(Chest. 2000;118:468-472.)
© 2000
American College of Chest Physicians
Reduction in Tracheal Lumen Due to Endotracheal Intubation and Its Calculated Clinical Significance*
Kevin R. Bock, MD;
Peter Silver, MD;
Maya Rom and
Mayer Sagy, MD, FCCP
*
From the Division of Critical Care Medicine, Schneider Children’s Hospital, Hyde Park, NY.
Correspondence to: Kevin R. Bock, MD, Division of Critical Care Medicine, Schneider Children’s Hospital, Hyde Park, NY 11040; e-mail: krbcmgb{at}massmed.org
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Abstract
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Background: The flow in the human trachea is turbulent.
Thus, the tracheal resistance (R) and the pressure gradient
(
P) required to maintain a given flow across the trachea is
inversely related to its radius raised to the fifth power. If the
caliber reduction ratio (X) after endotracheal intubation is calculated
as X = radius of the endotracheal tube (rETT)/radius of the
trachea (rT), then P and/or R will be increased by
(1/X)5.
Study objectives: To measure the
actual ratio between rETT and rT following endotracheal intubation of
pediatric patients with respiratory failure and to calculate the
resulting increase in the tracheal R and P for a given inspiratory
flow rate.
Design: Retrospective chart review.
Setting: Pediatric ICU in a tertiary-care teaching
children’s medical center.
Patient enrollment: Twenty
consecutive pediatric patients (mean [± SD] age, 6.4 ± 7.2
years) whose tracheas had been intubated for various causes of
respiratory failure, and who had received a CT scan, were included in
our study. All patients received an endotracheal tube the size of which
was derived from the following formula: (age in years/4) + 4.
Measurements and main results: rT and rETT were measured
from CT scan sections at and around the level of the thoracic inlet,
and the average values were used to calculate X. These values ranged
from 0.33 to 0.65 (mean, 0.55 ± 0.8). The factor (1/X)5
was calculated for each patient and then was multiplied by the known
normal value for tracheal R for adolescents and adults (0.07 cm
H2O/L/s) to obtain the value of R resulting from the
artificial airway, (1/X)5 x 0.07. Our results showed
that tracheal R increased due to caliber reduction of the trachea after
endotracheal intubation by 33.9 ± 52.5-fold (range, 8.6- to
255.5-fold). In order to maintain an inspiratory flow of 1 L/s, the
value of P for the intubated trachea would increase from 0.07 cm
H2O to a mean of 2.4 ± 3.7 cm H2O (range,
0.6 to 18 cm H2O). In two of our patients, the rT/rETT
ratios were < 0.5 (0.33 and 0.44, respectively); this translated into
a more significant increase in the calculated Ps, 18 and 4.2 cm
H2O, respectively.
Conclusions: The
common value of X due to endotracheal intubation is between 0.5 and
0.6, which in and of itself results in an increase in R across the
intubated trachea up to 32-fold. The calculated increase in P as a
result of this is between 2 and 3 cm H2O for adolescents or
young adults. The addition of pressure support of at least 3 cm
H2O during spontaneous ventilation via an endotracheal
tube, which is common practice in pediatric critical care, should
alleviate any respiratory distress emanating from the increased R.
However, a value for X < 0.5, which was found in 10% of our patients
(2 of 20 patients), results in a much higher calculated increase in the
pressure gradient and, therefore, a higher level of pressure support is
required to overcome this increase.
