## Abstract

The Coburn, Forster, Kane Equation (CFKE) describes a current understanding of the physiology of lung uptake and excretion of carbon monoxide (CO). The lung mean capillary P_{CO} is an important term in this equation because it drives CO excretion and functions as “back-pressure” during uptake of exogenous CO. Results of previous studies have indicated that the mean capillary P_{CO} of normal human lungs is equal to values calculated using the Haldane Equation, as described by the CFKE. The physiological explanation of how this parameter is set at this level is unknown. As a possible explanation, this study tested a hypothesis that a CO shuttle could be involved. Results of calculation-simulations indicate that a CO shuttle operates in a single alveolus model and imply that it could function as a determinant of the lung mean capillary P_{CO}.

- carbon monoxide shuttle
- carbon monoxide transfer factor of the lung
- the Coburn
- Forster
- Kane equation

## NEW & NOTEWORTHY

This study provides evidence regarding a physiological mechanism that determines the lung mean capillary P._{CO}that drives pulmonary CO excretion and functions as “back pressure” during CO uptake. Relevant to findings that CO is an intracellular signaling molecule and that there are clinical trials under way evaluating CO therapy, the goal of this study was to obtain a better understanding of the physiology of pulmonary CO exchanges that determine the body CO stores and intracellular P_{CO}values

## INTRODUCTION

the coburn, forster, kane Equation (CFKE) (2) describes a current understanding of the physiology of pulmonary CO uptake and excretion. This equation accurately predicts increases in the carboxyhemoglobin % saturation ([COHb]) in normal humans exposed to high ambient CO concentrations (15, 16, 26). A review sponsored by the National Academy of Science stated “The CFK Equation has been used by all regulatory agencies in the United States for setting CO standards” (11). This equation is given below, as used by Tikuisis et al. (27).
(1)
where β = (1/TL_{CO}) + (P_{B}-47/V_{A}). TL_{CO} is the lung transfer factor, mcapO_{2} is the mean pulmonary capillary PO_{2}, mcapO_{2}Hb is the mean pulmonary capillary oxyhemoglobin concentration, M is the equilibrium constant for the reaction of O_{2} + COHb ↔ CO + O_{2}Hb, Pi_{CO} is the saturated partial pressure of CO in inhaled air, P_{B} the barometric pressure minus vapor pressure of water, V_{A} the alveolar ventilation rate,V_{b} the blood volume, and V_{CO} the rate of endogenous CO production. The term ([COHb] × mcapPO_{2})/(mcapO_{2}Hb × M) is equal to the lung mean capillary P_{CO} (Lung-mcapP_{CO}) calculated from the Haldane Equation (5):
(2)
*Eq. 1* can also be given substituting “Lung-mcapP_{CO}” for its last term. Thus, the CFKE assumes—the Haldane assumption—that Po_{2}, P_{CO}, [O_{2}Hb], and [COHb] rapidly achieve chemical equilibrium in blood flowing in the pulmonary circulation. Experimental evidence that this assumption is valid in humans with normal lungs includes measurements made [using a rebreathing technique (3)] of the Lung-mcapP_{CO} and measurements of effects on the Lung-mcapP_{CO} of changing the alveolar PO_{2}. Reference 3 also cites other studies going back to the 1940s, which reported the use of the lung-mcapP_{CO} measured during breath holding to calculate the blood [COHb] with the Haldane Equation. The physiological importance of the Lung-mcapP_{CO} is that it is a driver of CO excretion and also functions as “back pressure” during CO uptakes.

The physiological basis of how Po_{2}, P_{CO}, [COHb], and [O_{2}Hb] could rapidly achieve chemical equilibrium in blood flowing in the pulmonary circulation is unknown. Experimental results (3) indicated that the P_{CO} increases as blood flows in the pulmonary circulation and that under a condition where there is little or no uptake or excretion of exogenous CO, there is only a small P_{CO} gradient between the Lung-mcapP_{CO} and the mean alveolar P_{CO}. How could this high Lung-mcapP_{CO} be achieved? It is argued that this requires a rapid P_{CO} increase to the lung-mcapP_{CO }level in blood flowing in first segments of lung capillaries. P_{CO} increases occur as a by-product of the reaction of O_{2} with COHb, but this reaction is too slow to evoke P_{CO} increases to the Lung-mcapP_{CO} level, even in blood exiting pulmonary capillaries (21). In the present study a possibility is considered that a rapid blood P_{CO} increase could be partially or completely explained by a CO shuttle occurring within individual alveoli where CO diffusing out of distal portions of capillaries into the alveolus would then diffuse into proximal capillary segments driven by the low P_{CO} in blood entering capillaries evoking a large alveolus- capillary P_{CO} gradient. Whether or not a shuttle of CO could occur and is significant depends on this gradient and the CO transfer factors of proximal and distal capillary segments.

CO is a signal transduction molecule (22), and induced expressions of heme oxygenase-1 have been estimated with measurements of the [CO] in expired gas (22). There is a potential for the use of CO therapy in patients with various inflammatory diseases (13). These findings give impetus to a need to obtain a better understanding of physiological mechanisms involved in CO uptake and excretion, which are determinants of the total body CO stores and the P_{CO} within body cells.

## METHODS

### Single Alveolus Model

Figure 1*A* shows schematically the proposed CO shuttle. The capillary shown in this figure, which represents all of the capillaries that feed a single alveolus, has been divided into proximal and distal segments. As indicated in the introduction, the proposed CO shuttle is operated by CO diffusing out of the distal capillary segment into the alveolus and then diffusing into the proximal capillary segment. The quantity of CO exiting from the distal segment blood into alveolus gas in a given time period, the TD-shuttle (TD-S), is assumed equal to the quantity of CO being transferred from the alveolus into the proximal capillary segment blood over the same time period, the TP-shuttle (TP-S). Mixing of CO in alveolus gas is assumed to be rapid and not limiting. It is assumed that shuttle-evoked CO transfers are limited by rates of diffusion out of distal segments and into proximal segments. The model used here is considered to be an average alveolus in a resting normal human where the alveolus gas Po_{2} is equal to a mean lung alveolar Po_{2} of 100 mmHg, and the time-dependent increase in the capillary blood Po_{2} of the alveolus is the same as described for the entire lung (23).

