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Eur Respir J 2001; 17:1167-1174
Copyright ©ERS Journals Ltd 2001

Noninvasive measurement of mean alveolar carbon dioxide tension and Bohr's dead space during tidal breathing

N.G. Koulouris, P. Latsi, J. Dimitroulis, B. Jordanoglou, M. Gaga and J. Jordanoglou

Dept of Respiratory Medicine, Respiratory Function Laboratory, University of Athens Medical School, "Sotiria" Hospital for Diseases of the Chest, Athens, Greece

CORRESPONDENCE: J. Jordanoglou, Dept of Respiratory Medicine, Respiratory Function Laboratory, University of Athens Medical School, "Sotiria" Hospital for Diseases of the Chest, 152, Mesogion Ave, Athens, GR-11527, Greece. Fax: 30 17770423

Keywords: alveolar carbon dioxide tension, arterial carbon dioxide tension, Bohr's dead space, chronic obstructive pulmonary disease, end-tidal carbon dioxide, physiological dead space

Received: July 13, 2000
Accepted January 30, 2001


   Abstract
TOP
 Abstract
Methods
 Results
 Discussion
 Appendix
 Acknowledgements
 References
 
The lack of methodology for measuring the alveolar carbon dioxide tension (PA,CO2) has forced investigators to make several assumptions, such as that PA,CO2 is equal to end-tidal (PET,CO2) and arterial CO2 tension (Pa,CO2).

The present study measured the mean PA,CO2 and Bohr's dead space ratio (Bohr's dead space/tidal volume (VD,Bohr/VT)) during tidal breathing. The method used is a new, simple and noninvasive technique, based on the analysis of the expired CO2 volume per breath (VCO2) versus the exhaled VT. This curve was analysed in 21 normal, healthy subjects and 35 chronic obstructive pulmonary disease (COPD) patients breathing tidally through a mouthpiece apparatus in the sitting position.

It is shown that: 1) PA,CO2 is similar to Pa,CO2 in normal subjects, whilst it is significantly lower than Pa,CO2 in COPD patients; 2) PA,CO2 is significantly higher than PET,CO2 in all subjects, especially in COPD patients; 3) VD,Bohr/VT is increased in COPD patients as compared to normal subjects; and 4) VD,Bohr/VT is lower than the "physiological" dead space ratio (VD,phys/VT) in COPD patients.

It is concluded that the expired carbon dioxide versus tidal volume curve is a useful tool for research and clinical work, because it permits the noninvasive and accurate measurement of Bohr's dead space and mean alveolar carbon dioxide tension accurately during spontaneous breathing.

The respiratory dead space is the concept in gas exchange derived by the investigators in their effort to determine the effectiveness of ventilation in health and disease. After the description of the dead space by Bohr 1, numerous papers on the subject followed, in which the methodology can be divided into two categories; the noninvasive studies from gas (nitrogen (N2), Helium (He), carbon dioxide (CO2)) concentration versus time or volume curves, and the invasive studies in which the arterial CO2 tension (Pa,CO2) instead of the alveolar CO2 tension (PA,CO2) was used 2–15. In the noninvasive methods, the "anatomical" dead space, i.e. Fowler's dead space (VD(F)), is determined from the expired gas concentration versus tidal volume or vital capacity curve, which is analysed by geometrical methods. The results obtained by this method may be doubtful since the junction of the phases II and III is difficult to define in disease, especially during tidal breathing. Furthermore, this analysis is based on the assumption that the end-tidal and alveolar CO2 fractions (FET,CO2 and FA,CO2) are identical. However, there is substantial evidence that FET,CO2 is lower than FA,CO2 in normal subjects and patients 16–18. The invasive methods permit the measurement of the "physiological" dead space ratio (physiological dead space/tidal volume (VD,phys/VT)), by using Pa,CO2 in Bohr's equation with the assumption that PA,CO2 is equal to Pa,CO2, which is valid only in normal subjects.

