Alveolar dead space (VDalv) impairs pulmonary

Transcription

1 Estimating Alveolar Dead Space from the Arterial to End-Tidal CO 2 Gradient: A Modeling Analysis Jonathan G. Hardman, FRCA, and Alan R. Aitkenhead, FRCA From the University Department of Anaesthesia, University Hospital, Nottingham, NG7 2UH, UK Using an original, validated, high-fidelity model of pulmonary physiology, we compared the arterial to endtidal CO 2 gradient divided by the arterial CO 2 tension (Pa-e'co 2 /Paco 2 ) with alveolar dead space expressed as a fraction of alveolar tidal volume, calculated in the conventional manner using Fowler s technique and the Bohr equation: (VDalv/VTalv) Bohr-Fowler. We examined the variability of Pa-e'co 2 /Paco 2 and of (VDalv/ VTalv) Bohr-Fowler in the presence of three ventilationperfusion defects while varying CO 2 production (V co 2 ), venous admixture, and anatomical dead space fraction (VDanat). Pa-e'co 2 /Paco 2 was approximately 59.5% of (VDalv/VTalv) Bohr-Fowler. During constant alveolar configuration, the factors examined (V co 2, pulmonary shunt fraction, and VDanat) each caused variation in (VDalv/VTalv) Bohr-Fowler and in Pa-e'co 2 / Paco 2. Induced variation was slightly larger for Pae'co 2 /Paco 2 during changes in VDanat, but was similar during variation of venous admixture and V co 2. Pa-e'co 2 /Paco 2 may be a useful serial measurement in the critically ill patient because all the necessary data are easily obtained and calculation is significantly simpler than for (VDalv/VTalv) Bohr-Fowler. (Anesth Analg 2003;97: ) Alveolar dead space (VDalv) impairs pulmonary gas exchange, increases the obligatory work of breathing and prevents or prolongs weaning from mechanical ventilation (1,2). Measurement of VDalv may facilitate estimation of disease progression, increase the efficacy of some interventions (particularly ventilatory), and improve perioperative outcome (3,4). Recent evidence suggests that pulmonary dead space fraction may be an independent predictor of mortality from acute respiratory distress syndrome (5). Therefore, its measurement may be important on the intensive care unit (ICU). However, the technical and time-consuming nature of measurement of VDalv prevents its routine use on the ICU. Nunn and Hill (6) have suggested that there is a relationship between the arterial to end-tidal CO 2 tension gradient (Pa-e'co 2 ) and the Vdalv fraction, but they did not investigate this relationship. In a previous investigation we used simple physiological modeling to examine the relationship between Pa-e'co 2 /Paco 2 and VDalv, calculated in the conventional manner using Fowler s technique and Enghoff s modification of the Bohr equation, expressed a fraction of alveolar Accepted for publication July 21, Address correspondence and reprint requests to Jonathan G. Hardman, Clinical Senior Lecturer, University Department of Anesthesia, University Hospital, Nottingham, NG7 2UH, UK. Address to j.hardman@nottingham.ac.uk. DOI: /01.ANE tidal volume: (VDalv/VTalv) Bohr-Fowler. We concluded in that investigation Pa-e'co 2 /Paco 2 had a roughly constant, linear relationship with (VDalv/VTalv) Bohr- Fowler as follows: (VDalv/VTalv) Bohr-Fowler 1.14 Pa-e'co 2 /Paco , and that it could be substituted acceptably for the conventional calculation (7). This investigation uses physiological models of much greater sophistication than those used previously. The advances in modeling that have made reevaluation important are detailed in the Appendix. Our aims were: 1. To examine the relationship between Pa-e'co 2 / Paco 2 and (VDalv/VTalv) Bohr-Fowler. 2. To determine the susceptibility of Pa-e'co 2 /Paco 2 and of (VDalv/VTalv) Bohr-Fowler to change induced by coincidental variation of physiological factors during a constant alveolar configuration (i.e., constant pulmonary ventilation and perfusion distributions). Such change is misleading because it causes the appearance of a change in alveolar configuration when such a change has not occurred. The better, independent measure of alveolar configuration is less susceptible to variation. Methods Physiological Models The models used in this investigation are based on the published and validated Nottingham Physiological 2003 by the International Anesthesia Research Society 1846 Anesth Analg 2003;97: /03