Key Words: airway resistance • endotracheal intubation • mechanical ventilator • trachea
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Introduction
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In
order for gas to flow into the lungs, a pressure gradient (P) must
develop to overcome the elastic and nonelastic airway resistance (R) of
the respiratory
system. The relationship between R and P across the airway is
expressed as
where V is the flow of gas.1
During laminar flow, the
resistance is calculated from the Hagen-Poiseuille equation, and the
above formula can be rearranged to
where L is the length of the airway, µ is the viscosity
of the gas, and r is the radius of the airway.2
However,
in the large airways, such as the trachea, V exceeds the critical
velocity and becomes turbulent.3
This transition to
turbulent V occurs at a Reynolds number of approximately 2,300, and V
becomes completely turbulent at a Reynolds number of
4,000.2
R across the trachea becomes directly proportional
to V2 and inversely proportional to the radius of
the trachea (rT) to the fifth power:
where p is the density of the gas and f is the frictional
factor.4
When a pediatric patient receives endotracheal intubation, the
endotracheal tube that is initially selected possesses an internal
diameter that is commonly derived from the following
formula5
:
The relationship of the internal diameter of the
endotracheal tube to the diameter of the tracheal lumen and the
implications of such a relationship for respiratory mechanics have not
been investigated fully in the pediatric population.
Pressure and R across the trachea for a constant V are inversely
related to rT5. If the tracheal X after
intubation is calculated as:
then R and P will be increased by
(1/X)5 in the intubated trachea. Our objectives
were to retrospectively measure the actual ratio between the rETTs and
the rTs following the intubation of pediatric patients with respiratory
failure and to calculate the derived increase in R and P across the
intubated tracheas. We hypothesize that our measured and calculated
data will help clinicians to understand better the difficulties that
some patients may encounter during periods of spontaneous breathing
through an endotracheal tube.
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Materials and Methods
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Twenty consecutive pediatric patients whose tracheas had been
intubated for respiratory failure and who received a CT scan of the
lung as part of their diagnostic evaluation were included in our study.
All patients had received placement of an endotracheal tube, with the
size of the tube derived from the following standard formula: (age in
years/4) + 4. Patient’s ages and the diagnoses they received are
listed in Table 1
. CT scan images of the trachea at and around the level of the thoracic
inlet were selected for each patient, and digital images were created
with a scanner (Scan Jet 5P; Hewlett Packard; Singapore) attached to a
personal computer (model 300GL; IBM; Austin, TX). The scanned CT images
then were magnified to allow for accurate measurements (Fig 1
). Two separate investigators (K.B. and M.R.) measured the rTs and
rETTs. There was no significant variance between measurements at
various cuts; the individual patient’s average value was used to
calculate X. The factor by which the tracheal R (or P) had increased
secondary to endotracheal intubation, (1/X)5, was
calculated for each patient. Data regarding tracheal R in the young
pediatric age group are unavailable. The known normal tracheal R in
adolescents and adults has been determined to be approximately 0.07 cm
H2O/L/s.6
Therefore, to obtain the
calculated value of R for an intubated trachea for this age group, we
multiplied (1/X)5 by the known normal value for
tracheal R:
Utilizing an inspiratory V of 1 L/s (60 L/min), the
P across the intubated trachea (Pint) becomes
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Figure 1. Top: an original CT scan image
(patient 1) at the level of the thoracic inlet. Bottom:
a magnified computer image of the CT scan made to enable accurate
measurements of rT and rETT.
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Results
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Data are presented as mean ± SD. The mean age of our patients
was 6.4 ± 7.2 years. The measured values of X ranged from 0.33 to
0.65 (mean, 0.55 ± 0.08) (Table 2 ). The factor (1/X)5 ranged from 8.6 to 255.5
(mean, 33.9 ± 52.5). Using an inspiratory flow of 1 L/s, the Ps
would be expected to increase from the known 0.07 cm
H2O for a nonintubated trachea for adolescents
and adults to a mean of 2.4 ± 3.7 cm H2O
(range, 0.6 to 18 cm H2O). In two of our patients
(10%), X was < 0.5 (0.33 and 0.44). In these patients, the
calculated P would be expected to significantly increase to 18 and
4.2 cm H2O, respectively. In two other patients
(10%), the ratio was 0.65, and, thus, the calculated
P was only 0.5 cm H2O.
