO levels and *2*) a rise in circulating COHb that in turn leads to decreased measures of Dl_{CO} similar to those seen with anemia. Although a CO backpressure correction was applied to address the rise in plasma CO levels, we did not directly measure circulating COHb levels. The exclusion of directly measured COHb levels throughout the experimental protocol is a limitation of the present study. Efforts to limit the buildup of COHb included a time separation of several minutes between rebreathing maneuvers and the periodic administration of hyperoxic gas (55% O_{2}) to promote the binding of O_{2} versus CO. Also, based on the works of Graham et al. (11) and Frey et al. (applying a COHb correction when using a rebreathe technique) (9), retrospective analysis of the present data set demonstrated that the maximum underestimation of the reported Dl_{CO} measures relative to the “true” Dl_{CO} was no more than 2% and considered by the authors to be relatively minor.

#### Other physiological considerations with presented methods.

An additional limitation to the present study is that dissimilarity in Dm and Vc results between the multiple- and single-Fi_{O2} methods may also arise from basic physiological considerations. It is known, for instance, that D_{LCO} measures are affected by ventilation-perfusion (V̇a/Q̇) mismatching within the lung (35–37, 39). Thus any functional measures of the lung involving the gas interactions between the alveolar and capillary spaces could be physiologically influenced by the changes in V̇a/Q̇ matching/mismatching known to occur with changes in Fi_{O2}.

Also, in using the disappearance of acetylene in the lung to measure cardiac output it was assumed that pulmonary capillary blood flow is equal to cardiac output. However, in a population of young, healthy subjects, pulmonary capillary blood flow is approximately equivalent to cardiac output and any error associated with this assumption is considered to be minimal (15, 38).

It is also possible that during exercise the lung-to-lung recirculation time may be less than the time needed to collect end-tidal gas concentration data over 6–8 breaths. There is a low risk that cardiac output, Dl_{CO}, and Dl_{NO} measurements may be underestimated because of a recirculation effect. Efforts to mitigate this risk included *1*) using only 6–8 breaths for the measurements so that the collection of data for each maneuver was completed before recirculation would be expected to occur and *2*) allowing a time of several minutes between rebreathing maneuvers in which some washout of the soluble gases is expected to occur.

Finally, it is important to note that the study and analytical exercise presented here was performed in normal, healthy individuals. Disease states such as chronic obstructive pulmonary disease (COPD), asthma, interstitial lung disease, heart failure, etc. may drastically alter the mechanics of uptake for each of the soluble gases used here. Application of the specific recommended equations and α-ratios should be used cautiously in the above-mentioned and other patient populations.

### Conclusions

We conclude that the parameters used to obtain Dm and Vc values from measures of Dl_{CO} or Dl_{NO} must be carefully considered before their experimental use. With this data set and for our specific laboratory, we have shown that the difference in Dm and Vc values calculated with a multiple-Fi_{O2} versus a single-Fi_{O2} method are minimized by using the θ_{CO} equation described by Reeves and Park (1991) and an α-ratio of ∼2.2. This parameter combination yields Dm and Vc values that are physiologically plausible in normal subjects at rest and when performing low-level exercise.

Although specific parameters apply directly to normal subjects and to the laboratory in which the data were collected, the implications of the study expand to all those who implement similar practices to calculate values for Dm and Vc. In the absence of standardization, we suggest that individual laboratories also compare the multiple- and single-Fi_{O2} methods so that subsequently published values for Dm and Vc are derived from empirically tested equations and technique parameters.

## GRANTS

This study was supported by National Heart, Lung, and Blood Institute Grant HL-71478 and by the Mayo Foundation.

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

## ACKNOWLEDGMENTS

The authors thank the subjects for their participation in our study.

- Copyright © 2010 the American Physiological Society