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J Appl Physiol 96: 1581-1588, 2004. First published December 12, 2003; doi:10.1152/japplphysiol.00328.2003
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Optimal hemoglobin concentration and high altitude: a theoretical approach for Andean men at rest

Francisco C. Villafuerte, Rosa Cárdenas, and Carlos Monge-C

Laboratorio de Transporte de Oxígeno, Facultad de Ciencias y Filosofía, Universidad Peruana Cayetano Heredia, Lima 31, Peru

Submitted 3 April 2003 ; accepted in final form 1 December 2003


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The beneficial role of erythrocytosis for O2 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 PO2 (PO2) and arterial O2 content, considering for both the relation between [Hb] and arterial PO2. Relations of [Hb] to other physiological variables such as cardiac output and convective arterial O2 transport were also discussed, revealing the importance of PO2 in this model. Our theoretical analysis suggests that increasing [Hb] allows increase and maintenance of PO2 with only moderate declines in arterial PO2 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 O2 content and O2 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 O2-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 O2 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 () markedly decreased along with increasing Hct and that blood O2 availability, expressed as the product of Hct and , 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 O2 availability above Hct of 40% resulted from decreased , 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 O2 transport in dogs was 40% and explained this optimal value as a balance between the opposing effects of Hct on viscosity and on blood O2 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 O2 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 high-altitude 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 so-called 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 O2 transport at high altitude, hence outweighing the advantage of increased O2-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 O2 transport.

In this regard, the hypothesis that any degree of erythrocytosis is not truly beneficial to O2 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 sea-level values while at altitude pulmonary ventilation improves and alveolar PO2 increases along with arterial PO2 (PaO2) and mean (mixed) venous PO2 (PO2); concomitantly, mean pulmonary artery pressure (MPAP) decreases (53, 54).

Evaluation of the role of erythrocytosis for O2 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 O2 transport that can be measured in vivo: PO2 and arterial O2 content (CaO2). We also discuss the relationship between convective arterial O2 transport (O2), expressed as the product of and CaO2, with [Hb] by analyzing data from studies in high-altitude Andean natives and sea-level residents.

To construct expressions describing PO2 and CaO2 as functions of [Hb], we use fundamental O2 transport equations and an empirical mathematical expression first derived by Monge and Whittembury (32), which expresses [Hb] as a function of PaO2. As previously shown (33), this expression better reflects the actual relation between these two variables in Andeans (Fig. 1). The use of PO2 for this analysis is based on the fact that it represents mean PO2 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 O2 transport. Additionally, PO2 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 CaO2 expressed as a function of PaO2 and [Hb], we can further analyze the issue at hand since it represents the arterial O2 availability and thus the potential O2 mass for tissue delivery. Finally, O2 and its relation with [Hb] is discussed. O2 is the product of and CaO2, thus representing an important variable for the analysis of O2 transport because it expresses the amount of O2 carried by arterial blood per time unit.



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  		Fig. 1. Hemoglobin concentration ([Hb]) as an inverse potential function of arterial PO2 (PaO2). We constructed the empirical curve using an empirical equation originally derived by Monge and Whittembury (32).

 

In summary, by employing mathematical functions expressing PO2 and CaO2 in terms of [Hb], which includes the relationship between [Hb] and PaO2, and discussing the relationship between O2 and with [Hb] from high-altitude literature data, we theoretically analyze optimal [Hb] and its physiological meaning to assess to what extent erythrocytosis is beneficial for O2 transport at altitude.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
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 normal1 [Hb] for different PaO2 values is best represented by an empirical equation that expresses [Hb] as a potential function of PaO2 and shows the inverse relation between both variables (Fig. 1; see APPENDIX). This empirical equation was obtained with [Hb] and PaO2 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 PaO2 change that [Hb] variation implies, we employ this relation in the construction of expressions describing PO2 and CaO2 as functions of [Hb].

To functionally correlate PO2 with PaO2 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 PO2 in terms of [Hb] and considers PaO2 as a function of [Hb].

