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In vitro evaluation of negative pressure generated during application of negative suction volumes by use of various syringes with and without thoracostomy tubes

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  • 1 1Summit Veterinary Referral Center, 2505 S 80th St, Tacoma, WA 98409.

Abstract

OBJECTIVE

To determine the amount of negative pressure generated by syringes of various sizes with and without an attached thoracostomy tube and whether composition of thoracostomy tubes altered the negative pressure generated.

SAMPLE

Syringes ranging from 1 to 60 mL and 4 thoracostomy tubes of various compositions (1 red rubber catheter, 1 polyvinyl tube, and 2 silicone tubes).

PROCEDURES

A syringe or syringe with attached thoracostomy tube was connected to a pneumatic transducer. Each syringe was used to aspirate a volume of air 10 times. Negative pressure generated was measured and compared among the various syringe sizes and various thoracostomy tubes.

RESULTS

The negative pressure generated decreased as size of the syringe increased for a fixed volume across syringes. Addition of a thoracostomy tube further decreased the amount of negative pressure. The red rubber catheter resulted in the least amount of negative pressure, followed by the polyvinyl tube and then the silicone tubes. There was no significant difference in negative pressure between the 2 silicone tubes. The smallest amount of negative pressure generated was −74 to −83 mm Hg.

CONCLUSIONS AND CLINICAL RELEVANCE

Limited data are available on the negative pressure generated during intermittent evacuation of the thoracic cavity. For the present study, use of a syringe of ≥ 20 mL and application of 1 mL of negative suction volume resulted in in vitro pressures much more negative than the currently recommended pressure of −14.71 mm Hg for continuous suction. Additional in vitro or cadaveric studies are needed.

Abstract

OBJECTIVE

To determine the amount of negative pressure generated by syringes of various sizes with and without an attached thoracostomy tube and whether composition of thoracostomy tubes altered the negative pressure generated.

SAMPLE

Syringes ranging from 1 to 60 mL and 4 thoracostomy tubes of various compositions (1 red rubber catheter, 1 polyvinyl tube, and 2 silicone tubes).

PROCEDURES

A syringe or syringe with attached thoracostomy tube was connected to a pneumatic transducer. Each syringe was used to aspirate a volume of air 10 times. Negative pressure generated was measured and compared among the various syringe sizes and various thoracostomy tubes.

RESULTS

The negative pressure generated decreased as size of the syringe increased for a fixed volume across syringes. Addition of a thoracostomy tube further decreased the amount of negative pressure. The red rubber catheter resulted in the least amount of negative pressure, followed by the polyvinyl tube and then the silicone tubes. There was no significant difference in negative pressure between the 2 silicone tubes. The smallest amount of negative pressure generated was −74 to −83 mm Hg.

CONCLUSIONS AND CLINICAL RELEVANCE

Limited data are available on the negative pressure generated during intermittent evacuation of the thoracic cavity. For the present study, use of a syringe of ≥ 20 mL and application of 1 mL of negative suction volume resulted in in vitro pressures much more negative than the currently recommended pressure of −14.71 mm Hg for continuous suction. Additional in vitro or cadaveric studies are needed.

Respiration is a complex process in which adequate ventilation and perfusion are dependent on pressure gradients of the various components within the system. The normal intrapleural pressure is −3.68 mm Hg (−5 cm H2O).1–4 Conditions that result in an accumulation of air or fluid in the thoracic cavity cause changes to the intrapleural pressure, which results in alterations of respiration. The conditions most commonly encountered in veterinary medicine are pneumothorax, chylothorax, pyothorax, hemo-thorax, and iatrogenic opening of the pleural space for surgical purposes.5–8

It is necessary to reestablish the normal intrapleural pressure to regain adequate ventilation and perfusion. This can be accomplished by intermittent thoracentesis, intermittent evacuation via a thoracostomy tube, or application of continuous suction within the pleural space. The recommended applied pressure for continuous suction systems is −3.68 to −18.39 mm Hg (−5 to −25 cm H2O).2,3,7 Although there are limited data to confirm the desired negative pressure applied for continuous suction, it was reported in 1 study9 that physicians typically use −14.71 mm Hg (-20 cm H2O) as the standard in practice.

