Pulmonary diseases impair gas exchange by inducing a ventilation/perfusion (V[Combining Dot Above]/Q[Combining Dot Above]) mismatch that may require ventilatory support.1–3 Such treatment aims to minimize lung areas of low V[Combining Dot Above]/Q[Combining Dot Above] and shunt but often at the expense of increasing the zones of high V[Combining Dot Above]/Q[Combining Dot Above] and dead space.4,5 Thus, the way a mechanical ventilator delivers gas during inspiration determines gas exchange.
Given the above scenario, detailed monitoring of ventilation should help in adjusting the ventilator settings to an individual patient's needs. A simple approach to this monitoring is the breath-wise analysis of carbon dioxide (CO2) kinetics applying the concept of dead space or “wasted” ventilation.6,7 The most popular technique for assessing dead space at the bedside is volumetric capnography (VCap) or the representation of expired CO2 over a tidal breath.7,8
In this article, we describe the rationale of dead space measurement by VCap and discuss its main clinical implications and the misconceptions surrounding it.
THE CONCEPT OF DEAD SPACE
A simple depiction of lung physiology is provided by Riley's 3-compartment model that helps in obtaining a basic understanding of the problem of dead space ventilation (Fig. 1).9,10 This model groups alveoli according to their V[Combining Dot Above]/Q[Combining Dot Above] ratios ranging from a normally perfused but not ventilated unit called “shunt” (unit A with a V[Combining Dot Above]/Q[Combining Dot Above] of 0) to a normally ventilated but not perfused unit called “dead space” (unit C with a V[Combining Dot Above]/Q[Combining Dot Above] of ∞). A normally ventilated and perfused alveolus called “ideal” unit (unit B with a V[Combining Dot Above]/Q[Combining Dot Above] of 1) can be found between the above extremes. It is important that certain amounts of high V[Combining Dot Above]/Q[Combining Dot Above] areas (similar to unit C, but with V[Combining Dot Above]/Q[Combining Dot Above] >1 but <∞) and low V[Combining Dot Above]/Q[Combining Dot Above] areas (similar to unit A, but with V[Combining Dot Above]/Q[Combining Dot Above] >0 but <1) can also be found in mechanically ventilated patients.1,2,4 Gas exchange will depend on the overall quantitative balance of all these different subpopulations of alveoli.
Dead space is the portion of ventilation that is not participating in gas exchange because it does not come in contact with the pulmonary capillary blood flow.6,7,11 Therefore, ventilation per unit of time, such as minute ventilation (V[Combining Dot Above]E), is formed by an effective portion called “alveolar ventilation” (V[Combining Dot Above]A) and an ineffective portion called dead space ventilation (V[Combining Dot Above]D)6,11:
Because dead space units are not perfused, their gas composition is not much different from inspired gases containing no CO2. This volume of gas free of CO2 is mixed with gases that come from ideal units with CO2, diluting the latter to decrease expired concentrations of CO2. The rationale of dead space analysis is to measure the degree of dilution.6
Dead space can be clinically expressed as an amount of breathing volume per unit of time (VD), as a fraction of a tidal volume (VD/VT), or as an absolute volume value contributing to 1 breath known as the physiological dead space (VDphys). VDphys is composed of 2 portions: the dead space of the conducting airways (VDaw) and the one within the alveolar compartment represented by the lung units C (VDalv).7,12–14Table 1 describes the main features of VDphys and its subcomponents.
THE TOOL TO MEASURE DEAD SPACE
VCaps are generated by specific capnography apparatuses that measure flow and CO2 with mainstream or sidestream sensors placed at the airway opening. The most frequently used clinical VCap device is the COSMO2 Plus and its newest version, the NICO (Philips Respironics, Wallingford, CT). The main difference between VCap and time-based capnography is that CO2 raw data are related point by point, not to time but to expiratory flow, which is then integrated to obtain volume. Using volume instead of time has the advantage of being able to directly derive volume-based variables such as dead space or the amount of CO2 eliminated per tidal breath.
Figure 2 shows the main features of VCaps. VCap is the breath-wise tidal elimination of CO2 by measuring the area under the curve or VTCO2,br (Fig. 2A). PETCO2, PACO2, and PēCO2 are defined as end-tidal, mean alveolar, and mixed expired partial pressures of CO2, respectively (Fig. 2B).