At rest, Andeans at high altitude have been considered to have mean values of O2 consumption (O2) and , and/or cardiac index (CI = corrected by body surface area), that are similar to those of sea-level residents (2, 38, 39, 42); therefore, we considered these as constants in the PO2 expression. In addition, the PO2 value at which hemoglobin is 50% saturated (P50) and the Hill parameter (nH), although with some variability in the former, have been shown to have similar values in Andean high-altitude natives and sea-level residents (53, 55); for this reason, they have also been considered as constants in both the PO2 and CaO2 expressions.

To obtain an equation that describes the changes in CaO2 when [Hb] rises as a consequence of decreasing PaO2 (increasing hypoxemia), we combined the Hill equation applied to arterial blood with the arterial saturation definition and placed PaO2 in terms of [Hb] as obtained from the empirical relationship. This allowed us to obtain a CaO2 expression as a function of [Hb] that considers the relationship between [Hb] and PaO2.

Although 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, high-altitude 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 or CI and [Hb] in high-altitude natives to then be combined with the CaO2 expression to obtain O2, we decided to empirically analyze O2 from CI and CaO2 data from different studies (37, 39, 42, 45). Finally, as shown in Fig. 4, we obtained a regression curve from the high-altitude Andean native and sea-level resident data sets.



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  		Fig. 4. Relationship between O2 transport (O2) and [Hb]. O2 was calculated from cardiac index (CI) and CaO2 data of sea-level, high-altitude, and CMS subjects and plotted with corresponding [Hb] values. Data appeared to fit an exponential equation (O2 = 425e0.032Hb; r = 0.50, P < 0.05). Healthy high-altitude natives ({circ}) and those suffering from CMS () tend to have higher O2 values with increasing Hb compared with sea-level residents ({square}). (Data are from Refs. 37, 39, 42, and 45.)

 

Because the PO2 and the CaO2 expressions consider PaO2 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 sea-level PaO2 of 95 Torr. To obtain the maximum of each function and find the [Hb] value at which PO2 and CaO2 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 PO2 curve described by Monge (25) overlooked the initial ascending portion, which gives that region of the curve a slight bell-shaped form and which clearly shows PO2 rising with increasing [Hb] despite decreasing PaO2 in the initial section as shown in Fig. 2.



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  		Fig. 2. Mean (mixed) venous PO2 (PO2) as a function of [Hb]. The PO2 model considers the change in [Hb] with varying PaO2. The theoretical curve passes through a maximum at an [Hb] value of 15 g/dl (14.7 g/dl), a "normal" sea-level value. See text.

 

Finally, we analyzed the sensitivity of the PO2 expression toward variations in its critical parameters: , O2, nH, and the Pa50/P50 pair. To achieve this and to make changes comparable among parameters, we chose to evaluate the fractional variation in maximum PO2 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 PO2 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
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 APPENDIX
 REFERENCES
 
Figure 2 shows that PO2 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 PaO2 from 95 to nearly 80 Torr (~2,000 m), increases PO2 from 40.4 up to a maximal value of 40.7 Torr. Above [Hb] of 15 g/dl, PO2 varies little until [Hb] values exceed 18 g/dl (PaO2 of 57 Torr). When PaO2 continues to decrease due to higher altitudes, PO2 significantly declines linearly regardless of the continuous rise in [Hb].

Figure 3 shows CaO2 as a function of [Hb]. The theoretical CaO2 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 best-fit curve obtained from CaO2 and from [Hb] mean values of healthy sea-level residents and high-altitude natives (1, 2, 9, 13, 22, 23, 27, 35, 37-40, 42, 43, 45) shows very close resemblance to our theoretical prediction.



