Calculating alveolar capillary conductance and pulmonary capillary blood volume: comparing the multiple- and single-inspired oxygen tension methods

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 O₂ tension [inspired fraction of O₂ (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.

“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.

$$\frac{1}{{\text{DL}}_{\text{CO}}}=\frac{1}{{\text{Dm}}_{\text{CO}}}+\frac{1}{\left({\theta }_{\text{CO}}·{\text{V}}_{\text{C}}\right)}$$ (1)

Since the binding of CO to Hb in blood has been shown to be dependent on O₂ 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 O₂ tensions (Pa_O2). For the “multiple-O₂ 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-O₂ 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.

$$\frac{1}{{\text{DL}}_{\text{NO}}}=\frac{1}{{\text{Dm}}_{\text{NO}}}+\frac{1}{\left({\theta }_{\text{NO}}·{\text{V}}_{\text{C}}\right)}$$ (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.

$$\frac{1}{{\text{DL}}_{\text{NO}}}=\frac{1}{{\text{Dm}}_{\text{NO}}}\therefore {\text{DL}}_{\text{NO}}={\text{Dm}}_{\text{NO}}$$ (3)

In the single-O₂ 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 O₂ 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 (C₂H₂), 0.3% of a stable isotope of carbon monoxide (C¹⁸O), 40 parts per million (ppm) NO (diluted immediately before the test into the bag from an 800-ppm NO source), and balance nitrogen (N₂). 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 C¹⁸O is nearly identical to that of N₂, 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 O₂ tension, subjects were given 18%, 35%, or 55% O₂ to breathe for 5 min before each maneuver, as appropriate.

Backpressure corrections for the gases CO and C₂H₂ were applied to the raw data from each rebreathe maneuver. Briefly, alveolar concentrations of CO and C₂H₂ were monitored in the air exhaled from the subject directly preceding each rebreathing maneuver. Residual CO or C₂H₂ was used in the calculation of Dl_CO and cardiac output as follows in Eq. 4:

$${\text{F}}_{\text{gas}{\left(\text{corrected}\right)}_i}=\frac{\left(\frac{{\text{F}}_{\text{gas,}i}-{\text{F}}_{\text{gas,}\text{lung}}}{{\text{F}}_{\text{gas,}\text{0}}}\right)}{{\text{F}}_{\text{He,}i}}$$ (4)

where F_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 (t₀) 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 C₂H₂ was noted during the analysis of each maneuver. A decrease in the rate of decline in breath-to-breath end-tidal C₂H₂ 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 C₂H₂ was always linear with high R² 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 O₂ 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.

$$\frac{1}{{\theta }_{\text{CO}}}=a·{\text{Po}}_{\text{2}}+b$$ (5)

Table 1.

θ_CO equations and their references

Equation Abbreviation	a	b	Reference	Assumptions
RF1.5	0.0058	1.00	Roughton and Forster (1957) (25)	pH = 8.0; λ = 1.5
RF2.5	0.0058	0.73	Roughton and Forster (1957) (25)	pH = 8.0; λ = 2.5
RFinf	0.0058	0.33	Roughton and Forster (1957) (25)	pH = 8.0; λ = ∞
RF7.4	0.0041	1.30	Forster (1987) (6)	pH = 7.4; λ = ∞
Hol	0.0065	1.08	Holland (1967) (13)
RP	0.008	0.0156	Reeves and Park (1992) (24)
Stam	0.0055	0.73	Stam et al. (1991) (30)	pH = 7.4; λ = ∞

θ_CO, reaction rate of CO with hemoglobin. λ denotes the ratio of permeability of the red cell membrane to the permeability of the red cell interior; a and b refer to parameters of the common equation 1/θ_CO = a·Po₂ + b.

