When Does Apparatus Dead Space Matter for the Pediatric Patient? Matthew F. Pearsall, MD, and Jeffrey M. Feldman, MD, MSE Physiologic dead space is defined as the volume of the lung where gas exchange does not occur. Apparatus dead space increases dead space volume, causing either increased Paco2 or the need to increase minute ventilation to maintain normocapnia. Children are especially vulnerable because small increases in apparatus dead space can significantly increase dead space to tidal volume ratio (Vd/Vt). The effect of changes in dead space on arterial CO2 (Paco2) and required minute ventilation were calculated for patients weighing 2 to 17 kg that corresponds to 0 to 36 months of age. Apparatus volumes for typical devices were obtained from the manufacturer or measured by the volume of water required to fill the device. The relationship between the fraction of alveolar CO2 (Faco2) and dead space volume (Vd) was derived from the Bohr equation, Faco2 = VCO2/(RR*(Vt − Vd)), where VCO2 is CO2 production, RR is respiratory rate, and Vt is tidal volume. VCO2 was estimated by using Brody’s equation for humans aged up to 36 months, (VCO2 = 5.56*(wt)1.05), where weight is in kilogram. Initial conditions were Vt = 8 mL/kg, Vd/Vt = 0.3, and a RR of 20 breaths per minute. The relationship between Paco2 and dead space was determined for increasing Vd. Rearranging the Bohr equation, the RR required to maintain Paco2 of 40 mm·Hg was determined as dead space increased. The apparatus Vd of typical device arrangements ranged from 8 to 55 mL, and these values were used for the dead space values in the model. Paco2 increased exponentially with increasing apparatus dead space. For smaller patients, the Paco2 increased more rapidly for small changes in Vd than that in larger patients. Similarly, RR required to maintain Paco2 of 40 mm·Hg increased exponentially with increasing dead space. Increasing apparatus Vd can lead to exponential increases in Paco2 and/or RR required to maintain normal Paco2. The effect on Paco2 is less as patient weight increases, but these data suggest it can be significant for typical circuit components up to at least 17 kg or aged 36 months. (Anesth Analg 2014;118:776–80)
“I
t 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 (Vd) of normal spontaneous respiration is normally about o ne-third of the tidal volume (Vt) and is expressed as a dead space to tidal volume ratio (Vd/Vt) 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 Vt is
From the General Anesthesia Division, Children’s Hospital of Philadelphia, Perelman School of Medicine/University of Pennsylvania, Philadelphia, Pennsylvania. Accepted for publication January 15, 2014. Funding: N/A. Conflict of Interest: See Disclosures at the end of the article. Reprints will not be available from the authors. Address correspondence to Matthew F. Pearsall, MD, General Anesthesia Division, Perelman School of Medicine/University of Pennsylvania, Children’s Hospital of Philadelphia, 9th Floor Main Building, 34th & Civic Center Boulevard, Philadelphia PA 19104. Address e-mail to [email protected]. Copyright © 2014 International Anesthesia Research Society DOI: 10.1213/ANE.0000000000000148
776 www.anesthesia-analgesia.org
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 Vd/Vt. 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 Vd/Vt ratio and adversely affect gas exchange. The goal of this model is to demonstrate the effect of apparatus dead space on CO2 elimination and ventilation requirements in pediatric patients.
METHODS
With the use of accepted mathematical models of the relationship between alveolar CO2 and Vd, the change in alveolar CO2 that results from an increasing dead space was determined. The change in minute ventilation that would be required to maintain a constant alveolar CO2 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 April 2014 • Volume 118 • Number 4
Figure 1. Basic anesthesia circuit schematic. Arrows indicate direction of gas flow and areas of bidirectional flow. The volume of components added to the breathing circuit on the patient side of the y-piece increases the total dead space and the dead space to tidal volume ratio.
Modeling the Effects of Apparatus Dead Space on Paco2 and Respiratory Rate
Figure 2. Circuit connections and filters that provide apparatus dead space with corresponding dead space volumes.
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.
April 2014 • Volume 118 • Number 4
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 Paco2 for increasing apparatus dead space was calculated along with the change in minute ventilation that would be required to maintain a normal Paco2. Stable hemodynamics, stable metabolic rate, and optimal V/Q relationships were assumed. The model is based on the relationship between the fraction of alveolar CO2 (Faco2), metabolic minute production of CO2 (VCO2) in milliliter of CO2 per minute and alveolar ventilation (VA) in milliliter per minute. This relationship can be described by the following equation:1
Faco 2 = VCO 2 / VA [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:
VA = RR * Vt − RR * Vd = RR * ( Vt − Vd ) [2]
Where RR is (in breaths per minute), Vt is (in milliliter), and Vd is (in milliliter). Substituting Equation 2 for VA into Equation 1 yields: Available at http://www.cdc.gov/growthcharts. Accessed November 20, 2013
a
www.anesthesia-analgesia.org 777
When Does Apparatus Dead Space Matter?
