c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 166–172

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Tidal breathing model describing end-tidal, alveolar, arterialand mixed venous CO2 and O2

Peter Poulsen, Dan S. Karbing, Stephen E. Rees, Steen Andreassen ∗

Center for Model-Based Medical Decision Support, Aalborg University, Niels Jernes Vej 14, DK-9220 Aalborg East, Denmark

a r t i c l e i n f o

Article history:

Received 21 December 2009

Received in revised form

13 March 2010

Accepted 30 March 2010

Keywords:

Rebreathing

Tidal breathing model

Carbon dioxide

Bohr&Haldane

a b s t r a c t

Thermodilution is the current standard for determination of cardiac output. The method is

invasive and constitutes a risk for the patient. As an alternative CO2 rebreathing allows non-

invasive cardiac output estimation using Ficks principle. The method relies on estimation of

arterial CO2 partial pressure from end-tidal CO2 pressure and estimation of mixed venous

CO2 partial pressure from end-tidal CO2 during rebreathing. Presumably the oxygenation of

blood in the lung capillaries increases lung capillary CO2 pressure due to the Haldane effect,

which during rebreathing may result in overestimation of the mixed venous CO2 pressure.

However, the Haldane effect is not discussed in the current literature describing cardiac

output estimation using CO2 rebreathing. The purpose of this study is to construct and verify

a compartmental tidal breathing lung model to investigate the physiological mechanisms

that influence the CO2 rebreathing technique. The model simulations show agreement with

End-tidal CO2 previous studies describing end-tidal to arterial differences in CO2 pressure and rebreathing

with high and low O2 fractions in the rebreathing bag. In conclusion the simulations show

that caution has to be taken when using end-tidal measurements to estimate CO2 pressures,

especially during rebreathing where the Haldane effect causes mixed venous CO2 partial

pressure to be substantially overestimated.

assumed to be in equilibrium with the blood in the pulmonarycapillaries [5].

The arterial CO2 partial pressure (PaCO2) can be determined

1. Introduction

The current standard for cardiac output monitoring is ther-modilution (TDCO) using a pulmonary arterial catheter (PAC)[1]. Studies have revealed that the information retrieved usinga PAC pre-, per- and postoperatively do not compensate for therisks involved [2]. Some studies even indicated a potential forincreased morbidity and mortality [3].

Ficks principle gives a non-invasive method to determinecardiac output (Q). To apply Ficks principle the exchange rate

of CO2 (VCO2), arterial (CaCO2) and mixed venous (CmvCO2)

∗ Corresponding author. Tel.: +45 99408764.E-mail address: sa@hst.aau.dk (S. Andreassen).

0169-2607/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights resdoi:10.1016/j.cmpb.2010.03.020

© 2010 Elsevier Ireland Ltd. All rights reserved.

CO2 concentrations must be known (Eq. (1)).

Q = VCO2

CmvCO2 − CaCO2(1)

Given the properties of blood [4] the mixed venous andarterial partial pressures of CO2 can be used to calculate theconcentrations. The partial pressure of CO2 in the alveoli is

using the end-tidal CO2 partial pressure (PETCO2), which is

erved.

i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 166–172 167

awtti

dhmgTc

bspObardoH

iCtpieaaabhdt

2

2

Tbttdl

2Tpofoff(h

Fig. 1 – An illustration of the model with flow of gasses inand out of the dead-space. The flow of N2 includes all inertgasses. The gas assumed to be at body temperature (TB)and fully saturated with water (SH2O,B) in the dead-space.The volume above the water and heat exchange is hencezero (V ≈ 0). The pressure of the dead-space is constant andequals the barometric pressure (Pb). The arrows indicate the

c o m p u t e r m e t h o d s a n d p r o g r a m s

good estimate for the alveolar PCO2[5,6]. During exercisehen the tidal volume is increased, PETCO2 has been shown

o overestimate PaCO2 significantly because the amplitude ofhe cyclic fluctuations in alveolar CO2 partial pressure (PACO2)ncreases when the tidal volume (VT) increases [5–8].

The mixed venous CO2 partial pressure (PmvCO2) can beetermined using PETCO2 during rebreathing. Several studiesave investigated the validity and reliability of the rebreathingethods to estimate PmvCO2 [9–13] and concluded that no sin-

le method is reliable and reproducible under all conditions.o avoid the PmvCO2 estimation, partial CO2 rebreathing [14]an be used.

