Clinical Significance of Elevated Diffusing Capacity

Clinical Significance of Elevated Diffusing Capacity* Ghulam Saydain, MD, FCCP; Kenneth C. Beck, PhD; Paul A. Decker, MS; Clayton T. Cowl, MD, MS, FCCP; and Paul D. Scanlon, MD, FCCP

Study objective: Single-breath diffusing capacity of the lung for carbon monoxide (DLCO) is used as a pulmonary function test (PFT) to assess gas transfer in the lungs. The implications of a low DLCO are well-recognized, but the clinical significance of a high DLCO is not clear. The aim of this study was to identify the clinical correlates of a high DLCO. Patients and methods: We identified 245 patients with a high DLCO (ie, > 140% predicted) and a matched group of 245 patients with normal DLCO (ie, 85 to 115% predicted), who were selected from a laboratory database of 45,000 patients tested between January 1997 and December 1999. We compared the demographic features, clinical diagnoses, and PFT data between the two groups. Settings: Large multispecialty group practice. Results: The patients in the high DLCO group were heavier (mean [ⴞ SD] weight, 96.0 ⴞ 22.9 vs 85.0 ⴞ 21.3 kg, respectively; p < 0.001), had a higher mean body mass index (32.9 ⴞ 7.4 vs 29.4 ⴞ 6.4 kg/m2, respectively; p < 0.001), larger body surface area (p < 0.001), and larger mean total lung capacity (p ⴝ 0.007) and alveolar volume (p < 0.001). The clinical diagnoses of obesity (p < 0.001) and asthma (p < 0.001) were more common among patients with high DLCO values. The majority of patients (62%) with a high DLCO had a diagnosis of obesity, asthma, or both. Polycythemia, hemoptysis, and left-to-right shunt were uncommon. Conclusion: A high DLCO on a PFT is most frequently associated with large lung volumes, obesity, and asthma. Other conditions are much less common. A clinical condition, which typically reduces (CHEST 2004; 125:446 – 452) DLCO, may deceptively normalize DLCO in such patients. Key words: asthma; diffusing capacity; obesity; pulmonary function test Abbreviations: BMI ⫽ body mass index; Dlco ⫽ diffusing capacity of the lung for carbon monoxide; PFT ⫽ pulmonary function test; RV ⫽ residual volume; SBVA ⫽ single-breath alveolar volume; TLC ⫽ total lung capacity

of the diffusing capacity of the lung M easurement for carbon monoxide (Dlco) provides information regarding pulmonary gas transfer, and is an important and widely used pulmonary function test (PFT). A reduced Dlco often signifies a pulmonary parenchymal or vascular disorder, and the clinical *From the Pulmonary and Critical Care Division (Dr. Saydain), Nassau University Medical Center, East Meadow, NY; Department of Radiology (Dr. Beck), University of Iowa, Iowa City, IA; Mayo Clinic and Mayo Medical School (Mr. Decker, and Drs. Cowl and Scanlon), Rochester, MN. This study was funded in part by National Heart, Lung, and Blood Institute grant HL-59248. Manuscript received March 20, 2003; revision accepted July 23, 2003. Reproduction of this article is prohibited without written permission from the American College of Chest Physicians (e-mail: [email protected]). Correspondence to: Ghulam Saydain MD, FCCP, Pulmonary and Critical Care Division, 10th floor, Nassau University Medical Center, 2201 Hempstead Tpk, East Meadow, NY, 11554; e-mail: [email protected] 446

implications of a low Dlco are well-recognized.1 Polycythemias as well as some physiologic variations like the Mu¨ller maneuver and exercise are known to increase the Dlco. During the routine measurement of Dlco, an adjustment for hemoglobin levels is applied and other physiologic variations are usually avoided.1–3 A high Dlco has been described in some clinical conditions such as asthma, obesity, and leftto-right intracardiac shunt. However, some studies4 –9 have shown conflicting results, and no large study has defined the relative frequency of these various conditions as a cause for a high Dlco. The use of Dlco for the diagnosis of pulmonary hemorrhage in Goodpasture syndrome has been described,10 however, in clinical practice not many patients with pulmonary hemorrhage may undergo pulmonary function testing at the time of bleeding. A low Dlco on a PFT sets forth the search for a cause. Should the same be true with a high Dlco? The present study was designed to define the relative Clinical Investigations

frequency of the clinical diagnoses associated with high single-breath Dlco values.

