Modification of the CO‐rebreathing method to determine haemoglobin mass and blood volume in patients suffering from chronic mountain sickness

What is the central question of this study? Is it necessary to modify the CO‐rebreathing method to acquire reliable measurements of haemoglobin mass in patients with chronic mountain sickness? What is the main finding and its importance? The CO‐rebreathing method must be modified because of the prolonged CO‐mixing time in patients with chronic mountain sickness. After adaptation of the blood sampling method, reliable and valid results were attained. With this modification, it is possible to quantify the extent of polycythaemia and to distinguish between a haemoconcentration and an exclusive enhancement of erythrocyte volume.

and bound to myoglobin or been exhaled via respiration (Garvican et al., 2010;Schmidt & Prommer, 2005). When applying the oCOR method to healthy subjects, these prerequisites are all fulfilled.
In some groups of patients, however, these preconditions are not guaranteed, e.g. in patients with chronic obstructive pulmonary disease, in patients with disturbances in peripheral arterial perfusion and in polycythaemia vera (Ahlgrim et al., 2014). Before applying the CO-rebreathing method to these patients, the above factors have to be verified, and the method might need to be modified.
In general, the [Hb] and haematocrit (Hct) depend on the Hbmass or red cell volume and the magnitude of plasma volume. In patients suffering from CMS, the size of the blood compartments is rarely investigated. There exists only one study of 11 CMS patients from 4350 ma.s.l. using Evans Blue for the determination of plasma volume (Claydon et al., 2004). Those authors described an almost normal plasma volume and calculated a massively increased red cell volume compared with healthy high-altitude residents. Although their study provided valuable information, there were some limitations influencing the validity of the data. The results were obtained from a small group of patients, and the red cell volume was determined indirectly, by measuring the plasma volume and calculating the red cell volume. Given that the cell factor describing the different distribution of cell mass and plasma in peripheral and central blood may change at altitude (Sánchez, Merino, & Figallo, 1970), direct measurements of Hbmass and/or red cell volume should be used. Exact Hbmass data would be valuable for quantifying the amount of haemoglobin and distinguishing between haemoconcentration attributable to reduced plasma volume and haemoconcentration attributable solely to an enhanced erythrocyte volume.
When applying the oCOR method for healthy subjects to CMS patients, the altered haemodynamics will probably affect the mixing time for the administered CO, leading to inaccurate or even false results. It is therefore mandatory to determine the exact mixing time to adjust the time points for blood sampling (Ahlgrim et al., 2014) and

New Findings
• What is the central question of this study?
Is it necessary to modify the CO-rebreathing method to acquire reliable measurements of haemoglobin mass in patients with chronic mountain sickness?
• What is the main finding and its importance?
The CO-rebreathing method must be modified because of the prolonged CO-mixing time in patients with chronic mountain sickness. After adaptation of the blood sampling method, reliable and valid results were attained. With this modification, it is possible to quantify the extent of polycythaemia and to distinguish between a haemoconcentration and an exclusive enhancement of erythrocyte volume.
to examine the amount of CO taken up by the blood and the amount of CO that diffuses from blood to myoglobin.
Additionally, the CO uptake during the rebreathing period might be altered, as can be assumed from the delayed CO uptake (Herbert et al., 1965), microembolisms in pulmonary arteries (Arias-Stella, 1971;Burgess & Bishop, 1963) and elevated blood volume in the pulmonary vascular bed (Greening, Patel, Goolden, Munro, & Hughes, 1982) observed in patients suffering from polycythaemia vera. In addition, a third source of error might be the loss of CO owing to diffusion from the vascular bed to myoglobin, which must be quantified, especially in CMS patients, for whom no related data are available.
The aim of the study was therefore to evaluate and, if necessary, to adapt the currently used CO-rebreathing method to be used in CMS patients. We analysed the optimal time points for blood sampling, we checked the extraction of CO from the lung and determined the loss of CO from blood to myoglobin. With the information obtained, we modified the CO-rebreathing method and demonstrated its reliability and validity for CMS patients.

Ethical approval
The subjects were informed about the requirements and possible risks of the study before giving written consent to participate. The subjects volunteered to participate in the study and were free to withdraw at any time without needing to provide a reason. The study conformed to the standards set by the Declaration of Helsinki, except for registration in a database. The study was approved by the Ethics Committee of the Universidad Mayor San Andres in La Paz, Bolivia.