In rebreathing trials a high oxygen fraction (>21%) in thereathing bag is often used to keep the patient’s oxygenaturation high throughout the trial [15]. However, the CO2

ressure is presumably affected by the oxygen saturation (S

2) of the blood. As the blood saturates with oxygen thelood releases CO2 due to the Haldane effect, resulting inn increased CO2 partial pressure. All rebreathing methodsely on the PETCO2 measure, which is influenced by the Hal-ane effect. The only commercial product to estimate cardiacutput using (partial) rebreathing [16] does not discuss thealdane effect.

The purpose of this study is to construct a tidal breath-ng model describing end-tidal to arterial differences and PO2 estimation using rebreathing maneuvers to give a bet-

er evaluation of the cardiac output determination using Ficksrinciple. The model will be based on the acid–base chem-

stry of blood as presented by [4] and a set of differentialquations describing state variables for the masses of CO2

nd O2 in the different compartments. The model is verifiedgainst data published in the literature describing end-tidal torterial differences during rest and exercise and the effect oflood oxygenation on the CO2 pressure during rebreathing. Weypothesize that the model results will show that the PETCO2

uring rebreathing is influenced by the Haldane effect leadingo an overestimation of PmvCO2.

. Methods

.1. Mathematical tidal breathing model

he tidal breathing model is based on the model of whole-ody O2 and CO2 described by [17]. This model consists ofhree major compartments representing the environment (E),he lungs, and the arterial blood (a). The lung compartment isivided into the lung alveoli (A), the dead-space (D) and the

ung capillaries (c). The model can be seen in Fig. 1.

.1.1. Model parameters and breathing patternhe tidal breathing model consists of a single alveolar com-artment and a serial dead-space. This model differs fromther similar models because the alveolar volume (VA) is aunction of time and includes a model of acid–base propertiesf blood [17]. The end-expiratory volume of the alveoli is the

unctional residual capacity (FRC). VA is dependent on severalactors: inspiration–expiration ratio (IE-ratio), the tidal volumeVT) and the respiratory frequency (f ). Furthermore the modelas to account for rebreathing of the volume of air in the dead-

positive flow direction.

space (VD) (Fig. 1) which takes place in every inspiration. Afraction of cardiac output (Q) is not involved in gas exchangein the lung capillaries. This fraction is the pulmonary shunt(s).

In the model simulations a sinusoidal respiratory flow isadjusted to the desired IE-ratio, VT and respiratory frequency.This flow profile gives similar results as a respiratory flow pro-

file during exercise [8]. The model simulations are made insteps of �t.

The acid–base properties of blood are determined bythe concentrations of haemoglobins, 2,3-diphosphoglycerate,

s i n

168 c o m p u t e r m e t h o d s a n d p r o g r a m

non-bicarbonate plasma buffer and base excess [4]. These areassumed to be constant in all blood compartments.

2.1.2. State variables and differential equationsFor the alveoli and the environment state variables describingthe moles of CO2 and O2 have been selected (e.g. nECO2, nEO2

and nEH2O for the environment). The state variables describ-ing arterial blood are the concentrations of CO2 and O2 (Ca

CO2 and Ca O2). All state variables have been selected so thatthey are additive making it easy to update their value usingdifferential equations.

To find the partial pressures of the environment and alveolidifferential equations for the number of moles of CO2 and O2

are written:

nECO2(t) = nCOD→E2 (t) (2)

nEO2(t) = nOD→E2 (t) (3)

nACO2(t) = nCOD→A2 (t) + nCOc→A

2 (t) (4)

nAO2(t) = nOD→A2 (t) − nOA→c

2 (t) (5)

The conversion from moles to partial pressure is done usingthe gas equation:

p = nRT

V

under the assumption of Daltons law. The gas equation isused both in this form and with the derivatives of moles andvolume (nRT = Vp) applied to both total pressures and partialpressures.

2.1.3. Initialization of the environmentThe environment compartment describes the gas in the inspi-ratory air. If the volume of the environment is finite itcorresponds to breathing into a bag.