Use of an intrapleural pressure lower than −14.71 mm Hg (−20 cm H2O) in humans results in an increase in chest discomfort and a possible increase in complications.10–13 A rare but possibly fatal complication of increased intrapleural negative pressure in humans is reexpansion pulmonary edema.14,15 The incidence of reexpansion pulmonary edema is reportedly between 0.5% and 14%16–20 with a mortality rate of up to 20%.14,17 Clinical signs associated with reexpansion pulmonary edema include cough, thoracic pain, dyspnea, foaming sputum, agitation, tachycardia, and tachypnea. If any of these clinical signs are noted, application of negative pressure should be discontinued and the patient evaluated further.14–16,19,20 Limiting the amount of negative pressure applied to the pleural cavity can reduce the risk of these complications.

No specific data have been provided regarding the recommended amount of pressure generated during intermittent evacuation of the thoracic cavity. It has been suggested that 5 to 10 mL of negative suction volume should be applied with a syringe during evacuation7,8; however, the amount of negative pressure generated with this negative suction volume has not been determined.

To the authors’ knowledge, no studies have been conducted to determine the amount of pressure generated during intermittent evacuation of the thoracic cavity via a thoracostomy tube. The purposes of the study reported here were to determine the negative pressure generated by syringes of various sizes with and without an attached thoracostomy tube and to determine whether the composition of the thoracostomy tube would alter the negative pressure generated. We hypothesized that there would be no difference in the negative pressure generated by syringes of various sizes for a fixed negative suction volume, that the addition of a thoracostomy tube would decrease the negative pressure generated, and that the composition of the thoracostomy tubes would affect the negative pressure generated.

Materials and Methods

Sample

Syringes that ranged from 1 to 60 mL were used to evaluate the amount of negative pressure generated. Syringes were used alone and also after attachment to 4 types of thoracostomy tubes.

Experimental procedures

The study was conducted in 2 phases to test the aforementioned hypotheses. Data collection for the study was performed at Summit Veterinary Referral Center. Because there were no documented standards for the amount of negative pressure applied during intermittent evacuation of a thoracostomy tube, the authors used the recommended amount of negative pressure applied for continuous suction as a guideline for the present study when comparing pressure obtained during intermittent evacuation of a thoracostomy tube to make recommendations for future studies and clinical application.

Phase 1—The first aspect of phase 1 was to determine the amount of negative pressure generated by syringes of various sizes at designated negative suction volumes. Commercially available syringesa of sizes ranging from 1 to 60 mL were connected directly to a pneumatic transducer.b A negative suction volume of 1 mL was applied with each syringe. Syringes were tested separately, and 10 pressure measurements were recorded for each syringe. The syringe was disconnected from the pneumatic transducer and then reconnected before each application of negative suction, and the transducer was calibrated to 0 before each recording to minimize measurement error. The same 1-mL negative suction volume was then applied 10 times with syringes of 3, 6, 12, 20, 35, and 60 mL.

The second aspect of phase 1 was to determine whether addition of a thoracostomy tube would alter the amount of negative pressure generated. A 12F red rubber catheterc was cut to a length of 40 cm; all fenestrations were removed. The catheter then was connected to the pneumatic transducer via a 3-way stopcock adaptor.d The previously used syringes were attached to the red rubber catheter via a female Luer lock-to-tapered catheter adaptor.e Data collection was performed for application of 1, 3, 6, 12, 20, 35, and 60 mL of negative suction volume 10 times with each syringe.

Phase 2—Phase 2 was designed to determine whether use of various thoracostomy tubes would result in different amounts of negative pressure. Four tubes of various composition were included in this phase of the study. Tube selection included the same 12F red rubber catheter used in phase 1, a 12F polyvinylf thoracostomy tube, and two 12F silicone thoracostomy tubes (silicone tube 1g and 2h). All tubes were cut to a length of 20 cm; all fenestrations were removed. The red rubber catheter and each of the 3 other tubes were attached to the pneumatic transducer via a 3-way stopcock adaptor. On the basis of the results for phase 1, it was determined that a negative suction volume > 12 mL generated a pressure amount greater than that recommended for the pneumatic transducer. Because such excessive negative pressures were generated, negative suction volumes of 20, 35, and 60 mL were not included in phase 2. Data collection was conducted in accordance with the same protocol described for phase 1. Data were collected for application of 1, 3, 6, and 12 mL of negative suction volume.