In previous reports 17, 18, Bohr's dead space ratio (Bohr's dead space/tidal volume (VD,Bohr/VT)) and PA,CO2 were not measured either simultaneously or within the volume domain. Since VD,Bohr/VT is in the volume domain, theoretically it appeared most appropriate to develop a new technique, i.e. the construction and mathematical analysis of the expired CO2 volume versus tidal volume curve (VCO2 versus VT curve). This curve, recorded at the mouth during expiration, has a curvilinear shape and the CO2 concentrations within the airways are lower than the alveolar one as a result of the "dilution effect" due to the pre-inspired atmospheric air (Appendix 1).

This technique allowed the simultaneous measurement of VD,Bohr/VT and PA,CO2. This simple and noninvasive method was applied in 21 normal subjects and 35 chronic obstructive pulmonary disease (COPD) patients breathing tidally through a mouthpiece apparatus. VD,Bohr/VT was compared to VD,phys/VT, and PA,CO2 to Pa,CO2 and end-tidal carbon dioxide tension (PET,CO2).


   Methods
TOP
 Abstract
 Methods
Results
 Discussion
 Appendix
 Acknowledgements
 References
 
Theoretical considerations
The VCO2 versus VT curve was derived from the expiratory flow and CO2 concentration versus time tracings measured at the mouth. It was constructed by plotting the exhaled VCO2 (the integral of CO2 fraction and flow with respect to time (VCO2={int}FCO2 V'dt)) versus the tidal volume (the integral of flow with respect to time (VT={int}V'dt)). The FET,CO2 was determined, by computer analysis, from the mean of 10 points of the last segment on the FCO2 versus time curve, at which the positive slope of the tangent with the horizontal line becomes zero. Beyond these points the curve started to have a consistent negative slope. The height of the mean of these points from the zero line of the curve represents the FET,CO2. The mixed expired CO2 fraction (FE,CO2) is the ratio of the total expired VCO2 per breath over VT (Appendix 1). The analysis of the VCO2 versus VT curve is described in detail in the Appendix section.

Study design
The experimental set-up consisted of a flanged semirigid plastic mouthpiece connected in series to a Fleisch No. 2 flow transducer head (Fleisch, Lausanne, Switzerland) via a metal piece (monitoring ring), on which the CO2 probe was attached (mouthpiece apparatus). The pneumotachograph (transducer and amplifier: Gould, Godart BV; No. 17212, Bilthoven, Holland) was connected with the Fleisch head via two semirigid plastic tubes 50 cm in length. The pneumotachograph system (rise time 10–90%=13 ms) was linear over the range of flows used. Volume was obtained by integration of the flow signal. An infrared capnograph (Jaeger; CO2 test III, Wuerzburg, Germany) (rise time 10–90%=100 ms) was connected to the monitoring ring through a thin polythene tube (length 50 cm, internal diameter 1.2 mm). The resistance of the mouthpiece apparatus to airflow was negligible. The rise time (10–90%) of the capnograph measured at the mouthpiece was ≥4.5 times faster than that of the fastest FCO2 versus time curve (FCO2/t), in normal subjects and COPD patients breathing at a frequency of 10–25·min–1. Calibration of the CO2 analyser was made using a standard mixture of CO2 (4.0%) in N2. The phase lag between the FCO2 versus t and V' versus t signals was determined by an abrupt change in flow of the above gas mixture generated through the experimental set-up. The measurement of the phase lag and the calibration of the CO2 analyser were repeated three times and the mean values were used. Airflow and CO2 signals were monitored on-line on a computer screen and sampled simultaneously at a rate of 150 Hz using a computer data acquisition system with a built-in 12-bit analogue-to-digital converter (National Instruments, AT-M10, Austin, Texas, USA). Collected data were stored on computer disk for subsequent analysis with custom-made computer analysis software. VCO2 and VT were expressed in mL body temperature and pressure, saturated (BTPS).