Subjects
In total, 51 male subjects participated in the study. Twenty-one of the subjects lived at high altitude (between 3600 and 4100 m a.s.l.) and were classified as CMS patients. Another four subjects living at

Study design
The project was divided into two substudies. The first part of the project dealt with the determination of the optimal blood sampling time points, which might differ from the known oCOR method owing to the possibly delayed CO mixing in CMS patients. The prerequisite for this calculation is knowledge about the amount of CO that diffuses from the blood to myoglobin and the amount of CO that is exhaled after disconnection of the subject from the spirometer. Taking these factors into account, we calculated the Hbmass every 2 min until 20 min and then every 5 min until 30 min after inhalation of the CO bolus. When the calculated Hbmass values reached a plateau, the CO mixing in blood was assumed to be complete. Based on these data, the time points for blood sampling were modified.
In the second part of the project, the reliability of the modified COrebreathing method was calculated by performing test-retests and calculating the typical error of the method. Furthermore, the validity of the method was determined by measuring the Hbmass before and after withdrawal of ∼500 ml of blood. The distribution of the subjects to the different substudies is illustrated in Table 2.
Given that Hbmass is ∼20% higher in natives to high altitude than in subjects from sea level (Heinicke et al., 2003), the CO bolus was increased to 1.5 ml (kg body mass) −1 in the control subjects from altitude (LP). For CMS patients and intermediates, the CO bolus was calculated according to the measurements in a pilot study as 1.7 ml (kg body mass) −1 . In overweight subjects, the theoretically derived body mass corresponding to a body mass index of 25 kg m −2 was used for the calculation. Capillary blood was sampled from an earlobe three times before and once every second minute after starting the rebreathing period until the 20 min mark and at the 25 and 30 min marks. From each blood sample, three replicates were analysed for carboxyhaemoglobin (COHb) using a CO haemoximeter (OSM3; Radiometer, Copenhagen, Denmark).
To calculate the amount of CO not taken up during the inhalation, a CO analyser (Draeger, Luebeck, Germany) was used to determine the CO remaining in the spirometer system. Additionally, the end-tidal CO concentration was measured 2, 6, 13 and 23 min after disconnecting the subject from the spirometer. Owing to the hyperventilation at altitude, the alveolar ventilation of controls-LP was adjusted by 10% (Hultgren, 1997). This adjustment was not performed for the CMS patients owing to the lack of increased hypoxic ventilation (Villafuerte & Corante, 2016). Unlike the Bolivian subjects, in controls-BT, the volume and the CO concentration of exhaled air were measured continuously after CO rebreathing up to 30 min. The Hbmass was determined using the following formula (Equation 1): Where K = current barometric pressure × 760 −1 × [1(0.003661 × current temperature)]; MCO = CO adm − (CO system+lung after disconnection + CO exhaled after disconnection ) − M Hb ; CO adm = CO volume administered into the system; CO system+lung after disconnection = CO concentration in the spirometer × (spirometer volume + lung residual volume); CO exhaled after disconnection = Δend-tidal CO concentration × alveolar ventilation × time; M Hb = CO diffusing to myoglobin; ΔCOHb% = difference between basal COHb% and COHb% in the blood samples after CO administration; and 1.39 = Hüfner's number (in millilitres of CO per gram of Hb; e.g. Gorelov, 2004). The Hbmass values were calculated every second minute until 20 min and at 25 and 30 min.
To quantify the diffusion of CO from blood to myoglobin, three different factors were used. We assumed that in the case of the bestfitting factor, the most constant plateau of Hbmass was achieved. The following three formulae (Equations 2-4) for calculating CO diffusion to myoglobin were used to verify the appropriate correction factor: When using OSM3 (Radiometer, Denmark) to analyse blood samples, one must take into account that percentage carboxyhaemoglobin (COHb%) values also depend on the S O 2 (Hütler, Beneke, Littschwager, & Böning, 2001). The majority of the tests were performed at high altitude, where the S O 2 in arterialized blood is reduced. After inhaling 3.5 l of pure oxygen during the rebreathing procedure, the S O 2 increases, which requires an adjustment in COHb%.
We used an individual correction factor for every subject according To determine the [Hb] and Hct, venous blood samples were drawn into an EDTA tube from a cubital vein after the subject had been sitting for ≥10 min and after the tourniquet was removed. The [Hb] was measured spectrophotometrically using the cyanmethaemoglobin method, and the Hct was measured by the microhaematocrit technique at 12,000 r.p.m. for 5 min.