Faco 2 = VCO 2 /(RR * ( Vt − Vd ))[3]
VCO2 is the metabolic production of CO2 (mL/min) and can be estimated by using Brody’s equation2 for basal energy metabolism of growing humans aged up to 36 months, where weight is in kilogram: 1.05 VCO 2 = 5.56 * ( wt ) [4]
The alveolar CO2 partial pressure at sea level (Paco2) in mm·Hg is found by multiplying Faco2 by the difference of atmospheric pressure and partial pressure of water vapor both in mm·Hg: Paco 2 = Faco 2 * (760 − 47 )[5]
Substituting Equation 4 and Equation 5 into Equation 3 yields Equation 6, thus allowing for the modeling of changes in Paco2 as apparatus dead space increases if weight, RR, and tidal volume are given:
(
Paco 2 = 713 * 5.56 * ( wt )
1.05
) /(RR * (Vd / Vt))[6]
Alternatively, rearranging Equation 6 to solve for the respiratory rate (RR) required to maintain a given Paco2 of 40 mm·Hg as dead space increases yields Equation 7, thus allowing for the modeling of RR required to maintain normocapnia (Paco2 = 40 mm·Hg) with increasing apparatus dead space:
(
RR = 713 * 5.56 * ( wt )
1.05
) /(40 * (Vd / Vt))[7]
The initial model conditions were set to be Vt 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 Paco2 range of 37 to 41 mm·Hg. A physiologic baseline Vd/Vt ratio of 0.3 was selected with further increases in cumulative Vd dependent on the amount of apparatus dead space. Cumulative Vd was increased to simulate increasing apparatus dead space, and the subsequent effect on Paco2 was calculated.
Sample Calculation Equation 6: Calculating Paco2 for a Given Apparatus Dead Space • A 10 kg child would have a Vt of 8 mL/kg equaling 80 mL. • Physiologic baseline Vd/Vt of 0.3 yields a baseline Vd of 24 mL. • If 30 mL apparatus is used the cumulative Vd is 30 + 24 mL = 54 mL. • Inputting these values into Equation 6 yields: ○○ Paco2 = (713*5.56*(10)1.05)/(20*(80 − 54)) = 85
Sample Calculation Equation 7: Calculating RR Necessary to Maintain Paco2 of 40 mm·Hg for a Given Apparatus Dead Space • A 10 kg child would have a Vt of 8 mL/kg equaling 80 mL. • Physiologic baseline Vd/Vt of 0.3 yields a baseline Vd of 24 mL.
778 www.anesthesia-analgesia.org
• If 30 mL apparatus is used, the cumulative Vd 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 Paco2, (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 Vd/Vt increases more rapidly for smaller patients as dead space increases. It is notable that the relationship between Paco2 and apparatus dead space or minute ventilation and apparatus dead space is exponential. Further analysis indicated that the inflection point where changes in Paco2 or RR began to increase very rapidly corresponded to the same Vd/Vt for each sized patient.
DISCUSSION
There are clinical studies that clearly indicate the impact of dead space changes on Paco2 and ventilation requirements.3 The goal of this model is to demonstrate the effect of apparatus dead space on CO2 elimination and ventilation requirements in pediatric patients. The results indicate that as apparatus dead space increases, CO2 elimination is significantly impaired as evidenced by a rapid increase in either Paco2 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 Paco2 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 Vt can avoid significant hypercapnia, and the model suggests limiting apparatus dead space to no more than one-third of Vt 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 Vd 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 Vd, 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
anesthesia & analgesia
Figure 3. Graph of Paco2 values for variable apparatus dead space and variable patient weight. Apparatus dead space to tidal volume ratios of 0.3 and 0.5 that correspond to cumulative Vd/Vt ratios of 0.6 and 0.8, respectively, are depicted.
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 (
“I
t 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 (Vd) of normal spontaneous respiration is normally about o ne-third of the tidal volume (Vt) and is expressed as a dead space to tidal volume ratio (Vd/Vt) 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 Vt is
From the General Anesthesia Division, Children’s Hospital of Philadelphia, Perelman School of Medicine/University of Pennsylvania, Philadelphia, Pennsylvania. Accepted for publication January 15, 2014. Funding: N/A. Conflict of Interest: See Disclosures at the end of the article. Reprints will not be available from the authors. Address correspondence to Matthew F. Pearsall, MD, General Anesthesia Division, Perelman School of Medicine/University of Pennsylvania, Children’s Hospital of Philadelphia, 9th Floor Main Building, 34th & Civic Center Boulevard, Philadelphia PA 19104. Address e-mail to [email protected]. Copyright © 2014 International Anesthesia Research Society DOI: 10.1213/ANE.0000000000000148
776 www.anesthesia-analgesia.org
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 Vd/Vt. 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 Vd/Vt ratio and adversely affect gas exchange. The goal of this model is to demonstrate the effect of apparatus dead space on CO2 elimination and ventilation requirements in pediatric patients.
METHODS
With the use of accepted mathematical models of the relationship between alveolar CO2 and Vd, the change in alveolar CO2 that results from an increasing dead space was determined. The change in minute ventilation that would be required to maintain a constant alveolar CO2 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 April 2014 • Volume 118 • Number 4
Figure 1. Basic anesthesia circuit schematic. Arrows indicate direction of gas flow and areas of bidirectional flow. The volume of components added to the breathing circuit on the patient side of the y-piece increases the total dead space and the dead space to tidal volume ratio.
