The Roughton-Forster equation for DL CO and DL NO re-examined

Adjusting diffusing capacity for anemia in patients undergoing allogeneic HCT: a comparison of two methodologies

BACKGROUND

Diffusing capacity (DLCO) measurements are affected by hemoglobin. Two adjustment equations are used: Cotes (recommended by ATS/ERS) and Dinakara (used in the hematopoietic stem cell transplantation comorbidity index [HCT-CI]). It is unknown how these methods compare, and which is better from a prognostication standpoint.

STUDY DESIGN

This is a retrospective cohort of 1273 adult patients who underwent allogeneic HCT, completed a pre-transplant DLCO and had a concurrent hemoglobin measurement. Non-relapse mortality was measured using competing risk analysis.

RESULTS

Patients had normal spirometry (FEV1 99.7% [IQR: 89.4-109.8%; FVC 100.1% [IQR: 91.0-109.6%] predicted), left ventricular ejection fraction (57.2[6.7]%) and right ventricular systolic pressure (30.1[7.0] mmHg). Cotes-DLCO was 85.6% (IQR: 76.5-95.7%) and Dinakara-DLCO was 103.6% (IQR: 90.7-117.2%) predicted. For anemic patients (Hb<10g/dL), Cotes-DLCO was 84.2% (IQR: 73.9-94.1%) while Dinakara-DLCO 111.0% (97.3-124.7%) predicted. Cotes-DLCO increased HCT-CI score for 323 (25.4%) and decreased for 4 (0.3%) patients. Cotes-DLCO was superior for predicting non-relapse mortality: for both mild (66-80% predicted, HR 1.55 [95%CI: 1.26-1.92, p < 0.001]) and moderate (<65% predicted, HR 2.11 [95%CI: 1.55-2.87, p<0.001]) impairment. In contrast, for Dinakara-DLCO, only mild impairment (HR 1.69 [95%CI 1.26-2.27, p < 0.001]) was associated with lower survival while moderate impairment was not (HR 1.44 [95%CI: 0.64-3.21, p = 0.4]). In multivariable analyses, after adjusting for demographics, hematologic variables, cardiac function and FEV1, Cotes-DLCO was predictive of overall survival at 1-year (OR 0.98 [95%CI: 0.97-1.00], p = 0.01), but Dinakara-DLCO was not (OR 1.00 [95%CI: 0.98-1.00], p = 0.20).

CONCLUSION

The ERS/ATS recommended Cotes method likely underestimates DLCO in patients with anemia, whereas the Dinakara (used in the HCT-CI score) overestimates DLCO. The Cotes method is superior to the Dinakara method score in predicting overall survival and relapse-free survival in patients undergoing allogeneic HCT.

Comparing in vitro nitric oxide blood uptake to its pulmonary diffusing capacity

Whether endothelium derived Nitric Oxide (NO) uptake by the blood is limited by a boundary layer, the red cell membrane or its interior is the subject of continued debate. Whether lung uptake of NO in the single-breath DLNO test is limited by blood or not is also debated. To understand which processes are limiting blood NO uptake we have modelled NO chemical kinetics and we have derived a shrinking core model, Thiele Modulus and FTCS (Euler) numerical solution. In a rapid reaction apparatus, NO uptake appears limited by a boundary layer, and throughout the red cell, by diffusion. In the single breath situation, and arguably with endogenous NO in vivo, NO uptake appears limited by a boundary layer and a pseudo first order chemical reaction in the outer molecular layers of the red cell. We have not found evidence to support red cell membrane limitation.

Week to week variability of pulmonary capillary blood volume and alveolar membrane diffusing capacity in patients with heart failure

BACKGROUND

Alveolar-capillary membrane diffusing capacity for carbon monoxide (DMCO) and pulmonary capillary volume (Vcap) can be estimated by the multi-step Roughton and Foster (RF, original method from 1957) or the single-step NO-CO double diffusion technique (developed in the 1980s). The latter method implies inherent assumptions. We sought to determine which combination of the alveolar membrane diffusing capacity for nitric oxide (DMNO) to DMCO ratio, an specific conductance of the blood for NO (θ_NO) and CO (θ_CO) gave the lowest week-to-week variability in patients with heart failure.

METHODS

44 heart failure patients underwent DMCO and Vcap measurements on three occasions over a ten-week period using both RF and double dilution NO-CO techniques.