Materials and Methods Study Population The subjects for the study were selected from the pulmonary function laboratory database at the Mayo Clinic in Rochester, MN. We selected adult patients (ie, those ⬎ 21 years old) who had performed a PFT (including spirometry, Dlco, and oximetry) between January 1997 and December 1999, and had a Dlco of ⬎ 85% predicted. From this patient population, two groups of patients were selected. The high Dlco group included patients who had a Dlco ⱖ 140% of the predicted value. We selected the 140% of the predicted Dlco as the cutoff for the selection of patients for the following reasons: (1) this is well outside the common range of intersubject variability; and (2) this increase in Dlco would be unlikely to be secondary to technical or physiologic variations during testing (eg, Muller maneuver).3 For each subject with a high Dlco, we selected a matching subject with a normal Dlco (ie, 85 to 115% of the predicted value) matched by a clinical history file number, which is a method described by Rosenbaum.11 Subjects matched by clinical history file number have comparable lengths of follow-up in their medical histories and are well-distributed with respect to other demographic characteristics (ie, age, gender, height, and weight). In case of multiple tests for the same patient, only the first test was analyzed. The institutional review board of the institution approved the study. Patients who had denied consent for the review of their medical records for research purposes were excluded. The medical record of each subject was reviewed, and the following data were collected: age; sex; height; weight; smoking history; clinical diagnoses; and PFT results. For statistical analysis, various clinical diagnoses were grouped into diagnostic categories depending on the body system involved. Conditions with a small number of patients (ie, ⬍ 20) in both groups (high Dlco patients and control patients) were combined with related diagnoses from the same body system in order to achieve a sufficient number for useful comparison. We reviewed the diagnostic list for each patient for conditions known to be associated with a high Dlco (polycythemia, left-to-right shunt, pulmonary hemorrhage, asthma, and obesity). PFTs Spirometry and Dlco measurements were performed in compliance with the American Thoracic Society (ATS) guidelines.1,12,13 Dlco was measured using a single-breath technique (model 1070; Medical Graphics; St. Paul, MN). The Dlco was routinely adjusted for hemoglobin1 if the value was outside the normal range or if a very low or very high hemoglobin level was suspected from clinical history, provided that the hemoglobin level was available at the time of testing. For the present study, Dlco was adjusted for hemoglobin for 234 of 245 patients (96%) in the high Dlco group. Reference values for predicted Dlco were from Miller et al.14 The total lung capacity (TLC) and other lung volumes were measured using a body plethysmograph (model 1085; Medical Graphics). The single-breath alveolar volume (SBVA) was obtained simultaneously with the Dlco, using neon as an inert tracer gas. Following the guidelines of the American Thoracic Society,1 an estimate of the patient’s anatomic dead space was subtracted from their inspired vital capacity before multiplying by the gas dilution ratio. Because gas dilution www.chestjournal.org

measurements of lung volumes can underestimate lung volumes in the presence of lung disease, an index of ventilation inhomogeneity was obtained from the mixing index (ie, TLC-SBVA)/ SBVA (see “Appendix”). The analysis of pulmonary function data compared the two groups for FVC, FEV1, FEV1/FVC ratio, plethysmographic TLC (when available), residual volume (RV), RV/TLC ratio, SBVA, mixing index, Dlco, Dlco/SBVA, heart rate, and pulse oximetry at rest and after moderate step exercise. Pulse oximetry was measured at rest and while patients performed a standardized step exercise on a 9-inch step walking up and down for a maximum of 3.0 min, one step for each beat of a metronome (60 beats/min). Quality Control Dlco tests were performed by trained technicians using equipment that was calibrated using a 3-L syringe twice per day. A rigorous biological quality control program was in place during the entire time of testing: a group of technicians who were free of cardiopulmonary disease performed full PFTs on themselves every Monday. If values were outside a 95% confidence interval for their established mean, a second technician was called in to perform the testing. If values from both tests were outside the 95% confidence limits, the particular testing station was not used until complete diagnostics could be performed and repeat testing gave values that were within limits. Patients performed at least one repeat Dlco test after the initial maneuver. If Dlco and SBVA values were not within 10%, the test was repeated a third time, and the values that were the closest match were used. Statistical Analysis Patient characteristics were compared between matched pairs using a paired t test for continuous variables and conditional logistic regression for categoric variables.15 The frequency of each specific medical diagnosis was compared between matched pairs using the sign test. In all cases, p values of ⱕ 0.05 were considered to be statistically significant.

