Tidal volume, cardiac output and functional residual capacity determine end-tidal CO₂ transient during standing up in humans

Abstract

In man assuming the upright position, end-tidal P_CO2 (P_ETCO2) decreases. With the rising interest in cerebral autoregulation during posture change, which is known to be affected by P_ETCO2, we sought to determine the factors leading to hypocapnia during standing up from the supine position. To study the contribution of an increase in tidal volume (V_T) and breathing frequency, a decrease in stroke volume (SV), a ventilation–perfusion (V/Q) gradient and an increase in functional residual capacity (FRC) to hypocapnia in the standing position, we developed a mathematical model of the lung to follow breath-to-breath variations in P_ETCO2. A gravity-induced apical-to-basal V/Q gradient in the lung was modelled using nine lung segments. We tested the model using an eight-subject data set with measurements of V_T, pulmonary O₂ uptake and breath-to-breath lumped SV. On average, the P_ETCO2 decreased from 40 mmHg to 36 mmHg after 150 s standing. Results show that the model is able to track breath-to-breath P_ETCO2 variations (r²= 0.74, P < 0.05). Model parameter sensitivity analysis demonstrates that the decrease in P_ETCO2 during standing is due primarily to increased V_T, and transiently to decreased SV and increased FRC; a slight gravity-induced V/Q mismatch also contributes to the hypocapnia. The influence of cardiac output on hypocapnia in the standing position was verified in experiments on human subjects, where first breathing alone, and then breathing, FRC and V/Q were controlled.

In man the carbon dioxide (CO₂) content of the alveolar air is lower in the upright position than in the supine position (Lilijestrand & Wollin, 1914). Main et al. (1937) confirmed this observation and explained it as being due to over-ventilation with resulting alkaemia. However, Hitchcock & Ferguson (1938) showed the drop in alveolar CO₂ partial pressure (P_CO2) upon assuming the erect posture to be independent of alterations in pulmonary ventilation. They attributed the lowered P_CO2 to an increase in functional residual capacity (FRC) in the upright position and an impairment of CO₂ transport from the dependent parts of the body.

In man assuming the upright position, cardiac output (Q) decreases (Stead et al. 1944). Variation in end-tidal partial P_CO2 (P_ETCO2) reflects variation in Q in the same direction, for example during acute haemodynamic perturbations in anaesthetized patients during constant ventilation (Shibutani et al. 1994). Airway CO₂ levels have been proposed as a monitor of Q during cardiovascular resuscitation (Blumenthal & Voorhees, 1997). We considered that the postural decrease in Q could well contribute to hypocapnia.

Previous studies have focused on the effect of gravity and body position on the distribution of ventilation (Zardini & West, 1966; Bryan et al. 1966; Milic-Emili et al. 1966), perfusion (West & Dollery, 1959; Anthonisen & Milic-Emili, 1966) and the ventilation–perfusion (V/Q) ratio (West, 1962; West et al. 1963; Musch et al. 2002) in the lung. Gravity induces a perfusion gradient in the upright lung, with a decrease in lung perfusion in apical regions and an increase in perfusion in basal regions. In the standing subject, air expired from alveoli active in gas exchange is diluted by air from apical lung segments which are relatively underperfused, resulting in a decrease in P_ETCO2. In the upright position, FRC and tidal volume (V_T) increase, due to lowering of the diaphragm and alveolar expansion due to the lungs' own weight. However, the relative contribution of each of these physiological phenomena to the postural decrease in P_ETCO2 is unknown.

With the rising interest in cerebral autoregulation during posture change (Birch et al. 1995; Cencetti et al. 1997; Novak et al. 1998; Harms et al. 2000; Hughson et al. 2001; Edwards et al. 2002), which is affected by P_CO2, we sought to determine the factors leading to transient P_ETCO2 variation during standing up from the supine position. We hypothesized that the reduction in Q, and the V/Q mismatch determine the decrease in P_ETCO2 upon standing up. To test this hypothesis, we developed a nine-compartment computer model of the lung to simulate breath-to-breath P_ETCO2 variations during active standing up. The model includes an FRC, V_T and anatomic dead space (V_D). Lung perfusion is modelled using stroke volume (SV) and heart rate (HR). Regional V/Q ratios are modelled for each lung compartment, accounting for effects of gravity. Input data to the model are Fick-calibrated breath-to-breath SV of the heart, pulmonary O₂ uptake (V̇_O2), respiratory interval (T_resp) and V_T.