2 ANESTH ANALG HARDMAN AND AITKENHEAD ;97: ALVEOLAR DEAD SPACE AND END-TIDAL CO2 Simulator (9 12). Briefly, the models are iterative, mass conserving, and arithmetical (rather than calculus based). The most fundamental processes of molecular movement and physical behavior, such as the constancy of pressure volume/temperature, were used to construct discrete program subunits, which are run repeatedly, with each iteration generating the tiny changes that have occurred since the last microsecond time-slice. These high-fidelity models are described in greater detail separately (13). The models have been validated for the performance of this investigation, and in particular, the poly-laminar series dead space and the poly-compartmental ventilationperfusion (VQ) aspects have been demonstrated to be robust and realistic (13). Experimental setup. The model was configured as follows: weight 75 kg, height 1.75 m, supine posture, inspired oxygen fraction (Fio 2 ) 21%, inspired CO 2 fraction (Fico 2 ) 0.1%, inspired gas temperature 37 C, inspired water fraction 6.2% (saturated at 37 C), cardiac index 2.73 L/min/m 2, oxygen consumption 250 ml/min (V o 2 ), respiratory quotient 0.8, anatomical dead space volume (VDanat) 65 ml (6), fixed (anatomical) pulmonary shunt 1% of cardiac output, ventilatory rate 12 breaths/min, inspired tidal volume (Vt) 500 ml. The sampling interval (see Appendix) was set to 1 ms and internal mass-conservation and error checking were enabled. The model included 500 alveolar gas-exchanging compartments and 250 series dead space laminae. Estimation of VDalv/VTalv. VDanat was derived by geometrically dividing the Pco 2 versus time capnogram, as per Fowler s technique (14). Physiological dead space (VDphys) was calculated using Enghoff s modification of the Bohr equation (15,16). (VDalv/ VTalv) Bohr-Fowler was estimated from the output of the model in the conventional manner: VDalv/VTalv ((1 (PE'CO 2 /Paco 2 ) VTexh) VDanat)/(VTexh VDanat), where PE'CO 2 represents the mixed expired CO 2 tension and VTexh is the exhaled Vt. Patterns of VQ mismatch. The relationship between (VDalv/VTalv) Bohr-Fowler and Pa-e'co 2 /Paco 2 was examined in the presence of three patterns of VQ mismatching. Each pattern of mismatch was created by varying the compartmental bronchiolar resistances and the compartmental arteriolar resistances in opposite directions, generating asynchronous alveolar ventilation and a realistic scatter of VQ ratios as follows: Small defect: vascular resistance (R v ) times normal, bronchial resistance (R b )2 0.5 times normal. Mean and standard deviation of compartmental VQ ratios were 1.42 and 0.57, respectively. Moderate defect: R v times normal, R b times normal. Mean and sd of compartmental VQ ratios were 2.23 and 1.47, respectively. Large defect: R v times normal, R b times normal. Mean and sd of compartmental VQ ratios were 3.15 and 2.50, respectively. Factor variation. Three factors were each varied independently to examine their effect on (VDalv/ VTalv) Bohr-Fowler and on Pa-e'co 2 /Paco 2. The factors, each of which had been found to cause significant disturbance in the relationship between VDalv and the Pa-e'co 2 gradient in our previous investigation, were as follows: CO 2 production (V co 2 values: 100, 200, and 300 ml/min). VDanat (values: 33, 65, and 130 ml). Fixed pulmonary shunt fraction (values: 1%, 15%, and 30% of cardiac output). Pulmonary VQ configuration was maintained during variation of shunt values by increasing cardiac output to keep intrapulmonary (nonshunted) blood flow constant. Each examination used a re-initialized scenario and (VDalv/VTalv) Bohr-Fowler and Pa-e'co 2 /Paco 2 were recorded after complete equilibration had been achieved for both CO 2 and O 2 (defined as total body CO 2 and O 2 flux 0.1 ml/min each). The distribution of variation induced in (VDalv/ VTalv) Bohr-Fowler and Pa-e'co 2 /Paco 2 are expressed as 95% confidence intervals of the variation: CI 95% mean (N (i 1ton) N 0 ) 1.95 sd (N (i 1ton) N 0 ), where mean (N (i 1 to n) N 0 ) is the mean of the variation from baseline and where N 0 is the original value before coincidental physiological variation. Results Normal conditions. Under normal physiological conditions (V co ml/min, shunt 1% of cardiac output, and VDanat 65 ml) while the VQ defect was varied, Pa-e'co 2 /Paco 2 had a linear relationship with (VDalv/VTalv) Bohr-Fowler ; it was consistently 59.5% of (VDalv/VTalv) Bohr-Fowler (Fig. 1). The CI 95% of the error in calculating (VDalv/VTalv) Bohr-Fowler from Pae'co 2 /Paco 2 using this formula was 13.0% to 11.5% in normal physiological conditions and 32.3% to 32.5% over all physiological conditions tested. CO 2 production. Variation in CO 2 production (from 200 ml/min down to 100 ml/min and up to 300 ml/ min) had very small effects on Pa-e'co 2 /Paco 2 and on (VDalv/VTalv) Bohr-Fowler (Fig. 1). The CI 95% of the induced variation are shown in Table 1. Fixed shunt fraction. Increasing fixed, pulmonary shunt fraction (from 1% of cardiac output to 15%, then 30%) in the presence of a constant alveolar configuration caused similar increases in Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr-Fowler (Fig. 2). The CI 95% of the induced variation are shown in Table 1.