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 O₂ (Pet_O2, a surrogate for alveolar O₂) 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 O₂ 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.

$$\frac{{\text{Dm}}_{\text{NO}}}{{\text{Dm}}_{\text{CO}}}=\left(\frac{\alpha {\text{B}}_{\text{NO}}}{\sqrt{{\text{MW}}_{\text{NO}}}}÷\frac{\alpha {\text{B}}_{\text{CO}}}{\sqrt{{\text{MW}}_{\text{CO}}}}\right)=\left(\frac{\alpha {\text{B}}_{\text{NO}}}{\alpha {\text{B}}_{\text{CO}}}\times \sqrt{\frac{{\text{MW}}_{\text{CO}}}{{\text{MW}}_{\text{NO}}}}\right)$$ (6)

$${\text{Dm}}_{\text{CO}}={\text{Dm}}_{\text{NO}}\times {\left(\frac{\alpha {\text{B}}_{\text{NO}}}{\alpha {\text{B}}_{\text{CO}}}\times \sqrt{\frac{{\text{MW}}_{\text{CO}}}{{\text{MW}}_{\text{NO}}}}\right)}^{-1}\therefore {\text{Dm}}_{\text{CO}}={\text{Dm}}_{\text{NO}}\times {\left({\alpha }_{\text{ratio}}\right)}^{-1}=\frac{{\text{Dm}}_{\text{NO}}}{\left({\alpha }_{\text{ratio}}\right)}\approx \frac{{\text{DL}}_{\text{NO}}}{\left({\alpha }_{\text{ratio}}\right)}$$ (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.

$$\frac{1}{{\text{V}}_{\text{c}}}={\theta }_{\text{CO}}·\left(\frac{1}{{\text{Dm}}_{\text{CO}}}-\frac{{\alpha }_{\text{ratio}}}{{\text{DL}}_{\text{NO}}}\right)$$ (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 (C¹⁸O) 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_Xi² is the variance of group i, and s_xixj is the covariance between 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.

$$\text{CCC}=\frac{2·s_{X_1{X}_2}}{s_{X_1}^2+s_{X_2}^2+{\left({\overline{\text{X}}}_1-{\overline{\text{X}}}_2\right)}^2}$$ (9)

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_Xi is the standard deviation of 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.

$$t=\frac{{\overline{\text{X}}}_1-{\overline{\text{X}}}_2}{S_{{\text{X}}_1{\text{X}}_2}·\sqrt{\left(2/n\right)}},\text{Where}{S}_{{\text{X}}_1{\text{X}}_2}=\sqrt{\frac{s_{x_1}^2+s_{x_2}^2}{2}}$$ (10)

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 [O₂ consumption (V̇o₂), minute ventilation (V̇e)] variables with exercise. Measures of Dl_CO and Dl_NO also increased with exercise.

Table 2.

Subject characteristics

Characteristics
No. of Subjects	8
Age, yr	27.4 ± 10.6
Height, cm	184.5 ± 8.7
Weight, kg	87.4 ± 7.6
BMI, kg/m2	25.7 ± 2.2
BSA, m2	2.1 ± 0.1
Inspiratory capacity, liter	4.0 ± 0.6

Values are reported as means ± SD. BMI, body mass index; BSA, body surface area.

Table 3.

Physiological monitoring measurements

	Workload
Physiological Monitoring	Rest	80-W Cycle Exercise
HR, beats/min	69 ± 9	106 ± 14
Cardiac output, l/min	6.7 ± 1.9	14.4 ± 1.7
Stroke volume, ml	100 ± 34	138 ± 22
DlCO, ml·min−1·mmHg−1	30.0 ± 3.9	37.4 ± 4.8
DlNO, ml·min−1·mmHg−1	105.0 ± 18.8	121.7 ± 15.8
DlNO/DlCO	3.51 ± 0.48	3.27 ± 0.38
V̇o2, ml·min−1·kg−1	5.7 ± 1.3	17.8 ± 1.5
V̇o2, ml/min	498 ± 139	1553 ± 120
V̇e, l/min	18.3 ± 7.4	44.7 ± 7.9

Values are reported as means ± SD. HR, heart rate; Dl_CO, Dl_NO, lung diffusing capacity for carbon monoxide, nitric oxide; V̇o₂, O₂ consumption; V̇e, minute ventilation.

