Abstract
The beneficial role of erythrocytosis for O_{2} transport has been questioned by evidence from bloodletting and hemodilution research as well as by studies suggesting the existence of an “optimal” hematocrit (Hct) or hemoglobin concentration ([Hb]) value. To assess to what extent erythrocytosis is beneficial in Andean men at high altitude, we examined and discussed optimal [Hb] using a mathematical approach by modeling the mixed (mean) venous Po_{2} (Pv̄_{O2}) and arterial O_{2} content, considering for both the relation between [Hb] and arterial Po_{2}. Relations of [Hb] to other physiological variables such as cardiac output and convective arterial O_{2} transport were also discussed, revealing the importance of Pv̄_{O2} in this model. Our theoretical analysis suggests that increasing [Hb] allows increase and maintenance of Pv̄_{O2} with only moderate declines in arterial Po_{2} as a consequence of moderate increases in altitude, reaching its maximum at the optimal [Hb] of 14.7 g/dl. Our analysis also shows that [Hb] corresponding to high arterial O_{2} content and O_{2} transport values is apparently not quite advantageous for improvement of oxygenation. Furthermore, chronic mountain sickness is discussed as an insightful example of the effects of excessive erythrocytosis at high altitude.
 oxygen transport
 hypoxia
 theoretical model
 mixed venous partial pressure of oxygen
erythrocytosis and hence elevated hematocrit (Hct) and hemoglobin concentration ([Hb]) have been considered a fundamental physiological response to hypoxia that occurs to increase blood O_{2}carrying capacity and to improve tissue oxygenation. The beneficial role of erythrocytosis, however, has been questioned by evidence from bloodletting and hemodilution studies (53, 54) as well as by several other studies on experimental anemia and erythrocytosis, all of which suggest the existence of an “optimal” hematocrit or maximal value above and below which O_{2} transport is affected (6, 10, 41).
Early questioning of the advantages of erythrocytosis is found in the works of Richardson and Guyton. In 1959, these researchers (41) studied the effects of normovolemic anemia and polycythemia in dogs by keeping blood volume constant and varying Hct from 20 to 68%. They showed that cardiac output (Q̇) markedly decreased along with increasing Hct and that blood O_{2} availability, expressed as the product of Hct and Q̇, was maximal at a Hct of 40% and decreased above and below this value. Their later study (10), also in normovolemic anemic and polycythemic dogs, showed that decreased O_{2} availability above Hct of 40% resulted from decreased Q̇, which resulted in turn from the marked decrease in venous return caused by rising Hct.
Crowell and colleagues (6) later showed that the optimal Hct for O_{2} transport in dogs was 40% and explained this optimal value as a balance between the opposing effects of Hct on viscosity and on blood O_{2} content. Crowell and Smith (7) subsequently obtained a theoretical expression from in vitro data that showed that the optimal Hct was inversely proportional to the decay constant of the exponential equation for blood viscosity. By combining this equation with a linear equation derived from previous experimental blood flow and Hct data, these researchers showed that the transport of O_{2} carried by the dispersed phase (erythrocytes) is maximal at a Hct level of 40%.
The relevance and uniqueness of these findings soon awoke further interest in this field. Most importantly, these works have become part of the ground work that has enabled the development of studies on human erythrocytosis, providing new insight that has led to a better understanding of physiological and pathophysiological states. One of the most widely known variations of erythrocytosis is the erythropoietic response of humans and other animals to highaltitude exposure. Moderate increases in Hct seem to be the “normal” response of humans undergoing prolonged exposure to a given altitude. However, more recent works have proven this is not always the case. Epidemiological studies have shown that some Andean individuals residing at a given altitude have [Hb] that are significantly higher than the socalled normal values. These higher values, grouped under the term “excessive erythrocytosis,” have been additionally allocated as the main sign of chronic mountain sickness (CMS), also known as “Monge's disease” (i.e., [Hb] > 21.3 g/dl in ∼15% of the population of Cerro de Pasco, Perú, 4,350 m; see Refs. 20, 26, and 30). From this group of the population, individuals who also suffer other symptoms that characterize CMS are diagnosed with the disease itself. Symptoms include headaches, insomnia, fatigue, confusion, and depression (20, 29, 31, 53). Phlebotomy and hemodilution have been shown to relieve these symptoms, suggesting that excessive erythrocytosis would play a detrimental rather than beneficial role in O_{2} transport at high altitude, hence outweighing the advantage of increased O_{2}carrying capacity (53). However, to evaluate the advantages and/or disadvantages of the erythropoietic response as a whole, it is necessary to also consider whether the normal increase in Hct occurring at high altitude is beneficial for O_{2} transport.