3 1848 HARDMAN AND AITKENHEAD ANESTH ANALG ALVEOLAR DEAD SPACE AND END-TIDAL CO2 2003;97: Figure 1. The relationship between arterial-end-tidal CO 2 gradient/ arterial CO 2 tension (Pa-e'co 2 /Paco 2 ) and alveolar deadspace/ alveolar tidal volume, calculated conventionally using Fowler s technique and the Bohr equation - (VDalv/VTalv) Bohr-Fowler. Solid lines show the behavior of Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr- Fowler during conditions that were constant other than changing alveolar configuration (i.e., changing VDalv). Dashed lines show the effect on Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr-Fowler of independently varying V co 2 while alveolar configuration remained constant. The vertical displacement along the dashed line reflects the change in alveolar configuration misleadingly implied by Pa-e'co 2 / Paco 2 and the horizontal displacement reflects the change in alveolar configuration misleadingly implied by conventionally calculated VDalv/VTalv. Anatomical dead space volume. An increase in anatomical dead space volume in the presence of a constant alveolar configuration significantly increased Pae'co 2 /Paco 2 but reduced (VDalv/VTalv) Bohr-Fowler (Fig. 3). The CI 95% of the induced variation are shown in Table 1. Discussion Although increasing fixed shunt fraction did not significantly alter the relationship between Pa-e'co 2 / Paco 2 and (VDalv/VTalv) Bohr-Fowler, it created a virtual dead space in both. This is in agreement with our previous study (7) and with previous clinical investigations (17 19). Correction may be made for the influence of changing fixed shunt fraction by estimating shunt fraction using iso-shunt diagrams (20) or a physiological model (10). Our methodology included the maintenance of nonshunted cardiac output while fixed shunt fraction varied. Clearly, reality is far less simple, and one cannot expect a patient to maintain their nonshunted pulmonary blood flow; this was necessary. If shunt is increased while cardiac output is unchanged then nonshunted blood flow decreases, automatically increasing the mean VQ ratio and thereby increasing VDalv. In our study, nonshunted blood flow was maintained during increasing venous admixture to keep alveolar configuration (and VDalv) constant, allowing examination of the robustness of measures representing VDalv during changing venous admixture. The dependence of the apparent VDalv on the VDanat has been noted previously in an elegant investigation using a four-compartment lung model (21). This model predicted that various combinations of serial and parallel dead spaces that should add up to identical VDphys values as calculated using Enghoff s modification of the Bohr equation in fact produced differing VDphys values. This area requires further investigation using high fidelity modeling. The dependence of both Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr-Fowler on VDanat does not imply the superiority of either method of representing VDalv, but highlights a potential problem with both. Large changes in VDanat are rare in clinical practice, and when such variations occur they are usually easily noted, and a change in the trend in Pa-e'co 2 /Paco 2 may be anticipated. The most important scenario in this context is probably that of VDanat conforming to a fraction of changing Vt (6). Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr-Fowler differ numerically, and although a conversion formula may be used as described in Results, it is probably unnecessary. Indeed, it is probably inappropriate because large variation was observed in the relationship between the two measures during physiological variation. It is clear that, despite constant alveolar configuration, (VDalv/VTalv) Bohr-Fowler is susceptible to variation while other physiological factors vary. Therefore, (VDalv/VTalv) Bohr-Fowler is not an independent representation of alveolar configuration. The question of whether (VDalv/VTalv) Bohr-Fowler or Pa-e'co 2 /Paco 2 is closer to the truth is difficult to answer. If lungs were constructed in a fashion similar to Riley s original lung model (22), consisting of a single dead space volume, a shunted volume, and an optimally ventilated and perfused volume, then there would be a simple, correct answer, but in the presence of a continuous distribution of variably perfused and ventilated alveoli the answer is less clear. The most clinically