Physiological Reports. 2023;11:e15806. 
 
  | 1 of 11
https://doi.org/10.14814/phy2.15806
wileyonlinelibrary.com/journal/phy2
1 | INTRODUCTION
Human activity is drastically constrained at extreme alti-
tudes due to low environmental oxygen availability. Few 
humans can reach the highest elevation on earth, the 
summit of Mt. Everest (~8850 m), without supplemental 
oxygen, and those who do are limited to such a degree that 
a slow uphill walk approaches the maximum capacity for 
oxygen uptake and utilization (V̇O2max).
Over millennia, several animal species have adapted to 
life at extreme altitudes, in part due to a high hemoglobin- 
oxygen affinity (Storz, 2007; Storz et al., 2010). The most 
common metric of hemoglobin- oxygen affinity is P50, the 
oxygen tension at which 50% of hemoglobin is saturated. 
Received: 10 August 2023 | Accepted: 11 August 2023
DOI: 10.14814/phy2.15806  
O R I G I N A L  A R T I C L E
The dependence of maximum oxygen uptake and 
utilization (V̇O2max) on hemoglobin- oxygen affinity and 
altitude
Kevin L. Webb1,2
 |   Michael J. Joyner1
 |   Chad C. Wiggins1
 |    
Timothy W. Secomb3
 |   Tuhin K. Roy1,2
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided 
the original work is properly cited.
© 2023 The Authors. Physiological Reports published by Wiley Periodicals LLC on behalf of The Physiological Society and the American Physiological Society.
1Department of Anesthesiology and 
Perioperative Medicine, Mayo Clinic, 
Rochester, Minnesota, USA
2Department of Physiology and 
Biomedical Engineering, Mayo Clinic, 
Rochester, Minnesota, USA
3Department of Physiology, University 
of Arizona, Tucson, Arizona, USA
Correspondence
Kevin L. Webb, Department of 
Anesthesiology and Perioperative 
Medicine, Mayo Clinic, Rochester, MN, 
USA.
Email: webb.kevin@mayo.edu
Funding information
National Institutes of Health, Grant/
Award Number: R35 HL139854
Abstract
Oxygen transport from the lungs to peripheral tissue is dependent on the affin-
ity of hemoglobin for oxygen. Recent experimental data have suggested that the 
maximum human capacity for oxygen uptake and utilization (V̇O2max) at sea 
level and altitude (~3000 m) is sensitive to alterations in hemoglobin- oxygen af-
finity. However, the effect of such alterations on V̇O2max at extreme altitudes 
remains largely unknown due to the rarity of mutations affecting hemoglobin- 
oxygen affinity. This work uses a mathematical model that couples pulmonary 
oxygen uptake with systemic oxygen utilization under conditions of high meta-
bolic demand to investigate the effect of hemoglobin- oxygen affinity on V̇O2max 
as a function of altitude. The model includes the effects of both diffusive and con-
vective limitations on oxygen transport. Pulmonary oxygen uptake is calculated 
using a spatially- distributed model that accounts for the effects of hematocrit and 
hemoglobin- oxygen affinity. Systemic oxygen utilization is calculated assuming 
Michaelis– Menten kinetics. The pulmonary and systemic model components are 
solved iteratively to compute predicted arterial and venous oxygen levels. Values 
of V̇O2max are predicted for several values of hemoglobin- oxygen affinity and 
hemoglobin concentration based on data from humans with hemoglobin muta-
tions. The model predicts that increased hemoglobin- oxygen affinity leads to in-
creased V̇O2max at altitudes above ~4500 m.
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WEBB et al.
A low P50 corresponds to a high hemoglobin- oxygen 
binding affinity and vice- versa. Recent investigation has 
highlighted a rare human population with hemoglo-
bin mutations causing high hemoglobin- oxygen affinity 
(low P50) (Charache et al., 1966; Thom et al., 2013). This 
human population has shown remarkable maintenance 
of exercise tolerance during normobaric hypoxia and at 
terrestrial high altitude (~3000 m) (Dominelli et al., 2020; 
Hebbel et al., 1978; Webb, Dominelli, et al., 2022a), per-
haps in part due to the elevated hemoglobin values ob-
served. Furthermore, there has been growing interest 
regarding the effects of pharmacologically altering the P50 
in healthy individuals with typical hemoglobin (Stewart 
et al.,  2021, 2020). Despite hemoglobin function being 
central to oxygen transport and utilization, much remains 
unknown regarding the effects of an altered P50.
Changes in P50 can markedly influence pulmonary ox-
ygen loading and peripheral offloading. For instance, a de-
crease in P50 may enhance pulmonary oxygen loading at 
the expense of blunted peripheral offloading. At sea level, 
where arterial blood is well- oxygenated, a low P50 likely 
hinders peripheral offloading leading to several compen-
satory adaptations (i.e., enhanced red blood cell produc-
tion and increased oxygen carrying capacity), as observed 
in humans with hemoglobin mutations (Webb, Domi-
nelli, et al., 2022a). Yet at high and extreme altitudes, a 
low P50 likely improves arterial blood oxygenation with 
subsequent preservation of V̇O2max. However, experi-
mental data regarding the influence of an altered P50 are 
largely limited to examination at high altitude conditions 
(~3000 m or 15% O2 in the laboratory setting). The ques-
tion remains: how would humans with a low P50 tolerate 
extreme altitudes (Bencowitz et al., 1982)?
Because hemoglobin mutations are exceedingly rare 
and research sojourns to extreme altitudes are challenging 
to achieve, we present a theoretical model of oxygen trans-
port to investigate the dependence of V̇O2max on P50 and 
altitude. We hypothesized that relative to a normal P50, a 
low P50 would result in a greater V̇O2max at high altitude 
and that this relationship would be further potentiated at 
extreme altitudes.
2 | METHODS
The V̇O2max achieved in any given situation reflects limi-
tations in both pulmonary oxygen uptake and systemic 
oxygen utilization. We therefore simulated whole- body 
oxygen uptake and utilization to investigate the varia-
tion in V̇O2max as a function of altitude in humans with 
normal and altered hemoglobin- oxygen affinity. A math-
ematical model for oxygen uptake in the lung was com-
bined with a model for oxygen utilization in the systemic 
circulation, as indicated in Figure 1, to predict arterial and 
venous oxygen tensions and oxygen consumption rate.