Part II: Reliability and validity of the modified method
To determine the reliability of the modified CO-rebreathing method, test-retests were performed. Based on the results of part I, the time points of blood sampling were set at 14, 16, 18 and 20 min, and the mean COHb value of this period was used for further calculations. The end-tidal CO concentration was measured before the tests and at 2, 6 and 13 min after disconnecting the subject from the spirometer. To calculate the amount of CO diffusing to myoglobin, the best-fitting factor from part I, i.e. 0.002 ml min −1 , was used.
The validity of the modified CO-rebreathing method was evaluated by measuring Hbmass immediately before and after withdrawal of

Statistics
Data are presented as the mean value ± SD. Student's paired t tests were applied to compare possible differences between the time points of blood sampling and between the three calculation possibilities for Hbmass by using the different equations for CO diffusion to myoglobin (Hopkins, 2003 When the outcomes of the ANOVA were significant (P < 0.05), Scheffé's tests were used to compare the individual groups with one another.
The typical error (TE) of the modified method was calculated according to Hopkins (2000). A correlation analysis was performed to check the reliability of the modified method by evaluating the relationship of Hbmass obtained in the test and retest.
F I G U R E 1 Carboxyhaemoglobin (COHb) kinetics during and up to 28 min after the CO-rebreathing protocols. The absolute differences from baseline values (a) and the percentage decrease from the peak value observed at minute 1 (b) are shown. Abbreviations: BT, Bayreuth; CMS, chronic mountain sickness; LP, La Paz; and SZ, Santa Cruz. ANOVA and post hoc tests (Scheffé's test) yielded significant differences in the percentage decrease between Controls-BT and CMS patients (P < 0.01) and Controls-LP (P < 0.05)

Part I: Modification of the CO-rebreathing method
In all groups, peak values for COHb concentration were observed 1 min after CO bolus inhalation (Figure 1a). Thereafter, the decline in COHb showed clear effects of a treatment × time interaction (P < 0.01), and post hoc tests (Scheffé's tests) yielded significant differences between Controls-BT and CMS (P < 0.01) and Controls-LP (P < 0.05) ( Figure 1b). Furthermore, we compared the CO content remaining in the spirometer after disconnection of the test subject to evaluate possible diffusion limitations. As demonstrated in Table 3, there were normal amounts of CO left in all groups, and in the spirometer of CMS patients the CO concentration was even lower than that of control subjects from La Paz and Santa Cruz.

CO-mixing time in blood
The In the subjects from high altitude, the time to reach the plateau was delayed, and no significant difference from previous values was found from 14 to 30 min (Figure 2c,d). Given that all four groups showed a plateau between 14 and 20 min, blood samples from this period of time were used to determine the real Hbmass. Figure 3 illustrates the difference in Hbmass between the conventional method (Prommer & Schmidt, 2007;Schmidt & Prommer, 2005) using the mean COHb values at 6 and 8 min for the calculation of Hbmass and the modified method, assuming a delayed mixing time, as mentioned above. No differences in Hbmass were found in the Controls-BT, whereas in all other groups, higher Hbmass values were obtained with the modified method (blood sampling after 14-20 min) than with the original method. The percentage differences were 4.4 ± 2.3% in Controls-SZ, 4.8 ± 1.9% in Controls-LP and 6.7 ± 2.5% in CMS patients. Values are presented as means ± SD. Abbreviations: BT, Bayreuth; LP, La Paz; and SZ, Santa Cruz. Significant differences in [CO] in the spirometer between the groups: * P < 0.05 compared with Controls-LP and † P < 0.05 compared with Controls-SZ. The difference between the conventional and modified methods is presented. Significant differences between the methods: *** P ≤ 0.001 Table 2). The TE was 23.1 g (1.6%; confidence limits, 1.2-2.5%).

Parts II and III: Reliability and validity of the modified method
There was an excellent correlation between the test and retest measurements of Hbmass (r = 0.995; P ≤ 0.001; Figure 4).
In four CMS patients, Hbmass was measured before and after withdrawal of 500 ml of blood, and the reduction in Hbmass was compared with the reduction calculated from the [Hb] in the transfusion bag. By this measure, Hbmass was reduced from 1779 ± 123 g to 1650 ± 129 g (7.2 ± 1.6%; measured) or to 1666 ± 122 g (6.3 ± 0.4%; calculated), and no difference between the two methods of determination was found ( Figure 5).