In this regard, the hypothesis that any degree of erythrocytosis is not truly beneficial to O_{2} transport in Andeans at high altitude goes beyond the concept of CMS and excessive erythrocytosis. The reasoning behind this concept is based on clinical observations of young and old adult subjects at high altitude and on the interpretation of exercise and functional studies at both the ventilatory and circulatory levels. Bloodletting and hemodilution studies have clearly shown that when Hct is reduced to sealevel values while at altitude pulmonary ventilation improves and alveolar Po_{2} increases along with arterial Po_{2} (Pa_{O2}) and mean (mixed) venous Po_{2} (Pv̄_{O2}); concomitantly, mean pulmonary artery pressure (MPAP) decreases (53, 54).
Evaluation of the role of erythrocytosis for O_{2} transport in Andeans at altitude in terms of optimal values was first attempted by Whittembury et al. in 1968 (50). By employing the optimal Hct expression by Crowell and Smith (7), Whittembury et al. calculated an optimal Hct from in vitro viscosity measurements of blood of Andeans living at different altitudes and obtained a Hct value of 34%, which is lower than the values commonly found in humans. Here, we theoretically analyze the optimal [Hb] issue in Andeans at high altitude through two important physiological variables of O_{2} transport that can be measured in vivo: Pv̄_{O2} and arterial O_{2} content (Ca_{O2}). We also discuss the relationship between convective arterial O_{2} transport (Ṫo_{2}), expressed as the product of Q̇ and Ca_{O2}, with [Hb] by analyzing data from studies in highaltitude Andean natives and sealevel residents.
To construct expressions describing Pv̄_{O2} and Ca_{O2} as functions of [Hb], we use fundamental O_{2} transport equations and an empirical mathematical expression first derived by Monge and Whittembury (32), which expresses [Hb] as a function of Pa_{O2}. As previously shown (33), this expression better reflects the actual relation between these two variables in Andeans (Fig. 1). The use of Pv̄_{O2} for this analysis is based on the fact that it represents mean Po_{2} of blood coming from all tissues to the lungs to become arterialized, thus representing the saturation starting point for blood oxygenation and for which reason it is considered a physiologically relevant variable for the study of O_{2} transport. Additionally, Pv̄_{O2} was chosen because, being in accordance with its wide use in clinical medicine (17, 24, 47), we consider it a useful indicator of overall state of tissue oxygenation and hence tissue hypoxemia. Also, by considering Ca_{O2} expressed as a function of Pa_{O2} and [Hb], we can further analyze the issue at hand since it represents the arterial O_{2} availability and thus the potential O_{2} mass for tissue delivery. Finally, Ṫo_{2} and its relation with [Hb] is discussed. Ṫo_{2} is the product of Q̇ and Ca_{O2}, thus representing an important variable for the analysis of O_{2} transport because it expresses the amount of O_{2} carried by arterial blood per time unit.
In summary, by employing mathematical functions expressing Pv̄_{O2} and Ca_{O2} in terms of [Hb], which includes the relationship between [Hb] and Pa_{O2}, and discussing the relationship between Ṫo_{2} and Q̇ with [Hb] from highaltitude literature data, we theoretically analyze optimal [Hb] and its physiological meaning to assess to what extent erythrocytosis is beneficial for O_{2} transport at altitude.
METHODS
For our analysis, we have chosen to employ [Hb] rather than Hct to calculate the optimal value because [Hb] is, in fact, the true functional variable.
Monge and Whittembury (32, 33) have previously shown that normal^{1} [Hb] for different Pa_{O2} values is best represented by an empirical equation that expresses [Hb] as a potential function of Pa_{O2} and shows the inverse relation between both variables (Fig. 1; see appendix). This empirical equation was obtained with [Hb] and Pa_{O2} values from studies of Hurtado and coworkers (14, 15) on healthy young men living at different altitudes in the Andes as well as from Monge and Whittembury's own data. Thus, to consider the Pa_{O2} change that [Hb] variation implies, we employ this relation in the construction of expressions describing Pv̄_{O2} and Ca_{O2} as functions of [Hb].
