anesth analg

SPECIAL ARTICLE

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Rationale of Dead Space Measurement byVolumetric CapnographyGerardo Tusman, MD,* Fernando Suarez Sipmann, MD, PhD,†‡§ and Stephan H. Bohm, MD�

Dead space is the portion of a tidal volume that does not participate in gas exchange becauseit does not get in contact with blood flowing through the pulmonary capillaries. It iscommonly calculated using volumetric capnography, the plot of expired carbon dioxide (CO2)versus tidal volume, which is an easy bedside assessment of the inefficiency of a particularventilatory setting. Today, Bohr’s original dead space can be calculated in an entirelynoninvasive and breath-by-breath manner as the mean alveolar partial pressure of CO2(Paco2) which can now be determined directly from the capnogram. The value derived fromEnghoff’s modification of Bohr’s formula (using Paco2 instead of Paco2) is a global index ofthe inefficiency of gas exchange rather than a true “dead space” because it is influenced by allcauses of ventilation/perfusion mismatching, from real dead space to shunt. Therefore, theresults obtained by Bohr’s and Enghoff’s formulas have different physiological meanings andclinicians must be conscious of such differences when interpreting patient data. In this article,we describe the rationale of dead space measurements by volumetric capnography anddiscuss its main clinical implications and the misconceptions surrounding it. (Anesth Analg2012;114:866–74)

Pulmonary diseases impair gas exchange by inducinga ventilation/perfusion (V/Q) mismatch that mayrequire ventilatory support.1–3 Such treatment aims

to minimize lung areas of low V/Q and shunt but often atthe expense of increasing the zones of high V/Q and deadspace.4,5 Thus, the way a mechanical ventilator delivers gasduring inspiration determines gas exchange.

Given the above scenario, detailed monitoring of ventila-tion should help in adjusting the ventilator settings to anindividual patient’s needs. A simple approach to this moni-toring 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 deadspace at the bedside is volumetric capnography (VCap) or therepresentation of expired CO2 over a tidal breath.7,8

In this article, we describe the rationale of dead spacemeasurement by VCap and discuss its main clinical impli-cations and the misconceptions surrounding it.

THE CONCEPT OF DEAD SPACEA simple depiction of lung physiology is provided byRiley’s 3-compartment model that helps in obtaining a

basic understanding of the problem of dead space ventila-tion (Fig. 1).9,10 This model groups alveoli according totheir V/Q ratios ranging from a normally perfused but notventilated unit called “shunt” (unit A with a V/Q of 0) to anormally ventilated but not perfused unit called “deadspace” (unit C with a V/Q of �). A normally ventilated andperfused alveolus called “ideal” unit (unit B with a V/Q of1) can be found between the above extremes. It is importantthat certain amounts of high V/Q areas (similar to unit C,but with V/Q �1 but ��) and low V/Q areas (similar tounit A, but with V/Q �0 but �1) can also be found inmechanically ventilated patients.1,2,4 Gas exchange willdepend on the overall quantitative balance of all thesedifferent subpopulations of alveoli.

Dead space is the portion of ventilation that is notparticipating in gas exchange because it does not come incontact with the pulmonary capillary blood flow.6,7,11

Therefore, ventilation per unit of time, such as minuteventilation (Ve), is formed by an effective portion called“alveolar ventilation” (Va) and an ineffective portion calleddead space ventilation (Vd)6,11:

Ve � Va � Vd (1)

Because dead space units are not perfused, their gas compo-sition is not much different from inspired gases containing noCO2. This volume of gas free of CO2 is mixed with gases thatcome from ideal units with CO2, diluting the latter to decreaseexpired concentrations of CO2. The rationale of dead spaceanalysis is to measure the degree of dilution.6

Dead space can be clinically expressed as an amount ofbreathing volume per unit of time (Vd), as a fraction of atidal volume (Vd/Vt), or as an absolute volume valuecontributing to 1 breath known as the physiological deadspace (Vdphys). Vdphys is composed of 2 portions: the deadspace of the conducting airways (Vdaw) and the one withinthe alveolar compartment represented by the lung units C(Vdalv).7,12–14 Table 1 describes the main features of Vdphys

and its subcomponents.