The study was performed in 21 normal subjects and 35 ambulatory COPD patients. Lung function data were obtained in the seated position with a flow-sensing spirometer (Fukuda; Spiroanalyzer ST300, Tokyo, Japan). Anthropometric and routine lung function data are given in table 1Go. Predicted values were those of Morris et al. 19. The subjects were studied while seated, breathing room air through the mouthpiece apparatus with a noseclip on, at their own resting VT and respiratory frequency. Each subject had an initial 10–15 min trial run to become accustomed to the apparatus and procedure. After regular breathing had been achieved, a series of breaths over a period of 1 min were recorded. At the end of the recording time, while the subject was still connected to the mouthpiece, an arterial blood sample (>1 mL) was taken for gas analysis. An expert physician using a 21 G needle, performed a quick (5–10 s) and direct puncture of the brachial artery. It is highly unlikely that a change in blood gases took place in such a short time interval. If the procedure of gas sampling was not successful after one single effort, the experiment was cancelled. The cancelled experiments were <7.5%. The Pa,CO2 was measured with a blood gas analyser (CIBA-CORNING; 288 Blood gas system, MA, USA) in 12 normal subjects and in all COPD patients.


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  		Table 1— Anthropometric and routine lung function data from 21 normal subjects and 35 chronic obstructive pulmonary disease (COPD) patients. Values are presented as mean±sd

 
The method was experimentally verified in three normal subjects during tidal breathing through different tubes of a known capacity. The dead space of the added tube (Vtube) was calculated from the difference VD–VD(o), where: VD and VD(o) are VD,Bohr of the subject breathing through the mouthpiece apparatus with and without the added tube, respectively. Three tubes were used, the capacities (Vcap) of which were 180, 337 and 504 mL calculated from the equation {pi}xr2xl ({pi}=3.14, r=radius and 1=length of the tube). The capacity of the tube deviated from the measured volume by <2.3% (table 2Go).


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  		Table 2— The capacity of the added tubes (Vcap={pi}xr2xl), the mean of the measured volume (Vtube, measured) in three normal subjects, and the calculated volume (Vtube, calculated) obtained by the regression equation (footnote) are shown.

 
The study had the approval of the local ethics committee and all subjects gave informed consent.


   Results
TOP
 Abstract
 Methods
 Results
Discussion
 Appendix
 Acknowledgements
 References
 
PA,CO2 and VD,Bohr/VT were measured by analysis of the VCO2 versus VT curve obtained from 21 normal subjects and 35 COPD patients during tidal breathing. It is noted that cardiogenic oscillations had no effect on the VCO2 versus VT curve, as this was consistently smooth in all subjects (Appendix 1). VD,Bohr/VT, VT, PET,CO2 and PA,CO2, were obtained for each subject by averaging all breaths during a 1-min data recording period.

The mean within-study, within-day and day-to-day coefficient of variation for VD,Bohr/VT was 6.5, 6.85 and 7.25% and for PA,CO2 1.57, 3.06, and 3.05%, respectively. These were determined in three normal subjects in whom measurements were repeated three times per day for 3 consecutive days.

VD,Bohr/VT and VD,phys/VT were not significantly different in the 12 normal subjects. In contrast, this difference was statistically significant in the COPD patients (p<0.001). The VD,Bohr/VT ratio in COPD patients was significantly higher than in normal subjects (p<0.001), (table 3Go; fig. 1Go). VD,Bohr/VT was higher than the dead space ratio measured from the FCO2 versus VT curve by Fowler's geometrical method of orthogonal projection (VD(F)/VT). In normal subjects, mean±sd VD(F)/VT was 28±8% and in COPD patients, 37±8%. The mean difference between VD,Bohr/VT and VD(F)/VT is 5±1% in normal subjects (p<0.001) and 7±2% in COPD patients (p<0.001).


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  		Table 3— Comparison of dead space ratios, in 21 normal subjects and 35 chronic obstructive pulmonary disease (COPD) patients.