The capnogram is divided into 3 phases: phase I, or the portion of tidal volume free of CO2; phase II, representing the CO2 coming from lung units with different rates of ventilation and perfusion; and phase III, the pure alveolar gas. The slopes of phases II and III contain important physiological information mainly related to the distribution of ventilation within the lungs7,15,16 (Fig. 2A). It is important to address here the difference in the slope of phase III between time-based and volume-based capnography. Because of the exponential passive nature of the expiratory flow, VCap shows a steeper alveolar slope than the corresponding time-based capnogram because most of the volume is exhaled early during expiration. The shallower alveolar slope of time-based capnography may lead to the erroneous assumptions of a relative equivalence of the PACO2 and PETCO2 values.
VCap separates the volume of gas that belongs to main airways from the one located within the alveolar compartment (Fig. 2B).7,12 Thus, VCap contains all of the information needed to calculate dead space on a breath-by-breath basis. A brief explanation of our systematic analysis of VCap17 can be found in the Online Supplement (see Supplemental Digital Content 1, http://links.lww.com/AA/A363).
THE CALCULATION OF DEAD SPACE
Following the above reasoning, dead space must be calculated by considering both gas from Riley's units C and the gas within the conducting airways. This is what Christian Bohr proposed in 1891 using a formula based on the principle of conservation of mass of CO2.6 Bohr's dead space (VDBohr)11 was thus calculated in the following way6,18:
VA in Equation 1 can also be expressed as the difference between VT and VD:
A simple rearrangement delivers:
Because inspired gases usually do not contain CO2 (FICO2 = 0), then the Bohr's formula can be simplified as:
In Bohr's equation, fractions or partial pressures of CO2 can be used interchangeably:
VDBohr constitutes the VD/VT ratio representing the dilution of the CO2 concentration by “dead air” stemming from both the main airways and from ventilated but not perfused alveoli. The absolute volume of dead space, however, is expressed as VDphys, which is calculated as:
VDBohr was originally obtained noninvasively using a Douglas bag.6 Because this technique is time-consuming, bothersome, and prone to handling errors, it has never reached broad clinical acceptance and has therefore rarely been applied systematically in mechanically ventilated patients. Currently, fast CO2 sensors and pneumotachographs placed at the airway opening allow VCap to be determined on a breath-by-breath basis.7,8,16 The recently validated noninvasive determination of PACO2 from VCap marks a turning point in the monitoring of VDBohr because it resolves a key limitation of the past.19 This implies that reliable and physiologically meaningful breath-by-breath dead space values can be obtained noninvasively using standard VCap.
Below, we describe how PACO2 and PēCO2, the 2 key constituents of Bohr's formula, can be determined from VCap.
The Measurement of PACO2
PACO2 is the mean value of CO2 within the alveolar compartment, which depends on the balance between pulmonary perfusion and VA. The classic alveolar air equation describes such relationship as:
where K is a constant and VCO2 is the amount of CO2 delivered to the lungs by the pulmonary circulation, which is then to be eliminated by VA.
By definition, PACO2 must be measured within the alveolar compartment, which in VCap is represented by the alveolar tidal volume (VTalv). Thus, PACO2 can be determined from VCap as the value located at the midpoint on the slope of phase III within VTalv.17,19 (Fig. 2B; for more details see Online Supplement, http://links.lww.com/AA/A363).
Two factors should be considered when measuring PACO2: (1) Any single lung unit has its own PACO2 depending on its individual V[Combining Dot Above]/Q[Combining Dot Above] ratio, meaning that a heterogeneous lung is represented by a broad spectrum of PACO2 values; and (2) PACO2 changes cyclically with the respiratory cycle. Experimental and theoretical studies showed that in normal lungs at rest, these tidal swings in alveolar PCO2 are in the order of 2 to 3 mm Hg and 4 to 5 mm Hg during exercise.20–22 Therefore, the precise moment during a breath at which a sample of alveolar CO2 is taken is crucial for the determination of representative dead space values, as seen in Figure 3. The calculated values differ depending on whether the alveolar sample is obtained at end-inspiration or at end-expiration.