To functionally correlate Pv̄_{O2} with Pa_{O2} and [Hb], we have used an expression originally derived by Monge (25) that combines the empirical equation mentioned above, the Hill equation applied to arterial and venous blood, the saturation definition, and the equation for Fick's principle. The final rearrangement of the expression predicts Pv̄_{O2} in terms of [Hb] and considers Pa_{O2} as a function of [Hb].
At rest, Andeans at high altitude have been considered to have mean values of O_{2} consumption (V̇o_{2}) and Q̇, and/or cardiac index (CI = Q̇ corrected by body surface area), that are similar to those of sealevel residents (2, 38, 39, 42); therefore, we considered these as constants in the Pv̄_{O2} expression. In addition, the Po_{2} value at which hemoglobin is 50% saturated (P_{50}) and the Hill parameter (n_{H}), although with some variability in the former, have been shown to have similar values in Andean highaltitude natives and sealevel residents (53, 55); for this reason, they have also been considered as constants in both the Pv̄_{O2} and Ca_{O2} expressions.
To obtain an equation that describes the changes in Ca_{O2} when [Hb] rises as a consequence of decreasing Pa_{O2} (increasing hypoxemia), we combined the Hill equation applied to arterial blood with the arterial saturation definition and placed Pa_{O2} in terms of [Hb] as obtained from the empirical relationship. This allowed us to obtain a Ca_{O2} expression as a function of [Hb] that considers the relationship between [Hb] and Pa_{O2}.
Although Q̇ has been shown to have similar mean values at sea level and high altitude, Winslow and Monge (53), after reviewing prior data obtained by Monge and colleagues (28), showed that, if taken separately, highaltitude CI points show a significant inverse linear relation with Hct. However, other studies in which CI and [Hb] values are given (39) do not show a similar relationship, probably due to differences in the methodology employed and to the high variability of values. Thus, in absence of an adequate expression to describe the true relationship between Q̇ or CI and [Hb] in highaltitude natives to then be combined with the Ca_{O2} expression to obtain Ṫo_{2}, we decided to empirically analyze Ṫo_{2} from CI and Ca_{O2} data from different studies (37, 39, 42, 45). Finally, as shown in Fig. 4, we obtained a regression curve from the highaltitude Andean native and sealevel resident data sets.
Because the Pv̄_{O2} and the Ca_{O2} expressions consider Pa_{O2} as a function of [Hb], we have chosen to plot both from an initial [Hb] value of 13.6 g/dl, which, as predicted by Eq. 1, corresponds to a sealevel Pa_{O2} of 95 Torr. To obtain the maximum of each function and find the [Hb] value at which Pv̄_{O2} and Ca_{O2} are greatest, we took the partial derivative of each equation with respect to [Hb] and equaled each to zero.
We must point out that the original Pv̄_{O2} curve described by Monge (25) overlooked the initial ascending portion, which gives that region of the curve a slight bellshaped form and which clearly shows Pv̄_{O2} rising with increasing [Hb] despite decreasing Pa_{O2} in the initial section as shown in Fig. 2.
Finally, we analyzed the sensitivity of the Pv̄_{O2} expression toward variations in its critical parameters: Q̇, V̇o_{2}, n_{H}, and the Pa_{50}/Pv̄_{50} pair. To achieve this and to make changes comparable among parameters, we chose to evaluate the fractional variation in maximum Pv̄_{O2} that result from the fractional variation of each of the parameters so that, if multiplied by 100, each of these fractional changes can be regarded as percent changes. The maximal Pv̄_{O2} and its corresponding starting parameter values have been taken as the unit (1.0 or 100%).
We used MATHEMATICA 4 software (Wolfram Research) for the mathematical analysis.
For a detailed description of all equations and mathematical procedures employed, see appendix.