CO application and CO diffusion in the lungs
Owing to the low ambient pressure, the volume of the CO bolus inhaled by the subjects at high altitude had to be increased by 35%. A further increase of ∼20% was implemented for the control subjects from F I G U R E 4 Correlation between test-retest measurements of haemoglobin mass (Hbmass; r = 0.991; P ≤ 0.001) by the modified CO-rebreathing method. Abbreviations: CMS, chronic mountain sickness; and LP, La Paz high altitude because their Hbmass was expected to be augmented in comparison to that of subjects from sea level (Heinicke et al., 2003).
Given that we did not want to expose the CMS patients to any risk, we did not increase the CO volume to the extent (∼2.4 ml kg −1 ) that would yield COHb concentrations matching those in the control subjects. The CMS patients, therefore, received CO at 1.7 ml (kg body mass) −1 , which resulted in a lower increase in COHb than that in the control groups (Figure 1a). To counteract a possible lower accuracy of the calculated Hbmass owing to a smaller difference in COHb after inhalation, we increased the number of replicate measures from six to nine for the baseline value and to 12 for the post-inhalation value using the four blood samples obtained between 14 and 20 min. The resulting analytical error was ∼1% (Alexander et al., 2011).
All patients and control subjects were asked whether they felt any side-effects from the CO-rebreathing procedure; none of the subjects complained or mentioned any discomfort.
The CO concentration in the air remaining in the spirometer after cessation of the rebreathing period was significantly lower for the CMS patients than for the control groups. Given that CO is used as a routine marker for lung diffusion (Salcedo Posadas, Villa Asensi, de Mir Messa, Sardón Prado, & Larramona, 2015), this indicates the absence of diffusion barriers in the lung, as could be expected from the chronically augmented pulmonary arterial constriction (Villafuerte & Corante, 2016) or multiple pulmonary arterial thrombi occurring in patients with polycythaemia vera (Ahlgrim et al., 2014;Arias-Stella, 1971). This finding, however, is in agreement with data from Groepenhoff et al. (2012), hinting at even greater CO-diffusion capacity in CMS patients than in subjects from near sea level. Therefore, we concluded that CO application to CMS patients is not limited by any problems with pulmonary diffusion.

CO diffusion to myoglobin
When CO is inhaled and bound to haemoglobin, a small amount of CO diffuses from the blood to extravascular spaces, i.e. mostly to myoglobin (Bruce & Bruce, 2003). In the present study, we determined the Hbmass by calculating the diffusion of CO from blood to myoglobin with the fixed factors 0.2% min −1 (Schmidt & Prommer, 2005) and 0.3% min −1 (Prommer & Schmidt, 2007) for inhaled CO and by using the model from Chada and Bruce (2012). Until 12 min after starting the inhalation, the three methods showed very similar results; thereafter, in all four groups, the factor 0.3% min −1 slightly underestimated the Hbmass, whereas the model of Chada and Bruce (2012) slightly overestimated the Hbmass in the high-altitude subjects. Using the factor of 0.2% min −1 yielded an Hbmass plateau for ≥30 min after CO inhalation, providing the best fit for all the groups investigated here.
Our calculation is, therefore, a strong approximation with low measurement error when applied to groups similar to those used in the present study, but different CO-diffusion factors might be more valid for other groups and patients.

F I G U R E 5
Haemoglobin mass (Hbmass) before and after withdrawal of 500 ml of blood in four chronic mountain sickness patients. Presented are the individual values of Hbmass measured with the modified CO-rebreathing method before and after the blood withdrawal and the Hbmass measured before and calculated after the blood withdrawal. On the right side, the mean values for the measured and calculated loss of Hbmass are demonstrated