To avoid errors in dead space calculation because of these factors, one intuitive solution is to use the mean PACO2 for a respiratory cycle. Therefore, before reliable PACO2-dependent calculations such as the one for dead space can be conducted, it is imperative to first agree on a standardized method to measure mean PACO2.
In the past, this measurement of PACO2 has been the cause of intense debates.23 DuBois et al.20,24 showed similar mean PACO2 values for inspiration and expiration despite the fluctuation of CO2 during the respiratory cycle (Fig. 3). Because the CO2 sensor is placed at the airway opening, mean PACO2 can only be determined from expiratory gases because PICO2 is zero. Fortunately, mean PACO2 has been shown to be represented most reliably by an alveolar sample taken shortly after mid-expiration time.24,25 Fletcher and Jonson7 extended the above concept by suggesting that mean PACO2 could theoretically be measured as the PCO2 value found at the midpoint of phase III of VCap. Later, Breen et al.26 confirmed that the mean PACO2 will correspond to the midpoint of phase III in volume-based but not in time-based capnography.
These rather theoretical ideas about the true mean value of PACO2 in VCap have recently been confirmed and validated in an experimental model of lung injury for a broad range of V[Combining Dot Above]/Q[Combining Dot Above] conditions.19 A strong correlation between mean PACO2 as measured by VCap and the one calculated by the alveolar air equation (Equation 8) using VCO2 values obtained from the multiple inert gas technique (MIGET) algorithms was found (r = 0.99, P < 0.0001). Pearson correlation between VCO2 from capnograms and MIGET was also good (r = 0.96, P < 0.0001). These data show that mean PACO2 can be calculated with accuracy even under conditions of high V[Combining Dot Above]/Q[Combining Dot Above] dispersion and irrespective of the resultant deformations of the shape of the capnogram.
Measurement of PēCO2
PēCO2 is determined by the dilution effect that the inspired VT, a volume normally free of CO2, has on the CO2 residing within the lungs. PĒCO2 is influenced not only by VDalv but also by VDaw and therefore, it is used in Bohr's equation to calculate VDphys.6 PĒCO2 is measured using VCap as:
This measurement has been validated comparing it against reference values derived either from indirect calorimetry27 or from MIGET.19
The Calculation of VDaw and VDalv
A complete dead space analysis requires a separation of VDphys into the airway and alveolar components. This is best done following Fowler's concept.12 Fowler described a concept based on the analysis of expired gases (irrespective of the tracer gas used)28 representing the mechanisms of gas transport within lungs. Thus, capnograms represent the way CO2 travels, either by convection within the main airways or by diffusion within the wide cross-sectional areas of the lung periphery29,30 (Fig. 2B). A limit or stationary interface between these 2 mechanisms of CO2 transport is found in each bronchiole, which, because of airway asymmetry, is located at the end of inspiration at different depths within the lungs. During expiration, these interfaces move mouthward and reach the gas sensor at different times, thereby causing the typical wide spread in gas concentrations of phase II. The mean value of these many individual interfaces defines the so-called airway-alveolar interface that allows the differentiation between main airway and the alveolar compartment.12,17,31 According to theoretical and experimental calculations, this mean interface is found at the midpoint of phase II.31–34
Several techniques to measure VDaw by means of VCap have been published.7,19,25,35–40 All of them use Fowler's original concept to determine the position of the airway-alveolar interface.12 The limitations of these methodologies were highlighted by Wolff et al.39 and Tang et al.41 Most approaches are based in a geometric calculation and their performances are affected by changes in the shape of VCap as observed in pulmonary diseases. Wolff et al.39 and our group17 have published methodologies that show a more stable and robust measurement of VDaw even in deformed capnograms.
Once VDphys and VDaw have been obtained sequentially by Bohr's equation and Fowler's concept, the next step is to calculate VDalv as follow:
How PACO2 Has Been Approximated in the Past
The direct measurement of PACO2 by VCap has not been validated until very recently. To create a feasible approximation of dead space, in the past clinicians have replaced the lacking PACO2 in Bohr's equation by the surrogates PETCO2 or arterial PCO2 (PaCO2).9,10,42 Both of these substitutes, however, lead to erroneous values for VDphys, especially under pathological lung conditions.