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.

Fig. 1.

Plotting the relationship between the inverse of the reaction rate of CO with hemoglobin (1/θ_CO) and the inverse of lung diffusing capacity for CO (1/Dl_CO) at rest and during exercise. Data were obtained from Dl_CO measures collected during rebreathe techniques using gas mixtures with 18%, 35%, and 55% O₂ concentration. In this graph, 1/θ_CO was calculated with the equation defined by Reeves and Park (24). Slope of the linear fit of the lines was subsequently used to define the inverse of pulmonary capillary blood volume (1/Vc); back-extrapolation of the linear fit curve to x = 0 was used to define the inverse of alveolar-capillary membrane conductance (1/Dm). Values are represented as means ± SE.

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.

Table 4.

Calculated Dm and Vc values: multiple-Fi_O2 method

	Resting Condition		80-W Cycle Ergometry
Equation	Dm	Vc	Dm	Vc
Predicted values	66.3 ± 5.0	94.9 ± 4.5
RF1.5	277.5 ± 406.4	74.6 ± 15.3	225.2 ± 152.2	79.5 ± 10.5
(% predicted)	(457 ± 722)	(78 ± 14)
RF2.5	92.9 ± 29.4	74.6 ± 15.3	112.4 ± 33.0	79.5 ± 10.5
(% predicted)	(143 ± 57)	(78 ± 14)
RFinf	58.9 ± 6.6	74.6 ± 15.3	69.4 ± 10.4	79.5 ± 10.5
(% predicted)	(89 ± 14)	(78 ± 14)
RF7.4	−297.0 ± 697.0	52.8 ± 10.8	200.2 ± 809.9	56.2 ± 7.5
(% predicted)	(−446 ± 1,055)	(55 ± 10)
Hol	186.6 ± 189.3	83.6 ± 17.2	194.2 ± 112.1	89.1 ± 11.8
(% predicted)	(299 ± 340)	(88 ± 15)
RP	46.4 ± 3.4	102.9 ± 21.1	53.8 ± 5.8	109.7 ± 14.5
(% predicted)	(70 ± 7)	(108 ± 19)
Stam	59.8 ± 7.0	70.8 ± 14.5	70.6 ± 10.9	75.4 ± 10.0
(% predicted)	(91 ± 15)	(74 ± 13)

Values are reported as group means ± SD. Predicted values for Dm and Vc at rest with rebreathing techniques were calculated from equations previously published by Crapo et al. (5).

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.]

Fig. 2.

Dm at rest and during exercise as a function of the α-ratio calculated with the single-inspired oxygen tension [inspired O₂ fraction (Fi_O2)] method. Calculated values for Dm at rest are shown in black; calculated values for Dm at rest are shown in gray. Data are shown as means ± SE.

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.

Fig. 3.

Vc as a function of the α-ratio calculated with the single-Fi_O2 method at rest (top) and during exercise (bottom). Each line represents the calculated Vc value obtained from the various θ_CO equations examined here. RF1.5, 1957 Roughton and Forester equation (low red cell permeability); RF2.5, 1957 Roughton and Forester equation (moderate red cell permeability); RFinf, 1957 Roughton and Forester equation (high red cell permeability); RF7.4, 1987 Forester equation (pH corrected to 7.4), Hol, Holland equation (1967); RP, Reeves and Park equation (1992); Stam, Stam et al. equation (1991). Data are shown as means ± SE.

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.

Table 5.