To represent conditions of maximal exercise, the tis-
sue oxygen demand and cardiac output were selected in 
accordance with observed sea- level V̇O2max values (see 
“Systemic oxygen utilization model” below). Arterial 
and venous oxygen tensions were then predicted at pro-
gressively lower atmospheric pressures (i.e., increasing 
altitude). The resulting arteriovenous oxygen content dif-
ferences were used to estimate oxygen consumption as a 
function of altitude and as a measure of functional capacity. 
To investigate the effects of hemoglobin- oxygen affinity on 
V̇O2max, calculations were performed for three cases of P50 
(low, normal, and high) with a range of potential changes 
in hemoglobin concentration as a function of altitude 
(Table 1). Further details of the mathematical model are 
given below, and parameter values are provided in Table 2.
2.1 | Pulmonary oxygen uptake model
The model for pulmonary oxygen uptake yields estimates 
of arterial oxygen tension (Pa
) for given values of alveo-
lar oxygen tension (PA
) and venous oxygen tension (Pv
). 
Oxygen uptake is calculated using a single- compartment 
model that accounts for the effects of capillary diameter 
and hematocrit based on simplified capillary and erythro-
cyte geometry (Roy & Secomb, 2019). The assumed value 
FIGURE 1 Schematic of modeling configuration, combining 
pulmonary oxygen uptake and systemic oxygen utilization. The 
dashed arrows indicate diffusive oxygen transport, and the solid 
arrows indicate convective oxygen transport within the blood. PA, 
alveolar oxygen tension; Pa, arterial oxygen tension; Pv, venous 
oxygen tension.
   | 3 of 11
WEBB et al.
for the lung diffusing capacity DLO2 (Table 2) was selected 
to account for the heterogeneity of perfusion present in 
the pulmonary circulation (Roy & Secomb, 2014). The dif-
fusion of oxygen from alveoli into the blood during pul-
monary capillary perfusion is represented by:
where Pb is blood oxygen tension, C0 is oxygen content of 
fully saturated blood (calculated as 1.34 × [Hb]), Q is mean 
capillary flow rate, x is distance, S(Pb
) describes the oxy-
hemoglobin dissociation curve, and Ltot is the total length 
of pulmonary capillaries. Setting t = x ∕L, where L is mean 
capillary length and Qtot is the total blood flow (i.e., cardiac 
output), yields:
This equation was integrated from t = 0 to t = 1 with 
the initial condition Pb(0) = Pv, to obtain Pa = Pb(1).
The cardiac output Qtot (L/min) was estimated based 
on a published correlation for measurements made over 
a range of ̇V O2 values (L/min) by averaging the results 
from two different experimental techniques (Calbet & 
Boushel, 2015):
To facilitate the calculation of PA via the alveolar gas 
equation, data for subjects at altitude were obtained from 
measurements performed on climbers summiting Mt. Ev-
erest, with an altitude of ~8850 m (Grocott et al., 2009). 
Values of hemoglobin concentration, PO2, and PCO2 were 
obtained by digitizing Figure 2 of Grocott et al. (Grocott 
et al., 2009) and a linear regression was used to fit these 
data as a function of altitude. The value of P50 was assumed 
to be 26.3 mmHg at sea level (see Table 1). To obtain an es-
timate of P50 at the summit, values of PO2 and saturation as 
reported in table 2 of Grocott et al. (2009) were fit using a 
nonlinear regression and an assumed value of 2.7 for the 
Hill coefficient n:
Values of barometric pressure were calculated from 
West et al. (1999).
where a is the altitude in kilometers. The simplified form of 
the alveolar gas equation was then used to calculate alveolar 
PO2 as a function of altitude:
where Pw represents water vapor pressure and R represents 
the respiratory quotient (see Table 2). The values of PCO2 
used in Equation 8, from Ref. (Grocott et al., 2009), were 
assumed to approximate the values under conditions of 
V̇O2max.
2.2 | Systemic oxygen utilization model
The systemic model yields estimates of Pv for given values 
of Pa and tissue oxygen demand. According to the model, 
(1)
QC0
dS(Pb
)
dx
=
DLO2
Ltot
(PA − Pb
)
(2)
dPb
dt =
DLO2
(PA − Pb
)
QtotC0S(Pb
)
(3)
Qtot = 4.37 + 5.33 ̇V O2
(4)
Qtot = 4.43 + 5.22 ̇V O2
(5)
S(P) =
Pn
Pn + P50
n
(6)
PB(a) = exp( − 0.00149a2 − 0.1112a + 6.63268)
(7)
PIO2 = FIO2
(PB(a) − Pw
)
(8)
PA(a) = PIO2 −
PCO2(a)
R
TABLE 1 Cases considered for modeling V̇O2max as a function of altitude. Data depict cases considered for variation in hemoglobin- 
oxygen affinity (P50) and hemoglobin concentration in humans during sojourn to extreme altitudes.
Normal hemoglobin- oxygen affinity
High hemoglobin- oxygen affinity
Low hemoglobin- oxygen affinity
P50 (mmHg)
Hemoglobin 
concentration  
(g/dL)
P50 (mmHg)
Hemoglobin 
concentration  
(g/dL)
P50 (mmHg)
Hemoglobin 
concentration 
(g/dL)
Case 1
26.3, Ref. (20)
14.8, Ref. (17)
Case 1
15.6, Ref. (5)
14.8
Case 1
37
14.8
Case 2
26.3
14.8 → 19.9, Ref. (17)
Case 2
15.6
18.7, Ref. (21)
Case 2
37
12.0
Case 3
26.3 → 24.8, Ref. (17)
14.8
Case 3
15.6
18.7 → 19.9*
Case 3
37
12 → 16.2*
Case 4
26.3 → 24.8
14.8 → 19.9
Case 4
15.6 → 14.7*
18.7
Case 4
37 → 34.9*
12.0
Case 5
15.6 → 14.7*
18.7 → 19.9*
Case 5
37 → 34.9*
12 → 16.2*
Note: Data were taken from experimental results when available. Arrows indicate changes in values from sea- level to an altitude of ~8400 m Ref (17).
*Indicates data for case of high or low hemoglobin- oxygen affinity was assumed to change proportionally to alterations observed during extreme altitude 
sojourn among humans with normal hemoglobin- oxygen affinity.