The initial fractions of CO2 and O2 in the environment(F∗

ECO2 and F∗EO2) are always given as dry gasses denoted with

an asterisk. For dry air F∗EO2 = 20.9% and F∗

ECO2 = 0.04%. Thesaturated water vapor pressure at temperature of the environ-ment PH2O@TE

and the water saturation of the environmentSH2O,E can be used to find the water vapor pressure of theenvironment (PEH2O):

PEH2O(t) = PH2O@TESH2O,E(t) (6)

The initial partial pressures of CO2 and O2 in the environ-ment can then be found [18]

PECO2(t = 0) = F∗ECO2 (Pb − PEH2O(t)) (7)

PEO2(t = 0) = F∗EO2 (Pb − PEH2O(t)) (8)

Pb is the barometric pressure (101.3 kPa).

2.1.4. Conversion of volumesThe alveolar ventilation (VA(t)) is the flow in and out of thealveoli and therefore this measure is at body temperature (TB

= 37 ◦C) and fully saturated with water (BTPS).

b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 166–172

The volume at the mouth during inspiration is calculatedat the temperature of the environment (TE) and at the watersaturation of the environment (SH2O,E). During expiration thevolume is at the temperature of the air expired from the dead-space (TED) and is fully saturated with water (SH2O,ED = 1).

To find the inspired and expired flow volume conversionfactors from BTPS to inspired air (VCA→E) and from BTPS toexpired air (VCA→ED) need to be found. In Fig. 1 all flows in andout of the dead-space can be seen. The total pressure beforeand after humidification and heating in the dead-space is thesame (Pb). The volume of air flowing between the dead-spaceand the environment during inspiration can be calculatedusing Daltons law and the gas equation (see Fig. 1):

Pb = nD→E(t)RTE

VE(t)

= (nD→E(t) − nH2OD→E(t))RTE

VE(t)+ nH2OD→E(t)RTE

VE(t)

= (nD→E(t) − nH2OD→E(t))RTE

VE(t)+ PEH2O(t)

�VE(t) = (nD→E(t) − nH2OD→E(t))RTE

Pb − PEH2O(t)

(9)

A similar derivation for the air flowing between the dead-space and alveoli gives:

VA(t) = (nD→A(t) − nH2OD→A(t))RTB

Pb − PH2O@TB

(10)

The volume, temperature and water saturation of the dead-space is constant meaning that the amount of water in thedead-space is constant (nDH2O(t) = 0). An expression for theconservation of water in the dead-space can be written as (seeFig. 1):

nDH2O(t) = nH2O→D(t) − nH2OD→A(t) − nH2OD→E(t)�nH2OD→A(t) = nH2O→D(t) − nH2OD→E(t)

(11)

An equation for the conservation of mass in the dead-spacecan be written as:

nD→E(t) = nH2O→D(t) − nD→A(t)

nD→E(t) − nH2OD→E(t) = nH2O→D(t) − nH2OD→E(t) − nD→A(t)(12)

Inserting Eq. (11) into Eq. (12) and rearranging gives:

nD→A(t) − nH2OD→A(t) = −(nD→E(t) − nH2OD→E(t)) (13)

Inserting Eq. (13) into Eq. (10) an expression for the volumeconversion factor from BTPS to inspiration can be found:

VCA→E(t) = VE(t)˙

=(nD→E(t) − nH2OD→E(t))RTE

Pb − PEH2O(t)

˙ D→E ˙ D→E

VA(t) −(n (t) − nH2O (t))RTB

Pb − PH2O@TB

= −TE(Pb − PH2O@TB)

TB(Pb − PEH2O(t))

(14)

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i

Fig. 2 – The dead-space is divided into M steps each withtd

s

V

t

V

2Ismosfitcibtm

ih

P

o(e

P

P

he volume Vstep(VD = M Vstep). The input/output sideepends on the flow direction.