Methods

Model

To assess the underlying physiology determining P_ETCO2 transients during posture change, we developed a breath-to-breath model, programmed in MATLAB (Release 5.2, The MathWorks, Natick, MA, USA). A detailed description of the mathematical model is given in the Appendix. The features of each breath (e.g. arterial and venous CO₂ concentrations) depend on the features of the previous breaths. Input data to the model are (Fick-calibrated) SV determined breath-to-breath, V̇_O2 and V_T. The model is ‘paced’ by the respiratory interval.

Ventilation

The model includes nine lung compartments (Fig. 1, right panel). Each compartment's share of the FRC and V_T is determined by its position with the apical compartments smaller than the basal compartments. The distributions of V_T and SV in the upright position, are approximations based on observations by West (1962) (Table 1). The model includes V_D. Using an established relation between anatomical V_D and height (Hart et al. 1963), we set the model V_D for men at a greater volume compared to the V_D for women (1.4 times), with the V_D at 200 ml for men and 140 ml for women in the supine position. In the upright position, these values were increased by 70 ml (see below). The respiratory quotient (RQ), defined as the ratio of carbon dioxide production (V̇_CO2) to V̇_O2, normally between 0.7 and 1.0, was set at 0.9.

Figure 1. Diagram of the P_ETCO2 model.

The left panel represents circulation with an arterial volume V_a, a venous volume V_v, a lung capillary volume V_cap, and circulating stroke volume per breath SV. The right panel represents ventilation with a functional residual capacity FRC, a respiratory dead space V_D, and a tidal volume V_T. The distribution of SV and V_T as shown here are for the upright position; in the supine position SV and V_T are equally distributed over apical and basal lung segments (1–9).

Table 1.

Parameters of nine-compartment lung model

		Lung compartment (apical to basal, respectively)
		1	2	3	4	5	6	7	8	9	Total
Supine	Perfusion (% SVk)	11.1	11.1	11.1	11.1	11.1	11.1	11.1	11.1	11.1	100
	Ventilation (%VTk)	11.1	11.1	11.1	11.1	11.1	11.1	11.1	11.1	11.1	100
	Alveolar vol. (% FRCk)	6.58	8.64	10.11	11.16	11.90	12.43	12.81	13.08	13.27	100
	Lung capil. (%Vcapk)	6.58	8.64	10.11	11.16	11.90	12.43	12.81	13.08	13.27	100
Standing	Perfusion (% SVk)	0.58	3.21	5.84	8.47	11.10	13.73	16.36	18.99	21.62	100
	Ventilation (%VTk)	4.58	6.63	8.48	10.13	11.62	12.96	14.17	15.25	16.22	100
	Alveolar vol. (% FRCk)	6.58	8.64	10.11	11.16	11.90	12.43	12.81	13.08	13.27	100
	Lung capil. (%Vcapk)	6.58	8.64	10.11	11.16	11.90	12.43	12.81	13.08	13.27	100

Distribution of stroke volume (SV), tidal volume (V_T), functional residual capacity (FRC) and lung capillary blood volume (V_cap) per lung segment k, in the supine and standing position. Upright distributions are based on measurements by West (1962).

Circulation

The model includes a simplified blood circulation with an arterial compartment (V_a), a venous compartment (V_v) and lung capillary gas-exchange compartments (V_cap) (see Fig. 1, left panel). The lung capillary volume and the small venule volume are lumped together, as gas exchange occurs in both. The major arteries of the lung are included in the venous compartment; the major veins of the lung are included in the arterial compartment. The total blood volume of 5.5 l is distributed over V_v (4.0 l), V_a (1.3 l) and V_cap (0.2 l) (Burton, 1972).

Effects of gravity

The effects of gravity are modelled as a gravity-induced perfusion gradient in the lung. The distribution of perfusion and ventilation in each lung compartment are based on measurements by West (1962). Distributions of V_T, SV, FRC and V_cap are summarized in Table 1. In the supine position, SV and V_T are distributed equally over all compartments. With nine compartments, in the supine position each lung compartment receives one-ninth of the breath-to-breath SV and V_T. In the upright position there is an apical-to-basal perfusion and ventilation gradient, with increased perfusion and ventilation at the lung base. The perfusion gradient is steeper than the ventilation gradient, resulting in a 7.9–0.8 apical-to-basal V/Q gradient. Furthermore, on going from supine to upright respiratory V_D increases (Bjurstedt et al. 1962; Rea et al. 1977). Bjurstedt et al. (1962) established an increase in V_D in the upright position of +53 ml (anatomical) and +81 ml (physiological). In the model, V_D increases by 70 ml in the upright position.