Using PETCO2 instead of PACO2 in Bohr's formula will increase the calculated value for VDphys. Whereas PACO2 is the average value for all ventilated alveoli, PETCO2 represents only those alveoli with the highest PCO2 resulting from ventilatory inhomogeneities within the lungs as witnessed by the positive sloping of phase III.29,30 Because PETCO2 is the value at the very top end of this slope, its value is higher than the value of PACO2 located at the middle of such slope (Figs. 2B and 3).19 Additionally, because these lung units have a longer expiratory time constant than the remainder of the alveoli, they have more time to equilibrate with the higher CO2 values of the incoming blood, thereby increasing the CO2 concentration within these units.43 From the above explanation, it becomes obvious that using PETCO2 in Bohr's formula will systematically overestimate VDphys in sicker lungs. Only in those healthy patients with flat slopes of phase III will the use of PETCO2 in Bohr's formula deliver dead space values similar to those where PACO2 is used.
Using PaCO2 instead of PACO2 in Bohr's formula also overestimates the true value of VDphys. Riley and Cournand9,10 proposed the concept of ideal lungs where PACO2 was considered identical with PaCO2 assuming that all lung units have a perfect V[Combining Dot Above]/Q[Combining Dot Above] matching. Subsequently, Enghoff ingeniously modified Bohr's equation applying this concept by rewriting the formula as44:
Any increase in the Bohr-Enghoff value (VDB-E) beyond normal reflects the degree by which a patient's lung deviates from the assumed ideal condition. Such deviation has long been thought to be attributable to dead space only. However, the main drawback of this concept of an ideal lung is that even perfectly healthy lungs are never ideal but always show certain amounts of anatomical shunt and dead space.1,4,45 The VDB-E equation not only measures the real VDalv but also includes all other causes of venous admixture because it considers arterial blood.7,18 This effect is easy to understand in Figure 1: if pulmonary artery blood with its high PCO2 bypasses the lungs via shunt pathways, PaCO2 will exceed that of PACO2, which in turn leads to an overestimation of dead space. Using Bohr's true dead space as a reference, Figure 4 shows how venous admixture increases dead space if Enghoff's approach is used. This was the reason why Suter et al.46 called this fictitious type of VDalv shunt dead space or why Fletcher and Jonson7 used the term apparent dead space. Following the same line of reasoning, Wagner47 highlighted the effect that low V[Combining Dot Above]/Q[Combining Dot Above] areas have on PaCO2.
These facts support the idea that VDB-E must be considered an index of global V[Combining Dot Above]/Q[Combining Dot Above] mismatching rather than a dead space.
COMMON MISCONCEPTIONS ABOUT DEAD SPACE
Having introduced the rationale for a meaningful dead space analysis, we discuss below the main misconceptions and misunderstandings around the topic.
Should Values Derived from Enghoff's Formula Be Called Dead Space?
We believe the main source of misconception is the use of the term dead space for the variables derived from Enghoff's modification of Bohr's original formula. By definition, only Bohr's formula is measuring true dead space (units C) because it is viewing the dilution of CO2 from only the alveolar side of the alveolar-capillary membrane.6 As we already stated above, because VDB-E includes information from both the blood and the alveolar gas side, it must not be called dead space (Table 2). Although these differences seem to be nothing more than simple semantic problems, the clinical implications, however, of the differences between VDBohr and VDB-E may be enormous (see below).
Does Bohr's Formula Measure Only Dead Space?
Alveoli with an excess of ventilation relative to perfusion (high V[Combining Dot Above]/Q[Combining Dot Above] areas) generate a VDalv-like effect and will contribute to the calculation of VDalv performed by VCap. It was postulated that this effect is caused by the intermediate solubility of CO2 in blood, making it impossible to differentiate high V[Combining Dot Above]/Q[Combining Dot Above] from pure dead space areas.14,18 From the physiological point of view, both V[Combining Dot Above]/Q[Combining Dot Above] mismatches have a similar diminishing effect on CO2 clearance and can thus be considered part of the same problem. Therefore, for clinical purposes, it seems legitimate to assume that dead space and high V[Combining Dot Above]/Q[Combining Dot Above] are the same thing, no matter which one of these V[Combining Dot Above]/Q[Combining Dot Above] mismatches prevails.