RESULTS
Figure 2 shows that Pv̄_{O2} initially rises slightly with increasing [Hb], graphically reaching a maximum at an [Hb] of ∼15 g/dl, and then begins to decrease above this value. This maximal value is mathematically confirmed by obtaining the maximum of the function, which corresponds to 14.7 g/dl. The curve shows that an increase in [Hb], from 13.6 to ∼15 g/dl due to a decrease in Pa_{O2} from 95 to nearly 80 Torr (∼2,000 m), increases Pv̄_{O2} from 40.4 up to a maximal value of 40.7 Torr. Above [Hb] of 15 g/dl, Pv̄_{O2} varies little until [Hb] values exceed 18 g/dl (Pa_{O2} of 57 Torr). When Pa_{O2} continues to decrease due to higher altitudes, Pv̄_{O2} significantly declines linearly regardless of the continuous rise in [Hb].
Figure 3 shows Ca_{O2} as a function of [Hb]. The theoretical Ca_{O2} curve rises with increasing [Hb] and reaches a maximum at [Hb] of 20.7 g/dl, a value after which the model predicts a parabolic decrease. A bestfit curve obtained from Ca_{O2} and from [Hb] mean values of healthy sealevel residents and highaltitude natives (1, 2, 9, 13, 22, 23, 27, 35, 3740, 42, 43, 45) shows very close resemblance to our theoretical prediction.
Figure 4 shows the relationship between Ṫo_{2} and [Hb] obtained from sealevel and highaltitude data sets. Ṫo_{2} values, expressed as the product of CI and Ca_{O2}, display an exponential relationship (r = 0.50, P < 0.05) with [Hb]. This relation illustrates how Ṫo_{2} increases with increasing [Hb] even when [Hb] values are very high, such as those observed in CMS subjects.
Results from the sensitivity analysis show the fractional variation in maximum Pv̄_{O2} values that result from the fractional variation of each of the parameters of the model. Figure 5A shows that Pv̄_{O2} is least sensitive to changes in n_{H} values within a limited range of 2.42.8. In this manner, an increase of 5% in n_{H} results in only a 0.48% decrease in maximal Pv̄_{O2}. P_{50} exerts the greatest change on maximum Pv̄_{O2}, but the magnitudes of these are limited by the P_{50} range we chose to consider (2430 Torr) so as not to stray from the physiological situation. In this case, a 5% increase in P_{50} (Pa_{50}/Pv̄_{50} pair) resulted in a 3.48% rise in the Pv̄_{O2} value.
Due to the range chosen for Q̇ and V̇o_{2} (Q̇ = 47 l/min; V̇o_{2} = 225800 ml/min), the sensitivity analysis allowed variation within a wider range of these parameters. However, to compare the changes exerted by each parameter on maximal Pv̄_{O2}, Fig. 5B shows the percent response in maximal Pv̄_{O2} when each parameter is varied slightly (5%). An increase of 5% in Q̇ resulted in a 2.10% increase in Pv̄_{O2}, whereas an increase of 5% in V̇o_{2} decreased Pv̄_{O2} in 1.98%.
The variation of maximum Pv̄_{O2} with each parameter is accompained by a variation of corresponding [Hb] values. The 5% increase in n_{H}, P_{50}, Q̇, and V̇o_{2} resulted in corresponding [HB] values of 14.9, 14.4, 14.6, and 14.8 g/dl, respectively.
DISCUSSION
Theoretical Pv̄_{O2} and Ca_{O2} as functions of [Hb]. Our analysis suggests that increases in [Hb] allow increase and maintenance of Pv̄_{O2} only while moderate declines in Pa_{O2} occur as a result of moderate increases in altitude. Hence, Pv̄_{O2} reaches a maximum at an [Hb] of nearly 15 g/dl (Hct of ∼45%), shows little variation up to an [Hb] of 18 g/dl (Pa_{O2} 57 Torr, ∼3,800 m), and afterward decreases linearly despite a continuously increasing [Hb] and augmented Ca_{O2}, suggesting that no additional protection to Pv̄_{O2} is offered by increasing [Hb].
Our theoretical curve shows that Ca_{O2} increases with increasing [Hb], reaching a maximum at an [Hb] of 20.7 g/dl, and then goes on to decrease above this value (Fig. 3). This finding is in agreement with a previous theoretical study in which Monge (26) showed that Ca_{O2} reached a maximum near a Pa_{O2} of 45 Torr, which would be equivalent to 4,500 m and according to Eq. 1 (see appendix) corresponds to an [Hb] of 20.6 g/dl. The decrease of Ca_{O2} predicted by our curve to occur above [Hb] of 20.7 g/dl and below Pa_{O2} of 45 Torr is a consequence of the shape of the O_{2} equilibrium curve. Because the mentioned Pa_{O2} value falls directly on the steeper portion of the O_{2} equilibrium curve, the increasing fall in saturation offsets the increase in Ca_{O2} that would be expected from increasing [Hb].