Data set

The physiological data we used to test our model are from eight healthy young subjects (2 women; median age 24 years (21–38 years); median height 183 cm (162–191 cm); median weight 78 kg (50–85 kg)), who participated in the study of van Lieshout et al. (2001) for which informed consent had been obtained from all participants, and which was approved by the ethics committee of Copenhagen (KF 01-120/96) and was performed in accordance with the guidelines laid down in the Declaration of Helsinki. Instrumentation occurred as previously described; after 5 min of supine rest, each subject actively assumed the upright position and remained standing for 5 min while continuous finger arterial blood pressure (ABP) and breath-to-breath online gas concentrations were recorded. The data we analysed were from a recording of each subject standing up just once. For the purpose of tracking short-term P_ETCO2 variations with posture change, we selected data starting 150 s prior to standing up and ending 150 s after standing up.

Mean arterial blood pressure was measured with a Finapres (Model 5; Netherlands Organization for Applied Scientific Research, Biomedical Instrumentation, TNO-BMI). The cuff was applied to the midphalanx of the middle finger of the dominant arm, which was placed at heart level. Beat-to-beat changes in SV were estimated by modelling flow from arterial pressure (Modelflow, TNO-BMI). This method computes an aortic waveform from a peripheral arterial pressure signal using a non-linear 3-element model of the aortic impedance (Jellema et al. 1999; Harms et al. 1999). Cardiac output was the product of SV and HR. To obtain absolute values of Q to calibrate Modelflow Q, a Fick-determined Q was obtained from arterial and central venous O₂ content and the V̇_O2 in the supine and in the standing position. Absolute values of Q were used to calibrate Modelflow Q, averaged during 150 s in the supine position, and during 150 s of standing.

Breath-to-breath online gas analysis was performed using a Medical-Graphics CPX/D metabolic cart. Respiratory gas was sampled continuously from a mouthpiece and partial gas pressures were obtained from a Zirkonia oxygen analyser (accuracy ± 0.03% O₂) and a non-dispersive infrared sensor for CO₂ (accuracy ± 0.05% CO₂) that thus delivered V̇_O2, V̇_CO2 and P_ETCO2.

Data processing and analysis

The ventilatory gas analysis was recorded as one value for every breath. All data were stored on a hard disk for off-line analysis. Mean ABP, HR and the ventilatory data were expressed in absolute values. Mean ABP was the integral of one beat. Heart rate was the inverse of the interbeat interval. Then, ventilatory data and Fick-calibrated Modelflow SV data were time aligned. For the duration of each breath, the sum of stroke volumes was taken to obtain breath-to-breath SV data.

Experiments

To verify the contribution of the postural reduction in Q to hypocapnia in the standing position, the following protocol was carried out in seven healthy non-smoking subjects (aged 29 ± 5 years, height 176 ± 8 cm, weight 71 ± 11 kg). Informed consent was obtained from all participants. The study was approved by the ethics committee of the Academic Medical Center (MEC 01-147) and performed in accordance with the guidelines laid down in the Declaration of Helsinki. First, the effect of increased ventilation was eliminated by using a protocol that involved standing up during controlled breathing. Second, we eliminated the effect of V/Q mismatch, FRC increase and increased ventilation. To achieve this we used a protocol involving standing with inflated leg splints (Pneumasplint, International deposit Nr. 844181), which augment venous return, followed by rapid leg splint deflation, with breathing frequency and V_T controlled. The subjects breathed through a mouthpiece connected to a two-way respiratory valve, and were instructed to breathe at a metronome-paced frequency (0.15 Hz). For each subject the airflow was adjusted to a comfortable level (8.2 ± 1 l min⁻¹). During expiration the inflow of air filled a bag, and during inspiration the subject was instructed to empty the bag, thus maintaining a constant V_T. Keeping the breathing fixed, 5 min of supine recording were followed by 5 min of recording in the standing position. Next, while in the standing position inflatable hip-to-toe leg splints were inflated to 60 mmHg. After 5 min recording during standing with inflated splints, the splints were deflated to atmospheric pressure within 4 s, followed by 5 min recording in standing position with deflated splints. The respiratory frequency and V_T were fixed throughout the procedures. We measured finger ABP (Finometer Model 1, TPD-BMI) and P_CO2 (Hewlett Packard Airway Adapter 1436 A). SV was derived from the peripheral arterial pressure signal using Modelflow as described above. Measurements of Q were carried out at the beginning and end of each procedure using the inert gas rebreathing technique (Innocor Model: SpO₂ & O₂ options; Gabrielsen et al. 2002). Rebreathing episodes were marked and Modelflow Q was level-corrected. The sum of FRC and V_D was measured in the supine and standing positions, also using the Innocor rebreathing technique. The calculation is based on the dilution of insoluble gas (SF6). Measurement of FRC and V_D combined, in both the supine and standing positions, allowed us to analyse the effect of FRC increase, as measured, on the P_ETCO2.