Results From the laboratory database of 45,000 patient encounters (January 1, 1997, to December 31, 1999) a total of 16,778 unique patients (aged ⬎ 21 years) had performed spirometry plus Dlco estimation and had a single-breath Dlco of ⬎ 85% of the predicted value. Of these, 251 patients had a Dlco of ⬎ 140% predicted. Six patients were excluded for lack of consent. The remaining 245 patients with high Dlco values were matched 1:1 with control patients with normal Dlco values (85 to 115% predicted). The demographic features of the high Dlco subjects and control patients are summarized in Table 1. There was no significant difference in age, gender, or height between the two groups. Compared with the control patients, patients with high Dlco values had a higher mean (⫾ SD) body weight (96.0 ⫾ 22.9 vs 85.0 ⫾ 21.3 kg, respectively; p ⬍ 0.001), body mass index (BMI) [32.9 ⫾ 7.4 vs CHEST / 125 / 2 / FEBRUARY, 2004

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Table 1—Patient Characteristics* Control Group (n ⫽ 245) Variables Age, yr Sex Female Male Height, cm Weight, kg BMI kg/m2 ⬎ 30 BSA, m2 Smokers Smoking, pack-yr

%

Mean ⫾ SD

High Dlco Group (n ⫽ 245) %

57.4 ⫾ 15.1 49 54

Mean ⫾ SD

p Value†

57.3 ⫾ 11.5

NS

170.8 ⫾ 10.2 96.0 ⫾ 22.9

NS NS ⬍ 0.001

51 46 169.6 ⫾ 9.4 85.0 ⫾ 21.3 29.4 ⫾ 6.4

40

32.9 ⫾ 7.4 58

2.0 ⫾ 0.3 49

2.1 ⫾ 0.3 34

15.3 ⫾ 25.6

Table 2—Comparison of PFT Results Between the High DLCO Group and the Control Group*

8.1 ⫾ 15.4

⬍ 0.001 ⬍ 0.001 ⬍ 0.001 0.002 ⬍ 0.001

*BSA ⫽ body surface area; NS ⫽ not significant (p ⬎ 0.10). In the control group 97% were white, 1% African American, 1% Native American, 1% Asian, and 1% were classified as “other” race. In the high Dlco group, 95% were white, 4% African American, 1% American Indian, and 1% Asian. †Taking into account the matched-pair design, the p values correspond to those obtained from the paired t test for continuous variables and from conditional logistic regression for categoric variables.

29.4 ⫾ 6.4 kg/m2, respectively; p ⬍ 0.001], and body surface area (2.1 ⫾ 0.3 vs 2.0 ⫾ 0.3 m2, respectively; p ⬍ 0.001). One hundred forty-three patients (58%) with high Dlco values were overweight (ie, BMI ⬎ 30 kg/m2) compared to 98 control patients (40%; p ⬍ 0.001). More patients in the control group smoked (49% vs 34%, respectively; p ⫽ 0.002), and the control group had a greater smoking history (15.3 ⫾ 25.6 vs 8.1 ⫾ 15.4 pack-years, respectively; p ⬍ 0.001). PFT results are presented in Table 2. FVC, FEV1, TLC, SBVA, and Dlco/SBVA ratio were all significantly higher in the high Dlco group. The patients with high Dlco values had a higher heart rate following exercise (111.9 ⫾ 17.0 vs 107.6 ⫾ 14.5 beats/min, respectively; p ⫽ 0.003), while the mixing index (an index of nonhomogeneous gas distribution) was higher in the control group (10.3 ⫾ 13.6 vs 4.9 ⫾ 7.6, respectively; p ⫽ 0.003). Diagnostic categories for the patients and control patients are summarized in Table 3. Of the 31 diagnostic categories, the clinical diagnosis of asthma (47% vs 23%, respectively; p ⬍ 0.001) and obesity (30% vs 14%, respectively; p ⬍ 0.001) were more common among the patients with high Dlco values than among the control patients. COPD (25% vs 8%, respectively; p ⬍ 0.001), pulmonary infections (12% vs 6%, respectively; p ⫽ 0.014), and liver and gall bladder disorders (13% vs 7%, respectively; p ⫽ 0.019) were more common among the control 448