 


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  		Fig. 1.— Scatter diagrams illustrating the relationship between Bohr's dead space ratio (Bohr's dead space/tidal volume (VD,Bohr)/VT)) and physiological dead space ratio (physiological dead space/tidal volume (VD,phys/VT)) in a) normal subjects and b) chronic obstructive pulmonary disease patients. Regression lines are shown: a) VD,Bohr/VT=0.151+0.508 (VD,phys/VT), r=0.584, n=12, p=0.046; b) VD,Bohr/VT=0.17+0.54 (VD,phys/VT), r=0.691, n=35, p<0.001. Dotted lines represent 95% confidence intervals of regression.

 
PA,CO2 and Pa,CO2 were compared in 12 normal subjects and in all patients. In the COPD patients, Pa,CO2 was significantly higher than PA,CO2 (p<0.001). In the 12 normal subjects, the difference between Pa,CO2 and PA,CO2 was not statistically significant (table 4Go; fig. 2Go). In all normal subjects and patients, PA,CO2 was significantly higher than PET,CO2 (table 4Go, fig. 3Go). The relationship between PET,CO2 and PA,CO2 is shown in figure 3Go.


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  		Table 4— Alveolar (PA,CO2) arterial (Pa,CO2), and end-tidal (PET,CO2) tension (kPa), in normal subjects and chronic obstructive pulmonary disease (COPD) patients.

 


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  		Fig. 2.— Scatter diagrams illustrating the relationship between alveolar (PA,CO2) and arterial carbon dioxide tensions (Pa,CO2) in a) normal subjects and b) chronic obstructive pulmonary disease patients. A significant regression was found for COPD: PA,CO2=1.38+0.64 Pa,CO2, r=0.551, n=35, p<0.001. Dotted lines represent 95% confidence intervals of regression.

 


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  		Fig. 3.— Scatter diagrams illustrating the relationship between end-tidal (PET,CO2) and alveolar carbon dioxide (PA,CO2) tension in a) normal subjects and b) chronic obstructive pulmonary disease patients. Regression lines are shown: a) PET,CO2=0.122+0.92 PA,CO2, r=0.972, n=21, p<0.001; b) PET,CO2=0.065+0.88 PA,CO2, r=0.976, n=35, p<0.001. Dotted lines represent 95% confidence intervals of regression.

 
The alveolar-end-tidal PCO2 ((A-ET) CO2) and the arterial-alveolar PCO2 ((a-A) CO2) differences were also related to the VD,Bohr/VT ratio. In all subjects, no statistical relationship was found between (a-A) CO2 and VD,Bohr/VT. In contrast, the (A-ET) CO2 was significantly related to the VD,Bohr/VT ratio in both groups of subjects, i.e. (A-ET) CO2=–0.050+(VD,Bohr/VT) (kPa) (r=0.79, SEE=0.072, p<0.001) in normal subjects and (A-ET) CO2=–0.261+1.852x(VD,Bohr/VT) (kPa) (r=0.83, SEE=0.122, p<0.001) in COPD patients.

The validity of the analysis of the VCO2 versus VT curve was also examined by calculating the expired VCO2 per breath from 1) the product FA,CO2xalveolar ventilation (V'A) (=VCO2(A)), and 2) the equation VCO2(B)=FslxVd+FET,CO2xalveolar volume (VA). The mean error between VCO2(A) and VCO2(B) was –0.02±1% in the normal subjects and 0.4±1% in the COPD patients (Appendix 3). The area A(A) differed from the area A(B) by 4±0.5% in normal subjects and 3±2% in COPD patients (Appendix 3).