4 of 11 |   
WEBB et al.
as altitude increases, levels of capillary PO2 are reduced, 
limiting the pressure gradient for diffusive transport to 
tissue, eventually resulting in tissue hypoxia. Under these 
conditions, oxygen consumption rate falls short of oxygen 
demand. The local rate of oxygen consumption is generally 
assumed to depend on tissue PO2 with Michaelis– Menten 
kinetics (Popel,  1989). Estimating distributions of tissue 
PO2 levels would require several additional assumptions re-
garding capillary density and oxygen transport properties. 
Thus, we employed a simplified approach, based on the as-
sumption that Pv can be used as an approximation for tissue 
PO2. In this approach, oxygen consumption is assumed to 
be a function of Pv with Michaelis– Menten kinetics:
where M is oxygen demand is oxygen demand, which is cal-
culated such that predicted ̇V O2 at sea level corresponded 
to a typical observed value of ̇V O2max = 2750 mL O2/min in 
healthy young adults (van der Steeg & Takken, 2021). The 
oxygen demand M represents mitochondrial oxygen con-
sumption capacity under conditions of unlimited oxygen 
supply.
The model for systemic oxygen utilization uses a sim-
plified approach, based on the assumption that Pv can be 
used as an approximation for tissue PO2. In reality, steep 
gradients in in tissue oxygen tensions around capillaries 
are present at V̇O2max, such that tissue PO2 is less than 
local capillary PO2. Also, intravascular PO2 declines in the 
axial direction along capillaries, such that venous PO2 
represents a lower bound on capillary PO2. From these 
considerations, it follows that Pv represents an interme-
diate value within the range of tissue PO2 levels and can 
be used as an approximate estimate of tissue PO2. The 
advantage of this approach, termed Fick– Michaelis– 
Menten (FickMM), is that it provides an estimate that is 
independent of capillary density and geometric arrange-
ment, which are highly variable and for which data are 
not generally available for human subjects.
According to the Fick principle, oxygen consumption 
rate must also satisfy:
where S(P) describes the oxyhemoglobin dissociation curve 
and other quantities are defined in the main text. For any 
given set of conditions, the predicted values of ̇V O2 and Pv 
correspond to the simultaneous solution of Equations 9 and 
10, as shown graphically in Figure 2.
To evaluate the validity of approximating tissue PO2 by 
venous PO2, comparisons with a model using a conven-
tional Krogh geometry and Michaelis– Menten kinetics 
were performed using the oxygen transport and geometric 
parameters described in Table  3. The calculations were 
performed by solving the radial diffusion equation in suc-
cessive slices of a cylinder surrounding a central capillary, 
as described elsewhere (McGuire & Secomb, 2001). These 
simulations take into account the variations in tissue PO2 
(9)
̇V O2 = M
Pv
Pv + P0
(10)
̇V O2 = QtotC0
(S(Pa
) − S(Pv
))
Parameter
Value
Units
Citation
Water vapor pressure Pw
47
mmHg
– 
Respiratory quotient R
0.8
– 
– 
Michaelis constant for 
oxygen consumption P0
10.5
mmHg
(Golub & Pittman, 2012)
Lung diffusing capacity DLO2
74
cm3 O2 min−1 mmHg−1
(Roy & Secomb, 2019)
Capillary length Ltot
0.5
mm
– 
Hill coefficient n
2.7
- 
(Hsia, 1998)
TABLE 2 Parameter values used for 
oxygen transport calculations.
FIGURE 2 Example of predicted maximal oxygen utilization 
rate using the systemic model. Conditions correspond to 
atmospheric pressure at sea level with typical hemoglobin- 
oxygen affinity and a hemoglobin concentration of 14.778 g/dL. 
Oxygen demand (M) was set as 4530 mL O2/min. The dashed 
line represents ̇VO2 calculated from Michaelis– Menten kinetics. 
The solid line represents ̇VO2 calculated from the Fick principle. 
Resulting predicted values at the intersection of the curves are ̇VO2 
= 2750 mL O2/min and a venous partial pressure of oxygen (Pv
) of 
16.2 mmHg. Pv, venous partial pressure of oxygen.
   | 5 of 11
WEBB et al.
with axial and radial position in the Krogh cylinder, when 
calculating the overall rate of oxygen consumption. From 
the results, the venous oxygen tension exiting the muscle 
compartment was estimated for a range of Pa, and for sev-
eral capillary densities (McGuire & Secomb, 2001). The 
entire cardiac output was assumed to be directed to the 
muscle compartment.
The results of these simulations (Figure 3) showed that 
the results for venous PO2 were similar to FickMM for 
capillary densities in the range of 1100– 1468 mm−2. While 
lower values of capillary density have been reported (Klau-
sen et al., 1981; Qu et al., 1997; Richardson, 1995), prior 
calculations by McGuire and Secomb (2003) demonstrate 
that higher values of capillary density (1100– 1468 mm−2) 
are consistent with measured oxygen uptake and utiliza-
tion rates, suggesting that histologically measured capil-
lary densities may underestimate functional values in vivo. 
For lower capillary densities, the FickMM model would 
exaggerate the V̇O2 levels that could be achieved. Similar 
results were seen for simulations performed with high and 
low affinity hemoglobin variants (P50 = 15.6 and 37 mmHg).
Corresponding calculations with a lower capillary den-
sity and not all cardiac output going to the muscle would 
require a higher oxygen demand to match the values of 
V̇O2max assumed at sea level. If the Krogh model were 
used with a lower capillary density, then the predicted 
values of V̇O2max would be lower than those obtained 
with the FickMM model, but would show similar trends 
with altitude. The value of oxygen demand assumed for 
FickMM was calculated on the basis of the entire cardiac 
output being directed to the muscle compartment. Includ-
ing effects of flow distribution to other organs would re-
sult in lower predicted V̇O2max values. For these reasons, 
the estimates of V̇O2max reported in the paper can be con-
sidered upper bounds.
The determinants of V̇O2max may be represented by 
plotting convective and diffusive limitations of O2 delivery 
as a function of venous PO2, in a graph referred to as a 
“Wagner diagram” (Poole et al., 2012; Wagner, 1996). The 
diffusive limitation on oxygen transport was estimated 
using the Krogh cylinder model, using assumed values of 
capillary density, capillary diameter, intracapillary diffu-
sion resistance, and blood and plasma oxygen diffusivity 
and solubility:
where rc is the capillary radius, K and Kpl are Krogh dif-
fusion coefficients in the tissue and the plasma, and Sh is 
the Sherwood number representing intravascular diffusion 
resistance. The tissue cylinder radius rt is computed based 
on an estimated capillary density obtained from Figure 3, 
such that the tissue PO2 matches the value obtained by the 
FickMM model. Convective oxygen delivery was calculated 
by the Fick principle as in Equation 10. Calculations were 
performed assuming that hemoglobin values did not change 
with altitude (Case 2) and that cardiac output was the same 
in all cases.