The conversion factor from BTPS to expired air from dead-pace (ED) can be found in a similar fashion:

CA→ED = VED(t)

VA(t)= −TED(Pb − PH2O@TB

)TB(Pb − (PH2O@TED

SH2O,ED))(15)

Given the alveolar flow an equation describing the flow athe mouth can now be derived:

˙ E(t) ={

VAVCA→E(t) inspirationVAVCA→ED expiration

(16)

.1.5. Dead-spacet is assumed that no mixing of gasses occurs in the dead-pace during inspiration and expiration. The dead-space isodeled as two FIFO buffers describing the partial pressures

f CO2 (PDCO2) and O2 (PDO2). Each buffer is divided into ‘M’teps. The volume of each step is Vstep = (VD/M) (see Fig. 2). Therst step corresponds to the Vstep of the dead-space closest tohe mouth and the M′th step is the Vstep of the dead-spacelosest to the alveoli. The direction from which the buffers filled depends on the the direction of the flow. The num-er of steps filled into and taken out of the opposite end ofhe buffer at time t depends on the flow (VA(t)) and equals(t) = (VA�t/Vstep). The partial pressure during the inspiration

s that of the environment corrected for humidification andeating using Eq. (7) (PECO2,BTPS)

PECO2,BTPS(t) = F∗ECO2(Pb − PH2O@TB

)

= PECO2(t)Pb − PH2O@TB

Pb − PEH2O(t)(17)

During the inspiration m(t) steps of the buffer is set to

ECO2,BTPS(t) and during the expiration m(t) steps is set to thatf the alveoli. The rest of the buffer is shifted m(t) steps. Eq.

18) is applied during inspiration and Eq. (19) is during thexpiration:

DCO2(i) ={

PECO2,BTPS(t) for i = 1 : m(t)PDCO2(i − m(t)) for i = (m(t) + 1) : M

(18)

DCO2(i) ={

PDCO2(i + m(t)) for i = 1 : (M − m(t))PACO2(t) for i = (M − m(t) + 1) : M

(19)

An equation identical to Eqs. (17)–(19) also applies for O2.

o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 166–172 169

2.1.6. Flow between environment and dead-spaceUsing the buffers described above the flow of CO2 and O2 overthe environment/dead-space border are:

nCOD→E2 (t) =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

VE(t)PECO2(t)RTE

inspiration

−VA(t)1

m(t)

m(t)∑i=1

PDCO2(i)

RTEDexpiration

(20)

Equations identical to Eq. (20) also apply for O2.Using Eqs. (2) and (3) and the gas equation, PECO2 and

PEO2 can now be calculated. If the environment is infinite(VE = ∞) the amount of CO2 and O2 removed or added to theenvironment is insignificant and all variables describing theenvironment are kept constant (PECO2 and PEO2).

2.1.7. Flow between alveoli and dead-spaceUsing the buffers described above the flow of CO2 and O2 overthe dead-space/alveoli border are:

nCOD→A2 (t) =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

VA(t)1

m(t)

M∑i=M−m(t)

PDCO2(i)

RTBinspiration

VA(t)PACO2(t)RTB

expiration

(21)

An equation identical to Eq. (21) also applies for O2.

2.1.8. Flow between the lung capillaries and alveoliMixed venous blood entering the lung capillaries has a higherPCO2 and lower P2 than the alveoli. When the blood flowsthrough the capillaries it is assumed that partial CO2 and O2

pressures (PcCO2 and PcO2) equilibrate with PACO2 and PAO2

Knowing PcCO2 and PcO2 and the properties of blooddescribing haemoglobins (cHb), base excess (BE), pH of plasma(pHp) and 2,3-diphospoglycerate (cDPG) equations describingthe acid–base chemistry of blood [4] can be used to calculateCcCO2 and CcO2.

Assuming mass balance the gas exchange between thealveoli and lung capillaries can be calculated. The cardiacoutput (Q), pulmonary shunt (s) and the mixed venous con-centration of CO2 and O2 are assumed to be constant.

nCOc→A2 (t) = Q(1 − s)(CmvCO2 − CcCO2(t)) (22)

nOA→c2 (t) = Q(1 − s)(CcO2(t) − CmvO2) (23)

Using Eqs. (4) and (5) and the gas equation, PACO2 and PAO2

can now be calculated.

2.2. Model parameters and initialization

The described model is implemented using MatLAB R2008a,The Mathworks. The model is initialized as described below.

The environment is only partially saturated with water (SH2O,E

= 0.5), but during rebreathing SH2O,E is assumed to be fully sat-urated with water. It is assumed that the temperature of theair inspired (TE = 20) and expired (TED = 25) are constant.

170 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 166–172

Table 1 – Data to initialise the model for simulations at rest and at exercise. VO2: O2 uptake (L min−1), VCO2: CO2production (L min−1), Q: cardiac output (L min−1), f: Respiratory frequency (min −1), VT : Tidal volume (L). means ± SD.