Winslow et al. (55) and Winslow and Monge (53), from several highaltitude studies and from their own experiences, have pointed out that a Pa_{O2} between 50 and 60 Torr corresponding to an altitude of ∼4,000 m can be considered as a critical value (critical Po_{2}) above which the effects of hypoxia become increasingly pronounced. This critical point is in very close correspondence to the [Hb] predicted by the Pv̄_{O2} expression, a value above which Pv̄_{O2} decreases linearly with increasing [Hb] and decreasing Pa_{O2}. In this regard, it is important to point out that, before Ca_{O2} reaches its maximum at 20.7 g/dl [Hb] and 45 Torr Pa_{O2}, the assumed critical Pa_{O2} value has already been reached. Additionally, at this [Hb] value, Pv̄_{O2} is also already low and decreasing linearly, which implies that increasing Ca_{O2} does not necessarily improve tissue oxygenation, in accordance with the fact that tissue O_{2} delivery mainly depends on Po_{2} and not on arterial content as its driving force. Therefore, the [Hb] value that corresponds to the maximum Ca_{O2} reached by our theoretical curve corresponds to a Pa_{O2} that is even lower than the assumed critical value and thus suggests it would be unable to offer protection against the increasing effects of hypoxemia, as shown by the linear Pv̄_{O2} decrease above 18 g/dl [Hb] (57 Torr Pa_{O2}).
Monge (25) previously suggested that a maximum Ca_{O2} would be reached at 24 g/dl [Hb]. However, our Ca_{O2} theoretical curve shows a maximum at 20.7 g/dl and better fits real literature data from healthy, young adult sealevel and Andean men (Fig. 3). Above the maximal Ca_{O2} value, our curve predicts a parabolic decrease for higher [Hb] values. Nevertheless, values over 20.7 g/dl (21 g/dl) usually correspond to subjects with excessive erythrocytosis or CMS, in whom the variability in arterial O_{2} saturation and [Hb] result in a wide range of Ca_{O2} and hence do not follow the theoretical prediction that should correspond to healthy men. In this regard, from their epidemiological studies in Cerro de Pasco, Perú (4,350 m), Monge et al. (27) demonstrated the lack of correlation between arterial O_{2} saturation and [Hb] in subjects over age 55 yr with excessive erythrocytosis or CMS, showing the different erythropoietic responses or overresponses to the same degrees of hypoxemia.
As shown in Fig. 3, the points corresponding to CMS subjects from different studies deviate significantly from the theoretical curve; some even show very high Ca_{O2} values. Therefore, CMS subjects may have very high Ca_{O2} values, but this does not necessarily mean improved oxygenation and rather could result in increased viscosity, vascular and cerebral congestion, and altered ventilationtoperfusion ratio (53, 54).
From all the above considerations, it is thus clear that the [Hb] value at which Ca_{O2} reaches a maximum cannot be considered as optimal. Rather, we tentatively suggest that optimal [Hb] can be defined as the [Hb] at which Pv̄_{O2} reaches a maximum despite decreasing Pa_{O2} or increasing altitude. Soon after this maximum, a loss of regulatory function occurs, as evidenced by the linear Pv̄_{O2} decrease that occurs above 18 g/dl [Hb]. Hence, [Hb] seems unable to efficiently maintain or protect Pv̄_{O2} and thus appears to be an ineffective or limited adaptive feature for life at high altitude.
Accordingly, Torrance et al. (46) compared highaltitude natives and sojourners at different altitudes and suggested that the increased [Hb] and O_{2} capacity of the former does not improve Pv̄_{O2} as effectively as does, for example, increased ventilation. According to our model, it is possible to assess to what extent Pv̄_{O2} is affected by other parameters besides [Hb]. The sensitivity analysis for this Pv̄_{O2} model demonstrates that maximal Pv̄_{O2} is most sensitive to variations in P_{50}, showing that a slightly greater affinity can cause a significant drop in Pv̄_{O2} and a slight increase in its corresponding [Hb], which in turn implies that just a bit more [Hb] is required to achieve a maximum Pv̄_{O2} due to the diminished unloading of O_{2} to tissues. In contrast, variations in n_{H} values affect Pv̄_{O2} and its corresponding [Hb] values minimally.
