Abstract
The Roughton–Forster equation of 1957 describes the transfer of oxygen and carbon monoxide from alveolar gas to pulmonary capillaries, as molecular diffusion across membranes and interstitium coupled to the reaction with haemoglobin in red cells https://bit.ly/380cg0D
Introduction
The transfer factor of the lung for carbon monoxide (TLCO) and spirometry are our two most valued tests in functional assessment. The understanding of the physiology underpinning TLCO (or DLCO) owes much to Robert Forster's research, including the formulation of the Roughton–Forster equation [1], the topic of this editorial. His other research involved oxygen and CO2 exchange, the role of carbonic anhydrase, and gas exchange in general. Robert (Bob) had a great sense of humour, and was delightful company (figure 1). He remained interested and engaged in the TLCO until a few months before his death in September 2021.
The Roughton–Forster equation has been one of the jewels of pulmonary gas exchange for 65 years: is it still relevant?
The Roughton–Forster equation for pulmonary diffusion
The TLCO, measured by the single breath and breath holding method, describes carbon monoxide (CO) transfer from alveolar gas to the haemoglobin (Hb) molecule in the pulmonary capillary red cells (CO being a surrogate for oxygen). TLCO is a conductance (mL·min−1·mmHg−1 in traditional units, mmol·min−1·kPa−1 in SI units) or “ease of transfer”; its reciprocal, 1/TLCO, is a resistance. In the Roughton–Forster equation [1], the resistance to transfer of gasx (O2, CO, etc.) from alveolus to capillary Hb (1/TLx) is presented as the sum of two resistances in series:
where 1/DMx is the diffusion resistance of the alveolar–capillary membranes and interstitium and plasma, and 1/θxVc is the reactive resistance of gasx with capillary blood; θx equals mL of gasx taken up per mL blood per unit time and partial pressure (Px): the units are mL·min−1·mmHg−1·mL−1 (or just min−1·mmHg−1); Vc is the pulmonary capillary blood volume.
The Roughton–Forster equation was a big step forward in the following ways:
1) Until that time (1957), the only resistance to oxygen and CO transfer from gas to blood was thought to be diffusive, meaning that 1/TLCO ∼ 1/DMCO.
2) The Roughton–Forster equation stressed the importance of the reactive resistance in pulmonary capillary red cells: approximately 75% of the total resistance to CO alveolar–capillary gas transfer (calculated from [2]). Thus, the low TLCO in anaemia and in idiopathic pulmonary hypertension could be explained.
3) Once the relationship between θCO and PO2 was established (but in vitro), the Roughton–Forster equation could be solved by measuring TLCO at different values of alveolar PO2, i.e. at different values of θCO. In a plot of 1/TLCO (y-axis) versus 1/θCO (x-axis), the intercept on the y-axis would be 1/DMCO and the slope 1/Vc.
1909–1957. How the Roughton–Forster equation came about
1909–1915. Copenhagen: the birth of DLCO
August and Marie Krogh introduced CO as a marker gas for measuring pulmonary diffusion, first with a steady state (ss) method [3] and, subsequently, in a famous paper [4], with a single breath (sb) technique, not so different from the TLCO measurement used in pulmonary function laboratories today. In using CO as a surrogate for O2, the Kroghs made two assumptions: first, that CO was an “indifferent” gas, traversing the alveolar membranes by diffusion alone, not transported by a “carrier” molecule. The absence of a “transporter” was confirmed some 80 years later [5]. The second assumption was that in low concentrations, CO taken up by capillary blood would combine instantaneously with Hb, meaning that no significant partial pressure for CO (PCO) would occur in the red cell. This meant that in the calculation of DLCO, only alveolar PCO needed to be measured. This assumption was reasonable at the time, since CO had been chosen for its very high affinity for Hb (215× the affinity of O2).