From the *Department of Anesthesiology, Hospital Privado de Comunidad,Mar del Plata, Argentina; †Department of Surgical Sciences, Section ofAnesthesiology & Critical Care, Uppsala University, Uppsala, Sweden;‡Instituto de Investigacion Sanitaria, Fundacion Jimenez Díaz, IIS-FJD,Madrid, Spain; §CIBERES; and �Swisstom AG, Landquart, Switzerland.

Accepted for publication December 7, 2011.

Supplemental digital content is available for this article. Direct URL citationsappear in the printed text and are provided in the HTML and PDF versionsof this article on the journal’s Web site (www.anesthesia-analgesia.org).

Conflicts of Interest: See Disclosures at the end of the article.

Reprints will not be available from the authors.

Address correspondence to Gerardo Tusman, MD, Department of Anesthe-siology, Hospital Privado de Comunidad, Mar del Plata, Argentina. Addresse-mail to [email protected].

Copyright © 2012 International Anesthesia Research SocietyDOI: 10.1213/ANE.0b013e318247f6cc

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THE TOOL TO MEASURE DEAD SPACEVCaps are generated by specific capnography appara-tuses that measure flow and CO2 with mainstream orsidestream sensors placed at the airway opening. Themost frequently used clinical VCap device is theCOSMO2 Plus and its newest version, the NICO (PhilipsRespironics, Wallingford, CT). The main difference be-tween VCap and time-based capnography is that CO2

raw data are related point by point, not to time but toexpiratory flow, which is then integrated to obtainvolume. Using volume instead of time has the advantageof being able to directly derive volume-based variables

such as dead space or the amount of CO2 eliminated pertidal breath.

Figure 2 shows the main features of VCaps. VCap is thebreath-wise tidal elimination of CO2 by measuring the areaunder the curve or Vtco2,br (Fig. 2A). Petco2, Paco2, andPe�co2 are defined as end-tidal, mean alveolar, and mixedexpired partial pressures of CO2, respectively (Fig. 2B).

The capnogram is divided into 3 phases: phase I, or theportion of tidal volume free of CO2; phase II, representingthe CO2 coming from lung units with different rates ofventilation and perfusion; and phase III, the pure alveolargas. The slopes of phases II and III contain importantphysiological information mainly related to the distributionof ventilation within the lungs7,15,16 (Fig. 2A). It is impor-tant to address here the difference in the slope of phase III

Figure 1. Riley’s model of the lungs and volumetric capnography(VCap). Adaptation of Riley’s 3-compartment model of the lungs with(A) representing shunt, (B) an ideal unit, and (C) dead space. Duringinspiration, physiological dead space (VDphys) is filled with air con-taining no CO2 shown as white area. VDphys is constituted by the sumof airway (VDaw) and alveolar dead space (VDalv or unit C), which aredelimited by the airway-alveolar interface (dotted line). VCap (top) iscollected by proper sensors placed at the airway’s opening. PETCO2,PACO2, and PE�CO2 are the end-tidal, mean alveolar, and mixed expiredpartial pressures of CO2, respectively.

Figure 2. Volumetric capnography (VCap) and derived variables.VCap is the plot of expired carbon dioxide (CO2) on the y-axis versusthe expired volume on the x-axis. A, VCap is divided into phases I, II,and III. SII and SIII are the lines following the slopes of phase II andIII, respectively. The area under the curve in gray is the VTCO2,br. B,VCap represents the transport of CO2 by convection (Conv) withinmain airways and by diffusion (Diff) within alveoli. The black dot inphase II is the inflection point of the whole VCap that marks theairway-alveolar interface (Aw-alv). According to Fowler’s concept, atidal volume is divided into an airway dead space (VDaw) and analveolar tidal volume (VTalv). PaCO2, PACO2, PETCO2, and PE�CO2 are thearterial, mean alveolar, end-tidal, and mixed expired partial pres-sures of CO2, respectively.