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  		Fig. 3. Arterial O2 content (CaO2) as function of [Hb]. The theoretical CaO2 curve (solid line) reaches a maximum at 21 g/dl [Hb]. {square}, CaO2 data of sea-level residents. {circ}, CaO2 data of high-altitude healthy natives. , CaO2 data of chronic mountain sickness (CMS) subjects. The theoretical curve from Monge (25) (dashed line) shows a maximum at 23.9 g/dl [Hb]. A best-fit curve of healthy sea-level and high-altitude residents data (dotted line) shows close resemblance to our theoretical curve. (Data are means from Refs. 1, 2, 9, 13, 22, 23, 27, 35, 37, 38, 39, 40, 42, 43, and 45.)

 

Figure 4 shows the relationship between O2 and [Hb] obtained from sea-level and high-altitude data sets. O2 values, expressed as the product of CI and CaO2, display an exponential relationship (r = 0.50, P < 0.05) with [Hb]. This relation illustrates how O2 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 PO2 values that result from the fractional variation of each of the parameters of the model. Figure 5A shows that PO2 is least sensitive to changes in nH values within a limited range of 2.4-2.8. In this manner, an increase of 5% in nH results in only a 0.48% decrease in maximal PO2. P50 exerts the greatest change on maximum PO2, but the magnitudes of these are limited by the P50 range we chose to consider (24-30 Torr) so as not to stray from the physiological situation. In this case, a 5% increase in P50 (Pa50/P50 pair) resulted in a 3.48% rise in the PO2 value.



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  		Fig. 5. PO2 model sensitivity analysis. A: fractional variation in maximal PO2 as a consequence of the fractional variation in each of its parameters (see text). B: comparison of the variations of maximal PO2, assuming a 5% increase in each of the parameters.

 

Due to the range chosen for and O2 ( = 4-7 l/min; O2 = 225-800 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 PO2, Fig. 5B shows the percent response in maximal PO2 when each parameter is varied slightly (5%). An increase of 5% in resulted in a 2.10% increase in PO2, whereas an increase of 5% in O2 decreased PO2 in 1.98%.

The variation of maximum PO2 with each parameter is accompained by a variation of corresponding [Hb] values. The 5% increase in nH, P50, , and O2 resulted in corresponding [HB] values of 14.9, 14.4, 14.6, and 14.8 g/dl, respectively.


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
APPENDIX
 REFERENCES
 
Theoretical PO2 and CaO2 as functions of [Hb]. Our analysis suggests that increases in [Hb] allow increase and maintenance of PO2 only while moderate declines in PaO2 occur as a result of moderate increases in altitude. Hence, PO2 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 (PaO2 57 Torr, ~3,800 m), and afterward decreases linearly despite a continuously increasing [Hb] and augmented CaO2, suggesting that no additional protection to PO2 is offered by increasing [Hb].

Our theoretical curve shows that CaO2 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 CaO2 reached a maximum near a PaO2 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 CaO2 predicted by our curve to occur above [Hb] of 20.7 g/dl and below PaO2 of 45 Torr is a consequence of the shape of the O2 equilibrium curve. Because the mentioned PaO2 value falls directly on the steeper portion of the O2 equilibrium curve, the increasing fall in saturation offsets the increase in CaO2 that would be expected from increasing [Hb].

Winslow et al. (55) and Winslow and Monge (53), from several high-altitude studies and from their own experiences, have pointed out that a PaO2 between 50 and 60 Torr corresponding to an altitude of ~4,000 m can be considered as a critical value (critical PO2) above which the effects of hypoxia become increasingly pronounced. This critical point is in very close correspondence to the [Hb] predicted by the PO2 expression, a value above which PO2 decreases linearly with increasing [Hb] and decreasing PaO2. In this regard, it is important to point out that, before CaO2 reaches its maximum at 20.7 g/dl [Hb] and 45 Torr PaO2, the assumed critical PaO2 value has already been reached. Additionally, at this [Hb] value, PO2 is also already low and decreasing linearly, which implies that increasing CaO2 does not necessarily improve tissue oxygenation, in accordance with the fact that tissue O2 delivery mainly depends on PO2 and not on arterial content as its driving force. Therefore, the [Hb] value that corresponds to the maximum CaO2 reached by our theoretical curve corresponds to a PaO2 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 PO2 decrease above 18 g/dl [Hb] (57 Torr PaO2).