RESULTS

When using the double diffusing method and applying θ_NO = infinity, the smallest week-to-week coefficient of variation for DMCO was 10 %. Conversely, the RF method derived DMCO had a much greater week-to-week variability (2x higher coefficient of variation) than the DMCO derived via the NO-CO double dilution technique. The DMCO derived from the double diffusion technique most closely matched the DMCO from the RF method when θ_NO = infinity and DMCO = DLNO/2.42. The Vcap measured week-to-week was unreliable regardless of the method or constants used.

CONCLUSIONS

In heart failure patients, the week-to-week DMCO variability was lowest when using the single-step NO-CO technique. DMCO obtained from double diffusion most closely matched the RF DMCO when DMCO/2.42 and θ_NO = infinity. Vcap estimation was unreliable with either method.

Modeling of Gas Exchange in the Lungs

This overview presents the recent progress in our understanding of gas transfer by the lungs during the respiratory cycle and during breath holding. Different phenomena intervene in gas transfer, convection and diffusion in the gas, dissolution, diffusion across the alveolar-capillary membrane, diffusion across blood plasma, and finally diffusion and reaction with hemoglobin inside blood cells. The different gases, O₂ , CO, and NO, have very different reaction times with hemoglobin ranging from a few microseconds to tens of milliseconds. This is leading to different outcomes. For O₂ , the solutions to the coupled nonlinear gas and blood equations are obtained at the acinus level. They include the fact that the acinar internal ventilation is strongly heterogeneous due to the arborescent structure. Also, in the dynamic calculation, one takes care of the delay between the start of inhalation and arrival of fresh air in the acinus. This "dead" time is the dynamic equivalent of the dead space ventilation. The question of the dependence of Vo₂ on ventilation and perfusion takes a different form. The results show that Vo₂ is not only a function of the ventilation/perfusion ratio but also depends on the variables: acinar ventilation VE_ac and perfusion Q_ac . The ratio VE_ac /Q_ac roughly determines arterial O₂ saturation and arterial and alveolar O₂ partial pressure. The classic Roughton-Forster interpretation of DLCO (separation between independent membrane and blood resistance) was a mathematical conjecture. It was shown recently that this conjecture was violated. This article presents an alternative interpretation that uses time concepts instead of resistance. © 2021 American Physiological Society. Compr Physiol 11:1289-1314, 2021.

Can DLNO/DLCO ratio offset prejudicial effects of functional heterogeneities in acinar regions?

OBJECTIVES

(1) To establish the general equation that describes relationship of DM_CO/Vc versus DL_NO/DL_CO under conditions with no functional heterogeneities. (2) To examine the effects of functional heterogeneities, including parallel and series (stratified) heterogeneities, on DL_NO/DL_CO.

RESULTS AND DISCUSSIONS

(1) Given that "true" θ_NO in pulmonary capillaries is represented by surface absorption-related θ_NO, relationship between DM_CO/Vc and DL_NO/DL_CO does not differ significantly from that obtained on premise of infinite θ_NO. DL_NO/DL_CO decided physiologically may mirror morphometric DM_CO/Vc actually working for gas exchange but not "total" morphometric ratio of DM_CO/Vc. (2) There are three parallel heterogeneities that affect diffusing capacity (D)-related parameters. Of them, only the heterogeneity of D/V_A, where V_A is alveolar volume, underestimates DL_CO and DL_NO. DL_NO/DL_CO does not alleviate negative impact of D/V_A heterogeneity, indicating that DM_CO/Vc estimated from DL_NO/DL_CO does not mirror "true" morphometric DM_CO/Vc in diseased lungs with D/V_A maldistribution. (3) Stratified heterogeneity underrates morphometric DM_CO, DM_NO, and DM_NO/DM_CO maximally by 1.4 %, 2.8 %, and 1.4 %, respectively, under conditions similar to single-breath D measurements, suggesting that effect of stratified heterogeneity on D measures is no longer needed to be considered in normal subjects but may be in patients having lung diseases with destructive lesions of acinar structures.

What are appropriate values of relative krogh diffusion Constant of NO against CO and of theta-NO in alveolar septa?

OBJECTIVES

To propose new physical constants for NO and CO (Krogh diffusion constant ratio (KD_NO/CO) and specific blood conductance for NO (θ_NO)) for calculating DMCO and Vc, according to Roughton-Forster's equation (Roughton and Forster, J. Appl. Physiol. 11: 290-302, 1957) from simultaneous DLNO and DLCO measurements.