Table 1. Dead Space ComponentsAbbreviation Name Limits Measurement Clinical presentation Factors that change it

VDphys Physiological deadspace

From ETT to the alveolar-capillary membrane ofunits C

Bohr’s formula(Eq. 7)

Absolute value or VD/VT It is affected by factors thatchange both VDalv and VDaw

VDalv Alveolar or paralleldead space

From airway-alveolar interfaceuntil the alveolar-capillarymembrane of units C

Bohr’s and Fowler’smethodologiestogether (Eq. 10)

Absolute value, VDalv/VT

or VDalv/VTalv

Increases with high PEEP and/or VT, hypovolemia, lunghypoperfusion, pulmonaryhypotension. Decreaseswith adequate treatment ofthe above conditions

VDaw Airway, anatomical, orseries dead space

From ETT to the airway-alveolar interface

Any method usingFowler’s concept

Absolute value orVDaw/VT

Increases with increased bodysize, VT, PEEP, and FRC.Decreases with inspiratorypause

VDinst Instrumental orapparatus deadspace

Any gadget between ETT andthe Y piece (humidifiers,connectors, mainstreamsensors, etc.)

Water displacementof gadget

Included in thecalculation of VDaw

Its clinical effect depends onthe size of gadget and thesize of VT applied. Veryimportant in pediatricpatients

ETT � endotracheal tube; PEEP � positive end-expiratory pressure; FRC � functional residual capacity; VD/VT measured by Bohr’s formula (VDBohr); VDphys �physiological dead space; VDaw � airway dead space and VDalv � alveolar dead space. Dead space values are commonly normalized by tidal volume (VT) to allowcomparison among patients with different VT size: VDaw/VT � airway dead space to tidal volume ratio and VDalv/VTalv � alveolar dead space to alveolar tidal volumeratio.

Dead Space Measured by Volumetric Capnography

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between time-based and volume-based capnography. Be-cause of the exponential passive nature of the expiratoryflow, VCap shows a steeper alveolar slope than the corre-sponding time-based capnogram because most of the vol-ume is exhaled early during expiration. The shalloweralveolar slope of time-based capnography may lead to theerroneous assumptions of a relative equivalence of thePaco2 and Petco2 values.

VCap separates the volume of gas that belongs to mainairways from the one located within the alveolar compart-ment (Fig. 2B).7,12 Thus, VCap contains all of the informationneeded to calculate dead space on a breath-by-breath basis. Abrief explanation of our systematic analysis of VCap17 can befound in the Online Supplement (see Supplemental DigitalContent 1, http://links.lww.com/AA/A363).

THE CALCULATION OF DEAD SPACEFollowing the above reasoning, dead space must be calcu-lated by considering both gas from Riley’s units C and thegas within the conducting airways. This is what ChristianBohr proposed in 1891 using a formula based on theprinciple of conservation of mass of CO2.6 Bohr’s deadspace (VdBohr)

11 was thus calculated in the followingway6,18:

Fe�co2 � Vt � Faco2 � Va � Fico2 � Vd (2)

Va in Equation 1 can also be expressed as the differencebetween Vt and Vd:

Fe�co2 � Vt � Faco2(Vt � Vd) � Fico2 � Vd (3)

A simple rearrangement delivers:

Vd/Vt � (Faco2 � Fe�co2)/(Faco2 � Fico2) (4)

Because inspired gases usually do not contain CO2

(Fico2 � 0), then the Bohr’s formula can be simplified as:

Vd/Vt � (Faco2 � Fe�co2)/Faco2 (5)

In Bohr’s equation, fractions or partial pressures of CO2

can be used interchangeably:

VdBohr or Vd/Vt � (Paco2 � Pe�co2)/Paco2 (6)

VdBohr constitutes the Vd/Vt ratio representing thedilution of the CO2 concentration by “dead air” stemmingfrom both the main airways and from ventilated but notperfused alveoli. The absolute volume of dead space,however, is expressed as Vdphys, which is calculated as:

Vdphys � VdBohr � Vt (7)

VdBohr was originally obtained noninvasively using aDouglas bag.6 Because this technique is time-consuming,bothersome, and prone to handling errors, it has neverreached broad clinical acceptance and has therefore rarelybeen applied systematically in mechanically ventilatedpatients. Currently, fast CO2 sensors and pneumotacho-graphs placed at the airway opening allow VCap to bedetermined on a breath-by-breath basis.7,8,16 The recentlyvalidated noninvasive determination of Paco2 from VCapmarks a turning point in the monitoring of VdBohr because

it resolves a key limitation of the past.19 This implies thatreliable and physiologically meaningful breath-by-breathdead space values can be obtained noninvasively usingstandard VCap.