Optimized comparison: multiple- vs. single-Fi_O2 methods

		Dm Optimal α-Ratio		Vc Optimal α-Ratio
θCO Equation	Observed DlNO/DmCO	t-Statistic [α-ratio (t-stat)]	CCC [α-ratio (CCC)]	t-Statistic [α-ratio (t-stat)]	CCC [α-ratio (CCC)]
Rest
RF1.5	0.82 ± 0.37	1.90 (1.448)	1.90 (<0.001)	2.50 (−1.779)	1.90 (0.105)
RF2.5	1.21 ± 0.31	1.90 (3.337)	1.90 (0.023)	2.50 (−1.695)	1.90 (0.168)
RFinf	1.79 ± 0.26	1.90 (1.130)	1.90 (0.354)	1.90 (−1.084)	1.90 (0.388)
RF7.4	−0.40 ± 0.60	2.50 (−1.286)	2.50 (<0.001)	2.50 (−1.931)	1.90 (0.043)
Hol	0.87 ± 0.36	1.90 (1.836)	1.90 (<0.002)	2.50 (−1.769)	1.90 (0.111)
RP	2.25 ± 0.27	2.26 (−0.008)	2.29 (0.519)	2.15 (0.011)	2.02 (0.324)
Stam	1.76 ± 0.26	1.90 (1.376)	1.90 (0.329)	1.90 (−1.259)	1.90 (0.377)
Exercise
RF1.5	0.71 ± 0.28	1.90 (3.119)	1.90 (0.033)	2.50 (−2.583)	1.90 (0.051)
RF2.5	1.13 ± 0.20	1.90 (5.268)	1.90 (0.120)	2.50 (−2.491)	1.90 (0.081)
RFinf	1.76 ± 0.12	1.90 (3.146)	1.90 (0.654)	2.50 (−2.252)	1.90 (0.243)
RF7.4	−0.61 ± 0.58	1.90 (0.473)	2.50 (−0.008)	2.50 (−2.738)	1.90 (0.022)
Hol	0.77 ± 0.33	1.90 (3.480)	1.90 (0.043)	2.50 (−2.573)	1.90 (0.054)
RP	2.26 ± 0.16	2.26 (−0.040)	2.27 (0.690)	2.08 (−0.027)	2.03 (0.408)
Stam	1.73 ± 0.12	1.90 (3.656)	1.90 (0.614)	2.50 (−2.267)	1.90 (0.229)

Values are reported as means ± SD. t-stat, t-statistic value, CCC, concordance correlation coefficient. For the CCC statistic, 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 value indicates a negative relationship between the methods. Values in bold indicate results that are significantly different between the multiple-Fi_O2 and single-Fi_O2 methods (paired t-test, P < 0.05).

Fig. 4.

Comparison of Dm and Vc between the multiple- and single-Fi_O2 methods: comparative t-statistic as a function of the α-ratio at rest (A, C) and during exercise (B, D). The shaded areas denote the boundaries with which paired t-tests between the 2 methods were statistically different. Each line represents the calculated t-statistic between the multiple-Fi_O2 and single-Fi_O2 methods for calculated Dm (A, B) and Vc (C, D) values obtained from the various θ_CO equations examined here.

Fig. 5.

Comparison of Dm and Vc between the multiple- and single-Fi_O2 methods: concordance correlation coefficient (CCC) as a function of the α-ratio at rest (A, C) and during exercise (B, D). A CCC of 1.0 indicates that there is a perfect matching of the collected data points between the methods; CCC of 0 indicates that there is no relationship of the collected data points between the methods. Each line represents the calculated CCC between the multiple-Fi_O2 and single-Fi_O2 methods for calculated Dm (A, B) and Vc (C, D) values obtained from the various θ_CO equations examined here.

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 Po₂. 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. Po₂ 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-Po₂ 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 O₂, CO, CO₂, and NO by red blood cells in blood considering an assortment of physiological variations, including that of Po₂. 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 O₂, 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 N₂ and O₂ with exposure to O₂, 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 Po₂ < 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 O₂ 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 O₂ 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% O₂) to promote the binding of O₂ 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).