The strategy was to calculate TP-S values for blood flowing in “proximal” capillary segments aimed at determining whether a CO shuttle could evoke P_{CO} increases. Calculations of shuttle-evoked P_{CO} increases in multiple segments just downstream from proximal segments were also performed. Blood volumes of each segment were = to 1% of the total capillary volume. To address the question of whether or not a P_{CO} increase driven by the shuttle could achieve the Alv-mcapP_{CO} level, TP-S values were compared with calculated CO uptakes into blood flowing in the same segments required to increase blood P_{CO} to the Alv-mcapP_{CO} level based on increases in dissolved + bound CO. This value was termed “CO Required” and abbreviated as CO-R. The % of the CO-R achieved by the TP-S is given by the term “R”. From the “R” value, the P_{CO} increase in blood flowing in a given segment and the P_{CO} in blood exiting from this segment were calculated. For the condition in which the total transit time for blood flowing in the capillary (TT_{Tot}) was 1,000 ms, the transit time for blood flowing in given proximal segments (TT_{Prox}) and each downstream segment (TT_{DS}) was 10 ms. When the TT_{Tot} was 500 ms, TT_{Prox} and TT_{DS} were 5 ms. The two different TT_{Tot} bordered a mean value found in the normal lung of 750 ms (10, 28). A [COHb] of 0.50% saturation (sat.), a normal value, was used in these calculations. Calculated values of Alv-mcapP_{CO} and the mixed venous P_{CO} are sensitive to the [COHb] used; however, calculated “R” values and conclusions made in this study were not changed using 0.50 to 1.0% sat. [COHb].

Three series of calculations were performed. In *Series A* calculations, the best available parameters were used. *Series B* and *C* calculations had the goal of assessing effects on results of changing major parameters.

### Proximal Segment Calculations: Parameters and Calculated Terms

#### The mean Po_{2} of blood flowing in proximal segments.

In *Series A*, proximal segment calculations, classical views of Po_{2} increases in blood flowing in the pulmonary circulation were followed. I used a plot showing time-dependent Po_{2} increases in blood flowing in the resting human pulmonary circulation with the subject breathing air published (Fig. 1) in an article by Staub (23). Po_{2} values were identified that corresponded to the 5 and 10 ms TT_{Prox} and represented the Po_{2} of blood leaving proximal segments. The mean Po_{2} in blood flowing in proximal segments were calculated from these values and a mixed venous Po_{2} of 40 mmHg (10). Effects of decreases in Pco_{2} and pH increases in blood flowing in proximal segments were not considered because of the short TT_{Prox} in 1% proximal segments.

#### Transfer factors and θ_{CO}.

The transfer factor of the lung (TL_{CO}) and the rate of CO uptake by erythrocyte hemoglobin (θ_{CO}) are major parameters used in calculations made here. Their relationship is given in the classic equation (20):
(3a)
where TL_{CO-M} is the membrane component of TL_{CO} and the Lung-Vc is the volume of blood in gas exchange capillaries. Other abbreviations were identified in the previous section of this article. Fig. 1*B* illustrates the intravascular and diffusion resistance to CO transfers depicted in this equation. To be relevant to CO uptake into proximal capillary segments of a single alveolus, *Eq. 3A* was converted to the following:
(3b)
where TF_{Prox} is the transfer factor of a proximal segment, TF_{Prox-M} is the membrane component of TF_{Prox}, Prox-θ_{CO} is the rate of CO uptake by erythrocyte hemoglobin in blood flowing in proximal segments, and Prox-Vc is the volume of blood in this segment. TF_{Prox} and TF_{Prox-M} were calculated by dividing TL_{CO} and TL_{CO-M} by 4.84 × 10^{8} and changing ml to µl and time units to ms TT_{Prox} so that TF_{Prox} and TF_{Prox-M} units are µl/(ms × mmHg). Prox-θ_{CO} units are µl/(TT_{Prox} × mmHg × µl). The blood volume of 1% proximal segments (Prox-Vc) was calculated by dividing the Lung-Vc by 4.84 × 10^{8}, converting units to microliters and multiplying by 0.01. 4.84 × 10^{8} is the number of alveoli in a normal lung, an average value found in six lungs fixed at their expiratory reserve volume: four from females and two from males (14).

#### Prox-θ_{CO} and its Po_{2} adjustment.

A θ_{CO} of 0.57 ml/(min × mmHg × ml) was used. This value is an average found in three different studies that reported data obtained with a continuous flow rapid mixing apparatus and double-beam spectrophotometry using human erythrocytes at pH 7.4, 38°C, a hemoglobin concentration of 15 g/100 ml blood, and a Po_{2} of 100 mmHg (6, 25). The 0.57 value was adjusted for increases that occur at Po_{2} < 100 mmHg using data reported by Reeves and Park (19). Po_{2}- adjusted θ_{CO} units were converted to Prox-θ_{CO }units, as described above. A Po_{2}-Prox-θ_{CO} plot for a proximal segment that had a TT_{Prox} of 10 ms is shown in Fig. 2*A*. A similar plot was constructed for use in calculations where the TT_{Prox} was 5 ms. These plots were used to adjust the TF_{Prox} in TP-S calculations, as described below.

#### TF_{Prox} and its Po_{2} adjustment.

The alveolus transfer factor (TF_{Alv}) was calculated as described above using a TL_{CO} of 30 ml/(min × mmHg) measured at a normal alveolar Po_{2} (1, 9). TF_{Alv} was then divided into the TF_{Prox} and the distal transfer factor (TF_{Dist}) as proportional to the % of the total capillary volume contained in proximal and distal segments. TF_{Prox} calculated in this manner needed to be adjusted to the low Po_{2} in blood flowing in proximal segments. Because there are no data published in the literature that quantifies the Po_{2} sensitivity of TL_{CO} over this Po_{2} range, the Po_{2} adjustment of the TF_{Prox} was determined using the Po_{2} sensitivity of Prox-θ_{CO}. Prox-θ_{CO} values for Po_{2} of 40, 50, 60, and 100 mmHg were identified from the plot shown in Fig. 2. Different TF_{Prox}were then calculated with *Eq. 3B* using Prox-θ_{CO} values that corresponded to each of these Po_{2}. TL_{CO}-_{M} and Lung-Vc values of 57 ml/(min × mmHg) and 80 ml (7), respectively, were used to calculate TF_{Prox-M} and Prox-Vc. A plot of TF_{Prox} vs. Po_{2} for 1% proximal segments, where the TT_{Prox} is 10 ms is shown in Fig. 2. Using mean Po_{2} values determined as described above, Po_{2}-corrected TF_{Prox} values used in TP-S calculations were read from this plot. Similar plots were constructed for use in calculations where the TT_{Prox} was 5 ms.

#### TF_{Dist}.

TF_{Dist} were calculated as equal to TF_{Alv} minus the Po_{2}-adjusted value of TF_{Prox}. This calculation assumes that the TF_{Dist} relevant to efflux of CO from distal segments is equal to the TF_{Dist} during CO uptake into this segment, an assumption discussed later in this article.

#### Alv-mcapP_{CO}.

*Alv-mcapP*_{CO} was calculated with *Eq. 2* using a Po_{2} 88 mmHg, [O_{2}Hb] 98%, M = 220, and [COHb] 0.50% sat., values typical of those used in CFKE calculations, giving an Alv-mcapP_{CO} = 2.040 × 10^{−3} mmHg.

