“It was realized in the nineteenth century that an appreciable part of each inspiration did not penetrate to the regions of the lungs in which gas exchange occurred and was therefore exhaled unchanged. This fraction of the tidal volume has long been known as the dead space…”

#### Nunn’s Applied Respiratory Physiology

In the spontaneously breathing patient, total or physiologic dead space includes the conducting airways, where there is no potential for gas exchange, and the alveoli that are ventilated but where gas exchange does not occur typically because of lack of perfusion. The dead space volume (V_{d}) of normal spontaneous respiration is normally about one-third of the tidal volume (V_{t}) and is expressed as a dead space to tidal volume ratio (V_{d}/V_{t}) of 0.3.

During controlled ventilation, managing dead space has significant potential implications for patient care. The physiologic dead space is subject to change when V_{t} is delivered mechanically, and ventilation/perfusion (V/Q) relationships are altered by positive pressure ventilation and hemodynamic changes. Furthermore, the various components of the apparatus used during mechanical ventilation can significantly increase dead space. Apparatus dead space can be defined as portions of the breathing circuit that have bidirectional flow (ventilation). Because gas exchange does not occur in the breathing circuit apparatus, apparatus dead space directly contributes to increasing the V_{d}/V_{t}. In a typical anesthesia circle system, the apparatus dead space is the internal volume of any apparatus on the patient side of the y-piece (Fig. 1).

The potential effect of dead space on gas exchange in pediatric patients is especially important because small increases in apparatus dead space can significantly increase the V_{d}/V_{t} ratio and adversely affect gas exchange. The goal of this model is to demonstrate the effect of apparatus dead space on CO_{2} elimination and ventilation requirements in pediatric patients.

#### METHODS

With the use of accepted mathematical models of the relationship between alveolar CO_{2} and V_{d}, the change in alveolar CO_{2} that results from an increasing dead space was determined. The change in minute ventilation that would be required to maintain a constant alveolar CO_{2} as dead space increases was also determined.

##### Measurement of Apparatus Dead Space

To determine the limits of apparatus dead space to be used in this analysis, the internal volume of circuit filters and connectors commonly used at our institution was determined from either documentation in the package insert (the 22-mL filter) or by measuring the volume of water in milliliter required to fill the internal volume (all other components) (Fig. 2).

On the basis of the volumes of the commonly available and used components, the amount of potential apparatus dead space used for the model was set to be from 0 to 55 mL. This range represents both the absolute minimum and reasonable maximum values in our clinical pediatric practice. The minimal apparatus dead space value of 0 mL represents the absence of a filter, elbow, and other connectors. The maximal value of 55 mL represents the largest apparatus dead space configuration (standard 8-mL elbow, 22-mL filter, and fully expanded 25-mL corrugated extension tubing) that would likely be used at our institution.

##### Modeling the Effects of Apparatus Dead Space on PaCO_{2} and Respiratory Rate

A mathematical model was implemented (Microsoft Excel 2007, Microsoft Corporation; Redmond WA) to estimate the effect of apparatus dead space on ventilation for patient weights from 2 to 17 kg. This weight range was selected because it is the approximate weight of the 5th to 95th percentile 0 to 36 month old boys and girls based on the most recent published Centers for Disease Control growth charts.a

For each patient weight, the change in PaCO_{2} for increasing apparatus dead space was calculated along with the change in minute ventilation that would be required to maintain a normal PaCO_{2}. Stable hemodynamics, stable metabolic rate, and optimal V/Q relationships were assumed.

The model is based on the relationship between the fraction of alveolar CO_{2} (FaCO_{2}), metabolic minute production of CO_{2} (VCO_{2}) in milliliter of CO_{2} per minute and alveolar ventilation (VA) in milliliter per minute. This relationship can be described by the following equation:^{1}

VA is the difference between total minute ventilation and dead space ventilation, which yields the portion of minute ventilation participating in gas exchange in the alveoli:

Where RR is (in breaths per minute), V_{t} is (in milliliter), and V_{d} is (in milliliter).