1922–1945. Cambridge (UK) and Boston (USA): Roughton and colleagues
F.J.W. Roughton (1899–1972) became, in 1921, an assistant to Hamilton Hartridge, a Senior Demonstrator in the Department of Physiology at Cambridge. Hartridge had a genius for invention, particularly of scientific apparatus: notably, the reversion spectroscope for measuring small quantities of CO combined with Hb (HbCO), and the continuous flow rapid reaction apparatus for monitoring the reactions of Hb with CO or O2 at the millisecond level (previously, the time resolution was minutes) [6]. Less than a year later, Hartridge and Roughton reported, in a letter to Nature [7]: “the combination (Hb with oxygen) was a very rapid one, being complete in one hundredth part of a second”. This was, for the time, an astonishing result. Roughton wanted to go on and measure the rate of uptake of CO with Hb. His mentor's put-down was “it would be a waste of time: CO is so tightly bound that the reaction would be too fast for us to measure it”. Cheekily, Roughton waited until Hartridge went away (to a meeting?), did the experiment, and found that the CO velocity (its association constant) was slower, not faster than oxygen! The reason for the high affinity of CO for Hb is that its dissociation constant is 1000 times slower than its association constant.
Roughton spent the rest of his life using the continuous flow rapid reaction apparatus to measure O2 and CO reaction times in dilute solutions of Hb and in intact red cells under hypoxic, normoxic and hyperoxic conditions. The velocity constants were fastest for O2 combining with deoxygenated Hb in solution and slowest for CO combining with oxyhaemoglobin in red cell suspensions (see table 1 in [6]); they convinced Roughton that the uptake of CO into blood was limited, particularly at high PO2, by diffusion plus reaction, and not by either process alone.
In World War II, Roughton worked in Boston at the Harvard Fatigue Laboratory. The practical problem was the build-up of CO to toxic levels in the confined spaces of tanks, cockpits and submarines. Roughton and his colleagues measured the rate of accumulation of HbCO in themselves at rest and on exercise, using a “bubble” apparatus designed by P.F. Scholander [8]. Under hyperoxic conditions, the rate of rise of HbCO was slowed by 25% [9]; qualitatively, the same was true for red cells in vitro [10]. In the last of three papers describing their research, Roughton made a most ingenious analysis of HbCO formation during steady state CO breathing (see Hughes and Bates [6], pp. 122–123), in which he calculated pulmonary capillary blood volume at rest (60 mL) and on exercise (95 mL) [11], values remarkably similar to the estimates when the Roughton–Forster equation came on stream 12 years later.
Roughton's work was of the greatest importance in our understanding pulmonary CO transfer and the DLCO, but he was actually more famous for his exposition of the reactions of CO2 and bicarbonate in lung and tissue gas exchange, and for his discovery (with Meldrum) of the vital enzyme, carbonic anhydrase [12].
1951–1954. Philadelphia (USA): Forster and colleagues; Copenhagen: Kruhoffer
When Robert Forster (1919–2021) started his research in the Department of Physiology and Pharmacology under Julius Comroe at the University of Pennsylvania, he was assigned a small laboratory in a basement with a new mass spectrometer and CO analyser. Comroe suggested he repeat the DLCO experiments which Marie Krogh had done 37 years earlier, but which had been largely ignored. With help from a more experienced colleague (Ward Fowler), Forster improved the Krogh DLCO (sb), making it practical for everyday use in pulmonary function laboratories [13]. Knowing of Roughton's work on CO in hyperoxia [10, 11], Forster and colleagues showed that DLCO (sb) was reduced as inspired oxygen (FIO2) was increased [14]; the more definitive paper was published in 1957 [15]. Forster realised that increasing FIO2 must have reduced the access of inspired CO to the O2–free (unliganded) Hb molecules, and that this quantity must be related to the instantaneous pulmonary capillary blood volume (Vc) [16]; in addition, the rate of reaction must have slowed, as Roughton had showed [10]. Forster and co-workers introduced a correction factor (C) to account for a significant red cell PCO, with the term θVc (the term θ appears only in a footnote!) where θ was, in essence, the diffusing capacity of 1 mL of blood, and Vc was the blood content of pulmonary capillaries accessible to the inhaled CO [16]. “C” included the ratio D/θVc, where D was DM, since Forster reasoned (as had Roughton) that red cell PCO (considered insignificant previously) would become important 1) if HbCO was high due to previous CO exposure (e.g. smoking), or 2) if membrane diffusion (DM) greatly exceeded the rate at which CO combined with the available Hb (∼ θVc). This rise of PCO would be “instantaneous” (i.e. confined to the pulmonary capillary transit) since the reaction Hb+CO would continue in arterial blood with a fall in PCO. These concepts were the essence of the Roughton–Forster equation.