#### The increase from the mixed venous blood P_{CO }to the alv-mcapP_{CO} (“↑ MV-P_{CO} to Alv-mcapP_{CO}”).

This value was used in determining different proximal mean capillary P_{CO} (Prox-mcapP_{CO}) values used in TP-S calculations, and in calculating CO-R. Because in mixed venous blood, the reaction O_{2} + COHb ↔ CO + O_{2}Hb is close to or in chemical equilibrium, the mixed venous blood P_{CO }was calculated using *Eq. 2* with a Po_{2} 40 mmHg, [O_{2}Hb] 75% sat.; M 220, and [COHb] 0.50% sat. This produced a value of 1.21 × 10^{−3} mmHg. The “↑ MV-P_{CO} to Alv-mcapP_{CO}” in blood flowing in proximal segments was calculated as 2.040 × 10^{−3} mmHg minus 1.21 × 10^{−3} mmHg = to 0.83 × 10^{−3} mmHg.

#### Prox-mcapP_{CO}.

Because values of this term are unknown, in *Series A*, proximal segment calculations of TP-S were calculated using four different Prox-mcapP_{CO}, which corresponded to 20, 30, 40, and 50% of the 0.83 × 10^{−3} mmHg “↑ MV-P_{CO} to Alv-mcapP_{CO}” calculated above. To illustrate this calculation, the 20% Prox-mcapP_{CO} was = to 0.2 × 0.83 × 10^{−3} + the mixed venous P_{CO} of 1.21 × 10^{−3} mmHg = 1.37 × 10^{−3} mmHg. Thirty, 40 and 50% Prox-mcapP_{CO} were 1.46, 1.54, and 1.63 × 10^{−3} mmHg, respectively. In *Series A* downstream calculations and *Series B* and *C* calculations, only the 40% Prox-mcapP_{CO} values were used.

#### Driving-P_{CO}.

This is the mean P_{CO} in blood flowing in proximal segments that drives the reaction of CO and erythrocyte hemoglobin. This term was used in determining the bound component of CO-R. Different Driving-P_{CO} values were calculated equal to different % of the “↑ MV-P_{CO} to Alv-mcapP_{CO}”. To illustrate this calculation a 20% Driving-P_{CO} was = to 0.2 × 0.83 × 10^{−3} mmHg = 0.167 × 10^{−3} mmHg. In most calculations the % of the “↑ MV-P_{CO} to Alv-mcapP_{CO}” used in calculating the Driving-P_{CO} was matched to the % of the “↑ MV-P_{CO} to Alv-mcapP_{CO}” used to calculate the Prox-mcapP_{CO}. For example, a 20% Prox-mcapP_{CO} of 1.37 × 10^{−3} mmHg was matched with the 20% Driving-P_{CO} 0.167 × 10^{−3} mmHg. The matched Driving P_{CO} was used as a best estimate of the actual mean driving P_{CO} operating in proximal segments, an estimate evaluated later in this article.

#### Dist-mcapP_{CO}.

This calculation follows the approach, given above, of dividing the TF_{Alv} into TF_{Prox} and TF_{Dist} as proportional to the fractions of the total capillary volume contained in proximal and distal segments. Therefore, considering mean blood P_{CO} to be average values:

Alv-mcapP_{CO} × TT_{Tot} = Prox-mcapP_{CO} × TT_{Prox} + Dist-mcapP_{CO} × TT_{Dist}. Thus,
(4)

#### AlvP_{CO}.

The derivation of *Eq. 5* is given in the
ix A: Equations and Example Calculations.
(5)

### Calculation of “R”

#### TP-S.

CO uptake in the lung can be expressed as: dCO/d*t* = TL_{CO} × ΔP_{CO }(5), where ΔP_{CO} is equal to the mean alveolar P_{CO} minus the lung-mcapP_{CO}. Analogous to this, we can consider CO uptake into proximal capillary segments of a single alveolus:
(6)
During each blood transit through the entire capillary, there is one transit of blood through a proximal segment; thus, the TF_{Prox} was described with TT_{Prox} time units and TP-S as μl/TT_{Prox}.

#### CO-R.

The CO-R is equal to increases in bound + dissolved CO per TT_{Prox} that would occur if the blood P_{CO} increased from the mixed venous P_{CO} to the Alv-mcapP_{CO}. Equations given below were used to calculate increases in bound CO and dissolved CO. As described above for TP-S calculations, the use of TT_{Prox} units in CO-R calculations was relevant to increases in bound and dissolved CO during one transit of blood flowing in a proximal segment and CO-R are given as μl/TT_{Prox}.
(7)
(8)
where BSCoef denotes the Bunsen solubility coefficient.

#### “R”.

The TP-S was divided by CO-R, multiplied by 100, and given as a percentage.

### Calculation of the P_{CO} ↑ in Blood Flowing in Proximal Segments

P_{CO} ↑ = “R” × 0.01 × the “↑ MV-P_{CO} to Alv-mcapP_{CO}”.

### Calculation of the End-Segment P_{CO} Given Both in mmHg P_{CO} and % of the Alv-mcapP_{CO}

The end-segment P_{CO} is = to the mixed venous P_{CO} + the segment P_{CO} ↑. The % of the Alv-mcapP_{CO} is obtained by dividing the end-segment P_{CO} by the Alv-mcapP_{CO} and multiplying by 100.

### Downstream Segment Calculations

The goal was to determine by extending the shuttle-evoked CO receiving segments how many additional 1% segments were required for blood P_{CO} to increase to the Alv-mcapP_{CO} level. The first DS segment (DS-1) was immediately downstream from the proximal segment, and the DS-2 segment was immediately downstream from DS-1. Each downstream segment had a transit time (TT_{DS}) of 10 ms (with 1,000 ms TT_{Tot} calculations) or 5 ms (with 500 ms TT_{Tot} calculations). Terms are abbreviated TF_{DS}, DS-θ_{CO}, DS-mcapP_{CO}, TT_{DS}. Instead of “↑ MV-P_{CO} to Alv-mcapP_{CO}”, the term “Inlet P_{CO} to Alv-mcapP_{CO}” is used. Mean DS segment Po_{2} were read from the plot cited above (23), reflecting 5- or 10-ms delays for blood to enter each downstream segment. Because the mean Po_{2} in blood flowing in DS segments were higher than found in proximal segments, different adjustments of DS-θ_{CO }and TF_{DS }were required.

#### How calculations were performed.

Examples are given in the Appendix A: Equations and Example Calculation section. Parameters and terms used in these examples, and other *Series A* and *B* calculations, are listed in Appendix B. As indicated above, *Series A* calculations were performed using four different Prox-mcapP_{CO} and matched Driving P_{CO}. For each Prox-mcapP_{CO}, calculating the end-segment P_{CO} required sequential calculations. First terms used in calculating TP-S and CO-R were determined; then TP-S, CO-R, and “R” were calculated. Values of “R” were used to calculate the P_{CO }↑ and end segment P_{CO}. With DS segment calculations, the Alv-P_{CO} was kept equal to the value calculated for the proximal segment. The calculation sequence was Inlet P_{CO} → “↑ Inlet P_{CO} to Alv-mcapP_{CO}” → 40% DS-mcapP_{CO} → DS-ΔP_{CO }- → TP-S → 40% DS Driving-P_{CO} → CO-R → “R” → P_{CO} ↑ in blood flowing in this segment → end-segment P_{CO}.