Does Bohr's Original Formula Measure VDalv or VDphys?
Until the end of the 19th century, the concept of alveolar dead space was ignored and VDBohr was thought to be related only to the anatomical dead space measured in cadavers. Ever since the work of Haldane and Priestley48 in the first years of the next century, alveolar gas could be clearly differentiated from the one within the VDaw. Consequently, using the Bohr-Enghoff formula, Fletcher found that VDBohr was always higher than VDaw but lower than VDphys.11 Hence he concluded, similar to many other researchers, that VDBohr had limited clinical value because it was not adequately representing the VDalv component. In other words, VDBohr was considered neither representative of VDaw nor of VDphys.
Therefore, the question arises what VDBohr really is. The answer to this key question can be found in the definition of PACO2. Because Fletcher and others used the ideal PACO2 in their dead space calculations, they overestimated VDphys because of the inadvertent addition of a fictitious VDalv from other sources. Today, we understand that these pioneers erroneously thought that VDBohr underestimated VDphys. Following this reasoning, we firmly believe that VDBohr encompasses a well-defined airway as well as an alveolar component provided that the mean PACO2 is used to calculate it. The following facts support this point of view.
First, it must be highlighted that the rationales behind the methodologies of both Fowler and Bohr have been clearly described and that the physiological meaning of VDaw and VDBohr have been clearly differentiated from one another.6,12 Fowler's concept determines VDaw, making use of phase II and thus detects the gas interface that marks the limit between conducting and gas-exchanging airways (Fig. 2B).12,31,33 Bohr's formula, however, measures VDphys based on the dilution effect of inspired gases on CO2 of the entire tidal breath, using phase III of the capnograms.6,19 Thus, it would not be plausible to confuse VDaw with VDBohr neither from a theoretical nor from a clinical point of view.
Second, data from MIGET calculations showed that the zones of dead space and high V[Combining Dot Above]/Q[Combining Dot Above] develop even in healthy patients undergoing anesthesia or mechanical ventilation.4 Using VCap and Bohr's formula, we found in 70 anesthetized patients with healthy lungs that VDalv constituted approximately one-third of the VDphys (personal unpublished data).
Third, to provide even stronger support for this point of view, we have reanalyzed part of our data from an animal model of acute lung injury and details of this analysis are given in the Online Supplement, http://links.lww.com/AA/A363. We hypothesized that Vphys obtained by Bohr's formula would be the same as the one obtained using Enghoff's approach, provided the latter was corrected for shunt effects using the formula described by Kuwabara and Duncalf49 as follow:
where PV[Combining Macron]CO2 is the partial pressure of CO2 in mixed venous blood and Qs/Qt the right-to-left shunt.
Correcting our experimental data this way revealed a Pearson correlation of r2 = 0.93 (P < 0.0001) between VDBohr and the corrected VDB-E. The corresponding Bland-Altman plot showed a mean bias of 0.0025 and limits of agreement between −0.0375 and 0.0425 (Fig. 5).
These results confirm that, by removing the effects of venous admixture from Enghoff's formula, VDphys becomes similar to the one obtained by Bohr's original equation. Thus, VDBohr comprises a true VDalv component and VDphys is not underestimated by this formula.
Issues Related to the Calculation of VA
The opposing twin concept of dead space is the effective part of ventilation within the alveolar compartment that is in close contact with the capillary blood (VA). The formula to calculate VA is a direct derivative of Equation (1)6,11:
Fletcher proposed that VA should be measured by Enghoff's approach and not by Bohr's original equation because he postulated that VDBohr underestimated VDphys.7,11 As has been pointed out above, we now know that VDBohr measures VDphys accurately and that VDB-E underestimates VA because of the addition of a shunt-related apparent or fictitious VDalv.18,19 Conceptually but also practically, VA is a real volume that can be adjusted on the ventilator whereas the fictitious volume is not. Therefore, the calculation of VA suffers from the same problem as dead space whenever the concept of ideal lung is included in the formula.