To complicate matters, Kruhoffer (from the same department the Kroghs had worked in) in the same year published measurements of DLCO at low and high alveolar PO2 using the radioisotope 14C [17]. Although Kruhoffer's equation for DMCO and Vc was almost the same as Roughton and Forster's, he had no reliable values for 1/θCO as a function of PO2 and was unable to calculate DMCO or Vc.
1954–1957. Forster contacts Roughton: the synthesis
Realising the importance of the DMCO/θVc ratio and knowing he needed information on the 1/θ–PO2 relationship in human blood, Forster wrote to Roughton in Cambridge. Roughton replied that his own measurements were not good enough, and could he come to Philadelphia with his own continuous flow rapid reaction apparatus and make the measurements there? It was arranged! Two years later, four papers appeared consecutively in the Journal of Applied Physiology, the first two documenting the kinetics of O2 and CO combination with Hb solutions and with intact red cells [18, 19], the third [15] investigating more rigorously the relationship between DLCO (sb) or DLCO (ss) and alveolar PO2, and the fourth [1] giving the formal proof of the Roughton–Forster equation and calculating DMCO and Vc from measurements of DLCO (sb) at different levels of alveolar PO2 and 1/θ (calculated from the in vitro data).
1957–2022. Clinical applications of the DMCO and Vc calculations
The physiological insight from the DMCO and Vc analysis has been considerable, but the diagnostic gain in various respiratory conditions has, on the whole, been disappointing. This is mainly because there is interdependence between DM and Vc, between the diffusion pathway and the distribution and shape of red cells in the capillary bed [20, 21]. Clearly, DMCO can only be recorded if Hb is in the vicinity to combine with the incoming CO; DM must be matched to Vc for CO exchange to take place. The only mismatch is in mild to moderate congestive heart failure in which a selective loss of DMCO occurs [22, 23].
The introduction of the diffusing capacity for nitric oxide (DLNO) in 1987–1989 [24, 25] has changed things [26, 27]. The ratio DLNO/TLCO is about 5.0. This is because 1) NO is twice as diffusible as CO (DMNO/DMCO is ∼2.0) and 2) the reactive resistance of NO is lower (1/θNO << 1/θCO). The DLNO/TLCO ratio is related to DMCO/Vc [28], and may act as a surrogate for the Roughton–Forster analysis. More measurements of DLNO and TLCO in a clinical context are awaited with interest.
Conclusion
This article is a tribute to the life and work of Robert E. Forster, the distinguished respiratory physiologist, who died in September 2021 at the age of 101. His work at the University of Pennsylvania led to the introduction in 1957 [13] of the single breath carbon monoxide diffusing capacity (DLCO (sb); now called the CO transfer factor, TLCO), which is used in pulmonary function laboratories throughout the world. The 1957 Roughton–Forster equation focused attention on the role of the pulmonary microcirculation in blood–gas transfer. The recent addition of the DLNO to the well-established TLCO has revived interest in the clinical application of Roughton and Forster's membrane diffusing capacity (DM) and capillary volume (Vc) analysis.
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Footnotes
Conflict of interest: None declared.
- Received April 14, 2022.
- Accepted May 13, 2022.
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