(11)
Pv = ̇V O2
[
rt
2 − rc
2
Kpl ∙ Sh −
rt2 − rc2 − 2rt2ln(rt∕rc
)
4K
]
TABLE 3 Assumed parameters and values used in the mathematical model.
Description
Parameter
Value
Units
Source
Sherwood number
Sh
2.5
(Hellums et al., 1996)
Plasma oxygen diffusivity
Dpl
2.18E- 5
cm2 s−1
(Hellums et al., 1996)
Plasma oxygen solubility
αpl
2.82E- 5
mL O2 cm−3 mmHg−1
(Christoforides et al., 1969)
Tissue capillary radius
rc
2.5
μm
(Roy & Secomb, 2014)
Tissue oxygen diffusivity
Dt
2.41E- 5
cm2 s−1
(Bentley et al., 1993)
Tissue oxygen solubility
αt
3.89E- 5
mL O2 cm−3 mmHg−1
(Bentley et al., 1993)
FIGURE 3 Estimates of venous oxygen tension (Pv) obtained 
using the Fick- Michaelis Menten (FickMM) model as compared to 
using a Krogh model with Michaelis– Menten kinetics for muscle 
oxygen utilization. Results are presented as a function of arterial 
oxygen tension (Pa) for various capillary densities (1468, 1100, 
and 700 mm−2) depicted in the figure legend. Computations were 
performed using the oxygen transport parameters in Table 3.
6 of 11 |   
WEBB et al.
2.3 | Cases considered
Cases of low P50, normal P50, and high P50 were investi-
gated. The variation of hemoglobin parameters with alti-
tude is not well established, particularly among humans 
with hemoglobin mutations. To encompass the likely 
range of variations in hemoglobin concentration and P50 
with altitude, various cases indicated in Table 1 were con-
sidered for each hemoglobin variant. These cases include 
ones in which the P50 was assumed to remain constant as 
a function of altitude, and others in which the P50 was as-
sumed to decrease with altitude, as was observed Grocott 
et al. (2009). Corresponding values of hemoglobin concen-
tration were assumed either to be constant or to vary with 
altitude according to the ratio observed experimentally, 
subject to the maximum value (Grocott et al., 2009).
3 | RESULTS
Model predictions of blood oxygenation and V̇O2max as a 
function of altitude are presented for cases of low, normal, 
and high P50, and for several different assumptions about 
the variations of P50 and hemoglobin concentration with 
altitude, as indicated in Table 1.
Profound blood gas alterations occur during human so-
journ to extreme altitudes. Figure 4 displays predicted ox-
ygen transport parameters for the three cases of P50 (low, 
normal, and high) as a function of altitude. The variation 
of arterial oxygen tension with increasing altitude is sim-
ilar for all cases considered. However, arterial oxygen sat-
uration and oxygen content are substantially increased at 
high and extreme altitudes for cases of low P50 compared 
to predicted values for cases of normal P50 and high P50.
The predicted V̇O2max as a function of altitude is de-
picted in Figure 5 for the cases of low, normal, and high P50. 
As expected, V̇O2max decreases with increasing altitude in 
all cases. However, the variation of V̇O2max with altitude is 
markedly dependent on hemoglobin- oxygen affinity. In the 
case of high P50, the predicted V̇O2max at sea level is greater 
than predicted values for normal P50, but markedly lower at 
altitudes above ~2500 m. Conversely, in the case of low P50, 
V̇O2max is lower than values predicted for normal P50 at sea 
level, but greater at altitudes above ~4500 m.
FIGURE 4 Predicted oxygen transport parameters as a function altitude for cases of low, normal, and high hemoglobin- oxygen affinity. 
Data are depicted for several cases of hemoglobin- oxygen affinity (low P50 in blue, normal P50 in red, and high P50 in yellow) with variable 
hemoglobin concentrations to account for potential differences in the hematological response to extreme altitude sojourn indicated in 
Table 1. These parameters are derived for a given tissue oxygen demand that corresponds with sea- level maximum oxygen uptake and 
utilization (V̇O2max). The elevation associated with the summit of Everest is depicted by the dashed vertical line. Parameters corresponding 
to altitudes above 8400 m are derived from the extrapolation of oxygen transport parameters in Grocott et al. (2009). P50, oxygen tension at 
which 50% of hemoglobin is saturated with oxygen.
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WEBB et al.
Predictions of V̇O2max from the present model are pre-
sented in Figure 6 together with lines and curves repre-
senting limitations on oxygen utilization according to the 
Wagner diagram. At sea level, V̇O2max shows small varia-
tions with P50, with a slight advantage at normal P50. At an 
altitude of ~8850 m, convective oxygen delivery is greatly 
reduced and shows a strong inverse dependence on P50. 
The higher rates of convective oxygen delivery at low P50 
result from two factors: higher arterial oxygen saturation 
(~45%, vs. ~30% for high P50) and higher hemoglobin val-
ues (~50% greater than for high P50).
4 | DISCUSSION
4.1 | Physiological implications
V̇O2max is determined by convective and diffusive oxygen 
transport, both of which are influenced by alterations in 
hemoglobin- oxygen affinity (Hebbel et al.,  1977; Webb, 
Elshaer, et al.,  2022b). Specifically, high hemoglobin- 
oxygen affinity tends to enhance pulmonary oxygen up-
take, particularly when alveolar oxygen tension is low, 
increasing convective oxygen transport. On the contrary, 
high hemoglobin- oxygen affinity implies a lower blood 
oxygen tension for a given level of oxygen saturation, 
such that the driving force for oxygen diffusion from 
blood to tissue is reduced. The relative influences of these 
two competing effects of high hemoglobin- oxygen affinity 
(low P50) on V̇O2max cannot easily be discerned by quali-
tative arguments. Therefore, we investigated this rela-
tionship using a mathematical model of oxygen transport 
that includes both pulmonary and systemic circulation 
and considers the effects of both convective and diffusive 
oxygen transport. The model also considers the influence 
of high altitude on oxygen availability and uptake in the 
lungs.