As listed in Appendix B, in *Series B* calculations the same parameters were used as in *Series A* calculations, except that the Lung-Vc was 120 ml, and the proximal blood mean Po_{2} 60 mmHg. The 120-ml Lung-Vc value was used because a morphometric measured value of this parameter (8) was larger than the calculated value listed above. The higher proximal segment mean Po_{2} was chosen because of evidence there is partial oxygenation of blood flowing in precapillary arterioles (4, 24).

In *Series C* calculations, “R” was calculated as described above but different values for major parameters were used; i.e., TL_{CO} was 25 ml/(min × mmHg); the 100 mmHg Po_{2} value of θ_{CO} was 0.67 ml/(min × mmHg × ml); mean Po_{2} was 60 mmHg; the number of lung alveoli was 3.6 × 10^{8}; and Lung-Vc was 120 ml. These calculations were made only for proximal segments.

## RESULTS

Table 1 lists *Series A* 1,000 ms TT_{Tot} results obtained using different Prox-mcapP_{CO} and matched Driving-P_{CO}. Major results are “R” and P_{CO} data consistent with large shuttle-evoked P_{CO }increases in blood flowing in proximal segments at each of the Prox-mcapP_{CO} and matched Driving-P_{CO}. Because “R” were determined by dividing TP-S by the CO-R, these results could be influenced by errors in the Driving-P_{CO} used to calculate the CO-R. Therefore, these values were recalculated using different Driving-P_{CO} and Prox-mcapP_{CO}. Results plotted in Fig. 3 show that “R” values remained > 40% over this entire range of Prox-mcapP_{CO} and Driving-P_{CO}.

Table 2 compares downstream and proximal segment results of *Series A* calculations. There were progressive shuttle-evoked P_{CO} increases in blood flowing into the DS-1, DS-2 and DS-3 segments. Under the condition in which the TT_{Tot} was 1,000 ms, end-segment blood P_{CO} reached >97% of the Alv-mcapP_{CO} level after flow through two DS segments. With 500-ms TT_{Tot} calculations, three DS segments were required for the end-segment blood P_{CO} to reach >97% of the Alv-mcapP_{CO} value. These P_{CO} increases are plotted in Fig. 4 vs. % total capillary volume. This plot emphasizes the progressive expansion of the CO receiving segment used in calculations that considered blood flowing from the proximal segment into downstream segments. These results predict that with both TT_{Tot} calculations, the shuttle could drive P_{CO} increases to >97% of the Alv-mcapP_{CO} level in blood flowing in the first 3 or 4% of the capillary.

Figure 4 also shows results of *Series B* calculations, where the mean proximal Po_{2} was increased to 60 mmHg and Lung-Vc increased to 120 ml. Blood P_{CO} increases in both proximal and DS segments were smaller than found in *Series A* calculations. Four DS segments were required for the P_{CO} to achieve >97% of the Alv-mcapP_{CO} of 2.040 × 10^{−3} mmHg.

Figure 5 shows results of *Series C* calculations, where effects on calculated “R” of changing one or two of the parameters used in *Series A* calculations were determined. All calculated “R”were >30%.

## DISCUSSION

Calculation-simulations using a single alveolus model evaluated the possibility that a CO shuttle could exist in the normal human lung and be large enough to evoke blood P_{CO} increases in blood flowing in the pulmonary circulation sufficient to approach the Alv-mcapP_{CO} level. The goal was to possibly explain the physiological basis of the Haldane assumption made in deriving the CFKE. “R” values calculated for proximal and for DS segments indicate the % of blood P_{CO} increases evoked by the proposed CO shuttle of the value that would occur if the P_{CO} increased from the inlet P_{CO} to the Alv-mcapP_{CO} level of 2.040 × 10^{−3} mmHg.

Major results are the large “R” found in proximal segment calculations determined under all conditions studied and that shuttle-evoked P_{CO} increases nearly reached the Alv-mcapP_{CO} level after blood flowed through two to four segments immediately downstream from proximal segments. Shuttle-evoked blood P_{CO} increases in CO receiving segments (proximal + DS) segments) were a result of large Prox-ΔPco and DS-ΔP_{CO} values, the increase in TF_{Prox} and TF_{DS} resulting from the low Po_{2} in blood flowing in these segments, and small Prox-Vc and DS-Vc values, so that only a small influx of CO was required to evoke blood P_{CO} increases.

Two different approaches assessed variations in results. These include results obtained in *Series A* calculations (Table 1, Fig. 3) that compared effects of different Prox-mcapP_{CO} and Driving P_{CO}, as well as results obtained in *Series B* and *C* calculations (Table 1, Fig. 5) that assessed effects of changing other parameters. “R” values were 35 to 121%. It is still possible that these values are too high. If this occurred, more downstream segments would be required for their end-segment blood P_{CO} to achieve >97% of the Alv-mcapP_{CO}. For example, if a proximal segment “R” was 20%, it would take flow into as many as 20 1% DS segments, accounting for 21% of the total capillary volume, for the blood P_{CO} to increase to >97% of the Alv-mcapP_{CO}.

The finding of evidence that shuttle-evoked P_{CO} increases in blood flowing in DS segments reached the Alv-mcapP_{CO} level, although supporting the shuttle hypothesis does not produce a complete physiological description of how the Alv-mcapP_{CO} might be determined. This is because P_{CO} changes in distal segments were not considered in these calculations other than predicting that the P_{CO} in blood entering the distal segment is = to the Alv-mcapP_{CO}. To evaluate possible P_{CO} changes in blood flowing in distal segments, calculations of the Dist-mcapP_{CO} were performed using *Eq. 4*, an equation that describes that for given % proximal and % distal segment, Prox-mcapP_{CO}, and Alv-mcapP_{CO}, there is a unique Dist-mcapP_{CO}. Calculated Dist-mcapP_{CO} values were only 0.007 to 0.010 × 10^{−3} mmHg larger than the AlvP_{CO}, a finding that suggests that when the P_{CO} in blood flowing in CO-receiving segments approaches the Alv-mcapP_{CO} level, only small further net P_{CO} increase would occur in blood flowing in distal segments. These preliminary results imply the importance of shuttle-evoked P_{CO} increases in blood flowing in CO receiving segments in setting the Alv-mcapP_{CO}.