CO-mixing time
For healthy subjects, complete mixing of an inhaled CO bolus was determined to occur within 6 min (Prommer & Schmidt, 2007;Schmidt & Prommer, 2005). Therefore, blood samples from minute 7 after CO inhalation (mean from samples drawn at minutes 6 and 8) are routinely used in the optimized CO-rebreathing method to calculate the Hbmass (Prommer & Schmidt, 2007). This concept was criticized by Keiser et al. (2013), who claimed that the mixing was not complete at this time point, thereby leading to the overestimation of Hbmass. Complete mixing of a CO bolus with high interindividual variation was found after 10 min by Garvican et al. (2010) and Gore et al. (2006), but because of only small differences compared with the findings of Prommer and Schmidt (2007), the method was not modified for healthy subjects from sea level. Both groups describing the extended period for mixing, however, recommended checking the mixing time for the investigation of special populations.
In the present study, complete mixing was achieved after 6 min in the control subjects from near sea level (Controls-BT) but complete mixing was not achieved until 12 min in the CMS patients and control subjects from high altitude. For the CMS patients, this delay might be explained by the impaired haemodynamics owing to higher blood viscosity (Kwaan & Wang, 2003) as a consequence of haematocrit values ranging between 63 and 78%; this impairment probably results in reduced peripheral and organ perfusion, as can be assumed from the reduced blood flow velocity in CMS patients (Claydon et al., 2005).
According to the model of Bruce and Bruce (2003), CO mixing and CO distribution in the body depends on five compartments, four of which are vascular: arterial blood, mixed venous blood, muscle tissue and non-muscle tissue. The time for blood to pass through each of these compartments and therefore to become mixed depends on the volume of the compartment and the blood flow through each compartment (Bruce & Bruce, 2003;Garvican et al., 2010). Despite the higher blood volume (Claydon et al., 2004) the difference in Hbmass amounts to ∼100 g, which corresponds to 6.7% (Figure 3). Therefore, these data strongly suggest that the oCOR method should be modified when it is applied to patients suffering from erythrocytosis.
A delayed mixing time was also observed in control subjects from high altitude, who have haematocrit values between 46 and 58%. Although the difference in calculated Hbmass between the two protocols was smaller (∼50 g), we recommend the modified protocol for further investigation of subjects from high altitude.
A possibility for reduction of the mixing time might be to conduct the CO-rebreathing tests in the supine position, in which increased venous return from the lower extremities (e.g. Truijen, Bundgaard-Nielsen, & Van Lieshout, 2010) and more homogeneous lung perfusion could facilitate CO mixing.

Reliability and validity
Test-retest with the modified protocol was performed on subjects from high altitude, i.e. CMS patients, patients with previous CMS diagnoses who did not fulfil the criterion [Hb] >21 g dl −1 and control subjects. As shown in Figure 4, the reliability was very good in all groups, resulting in a TE of 1.6%. Similar TE values were also described for CO-rebreathing tests at sea level [TE between 1.1 (Gore et al., 2006) and 2.3% (Eastwood, Bourdon, Withers, & Gore, 2009)] and at altitude [TE = 1.4% (Wachsmuth et al., 2013)], proving the reliability of the modified method when applied to high-altitude populations, similar to the established method.
The validity of the modified method was checked by phlebotomy of a known blood volume and known Hbmass. The difference between the measured and calculated volumes (0.9%) was in the same range as that reported by Schmidt and Prommer (2005) immediately after a blood donation. Both the reliability and the validity of the modified method for CMS patients showed that the quality of data was the same as that achieved using the established CO-rebreathing method for healthy subjects and patients at sea level. Unfortunately, we did not determine validity after blood sampling at minutes 6-8, which could have confirmed the prolonged mixing time in CMS patients.

Possible practical importance
As our preliminary data show, the mean Hbmass of CMS patients was expanded twofold, and the individual Hbmass was increased threefold, compared with healthy subjects from sea level. This increase might be accompanied by blood volume expansion, which in turn strongly influences cardiovascular function via volume overloading and hyperviscosity. Similar pathophysiological mechanisms might exist in polycythaemia vera, in which plasma volume is also frequently expanded, which masks the high red cell volume (Spivak, 2019). The modified CO-rebreathing method might therefore represent a simple tool for diagnosing the degree of erythrocytosis and the risk of possible negative consequences in CMS patients and in patients with polycythaemia of other origins, e.g. polycythaemia vera.

Conclusions
Application of the CO-rebreathing method to CMS patients and healthy residents from high altitude (3600-4100 m a.s.l.) requires modification of the established CO-rebreathing method. Although CO uptake in the lungs and CO diffusion from blood to myoglobin are similar between CMS patients and healthy subjects from sea level, the