Previous analyses of effects of P50 on oxygen transport 
at extreme altitude suggested that V̇O2max is insensitive to 
P50 over a considerable range (Bencowitz et al., 1982; Wag-
ner, 1997). The present model differs from those analyses 
in two significant respects. First, it includes effects of vari-
ations in hemoglobin levels in individuals with altered P50, 
which results in increased convective oxygen delivery in 
the case of low P50. Second, it takes into account the non-
linear Michaelis– Menten kinetics of oxygen utilization as 
a function of tissue PO2, representing the finite rate of mi-
tochondrial oxygen consumption when oxygen is not rate- 
limiting. Both of these effects result in increased predictions 
FIGURE 5 The dependence of predicted maximum oxygen 
uptake and utilization (V̇O2max) on hemoglobin- oxygen 
affinity (P50) and altitude. Data are depicted for several cases of 
hemoglobin- oxygen affinity (low P50 in blue, normal P50 in red, 
and high P50 in yellow) with variable hemoglobin concentrations 
to account for potential differences in the hematological 
response to extreme altitude sojourn indicated in Table 1. These 
parameters are derived for a given tissue oxygen demand that 
corresponds with sea- level V̇O2max. The elevation associated 
with the summit of Everest is depicted by the dashed vertical line. 
Parameters corresponding to altitudes above 8400 m are derived 
from the extrapolation of oxygen transport parameters in Grocott 
et al. (2009). P50, oxygen tension at which 50% of hemoglobin is 
saturated with oxygen.
FIGURE 6 Predicted oxygen uptake and utilization (V̇O2) 
presented as a Wagner diagram for cases of low, normal, and high 
P50. Data for each group are presented at sea- level (solid lines) 
and an altitude of ~8850 m (summit of Mt. Everest, represented by 
dashed lines). The V̇O2max value is depicted by the intersection 
between convective oxygen transport (curved lines obtained via 
Fick principle) and diffusive oxygen transport (dotted line passing 
through the origin). Open circles plotted on curved lines denote the 
predicted V̇O2max as determined using Michaelis– Menten kinetics. 
Pa, arterial oxygen tension; V̇O2, oxygen uptake and utilization, 
P50; oxygen tension at which 50% of hemoglobin is saturated with 
oxygen. Values of Pa and P50 are in units of mmHg.
8 of 11 |   
WEBB et al.
of V̇O2max at extreme altitude for reduced P50, and account 
for the apparent discrepancy with the earlier work.
The diffusive limitation of oxygen transport, Equa-
tion  11, is computed assuming a uniform rate of oxy-
gen consumption throughout the tissue. In contrast, the 
FickMM model allows for variations of oxygen levels and 
oxygen consumption rates in the tissue, including possi-
ble hypoxic regions. The resulting estimates of V̇O2max at 
altitude are slightly higher than those obtained from the 
intersections of the diffusive limitation line and the con-
vective delivery curves, as shown in Figure 6. This differ-
ence is most evident in the case of low P50. The diffusive 
limitation line shown in Figure 6 is based on the assump-
tion that PO2 values approach zero only at the point in 
the tissue furthest from the distal end of the supplying 
capillary. If oxygen demand is further increased, overall 
oxygen consumption can increase beyond the value im-
plied by diffusive limitation, even if some regions of tis-
sue are hypoxic (McGuire & Secomb, 2001).
Humans at high altitude experience a range of acute 
(dehydration, alkalosis, hypocapnia) and chronic (train-
ing, acclimatization) effects, both of which may be 
associated with variations in P50 and hemoglobin con-
centration (Mairbaurl & Weber, 2012; Monge & Leon- 
Velarde, 1991; Windsor & Rodway, 2007). Because these 
effects are not widely characterized among humans 
with hemoglobin mutations, we considered a range of 
cases for each case of hemoglobin- oxygen affinity (low, 
normal, and high P50). Thus, the predicted V̇O2max is 
provided with a range of values for each altitude and 
case examined, providing an indication of the sensitivity 
of the model to these potential variations in P50 and he-
moglobin concentration. Individual variations in phys-
iological parameters such as capillary density and lung 
diffusing capacity, as well as potential alterations of 
these parameters during extreme altitude sojourn, may 
be substantial and would obviously affect the predictions 
of this model. However, the primary trends in V̇O2max 
as a function of altitude are likely to remain similar even 
if baseline values are notably different. Other parame-
ters of oxygen transport, such as lung diffusing capacity 
and the respiratory quotient, may vary with altitude but 
are assumed to be constant in the model. Additionally, 
the effects of non- muscle blood flow on overall oxy-
gen transport are not considered, as the entire cardiac 
output is assumed to be directed to the skeletal muscle 
during maximal exercise.
Our results revealed that at low altitudes, where at-
mospheric pressure is more than sufficient to cause 
nearly complete saturation of hemoglobin, a low P50 does 
not confer an advantage in terms of oxygen utilization 
since convective transport is sufficient to supply skeletal 
muscle. At high altitudes, however, a low P50 increases 
convective oxygen delivery due to higher oxygen satu-
ration values, despite the diffusion limitation resulting 
from lower blood oxygen tension. This improved oxy-
gen delivery allows for better preservation of V̇O2max at 
high altitudes. In summary, a low P50 leads to a reduced 
driving force for oxygen diffusion from blood to tissue at 
low altitudes yet increased convective oxygen delivery 
at high altitudes. These two competing tendencies ap-
proximately cancel at an altitude of ~4500 m such that 
high hemoglobin- oxygen affinity confers an advantage 
at higher altitudes.
In the results presented here, the effects of capillary 
density are not explicitly considered under the approx-
imation that venous oxygen tension is representative of 
tissue oxygen tension. More detailed calculations show 
that high capillary densities can lead to greater tissue 
oxygen tensions values than assumed here. A high cap-
illary density may facilitate the advantage conferred by 
a low P50 due to decreased diffusion limitation. Con-
versely, a low capillary density may negate the advan-
tage of a low P50 at high and extreme altitude because 
oxygen delivery would then be limited by reduced mus-
cle diffusing capacity.
Practical applications
Studies in comparative physiology show a wide range 
of adaptations to altitude, some of which have sup-
ported that an increase in hemoglobin- oxygen affinity 
is likely beneficial for species adapted to high and ex-
treme altitude (Natarajan et al., 2018; Storz, 2007; Storz 
et al., 2010). Across species, multiple factors including 
evolutionary pressures may influence the observed ad-
aptations in hemoglobin- oxygen affinity. Further de-
tailed investigation of this topic in terms of convective 
versus diffusive oxygen transport limitations would be 
appropriate, and the theoretical approach developed 
here may be applicable to such studies.