   Discussion
TOP
 Abstract
 Methods
 Results
 Discussion
Appendix
 Acknowledgements
 References
 
The present study used the expired VCO2 versus the exhaled VT curve for the noninvasive measurement of VD,Bohr/VT and mean PA,CO2 in normal subjects and COPD patients during tidal breathing. According to the results: 1) VD,Bohr/VT is increased in COPD patients as compared to normal subjects; 2) VD,Bohr/VT is lower than VD,phys/VT in COPD patients; 3) PA,CO2 is closely similar to Pa,CO2 in normal subjects, whilst it is significantly lower than Pa,CO2 in COPD patients; and 4) PA,CO2 is significantly higher than PET,CO2 in all subjects, especially in COPD patients. This curve overcomes: 1) the assumption inherent in the analysis of the FCO2 versus V curve, i.e. that FA,CO2 is equal to FET,CO2; and 2) the difficulty in drawing the extrapolated line of the sloping alveolar plateau in disease, especially during tidal breathing.

At a steady state, regardless of the actual value of the V'A/perfusion (Q') ratio, the CO2 molecules within the residual air define FA,CO2. This is dependent on the dynamic equilibrium within the alveolar space between the inflow and outflow of the CO2 molecules, and the overall V'A/Q' ratio of the lungs at the existing functional residual capacity. A portion of the CO2 molecules is exhaled with the VT constituting the expired VCO2 per breath. During expiration, these molecules move out from the alveolar space mainly by bulk movement but also by diffusion, and at the same time they are replaced by CO2 molecules originating from blood through the alveolar membrane. The concentrations of the CO2 molecules within the airways, diluted by pre-inspired atmospheric air, are lower than the alveolar concentration. As a result of the "dilution effect", the VCO2 versus VT curve gets the curvilinear shape recorded at the mouth (Appendix 1).

The analytical procedure of the VCO2 versus VT curve was verified, both theoretically and practically i.e. 1) The measurement of the volume of the added tubes with a deviation of <2.3% from the capacity of the tubes denotes the validity and the accuracy of the described method. The added tube affects the entire VCO2 versus VT curve and its volume was calculated from the change of VD,Bohr. 2) The nonsignificant difference in normal subjects between PA,CO2 and Pa,CO2 is strong evidence for the accuracy of the method. 3) The Equations 9 and 10GoGo in Appendix 1, derived from the VCO2 versus VT curve, are identical to those widely accepted in the literature 1–18. 4) The mean error between VCO2(A) and VCO2(B) is <0.4%, i.e. VCO2(A)=VCO2(B). This equality means that the points b, d and a are correctly positioned and not arbitrarily taken (Appendix 1, 3). Furthermore, the mean deviation of the area A(A) from the area A(B) is very small (Appendix 3).

The repeatability of the measurements for VD,Bohr/VT was ~7% and for PA,CO2 ~3%. However, the increase of the coefficient of variation of the VT per se beyond the value of 16% reduces the repeatability especially of VD,Bohr/VT.

VD,Bohr(=segment ia; Appendix 1) is higher than VD(F), measured from the FCO2 versus V curve (Fowler's method), by the amount of the volume segment Vda (=VCO2(d)/FET,CO2), if the analysis of the FCO2 versus V curve is performed according to the method of orthogonal projection of the curve (Appendix 2). So, the ratio VD,Bohr/VT is higher than usually referred to in the literature 1–18. If, however, the FCO2 versus V curve is analysed by the method of the "sloping alveolar plateau", the difference between VD,Bohr and VD(F) is even higher (Appendix 2).

The alveolar CO2 and the mixed expired CO2 concentrations are the two ends of a spectrum of gas fractions influenced by several mechanisms affecting the homogeneity of ventilation. According to the law of conservation of mass, the product FE,CO2xVT is equal to FA,CO2xVA or to the intermediate products FslxVbe or FET,CO2xVde (Appendix 1). That is, VCO2 per breath is exhaled with the VT at the mixed expired gas concentration or with smaller volumes at increased gas concentrations until the minimal volume (alveolar, VA) at the highest gas concentration (FA,CO2). Mean FA,CO2 cannot be greater than a maximal value determined by the overall V'A/Q' ratios of the lungs.