Below, we describe how Paco2 and Pe�co2, the 2 keyconstituents of Bohr’s formula, can be determined fromVCap.

The Measurement of PACO2Paco2 is the mean value of CO2 within the alveolarcompartment, which depends on the balance betweenpulmonary perfusion and Va. The classic alveolar airequation describes such relationship as:

Paco2 � K � Vco2/Va (8)

where K is a constant and Vco2 is the amount of CO2

delivered to the lungs by the pulmonary circulation, whichis then to be eliminated by Va.

By definition, Paco2 must be measured within thealveolar compartment, which in VCap is represented bythe alveolar tidal volume (Vtalv). Thus, Paco2 can bedetermined from VCap as the value located at themidpoint 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 measuringPaco2: (1) Any single lung unit has its own Paco2 depend-ing on its individual V/Q ratio, meaning that a heteroge-neous lung is represented by a broad spectrum of Paco2

values; and (2) Paco2 changes cyclically with the respira-tory cycle. Experimental and theoretical studies showedthat in normal lungs at rest, these tidal swings in alveolarPco2 are in the order of 2 to 3 mm Hg and 4 to 5 mm Hgduring exercise.20–22 Therefore, the precise moment duringa breath at which a sample of alveolar CO2 is taken iscrucial for the determination of representative dead spacevalues, as seen in Figure 3. The calculated values differdepending on whether the alveolar sample is obtained atend-inspiration or at end-expiration.

To avoid errors in dead space calculation because ofthese factors, one intuitive solution is to use the meanPaco2 for a respiratory cycle. Therefore, before reliablePaco2-dependent calculations such as the one for deadspace can be conducted, it is imperative to first agree on astandardized method to measure mean Paco2.

In the past, this measurement of Paco2 has been thecause of intense debates.23 DuBois et al.20,24 showed similarmean Paco2 values for inspiration and expiration despitethe 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 gasesbecause Pico2 is zero. Fortunately, mean Paco2 has beenshown to be represented most reliably by an alveolarsample taken shortly after mid-expiration time.24,25

Fletcher and Jonson7 extended the above concept by sug-gesting that mean Paco2 could theoretically be measuredas the Pco2 value found at the midpoint of phase III ofVCap. 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.

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These rather theoretical ideas about the true mean valueof Paco2 in VCap have recently been confirmed andvalidated in an experimental model of lung injury for abroad range of V/Q conditions.19 A strong correlationbetween mean Paco2 as measured by VCap and the onecalculated by the alveolar air equation (Equation 8) usingVco2 values obtained from the multiple inert gas technique(MIGET) algorithms was found (r � 0.99, P � 0.0001).Pearson correlation between Vco2 from capnograms andMIGET was also good (r � 0.96, P � 0.0001). These datashow that mean Paco2 can be calculated with accuracyeven under conditions of high V/Q dispersion and irre-spective of the resultant deformations of the shape of thecapnogram.

Measurement of PE�CO2Pe�co2 is determined by the dilution effect that the inspiredVt, a volume normally free of CO2, has on the CO2 residingwithin the lungs. Pe�co2 is influenced not only by Vdalv butalso by Vdaw and therefore, it is used in Bohr’s equation tocalculate Vdphys.

6 Pe�co2 is measured using VCap as:

Pe�co2 � Fe�co2 � barometric pressure (9)

This measurement has been validated comparing itagainst reference values derived either from indirect calo-rimetry27 or from MIGET.19

The Calculation of VDaw and VDalvA complete dead space analysis requires a separation ofVdphys into the airway and alveolar components. This is

best done following Fowler’s concept.12 Fowler described aconcept based on the analysis of expired gases (irrespectiveof the tracer gas used)28 representing the mechanisms ofgas transport within lungs. Thus, capnograms represent theway CO2 travels, either by convection within the mainairways or by diffusion within the wide cross-sectionalareas of the lung periphery29,30 (Fig. 2B). A limit or station-ary interface between these 2 mechanisms of CO2 transportis found in each bronchiole, which, because of airwayasymmetry, is located at the end of inspiration at differentdepths within the lungs. During expiration, these interfacesmove mouthward and reach the gas sensor at differenttimes, thereby causing the typical wide spread in gasconcentrations of phase II. The mean value of these manyindividual interfaces defines the so-called airway-alveolarinterface that allows the differentiation between main air-way and the alveolar compartment.12,17,31 According totheoretical and experimental calculations, this mean inter-face is found at the midpoint of phase II.31–34