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Discussion
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The substitution of an endotracheal tube for the trachea in
critically ill patients results in an additional resistive load imposed
on the respiratory muscles and, thus, a possible increase in the work
of breathing (WOB).7
Calculating the actual WOB during the
process of weaning from mechanical ventilation might be clinically
valuable when selecting the appropriate amount of pressure support
ventilation required to reduce the WOB to a specific
level.8
However, calculating the WOB based on the Campbell
diagram entails the use of a pneumotachograph and the insertion of an
intraesophageal balloon catheter to obtain the intrapleural
pressure.9
While this is a simple method, it is invasive.
The determination of the pressure drop across the endotracheal
tube in order to calculate R or its contribution to the WOB for various
rates of V is similarly invasive; it requires the insertion of a
catheter into the distal tip of the endotracheal tube for pressure
measurements10
and is dependent on the level at which the
catheter tip is located.11
Additionally, the intraluminal
catheter reduces the cross-sectional area of the endotracheal tube,
thus artificially increasing R.11
The Blasius resistance
formula and the acoustic Blasius technique provide noninvasive methods
to calculate the pressure drop across an endotracheal tube, but
requires an accurate determination of the viscosity, density, and V of
the delivered gas in addition to the endotracheal tube
diameter.12
13
These methods could have been considered
for our patients had we planned a prospective study. Chowienczyk et
al14
describe a noninvasive flow-interruption device to
determine the level of airway R; however, the data generated are for
the complete airway and not the trachea alone. Likewise, the body
plethysmograph technique measures not just the tracheal R, but R for
the entire airway14
; additionally, this method would not
be technically feasible in our ICU patients.
Our retrospective study was based on the assumption that endotracheal
intubation results in a measurable reduction in the lumen of the airway
through which gas is delivered to the smaller airways and alveoli. The
extent of this reduction has not been studied fully in the pediatric
age group and, thus, became one of the goals of our study. Various
techniques have been described to measure the airway caliber, including
quantitative videobronchoscopy,15
CT
scanning,16
and the acoustic reflection
method.17
However, there is a paucity of reports in which
artificial airway calibers are measured in relation to the tracheal
calibers in pediatric patients whose tracheas were intubated. Our
results indicate that the commonly used formula, (age in
years/4) + 4, to determine the endotracheal tube size prior to
intubation, leads to the selection of endotracheal tubes with diameters
that are 40 to 50% smaller than the trachea. These findings are
supported by previous measurements of tracheal calibers.16
An evaluation of the clinical significance of the reduction of the
tracheal caliber with respect to airway R was the second goal of our
study.
R across a large artificial airway is inversely related to the internal
radius of that airway raised to the fifth power. During
positive-pressure mechanical ventilation, adjustments in the ventilator
settings easily can overcome the R of a narrow artificial airway.
However, during spontaneous ventilation, the patient has to generate
the necessary P to overcome the added R of an endotracheal tube;
this might result in signs of increased effort and discomfort. The
inverse (1/X)5
indicates that even a slight difference between the caliber of the
endotracheal tube and the trachea might result in significantly higher
R. In spontaneously breathing patients, pressure support is often
utilized to alleviate this additional WOB. Brochard et
al18
reported that during the weaning process from
mechanical ventilation and extubation of the trachea the addition of
pressure support resulted in the greatest success compared to other
weaning strategies.
Our data revealed three interesting facts. First, in the majority of
our patients (70%), X was similar, between 0.5 and 0.6. Therefore, the
factor (1/X)5 predicted an increase in tracheal R
between 11- and 32-fold. Second, this common X was similar among all
ages studied. Last, when X is < 0.5, the factor
(1/X)5 becomes extremely high, as found in two of
our patients (patients 1 and 9). In these patients, the resistance of
their intubated tracheas had increased by 255- and 60-fold,
respectively. Assuming that pressure and R are directly proportional,
then the P required to overcome R would increase by the same factor.