Parameter sensitivity analysis

To assess the relative contribution of the various physiological phenomena contributing to P_ETCO2 variations, the parameter sensitivity of the model was analysed. First, the effect of variations in V_T, V_D, SV, V̇_O2, RQ, FRC, V_v, V_a, T_RESP and V/Q on model output (M-P_ETCO2) were evaluated by carrying out a series of simulations in which a steady-state period of 200 s was followed by a 900 s period with one input parameter set at a value ranging from –10 to +10% of baseline value. An exception is the V/Q parameter sensitivity, which was determined starting with 200 s steady-state ‘supine’ settings, followed by 900 s with ‘upright’ settings. Steady-state values were: V_T = 484 ml; V_D = 200 ml; SV = 550 ml;V̇_O2 = 250 ml min⁻¹; RQ = 0.9; FRC = 2.5 l; V_v= 4.0 l; V_a= 1.3 l; T_RESP= 4 s and V/Q =‘supine’. The output value used in the analysis was M-P_ETCO2 at maximum value or at end-point. Second, the analysis was also performed with the input starting at baseline and varying each input variable as occurs during posture change, with an increase in V_T, V_D and FRC, a reduction in SV, and a shift in V/Q.

Statistical analysis

Haemodynamic and respiratory variables were tested for normality (Shapiro-Wilk test) and, where distribution was not normal, the median was computed for each body position. Results were expressed as means and standard deviation (s.D.) or as median and range, as appropriate. Supine and upright values were compared by paired t test. Agreement between P_ETCO2 and M-P_ETCO2 was judged by plotting the difference between M-P_ETCO2 and P_ETCO2 against their means, and computing Pearson's correlation coefficient. The mean difference (bias) and s.D. (precision) between M-P_ETCO2 and P_ETCO2 was tested by paired t test. A P value < 0.05 was considered to indicate a statistically significant difference.

Results

Input to the model

The group average haemodynamic and ventilatory responses to standing up from the test database are given in Table 2. Upon standing, Q decreased from 6.5 ± 1.1 l min⁻¹ to 4.0 ± 0.9 l min⁻¹ in the standing position. The Q response ranged from −0.6 l min⁻¹ to −4.5 l min⁻¹. V_T increased on standing up, while the respiratory rate decreased. V_E increased on standing up in all subjects, with a range of 0.3–5.9 l min⁻¹. The P_ETCO2 decreased from 40 ± 1 to 36 ± 2 mmHg.

Table 2.

Haemodynamic and ventilatory responses to standing up in eight normal subjects

	Q (l min−1)	V̇CO2 (ml min-1)	V̇O2 (ml min−1)	PETCO2 (mmHg)	R-R (min−1)	VT (ml)	VE (l min−1)
Supine	6.5 ± 1.1	217 ± 36	263 ± 60	40 ± 1	16 ± 4	490 ± 105	7.9 ± 1.4
Standing	4.0 ± 0.9	248 ± 53	263 ± 65	36 ± 2	13 ± 3	734 ± 199	9.8 ± 2.7
P value*	0.002	n.s.	n.s.	< 0.001	0.03	0.005	0.03

Group average values (mean ± s.D.) for cardiac output (Q), CO₂ output (V̇_CO2), oxygen uptake (V̇_O2), end-tidal CO₂ pressure (P_ETCO2), respiratory rate (R-R), tidal volume (V_T) and expired ventilation (V_E) as determined from 150 s in the supine position followed by 150 s of standing. Data from the study of van Lieshout et al. (2001).

^*Standing versus supine, paired t test.

Model simulation

Inputs to the model were (measured) breath-to-breath values of V_T, SV (summed per breath) and V̇_O2. Starting values for P_CO2 in the venous and the arterial blood and in the various lung compartments were set for each test subject, corresponding to their starting measured P_ETCO2. Venous CO₂ concentrations were set at a starting value ranging from 52 to 55%. The P_CO2 starting values in arterial blood and the lung compartments ranged from 40 to 42 mmHg. The first breaths of each model run were excluded from analysis. The P_ETCO2 and the M-P_ETCO2 during 150 s in the supine position followed by 150 s of standing of all individual subjects are given in Fig. 2. The model tracks P_ETCO2 during standing up, and it also follows non-posture-related variations in P_ETCO2(r²= 0.43–0.86), with those registrations with the greatest variance in measured P_ETCO2 resulting in the best correlations of M-P_ETCO2 with P_ETCO2(P < 0.01).