Monge (25) previously suggested that a maximum CaO2 would be reached at 24 g/dl [Hb]. However, our CaO2 theoretical curve shows a maximum at 20.7 g/dl and better fits real literature data from healthy, young adult sea-level and Andean men (Fig. 3). Above the maximal CaO2 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 O2 saturation and [Hb] result in a wide range of CaO2 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 O2 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 CaO2 values. Therefore, CMS subjects may have very high CaO2 values, but this does not necessarily mean improved oxygenation and rather could result in increased viscosity, vascular and cerebral congestion, and altered ventilation-to-perfusion ratio (53, 54).

From all the above considerations, it is thus clear that the [Hb] value at which CaO2 reaches a maximum cannot be considered as optimal. Rather, we tentatively suggest that optimal [Hb] can be defined as the [Hb] at which PO2 reaches a maximum despite decreasing PaO2 or increasing altitude. Soon after this maximum, a loss of regulatory function occurs, as evidenced by the linear PO2 decrease that occurs above 18 g/dl [Hb]. Hence, [Hb] seems unable to efficiently maintain or protect PO2 and thus appears to be an ineffective or limited adaptive feature for life at high altitude.

Accordingly, Torrance et al. (46) compared high-altitude natives and sojourners at different altitudes and suggested that the increased [Hb] and O2 capacity of the former does not improve PO2 as effectively as does, for example, increased ventilation. According to our model, it is possible to assess to what extent PO2 is affected by other parameters besides [Hb]. The sensitivity analysis for this PO2 model demonstrates that maximal PO2 is most sensitive to variations in P50, showing that a slightly greater affinity can cause a significant drop in PO2 and a slight increase in its corresponding [Hb], which in turn implies that just a bit more [Hb] is required to achieve a maximum PO2 due to the diminished unloading of O2 to tissues. In contrast, variations in nH values affect PO2 and its corresponding [Hb] values minimally.

Increasing O2 while keeping constant decreases PO2 so that a greater [Hb] is needed to attain a maximal PO2 due to the greater demand of tissues. Conversely, if increases and O2 is kept constant, PO2 increases and less [Hb] is required.

Erythrocytosis, , and O2. In an optimal [Hb] discussion, it is important to also review the effect of Hct and [Hb] over other key variables of O2 transport. Because represents the convective link in the O2 transport chain, it is thus an important variable to consider when assessing O2 transport at high altitude. Researchers have shown mean or CI values to be similar in sea-level residents and high-altitude natives (2, 38, 39, 42). Monge et al. (28) found a slightly increased CI mean value in high-altitude natives compared with sea-level 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 sea-level group, which showed wide variability. However, they noted that if taken separately high-altitude 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 deserves particular discussion. The results of normovolemic hemodilution studies made in high-altitude natives by Winslow and coworkers (Ref. 54, summarized in Ref. 53) and by others (48) in which Hct and [Hb] were reduced to sea-level values showed that increased as Hct was diminished, suggesting that may be regulated in part by erythrocytosis and thus the latter could have a detrimental effect over . This finding is consistent with Guyton and Richardson's work (10) in dogs in which they showed how 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 . However, besides large variability and different methodology, the reason for similar 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 high-altitude 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 , could be partially or totally offset by the increase in blood volume finally resulting in similar values for high-altitude natives and sea-level 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 in high-altitude natives.