Pharmacological agents have been developed that 
can alter P50 in healthy individuals (Henry et al., 2021; 
Safo & Kato, 2014; Woyke et al., 2021). Although these 
agents are mainly investigated for treatment of sickle- cell 
disease, they have also been used in healthy individuals 
(Stewart et al., 2021, 2020). According to the present re-
sults, decreasing the P50 has significant effects on blood 
oxygenation and V̇O2max at altitude, some of which 
may prove beneficial depending on the environmental 
context. For instance, pharmacologically decreasing the 
P50 may have an ergogenic effect at high and extreme 
altitudes by increasing arterial blood saturation and im-
proving convective oxygen delivery. This raises the pos-
sibility that such agents could be used for “blood doping” 
in competitive sports. In military operations at high and 
extreme altitudes, environmental conditions may limit 
   | 9 of 11
WEBB et al.
physical performance and cognitive function (McLaugh-
lin et al., 2017). Pharmacological reduction in P50 may in-
crease hypoxia tolerance (Dufu et al., 2021) and prevent 
decrements in physical performance (Stewart et al., 2021). 
However, further work is needed to examine the advan-
tages or disadvantages of pharmacologically altering P50 
in healthy individuals in various contexts. The present 
model may be useful for predicting the change in P50 at a 
given altitude that maximizes the ergogenic effect.
4.3 | Limitations
A major simplification of this model is the use of venous 
PO2 as a measure of tissue PO2 for the purpose of cal-
culating oxygen consumption according to Michaelis– 
Menten kinetics. The rationale for this assumption is 
that venous PO2 typically lies within the range of the 
minimum and maximum tissue PO2. As shown in Fig-
ure 3, oxygen consumption rates calculated under this 
assumption show reasonable agreement with more de-
tailed calculations using a Krogh cylinder model. This 
approach avoids the need to specify the geometry of the 
capillary network, since such detailed information is 
generally not available. However, the limitation of this 
approach is that it does not include the effects of capil-
lary network geometry.
Previous studies have indicated that the Bohr effect (pH 
dependent change in the P50) may play a notable role in 
the determination of V̇O2max (Severinghaus, 1994). How-
ever, this effect was not considered in the present model. 
Because the magnitude of the Bohr effect at extreme alti-
tudes is not known, it was excluded to facilitate comparisons 
across altitudes. Given that the Bohr effect is generally pre-
served among humans with hemoglobin mutations (Boyer 
et al., 1972), its effect on V̇O2max values would likely be uni-
directional and comparable between the groups examined. 
Additionally, past investigations have described aberrations 
in metabolic processes during exercise among humans with 
low P50 and suggested that skeletal muscle and mitochon-
drial adaptations may compensate for the blunted oxygen 
offloading (Wranne et al., 1983). At extreme altitude, how-
ever, V̇O2max is severely limited by the reduced oxygen 
availability, such that changes in maximal mitochondrial 
oxygen consumption are unlikely to affect V̇O2max. There-
fore, the present model assumes similar mitochondrial 
function between groups with normal and altered P50.
5 | CONCLUSION
The presented analyses leverage experimental data 
among 
humans 
with 
hemoglobin 
mutations 
to 
predict blood oxygenation and V̇O2max as a function 
of hemoglobin- oxygen affinity and altitude. We posit 
that high hemoglobin- oxygen affinity leads to improved 
blood oxygenation and better preserved V̇O2max values 
at extreme altitudes compared to values associated with 
normal hemoglobin- oxygen affinity. Additionally, we 
provide theoretical estimates for V̇O2max as a function 
of altitude among humans with mutations causing low 
hemoglobin- oxygen affinity, which has yet to be exam-
ined experimentally.
AUTHOR CONTRIBUTIONS
Kevin L. Webb and Tuhin K. Roy conceived the presented 
idea. All author contributed to the methodological design 
of this work. Kevin L. Webb, Tuhin K. Roy, and Timothy 
W. Secomb contributed to model development, analyses, 
and data visualization. Kevin L. Webb and Tuhin K. Roy 
constructed the initial manuscript draft. All authors con-
tributed to manuscript revising and have approved the 
final submission.
ACKNOWLEDGMENTS
The authors would like to thank the members of the 
Human and Integrative Physiology and Clinical Pharma-
cology Laboratory at the Mayo Clinic for intellectual dis-
cussion and feedback.
FUNDING INFORMATION
This work was funded by the National Institutes of Health 
grant R35- HL139854 (M.J.J.).
CONFLICT OF INTEREST STATEMENT
The authors have no conflict of interest to declare.
ETHICS STATEMENT
The presented study was exempt from obtaining IRB 
approval and does not present novel data pertaining to 
human nor animal subjects.
DATA AVAILABILITY STATEMENT
All pertinent data are presented within the manuscript. 
All code used to perform calculations will be shared upon 
reasonable request.
ORCID
Kevin L. Webb 
 https://orcid.org/0000-0003-3015-6076 
Michael J. Joyner 
 https://orcid.org/0000-0002-7135-7643 
Chad C. Wiggins 
 https://orcid.org/0000-0002-6458-0142 
Timothy W. Secomb 
 https://orcid.
org/0000-0002-0176-5502 
Tuhin K. Roy 
 https://orcid.org/0000-0002-8182-7629 
10 of 11 |   
WEBB et al.
REFERENCES
Bencowitz, H. Z., Wagner, P. D., & West, J. B. (1982). Effect of 
change in P50 on exercise tolerance at high altitude: A theoret-
ical study. Journal of Applied Physiology (1985), 53, 1487– 1495. 
https://doi.org/10.1152/jappl.1982.53.6.1487
Bentley, T. B., Meng, H., & Pittman, R. N. (1993). Temperature 
dependence of oxygen diffusion and consumption in mam-
malian striated muscle. American Journal of Physiology, 264, 
H1825– H1830.
Boyer, S. H., Charache, S., Fairbanks, V. F., Maldonado, J. E., Noyes, 
A., & Gayle, E. E. (1972). Hemoglobin Malmö β- 97 (FG- 4) his-
tidine→glutamine: A cause of polycythemia. The Journal of 
Clinical Investigation, 51, 666– 676.