Figure 2. Individual P_ETCO2 recordings and model simulations during lying down and standing.

Plots of breath-to-breath P_ETCO2 of each individual subject. Subjects 1–8 are represented in panels A–H, respectively. Each panel contains a plot of breath-to-breath P_ETCO2 measurements (•) during 150 s supine and 150 s of standing, and a model simulation (^) of the same period. Arrows indicate posture change from supine to standing at time zero.

Figure 3A shows the pooled results of breath-to-breath M-P_ETCO2, plotted against the pooled P_ETCO2 measurements. There was a significant correlation between M-P_ETCO2 and P_ETCO2(r²= 0.74, P < 0.05). The difference between P_ETCO2 and M-P_ETCO2, versus the average P_ETCO2 is shown in Fig. 3B. Accuracy (group-averaged M-P_ETCO2–P_ETCO2 difference) and precision (s.D. of the M-P_ETCO2–P_ETCO2 difference) of the model during the simulation were –0.16 and 1.93 mmHg, respectively (95% limits of agreement were −3.95 and + 3.63 mmHg).

Figure 3. Pooled data of 300 s of P_ETCO2 registration in 8 subjects, 150 s supine and 150 s standing, plotted against the output of a model run of the same time period.

The number of data points is 583, representing the total of 583 breaths. A, pooled data of computed P_ETCO2 (M-P_ETCO2) plotted against measured P_ETCO2. B, pooled data scatter diagram of differences between measured P_ETCO2 and computed P_ETCO2 (M-P_ETCO2) against their mean. Horizontal lines indicate mean ± 1.96 s.d.

Experiments

To verify the contribution of the postural reduction in Q to hypocapnia in the standing position, a protocol of standing up during controlled breathing, and the deflation of leg splints was applied on seven subjects. Throughout standing up and deflation of leg splints, the minute ventilation was fixed (the level ranged from 7 to 9.5 l min⁻¹) and breathing frequency was maintained at 0.15 Hz.

Supine versus standing

On average the sum of FRC and V_D increased from 2.8 ± 0.8 l in the supine position to 3.3 ± 0.3 l in the upright position (P = 0.22). The group average mean ABP was 84 ± 8 mmHg supine versus 87 ± 13 mmHg standing (n.s.), whereas HR increased from 74 ± 5 to 89 ± 7 beats min⁻¹ (P < 0.001). With V_T and T_RESP fixed, both Q (–0.6 to –3.1 l min⁻¹) and P_ETCO2 (–2.3 to –3.5 mmHg) decreased on going from supine to standing (Fig. 4). In other words, P_ETCO2 decreased in the upright position even though the depth and rate of breathing were kept constant. However, the decrease in P_ETCO2 and the decrease in Q showed a correlation coefficient (r²) of only 0.06.

Figure 4. P_ETCO2 and Q during controlled breathing in 7 healthy subjects.

Results of supine and standing (A) and inflated and deflated leg cuffs (B) protocols. Symbols represent average end-tidal P_CO2 (top) and cardiac output (Q, bottom) during 5 min. The lines link the results of a particular subject. Asterisk indicates P < 0.01.

Inflated versus deflated leg splints

The group average mean ABP was 88 ± 11 mmHg with inflated splints versus 86 ± 10 mmHg with deflated splints (n.s.), whereas HR increased from 80 ± 8 to 93 ± 10 beats min⁻¹ (P = 0.02). Following deflation of splints, Q decreased (−0.1 to −1.1 l min⁻¹) and P_ETCO2 decreased (ranging from –1.4 to −3.6 mmHg) in all subjects, while V_T and T_resp were fixed (Fig. 4). The correlation between the decrease in Q and P_ETCO2 yielded a correlation coefficient of r²= 0.80.

Parameter sensitivity analysis

The sensitivity of the model output to variations in parameters and model input was analysed. This resulted in a transient change in model output, a progressive variation or no variation in the output.

Transient M-P_ETCO2 change.

A decrease in SV resulted in a transient reduction in P_ETCO2 with a peak after six breaths (Fig. 5A). The model response to SV change was asymmetrical: a decrease in SV had a greater effect on P_ETCO2 than an increase in SV of similar magnitude. The model response to an increase in FRC was transient, the peak response occurred at the first breath and rapidly decayed (Fig. 5B). The model response to FRC variation also showed asymmetry; a decrease in FRC yielded a greater M-P_ETCO2 variation than an increase in FRC of the same magnitude.