The real VCO2 versus VT curve functionally can be represented by the line iac (Appendix 1). The segment ia is VD,Bohr, which if considered without CO2 gas, then the segment ae (=projection of the line ac on the horizontal axis with the angle cae (=FA,CO2)) is the mean VA transferring out all the VCO2 per breath with the maximal concentration (FA,CO2).

VD,Bohr/VT is considered as an index of maldistribution of the expired air within the lungs, i.e. within the space between the inner surface of the alveolar membrane and the mouth. The VD,phys/VT is influenced not only by the mechanisms of uneven ventilation, but also by the mechanisms of inhomogeneous distribution of Q'. In normal subjects, in whom Pa,CO2 is approximately equal to PA,CO2, the difference between VD,phys/VT and VD,Bohr/VT was not statistically significant. This may be a true result or is more likely due to the small number of observations (power of paired t-test=0.201). In the COPD patients, in whom Pa,CO2 was higher than PA,CO2, the difference between the two dead space ratios was considerable (table 3Go).

Pa,CO2 in normal subjects was not significantly different from PA,CO2. However, in COPD patients (a-A) CO2 was significantly higher than in normal subjects (table 4Go). This may be explained as follows. An increased PA,CO2 in regions with low V'A/Q' ratio is followed by an increase of the end-capillary PCO2 (Pc,CO2) locally, while in regions with a high V'A/Q' ratio, the decrease of PA,CO2 is accompanied by a local decrease of Pc,CO2. If the arterial blood is composed mainly from blood perfusing regions with a low V'A/Q' ratio, Pa,CO2 will be increased. At the same time, when the exhaled VT contains air coming mostly from regions with high V'A/Q' ratio, PA,CO2 will be decreased. The combination of these two conditions probably results in the increased (a-A) CO2 in patients with COPD. This is compatible with the results obtained, i.e. that the (a-A) CO2 is not statistically related to VD,Bohr/VT in the subjects studied. In contrast, (A-ET) CO2 is significantly related to VD,Bohr/VT in all subjects, due to the existing inhomogeneity of ventilation, especially in the COPD patients. The (A-ET) CO2 was higher in COPD patients than in normal subjects (table 4Go). In addition, PA,CO2 was linearly related to PET,CO2, and PA,CO2 was higher than PET,CO2 in all subjects (fig. 3Go). The (A-ET) CO2 difference was strongly related to VD,Bohr/VT in normal subjects and COPD patients, as is described in Equation 11Go (Appendix 1).

PA,CO2 is VCO2/VA times the factor (barometric pressure-47), as conventionally referred to in the literature. It is mentioned that the measured value of PA,CO2 per breath is a mean value from all the regions of the lungs with different V'A/Q' ratios. Furthermore, the values of PA,CO2 shown in the Results section are mean values from all breaths during the 1-min sampling period.

It is concluded that the carbon dioxide output versus tidal volume curve obtained during tidal breathing with minimal cooperation on the patient's part, is useful in clinical practice and research work. It allows, with accuracy and precision, the noninvasive measurement and monitoring of the mean alveolar carbon dioxide tension and Bohr's dead space volume. The alveolar carbon dioxide tension can be safely used instead of the arterial one in normal subjects, but not in chronic obstructive pulmonary disease patients. In all subjects, end-tidal carbon dioxide tension cannot be used instead of alveolar carbon dioxide tension.



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  		Fig. 4.— The expired carbon dioxide (CO2) volume versus the exhaled volume curve (VCO2 versus VT) obtained from a chronic obstructive pulmonary disease patient. The volume segment ie is the tidal volume (VT). The point I is the beginning of expiration and the point e the end of it. Angle cie is the mixed expired CO2 concentration (FE,CO2). Angle cbe (Fsl) is the average slope of the curve. The area under the whole curve (area E) is equal to the area of the triangle cbe. The areas K and M are equal to each other. Vbe: volume segment be.

