A method for modelling the oxyhaemoglobin dissociation curve at the level of the cerebral

capillary in humans

Rasmus H. Dahl,1 MD; Sarah Taudorf,2 MD, PhD; Damian M. Bailey,3 PhD;Kirsten Møller,1,4 MD, PhD, DMSc; Ronan M. G. Berg,3,5,6 MD, PhD

1Department of Neuroanaesthesiology, University Hospital Rigshospitalet, Copenhagen, Denmark; 2Department of Neurology, University Hospital Rigshospitalet, Copenhagen, Denmark; 3Neurovascular Research Laboratory, Faculty of Life Sciences and Education, University of South Wales, Pontypridd, United Kingdom; 4Department of Clinical Medicine, Faculty of Health Sciences, University of Copenhage;5Department of Biomedical Sciences, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark;6Department of Clinical Physiology, Nuclear Medicine & PET and Centre for Physical Activity Research, University Hospital Rigshospitalet, Copenhagen, Denmark.

Running head: Cerebral capillary ODCWord count (including abstract and references): 3430; Figures: 4; Tables: 0; References: 18Target journal: Experimental Physiology (Short communication)

Corresponding Author:Dr. Ronan M. G. Berg, Associate ProfessorDepartment of Biomedical SciencesThe Panum Institute, room 10.5.19Faculty of Health and Medical SciencesUniversity of CopenhagenBlegdamsvej 32200 Copenhagen NCopenhagenE-mail: ronan@sund.ku.dkORCID ID: 0000-0002-5757-9506

Co-author e-mails:Rasmus H. Dahl: rhd@dadlnet.dkSarah Taudorf: sarahtaudorf@dadlnet.dkDamian M. Bailey: damian.bailey@southwales.ac.ukKirsten Møller: kirsten.moller@dadlnet.dk

Conflicts of Interest: The authors have no conflicts of interest to declare.

Keywords: brain oxygenation; half-saturation constant; Hill coefficient; Hill slope; oxyhaemoglobin dissociation curve

1

Abstract

In the present paper, we provide a method for modelling the oxyhaemoglobin dissociation curve

(ODC) in the cerebral capillary in humans. In contrast to previous approaches, where the cerebral

capillary ODC is assumed to be identical to either a standard or measured arterial ODC, our

method involves the construction of an averaged ODC based on paired arterial-jugular venous

blood gas values. The averaged ODC enables estimation of oxygen parameters in the cerebral

capillary blood.

The method was used to determine the mean cerebral capillary oxygen saturation and

tension, as well as mean mitochondrial oxygen tension in 30 healthy volunteers. The averaged

ODC provided systematically higher capillary and mitochondrial oxygen tensions than when

assuming a ‘fixed’ standard arterial ODC. When the averaged and measured arterial ODC were

used for constructing the capillary ODC, similar values were obtained during resting breathing,

but not when the arterial ODC was modulated by hypocapnia.

The findings suggest that our method for modelling the cerebral capillary ODC provides

robust and physiologically reliable estimates of cerebral capillary and mitochondrial oxygen

tensions in humans both during normal resting conditions and during voluntary hyperventilation.

We furthermore introduce a revised model for capillary oxygen transport considering the

dissolved oxygen. Altogether, we provide a method to credibly estimate the cerebral capillary

oxygen tension, both in normo- and pathophysiological states.

2

Introduction

A change in the oxygen affinity of haemoglobin (Hb) during the red blood cell’s passage through

target tissue capillaries is a fundamental aspect of oxygen transfer to target tissues (Woodson,

1988; Gjedde et al., 2011). However, in human-experimental studies of brain oxygenation, the

underlying configurational changes in the oxyhaemoglobin curve (ODC) are rarely considered,

probably because no method currently exists for determining the ODC at the level of the cerebral

capillary. In several previous studies conducted by us and others, this has been resolved by

assuming that the ODC does not change between the arterial and cerebral capillary bed (Vafaee

& Gjedde, 2000; Rasmussen et al., 2006, 2010; Gjedde et al., 2011; Bailey et al., 2011).

In the present paper, we provide a novel method which models changes in the ODC in the

cerebral microvasculature, so that the cerebral capillary ODC can be reconstructed from paired

arterial-jugular venous P O2 and S O2-values. We use this method to estimate average cerebral

capillary and mitochondrial oxygen tensions during normo- and hyperventilation in healthy

humans and evaluate to which extent these estimates differ from values obtained when no

configurational changes in the ODC are considered. We hypothesize that capillary oxygen

parameters will be systematically underestimated when using the arterial or standard ODCs

compared to the averaged ODC calculated from paired arterial-jugular venous blood gas values.

