_{phys}) provides important insight regarding the efficiency of ventilation and its relation to pulmonary perfusion.

^{1}Respiratory dead space measurement has found wide applications in respiratory physiology, clinical anesthesia, and critical care medicine. It has been used in the diagnosis of pulmonary embolism

^{2}and as a predictor of lung volume during controlled ventilation.

^{3}A physiologic dead space to tidal volume ratio higher than 0.6 was associated with a 1.5-fold increase in mortality rate in infants with congenital diaphragmatic hernia.

^{4}In a prospective study of adults with acute respiratory distress syndrome, patients who died showed a significantly higher mean dead space fraction compared with survivors (0.63

*vs.*0.54, respectively;

*P*< 0.05).

^{5}Coss-Bu

*et al.*

^{6}found similar results in critically ill children with lung injury. Routine monitoring of dead space to tidal volume ratio in pediatric patients has been demonstrated to permit earlier extubation and to reduce unexpected extubation failures.

^{7}

^{8}The total respiratory dead space can be portioned into two parts: the anatomical dead space (airway, serial, or Fowler dead space, Vd

_{anat}), and alveolar or parallel dead space (Vd

_{alv}).

^{9}Because alveolar dead space cannot be measured directly, it is commonly estimated by subtracting the anatomical dead space from the physiologic dead space.

^{2}

^{10}A graphical method for calculating and representing anatomical, physiologic, and alveolar dead space was reported by Fletcher

*et al.*,

^{11}in which the dead spaces are represented by areas of trapezoids.

#### Materials and Methods

##### Physiologic Dead Space

^{12}:

_{phys}be is physiologic dead space calculated by the Bohr-Enghoff equation, Fēco

_{2}is mixed expired concentration of carbon dioxide, Faco

_{2}is the carbon dioxide fraction of a gas in equilibrium with arterial blood, and Vt is tidal volume. Arterial and mixed expired carbon dioxide partial pressures can also be used in this equation instead of Faco

_{2}and Fēco

_{2}.

*ik*is drawn intersecting the expirogram at

*j*such that areas A

_{qjk}and A

_{ichj}are equal (fig. 1). Then,

_{phys}ea =

*ok*,

_{phys}ea is physiologic dead space calculated by the new equal area method and

*ok*is the distance between the origin and the point

*k*. Vd

_{phys}ea may be shown to equal Vd

_{phys}be.

_{ohd}is the area under the expirogram, which is the total expired carbon dioxide (Vco

_{2}). Substituting equation 2 into 1,

_{icdk}can be expressed as

Equation 5 Image Tools |
Equation 6 Image Tools |
Equation (Uncited) Image Tools |

_{ojk}equal to area A

_{ichj}intersects the x-axis at a point (

*k*) that represents the physiologic dead space.

##### Anatomical Dead Space

*mh*is fitted to phase III of the expirogram and extrapolated to

*r*. The vertical line

*rb*intersects the expirogram and the x-axis at points

*n*and

*b*respectively, making areas A

_{nrm}and A

_{qnb}equal. The point

*b*on the expired volume axis is the anatomical dead space.

##### Alveolar Dead Space

*ok*) and anatomical dead space (

*ob*) is

*bk*, which therefore represents alveolar dead space, Vd

_{alv}. Hence anatomical, physiologic, and alveolar dead spaces are calculated by similar equal areas principles and displayed graphically on the same x-axis.

##### Fletcher Graphical Method and Representation

^{11}physiologic, anatomical, and alveolar dead spaces are calculated as follows:

Equation 8 Image Tools |
Equation 10 Image Tools |

*rhdb*, Y is the area of trapezoid

*schr*, Z is the area of rectangle

*asbo*(fig. 1), and f indicates the Fletcher method. Equation 8 is analytically identical to the Bohr-Enghoff equation (equation 1), and equation 10 is analytically identical to the Fowler equal area method.

##### Clinical Study

_{2}O; and inspired oxygen concentration, 35%.

^{13}The carbon dioxide analyzer was calibrated with known concentrations of carbon dioxide and was cross-calibrated with the blood gas analyzer (ABL 700; Radiometer, Copenhagen, Denmark). The synchronization of flow and carbon dioxide signals of the NICO monitor was verified by rapid injection of carbon dioxide at 1 l/min into the airway immediately upstream of the carbon dioxide analyzer while 5 l/min of oxygen was flowing.

^{14,15}were adjusted one at a time from the baseline in random order to one of the following settings: tidal volume 80, 100, and 120% of baseline tidal volume; end-expiratory pressure 0, 5, and 10 cm H

_{2}O; inspiratory-to-expiratory ratio 1:1.7, 1:1, and 2:1; inspiratory hold 10, 30, and 50% of the inspiratory time. After 15 min at each setting, 10 carbon dioxide expirograms were recorded for analysis, and at the same time, arterial blood was drawn into a heparinized syringe (PICO70; Radiometer) and stored in ice slush for blood gas analysis.