Several techniques to measure Vdaw by means of VCaphave been published.7,19,25,35–40 All of them use Fowler’soriginal concept to determine the position of the airway-alveolar interface.12 The limitations of these methodologieswere highlighted by Wolff et al.39 and Tang et al.41 Mostapproaches are based in a geometric calculation and theirperformances are affected by changes in the shape of VCapas observed in pulmonary diseases. Wolff et al.39 and ourgroup17 have published methodologies that show a morestable and robust measurement of Vdaw even in deformedcapnograms.

Once Vdphys and Vdaw have been obtained sequentiallyby Bohr’s equation and Fowler’s concept, the next step is tocalculate Vdalv as follow:

Vdalv � Vdphys � Vdaw (10)

How PACO2 Has Been Approximated in the PastThe direct measurement of Paco2 by VCap has not beenvalidated until very recently. To create a feasible approxi-mation of dead space, in the past clinicians have replacedthe lacking Paco2 in Bohr’s equation by the surrogatesPetco2 or arterial Pco2 (Paco2).9,10,42 Both of these substi-tutes, however, lead to erroneous values for Vdphys, espe-cially under pathological lung conditions.

Using Petco2 instead of Paco2 in Bohr’s formula willincrease the calculated value for Vdphys. Whereas Paco2 isthe average value for all ventilated alveoli, Petco2 repre-sents only those alveoli with the highest Pco2 resultingfrom ventilatory inhomogeneities within the lungs as wit-nessed by the positive sloping of phase III.29,30 BecausePetco2 is the value at the very top end of this slope, itsvalue is higher than the value of Paco2 located at themiddle of such slope (Figs. 2B and 3).19 Additionally,because these lung units have a longer expiratory timeconstant than the remainder of the alveoli, they have moretime to equilibrate with the higher CO2 values of theincoming blood, thereby increasing the CO2 concentrationwithin these units.43 From the above explanation, it be-comes obvious that using Petco2 in Bohr’s formula willsystematically overestimate Vdphys in sicker lungs. Only inthose healthy patients with flat slopes of phase III will the

Figure 3. Alveolar CO2 during the respiratory cycle and its relation-ship with volumetric capnography. Changes in the partial pressure ofCO2 within the alveolar compartment during the respiratory cycle arerepresented by the dotted line. Point a represents the reinhalation ofCO2 at the beginning of inspiration coming from the airways and frominstrumental dead spaces. Point b is the lowest PCO2 found at theend of inspiration, which is the result of the dilution by the CO2-freeinhaled tidal volume. Point c is the highest PCO2 found at the end ofexpiration. Black dots represent the mean PACO2 during both inspi-ration and expiration. As the CO2 sensor is placed at the airwayopening, it does not measure any CO2 in the inspired fresh gas(PICO2 � 0). Once the gas in the airway dead space has been washedout during expiration, alveolar gas is sampled and PACO2 can bemeasured directly in capnograms at the middle point of phase III(modified from DuBois et al.20).



use of Petco2 in Bohr’s formula deliver dead space valuessimilar to those where Paco2 is used.

Using Paco2 instead of Paco2 in Bohr’s formula alsooverestimates the true value of Vdphys. Riley and Cour-nand9,10 proposed the concept of ideal lungs where Paco2

was considered identical with Paco2 assuming that all lungunits have a perfect V/Q matching. Subsequently, Enghoffingeniously modified Bohr’s equation applying this con-cept by rewriting the formula as44:

VdB-E or Vd/Vt � (Paco2 � Pe�co2)/Paco2 (11)