Increasing V̇o_{2} while keeping Q̇ constant decreases Pv̄_{O2} so that a greater [Hb] is needed to attain a maximal Pv̄_{O2} due to the greater demand of tissues. Conversely, if Q̇ increases and V̇o_{2} is kept constant, Pv̄_{O2} increases and less [Hb] is required.
Erythrocytosis, Q̇, and Ṫo_{2}. In an optimal [Hb] discussion, it is important to also review the effect of Hct and [Hb] over other key variables of O_{2} transport. Because Q̇ represents the convective link in the O_{2} transport chain, it is thus an important variable to consider when assessing O_{2} transport at high altitude. Researchers have shown mean Q̇ or CI values to be similar in sealevel residents and highaltitude natives (2, 38, 39, 42). Monge et al. (28) found a slightly increased CI mean value in highaltitude natives compared with sealevel residents but regarded this difference with doubtful significance. Later, Winslow and Monge (53), after reviewing CI data from the same study, found no relation between CI points and Hct values for the sealevel group, which showed wide variability. However, they noted that if taken separately highaltitude CI points (excluding one case) showed a significant inverse linear relationship with Hct values above 55%. Nevertheless, we cannot draw an overall pattern from this study because this finding has not been supported by other studies.
Nevertheless, the true effect Hct and thus [Hb] may have over Q̇ deserves particular discussion. The results of normovolemic hemodilution studies made in highaltitude natives by Winslow and coworkers (Ref. 54, summarized in Ref. 53) and by others (48) in which Hct and [Hb] were reduced to sealevel values showed that Q̇ increased as Hct was diminished, suggesting that Q̇ may be regulated in part by erythrocytosis and thus the latter could have a detrimental effect over Q̇. This finding is consistent with Guyton and Richardson's work (10) in dogs in which they showed how Q̇ decreased as Hct was elevated (at constant blood volumes) by means of increased viscosity and diminished venous return. In this regard, it is important to note that Winslow and Monge (53) have shown that blood viscosity increases exponentially with Hct above 55% in Andeans (53) and thus could potentially cause the same effect over Q̇. However, besides large variability and different methodology, the reason for similar Q̇ mean values at sea level and high altitude most probably resides in the complex interrelation and balance between blood volume, blood viscosity, and peripheral resistance.
In chronic erythrocytosis, as found in highaltitude natives, blood volume is increased and, because of it, venous return and systemic pressure are increased as well. Additionally, peripheral resistance is decreased due to increased vascularization of the capillary beds. Thus the effect of blood viscosity, the consequence of increased Hct on venous return and hence Q̇, could be partially or totally offset by the increase in blood volume finally resulting in similar Q̇ values for highaltitude natives and sealevel residents.
However, further experimental work with similar methodology is needed to achieve a complete and satisfactory description of the effect of Hct and [Hb] on Q̇ in highaltitude natives.
Figure 4 shows that Ṫo_{2} rises with increasing [Hb] ranging from sea level to excessive erythrocytosis/CMS values. It is interesting that CMS subjects tend to have the higher Ṫo_{2} values, which may at first seem paradoxical. However, with very high Ṫo_{2}, which, if assuming Q̇ constant, would be consequence of increased Ca_{O2}, subjects present a variety of signs and symptoms that imply no improvements in oxygenation. Thus it is clear that an increased Ṫo_{2} cannot be considered a good indicator of improved oxygenation.
CMS and excessive erythrocytosis. Although our analysis is intended for healthy Andean men, CMS constitutes an insightful example of the effects of excessive erythrocytosis and provides an important point regarding the effects of Hct and [Hb] reduction at high altitude.
Although evidence is still controversial, a decreased ventilatory drive is probably the primary cause or a significant risk factor for CMS with important contributions from sleep hypoxia and age (Refs. 19, 44, 51, see also Ref. 11). These factors act in conjunction and “overshoot” erythropoiesis, leading to excessive erythrocytosis, which in turn results in a drift toward higher [Hb] values from what would be expected for a given altitude of residence.