Substituting Equation 2 for VA into Equation 1 yields:

VCO_{2} is the metabolic production of CO_{2} (mL/min) and can be estimated by using Brody’s equation^{2} for basal energy metabolism of growing humans aged up to 36 months, where weight is in kilogram:

The alveolar CO_{2} partial pressure at sea level (PaCO_{2}) in mm·Hg is found by multiplying FaCO_{2} by the difference of atmospheric pressure and partial pressure of water vapor both in mm·Hg:

Substituting Equation 4 and Equation 5 into Equation 3 yields Equation 6, thus allowing for the modeling of changes in PaCO_{2} as apparatus dead space increases if weight, RR, and tidal volume are given:

Alternatively, rearranging Equation 6 to solve for the respiratory rate (RR) required to maintain a given PaCO_{2} of 40 mm·Hg as dead space increases yields Equation 7, thus allowing for the modeling of RR required to maintain normocapnia (PaCO_{2} = 40 mm·Hg) with increasing apparatus dead space:

The initial model conditions were set to be V_{t} of 8 mL/kg, a RR of 20 breaths per minute, and an initial apparatus dead space of 0 mL. Whole numbers were used for these initial conditions to provide a more realistic clinical scenario. These initial conditions provided an initial normocapnic model condition yielding a PaCO_{2} range of 37 to 41 mm·Hg.

A physiologic baseline V_{d}/V_{t} ratio of 0.3 was selected with further increases in cumulative V_{d} dependent on the amount of apparatus dead space. Cumulative V_{d} was increased to simulate increasing apparatus dead space, and the subsequent effect on PaCO_{2} was calculated.

##### Sample Calculation Equation 6: Calculating PaCO_{2} for a Given Apparatus Dead Space

* A 10 kg child would have a V_{t} of 8 mL/kg equaling 80 mL.

* Physiologic baseline V_{d}/V_{t} of 0.3 yields a baseline V_{d} of 24 mL.

* If 30 mL apparatus is used the cumulative V_{d} is 30 + 24 mL = 54 mL.

* Inputting these values into Equation 6 yields:

* PaCO_{2} = (713*5.56*(10)^{1.05})/(20*(80 − 54)) = 85

##### Sample Calculation Equation 7: Calculating RR Necessary to Maintain PaCO_{2} of 40 mm·Hg for a Given Apparatus Dead Space

* A 10 kg child would have a V_{t} of 8 mL/kg equaling 80 mL.

* Physiologic baseline V_{d}/V_{t} of 0.3 yields a baseline V_{d} of 24 mL.

* If 30 mL apparatus is used, the cumulative V_{d} is 30 + 24 mL = 54 mL.

* Inputting these values into Equation 7 yields:

* RR = (713*5.56*(10)^{1.05})/(40*(80 − 54)) almost equal to 43 breaths per minutes.

#### RESULTS

The model demonstrated that increasing apparatus dead space increases the PaCO_{2}, (Fig. 3) or the need to increase RR if normocapnia is to be maintained (Fig. 4). Not surprisingly, patient weight is a very important factor, because the V_{d}/V_{t} increases more rapidly for smaller patients as dead space increases. It is notable that the relationship between PaCO_{2} and apparatus dead space or minute ventilation and apparatus dead space is exponential. Further analysis indicated that the inflection point where changes in PaCO_{2} or RR began to increase very rapidly corresponded to the same V_{d}/V_{t} for each sized patient.

Figure 3 Image Tools |
Figure 4 Image Tools |

#### DISCUSSION

There are clinical studies that clearly indicate the impact of dead space changes on PaCO_{2} and ventilation requirements.^{3} The goal of this model is to demonstrate the effect of apparatus dead space on CO_{2} elimination and ventilation requirements in pediatric patients. The results indicate that as apparatus dead space increases, CO_{2} elimination is significantly impaired as evidenced by a rapid increase in either PaCO_{2} or RR required to maintain normocapnia, and furthermore, that smaller patients are more sensitive to increases in apparatus dead space. Although these data are based purely on a mathematical model, the change in PaCO_{2} and required RR to maintain normocapnia would be expected to be qualitatively similar for patients of similar weight with similar ventilation variables. One can therefore gain insight from these results into the degree to which the effectiveness of ventilation can be influenced by adding additional dead space apparatus.