Figure 5. Parameter sensitivity analysis of SV and FRC.

Each line represents a model run where after 200 breaths under baseline conditions the input is changed from its baseline value by –10 to +10%, in steps of 2%. In A the input is SV of the heart, in B the input is FRC. Note difference in ordinate scale.

Progressive M-P_ETCO2 change.

A strong influence on model output was exerted by changes in V_T, T_resp, V̇_O2, RQ and V_D (Fig. 6). The effects of T_resp, V̇_O2 and RQ on M-P_ETCO2 were equal, as can be expected from eqn (4) (see Appendix), where the V̇_CO2 per breath is determined by V̇_O2,n, the RQ and the breath duration. The V/Q gradient was analysed by comparing a model run with homogeneous perfusion distribution (as in the supine position) to a model run with a gravity-induced lung-perfusion gradient (as in the standing position). The steady-state model run with ‘supine’V/Q distribution resulted in a baseline P_ETCO2 of 40 mmHg. After the model run with ‘upright’V/Q distribution, the P_ETCO2 was 38.4 mmHg after 900 s.

Figure 6. Analysis of effect of each input variable on P_ETCO2.

Parameter sensitivity analysis of model input (T_resp, V_T, V̇_O2) and model parameters (V_D and RQ). Model input is changed from baseline by –10 to +10% (see Methods) and model output (P_ETCO2) determined after 900 s.

Appendix

Symbols	Definition	Units
[CO2]a	Arterial CO2 content	%
[CO2]v	Venous partial CO2 content	%
ABP	Arterial blood pressure	mmHg
FRC	Functional residual capacity	ml
HR	Heart rate	beats min−1
PETCO2	End-tidal partial CO2 pressure	mmHg
M-PETCO2	Model output end-tidal partial CO2 pressure	mmHg
PkCO2	Lung compartment k partial CO2 pressure	mmHg
PtcCO2	PCO2 of blood draining the lungs	mmHg
Q	Cardiac output	l min−1
RQ	Respiratory quotient	unitless
R-R	Respiratory rate	min−1
SV	Stroke volume per breath	ml
TRESP	Respiratory interval	s
Va	Arterial blood volume	ml
Vcap	Lung capillary blood volume	ml
VD	Anatomical dead space	ml
VE	Ventilation	l min−1
V̇o2	Pulmonary O2 uptake	ml min−1
V/Q	Ventilation/perfusion ratio	unitless
VT	Tidal volume	ml
Vv	Venous blood volume	ml

No M-P_ETCO2 change.

A 10% increase or decrease in V_v or V_a did not influence model outcome of P_ETCO2. However, an increase in V_a or V_v results in increased damping of breathing pattern-related variation in P_ETCO2.

Posture-induced variations

The contribution of each parameter on P_ETCO2 as is likely to occur during posture change is given in Fig 7. For example, a 20% increase in V_T resulted in a progressive decrease in P_ETCO2 which dropped from 40 to 34 mmHg after a 300 s model run. An increase in FRC resulted in acute hypocapnia which lasted for several breaths. After 300 s, however, the P_ETCO2 was only 1 mmHg below supine levels. The posture-dependent change in the V/Q mismatch per se had a limited effect on the decrease in P_ETCO2.

Figure 7. Effect of active-standing induced variations in model input variables on P_ETCO2.

Each thin line indicates the output of a model run starting with supine settings and with parameter settings varied at 200 s as is likely to occur on standing up: Q, output when Q was reduced by 40%, V_T, output when V_T was increased by 20%, FRC, output when FRC was increased by 20%, V_D, output when V_D was increased by 70 ml, V/Q, output when V/Q shifted from equal distribution to model settings for a gravitationally induced V/Q mismatch. The thick line labelled ALL indicates model P_ETCO2 levels when all of these changes occurred simultaneously.

Computed effect of FRC and V_D increase upon standing

We conducted an additional analysis of the increase in FRC and V_D, which occur simultaneously during tilt. On average the sum of FRC and V_D increased from 2.8 ± 0.8 l in the supine position to 3.3 ± 0.3 l in the upright position (P = 0.22). We used model (male) supine steady state settings (see above) to analyse the effect on P_ETCO2, where an FRC of 2.5 l and V_D at 0.2 l results in a P_ETCO2 of 40 mmHg. By increasing FRC to 2.93 l and V_D increased to 0.27 (V_D is known to increase by ∼70 ml in the upright position; together V_D and FRC now amount to 3.2 l), computed P_ETCO2 transiently decreased by 12% in the first breath. However, after 9 breaths the hypocapnia had completely disappeared, and after 13 breaths P_ETCO2 had increased to above steady state levels. Therefore, an increase in FRC and V_D combined induce hypocapnia only in the first 40 s.