Winslow (52) has pointed out that increased viscosity and a possible association of excessive erythrocytosis to impaired blood lung oxygenation are factors contributing to a selfpropagating “viciouscycle” of lower Pa_{O2}, desaturation, lower Pv̄_{O2}, and augmented erythropoietin secretion, which further contribute to CMS (see also Ref. 53), thus showing the detrimental role that excessive erythrocytosis could play. This becomes evident when CMS subjects undergo hemodilution. Winslow et al. (54) and Winslow and Monge (53) have shown that, after reduction of Hct from excessive to sealevel values while at high altitude, subjects experience remarkable symptomatic improvement, stimulation of ventilation, and improved ventilationperfusion matching, thus increasing alveolar Po_{2}, Pa_{O2}, arterial O_{2} saturation, Pv̄_{O2}, and venous O_{2} saturation while decreasing MPAP (53, 54). The latter finding is consistent with the study by Peñaloza et al. (40), in which a significant increase in arterial O_{2} saturation and a significant decrease in MPAP was found in six CMS subjects in Cerro de Pasco after phlebotomy, suggesting an improvement of pulmonary perfusion despite the drop in MPAP.
Exercise performance and Hct reduction at high altitude. The integration of all O_{2} transport mechanisms is comprised in the study of overall exercise performance, because the latter is a good indicator of O_{2} transport efficiency. The most striking result of overall exercise performance studies by Winslow and coworkers (Ref. 54, see also Ref. 53) is that in no case did Hct and [Hb] reduction, whether achieved by phlebotomy or hemodilution, decrease the maximal exercise level. This finding suggests that increased O_{2} capacity resulting from excessive erythrocytosis in these highaltitude natives serves no useful purpose during exercise. This contradicts the study by Horstmann et al. (12) on the effect of hemodilution over V̇o_{2 max} at high altitude, which showed that Hct reduction decreased V̇o_{2 max}. However, the latter study was in 3wk acclimatized lowlanders at 4,300 m and is not strictly comparable to natives born and raised at high altitude due to a number of structural and functional differences that exist between shortterm acclimatized lowlanders and highaltitude natives. Wagner (49) compared the influence of several O_{2} transport variables in determining V̇o_{2 max} at sea level and at high altitude via a theoretical analysis. His analysis showed that in sojourners at altitude V̇o_{2 max} was least influenced by [Hb] and Q̇ and mostly determined by inspired Po_{2} and ventilation, thus suggesting that changes in [Hb] would not cause major variations in V̇o_{2 max} at high altitude.
Adaptative capacity of erythrocytosis: an evolutionary outlook. From an evolutionary physiology point of view, natural selection does not seem to have acted on Andean humans as much as on other highaltitude species. This fact is most probably due to the migratory habits of Andean people, their greater admixture with lowland groups, and most importantly less evolutionary time exposure to highaltitude environments (34). In contrast to Andeans, Himalayans at the same altitude maintain lower [Hb] values because of apparently lower erythropoietic response sensitivity to hypoxia and because of higher hypoxic ventilatory responsiveness (34, 36) and could hence be considered as a true adaptive trait for high altitude. This fact also favors and supports the hypothesis that for Andeans erythrocytosis has a limited beneficial function and could even be considered as an ineffective adaptive mechanism and a sign of limitation and nonadaptation to high altitude.
Still, it is interesting to note that the optimal [Hb] resulting from our Pv̄_{O2} expression corresponds to a [Hb] value within the normal range of values known for humans at sea level. This value corresponds to a maximum Pv̄_{O2}, supporting the idea that an increased [Hb] is evidence of the possible limited adaptive capacity of erythrocytosis. Moreover, the fact that the optimal [Hb] value for Andeans obtained through our theoretical analysis is within a normal range of values known for humans at sea level and the overall symptomatic and physical improvement that comes from reducing Hct to sealevel values while at high altitude suggest that Andean humans would be better suited for life at high altitudes if they could maintain an [Hb] within the sealevel range.
As Niermeyer et al. (36) have pointed out, it is apparently as a result of the establishment of sea level physiological traits that Himalayans present such an overall pattern of successful adaptation to life at high altitude. Hence, if these traits can make a single highaltitude population have close resemblance to one at sea level, then the similarities among developmental characteristics, [Hb], and pulmonary arterial pressures indicate that physiological responses such as erythrocytosis, decreased ventilatory drive, and increased pulmonary artery pressure commonly observed in sealevel sojourners to high altitude as well as in Andean highaltitude residents are not actually adaptive.