##### Data Analysis

_{2}was calculated according to Faco

_{2}= Paco

_{2}/(P

_{b}− P

_{w}), where P

_{b}is barometric pressure, P

_{w}is the saturated water vapor pressure at body temperature,

^{16}and Paco

_{2}is arterial partial pressure of carbon dioxide corrected to the patient's body temperature.

^{17}Total expired carbon dioxide volume (Vco

_{2}= A

_{ohd}) was calculated by integrating the expired carbon dioxide concentration with respect to expired volume. For each carbon dioxide expirogram, physiologic dead space was calculated by using the Bohr-Enghoff equation (equation 1), the new equal area method, and the Fletcher area method (equation 8). All methods were implemented without interpolating between data points. The points

*b*and

*k*were assigned by selecting the sampled data points that minimized the difference between the areas. The average and SD of each set of 10 dead spaces were calculated.

^{18}The limits of agreement were defined as the mean difference ± 2 SD and describe the range that includes 95% of the differences between the two methods compared. All other results are reported as mean ± SD.

*P*< 0.05 was considered to be statistically significant. All calculations were performed by software written in MATLAB.

#### Results

^{2}(range, 23.6–30.4 kg/m

^{2}). A total of 120 sets of 10 expirograms were obtained from the 10 patients. Calculated Vd

_{anat}, Vd

_{phys}be, Vd

_{phys}f, and Vd

_{phys}ea were 197.7 ± 33.2, 313.6 ± 80.1, 313.6 ± 80.1, and 313.5 ± 80.1 ml, respectively. Intraindividual dead space measurements varied by −15.9 ± 5.1 to 18.4 ± 7.3% due to changes in tidal volume, by 0 to 6.7 ± 1.7% due to changes in end-expiratory pressure, by 0 to −9.7 ± 2.9% due to changes in inspiratory-to-expiratory ratio, and by 0 to −18.4 ± 6.9% due to changes in inspiratory hold. The mean intraindividual coefficient of variation of the 120 sets of 10 dead space measurements at each ventilation setting was 2.0% (range, 0.7–5.0%).

_{phys}ea and Vd

_{phys}be ranged from −1.65 to 0.79 ml (mean, −0.07 ml; limits of agreement, −1.27 to 1.13 ml; fig. 2A). Differences between Vd

_{phys}ea and Vd

_{phys}f ranged from −2.08 to 1.19 ml (mean, −0.09 ml; limits of agreement, −1.52 to 1.34 ml; fig. 2B). The differences were all randomly distributed over the range of dead spaces, and the mean differences were not statistically significantly different from zero in either comparison. Pearson correlation analysis showed correlation coefficients of 0.999 (

*P*< 0.05) between Vd

_{phys}be and Vd

_{phys}ea and between Vd

_{phys}f and Vd

_{phys}ea. Analysis of variance showed that (Vd

_{phys}be − Vd

_{phys}ea) and (Vd

_{phys}f − Vd

_{phys}ea) were not statistically different from zero (

*P*> 0.05) over all ventilator settings (means, −0.07 and −0.09 ml; ranges, −0.25 to 0.11 and −0.30 to 0.15 ml, respectively).

Fig. 3 Image Tools |
Table 1 Image Tools |

#### Discussion

_{anat}, Vd

_{alv}, Vd

_{phys}, Vt, Vd

_{anat}/Vt, Vd

_{alv}/Vt, Vd

_{phys}/Vt, and Vd

_{alv}/Vt

_{alv}, which is especially helpful for the visualization of dead spaces during bedside monitoring of patients; (2) the use of a principle similar to that used in the Fowler equal area method, which makes the calculation of anatomical and physiologic dead spaces on the carbon dioxide expirogram consistent; (3) the use of a more straightforward method than the partitioning of areas on a carbon dioxide expirogram proposed by Fletcher

*et al.*

^{11}; (4) the equal area method is simpler than the classic Douglas bag method, an advantage it shares with other open-circuit methods, although all three methods require arterial blood sampling. In addition, this new equal area method emphasizes the relations that exist between the various respiratory dead spaces and thus will greatly assist in understanding and teaching of their concepts. Once synchronized flow and carbon dioxide signals are digitized, the new method requires a few lines of code more than the open-circuit Bohr-Enghoff method, but it is not difficult to implement. With the advance of computing technology, the calculation and visualization of the dead spaces can be easily implemented for clinical application.

^{19}The delay between carbon dioxide analyzer and flow signals and the rise time of the carbon dioxide analyzer, especially in sidestream carbon oxide analyzers, should be corrected to reduce error.

^{19}