Calbet, J. A. L., & Boushel, R. (2015). Assessment of cardiac output 
with transpulmonary thermodilution during exercise in hu-
mans. Journal of Applied Physiology (1985), 118, 1– 10. https://
doi.org/10.1152/jappl physi ol.00686.2014
Charache, S., Weatherall, D. J., & Clegg, J. B. (1966). 
Polycythemia associated with a hemoglobinopathy. The 
Journal of Clinical Investigation, 45, 813– 822. https://doi.
org/10.1172/JCI10 5397
Christoforides, C., Laasberg, L. H., & Hedley- Whyte, J. (1969). Effect 
of temperature on solubility of O2 in human plasma. Journal of 
Applied Physiology, 26, 56– 60.
Dominelli, P. B., Wiggins, C. C., Baker, S. E., Shepherd, J. R. A., 
Roberts, S. K., Roy, T. K., Curry, T. B., Hoyer, J. D., Oliveira, 
J. L., & Joyner, M. J. (2020). Influence of high affinity haemo-
globin on the response to normoxic and hypoxic exercise. The 
Journal of Physiology, 598, 1475– 1490. https://doi.org/10.1113/
JP279161
Dufu, K., Williams, A. T., Muller, C. R., Walser, C. M., Lucas, A., 
Eaker, A. M., Alt, C., Cathers, B. E., Oksenberg, D., & Cabrales, P. 
(2021). Increased hemoglobin affinity for oxygen with GBT1118 
improves hypoxia tolerance in sickle cell mice. American 
Journal of Physiology. Heart and Circulatory Physiology, 321, 
H400– H411. https://doi.org/10.1152/ajphe art.00048.2021
Golub, A. S., & Pittman, R. N. (2012). Oxygen dependence of respi-
ration in rat spinotrapezius muscle in situ. American Journal 
of Physiology. Heart and Circulatory Physiology, 303, H47– H56. 
https://doi.org/10.1152/ajphe art.00131.2012
Grocott, M. P. W., Levett, D. Z. H., & Windsor, J. (2009). Arterial 
blood gases and oxygen content in climbers on Mount Everest. 
The New England Journal of Medicine, 360, 140– 149. https://
doi.org/10.1056/NEJMo a0801581
Hebbel, R. P., Eaton, J. W., Kronenberg, R. S., Zanjani, E. D., Moore, 
L. G., & Berger, E. M. (1978). Human llamas: Adaptation to 
altitude in subjects with high hemoglobin oxygen affinity. 
The Journal of Clinical Investigation, 62, 593– 600. https://doi.
org/10.1172/JCI10 9165
Hebbel, R. P., Kronenberg, R. S., & Eaton, J. W. (1977). Hypoxic 
ventilatory response in subjects with normal and high oxygen 
affinity hemoglobins. The Journal of Clinical Investigation, 60, 
1211– 1215. https://doi.org/10.1172/JCI10 8874
Hellums, J. D., Nair, P. K., Huang, N. S., & Ohshima, N. (1996). 
Simulation of intraluminal gas transport processes in the mi-
crocirculation. Annals of Biomedical Engineering, 24, 1– 24. 
https://doi.org/10.1172/JCI10 8874
Henry, E. R., Metaferia, B., Li, Q., Harper, J., Best, R. B., Glass, K. E., 
Cellmer, T., Dunkelberger, E. B., Conrey, A., Thein, S. L., Bunn, 
H. F., & Eaton, W. A. (2021). Treatment of sickle cell disease 
by increasing oxygen affinity of hemoglobin. Blood, 138, 1172– 
1181. https://doi.org/10.1182/blood.20210 12070
Hsia, C. C. W. (1998). Respiratory function of hemoglobin. New 
England Journal of Medicine, 338, 239– 248. https://doi.
org/10.1056/NEJM1 99801 22338 0407
Klausen, K., Andersen, L. B., & Pelle, I. (1981). Adaptive changes in 
work capacity, skeletal muscle capillarization and enzyme levels 
during training and detraining. Acta Physiologica Scandinavica, 
113, 9– 16. https://doi.org/10.1111/j.1748- 1716.1981.tb068 54.x
Mairbaurl, H., & Weber, R. E. (2012). Oxygen transport by hemo-
globin. Comprehensive Physiology, 2, 1463– 1489. https://doi.
org/10.1002/cphy.c080113
McGuire, B. J., & Secomb, T. W. (2001). A theoretical model for 
oxygen transport in skeletal muscle under conditions of high 
oxygen demand. Journal of Applied Physiology, 91, 2255– 2265. 
https://doi.org/10.1152/jappl.2001.91.5.2255
McGuire, B. J., & Secomb, T. W. (2003). Estimation of capillary 
density in human skeletal muscle based on maximal oxygen 
consumption rates. American Journal of Physiology. Heart 
and Circulatory Physiology, 285, H2382– H2391. https://doi.
org/10.1152/ajphe art.00559.2003
McLaughlin, C. W., Skabelund, A. J., & George, A. D. (2017). Impact 
of high altitude on military operations. Current Pulmonology 
Reports, 6, 146– 154. https://doi.org/10.1007/s1366 5- 017- 0181- 0
Monge, C., & Leon- Velarde, F. (1991). Physiological adaptation 
to high altitude: Oxygen transport in mammals and birds. 
Physiological Reviews, 71, 1135– 1172. https://doi.org/10.1152/
physr ev.1991.71.4.1135
Natarajan, C., Jendroszek, A., Kumar, A., Weber, R. E., Tame, J. R. 
H., Fago, A., & Storz, J. F. (2018). Molecular basis of hemoglobin 
adaptation in the high- flying bar- headed goose. PLoS Genetics, 
14, e1007331. https://doi.org/10.1371/journ al.pgen.1007331
Poole, D. C., Hirai, D. M., Copp, S. W., & Musch, T. I. (2012). Muscle 
oxygen transport and utilization in heart failure: Implications 
for exercise (in)tolerance. American Journal of Physiology. 
Heart and Circulatory Physiology, 302, H1050– H1063. https://
doi.org/10.1152/ajphe art.00943.2011
Popel, A. S. (1989). Theory of oxygen transport to tissue. Critical 
Reviews in Biomedical Engineering, 17, 257– 321.
Qu, Z., Andersen, J. L., & Zhou, S. (1997). Visualisation of capillaries 
in human skeletal muscle. Histochemistry and Cell Biology, 107, 
169– 174. https://doi.org/10.1007/s0041 80050101
Richardson, R. (1995). Oxygen transport to tissue XVI (1st ed.). 
Springer.