Variables FVC, % predicted FEV1, % predicted FEV1/FVC ratio TLC,‡ % predicted SBVA, % predicted Dlco, % predicted Dlco/SBVA ratio RV/TLC‡ Mixing index‡§ Sao2 % At rest Exercise Heart rate, min At rest After exercise

Control Group (n ⫽ 245)

High Dlco Group (n ⫽ 245)

p Value†

88.8 ⫾ 14.1 82.3 ⫾ 18.2 73.5 ⫾ 10.3 103.6 ⫾ 14.5 96.3 ⫾ 11.4 99.4 ⫾ 8.3 4.5 ⫾ 0.7 42.3 ⫾ 11.3 10.3 ⫾ 13.6

95.6 ⫾ 15.8 89.2 ⫾ 17.7 74.1 ⫾ 8.4 110.8 ⫾ 15.7 107.1 ⫾ 13.1 147.3 ⫾ 7.0 5.9 ⫾ 0.8 41.4 ⫾ 8.7 4.9 ⫾ 7.6

⬍ 0.001 ⬍ 0.001 NS 0.007 ⬍ 0.001 ⬍ 0.001 ⬍ 0.001 NS 0.003

95.5 ⫾ 1.5 94.6 ⫾ 1.9

95.3 ⫾ 1.5 94.9 ⫾ 1.9

NS NS

81.3 ⫾ 13.0 107.6 ⫾ 14.5

83.7 ⫾ 14.8 111.9 ⫾ 17.0

0.056 0.003

*Values given as mean ⫾ SD, unless otherwise indicated. See Table 1 for abbreviations not used in text. †Two-tailed p value from a paired t test. ‡TLC and RV data were not available for some subjects. Sixty-four matched sets were used in comparison of RV and TLC. §Mixing index (an index of nonhomogeneous gas distribution), defined as ([TLC ⫺ SBVA]/SBVA).

patients. There were no significant differences for the remaining diagnostic categories. Review of the individual diagnostic list for each patient in the high Dlco group for the possible explanation of high Dlco values showed that 80 (33%) had a diagnosis of asthma (without obesity), 39 (16%) had obesity (without asthma), and 34 (14%) had asthma as well as obesity. Thus, 62.4% of the patients had a diagnosis of asthma or obesity. An additional 49 patients (20%), although not clinically diagnosed as obese, had BMI values of ⬎ 30 kg/m2. Only three patients (1.2%) had a history of hemoptysis, three patients (1.2%) had left-to-right shunt due to atrial septal defect, and one patient (0.5%) had a clinical diagnosis of polycythemia (current hemoglobin level, 14.3 g/dL). This patient also had history of asthma and a BMI of 34.3 kg/m2. Correlation analysis revealed strong and significant correlations between Dlco and SBVA (r ⫽ 0.68; p ⬍ 0.001). The strength of this correlation was less when Dlco and SBVA were expressed as a percentage of the predicted value (r ⫽ 0.42; p ⬍ 0.001), indicating that the strong absolute correlation was largely due to correlation with height, with which both Dlco and SBVA are positively associated. There was a weak but statistically significant correlation between Dlco (percent predicted) and BMI when the groups were combined (r ⫽ 0.26; p ⬍ 0.001), but not when groups were analyzed separately. Clinical Investigations

Table 3—Comparison of Diagnostic Categories Between the Control Group and the High DLCO Group* Control Group (n ⫽ 245)

High Dlco Group (n ⫽ 245)

Diagnostic Category

No.

%

No.