 



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  		Fig. 5.— The same curve as in figure 4Go. The slope of the line cd represents the end-tidal concentration (FET,CO2), measured directly from the carbon dioxide fraction (FCO2) versus time curve. Area D is equal to the area of the triangle bcd (=1/2VCO2xVd), where VCO2 is expired CO2 and Vd is the volume segment bd (=Vbe–Vde). The gas volume VCO2(d) (=gas volume segment xd=ya=ee') is calculated from Equation 4Go. The segment iu contains no CO2 gas (=Vo) and it represents the upper airways dead space volume. The volume segment ua represents the transitional volume (Vtr). VD,Bohr: Bohr's dead space; VA: alveolar ventilation.

 



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  		Fig. 6.— The same curve as in figure 4Go. The point y on the line cd is the limit, below which the gas volume is expired at the mean concentration Fd (=VCO2(d)/(VD,Bohr)) (smaller than end-tidal carbon dioxide fraction (FET,CO2)) and above which at a constant concentration equal to FET,CO2. The segment yc projected horizontally with the slope FET,CO2 gives the volume segment ye', which is equal to the volume segment ae representing the alveolar volume (VA). The triangular area cae is equal to the sum of the areas iya and cye'. VCO2 per breath forms with the VA the angle cae, which represents the mean alveolar CO2 concentration (FA,CO2). The volume segment ia represents Bohr's dead space volume (VD,Bohr).

 


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  		Fig. 7.— The carbon dioxide concentration versus the exhaled volume curve (FCO2 versus VT) (upper curve) obtained from a chronic obstructive pulmonary disease patient and the expired CO2 versus exhaled volume (VCO2 versus VT) curve (lower curve), which is derived from the upper curve. FCO2 is expressed in %, VT in litres, and VCO2 in mL. In this patient, Bohr's dead space ratio (Bohr's dead space/tidal volume (VD,Bohr/VT)) is 0.60. According to the geometrical method of orthogonal projection, anatomical dead space measured by Fowler's technique/tidal volume ratio (VD(F)/VT) is equal to 0.53. If the extrapolation of the "sloping alveolar plateau" is drawn, the ratio VD(F)/VT becomes even smaller than when measured by the technique of orthogonal projection and is equal to 0.48.

 


   Appendix
TOP
 Abstract
 Methods
 Results
 Discussion
 Appendix
Acknowledgements
 References
 
1. The expired carbon dioxide volume versus tidal volume curve

The simplified analysis of the VCO2 versus VT curve, presented in geometrical terms, is as follows. The total area under the VCO2 versus VT curve (E) is equal to the area of the triangle bce. In either side of the line bc (hypotenuse) the areas K and M are equal to each other (fig. 4Go). Accordingly, the volume segment be (Vbe) on the VT axis is equal to (fig. 5Go):


(001)

The angle cbe represents the average slope (Fsl=VCO2/Vbe) of the VCO2 versus VT curve (figs. 4 and 5GoGo). FET,CO2 is measured directly at the end of the FCO2 versus time curve. The ratio VCO2/FET,CO2 determines the volume segment de (Vde) on the horizontal axis (fig. 5Go), i.e.


(002)

The line cd, the volume segment id and the curve itself confine the one-sided area D, which is equal to the area of the triangle bcd (fig. 5Go), i.e.


(003)
where: (Vbe-Vde) is the base (volume segment bd=Vd) of the triangle bcd. The area D denotes that a part of VCO2 (VCO2(d)) is exhaled at smaller concentrations than FET,CO2. The gas volume VCO2(d) (segment xd) is calculated from the average slope of the curve (Fsl) and the volume segment Vd (fig. 5Go), i.e.


(004)

The gas volume VCO2, as already described, is expired in two parts, the initial one (VCO2(d)) with a mean concentration Fd and the rest (VCO2-VCO2(d)) with concentration equal to FET,CO2 (fig. 6Go). The meeting point (y) of these two slopes (Fd and FET,CO2) lies on the line cd and the gas volume segments xd, ya and ee' are equal to each other (=VCO2(d)) (figs. 5 and 6GoGo). The volume segment ye' is equal to the segment ae, and represents the alveolar part of the VT with which the gas volume (VCO2-VCO2(d)) is expired at the end-tidal concentration (FET,CO2), i.e.