Roy, T. K., & Secomb, T. W. (2014). Theoretical analysis of the deter-
minants of lung oxygen diffusing capacity. Journal of Theoretical 
Biology, 351, 1– 8. https://doi.org/10.1016/j.jtbi.2014.02.009
Roy, T. K., & Secomb, T. W. (2019). Effects of pulmonary flow 
heterogeneity on oxygen transport parameters in exercise. 
Respiratory Physiology & Neurobiology, 261, 75– 79. https://doi.
org/10.1016/j.resp.2018.10.004
Safo, M. K., & Kato, G. J. (2014). Therapeutic strategies to Alter oxy-
gen affinity of sickle hemoglobin. Hematology/Oncology Clinics 
of North America, 28, 217– 231. https://doi.org/10.1016/j.
hoc.2013.11.001
Severinghaus, J. W. (1994). Exercise O2 transport model assum-
ing zero cytochrome PO2 at VO2max. Journal of Applied 
Physiology (1985), 77, 671– 678, 678. https://doi.org/10.1152/
jappl.1994.77.2.671
   | 11 of 11
WEBB et al.
Stewart, G. M., Chase, S., Cross, T. J., Wheatley- Guy, C. M., Joyner, 
M., Curry, T., Lehrer- Graiwer, J., Dufu, K., Vlahakis, N. E., & 
Johnson, B. D. (2020). Effects of an allosteric hemoglobin af-
finity modulator on arterial blood gases and cardiopulmonary 
responses during normoxic and hypoxic low- intensity exercise. 
Journal of Applied Physiology (1985), 128, 1467– 1476. https://
doi.org/10.1152/jappl physi ol.00185.2019
Stewart, G. M., Cross, T. J., Joyner, M. J., Chase, S. C., Curry, T., 
Lehrer- Graiwer, J., Dufu, K., Vlahakis, N. E., & Johnson, B. D. 
(2021). Impact of pharmacologically left shifting the oxygen– 
hemoglobin dissociation curve on arterial blood gases and 
pulmonary gas exchange during maximal exercise in hypoxia. 
High Altitude Medicine & Biology, 22(3), 249– 262.
Storz, J. F. (2007). Hemoglobin function and physiological adaptation 
to hypoxia in high- altitude mammals. Journal of Mammalogy, 
88, 24– 31. https://doi.org/10.1644/06- MAMM- S- 199R1.1
Storz, J. F., Scott, G. R., & Cheviron, Z. A. (2010). Phenotypic plas-
ticity and genetic adaptation to high- altitude hypoxia in ver-
tebrates. The Journal of Experimental Biology, 213, 4125– 4136. 
https://doi.org/10.1242/jeb.048181
Thom, C. S., Dickson, C. F., Gell, D. A., & Weiss, M. J. (2013). 
Hemoglobin variants: Biochemical properties and clinical cor-
relates. Cold Spring Harbor Perspectives in Medicine, 3, a011858. 
https://doi.org/10.1101/cshpe rspect.a011858
van der Steeg, G. E., & Takken, T. (2021). Reference values for 
maximum oxygen uptake relative to body mass in Dutch/
Flemish subjects aged 6– 65 years: The LowLands fitness reg-
istry. European Journal of Applied Physiology, 121, 1189– 1196. 
https://doi.org/10.1007/s0042 1- 021- 04596 - 6
Wagner, P. D. (1996). Determinants of maximal oxygen transport 
and utilization. Annual Review of Physiology, 58, 21– 50. https://
doi.org/10.1146/annur ev.ph.58.030196.000321
Wagner, P. D. (1997). Insensitivity of VO2max to hemoglobin- P50 
at sea level and altitude. Respiration Physiology, 107, 205– 212. 
https://doi.org/10.1016/s0034 - 5687(96)02512 - 1
Webb, K. L., Dominelli, P. B., Baker, S. E., Klassen, S. A., Joyner, 
M. J., Senefeld, J. W., & Wiggins, C. C. (2022a). Influence of 
high hemoglobin- oxygen affinity on humans during hypoxia. 
Frontiers in Physiology, 12, 763– 933. https://doi.org/10.3389/
fphys.2021.763933
Webb, K. L., Elshaer, A. N., Dominelli, P. B., Senefeld, J. W., Hammer, 
S. M., Baker, S. E., Shepherd, J. R. A., Roy, T. K., Joyner, M. J., 
& Wiggins, C. C. (2022b). Muscle oxygenation during normoxic 
and hypoxic cycling exercise in humans with high- affinity hae-
moglobin. Experimental Physiology, 107, 854– 863. https://doi.
org/10.1113/EP090308
West, J. B. (1999). Barometric pressures on Mt. Everest: New data and 
physiological significance. Journal of Applied Physiology (1985), 
86, 1062– 1066. https://doi.org/10.1152/jappl.1999.86.3.1062
Windsor, J. S., & Rodway, G. W. (2007). Heights and haematology: The 
story of haemoglobin at altitude. Postgraduate Medical Journal, 
83, 148– 151. https://doi.org/10.1136/pgmj.2006.049734
Woyke, S., Mair, N., Ortner, A., Haller, T., Ronzani, M., Rugg, C., 
Ströhle, M., Wintersteiger, R., & Gatterer, H. (2021). Dose-  and 
sex- dependent changes in hemoglobin oxygen affinity by the 
micronutrient 5- Hydroxymethylfurfural and α- ketoglutaric 
acid. Nutrients, 13, 3448. https://doi.org/10.3390/nu131 03448
Wranne, B., Berlin, G., Jorfeldt, L., & Lund, N. (1983). Tissue ox-
ygenation and muscular substrate turnover in two subjects 
with high hemoglobin oxygen affinity. The Journal of Clinical 
Investigation, 72, 1376– 1384. https://doi.org/10.1172/JCI11 
1094
How to cite this article: Webb, K. L., Joyner, M. 
J., Wiggins, C. C., Secomb, T. W., & Roy, T. K. 
(2023). The dependence of maximum oxygen 
uptake and utilization (V̇O2max) on hemoglobin- 
oxygen affinity and altitude. Physiological Reports, 
11, e15806. https://doi.org/10.14814/phy2.15806

The dependence of maximum oxygen uptake and utilization (V̇O<sub>2</sub> max) on hemoglobin-oxygen affinity and altitude.
Webb, Kevin L,Joyner, Michael J,Wiggins, Chad C,Secomb, Timothy W,Roy, Tuhin K