### Are Results Relevant to the Intact Lung?

Different alveoli in a normal lung have different parameters that would determine shuttle-evoked blood P_{CO} increases in proximal and DS segments. Considering variations of alveolus Po_{2} that occur in a normal lung, “R” remained >30% as the mean proximal segment Po_{2} was varied from 40 to 60 mmHg (see Fig. 5 for the 60 mmHg value). Effects on “R” of changes in other parameters that would operate in different alveoli, shown in Table 1 and Fig. 5, are also consistent with a preliminary conclusion that a shuttle-evoked blood P_{CO} increase in CO-receiving segments could operate in most alveoli in a normal lung.

### Implications

The major importance of results described here is that they provide at least a partial physiological explanation for the Haldane assumption made in deriving the CFKE. If the shuttle hypothesis is correct, results suggest that more variables are involved in the physiology of lung CO exchanges than described by the CFKE; i.e., those involved in driving the TP-S. Results also show that the TP-S in proximal and DS segments of a normal alveolus are able to drive blood P_{CO} to the Alv-mcapP_{CO}, evidence that explains how the CFKE can be used to calculate CO uptake or excretion rates in humans with normal lungs without considering additional variables that drive the TP-S. However, I emphasize that this conclusion is only relevant to normal lungs and not necessarily correct for diseased lungs. As discussed in the introduction, the CFKE is used to quantify blood [COHb] increases in humans exposed to elevated air CO levels. The physiological explanation for the Haldane assumption provided by results given here strengthens the use of the CFKE for this purpose in humans with normal lungs. Because the Lung-mcapP_{CO} is a driving force for excretion, results of the present calculations are relevant to a better understanding of the physiology of CO excretion and recovery from CO poisoning. Findings given here are relevant to the physiology of CO therapy effected by inhalation because therapeutic effects are dependent on [COHb] increases and how long the [COHb] remains elevated following decreases in inhaled [CO] to ambient levels.

So far, calculation simulations have been made only for a normal lung alveolus. It has never been established that the CFKE is valid for use in calculating CO exchanges in diseased lungs. The issue considering diseased lungs is whether or not the Haldane assumption is valid in setting the Lung-mcapP_{CO}; i.e., whether the Lung-mcapP_{CO} is maintained in these lungs. The identification of parameters that determine the TP-S in the present study should allow future studies to be performed that consider CO exchanges in diseased lungs.

Results provide a possible physiological basis for the use of “CO back pressure”, calculated by making the Haldane assumption, in correcting TL_{CO} measurements determined in pulmonary function laboratories. Results also provide a possible explanation for the finding that the TL_{CO} measured during CO uptake and during CO excretion are identical (3, 17), an expected finding if the Lung-mcapP_{CO} is set by the shuttle mechanism proposed here.

### Discussion of Major Assumptions

#### The division of TF_{Alv} into TF_{Prox} or TF_{DS}, and TF_{Dist}, is proportional to capillary segment volumes and transfer factors are uniform in different capillary segments.

(These are similar to assumptions made in Bohr integration calculations of time-dependent Po_{2} increases in blood flowing in the pulmonary circulation summarized in Ref. 23). These assumptions were tested by calculating effects on “R” of decreasing or increasing TF_{Prox}, keeping the TF in distal 1% segments largely unchanged. Decreasing TF_{Prox} to 75 or 50% of values used in *Series A* 1,000-ms TT_{Tot} calculations decreased “R” from 59.8 to 45.8 and 30.4%, respectively, values still consistent with operation of the shuttle that would evoke P_{CO} increases in blood flowing downstream segments to the Alv-mcapP_{CO }level. Increasing the TF_{Prox} > TF in 1% distal segments resulted in increases in the TP-S and in “R” that made the shuttle even more efficient in driving proximal segment blood P_{CO} increases.

#### The TF_{Dist} is the same during CO efflux from distal segments and CO influx into these segments.

TF_{Dist} is calculated from TL_{CO} values made during measurements of CO uptake, but operation of the shuttle involves CO diffusion out of distal segments. The above assumption is supported by the previous finding that the TL_{CO} of normal human subjects (at a normal alveolar Po_{2}) is the same measured during CO uptake or during CO excretion (3, 17).

#### CO mixing within a single alveolus is rapid enough to obviate a significant gas P_{CO} gradient.

This assumption is based on calculations (6) that indicated that because of small alveolus dimensions, 90% mixing of N_{2 }in a single alveolus occurs within 5 ms. This is relevant to CO mixing because N_{2} and CO have similar self-diffusion coefficients. Because the 90% mixing time of 5 ms is short compared with the time during which CO is diffusing out of the distal segments into the alveolus (495 to 990 ms), a significant alveolus gas P_{CO} gradient resulting from CO transfer out of distal segments is unlikely to occur. However, because the TT_{Prox} is only 5 and 10 ms, it cannot be excluded that there is a significant P_{CO} gradient in gas in close proximity to proximal capillary segments that would decrease Prox-ΔP_{CO} and TP-S values. The finding that calculations (not given) that used 5% proximal segments, where TT_{Prox} were 25-50 ms, produced “R” >50% argues against this possibility.

#### The value of θ_{CO} usually measured after P_{CO} step increases from 0 to 50–70 mmHg is relevant to a condition in which the driving P_{CO} was 0.167 to 0.415 × 10^{−3} mmHg.

This assumption, similar to that made by investigators who calculated the TL_{CO-M} and Lung-Vc using *Eq. 3A* (9, 20), follows findings that θ_{CO} values are unchanged as a function of different P_{CO} step changes made during the measurement; i.e., that initial rates of the reaction are proportional to the P_{CO} (9, 19).

#### TP-S is equal to the TD-S, a condition where there is no CO uptake or excretion of exogenous CO and where endogenously produced CO is insignificant.

Results speak only for this condition. However, this condition is not different from that occurring in several subjects (described in Ref. 3), who were at or near a steady state regarding uptake and excretion of exogenous CO. The endogenously produced CO excretion rate is too small to influence these calculations.

#### Single alveolus model data are applicable to the normal alveolus in intact lungs.

The model ignores the complexity of capillary networks within single alveoli (8, 12). However, this assumption is supported by the finding that “R” values remained >30% in calculations where TT_{Tot}, and Prox-mcapP_{CO} were varied over ranges likely found in different capillaries feeding individual alveoli.

#### Shuttle-evoked CO uptake into blood flowing in precapillary arterioles does not occur.

If this assumption is not correct, and the shuttle drives CO into precapillary arterioles, TP-S and “R” values reported here would be underestimated. Thus, the shuttle would be even more efficient in driving blood P_{CO} to the Alv-mcapP_{CO}. However, this cannot be quantified because transfer factors of these arterioles are unknown.

### Conclusions

Results of calculation-simulations that used a single “normal” alveolus model *1*) support operation of a CO shuttle that evokes P_{CO} increases in blood flowing in proximal and DS segments, and *2*) indicate that these increases can reach the Alv-mcapP_{CO} level.

The CO shuttle hypothesis explains how the Lung-mcapP_{CO} could be determined; i.e., the physiological basis of the Haldane assumption made in deriving the CFKE.

