TRANSTRACHEAL PRESSURE BY ENDOTRACHEAL TUBE JAMES
Department of
Ph~s~olog!.
Lo!&
Mrdul
tXn LIZ:
M.
School.
EXERTED CUFFS*+
II60
South
First .Avenue.
Mayuood.
Illtnors. 1~S.A
and PHILIP
B.
~H3RIN
Department oC Physmlog~. Loyola Medrcal School: and Departments of Surgery. Loyola Hospital and Hints V. A. Hospital. Maywood. Illtnots hOI5i. L’.S.A. AbstractInllated rndotrachcal tubes may compress the tracheal mucosa causing ischemtc ttssue damage. In the present study. finite deformation analysts of the CURwas made assummg a rigid trachea. This solution provided transtracheal pressure as a fraction of the cuff inflation pressure. This ratio was exammed at varrous degrees of contact between the cuff and trachea. inflatton pressure and contact pressures were obtained experimentally for cndotracheal tubes inserted into rigid transparent cylinders about the SIX of tracheas. I sing these data. it was possible to evaluate the estimates ohtained from fimtr deformation analysis hy comparing these esttmates vvith expertmentally-recorded data.
I. I\TRODL’CTIO\
endotracheal and tracheostomy tubes are employed clinically to provide an airway in anesthetized and unconscious patients. These tubes are inserted into the trachea and then sealed with an inflatable. balloon-like cuff which surrounds the airway tube. However. the inflatable cuff exerts pressure against the trachea. This may impede blood flow and cause tissue damage (Chance cotul.. 1964: Silen ef al.. 1965; Deveral. 1967: Hedden. 1969; Hilding. 1971: Peagle. 19731. Expertments have been performed to evaluate the pressure exerted against the tracheal mucosa. In one type of experiments. a small pressure transducer was inserted through the tracheal wall to directly measure pressures (Carroll and Hedden. 19691. However the pressure recorded depends upon the precise placement of the sensor. and the extent to which the cuff artifactually compresses the intruding sensor. In other studies. transtracheal pressure was estimated. neglecting the stiffness of the inflated cuff after it was in contact with the tracheal wall lDobrin er al.. 1974). Obviously the pressure-deformation characteristics of the cuff play a part in determining how much pressure actually is transmitted across the tracheal wall. Accordingly. the present analysis was undertaken to examine this problem. An analytic solution then was obtained to determine what portion of the prcssurc aithin the inflated cuff is transmitted outward against the trachea. and this was supported Cuffed
by model experiments using a lucite mock ‘trachea’ and cuffed endotracheal tubes. 2. AXALI’TICAL
Three idealizations of the trachea were made m the present analysis. The first was that the lumen was circular and concentric with the tube; the second was the assumption that the trachea was rigid and did not deform when in contact with the cuff; the third was that friction between the cuff and the tracheal wall was negligible. A schematic of the various stages of inflation under these conditions is shown in Fig. 1. Due to symmetry. only one-half of the cuff needs to be considered in the analysis. Figure 2 shows pertinent dimensions of that portion treated in what follows. The line .4BC represents the cuff membrane in the uninflated state, while the curve ADE stands for a. p:o
b
Fwrt cont..3
p=p, .,.................. .:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.~~~:.~:.~:.:.:.:.:.:.:.:.~:.~:.:.:... ( ‘. ....’
--~__~~
* Rrw~wd 2 I Juwrr~~
~_
1971.
+
This study was supported by NIH Grant HE08682 + Research performed while Dr. Doyle was on sabbatical lea+ve m Department of Physiology. Dr. Doyle’s present address IS Bert B. Hanson & Associates. West Union. Iowa. Send reprint requests to P. B. Dobrin. Department of Physiology. Loyola Medical School. Maywood. Illinois. 247
Fig. I. Schematic of endotracheal tube within the trachea with the cuff at various stages of inflation.
248
JAMESM. DOYLEand
PHILIP
B. Dotutt~
in which r is the deformed radius, < is the length along a meridion, P is the internal pressure and K, and K* are the principal curvatures. Extension ratios in the three principal directions are given by:
,A
#I
Fig. 2. Dimensions of the endotracheal tube cuff with the tube located within the trachea. Line ABC represents the cuff membrane in the uninflated state. Curve ADE represents the cuff membrane after inflation. the membrane position after inflation. Since there is a discontinuity in curvature at point D, the deformation analysis must be done in two parts. The cuff is initially a right circular cylinder. In the inflated state it consists of the surface of revolution AD (Part I), and the enlarged right circular cylinder DE (Part II). In the original configuration Part I is represented by AB and Part II by BC. In brief, the procedure for solution involves solving Part I and Part II separately and then enforcing geometric compatibility and equality of meridional force components at the junction designated by point D. A method for calculating deformation of axi-symmetric loaded membranes has been developed by Kydoniefs and Spencer (1969). Their work is applicable to the problem arising in Part I of this case, and was utilized in obtaining the solution. Only the main parts of their analysis are included here. The coordinates in the deformed and undeformed state of the membrane are shown in Fig. 3. It is assumed that the membrane is in plane stress, that is. all stress components perpendicular to surface are disregarded. The normal stress in the meridional direction is designated by a cl while that in the circumferential direction is c2. The corresponding stress resultants are given by: T, = 2hu, T, = Zha,,
(1)
j.s.$.,
i2=r;
Department of
Ph~s~olog!.