3

Methods

Capillary oxyhaemoglobin dissociation curve

The Hill equation represents a simple model of the sigmoid shape of the ODC, where the ODC-

defining parameters are the P50-value, which reflects the dissociation constant, and the Hill

coefficient, h, which is the cooperativity. P50 is defined as the oxygen tension when Hb is half-

saturated and h is the maximum slope of the ODC (Hill, 1910; Mairbäurl & Weber, 2012). The

Hill equation relates these ODC-defining parameters to the oxygen tension, P O2, and oxygen

saturation, S O2.

The physiological increase in the acidity and carbon dioxide tension from the arterial inlet

to the venous outlet changes the P50-value and Hill’s coefficient throughout the capillary (Gjedde

et al., 2011). However, an averaged ODC with constant ODC-defining parameters is required for

modelling the capillary oxygen transport. This can be estimated from paired arterial and jugular-

venous blood gas values by assuming that they fulfil the Hill equations in both vascular beds.

Hill’s coefficient is

h=

ln( Sa O2

1−SaO2)−ln ( Sv O2

1−SvO2)

ln ( PaO2 )−ln ( Pv O2 )

(Eq. 1)

and P50 can be calculated by insertion of the Hill coefficient into the Hill equation using arterial

or jugular-venous blood gas values.

P50=Pa O2⋅( Sa O2

1−Sa O2)−1

h =Pv O2 ⋅( Sv O2

1−Sv O2)−1h

(Eq. 2)

4

Here, PaO2 and Pv O2 are the oxygen tensions, and SaO2 and SvO2 are the oxygen saturations

measured in arterial and jugular-venous blood, respectively. We assume that values measured in

arterial and jugular-venous blood approximate the oxygen tension and saturation in the arterial

and venous end of the capillary, respectively.

Modelling capillary oxygen transport

The mean capillary oxygen tension, P cap O2, and saturation, Scap O2, may be determined

following modification of established mathematical formalism (Gjedde et al., 2011). The

cerebral transfer of oxygen was originally assumed to occur uniformly throughout the cerebral

capillary bed, because the microvascular anatomy ensures that every capillary segment supplies

equivalent brain volumes (Kety, 1957; Weibel, 1984; Gjedde et al., 2011). As blood flows

through the capillary from the arterial inlet to the venous outlet, the capillary oxygen extraction,

E O2, increases and the total capillary oxygen content, Ccap O2, decreases proportionally with the

distance traversed.

Now let the fraction of the capillary bed already served by the blood stream be denoted

by z, which ranges from 0 to 1. The full capillary range spans from the arterial inlet (z = 0) to the

venous outlet (z = 1). The assumption of uniform oxygen transfer ensures that the capillary

oxygen extraction fraction at position z, equals the fraction, z, of the arterial to jugular-venous

oxygen extraction fraction, EO 2. From the definition of the oxygen extraction fractions we have:

z=CaO2−Ccap O2

CaO2−Cv O2

(Eq. 3)

5

Here, CaO2, Cv O2 and Ccap O2 are the total oxygen contents in arterial, jugular-venous, and

capillary blood. The total oxygen content is defined as the sum of haemoglobin-bound and

dissolved oxygen, such that the capillary oxygen content equals:

Ccap O2=Hb ⋅ ScapO2+α O2⋅Pcap O2

(Eq. 4)

where Hb is the haemoglobin concentration, Scap O2 is the capillary oxygen saturation,Pcap O2

is the capillary oxygen tension and α is the solubility coefficient of oxygen in blood. Insertion of

the above expression into Eq. 3 shows that z can be expressed in term of the capillary variables

Pcap O2 and Scap O2, and the arterial and jugular-venous oxygen content:

z=CaO2−(Hb⋅ ScapO2+α O2

⋅Pcap O2)CaO2−Cv O2

(Eq. 5)

This expression shows the relationship between z, Pcap O2, and Scap O2. The ODC finally

relates the ScapO2 to Pcap O2, which can be used to eliminate either Scap O2 or Pcap O2 in the

above formula. The averaged ODC can be estimated from paired arterial-jugular venous blood

gas values using Eqs. 1 and 2. The Hill equation is shown in two different forms, which can be

inserted directly into Eq. 5.