applicable measure is probably that whichever is most independent of coincidental physiological variation. As (VDalv/VTalv) Bohr-Fowler is marginally more robust in the presence of variation in VDanat then it may be considered the superior measure. However, calculation of (VDalv/VTalv) Bohr-Fowler requires the collection and analysis of expired gas (over a significant time period), the calculation of VDanat using a partial pressure versus volume capnogram and arterial gas tension analysis. Calculation of Pa-e'co 2 / Paco 2, however, requires only measurement of Pae'co 2 tension. Additionally, Pa-e'co 2 /Paco 2 may be updated in real time. The appropriate use of Pa-e'co 2 / Paco 2 may include its daily calculation on the ICU as

4 ANESTH ANALG HARDMAN AND AITKENHEAD ;97: ALVEOLAR DEAD SPACE AND END-TIDAL CO2 Table 1. Variation Induced in Arterial-End-Tidal CO 2 Gradient/Arterial CO 2 Tension (Pa-e co 2 /Paco 2 ) and in Alveolar Deadspace/Alveolar Tidal Volume (Calculated Conventionally Using Fowler s Technique and the Bohr Equation) During Coincidental Variation of Physiological Factors CI 95% of induced misleading variation Varying factor Pa-e co 2 /Paco 2 Conventional VDalv/VTalv Vco % 0.20% 0.33% 0.34% Pulmonary shunt fraction 3.00% 2.40% 2.80% 2.37% VDanat 2.50% 1.87% 1.00% 1.67% Figure 2. The relationship between arterial-end-tidal CO 2 gradient/ arterial CO 2 tension (Pa-e'co 2 /Paco 2 ) and alveolar deadspace/ alveolar tidal volume, calculated conventionally using Fowler s technique and the Bohr equation - (VDalv/VTalv) Bohr-Fowler. Solid lines show the behavior of Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr- Fowler during conditions that were constant other than changing alveolar configuration (i.e., changing VDalv). Dashed lines show the effect on Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr-Fowler of independently varying fixed pulmonary shunt fractio, while alveolar configuration remained constant. The vertical displacement along the dashed line reflects the change in alveolar configuration misleadingly implied by Pa-e'co 2 /Paco 2 and the horizontal displacement reflects the change in alveolar configuration misleadingly implied by conventionally calculated VDalv/VTalv. an estimate of disease progression or to assess the efficacy of interventions. It is obvious that use of Pae'co 2 /Paco 2 should not replace the use of (VDalv/ VTalv) Bohr-Fowler, but its simplicity of calculation may allow easier clinical application of VDalv estimation. Indeed, its ease of use may encourage the more widespread use of VDalv monitoring to quantify disease progression and to assess the effects of interventions. It is probably inappropriate to refer to Pa-e'co 2 / Paco 2 as the alveolar dead space fraction because this is widely accepted as being represented by the conventional calculation. It may be more appropriate to refer to it by its formula if it is recorded in trends in daily ICU patient management. It is widely recognized that the VDphys, calculated using Enghoff s modification of Bohr s equation, does not refer to any discrete part of the respiratory system, and has been termed by some the Bohr dead space (23). The limitations of this investigation include the following: Figure 3. The relationship between arterial-end-tidal CO 2 gradient/ arterial CO 2 tension (Pa-e'co 2 /Paco 2 ) and alveolar dead space/ alveolar tidal volume, calculated conventionally using Fowler s technique and the Bohr equation - (VDalv/VTalv) Bohr-Fowler. Solid lines show the behavior of Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr- Fowler during conditions that were constant other than changing alveolar configuration (i.e., changing VDalv). Dashed lines show the effect on Pa-e'co 2 /Paco 2 and (VDalv/VTalv) Bohr-Fowler of independently varying anatomical dead space volume while alveolar configuration remained constant. The vertical displacement along the dashed line reflects the change in alveolar configuration misleadingly implied Pa-e'co 2 /Paco 2 and the horizontal displacement reflects the change in alveolar configuration misleadingly implied by conventionally calculated VDalv/VTalv. 1. The use of only three discrete VQ defects. Clearly, the patient population includes a nearinfinite number of discrete VQ defects. Our models were chosen to represent large, heterogeneous groups rather than individuals, and we expect that each defect modeled will adequately represent patients whose VQ defects are similar. The results of this investigation may not be applicable to those patients whose VQ defects are grossly dissimilar to those examined in this investigation. This includes patients with the most severe lung pathology, whose VQ configurations we have not reproduced in this study. 2. The use of a limited number of alveolar compartments (500) and series dead space laminae (250). This is unlikely to represent a serious flaw, and will achieve greater accuracy than any other currently investigated pulmonary model. 3. The use of a mathematical model rather than a patient group. This criticism may be directed at