Any increase in the Bohr-Enghoff value (VdB-E) beyondnormal reflects the degree by which a patient’s lungdeviates from the assumed ideal condition. Such deviationhas long been thought to be attributable to dead space only.However, the main drawback of this concept of an ideallung is that even perfectly healthy lungs are never ideal butalways show certain amounts of anatomical shunt anddead space.1,4,45 The VdB-E equation not only measures thereal Vdalv but also includes all other causes of venousadmixture because it considers arterial blood.7,18 This effectis easy to understand in Figure 1: if pulmonary artery bloodwith its high Pco2 bypasses the lungs via shunt pathways,Paco2 will exceed that of Paco2, which in turn leads to anoverestimation of dead space. Using Bohr’s true dead spaceas a reference, Figure 4 shows how venous admixtureincreases dead space if Enghoff’s approach is used. Thiswas the reason why Suter et al.46 called this fictitious typeof Vdalv shunt dead space or why Fletcher and Jonson7

used the term apparent dead space. Following the sameline of reasoning, Wagner47 highlighted the effect that lowV/Q areas have on Paco2.

These facts support the idea that VdB-E must be consid-ered an index of global V/Q mismatching rather than adead space.

COMMON MISCONCEPTIONS ABOUT DEAD SPACEHaving introduced the rationale for a meaningful deadspace analysis, we discuss below the main misconceptionsand misunderstandings around the topic.

Should Values Derived from Enghoff’s FormulaBe Called Dead Space?We believe the main source of misconception is the use ofthe term dead space for the variables derived from Eng-hoff’s modification of Bohr’s original formula. By defini-tion, only Bohr’s formula is measuring true dead space(units C) because it is viewing the dilution of CO2 fromonly the alveolar side of the alveolar-capillary membrane.6

As we already stated above, because VdB-E includes infor-mation from both the blood and the alveolar gas side, itmust not be called dead space (Table 2). Although thesedifferences seem to be nothing more than simple semanticproblems, the clinical implications, however, of the differ-ences between VdBohr and VdB-E may be enormous (seebelow).

Figure 4. Graphical representation of the ap-proaches of Bohr and Enghoff. VDaw � airwaydead space and VDalv � alveolar dead space.PaCO2, PETCO2, and PACO2 are the arterial, end-tidal, and mean alveolar partial pressures ofcarbon dioxide, respectively.

Table 2. Differences Between the Approaches of Bohr and EnghoffBohr’s approach Enghoff’s approach

Formula VDBohr � (PACO2 � PE�CO2)/PACO2 VDB-E � (PaCO2 � PE�CO2)/PaCO2

Origin of PACO2 Mean PACO2 as the average PCO2 coming from alllung units

PaCO2 replaces PACO2 following Riley’s concept of anideal lung

Type of V/Q analyzed V/Q of � (units C) V/Q of � (units C)High V/Q �1 but �� High V/Q �1 but ��

V/Q of 0 (unit A)Low V/Q �1 but �0

Type of measurement Noninvasive, continuous, breath by breath Invasive, discontinuous provides information only whenarterial blood samples are obtained

Physiological factors having aninfluence on parameter

Alveolar overdistension by excessive PEEP and/or VT, pulmonary embolism, hypovolemia,pulmonary hypotension

Idem Bohr’s approach plus all causes of shunt and lowV/Q: atelectasis, pneumonia, COPD, asthma, etc.

VDBohr � VD/VT measured by Bohr’s formula; VT � tidal volume; PEEP � positive end-expiratory pressure; V/Q � ventilation/perfusion ratio; PaCO2, PETCO2, PACO2,and PE�CO2 � the arterial, end-tidal, mean alveolar, and mixed expired partial pressures of carbon dioxide, respectively; COPD � chronic obstructive pulmonarydisease.

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Does Bohr’s Formula Measure OnlyDead Space?Alveoli with an excess of ventilation relative to perfusion(high V/Q areas) generate a Vdalv-like effect and willcontribute to the calculation of Vdalv performed by VCap. Itwas postulated that this effect is caused by the intermediatesolubility of CO2 in blood, making it impossible to differ-entiate high V/Q from pure dead space areas.14,18 From thephysiological point of view, both V/Q mismatches have asimilar diminishing effect on CO2 clearance and can thus beconsidered part of the same problem. Therefore, for clinicalpurposes, it seems legitimate to assume that dead spaceand high V/Q are the same thing, no matter which one ofthese V/Q mismatches prevails.