Figure 4 shows that O2 rises with increasing [Hb] ranging from sea level to excessive erythrocytosis/CMS values. It is interesting that CMS subjects tend to have the higher O2 values, which may at first seem paradoxical. However, with very high O2, which, if assuming constant, would be consequence of increased CaO2, subjects present a variety of signs and symptoms that imply no improvements in oxygenation. Thus it is clear that an increased O2 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 self-propagating "vicious-cycle" of lower PaO2, desaturation, lower PO2, 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 sea-level values while at high altitude, subjects experience remarkable symptomatic improvement, stimulation of ventilation, and improved ventilation-perfusion matching, thus increasing alveolar PO2, PaO2, arterial O2 saturation, PO2, and venous O2 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 O2 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 O2 transport mechanisms is comprised in the study of overall exercise performance, because the latter is a good indicator of O2 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 O2 capacity resulting from excessive erythrocytosis in these high-altitude natives serves no useful purpose during exercise. This contradicts the study by Horstmann et al. (12) on the effect of hemodilution over O2 max at high altitude, which showed that Hct reduction decreased O2 max. However, the latter study was in 3-wk 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 short-term acclimatized lowlanders and high-altitude natives. Wagner (49) compared the influence of several O2 transport variables in determining O2 max at sea level and at high altitude via a theoretical analysis. His analysis showed that in sojourners at altitude O2 max was least influenced by [Hb] and and mostly determined by inspired PO2 and ventilation, thus suggesting that changes in [Hb] would not cause major variations in O2 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 high-altitude 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 high-altitude 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 PO2 expression corresponds to a [Hb] value within the normal range of values known for humans at sea level. This value corresponds to a maximum PO2, 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 sea-level 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 sea-level 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 high-altitude 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 sea-level sojourners to high altitude as well as in Andean high-altitude residents are not actually adaptive.

It would be insightful to obtain PO2 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 PO2 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 PO2 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 PO2 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.


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  		Table 1. Hb and PO2 values from high-altitude literature

 

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
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
REFERENCES
 
The empirical equation that expresses [Hb] as an inverse potential function of PaO2 was originally obtained by Monge and Whittembury (31) from [Hb] and PaO2 data from Hurtado and coworkers (14, 15) on healthy Andean men at different altitudes

(1)

The Hill equation expresses hemoglobin oxygen saturation (SaO2) as a function of PO2

(2)

The saturation definition corresponds to the relation between blood O2 content and blood O2 capacity

(3)

where CO2 is the blood O2 content and 1.34 Hb represents the blood O2 capacity (O2 capacity = 1.34 ml O2/g Hb).

The Fick principle expresses O2 flux (O2) as the product of and arterial - mean venous O2 content difference (CaO2 - CO2)

(4)

By equaling Eqs. 2 and 3, we obtain

(5)

Equation 5 constitutes the starting point for the construction of PO2 and CaO2 expressions. Rearranging and applying Eq. 5 to arterial blood and placing PaO2 in terms of [Hb] according to Eq. 1, we obtain an expression of CaO2 as a function of [Hb] that considers the variation of [Hb] as a function of PaO2

(6)

where Pa50 is the arterial P50 value and nHa is the arterial Hill parameter. Pa50 and nHa values were obtained from Brown et al. in the Peruvian Andes (4).

To obtain the PO2 expression, Eq. 5 was rearranged and then applied to arterial and venous blood

(7)

where P50 corresponds to mixed venous P50 and nH to the Hill parameter for mixed venous blood. The value for nH was considered the same as nHa assuming a similar 2,3-DPG-to-Hb molar ratio in arterial and venous blood. P50 value was calculated assuming an arterial-mixed venous pH difference of 0.02 and a Bohr factor (dlogP50/dpH) of -0.387 (54).

By rearranging Eq. 7, replacing Eqs. 1 and 3 in it, and replacing the constant values (Pa50 = 27.6 Torr, nHa = 2.62, P50 = 28.6 Torr, nH = 2.62, O2= 0.250 l/min, = 5.5 l/min), the expression that predicts PO2 in terms of [Hb], considering [Hb] variation as a function PaO2, 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
 

Address for reprint requests and other correspondence: C. Monge-C, Laboratorio de Transporte de Oxígeno, Facultad de Ciencias y Filosofía, Universidad Peruana Cayetano Heredia, Av.Honorio Delgado 430, Lima 31, Perú (E-mail: cmonge{at}upch.edu.pe).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1 It is assumed that for any given altitude, the average [Hb] of young high-altitude 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). Back


   REFERENCES
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

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