## DISCLOSURES

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

## AUTHOR CONTRIBUTIONS

R.F.C. conception and design of research; R.F.C. performed experiments; R.F.C. analyzed data; R.F.C. interpreted results of experiments; R.F.C. prepared figures; R.F.C. drafted manuscript; R.F.C. edited and revised manuscript; R.F.C. approved final version of manuscript.

## Glossary General

- CFKE
- Coburn, Forster, Kane Equation
- Haldane assumption
- Alv-mcapP
_{CO}is equal to the chemical equilibrium value of the reaction of O_{2}+ COHb calculated using mean capillary values of Po_{2}, [O_{2}Hb], and [COHb].

## Proximal Segment Calculations

- Alv-mcapP
_{CO} - Mean P
_{CO}in capillaries servicing a single alveolus - AlvP
_{CO} - P
_{CO}in alveolus gas - Alv-Vc
- Volume of blood in capillaries servicing a single alveolus
- CO-R
- Quantity of CO entering blood flowing in a proximal capillary segment per TT
_{Prox}, required to increase the P_{CO}from the mixed venous level to the level of the Alv-mcapP_{CO}. - Dist-ΔP
_{CO} - P
_{CO}gradient (Dist-mcapP_{CO}− Alv-P_{CO}) effecting transfer of CO from the distal capillary segment into alveolus gas - Dist-mcapP
_{CO} - Mean P
_{CO}in blood flowing in a distal segment - Driving-P
_{CO} - P
_{CO}that is “driving” the reaction of CO with erythrocyte hemoglobin - Lung-mcapP
_{CO} - Lung mean capillary P
_{CO} - Lung-Vc
- Lung capillary volume
- “↑ MV-P
_{CO}to Alv-mcapP_{CO}” - Increase from the mixed venous P
_{CO}to the Alv-mcapP_{CO}level in blood flowing in a proximal segment - % proximal segment and % distal segment
- % of the total capillary volume in a proximal and in a distal capillary segment
- Prox-ΔP
_{CO} - P
_{CO}gradient (AlvP_{CO}− Prox-mcapP_{CO}) effecting transfer of CO into a proximal segment - Prox-mcapP
_{CO} - Mean P
_{CO}in blood flowing in a proximal capillary segment - Prox-θ
_{CO} - Reaction rate of CO with erythrocyte hemoglobin in blood flowing in a proximal capillary segment
- Prox-Vc, Dist-Vc
- Blood volumes of proximal and distal capillary segments
- “R”
- Ratio of TP-S to CO-R, multiplied by 100; i.e., the % of the CO-R achieved by the TP-S
- TD-S
- Quantity of CO exiting into the alveolus from blood flowing in a distal capillary segment per TT
_{Prox}effected by a CO shuttle - TF
_{Alv}, TF_{Prox}, and TF_{Dist} - Transfer factors of a single alveolus, a proximal capillary segment, and a distal capillary segment
- TL
_{CO-M} - Membrane transfer factor of the lung
- TF
_{Prox-M} - Membrane transfer factor of the proximal segment
- θ
_{CO} - Reaction rate of CO with erythrocyte hemoglobin
- TL
_{CO} - Transfer factor of the human lung
- TP-S
- Quantity of CO transferred from an alveolus into blood flowing in a proximal capillary segment per TT
_{Prox}effected by a CO shuttle - TT
_{Prox}and TT_{Dist} - Transit times for blood flowing in a proximal capillary segment and in a distal capillary segment
- TT
_{Tot} - Total transit time for blood flowing in the alveolus capillaries

## Downstream Segment Calculations

- DS-θ
_{CO} - Reaction rate of CO with erythrocyte hemoglobin in blood flowing in a downstream capillary segment
- DS-mcapP
_{CO} - Mean P
_{CO}in blood flowing in a downstream capillary segment - DS-ΔP
_{CO} - P
_{CO}gradient (AlvP_{CO}− DS-mcapP_{CO}) effecting transfer of CO into a downstream segment - “↑ Inlet-P
_{CO}to Alv-mcapP_{CO}” - Increase from the Inlet P
_{CO}to the Alv-mcapP_{CO}level in blood flowing in a downstream segment - % DS segment
- % of the total capillary volume in a downstream capillary segment
- TT
_{DS} - Transit time for blood flowing in a downstream capillary segment
- TF
_{DS} - Transfer factor of a downstream capillary segment

## Values Taken from the Literature

- Bunsen Solubility Coefficient (BSCoef) for CO in human blood at 37°C
- 2.49 × 10
^{−5}μl/(mmHg × μl blood) (18) - TL
_{CO-M} - 57 ml/(min × mmHg) (7)
- Lung-Vc
- 80 ml (7)
- θ
_{CO}measured at a Po_{2}of 100 mmHg and 37°C - 0.57 ml/(min × mmHg × ml blood) (7, 25)
- TL
_{CO} - 30 ml/(min × mmHg) (1, 9)
- Total number of alveoli in the normal lung
- 4.84 × 10
^{8}(14)

## Appendix A

*Derivation of Eq. 5 used to calculate the AlvP*_{CO}

*Derivation of Eq. 5 used to calculate the AlvP*

_{CO}During the 5 or 10 ms TT_{Prox} TP-S is assumed to = TD-S

(i) TP-S = TF_{Prox} × (AlvP_{CO} – Prox-mcapP_{CO}) and TD-S = TF_{Dist} × (Dist-mcapP_{CO} – AlvP_{CO})

(ii) TF_{Prox} × (AlvP_{CO} – Prox-mcapP_{CO}) = TF_{Dis}
(Dist-mcapP_{CO} – AlvP_{CO})

(iii) TF_{Prox} × AlvP_{CO} – TF_{Prox} × Prox-mcapP_{CO} = TF_{Dist} × Dist-mcapP_{CO} – TF_{Dist} × AlvP_{CO}

(iv) TF_{Prox} × AlvP_{CO} + TF_{Dist} × AlvP_{CO} = TF_{Dist} × Dist-mcapP_{CO} + TF_{Prox} × Prox-mcapP_{CO}

(v) AlvP_{CO} × (TF_{Prox} + TF_{Dist}) = TF_{Dist} × Dist-mcapP_{CO} + TF_{Prox} × Prox-mcapP_{CO}

**∴ AlvP**_{CO} **= (TF**_{Dist} **× Dist-mcapP**_{CO} **+ TF**_{Prox} **× Prox-mcapP**_{CO}**)/(TF**_{Prox}**+ TF**_{Dist}**)**

Because this derivation considers events occurring during TT_{Prox}, both TF_{Prox} and TF_{Dist} are given as μL/(TT_{Prox} × mmHg). AlvP_{CO}, Dist-mcapP_{CO} and Prox-mcapP_{CO} are given in mmHg.