Does Bohr’s Original Formula MeasureVDalv or VDphys?Until the end of the 19th century, the concept of alveolardead space was ignored and VdBohr was thought to berelated only to the anatomical dead space measured incadavers. Ever since the work of Haldane and Priestley48 inthe first years of the next century, alveolar gas could beclearly differentiated from the one within the Vdaw. Con-sequently, using the Bohr-Enghoff formula, Fletcher foundthat VdBohr was always higher than Vdaw but lower thanVdphys.

11 Hence he concluded, similar to many otherresearchers, that VdBohr had limited clinical value becauseit was not adequately representing the Vdalv component. Inother words, VdBohr was considered neither representativeof Vdaw nor of Vdphys.

Therefore, the question arises what VdBohr really is. Theanswer to this key question can be found in the definitionof 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 thesepioneers erroneously thought that VdBohr underestimatedVdphys. Following this reasoning, we firmly believe thatVdBohr encompasses a well-defined airway as well as analveolar component provided that the mean Paco2 is usedto calculate it. The following facts support this point ofview.

First, it must be highlighted that the rationales behindthe methodologies of both Fowler and Bohr have beenclearly described and that the physiological meaning ofVdaw and VdBohr have been clearly differentiated from oneanother.6,12 Fowler’s concept determines Vdaw, making useof phase II and thus detects the gas interface that marks thelimit 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 theentire tidal breath, using phase III of the capnograms.6,19

Thus, it would not be plausible to confuse Vdaw withVdBohr neither from a theoretical nor from a clinical point ofview.

Second, data from MIGET calculations showed that thezones of dead space and high V/Q develop even in healthypatients undergoing anesthesia or mechanical ventilation.4

Using VCap and Bohr’s formula, we found in 70 anesthe-tized patients with healthy lungs that Vdalv constituted

approximately one-third of the Vdphys (personal unpub-lished data).

Third, to provide even stronger support for this pointof view, we have reanalyzed part of our data from ananimal model of acute lung injury and details of thisanalysis are given in the Online Supplement,http://links.lww.com/AA/A363. We hypothesized thatVphys obtained by Bohr’s formula would be the same asthe one obtained using Enghoff’s approach, provided thelatter was corrected for shunt effects using the formuladescribed by Kuwabara and Duncalf49 as follow:

Vd/Vt �

�PvCO2 �PvCO2 � PaCO2

1 � Qs/Qt� � PE� CO2

�PvCO2 �PvCO2 � PaCO2

1 � Qs/Qt�

(12)

where Pv�co2 is the partial pressure of CO2 in mixed venousblood and Qs/Qt the right-to-left shunt.

Correcting our experimental data this way revealed aPearson correlation of r2 � 0.93 (P � 0.0001) betweenVdBohr and the corrected VdB-E. The corresponding Bland-Altman plot showed a mean bias of 0.0025 and limits ofagreement between �0.0375 and 0.0425 (Fig. 5).

These results confirm that, by removing the effects ofvenous admixture from Enghoff’s formula, Vdphys becomessimilar 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 VAThe opposing twin concept of dead space is the effectivepart of ventilation within the alveolar compartment that isin close contact with the capillary blood (Va). The formulato calculate Va is a direct derivative of Equation (1)6,11:

Va � Ve � Vd (13)

Fletcher proposed that Va should be measured by Eng-hoff’s approach and not by Bohr’s original equation becausehe postulated that VdBohr underestimated Vdphys.

7,11 As hasbeen pointed out above, we now know that VdBohr mea-sures Vdphys accurately and that VdB-E underestimates Vabecause of the addition of a shunt-related apparent orfictitious Vdalv.18,19 Conceptually but also practically, Va isa real volume that can be adjusted on the ventilatorwhereas the fictitious volume is not. Therefore, the calcu-lation of Va suffers from the same problem as dead spacewhenever the concept of ideal lung is included in theformula.

CLINICAL IMPLICATIONS OF THE APPROACHESOF BOHR AND ENGHOFFTable 2 shows the main differences between the formulas ofBohr and Enghoff that are of clinical relevance. The inten-tion of this report is to highlight these important differencesbut not to judge whether Bohr’s equation is better thanEnghoff’s or vice versa. What we are trying to convey is thesimple fact that true dead space can only be determined by




Bohr’s formula. However, it is obvious why Enghoff’sapproach is clinically useful because it provides a goodglobal estimate of a lung’s state of V/Q. Therefore, thequestion of which formula we must use at the bedsidedeserves an answer. This answer is, both, depending on theclinical problem or disease to be addressed.