It would be insightful to obtain Pv̄_{O2} and [Hb] data at different altitudes in the Andes for a complete validation of this theoretical model and also to experimentally determine the optimal [Hb] in Andean and Himalayan humans for comparative purposes as well as in different species genetically adapted and not adapted to high altitudes. Unfortunately sufficient Pv̄_{O2} data of Andean humans living at different altitudes is not widely available for a full validation of this theoretical model. Also important to take into account is the fact that most studies from which Pv̄_{O2} data can be obtained, calculated, or estimated took place mainly in two locations in the Peruvian Andes (Cerro de Pasco, 4,350 m; and Morococha, 4,500 m) and one location in the Bolivian Andes (La Paz, 3,700 m), which is why covering all of the curve's range is a difficult task. Nevertheless, the limited Pv̄_{O2} values obtained or estimated from previous studies are very similar to those predicted by our theoretical curve (see Table 1). Further experimental work, however, is needed to satisfactorily determine whether erythrocytosis is truly an ineffective adaptive mechanism for life at high altitude.
Finally, a word of caution must be mentioned. The present work is focused on trying to acquire a better theoretical understanding of a natural physiological/pathophysiological phenomenon and is not intended to have prescriptive purposes.
APPENDIX
The empirical equation that expresses [Hb] as an inverse potential function of Pa_{O2} was originally obtained by Monge and Whittembury (31) from [Hb] and Pa_{O2} data from Hurtado and coworkers (14, 15) on healthy Andean men at different altitudes 1
The Hill equation expresses hemoglobin oxygen saturation (Sa_{O2}) as a function of Po_{2} 2
The saturation definition corresponds to the relation between blood O_{2} content and blood O_{2} capacity 3
where Co_{2} is the blood O_{2} content and 1.34 Hb represents the blood O_{2} capacity (O_{2} capacity = 1.34 ml O_{2}/g Hb).
The Fick principle expresses O_{2} flux (V̇o_{2}) as the product of Q̇ and arterial  mean venous O_{2} content difference (Ca_{O2}  Cv̄_{O2}) 4
By equaling Eqs. 2 and 3, we obtain 5
Equation 5 constitutes the starting point for the construction of Pv̄_{O2} and Ca_{O2} expressions. Rearranging and applying Eq. 5 to arterial blood and placing Pa_{O2} in terms of [Hb] according to Eq. 1, we obtain an expression of Ca_{O2} as a function of [Hb] that considers the variation of [Hb] as a function of Pa_{O2} 6
where Pa_{50} is the arterial P_{50} value and n_{Ha} is the arterial Hill parameter. Pa_{50} and n_{Ha} values were obtained from Brown et al. in the Peruvian Andes (4).
To obtain the Pv̄_{O2} expression, Eq. 5 was rearranged and then applied to arterial and venous blood 7
where Pv̄_{50} corresponds to mixed venous P_{50} and n_{Hv̄} to the Hill parameter for mixed venous blood. The value for n_{Hv̄} was considered the same as n_{Ha} assuming a similar 2,3DPGtoHb molar ratio in arterial and venous blood. Pv̄_{50} value was calculated assuming an arterialmixed venous pH difference of 0.02 and a Bohr factor (dlogP_{50}/dpH) of 0.387 (54).
By rearranging Eq. 7, replacing Eqs. 1 and 3 in it, and replacing the constant values (Pa_{50} = 27.6 Torr, n_{Ha} = 2.62, Pv̄_{50} = 28.6 Torr, n_{Hv̄} = 2.62, V̇o_{2}= 0.250 l/min, Q̇ = 5.5 l/min), the expression that predicts Pv̄_{O2} in terms of [Hb], considering [Hb] variation as a function Pa_{O2}, is obtained 8
By taking the partial derivative with respect to [Hb] of Eqs. 6 and 8 and by equaling to zero, we obtain the maximum of each function 9 10
Footnotes

↵1 It is assumed that for any given altitude, the average [Hb] of young highaltitude natives defines normal values and that more than two standard deviations above average for each altitude of residence is considered excessive (20, 21, 27, 31).
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