Pcap O2=P50⋅( Scap O2

1−ScapO2)

1h Scap O2=

1

1+( P50

Pcap O2 )h

(Eqs. 6 and 7)

In the following we define three profile curves showing the oxygen tension P(z ), oxygen

saturation S(z ) and total oxygen content C (z) as function of the fractional distance traversed.

Insertion of Eqs. 6 or 7 into Eq. 5 allow the construction of profile curves for the oxygen tension

6

and saturation, while Eq. 3 shows that there is a linear relationship between the total oxygen

content and z. All profile curves decrease throughout the capillary as the oxygen is delivered to

the tissue (Fig. 1).

Mean capillary oxygen tension and saturation

The mean capillary oxygen tension, P cap O2, and oxygen saturation, S cap O2, equals the area

under the respective profile curves, but due to the complexity of Eq. 5, the profile curves can not

be expressed in simple terms. Instead, the area under the profile curves may be calculated by

integration of the inverse function of the profile curves by shifting the interval of integration.

Since the inverse function of the profile curves equal Eq. 5, we have:

P capO2=∫0

1

P(z )dz=Pv O2+ ∫Pv O2

Pa O2

z dPcap O2

S capO2=∫0

1

S(z )dz=SvO2+ ∫Sv O2

Sa O2

z dScap O2

(Eqs. 8 and 9)

Formulas for the mean oxygen tension and saturation are derived:

P cap O2=Pv O2+( Pa O2−Pv O2 ) ⋅CaO2−C '

Ca O2−Cv O2

S cap O2=Sv O2+( SaO2−Sv O2 )⋅CaO2−C ' '

Ca O2−Cv O2

(Eqs. 10 and 11)

where C ' and C ' ' are defined:

C '=α O2 ⋅Pa O2+ Pv O2

2+Hb ⋅SODC

7

C ' '=α O 2⋅PODC+Hb⋅Sa O2+SvO2

2

(Eqs. 12 and 13)

Here SODC and PODC are the mean oxygen saturation and tension measured on the ODC curves

defined in Eqs. 6 and 7. These mean values are calculated by integration of the Hills equations

from the arterial inlet to venous outlet.

SODC=1

PaO2−Pv O2⋅ ∫

Pv O2

Pa O2 (1+( P50

Pcap O2 )h

)−1

dPcap O2

PODC=1

Sa O2−Sv O2∫

SvO 2

SaO 2

P50⋅( Scap O2

1−ScapO2 )1h dScap O2

(Eqs. 14 and 15)

We specifically use the Hill equation to estimate the ODC, notwithstanding that other

mathematical models are available in the literature (Adair, 1925; Severinghaus, 1979; Siggaard-

Andersen et al., 1984). By changing the integrand in Eq. 14 and 15, the method described above

may also be used with other ODC models.

Mean mitochondrial oxygen tension

The oxygen delivery to target tissue mitochondria depends on the oxygen tension gradient over

the capillary wall and the oxygen diffusion capacity in the segment z of the capillary (Gjedde,

2005). No methods currently exist for direct measurement of the mitochondrial oxygen tension.

Therefore, our calculations are based on the mean oxygen diffusion capacity, L O2, that have

been estimated during hypoxia under assumptions described elsewhere (Gjedde et al., 2011). The

mean mitochondrial oxygen tension is:

8

P mit O2=P capO2−J O2

LO2

(Eq. 17)

The cerebral metabolic rate of oxygen, J O2, is calculated from the cerebral blood flow (CBF)

and the arterial-to-jugular venous oxygen content difference according to the Fick principle.

J O2=(CaO2−Cv O2 )⋅CBF

(Eq. 18)

Experimental setup

We included data from two previously published experimental studies that were approved by the

Scientific-Ethical Committee of Copenhagen and Frederiksberg Municipalities (file number KF-

01-207/04 and KF-01-144/98 with amendment KF-11-095/00). The current study describes

entirely separate measurements to address an independent working hypothesis.

Study A included 22 male volunteers aged 31 (7) years in which cerebral blood flow

(CBF) was determined by the Kety-Schmidt technique using inhaled N2O (5 %) as the tracer in

the desaturation phase and by discontinuous blood sampling during resting breathing at sea level

(Taudorf et al., 2009). Paired blood samples were obtained from a radial artery and the right

internal jugular vein. Blood samples were then analysed on a blood gas analyser (ABL 605 and

OSM 3, Radiometer, Brønshøj, Denmark).