Modeling the Effects of Apparatus Dead Space on Paco2 and Respiratory Rate
Figure 2. Circuit connections and filters that provide apparatus dead space with corresponding dead space volumes.
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.
April 2014 • Volume 118 • Number 4
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 Paco2 for increasing apparatus dead space was calculated along with the change in minute ventilation that would be required to maintain a normal Paco2. Stable hemodynamics, stable metabolic rate, and optimal V/Q relationships were assumed. The model is based on the relationship between the fraction of alveolar CO2 (Faco2), metabolic minute production of CO2 (VCO2) in milliliter of CO2 per minute and alveolar ventilation (VA) in milliliter per minute. This relationship can be described by the following equation:1
Faco 2 = VCO 2 / VA [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:
VA = RR * Vt − RR * Vd = RR * ( Vt − Vd ) [2]
Where RR is (in breaths per minute), Vt is (in milliliter), and Vd is (in milliliter). Substituting Equation 2 for VA into Equation 1 yields: Available at http://www.cdc.gov/growthcharts. Accessed November 20, 2013
a
www.anesthesia-analgesia.org 777
When Does Apparatus Dead Space Matter?
Faco 2 = VCO 2 /(RR * ( Vt − Vd ))[3]
VCO2 is the metabolic production of CO2 (mL/min) and can be estimated by using Brody’s equation2 for basal energy metabolism of growing humans aged up to 36 months, where weight is in kilogram: 1.05 VCO 2 = 5.56 * ( wt ) [4]
The alveolar CO2 partial pressure at sea level (Paco2) in mm·Hg is found by multiplying Faco2 by the difference of atmospheric pressure and partial pressure of water vapor both in mm·Hg: Paco 2 = Faco 2 * (760 − 47 )[5]
Substituting Equation 4 and Equation 5 into Equation 3 yields Equation 6, thus allowing for the modeling of changes in Paco2 as apparatus dead space increases if weight, RR, and tidal volume are given:
(
Paco 2 = 713 * 5.56 * ( wt )
1.05
) /(RR * (Vd / Vt))[6]
Alternatively, rearranging Equation 6 to solve for the respiratory rate (RR) required to maintain a given Paco2 of 40 mm·Hg as dead space increases yields Equation 7, thus allowing for the modeling of RR required to maintain normocapnia (Paco2 = 40 mm·Hg) with increasing apparatus dead space:
(
RR = 713 * 5.56 * ( wt )
1.05
) /(40 * (Vd / Vt))[7]
The initial model conditions were set to be Vt 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 Paco2 range of 37 to 41 mm·Hg. A physiologic baseline Vd/Vt ratio of 0.3 was selected with further increases in cumulative Vd dependent on the amount of apparatus dead space. Cumulative Vd was increased to simulate increasing apparatus dead space, and the subsequent effect on Paco2 was calculated.
Sample Calculation Equation 6: Calculating Paco2 for a Given Apparatus Dead Space • A 10 kg child would have a Vt of 8 mL/kg equaling 80 mL. • Physiologic baseline Vd/Vt of 0.3 yields a baseline Vd of 24 mL. • If 30 mL apparatus is used the cumulative Vd is 30 + 24 mL = 54 mL. • Inputting these values into Equation 6 yields: ○○ Paco2 = (713*5.56*(10)1.05)/(20*(80 − 54)) = 85
Sample Calculation Equation 7: Calculating RR Necessary to Maintain Paco2 of 40 mm·Hg for a Given Apparatus Dead Space • A 10 kg child would have a Vt of 8 mL/kg equaling 80 mL. • Physiologic baseline Vd/Vt of 0.3 yields a baseline Vd of 24 mL.
778 www.anesthesia-analgesia.org
• If 30 mL apparatus is used, the cumulative Vd 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 Paco2, (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 Vd/Vt increases more rapidly for smaller patients as dead space increases. It is notable that the relationship between Paco2 and apparatus dead space or minute ventilation and apparatus dead space is exponential. Further analysis indicated that the inflection point where changes in Paco2 or RR began to increase very rapidly corresponded to the same Vd/Vt for each sized patient.
DISCUSSION
There are clinical studies that clearly indicate the impact of dead space changes on Paco2 and ventilation requirements.3 The goal of this model is to demonstrate the effect of apparatus dead space on CO2 elimination and ventilation requirements in pediatric patients. The results indicate that as apparatus dead space increases, CO2 elimination is significantly impaired as evidenced by a rapid increase in either Paco2 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 Paco2 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 Vt can avoid significant hypercapnia, and the model suggests limiting apparatus dead space to no more than one-third of Vt 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 Vd 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 Vd, 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
anesthesia & analgesia
Figure 3. Graph of Paco2 values for variable apparatus dead space and variable patient weight. Apparatus dead space to tidal volume ratios of 0.3 and 0.5 that correspond to cumulative Vd/Vt ratios of 0.6 and 0.8, respectively, are depicted.
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 (