%

p Value†

Obesity Asthma COPD Pulmonary infection Liver/gallbladder disorders Musculoskeletal Sleep disorders Pulmonary nodules/malignancy Pulmonary miscellaneous Interstitial and restrictive disorders Pulmonary obstructive disorders (other than COPD and asthma) Abdomen/GI Endocrine Ear, nose, and throat Dermatology Renal Hypertension Cardiac Neurological Psychiatric Ophthalmology Oncology Hematology Vascular Breast disorders Gynecologic disorders Trauma

35 57 62 30 33 117 35 21 81 13 12

14 23 25 12 13 48 14 9 33 5 5

73 114 19 15 17 135 49 23 80 12 8

30 47 8 6 7 55 20 9 33 5 3

⬍ 0.001 ⬍ 0.001 ⬍ 0.001 0.014 0.019 0.095 0.094 NS NS NS NS

119 117 105 77 92 66 85 78 52 42 33 42 27 15 19 11

49 48 43 31 38 27 35 32 21 17 13 17 11 6 8 4

116 112 104 83 78 78 73 65 59 44 31 30 22 21 15 12

47 46 42 34 32 32 30 27 24 18 13 12 9 9 6 5

NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS NS

*See Table 1 for abbreviations not used in the text. The following diagnoses were omitted from Table 3 because of small sample size: pulmonary artery hypertension (1 control, 4 cases); laboratory test only (0 controls, 1 case); and pleural disease (4 controls, 0 cases). †From sign test taking into account the 1:1 matched study design.

Discussion Our results indicate that patients with high Dlco values tend to be overweight with higher BMIs and larger body surface areas. High Dlco was associated with both large lung volumes (ie, TLC and SBVA) as well as higher gas transfer (ie, Dlco/SBVA). Obesity, asthma, or both were observed in a majority of the patients with high Dlco values. Other known causes of high Dlco (ie, pulmonary hemorrhage, left-to-right shunt, and polycythemia) accounted for a very small fraction of the patients. In clinical practice, high Dlco is likely to be due to large lung volume, obesity, or asthma often in combination. Although a high Dlco may not warrant further extensive investigation, a disease known to lower Dlco may reduce Dlco in these patients (with high Dlco) to deceptively normal levels. A single measurement of Dlco in such patients may not reflect the severity of the gas exchange impairment. Under such circumstances, comparison with a previously measured Dlco value or a change over time would be necessary to evaluate the gas exchange abnormality. www.chestjournal.org

Variations in Dlco may be associated with ethnicity, age, gender, height, cigarette smoking, and variations in the technique of measurement, physiologic changes, and different disease states.1,2 Age, height, ethnicity, and gender were similar in both groups of patients and do not explain the difference in Dlco among our patients. Smokers tend to have lower Dlco values,1 and there were more smokers (with a greater average pack-year smoking history) in the control group (ie, normal Dlco). COPD and pulmonary infections may be associated with low Dlco,1,2 and these conditions were more common among patients in the control group compared with the high Dlco group. We also observed increased frequency of liver and gall bladder diseases in the control group. Liver disease is sometimes associated with pulmonary conditions characterized by low Dlco.16 Polycythemia, exercise, or technical variations (eg, Mu¨ ller maneuver) may lead to increased Dlco.1,3 In our patients, Dlco was measured in the resting state and was adjusted for hemoglobin level when possiCHEST / 125 / 2 / FEBRUARY, 2004