*Example calculations of “R” and the P*_{CO} in blood exiting from proximal and DS-1 segments

*Example calculations of “R” and the P*

_{CO}in blood exiting from proximal and DS-1 segmentsThese calculations used Series A 1000 ms TT_{Tot} parameters and terms listed in the Appendix B. 40% Prox-mcapP_{CO} and Driving P_{CO} were used in these calculations.

*Proximal segment calculations*

*Proximal segment calculations*

*(i) Dist-mcapP*_{CO}**:** Dist-mcapP_{CO} = (Alv-mcapP_{CO} × TT_{Tot} – Prox-mcapP_{CO} × TT_{Prox})/TT_{Dist} (**Eq. 4**)

Dist-mcapP_{CO} = (2.040 × 10^{−3} × 1000 – 1.54 × 10^{−3} × 10)/990

= 2.045 × 10^{−3} mmHg

*(ii) AlvP*_{CO} = (TF_{Dist} × Dist-mcapP_{CO} + TF_{Prox} × Prox-mcapP_{CO})/(TF_{Prox }+ TF_{Dist}) (**Eq. 5**)

AlvP_{CO} = (10.17 × 10^{−9} × 2.045 × 10^{−3} + 0.130 × 10^{−9} × 1.54 × 10^{−3})/(0.130 × 10^{−9} + 10.17 × 10^{−9})

= 2.038 × 10^{−3} mmHg

*(iii) Prox-ΔP*_{CO} = AlvP_{CO} – Prox-mcapP_{CO} = 2.038 × 10^{−3} – 1.54 × 10^{−3}

= 0.498 × 10^{−3} mmHg

** (iv) TP-S** = (TF

_{Prox}× Prox-ΔP

_{CO})/TT

_{Prox }(

**Eq. 6**)

= (0.130 × 10^{−9} **×** 0.498 × 10^{−3})/10 ms = 0.064 × 10^{−12} μl CO/10 ms

**(v) CO-R:**

**↑ bound CO** in TT

_{Prox}= (Prox-θ

_{CO}× Driving-P

_{CO}× Prox-Vc) (

**Eq. 7**)

= (1.48 × 10^{−4} × 0.330 × 10^{−3} × 1.55 × 10^{−6})

= 0.076 × 10^{−12} μl

**↑ dissolved CO** in TT

_{Prox}= (BSCoef × “↑ MV-P

_{CO}to Alv-mcapP

_{CO}“ × Prox-Vc) (

**Eq. 8**)

= (2.49 × 10^{−5} × 0.83 × 10^{−3} × 1.55 × 10^{−6}) in 10 ms

= 0.032 × 10^{−12} μl in 10 ms

**CO-R (↑ bound CO + ↑ dissolved CO) in 10 ms**

= 0.076 × 10^{−12} + 0.032 × 10^{−12} μl/10 ms

= 0.107 × 10^{−12} μl/10 ms.

** (vi) “R”** (terms given per TT

_{Prox}of 10 ms)

**= [TP-S/CO-R] × 100**

= [0.064 × 10^{−12}/ 0.107 × 10^{−12}] × 100 = 59.8%

*(vii) P*_{CO} **↑ in blood flowing in this segment**

= *“R” × 0.01 × “MV-P*_{CO} *to Alv-mcapP*_{CO}*”*

= 59.8 × 0.01 × 0.83 × 10^{−3} = 0.496 × 10^{−3} mmHg

**(viii) End-segment P**_{CO} = Inlet P_{CO} + P_{CO} ↑

= 1.21 × 10^{−3} + 0.496 × 10^{−3}

= 1.706 × 10^{−3} mmHg. This value is 83.3% of the Alv-mcapP_{CO} of 2.040 × 10^{−3} mmHg.

*DS-1 segment calculations*

*DS-1 segment calculations*

**(i)** *Inlet P*_{CO} = to the P_{CO} of blood exiting from the proximal segment = 1.706 × 10^{−3} mmHg

*(ii) “↑ Inlet-P*_{CO} *to Alv-mcapP*_{CO}**”** = Alv-mcapP_{CO} – Inlet P_{CO}

= 2.040 × 10^{−3} – 1.70 × 10^{−3} = 0.34 × 10^{−3} mmHg

*(iii) 40% DS-1-mcapP*_{CO} = 0.40 × “↑ Inlet-P_{CO} to Alv-mcapP_{CO}” + the Inlet P_{CO}

= 0.40 × 0.34 × 10^{−3} + 1.70 × 10^{−3} = 1.84 × 10^{−3} mmHg

*(iv) DS-1-ΔP*_{CO} = AlvP_{CO} – DS-mcapP_{CO}

= 2.038 × 10^{−3} – 1.84 × 10^{−3} = 0.198 × 10^{−3} mmHg

** (v) TP-S** = (DS-1-ΔP

_{CO}× TF

_{DS-1})/TT

_{DS}

= (0.198 × 10^{−3} × 0.128 × 10^{−9} μl)/10 ms

= 0.0253 × 10^{−12} μl/10 ms

*(vi) 40% Driving- P*_{CO} = 0.4 × “↑ Inlet-P_{CO} to Alv-mcapP_{CO}” = 0.40 × 0.34 × 10^{−3}

= 0.136 × 10^{−3} mmHg

*(vii) CO-R***:**

**↑ bound CO** ** in 10 ms** = (DS-1-θ

_{CO }× Driving-P

_{CO}× DS-Vc)

= (1.42 × 10^{−4} × 0.136 × 10^{−3} × 1.55 × 10^{−6})

= 0.029 × 10^{−12} μl

↑ **dissolved CO** in 10 ms = (BSCoef × “↑ Inlet-P_{CO} to Alv- mcapP_{CO}” × DS-Vc)

= (2.49 × 10^{−5} × 0.34 × 10^{−3} × 1.55 × 10^{−6})

= 0.013 × 10^{−12} μl

*CO-R = (↑ bound CO + ↑ dissolved CO) in 10 ms*

= (0.0.029 × 10^{−12} + 0.013 × 10^{−12}) = 0.042 × 10^{−12} μl

** (viii) “R”** (terms given per TT

_{Prox}10 ms)

**= [TP-S/CO-R] × 100**

= [(0.025 × 10^{−12}/(0.042 × 10^{−12}] × 100

= 60.2%

*(ix) P*_{CO} *↑ in blood flowing in this segment*

= “R” × 0.01 × “Inlet-P_{CO} to Alv-mcapP_{CO}”)/TT_{DS}

= (60.2 × 0.01 × 0.34 × 10^{−3})/10 ms

= 0.204 × 10^{−3} mmHg/10 ms

*(x) End-segment P*_{CO} = Inlet P_{CO} + P_{CO }↑

= 1.70 × 10^{−3} + 0.204 × 10^{−3}

= 1.904 × 10^{−3} mmHg

## Appendix B

*Parameters and terms used in Series A calculations*

*Parameters and terms used in Series A calculations*

**Parameters used in all Series A calculations:** mixed venous PO_{2} 40 mmHg; mixed venous P_{CO} 1.21 × 10^{−3} mmHg; the BSCoef 2.49 × 10^{−5} μl/(mmHg × μl blood); TL_{CO} 30 ml/(min × mmHg); Lung-Vc 80 ml; TL_{M} 57 ml/(min × mmHg); θ_{CO} 0.57 ml/(min × mmHg × ml); # lung alveoli 4.84 × 10^{8}; the
Alv-mcapP_{CO} 2.040 × 10^{−3} mmHg, TF_{Alv} 1.70 × 10^{−9} μl/(10 ms × mmHg); Vc of proximal and DS segments - 1.55 × 10^{−6} μl.