RESULTS AND CONCLUSIONS

(1) The Graham's law is unacceptable for determining KD_NO/CO because CO does not fulfil all the conditions of an "ideal" gas. We have re-estimated KD_NO/CO in a new way based on difference in molar volumes of two gases (molar volume theory). The KD_NO/CO thus decided is 2.34. (2) θ_NO measured with rapid-reaction, constant-flow method by Carlsen and Comroe (J. Gen. Physiol. 42: 83-107, 1958) may be underestimated by about 40 % due to unstirred water layer surrounding the erythrocyte. (3) Erythrocyte θ_O2 can be harvested from O₂ release kinetics in presence of high concentration of dithionite, which effectively removes the unstirred water layer-elicited effect. Multiplication of erythrocyte θ_O2 by erythrocyte KD_NO/O2 equals erythrocyte θ_NO, the value of which is 6.2 mL/min/mmHg/(mL⋅blood). According to the concepts of Kang et al. (RESPNB. 241: 62-71, 2017) and Borland et al. (RESPNB. 241: 58-61, 2017), in vitro θ_NO decided from rapid-mixing experiments may mirror bulk absorption of NO by erythrocytes. (4) In pulmonary capillaries, NO uptake takes place predominantly in the surface rim of the erythrocyte. This surface absorption of NO increases the θ_NO 10-fold versus bulk absorption of NO to about 60 mL/min/mmHg/(mL⋅blood).

Lung Diffusing Capacities (DL ) for Nitric Oxide (NO) and Carbon Monoxide (CO): The Evolving Story

Nitric oxide and carbon monoxide diffusing capacities (D_LNO and D_LCO ) obey Fick's First Law of Diffusion and the basic principles of chemical kinetic theory. NO gas transfer is dominated by membrane diffusion (D_M ), whereas CO transfer is limited by diffusion plus chemical reaction within the red cell. Marie Krogh, who pioneered the single-breath measurement of D_LCO in 1915, believed that the combination of CO with red cell hemoglobin (Hb) was instantaneous. Roughton and colleagues subsequently showed, in vitro, that the reaction rate was finite, and prolonged in the presence of high P O 2 . Roughton and Forster (R-F) proposed that the resistance to transfer (1/D_L ) was the sum of the membrane resistance (1/D_M ) and (1/θVc), the red cell resistance (θ being the CO or NO conductance for blood uptake and Vc the capillary volume). From this R-F equation, D_M for CO and Vc can be solved with simultaneous NO and CO inhalation. At near maximum exercise, D_MCO and Vc for normal subjects were 88% and 79%, respectively, of morphometric values. The validity of these calculations depends on the values chosen for θ for CO and NO, and on the diffusivity of NO versus CO. Recent mathematical modeling suggests that θ for NO is "effectively" infinite because NO reacts only with Hb in the outer 0.1 μM of the red cell. An "infinite θ_NO " recalculation reduced D_MCO to 53% and increased Vc to 95% of morphometric values. © 2020 American Physiological Society. Compr Physiol 10:73-97, 2020.

Assessment of concordance between diffusion of carbon monoxide through the lung using the 10 s breath-hold method, and the simultaneous NO/CO technique, in healthy participants

INTRODUCTION

There is limited, large sample size, healthy control data comparing measurement of diffusing capacity of the lungs for carbon monoxide (DLCO) via the 10 s single-breath carbon monoxide uptake method (DLCO₁₀) and using a DLCO-DLNO double diffusion test performed with a 5 s time of apnoea (DLCO₅).

OBJECTIVES

The primary objective was to compare DLCO₅ and DLCO₁₀ in healthy participants. The secondary objective was to evaluate the reproducibility of DLCO₅.

MATERIAL AND METHODS

We included medical students at Caen University Hospital, from 2008 to 2011. We performed a standard single-breath carbon monoxide uptake and combined DLCO and DLNO measurement for each participant. The combined test was repeated one week later.

RESULTS

Among the 153 study participants, there was no statistically significant difference between the mean values of DLCO₁₀ (10.2 ± 2.2 mmol.min^-1 kPa^-1) and DLCO₅ (10.3 ± 2.2 mmol.min^-1 kPa^-1; paired t-test p = 0.19). Corrected for the same FiO₂, DLCO₅ was calculated at 10.5 ± 2.3 mmol.min^-1 kPa^-1 and was significantly different from DLCO₁₀ (paired t-test p < 0.001). DLCO₅ deviates from 1,6 mmol.min^-1 kPa^-1 (4,6 mL.min^-1. mmHg^-1) or 15 % of DLCO₁₀ (17 % above and 13% below, for 95 % of the subjects). Forty-seven participants were included in the DLCO₅ reproducibility test. The 2 test sessions were carried out at 6 ± 2 day intervals. Reproducibilities for DLCO, DLNO, DmCO and Vc was respectively 1.2 (11 %), 6.8 (13%), 16.5 (32 %), 12.5 (17 %) mmol.min^-1 kPa^-1.