Study B included 8 healthy volunteers (one female) aged 25 (3) years, in which CBF was

determined by the Kety-Schmidt technique using intravenous 133Xe dissolved in saline as the

tracer in the desaturation phase, while paired blood samples were obtained from a radial artery

and the right internal jugular vein, and analysed on a blood gas analyser (ABL 610 and OSM 3,

9

Radiometer, Brønshøj, Denmark). Measurements were done at sea level during resting breathing

and following 15 minutes of voluntary hyperventilation (Møller et al., 2002).

Calculations

In all volunteers (Study A + B), the ODC-defining parameters h and P50 were determined by

insertion of measured arterial and jugular-venous oxygen tensions and saturations into Eqs. 1

and 2. These values were then used to calculate the mean oxygen tension, PODC, and saturation,

SODC, of the ODC by Eqs. 14 and 15.

The mean capillary oxygen tension and saturation were subsequently calculated using

Eqs. 10-15. First SODC and PODC were inserted into Eq. 12 and 13 for calculation of the

parameters C ' and C ' ' , and these were finally inserted into Eqs. 10 and 11 for determination of

P capO2 and S capO2.

In Eqs. 12 and 13, and for calculation of arterial and jugular-venous oxygen content, the

arterial haemoglobin values were used, and α O2 was assumed to be 0.01 mmol L−1 kP a−1.

P capO2-values were furthermore used to calculate P mit O2 values by Eq. 17, where the mean

cerebral oxygen diffusion capacity, L O2, was assumed to be 33.0 μmol (100 g )−1 min−1 kP a−1

(Vafaee & Gjedde, 2000; Rasmussen et al., 2006).

ODC-defining parameters

The impact of a ‘fixed’ ODC from the arterial to the cerebral capillary level was examined using

either standard arterial or measured arterial P50- and h-values. Henceforth, values obtained by the

former method will be noted by the subscript std, while the latter will be noted by the subscript

meas. Furthermore, the subscript cap will be used for the capillary ODC-defining parameters

10

estimated by Eqs. 1 and 2. We calculated Pcap O2 ,std, ScapO2, std, and Pmit O2 ,std in Study A + B

by inserting P50 , std- and hstd-values of 3.5 kPa and 2.8, respectively, rather than using Eqs. 1 and

2 as above. The approach for determining Pcap O2 ,std, Scap O2, std, and Pmit O2 ,std was otherwise

identical to that described above for P capO2, S capO2, and P mit O2.

The blood gas analyser used in Study B was set up to provide individual P50-values, so

that arterial P50 ,meas-values from this study could be reported; hmeas-values were subsequently

calculated by rearranging the Hill equation (Eq. 6 and 7), and using measured PaO2- and SaO2-

values. The approach for determining Pcap O2 ,meas, Scap O2, meas, and Pmit O2 ,meas was otherwise

identical to that described above for P cap O2, S cap O2, and P mit O2.

Statistics

Normality of data was confirmed by visual inspection of normality plots and by means of the

Shapiro-Wilk W-test and parametric tests were thus used throughout. Data are presented as mean

(SD), and differences are presented as mean (95% CI). Significance was established at p < 0.05

after adjustment by Holm’s sequential Bonferroni correction. All analyses were performed using

SAS statistical software version 9.2 (SAS Institute Inc., Cary, NC, USA).

11

Results

Mean capillary vs. standard arterial ODC-defining parameters and derived indices of cerebral

oxygenation

P50 ,cap was 3.7 (0.2) kPa and hcap was 2.4 (0.2) during resting ambient breathing, so that the

former was higher, and the latter was lower than the P50 , std- and hstd-values of 3.5 kPa and 2.8,

respectively (both p < 0.001). S capO2 and Scap O2, std were similar (both 0.80 (0.02)), while

P capO2 was 7.6 (0.5) kPa, and P mit O2 2.0 (1.3) kPa, respectively, values that were higher than

Pcap O2 ,std and Pmit O2 ,std at 6.2 (0.3) kPa and 0.5 (1.1) kPa, respectively (p < 0.001 for both). In

terms of P capO2 vs. Pcap O2 ,std, a Bland-Altman plot-based analysis showed a bias of 1.4 kPa

with limits of agreement of 0.5 kPa to 2.4 kPa (Fig. 2).