On the one hand, Bohr’s approach is useful to determinethe balance between effective and wasted ventilation. It willdetect an excess of ventilation caused by large Vt and/or toomuch positive end-expiratory pressure (PEEP) or at a fixedventilatory setting a respective deficit in lung perfusioncaused by hypovolemia, pulmonary hypotension, or embo-lism.50 Enghoff’s approach includes a similar but less specificcalculation, i.e., it can give a false-positive diagnosis of anincrement in dead space or type C units. This is the case, forexample, in atelectatic lungs where the fictitious Vdalv isincreased by high shunt and low V/Q. If clinicians misinter-pret such a scenario as PEEP-induced lung “overdistension,”they might want to decrease the level of PEEP while in factmore PEEP is needed to overcome the atelectatic and shuntingstate.

Bohr’s formula cannot detect what is happening at thecapillary side of the alveolar-capillary membrane. Eng-hoff’s approach has a notable clinical advantage because itprovides a good idea of the global state of gas exchangefrom using just one single arterial blood sample. Thus,Enghoff’s approach has important clinical applications: ithas been used to diagnose pulmonary embolism,51,52 toguide the weaning process and to predict tracheal extuba-tion,53 to adjust PEEP,54 to detect lung collapse,55 or topredict survival in acute respiratory distress syndromepatients.56 Despite these ample publications, we encouragecaution and a critical reappraisal of some of these results.For example, Nuckton et al.56 demonstrated that Vd/Vtobtained by Enghoff’s approach seems to be a predictor ofmortality in acute respiratory distress syndrome patients.Was mortality really related to dead space or was it morerelated to the amount of shunt? What would happen if wedetermined true dead space using Bohr’s equation? Can alink between overdistension and mortality be established?

In future studies, all of these questions need to beaddressed by appropriate methodologies considering thatthe clinical role of VCap in monitoring lung function isgrossly enriched if both Bohr’s and Enghoff’s approachesare used synergistically.

CONCLUSIONSVCap is clinically useful to monitor the V/Q relationshipin mechanically ventilated patients. Although this tech-nique may not be as precise and detailed as the investi-gational “gold standard” of MIGET, it can easily beapplied at the bedside.

Currently, the novel direct determination of Paco2 byVCap allows the calculation of wasted ventilation (true deadspace together with areas of high V/Q) using Bohr’s equationon a breath-by-breath basis. Contrarily, Enghoff’s approachuses an arterial blood sample and delivers an index of globalV/Q matching considering both, wasted ventilation andwasted perfusion (shunt plus low V/Q areas). Therefore, toavoid misunderstanding using dead space as a descriptor ofthe output of Enghoff’s formula is no longer justified.

Following both approaches separately provides the cli-nician with useful complementary information when moni-toring mechanically ventilated patients at the bedside. Wethink it is time to call these important physiological vari-ables by their appropriate names.

DISCLOSURESName: Gerardo Tusman, MD.Contribution: This author helped prepare the manuscript,figures, and tables.Conflicts of Interest: Gerardo Tusman is the inventor andapplicant of patent EP 04007355.3: non-invasive method andapparatus 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 todeclare.

Figure 5. Relationship between VDBohr and VDB-E corrected for shunt fraction of a tidal volume (VD/VT) measured by Bohr’s formula (VDBohr)versus the one calculated by the Enghoff approach but corrected for the effect of shunt using the formula described by Kuwabara and Duncalf49

(VDB-Ecorr). (A) Pearson correlation and (B) Bland-Altman plot showing the mean bias and limit of agreement between variables. Data wereobtained in an experimental model of acute lung injury (n � 12 pigs, 144 data points).

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Name: Stephan H. Bohm, MD.Contribution: This author helped prepare the manuscript.Conflicts of Interest: Stephan H. Bohm is the inventor andapplicant of patent EP 04007355.3: non-invasive method andapparatus for optimizing the respiration of atelectatic lungs.This manuscript was handled by: Steven L. Shafer, MD.

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