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ble. In the high Dlco group, one patient had history of polycythemia, however, the hemoglobin was within normal range at the time of pulmonary function testing, and the patient was obese and had a history of asthma. The Mu¨ ller maneuver may account for an increase in measured Dlco by as much as 22.5% (average increase, 5.7%), however, this would not likely result in as high a Dlco value as that observed in our patients.2,3 Strict quality control measures are enforced in our laboratory to avoid technical variations, and to ensure the validity and reproducibility of the test results. Patients with high Dlco values had larger TLC, FVC, and SBVA values compared to the control group. This is attributable, in part, to selection bias from the study design. Larger lung volumes have been associated with higher Dlco.17,18 However, this does not seem to be the only explanation for high Dlco, since the Dlco/SBVA ratio also was higher among these patients, thus indicating enhanced conductance of carbon monoxide in addition to larger lung volumes as an explanation for the very high Dlco value. Obesity was strongly associated with high Dlco. The high Dlco group had a larger number of patients with clinical diagnosis of obesity (30% vs 14%, respectively; p ⬍ 0.001) and with a BMI of ⬎ 30 (58% vs 40%, respectively; p ⬍ 0.001) compared to the control group. Obesity has been associated with higher blood volume and cardiac output.19,20 The increased blood volume and cardiac output in obese patients will increase the capillary blood volume, and may thereby increase Dlco. High Dlco has been observed in obese patients previously.8,21 Ray et al8 studied 43 otherwise healthy obese patients and classified them into various groups based on their weight/height ratio. The mean Dlco for all patients was 105.7% predicted (range, 79 to 145% predicted), and the mean Dlco/ SBVA ratio was 119.6% predicted. The mean Dlco percent predicted was not significantly different in various groups. Only four patients had a mean Dlco/SBVA ratio of 140 ⫾ 19% predicted, and these patients had a weight/height ratio of ⬎ 1.10. These individuals had a low vital capacity. In contrast, in another study of 43 obese patients by Biring et al9 Dlco and Dlco/SBVA ratio were within normal range, and there was no correlation to weight/height ratio. Baylor and Goebel22 studied 18 patients with high Dlco/SBVA ratio and attributed the increased Dlco/SBVA ratio in 16 patients to a reduction in vital capacity secondary to obesity, pleural disease, or diaphragmatic dysfunction. No study has specifically addressed high Dlco per se in obese patients. Our study is different in that regard, as our patients were selected for a high Dlco not 450

just a high Dlco/SBVA. More importantly, the large number of subjects in our study allows us to address a variety of other contributory factors. Asthma is the other common clinical diagnosis among our patients with high Dlco. This accounted for 47% of our subjects. Of the 114 patients with asthma in the high Dlco group, 34 were also obese. Asthma has previously been reported as a cause for increased Dlco and Dlco/SBVA ratio.5,6 Different mechanisms have been postulated to account for high Dlco in asthma, and these include overestimation of Dlco due to airflow obstruction,23 increased perfusion of apices of the lungs due to increased pulmonary arterial pressure or more negative pleural pressure as a consequence of bronchial narrowing.5,6 Weitzman and Wilson6 found an elevated Dlco in a majority of their patients with asthma, which they asserted did not seem to be due to airway obstruction, hyperinflation, increased pulmonary blood flow, or membrane component. They attributed increased Dlco to greater perfusion of the apices of the lungs in asthmatic patients.6 Other known causes of high Dlco (ie, polycythemia, left-to-right shunt, and pulmonary hemorrhage) were observed in very few of our patients. In these conditions, high Dlco is due to increased capillary blood volume or to the presence of extravascular blood in the lungs.1,2,10 Patients with high Dlco had significantly higher heart rates after exercise compared to those in the control group. This is probably related to asthma and obesity, both of which are associated with increased work demand of exercise, deconditioning, and poor exercise tolerance. In conclusion, high Dlco is commonly associated with a clinical diagnosis of obesity and asthma. Other known causes of high Dlco, such as pulmonary hemorrhage, polycythemia, and left-to-right shunt, are uncommon causes of a high Dlco. A very high Dlco is the result of both large lung volume (ie, SBVA) as well as increased conductance for carbon monoxide (ie, Dlco/SBVA ratio). ACKNOWLEDGMENT: The authors wish to acknowledge the foresight of our former laboratory director, Dr. Joseph R. Rodarte, who had the wisdom and insight to develop a laboratory database that was designed to be useful for both patient care and clinical investigation.

Appendix The following derivation describes how ventilation inhomogeneity can produce an underestimate of the SBVA that is associated with the single-breath Dlco test. The underestimate comes about because the exhaled concentration of insoluble gas (neon) in a mixed expired sample obtained after inhaling a vital capacity breath of test gas and exhaling, as in the maneuver required by the single-breath Dlco test, is higher in a lung with ventilation Clinical Investigations