CLINICAL IMPLICATIONS OF THE APPROACHES OF BOHR AND ENGHOFF
Table 2 shows the main differences between the formulas of Bohr and Enghoff that are of clinical relevance. The intention of this report is to highlight these important differences but not to judge whether Bohr's equation is better than Enghoff's or vice versa. What we are trying to convey is the simple fact that true dead space can only be determined by Bohr's formula. However, it is obvious why Enghoff's approach is clinically useful because it provides a good global estimate of a lung's state of V[Combining Dot Above]/Q[Combining Dot Above]. Therefore, the question of which formula we must use at the bedside deserves an answer. This answer is, both, depending on the clinical problem or disease to be addressed.
On the one hand, Bohr's approach is useful to determine the balance between effective and wasted ventilation. It will detect an excess of ventilation caused by large VT and/or too much positive end-expiratory pressure (PEEP) or at a fixed ventilatory setting a respective deficit in lung perfusion caused by hypovolemia, pulmonary hypotension, or embolism.50 Enghoff's approach includes a similar but less specific calculation, i.e., it can give a false-positive diagnosis of an increment in dead space or type C units. This is the case, for example, in atelectatic lungs where the fictitious VDalv is increased by high shunt and low V[Combining Dot Above]/Q[Combining Dot Above]. If clinicians misinterpret such a scenario as PEEP-induced lung “overdistension,” they might want to decrease the level of PEEP while in fact more PEEP is needed to overcome the atelectatic and shunting state.
Bohr's formula cannot detect what is happening at the capillary side of the alveolar-capillary membrane. Enghoff's approach has a notable clinical advantage because it provides a good idea of the global state of gas exchange from using just one single arterial blood sample. Thus, Enghoff's approach has important clinical applications: it has been used to diagnose pulmonary embolism,51,52 to guide the weaning process and to predict tracheal extubation,53 to adjust PEEP,54 to detect lung collapse,55 or to predict survival in acute respiratory distress syndrome patients.56 Despite these ample publications, we encourage caution and a critical reappraisal of some of these results. For example, Nuckton et al.56 demonstrated that VD/VT obtained by Enghoff's approach seems to be a predictor of mortality in acute respiratory distress syndrome patients. Was mortality really related to dead space or was it more related to the amount of shunt? What would happen if we determined true dead space using Bohr's equation? Can a link between overdistension and mortality be established?
In future studies, all of these questions need to be addressed by appropriate methodologies considering that the clinical role of VCap in monitoring lung function is grossly enriched if both Bohr's and Enghoff's approaches are used synergistically.
VCap is clinically useful to monitor the V[Combining Dot Above]/Q[Combining Dot Above] relationship in mechanically ventilated patients. Although this technique may not be as precise and detailed as the investigational “gold standard” of MIGET, it can easily be applied at the bedside.
Currently, the novel direct determination of PACO2 by VCap allows the calculation of wasted ventilation (true dead space together with areas of high V[Combining Dot Above]/Q[Combining Dot Above]) using Bohr's equation on a breath-by-breath basis. Contrarily, Enghoff's approach uses an arterial blood sample and delivers an index of global V[Combining Dot Above]/Q[Combining Dot Above] matching considering both, wasted ventilation and wasted perfusion (shunt plus low V[Combining Dot Above]/Q[Combining Dot Above] areas). Therefore, to avoid misunderstanding using dead space as a descriptor of the output of Enghoff's formula is no longer justified.
Following both approaches separately provides the clinician with useful complementary information when monitoring mechanically ventilated patients at the bedside. We think it is time to call these important physiological variables by their appropriate names.
Name: Gerardo Tusman, MD.
Contribution: This author helped prepare the manuscript, figures, and tables.
Conflicts of Interest: Gerardo Tusman is the inventor and applicant of patent EP 04007355.3: non-invasive method and apparatus for optimizing the respiration of atelectatic lungs.
Name: Fernando Suarez Sipmann, MD, PhD.
Contribution: This author helped prepare the manuscript.
Conflicts of Interest: This author has no conflicts of interest to declare.
Name: Stephan H. Bohm, MD.
Contribution: This author helped prepare the manuscript.
Conflicts of Interest: Stephan H. Bohm is the inventor and applicant of patent EP 04007355.3: non-invasive method and apparatus for optimizing the respiration of atelectatic lungs.
This manuscript was handled by: Steven L. Shafer, MD.
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