VO2 VCO2 Q f VT

Rest 0.4 ± 0.06 0.3 ± 0.04 7.0 ± 1.3 19.7 ± 3.9 0.8 ± 0.1˙

40% VO2,max 1.4 ± 0.2 1.2 ± 0.2

50% VO2,max 1.8 ± 0.5 1.8 ± 0.565% VO2,max 2.6 ± 0.6 2.4 ± 0.575% VO2,max 2.4 ± 0.4 2.5 ± 0.4

FRC and VD were set to 2.5 L and 0.15 L respectively [19]and the properties of blood were set to standard values [4].Shunt was set to 5 % and I:E-ratio was 1:2 during rest and1:1 during exercise. The tidal volume VT and respiratory fre-quency (f ) can be found in Table 1. The partial pressures of theenvironment were set to standard values when not rebreath-ing and as the initial pressures of the rebreathing bag (unlessother is stated). Initial concentrations of CO2 and O2 in arterialblood, CaCO2 and CaO2, were calculated using the blood model[4] assuming that the arterial blood is in equilibrium with thealveolar gas pressures. Knowing Q , VCO2 and VO2 (see Table 1),CmvCO2 and CmvO2 were initialized using Ficks principle[8].

The simulations were run until O2 and CO2 pressures in theexpired air differed between two subsequent breaths by lessthan 0.0001 kPa during normal ventilation. The rebreathingsimulations were run for a 20 s period. The simulations wererun with an incremental time �t of 10 ms using rectangularintegration.

3. Results

The model was validated by comparing model simulationswith results from two studies [19,20].

3.1. Validation of end-tidal to arterial PCO2 difference

[19] investigated the end-tidal to arterial PCO2 differences dur-ing rest and exercise. A tidal breathing model was used withinput data for VT , respiratory frequency, VCO2, VO2 and Q .These data were collected from trials made with 17 subjects

Fig. 3 – The leftmost plot is a simulated breath cycle during restthe arterial CO2 pressure, which is assumed to be equal the meamouth, is plotted. In this example the end-tidal to arterial differe(time = 1.6).

12.9 ± 2.7 23.7 ± 3.2 1.6 ± 0.213.8 ± 2.7 28.1 ± 4.5 1.9 ± 0.317.7 ± 2.3 33.3 ± 3.1 2.2 ± 0.217.1 ± 2.3 36.7 ± 4.6 2.3 ± 0.3

on a cycle ergometer. The data were reported as mean ± SD(Fig. 4).

Values for VCO2, VO2, Q , respiratory frequency (f ) and VT

were initialised using data by [19]. To test whether the modelin this study produces correct values during different condi-tions, 17 sets of data for each exercise level were constructed(see Table 1). These data were randomly selected to lie withinthe values reported by [19] and to have physiologically correctrespiratory quotient (RQ) [21] and alveolar ventilation (VA) [18]for the given exercise level.

The simulated end-tidal to arterial difference is illustratedin Fig. 3 during rest and exercise. The end-tidal to arterial PCO2

differences simulated at rest and during exercise are plotted inFig. 4. The ANOVA analysis of the model simulated differencescompared with the validation study of [19] shows that they arenot statistically different (P > 0.05). The end-tidal to arterialdifferences increased significantly from (mean ± SD) 0.12 ±0.02 kPa at rest to 0.67 ± 0.07 kPa at 75% of VO2,max (P < 0.0001)as reported by [19].

3.2. Validation of end-tidal to mixed venous PCO2

difference

The study of [20] investigated rebreathing with high and lowalveolar oxygen during rest and exercise. They achieved lowalveolar oxygen by filling the rebreathing bag with nitrogen,primed with a suitable fraction of CO2 to reduce the timeto equilibrium between P CO and P CO . Rebreathing was

mv 2 A 2

continued until equilibrium was achieved also between Pmv O2

and PAO2. At this time the venous blood is not oxygenated inthe lungs. Therefore there is no Haldane effect, and the PACO2

of the expired alveolar gas should represent PmvCO2.

and the rightmost is during high intensity exercise. PACO2,n alveolar CO2 pressure and the CO2 capnogram at thence is 0.05 kPa during rest (time = 3) and 0.5 during exercise