CONCLUSION

In healthy participants, discrepancies between DLCO measured during the double diffusion and DLCO measured on an apnoea of 10 s are quite large. It may be an indication that the Roughton and Forster interpretation to describe this type of measurements is inadequate.

Permeability and diffusivity of nitric oxide in human plasma and red cells

A simple diffusion cell was made to measure the permeability and diffusivity of Nitric Oxide in human plasma and red cells. Nitric oxide was passed through the cell containing plasma or nitrited red cells enclosed by silicone membranes. Steady state permeability (α_NOD_NO ) was calculated from the cell dimensions and from the NO bulk flow entering and leaving the cell. The diffusion coefficient (D_NO) was calculated in three ways: (i) by dividing the steady state permeability by published values for solubility (α_NO ) in water at 26 °C and 37 °C (ii) by a numerical method and (iii) by an analytical method. Mean steady state permeability (95% confidence intervals) were plasma (26 °C) 5.57 × 10^-11 (2.35 × 10^-11-1.32 × 10^-10) and (37 °C) 5.48 × 10^-11 (2.13 × 10^-11-1.41 × 10^-10) mol cm^-1 s^-1 atm^-1 and red cells (26 °C) 6.74 × 10^-12 (1.29 × 10^-12-3.53 × 10^-11) and (37 °C) 3.93 × 10^-11 (1.39 × 10^-11-1.11.10^-10) mol cm^-1 s^-1 atm^-1. Median Diffusion Coefficients (D_NO) for plasma at 37 °C ranged from 3-3.36 × 10^-5 cm² s^-1 and red cells 2.41-2.94 × 10^-5 cm² s^-1 depending on the method used. These values may be used for modelling NO transport in vivo in the human lung and capillary. Parameters used for modelling in vivo should be measured at 37 °C.

Combined measurement of carbon monoxide and nitric oxide lung transfer does not improve the identification of pulmonary hypertension in systemic sclerosis

Screening is important to determine whether patients with systemic sclerosis (SSc) have pulmonary hypertension because earlier pulmonary hypertension treatment can improve survival in these patients. Although decreased transfer factor of the lung for carbon monoxide (TLCO) is currently considered the best pulmonary function test for screening for pulmonary hypertension in SSc, small series have suggested that partitioning TLCO into membrane conductance (diffusing capacity) for carbon monoxide (DMCO) and alveolar capillary blood volume (VC) through combined measurement of TLCO and transfer factor of the lung for nitric oxide (TLNO) is more effective to identify pulmonary hypertension in SSc patients compared with TLCO alone. Here, the objective was to determine whether combined TLCO–TLNO partitioned with recently refined equations could more accurately detect pulmonary hypertension than TLCO alone in SSc.

For that purpose, 572 unselected consecutive SSc patients were retrospectively recruited in seven French centres.

Pulmonary hypertension was diagnosed with right heart catheterisation in 58 patients. TLCO, TLNO and VC were all lower in SSc patients with pulmonary hypertension than in SSc patients without pulmonary hypertension. The area under the receiver operating characteristic curve for the presence of pulmonary hypertension was equivalent for TLCO (0.82, 95% CI 0.79–0.85) and TLNO (0.80, 95% CI 0.76–0.83), but lower for VC (0.75, 95% CI 0.71–0.78) and DMCO (0.66, 95% CI 0.62–0.70).

Compared with TLCO alone, combined TLCO–TLNO does not add capability to detect pulmonary hypertension in unselected SSc patients.

Diffusion Reaction of Carbon Monoxide in the Human Lung

The capture of CO, a standard lung function test, results from diffusion-reaction processes of CO with hemoglobin inside red blood cells (RBCs). In its current understanding, suggested by Roughton and Forster in 1957, the capture is represented by two independent resistances in series, one for diffusion from the gas to the RBC periphery, the second for internal diffusion reaction. Numerical studies in 3D model structures described here contradict the independence hypothesis. This results from two different theoretical reasons: (i) The RBC peripheries are not equi-concentrations; (ii) diffusion times in series are not additive.