5 1850 HARDMAN AND AITKENHEAD ANESTH ANALG ALVEOLAR DEAD SPACE AND END-TIDAL CO2 2003;97: any investigation using mathematical modeling. However, the stratification of physiological factors that was crucial to this investigation could not be performed in vivo. The modeling used in this investigation included dynamic and static lung inhomogeneity. Viscoelasticity, nonsynchronous alveolar exhalation, poly-laminar dead space, poly-compartmental lung and microtimeslicing all contributed to a very credible, high-fidelity model of pulmonary physiology. In addition, performance of this investigation in vivo would be very difficult because achieving CO 2 equilibrium after changes in physiological factors would take too long for the investigation to be feasible (24). Finally, it is impossible in vivo to vary a physiological value independently. Without this independent variation, clear conclusions of causal relationships cannot be drawn, particularly within a heterogeneous patient group. 4. Other techniques of VDalv estimation. A further criticism that may be leveled at this investigation is that VDalv may be measured almost in realtime using a technique of continuous expired gas analysis, such as the single-breath CO 2 test (25). Therefore, why should we require a further method of quantifying alveolar configuration? First, most ICUs do not have a single-breath CO 2 analyzer, and thus cannot use that method. Second, the technique of single-breath capnographic VDalv quantification is validated only in animals and has not been demonstrated to be independent of variation in the factors presented here, such as VDanat. VDalv measured by the singlebreath test may, in fact, be just as variable as either of the measures presented in this investigation. Several conclusions drawn from this modeling investigation contrast with conclusions based on our previous investigation in this area (7). These differences are explained by the increase in complexity and fidelity of the modeling. However, several of our previous conclusions are supported by this investigation, and this includes the recommendation Pa-e'co 2 / Paco 2 may be useful in clinical practice, particularly as a monitor of trends in pulmonary condition. Appendix The following advances in physiological modeling make re-evaluation of this topic important: Nonsynchronous alveolar exhalation. This is responsible for much of the variation in Pa-e'co 2 in vivo. In contrast to the previous modeling, the current model includes alveolar units with unique time constants generated by independent inlet resistances and compliance curves. Thus, the full spectrum of respiratory disturbance may be accurately recreated. Poly-compartmental lung. Each of the 500 alveolar compartments has a unique ventilationperfusion (VQ) ratio. The modeling used in the previous investigation used only 3 compartments: a true shunt, a true dead space and an optimally ventilated and perfused compartment. The large number of compartments allows the smooth distribution of VQ ratios, avoiding the production of step-artifacts. The validated modeling used in this investigation more closely resembles in vivo lung anatomy and physiology. Inclusion in the model of a poly-laminar anatomical dead space. The previous modeling used a single, immediate-mixing, fixed-volume compartment. This modeling was expedient and computationally efficient, but with the advent of greater computer power a more sophisticated and credible model is possible. The use of micro-timeslicing (1 ms) for far greater accuracy (8). The fidelity of the model is greatly increased by considering, during each iteration of the model algorithms, the changes that occur in the system each millisecond. 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