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 1 ( 2 0 1 1 ) 166–172 171

Fig. 4 – Plot of the PETCO2-PaCO2 differences simulated with the model at rest and during exercise (∗). The measuredd (Mea

fiDvrtiaP

rrthi�

aErleitt

Fr

ifferences from the validation study [3] are shown with ‘×’

During rebreathing with high O2 the rebreathing bag waslled with oxygen, also primed with a suitable fraction of CO2.ue to the resulting elevated alveolar oxygen pressure, theenous blood will continue to be oxygenated throughout theebreathing period. The Haldane effect must thus be expectedo raise CO2 partial pressure PcCO2 of the oxygenated bloodn the lung capillaries, and the equilibrium between PcCO2

nd PACO2 should therefore be at a CO2 pressure that exceeds

mvCO2.[20] compared the equilibrium obtained during low oxygen

ebreathing (PACO2@lowO2) with that obtained during high O2

ebreathing (PACO2@highO2). Fig. 5 shows their results, wherehe difference �PACO2

high–lowO2 = PACO2@highO2–PACO2@lowO2

as been plotted versus the arterio-venous differencen oxygen saturation (Sa−vO2). Their results show thatPACO2

high–lowO2 is positive and that it increases with Sa−vO2,s would be expected due to the Haldane effect (Fig. 5).xperimentally [20] used exercise to increase Sa−vO2 aboveesting value. Simulations by the model were used to calcu-ate equilibrium CO2 pressure under conditions equal to thexperiments by [20]. Simulations results (Fig. 5) also showed an

ncrease in �PACO2

high–lowO2 with increasing Sa−vO2, althoughhe slope of the increase was significantly smaller (P < 0.01)han in the experiments by [20].

ig. 5 – Difference between equilibrium PACO2 in high and low aesults are shown with asterisks (∗) and the data by [13] are show

n ± SD).

4. Discussion

The end-tidal to arterial CO2 pressure difference, simulatedwith the model initialized using data from the validation study[19], showed that they were not statistically different from thedifference measured by [19].

The end-tidal to arterial differences simulated with thismodel showed better correlation with the measured data thanthe model used in the study by [19], which simulated a differ-ence that were significantly higher than the measured data.The model used by [19] uses fractions to describe the gascompositions in the different compartments. Fractions canonly be used under the assumption that the temperatureand water vapor pressure is constant in all compartments,else fractions are not additive. The model presented inthis study simulates the changes of temperature and watervapor pressure of the air in different compartments, whichcould explain the better correlation with the measured datafrom [19].

Furthermore the rebreathing simulation showed that the

model described the difference in capillary CO2 partial pres-sure between simulations during rebreathing of CO2 in O2 andCO2 in N2 in agreement with the results reported by [20].

lveolar O2 experiments versus Sa–vO2. The model simulatedn with ‘ב.

s i n

r

Alveolar-to-blood, PCO2 difference during rebreathing in

172 c o m p u t e r m e t h o d s a n d p r o g r a m

The difference between simulations with high and low O2

can be explained by the Haldane effect. As the blood saturateswith oxygen the blood releases CO2 resulting in an increasedCO2 partial pressure. The results showed an increase in�PACO2

high–lowO2 with increasing Sa−vO2. The slope of theincrease was significantly smaller in the simulations than inthe experiments by [20] indicating not only that the Haldaneeffect increases PACO2, but that the increase observed exper-imentally may exceed the increase predicted by the model.Since PACO2 during rebreathing is used as an estimate ofPmvCO2, a Haldane effect mediated increase of PACO2 wouldlead to an overestimation of PmvCO2. The overestimationduring normal ventilation (Sa−vO2 = 25 %) would be approx-imately 0.6 kPa (Fig. 5). This error is approximately the sameas a normal mixed venous to arterial PCO2 difference andwould thus contribute to an erroneous Q estimation usingFicks principle (see Eq. (1)).

In conclusion, the model is capable of simulating CO2 pres-sures during normal respiration, exercise and rebreathing,showing that the end-tidal to arterial difference has to beaccounted for during exercise when the end-tidal value is usedas an estimate for the arterial PCO2. Furthermore the Haldaneeffect has influence on the estimated PCO2 using all rebreath-ing techniques. As a consequence correction for the Haldaneeffect has to be made when using rebreathing techniques toestimate PmvCO2 in cardiac output measurements.

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