Mean capillary vs. measured arterial ODC-defining parameters

P50 ,meas was 3.9 (0.3) kPa with a hmeas of 2.5 (0.1) during resting ambient breathing, and neither

differed significantly from the corresponding and P50 ,cap- and hcap-values (p = 0.14 for both) (Fig.

3A-B); the resultant ODCs at the arterial and cerebral capillary level are provided in Fig 3C.

During voluntary hyperventilation, PaC O2 was reduced by 2.1 (1.7-2.5) kPa from 5.4 (0.3) to

3.3 (0.5) kPa (p < 0.001), while arterial pH was increased by 0.16 (0.13-0.19) from 7.42 (0.01) to

7.57 (0.04) (p < 0.001). This changed the ODC curve both at the arterial and capillary level, such

that arterial P50 ,meas was reduced by 0.9 (0.7-1.2) kPa and hmeas was reduced by 0.4 (0.3-0.6),

while P50 ,cap was reduced by 0.3 (0.2-0.4) kPa, and hcap was reduced by 0.2 (0.1-0.2), and P50 ,cap

and hcap both became higher than P50 ,meas and hmeas (Fig. 3D-E). The resultant configurational

change in the ODC from the arterial to the cerebral capillary level is illustrated in Fig. 3F.

12

Mean capillary vs. measured arterial ODC-derived indices of cerebral oxygenation

Scap O2, meas was 0.80 (0.02), Pcap O2 ,meas was 7.4 (0.6) kPa, and Pmit O2 ,meas was 2.4 (2.3) kPa,

and none of these differed from the corresponding S cap O2- (p = 0.10), P cap O2- (p = 0.12), or

P mit O2-values (p = 0.12) during resting ambient breathing.

During voluntary hyperventilation, Scap O2, meas was 0.72 (0.02), Pcap O2 ,meas was 5.7

(0.3) kPa, and Pmit O2 ,meas 0.7 (2.1) kPa, and thus all reduced compared to resting breathing (p <

0.001). Meanwhile, S cap O2 was 0.72 (0.02) (p < 0.001 vs. resting breathing), P capO2 was 6.1

(0.3) kPa (p < 0.001 vs. resting breathing), and P mit O2 was 1.1 (2.1) kPa (p < 0.05 vs. resting

breathing). Scap O2, meas was similar to ScapO2 (p = 1.00), while Pcap O2 ,meas and Pmit O2 ,meas

were both lower than P capO2 and P mit O2, respectively (both p < 0.001). Accordingly, a

Bland-Altman plot-based analysis also showed no systematic difference between P capO2 and

Pcap O2 ,meas with a bias of -0.71 and limits of agreement of -1.68 to 0.37 kPa during resting

breathing, while P cap O2 was systematically higher than Pcap O2 ,meas with a bias of 0.45 and

limits of agreement of 0.35 to 0.54 during hyperventilation (Fig. 4).

13

Discussion

The method provided in the present paper considers the change in haemoglobin’s affinity for

oxygen that occurs as blood passes through the brain microvasculature, and thus permits

modelling the ODC at the cerebral capillary level.

Our findings indicate that assuming a ‘fixed’ standard arterial ODC that does not change

throughout the cerebral microvasculature leads to a systematic underestimation of cerebral

capillary and mitochondrial oxygen tensions. If the ODC-defining parameters P50 and h are

measured in arterial blood, which is possible in some arterial blood gas analysers, these

nonetheless provide acceptable estimates of the corresponding cerebral capillary ODC-defining

parameters and subsequently of the cerebral capillary and mitochondrial oxygen tensions, at least

during resting ambient breathing. However, when the arterial ODC is physiologically modulated,

for example by voluntary hyperventilation, the configurational change in the ODC from the

arterial to the capillary level may become substantial. It would thus have been expedient to

compare our P cap O2- and P mit O2-estimates to cerebral capillary blood sample values or

intracerebral oxygen tension measurements, but this is not ethically feasible in studies on healthy

volunteers. In future studies, it may however be brought to the test in selected patient groups,

such as intensive care patients subjected to multimodal neuromonitoring.

Our estimates are based on measurements on arterial and jugular-venous blood, and thus

provide an ‘ideal’ cerebral capillary ODC that does not consider the marked heterogenicity of

capillary flow and brain tissue metabolism. The variation in blood flow and oxygen extraction in

the different cerebral vascular territories imply that the ODCs may vary among capillary beds

(Catafau et al., 1996; Vovenko, 1999). However, when considered on a global level, we found

that the changes in the ODC-defining parameters from standard arterial values to the calculated

14

mean capillary values favoured a rightward shift in the ODC by simultaneously increasing the

P50-value and decreasing the Hill coefficient.