(005)
VD,Bohr is equal to:


(006)

This is divided into two portions, the initial volume Vo (=volume segment iu) and the transitional volume Vtr (=volume segment ua) (figs. 5 and 6GoGo). The volume Vo is the initial part of the VT with no CO2 gas in it. The transitional volume contains the gas volume VCO2(d) and is equal to (figs. 5 and 6GoGo):


(007)
and


(008)

The volume Vo is directly measured by the computer as the volume segment from the beginning of expiration (point i) to point u, at which CO2 gas starts appearing in the expired air.

VA is calculated from Equation 5Go. If FCO2 is considered as zero in VD,Bohr (Vo+Vtr), then all the VCO2 per breath should be expired with the VA (fig. 6Go). So, the mean alveolar FCO2 is calculated from the equation:


(009)
By substituting in Equation 9Go the term VCO2 by its equal FE,CO2xVT, the equation for the VA/VT ratio is the following:


(010)
where FE,CO2 is the mixed expired CO2 fraction (=({Sigma}on(dVCO2/dV)]/n=angle cie) (fig. 4Go). Since the VA is smaller than the volume segment Vde by the volume segment da (Vda=VCO2(d)/FET,CO2), FA,CO2 is greater than FET,CO2 (fig. 6Go), i.e.


(011)
Equation 11Go is derived from Equations 5 and 9GoGo.

2. Relationship between the expired carbon dioxide versus tidal volume and carbon dioxide fraction versus tidal volume

The gas volume versus VT curve (lower curve) and the corresponding gas concentration versus VT curve (upper curve) are obtained from a single breath of a COPD patient (fig. 7Go). In the upper curve (FCO2 versus VT curve), the vertical line dd' corresponds to the point d of the lower curve. The line dd' separates the FCO2 versus VT curve to the areas A and B, which are equal to each other. It is evident that VD(F), measured by Fowler's technique of orthogonal projection, is smaller than VD,Bohr by the volume segment Vda. It is mentioned that if VCO2(d) is zero, VD(F) is equal to VD,Bohr. In the upper curve (FCO2 versus VT), the drawing of the line of the "sloping alveolar plateau" is very difficult. However, if the last part of the FCO2 versus VT, which by no means is a straight line, is extrapolated, VD(F) becomes even smaller as compared to VD,Bohr by the volume segment Vda (fig. 7Go).

3. Verification of the method

The analysis of the VCO2 versus VT curve was verified as follows: 1) In three normal subjects breathing tidally through tubes of known capacity (Vcap) interposed between the mouthpiece and the monitoring ring, the dead space volume was measured without (VD(o)) and with the added tube (VD). The difference VD-VD(o) was compared with the capacity of the added tube (Results). 2) The gas volume VCO2(A) (=FA,CO2xVA) was compared to the volume VCO2(B) (=FslxVd+FET,CO2xVA) (fig. 6Go). The error between VCO2(A) and VCO2(B) was calculated from (l-(VCO2(B)/VCO2(A)))x100 (Results). 3) The area A(A) (=1/2VAxVCO2) was compared to the area A(B) (=1/2VD,BohrxVCO2(d)+1/2VAx(VCO2-VCO2(d))) with an error calculated from [1-(A(B)/A(A))]x100 (Results) (fig. 6Go). 4) In normal subjects, PA,CO2 did not differ significantly from Pa,CO2 (Results).


   Acknowledgements
TOP
 Abstract
 Methods
 Results
 Discussion
 Appendix
 Acknowledgements
References
 
The authors are grateful to N.B. Pride, M. Hughes, and P.T. Macklem for their most constructive criticism.


   References
TOP
 Abstract
 Methods
 Results
 Discussion
 Appendix
 Acknowledgements
 References
 

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