Had we known the normal tracheal R of every patient in our study, the
calculated increase in R could have been converted into real P
values for specific rates of inspiratory V. Moreover, an appropriate
level of pressure support could have been chosen to balance the
calculated increase in Ps and to minimize the effect of the added R
due to the endotracheal tube.
Data regarding the dimensions of the pediatric and
adolescent16
19
20
airways have been reported. The R of
infant endotracheal tubes21
is known as well. However, the
tracheal R in pediatric patients is unknown. Pedley et al6
have determined the tracheal resistance in adults to be approximately
0.07 cm H2O/L/s. Since our data showed that the
tracheal caliber reduction factor is similar among all ages, we used
this value to calculate the resistance of the intubated trachea for the
various values of X found in our patients. Our results show that we can
expect tracheal R to increase due to intubation by 33.9 ± 52.5-fold
(range, 8.6- to 255-fold). To maintain an inspiratory flow rate of 1
L/s, the P across the intubated trachea would increase from the
known 0.07 cm H2O to a mean of 2.4 ± 4.5 cm
H2O (range, 0.6 to 18 cm
H2O). In two of our patients, the rT/rETT ratios
were < 0.5 (0.33 and 0.44, respectively); this translated into a much
greater increase in the calculated P, 18 and 4.2 cm
H2O, respectively. When X is between 0.5 and 0.6,
a pressure support of 2 to 3 cm H2O is sufficient
to offset the increase in the P required to maintain a V of 1 L/s.
If rates of inspiratory V increase or decrease, then the pressure
support would need to be adjusted accordingly. Similarly, large values
of X would dictate that a large amount of pressure support is needed.
In patient 1, X was 0.33. In this patient, approximately 18 cm
H2O of pressure support would be required to
offset the tracheal tube R. These data are similar to those of Banner
et al,22
who described a mean pressure support of
13.5 ± 4.5 cm H2O to reduce the WOB to 0 in
their study of 11 adult patients and 4 pediatric patients.
The limitations of our study emanate from the fact that it was
retrospectively conducted and, therefore, actual measurements of
parameters, such as pressure drops across the endotracheal tube,
tracheal R, and rates of V, were not obtained. Moreover, we used a
previously published value for tracheal R (0.07 cm
H2O/L/s) in studied adults6
as the
basis for our calculations. While no data are available for the
tracheal R in the pediatric population, the value obtained by Pedley et
al6
is similar to the values extrapolated from the Moody
diagram plots of adult endotracheal tubes published by Lofaso et
al.12
An additional limitation of our study is the
assumption of a constant flow rate for our calculations, as opposed to
integrating the V differential across time. While patients’ V rates
are not constant,23
our hypothetical mean V rate of 1 L/s
is consistent with the V levels utilized for the in vivo and
in vitro testing of endotracheal Rs.10
11
12
13
Lastly, the fact that endotracheal tubes are frequently curved or bent
was ignored in our study, yet this may have a significant effect on
respiratory mechanics.23
In summary, calculating the endotracheal tube size by using the formula
(age in years/4) + 4 may occasionally result in the insertion of an
endotracheal tube that imposes a high R and does not permit comfortable
spontaneous breathing. During assisted mechanical ventilation, the
problems of increased R secondary to a small endotracheal tube are
usually overcome by the ventilator’s power. However, during
spontaneous ventilation, increased patient effort may be due in part to
a large reduction in airway caliber. In such instances, a CT scan of
the chest can provide data to calculate this factor. Based on our
results, if X < 0.5, the clinician should be advised that the
pressure support level required to achieve comfortable breathing is
likely to exceed what he or she is accustomed to delivering.
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Footnotes
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Abbreviations: P = pressure
gradient; rETT = radius of the endotracheal tube; R = resistance;
rT = radius of the trachea; V = flow; WOB = work of breathing;
X = caliber reduction ratio
Received for publication September 27, 1999.
Accepted for publication February 24, 2000.
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Abstract
Introduction