Lo!&
Mrdul
tXn LIZ:
M.
School.
EXERTED CUFFS*+
II60
South
First .Avenue.
Mayuood.
Illtnors. 1~S.A
and PHILIP
B.
~H3RIN
Department oC Physmlog~. Loyola Medrcal School: and Departments of Surgery. Loyola Hospital and Hints V. A. Hospital. Maywood. Illtnots hOI5i. L’.S.A. AbstractInllated rndotrachcal tubes may compress the tracheal mucosa causing ischemtc ttssue damage. In the present study. finite deformation analysts of the CURwas made assummg a rigid trachea. This solution provided transtracheal pressure as a fraction of the cuff inflation pressure. This ratio was exammed at varrous degrees of contact between the cuff and trachea. inflatton pressure and contact pressures were obtained experimentally for cndotracheal tubes inserted into rigid transparent cylinders about the SIX of tracheas. I sing these data. it was possible to evaluate the estimates ohtained from fimtr deformation analysis hy comparing these esttmates vvith expertmentally-recorded data.
I. I\TRODL’CTIO\
endotracheal and tracheostomy tubes are employed clinically to provide an airway in anesthetized and unconscious patients. These tubes are inserted into the trachea and then sealed with an inflatable. balloon-like cuff which surrounds the airway tube. However. the inflatable cuff exerts pressure against the trachea. This may impede blood flow and cause tissue damage (Chance cotul.. 1964: Silen ef al.. 1965; Deveral. 1967: Hedden. 1969; Hilding. 1971: Peagle. 19731. Expertments have been performed to evaluate the pressure exerted against the tracheal mucosa. In one type of experiments. a small pressure transducer was inserted through the tracheal wall to directly measure pressures (Carroll and Hedden. 19691. However the pressure recorded depends upon the precise placement of the sensor. and the extent to which the cuff artifactually compresses the intruding sensor. In other studies. transtracheal pressure was estimated. neglecting the stiffness of the inflated cuff after it was in contact with the tracheal wall lDobrin er al.. 1974). Obviously the pressure-deformation characteristics of the cuff play a part in determining how much pressure actually is transmitted across the tracheal wall. Accordingly. the present analysis was undertaken to examine this problem. An analytic solution then was obtained to determine what portion of the prcssurc aithin the inflated cuff is transmitted outward against the trachea. and this was supported Cuffed
by model experiments using a lucite mock ‘trachea’ and cuffed endotracheal tubes. 2. AXALI’TICAL
Three idealizations of the trachea were made m the present analysis. The first was that the lumen was circular and concentric with the tube; the second was the assumption that the trachea was rigid and did not deform when in contact with the cuff; the third was that friction between the cuff and the tracheal wall was negligible. A schematic of the various stages of inflation under these conditions is shown in Fig. 1. Due to symmetry. only one-half of the cuff needs to be considered in the analysis. Figure 2 shows pertinent dimensions of that portion treated in what follows. The line .4BC represents the cuff membrane in the uninflated state, while the curve ADE stands for a. p:o
b
Fwrt cont..3
p=p, .,.................. .:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.~~~:.~:.~:.:.:.:.:.:.:.:.~:.~:.:.:... ( ‘. ....’
--~__~~
* Rrw~wd 2 I Juwrr~~
~_
1971.
+
This study was supported by NIH Grant HE08682 + Research performed while Dr. Doyle was on sabbatical lea+ve m Department of Physiology. Dr. Doyle’s present address IS Bert B. Hanson & Associates. West Union. Iowa. Send reprint requests to P. B. Dobrin. Department of Physiology. Loyola Medical School. Maywood. Illinois. 247
Fig. I. Schematic of endotracheal tube within the trachea with the cuff at various stages of inflation.
248
JAMESM. DOYLEand
PHILIP
B. Dotutt~
in which r is the deformed radius, < is the length along a meridion, P is the internal pressure and K, and K* are the principal curvatures. Extension ratios in the three principal directions are given by:
,A
#I
Fig. 2. Dimensions of the endotracheal tube cuff with the tube located within the trachea. Line ABC represents the cuff membrane in the uninflated state. Curve ADE represents the cuff membrane after inflation. the membrane position after inflation. Since there is a discontinuity in curvature at point D, the deformation analysis must be done in two parts. The cuff is initially a right circular cylinder. In the inflated state it consists of the surface of revolution AD (Part I), and the enlarged right circular cylinder DE (Part II). In the original configuration Part I is represented by AB and Part II by BC. In brief, the procedure for solution involves solving Part I and Part II separately and then enforcing geometric compatibility and equality of meridional force components at the junction designated by point D. A method for calculating deformation of axi-symmetric loaded membranes has been developed by Kydoniefs and Spencer (1969). Their work is applicable to the problem arising in Part I of this case, and was utilized in obtaining the solution. Only the main parts of their analysis are included here. The coordinates in the deformed and undeformed state of the membrane are shown in Fig. 3. It is assumed that the membrane is in plane stress, that is. all stress components perpendicular to surface are disregarded. The normal stress in the meridional direction is designated by a cl while that in the circumferential direction is c2. The corresponding stress resultants are given by: T, = 2hu, T, = Zha,,
(1)
j.s.$.,
i2=r;