Attention to the amount of apparatus dead space added relative to the desired V_{t} can avoid significant hypercapnia, and the model suggests limiting apparatus dead space to no more than one-third of V_{t} or lower if possible. Minimizing apparatus dead space can be easily accomplished with careful selection of the devices added to the circuit after the y-piece. The apparatus V_{d} used in the model were based on the internal volume of circuit elbows, filters, and extensions that are readily available and frequently used at our institution. There are commercially available products with smaller V_{d}, but these devices typically do not provide gas sampling ports that facilitate capnography and inhaled agent analysis. The default and most common apparatus setup at our pediatric institution is the 8-mL elbow and 22-mL filter, yielding 30 mL apparatus dead space. Also, flexible corrugated extension tubing may be added to facilitate a less intrusive profile of the breathing circuit, creating additional apparatus dead space of 13 to 25 mL depending on the degree of extension used. For neonates and infants younger than 6 months of age, our institutional default setup is to use a smaller 9-mL filter with the 8-mL elbow instead of the larger 22-mL filter, which decreases apparatus dead space from 30 to 17 mL. Often after induction, intubation and positioning of our smaller patients (<5 kg) the 8-mL elbow is removed to reduce apparatus dead space to 9 mL.

The model results indicate that commonly used circuit components can easily increase apparatus dead space, leading to hypercarbia in small patients. In addition, hypercarbia may go unrecognized if end tidal capnography is relied on as the sole monitor of effective ventilation when V_{d}/V_{t} increases.^{4} Although it is possible to increase minute ventilation to offset the hypercarbia, modern approaches to lung-protective ventilation dictate that V_{t} and ventilator cycles should be limited to minimize the risk of ventilator-induced lung injury.^{5} Given the smaller V_{t} required by a lung-protective strategy, managing dead space in small patients is important to avoid unintended increases in V_{d}/V_{t}.^{3}

There are a number of limitations to this model that prevent quantitative validation against physiologic measurements in living beings. The model assumes a single compartment in the lung where gases are mixed instantaneously. Given the fact that regions of the human lung receive differential amounts of ventilation during each breath, the single compartment model is not likely to predict physiologic values exactly. Multiple other factors that are not included in the model and are difficult to control in vivo include fluctuations in physiologic dead space directly due to mechanical ventilation or indirectly due to perfusion changes. Since CO_{2} elimination depends on the effectiveness of ventilation, and the model assumes the best conditions for gas exchange, one would expect that the predicted values for PaCO_{2} by the model would likely be lower than expected during actual patient care.

This model does not attempt to describe any potential effects of apparatus dead space on oxygenation. However, increased apparatus dead space can be detrimental to oxygenation. Reduced VA results in less oxygen delivery to the alveolus. Furthermore, if a significant portion of CO_{2} in the exhaled V_{t} is rebreathed which is possible with higher cumulative V_{d}/V_{t}, CO_{2} accumulates in the alveolus and reduces the partial pressure of oxygen. This model also assumes normal metabolic rate and V/Q relationships in the lung or the optimal conditions to support gas exchange. Abnormal V/Q relationships or higher metabolic rates would likely lead to even worse predictions for the effect of dead space on gas exchange, but a different and more complex model would be required.

The model presented here predicts that CO_{2} elimination will be more effective if apparatus dead space is carefully managed. When caring for small patients, simply identifying and removing unnecessary components (such as eliminating the 8-mL elbow or extensions) or by using components with smaller V_{d} (switching to a 9-mL filter from a 22-mL filter) is predicted to improve the efficiency of mechanical ventilation.

#### DISCLOSURES

**Name:** Matthew F. Pearsall, MD.

**Contribution:** This author is the first author.

**Attestation:** Matthew Pearsall approves the final manuscript.

**Conflicts of Interest:** The author has no conflicts of interest to declare.

**Name:** Jeffrey M. Feldman, MD, MSE.

**Contribution:** This author is the second author.

**Attestation:** Jeffrey Feldman approves the final manuscript.

**Conflicts of Interest:** This author is the consultant for Draeger Medical Inc.

**This manuscript was handled by:** Maxime Cannesson, MD, PhD.

#### FOOTNOTES

a Available at http://www.cdc.gov/growthcharts. Accessed November 20, 2013 Cited Here...