Discussion

The present study determined the relative contributions of increased ventilation and FRC, slight V/Q mismatch, and decreased cardiac output to the postural decrease in P_ETCO2. For this we developed a mathematical model based on respiratory and circulatory physiology, which predicted P_ETCO2 variations during the transition from supine to standing and for 2.5 min in the upright position. The model is sensitive to changes in V_T, FRC and V_D, SV, T_resp, V̇_O2, RQ, and V/Q, all of which affect model output, i.e. P_ETCO2 (Figs 5, 6 and 7). Stroke volume transiently affects model P_ETCO2 with a maximal effect after several breaths (Fig. 5A). This response is asymmetrical, with a greater effect from a decrease in SV compared to an increase in SV. An increase in FRC causes a transient decrease in model P_ETCO2 (Fig. 5B). However, with the concomitant increase in V_D, the FRC-induced hypocapnia is of limited duration (∼40 s). A gravitation-induced slight V/Q mismatch as occurs during standing up (Fig. 1, Table 1) contributes to the decrease in P_ETCO2. RQ affects model P_ETCO2 levels, but does not vary on a breath-to-breath basis. Thus, the V_T increase and SV reduction when standing up are the physiological events primarily responsible for the decrease in P_ETCO2, whereas a gravity-induced V/Q mismatch and, transiently, an increase in FRC contribute to hypocapnia.

The predominant influence of Q on hypocapnia in the standing position was verified in experiments on human subjects, using a protocol in which first breathing alone and then breathing, FRC and V/Q were controlled. The correlation between the decrease in Q and in P_ETCO2 (r²= 0.80), in the absence of alternations in breathing, FRC and V/Q indicates that the postural decrease in Q contributes to hypocapnia.

Limitations

The lung model presented is, by design, a simplified representation of lung ventilation and perfusion, and has limitations. First, the model circulation is simplified into a venous, an arterial and a lung capillary compartment. There is no bronchial arterial shunt included, because its effect on the P_ETCO2 is thought to be small and not likely to vary with posture change. Autoregulation of the lung is not included in our model, and the model circulation does not include a venous pooling reservoir, although venous pooling has profound effects on P_ETCO2 (Hitchcock & Ferguson, 1938). We considered a pooled venous reservoir with high P_CO2 levels in blood and interstitium likely to affect the P_ETCO2 when assuming the supine position after prolonged standing rather than on going from a supine position to standing up. When pooled blood with elevated P_CO2 returns to the heart and subsequently reaches the lungs, this will result in a P_ETCO2‘overshoot’. Interstitial space and CO₂ transfer to and from extracellular space are not modelled, nor are changes in haemoglobin concentration due to haemoconcentration during standing. The model was designed for short-term P_ETCO2 variability and we assumed that changes in haemoglobin concentration are minor.

The apex-to-base V/Q distribution inequality in the standing position results in a decrease in P_ETCO2 because the air expired from alveoli active in gas exchange is diluted by air from apical lung segments which are relatively underperfused, suggesting that the reduction in P_ETCO2 will be more pronounced than the reduction in arterial P_CO2 when standing up. In 1962 Bjurstedt et al. observed that changing from the supine to the standing position was associated with a significant rise in the arterial-to-end-tidal P_CO2 difference. However, our current model and experimental data do not allow us to analyse the arterial-to-end-tidal P_CO2 difference due to the afore-mentioned model limitations, including the absence of a bronchial arterial shunt, a venous pooling reservoir and lung-autoregulation.

To convert [CO₂] to P_CO2 and vice versa, we fitted blood CO₂ equilibrium curves (see Appendix), without accounting for O₂ dependency. We did not implement Kelman's digital computer procedure for conversion of P_CO2 into blood CO₂ content, which in our model would yield a linear relationship because haemoglobin concentration and temperature are assumed to remain constant (Kelman, 1967).

Step changes in V_v and in V_a did not influence P_ETCO2 in the sensitivity analysis, where all other model settings were kept constant. This does not imply that settings for V_v and V_a are of no consequence. These compartments act as buffers for P_ETCO2 changes brought about by variations in V_T, SV, etc. Therefore, a larger V_v or V_a will result in damping of P_ETCO2 variations.