*1000 msecs TT*_{Tot} calculations

*1000 msecs TT*

_{Tot}calculations**Proximal segment:** mean segment PO_{2} 42 mmHg, TT_{Prox }10 msecs, TT_{Dist }990 ms. **Terms:** TF_{Prox} 0.130 × 10^{−3} μl/10 ms × mmHg), TF_{Dist} 10.17 × 10^{−9} μl/(10 ms × mmHg); Prox-θ_{CO }1.48 × 10^{−4} μl/(10 ms × mmHg × μl), inlet P_{CO} - the MV-P_{CO}.

**DS-1 segment:** mean segment PO_{2} 43 mmHg, TT_{DS-1} 10 ms, TT_{Dist} 980 ms. **Terms:** TF_{DS-1} 0.128 × 10^{−9} μl/(10 ms × mmHg), DS-1-θ_{CO} 1.42 × 10^{−4} μl/(10 ms × mmHg × μl), inlet P_{CO} - the end segment P_{CO} of the proximal segment.

**DS-2 segment:** mean segment PO_{2} 52 mmHg, TT_{DS-2} 10 ms, TT_{Dist} 970 ms. **Terms:** TF_{DS-2} 0.126 × 10^{−9} μl/(10 ms × mmHg), DS-2-θ_{CO }1.32 × 10^{−4} μl/(10 ms × mmHg × μl), inlet P_{CO} - the end segment P_{CO} of the DS-1 segment.

*500 msecs TT*_{Tot}*calculations*

*500 msecs TT*

*calculations*

**Proximal segment:** mean segment PO_{2} 41 mmHg, TT_{Prox} 5 ms, TT_{Dist} 495 ms. **Terms:** TF_{Prox} 0.066 × 10^{−9} μl/(5 ms × mmHg), TF_{Dist} 5.085 × 10^{−9} μl/(5 ms × mmHg)**,** Prox θ_{CO }0.75 × 10^{−4} μl/(5 ms × mmHg × μl).

**DS-1 segment:** mean segment PO_{2} 42 mmHg, TT_{DS-1} 5 ms, TT_{Dist} 985 ms. **Terms:** TF_{DS-1} 0.066 × 10^{−9} μl/(5 ms × mmHg), DS-1- θ_{CO }0.73 × 10^{−4} μl/(5 ms × mmHg × μl), inlet P_{CO} - the end segment P_{CO} of the proximal segment.

**DS-2 segment:** mean segment PO_{2} 43 mmHg, TT_{DS-2} 5 ms, TT_{Dist} 980 ms. **Terms:** TF_{DS-2 }0.065 × 10^{−9} μl/(5 ms × mmHg), DS-2**-**θ_{CO }0.72 × 10^{−4} μl/(5 ms × mmHg × μl), inlet P_{CO} - the end segment P_{CO} of the DS-1 segment.

**DS-3 segment:** mean segment PO_{2} 45 mmHg, TT_{DS-3} 5 ms, TT_{Dist} 975 ms. **Terms:** TF_{DS-3} 0.065 × 10^{−9} μl/(5 ms × mmHg), DS-3**-** θ_{CO }0.73 × 10^{−4} μl/(5 ms × mmHg × μl), inlet P_{CO} - the end segment P_{CO} of the DS-2 segment.

**DS-4 segment:** mean segment PO_{2} 47 mmHg, TT_{DS-4} 5 ms, TT_{Dist} 970 μl. **Terms:** TF_{DS-4} 0.064 × 10^{−9} μl/(5 ms × mmHg), DS-4**-** θ_{CO} 0.71 × 10^{−4} μl/(5 ms × mmHg × μl), inlet P_{CO} - the end segment P_{CO} of the DS-3 segment.

*Parameters and terms used in Series B calculations*

*Parameters and terms used in Series B calculations*

**Parameters used in all calculations:** TT_{Tot} 1000 ms, TT_{Prox} and TT_{DS} segments 10 ms, mixed venous P_{CO} 1.21 × 10^{−3} mmHg, the BSCoef 2.49 × 10^{−5}, μl/(mmHg × μl blood), TL_{CO} 30 ml/(min × mmHg); Lung-Vc 120 ml, TL_{M} 57 ml/(min × mmHg), # alveoli in the normal lung 4.84 × 10^{8}, θ_{CO} 0.57 ml/(min × mmHg × ml), TF_{Alv} 1.68 × 10^{−9} μl/(10 ms, × mmHg), Vc of proximal and DS segments - 2.33 × 10^{−6} μl.

** Proximal segment:** mean proximal segment PO

_{2}60 mmHg.

**Terms:**TF

_{Prox}0.121 × 10

^{−9}μl/(10 ms × mmHg), TF

_{Dist}10.56 × 10

^{−9}μl/(10 ms × mmHg), Prox-θ

_{CO }1.28 × 10

^{−4}μl/(10 ms × mmHg × μl), inlet P

_{CO}: the MV-P

_{CO}.

** DS-1 segment:** mean segment PO

_{2}63 mmHg.

**Terms**:TF

_{DS-1}0.121 × 10

^{−9}μl/(10 ms × mmHg × μl), TF

_{Dist}10.56 × 10

^{−9}μl/(10 ms × mmHg), DS

_{1}-θ

_{CO}1.25 × 10

^{−4}μl/(10 ms × mmHg × μl), inlet P

_{CO}- the end segment P

_{CO}of the proximal segment.

** DS-2 segment:** mean segment PO

_{2}67 mmHg

**, Terms:**TF

_{DS-2}0.120 × 10

^{−9}μl/(10 ms × mmHg, TF

_{Dist}10.56 × 10

^{−9}μl/(10 ms × mmHg), DS

_{2}-θ

_{CO }1.25 × 10

^{−4}μl(10 ms × mmHg × μl), inlet P

_{CO}- the end-segment P

_{CO}of DS-1.

**DS-3 segment:** mean PO_{2} 71 mmHg. **Terms:** TF_{DS-3} 0.117 μl/(10 ms × mmHg), TF_{Dist} 10.56 × 10^{−9} μl/(10 ms × mmHg), DS_{3}-θ_{CO }1.11 × 10^{−4} μl/(10 ms × mmHg × μl), inlet P_{CO} - the end-segment P_{CO} of DS-2.

- Copyright © 2016 the American Physiological Society