inhomogeneity compared with a lung with uniform ventilation and the same overall gas volume. To prove this, consider the lung to be divided into a large number, N, of terminal units that have equal volume, VA,r, when the lungs are fully inflated. During inspiration, each unit receives first a mixture of dead space gas followed by fresh gas. The amount of fresh gas received by a given unit will depend on the dead space volume and the relative volume expansion, ⌬VT,i, of the unit compared to its original volume. All units do not have the same relative volume expansion, and the effect of this inhomogeneity of relative expansion is to make gas concentration in the units after the inspiration nonuniform. A mixed expired sample will contain a mixed sample of regional gases, weighted by the volume contributions in the expirate. For the following derivation, the symbol with subscript “i” (eg, VA,i) is used in a summation operation as a means for counting individual lung units (ith lung units), where “i” ranges from 1 to the total number of terminal gas exchanging units in the lung. Symbols with superscript “i” or “e” refer to inspiration and expiration, respectively. The SBVA is usually calculated from the following simple relationship: FI SBVA ⫽ (IVC ⫺ Vd) ⫻ Fm where IVC is the inspired vital capacity (equal to the sum of i changes in volumes of all the terminal lung units, 兺N i ⌬VT,i), VD is total anatomic dead space volume, and FI and Fm are the inhaled and exhaled gas concentrations, respectively. The exhaled gas concentration, Fm, is a weighted sum of concentrations from all alveoli, as follows:

冘 N

Fm ⫽

FA,i ⫻

i

⌬V ⌬V

e A,i e A

e ⌬VA,i

where is the expiratory change in alveolar volume of the ith e unit and ⌬VeA is the total alveolar gas sample volume 兺N i ⌬VA,i. The end-inspiratory gas concentration in each unit, FA,i is given by i ⌬VA,i ⫻ FI FA,i ⫽ VA,r

where VA,r is the volume at end inspiration, which is assumed to be equal for all units. The true total alveolar gas volume, VA,true, i is equal to N ⫻ VA,r. ⌬VA,i is the volume of fresh gas (ie, tidal volume change less dead space) to the ith unit. The gas concentration at the mouth then becomes as follows:

冘 N

Fm ⫽ FI ⫻

i

⫽

i e ⌬VA,i ⌬VA,i ⫻ ⌬VA,r ⌬VeA

FI ⫻ ⌬VeA ⫻ VA,r

冘 N

i e ⌬VA,i ⫻ ⌬VA,i

i

The changes in fresh gas volume of all alveoli are not the same because of the inhomogeneity of volume expansion i i i ⫽ ⌬VA,i ⫹ ␯ii ⫽ (1 ⫹ fi) ⫻ ⌬VA,i ⌬VA,i e e e ⌬VA,i ⫽ ⌬VA,i ⫹ ␯ei ⫽ (1 ⫹ fi) ⫻ ⌬VA,i

where a bar over a symbol indicates an average over all units, and ␯ii and ␯ei represent the deviation in volume expansion from the mean for inspiration and expiration, respectively. fi denotes fractional volume expansion, which is assumed to be equal for www.chestjournal.org

inspiration and expiration for this derivation. Note that the sum of all fractional volume expansions is zero (there are equal deviations from the mean in positive and negative directions, implying a symmetrical distribution of volume expansions). Thus, gas concentration at the mouth becomes

冘 N

i e ⌬VA,i ⫻ ⌬VA,i ⫻ ⌬VeA ⫻ VA,r

Fm ⫽ FI ⫻

(1 ⫹ f2i )

i

i We can now substitute IVC ⫽ ⌬VA,i ⫻ N ⫹ VD, VA,r ⫽ VA,true/N, i and ⌬VA,I ⫽ ⌬VeT/N one can arrive at:

Fm ⫽ FI ⫻

(IVC ⫺ VD) ⫻ VA,true ⫻ N

冘 N

(1 ⫹ f2i )

i

A rearrangement expresses the VA,true in terms of measured variables times the mean of (1 ⫹ f2i )

冘 N

(IVC ⫺ Vd) VA,true ⫽ FI ⫻ ⫻ Fm

(1 ⫹ f2i )

i

N

冋 册

⫽ SBVA ⫻ 1 ⫹

f2i N

⫽ SBVA ⫻ 关1 ⫹ f2i 兴 The alveolar volume as traditionally measured, SBVA, is thus an underestimate of the true alveolar volume due to regional inhomogeneities of volume expansion. The difference between VA,true and SBVA is equal to the mean square deviations of the fractional volume expansions from the mean. If we take the plethysmographically measured TLC to represent VA,true, then a mixing efficiency index (MI) can be derived from the last equation, as follows: MI ⫽

(TLC ⫺ SBVA) ⫽ f2i SBVA

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Clinical Investigations