The model for capillary oxygen transfer presented in the present paper considers the

physically dissolved oxygen, which has been omitted in previous models (Vafaee & Gjedde,

2000; Gjedde et al., 2011). Dissolved oxygen represented 1.8 (0.2) % of the total blood oxygen

content during normoxia in the present study, and its effect on the mean capillary oxygen tension

and saturation can easily be assessed by setting α O2=0 in Eqs. 13 and 14. For α O2

=0, Eq. 14 is

simplified to ScapO 2=( Sa+Sv) /2, which only differs by 0.3 (0.1) % from our ScapO 2 estimate.

Hence, ScapO 2-values can accurately be calculated as the mean arterial to jugular-venous oxygen

saturation, but unfortunately no simple expression can be obtained for the corresponding

P capO2, which is 1.0 (0.3) % lower when the dissolved oxygen is not considered. Although the

dissolved oxygen is of less importance during normoxia, it may be crucial when modelling the

cerebral oxygen transfer in patients with diseases requiring higher fractions of inspired oxygen,

for example during mechanical ventilation in the intensive care unit.

In conclusion, physiologically meaningful and consistent P capO2- and P mit O2-values

may be obtained in humans when the mathematical formalism provided in this paper is used to

construct an ‘ideal’ cerebral capillary ODC from paired arterial and jugular-venous blood gases.

15

Figure 1. Capillary oxygen profiles. Solid lines show the total oxygen content (A), oxygen

saturation (B), and oxygen tension (C) as function of the segment of capillary. Hatched lines

illustrate the mean capillary values estimated by the area under the profile curves. All profile

curves decrease from the arterial (z = 0) to venous (z = 1) end of the capillary due to the delivery

of oxygen from brain capillary to the tissue. The graphs are constructed by averaging oxygen

profile curves defined by Eq. 3-6 (see text) and obtained in 30 healthy humans during resting

ambient breathing.

16

Figure 2. Capillary oxygen tension based on standard arterial or estimated capillary values.

The capillary oxygen tension was estimated using either the calculated mean capillary or the

standard arterial Hill coefficient and P50-value (‘capillary’ and ‘arterial’, respectively). The mean

difference (solid line) and the limits of agreement (hatched lines) are shown. Two outliers are

found.

17

Figure 3. Cerebral oxyhaemoglobin dissociation during normo- and hyperventilation. P50

was measured in arterial (white bars) and jugular venous (grey bars) blood and Hill’s coefficient

(h) was subsequently calculated by Hill’s equation. Cerebral capillary (hatched bars) P50 and h

were calculated by the mathematical approach presented in the current paper. A: P50, B: h, and

C: configurational change in the oxyhaemoglobin dissociation curve from artery (solid line) to

cerebral capillary (hatched line) during ambient resting breathing; D: P50, E: h, and F:

configurational change in the oxyhaemoglobin dissociation curve from artery (solid line) to

cerebral capillary (hatched line) during voluntary hyperventilation. The data are based on paired

arterial-jugular venous blood gases in eight healthy volunteers during resting ambient breathing

(‘normoventilation’) and voluntary hyperventilation.

*p < 0.05 vs. artery; †p< 0.05 vs. cerebral capillary; ‡p < 0.05 vs. normoventilation at same

site

18

Figure 4. Capillary oxygen tension based on measured arterial or estimated capillary

values during normo- and hyperventilation. Capillary oxygen tension estimated using either

the calculated mean capillary or the measured arterial Hills coefficient and P50-value (‘capillary’

and ‘arterial’, respectively). The mean differences (solid lines) and the limits of agreements

(hatched lines) are shown for resting breathing (black) and hyperventilation (grey).

19

Author Contributions

RHD performed mathematics, interpreted the data, prepared tables and figures, performed

statistical analyses and drafted the manuscript. ST and DMB conducted the study and acquired

and interpreted the data. KM conceived and designed the research, conducted the study,

acquired, analysed and interpreted the data, drafted the manuscript, and handled funding and

supervision. RMGB conducted and conceived the study, designed the research, handled

supervision, interpreted the data and drafted the manuscript. All authors made critical revisions

and read and approved the final manuscript.

Acknowledgements

None

Conflicts of interest

None of the authors have any conflicts of interest to disclose

Funding

None

20

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