Several model parameters are estimated based on previous studies. The distribution of ventilation and perfusion in the upright position are based on measurements of West (1962). The distribution of ventilation and perfusion over the lung are influenced by a gravity-invoked hydrostatic pressure gradient (perfusion) and a pleural pressure gradient influencing the alveolar pressure–volume relationship (ventilation). Although in the supine position there is still some effect of gravity, this will be less because the vertical height of the lung is less than in the upright position. Therefore, we chose to model the distribution of ventilation and perfusion in the supine position as equally distributed from apex to base.

Conclusions

In human subjects assuming the upright position, end-tidal CO₂ levels drop. The present study shows that the CO₂ levels during posture change can be tracked using a mathematical model, with breath-to-breath values for tidal volume, stroke volume, pulmonary O₂ uptake and respiratory interval as input variables. We found that the decrease in end-tidal CO₂ level in the standing position is due to increased tidal volume and transiently decreased cardiac output, and increased FRC. The gravity-induced slight ventilation–perfusion mismatch contributes to hypocapnia.

Model equations

Conversion and weight functions

The CO₂ equilibrium curve relating blood CO₂ content ([CO₂]) to blood partial CO₂ pressure (P_CO2) is described as [CO₂]=f(P_CO2), with

To compute P_CO2 from [CO₂] in blood, we use the inverse function

To convert P_CO2 in air (mmHg) to [CO₂] (%), we use the conversion factor c, which amounts to 0.1316% mmHg⁻¹. The distribution of SV and V_T over each lung compartment k (k = 1…9) is described by functions g and h, respectively. These functions, which are different for the supine and upright positions and yield the fractions for SV and V_T listed in Table 2, are given by

and

Each lung compartment's share of FRC, V_cap and V_D is given by the weight function

which yields the fractions for FRC and V_cap listed in Table 2.

Venous CO₂

For each breath n, the venous CO₂ content ([CO₂]_v,n) is calculated from its previous value [CO₂]_v,n-1 according to eqns (1)–(4). The amount of CO₂ in the venous compartment increases by the amount that arrives from the arterial compartment (A) and the amount created by the basal metabolism (B), and decreases by the amount that leaves the compartment (C). Thus, we have

(1)

where

(2)

(3)

with [CO₂]_a denoting the arterial CO₂ content, and

(4)

where V̇_O2,n is the oxygen extraction for breath n (in ml min⁻¹) and RQ is the respiratory quotient, which is set at 0.9 (the average as approximated from subject data, by dividing V_co2by V̇_O2). The term is multiplied by the breath duration (in min) (T_resp,n/60) to estimate the CO₂ produced per breath.

Arterial CO₂

The arterial blood CO₂ content for breath n ([CO₂]_a,n) is calculated from its previous value [CO₂]_a,n-1 according to eqns (5)–(7). The amount of CO₂ in the arterial compartment increases by the amount of CO₂ arriving from the lungs (D) and decreases by the amount of CO₂ leaving the arterial compartment (E)

(5)

The amount D can be estimated from the end-tidal partial CO₂ pressure in each lung compartment k (P_kCO2k = 1…9) through

(6)

Where f is the above function that relates blood CO₂ content to the blood partial CO₂ pressure and g is the above function that defines the distribution of SV over the nine lung compartments. The amount E is given by

(7)

Lung CO₂

The P_CO2 of blood draining the lungs (P_tcCO2) is dependent on the gravity-induced perfusion and ventilation gradients, as described by the above functions g and h. For each breath, the P_CO2 in each lung segment k (P_kCO2,n) is calculated according to eqns (8)–(13). At FRC, the amount of CO₂ in lung segment k (F) is determined by the CO₂ content in the lung capillaries, in the FRC and in the V_D

(8)

with the weight function w and conversion factor c as described above. The contribution of CO₂ in dead space (the right-most term) is computed noting that end-tidal air from the previous breath is returned to the lungs from dead space. The amount of CO₂ carried to the lungs from the venous compartment (G) is given by

(9)

The ratio a of [CO₂] in blood and [CO₂] in air is approximated from the previous breath, n– 1, according to

(10)

The ratio b of the end-tidal amount of CO₂ in air and the total amount of CO₂ is given by

(11)

The end-tidal [CO₂] in each lung compartment k is determined by the total amount of CO₂ (F+G), which is distributed over air and blood with ratio b, and the end-tidal volume of air in compartment k

(12)

A simple conversion using the above constant c then yields P_kCO2,n. The P_ETCO2 depends on the distribution of tidal volume, which is given by the fraction h(k),k = 1..9, and differs between the supine and the standing position, and is computed as

(13)