Data analysis

Data were evaluated by use of commercially available software.i For each group of data collected, mean and SD of the negative pressure generated were calculated. The Bartlett test for equal variances was performed before the performance of additional statistical tests.

Comparisons of negative pressure generated for each syringe size and negative suction volume were performed by use of a 1-way ANOVA, which was followed by pairwise Bonferroni multiple comparisons when the ANOVA revealed significant (P 0.05) differences. Comparisons among syringe sizes and negative suction volume were performed by use of 2-sample t tests for phase 1 and a 1-way ANOVA for phase 2 that was followed by pairwise Bonferroni multiple comparisons when the ANOVA revealed significant differences. Comparisons among negative suction volumes were performed by use of an ANOVA for each syringe size, which was followed by pairwise Bonferroni multiple comparisons when the ANOVA revealed significant differences.

Results

Phase 1

Mean and SD values for the amount of negative pressure generated by use of the syringes alone and by use of the syringes connected to a 40-cm-long 12F red rubber catheter were calculated (Table 1). Comparison of the various syringe sizes for a fixed negative suction volume revealed that the amount of negative pressure generated became significantly (P < 0.001) more negative as the size of the syringe increased. This was true for 1, 3, 6, and 12 mL of negative suction volume, but not for 20 (P = 0.913) or 35 (P = 1.000) mL of negative suction volume. Addition of the 12F red rubber catheter resulted in a significant (P < 0.001) decrease in the amount of negative pressure generated as the size of the syringe increased for negative suction volumes of 1, 3, and 6 mL but not for negative suction volumes of 12 (P = 0.046), 20 (P = 1.000), or 35 (P = 0.331) mL. Although the overall ANOVA for negative suction volume of 12 mL indicated that there should be at least 1 significant difference among sizes of the syringe (P = 0.046), the Bonferroni pairwise comparisons procedure failed to detect any significant differences (P ≥ 0.123). Subsequent analysis revealed that the amount of negative pressure generated was significantly (P < 0.001) less after addition of the red rubber catheter, compared with the negative pressure generated with the syringe alone. This significant (P < 0.001) finding was consistently true for data collected for 1, 3, 6, 12, 20, and 35 mL of negative suction volume.

Table 1—

Negative pressure generated by application of various negative suction volumes with various syringes and with those syringes connected to a 40-cm-long red rubber catheter.

Negative suction volume (mL)Syringe size (mL)Pressure with syringe (mm Hg)Pressure with syringe and red rubber catheter (mm Hg)*
11−132.4 ± 0.52a−84.3 ± 0.48a
 3−129.2 ± 0.63b−80.0 ± 0.67b
 6−121.8 ± 0.79c−80.0 ± 0.67b
 12−118.1 ± 0.88d−79.9 ± 0.74b
 20−103.0 ± 0.82e−69.3 ± 0.67c
 35−99.4 ± 0.84f−69.3 ± 0.67c
 60−96.6 ± 0.70g−69.2 ± 0.79c
33−287.8 ± 0.79a−209.3 ± 0.48a
 6−284.2 ± 0.63b−206.2 ± 0.63b
 12−280.8 ± 0.92c−206.3 ± 0.48b
 20−269.8 ± 1.55d−199.5 ± 0.53c
 35−266.7 ± 0.48e−199.5 ± 0.53c
 60−263.1 ± 0.99f−199.0 ± 0.67c
66−415.7 ± 0.82a−331.2 ± 0.79a
 12−415.5 ± 0.53a−331.2 ± 0.63a
 20−410.1 ± 0.99b−323.7 ± 0.67b
 35−407.5 ± 0.53c−323.6 ± 0.70b
 60−404.4 ± 0.52d−321.5 ± 0.53c
1212−537.5 ± 0.71a−455.4 ± 0.70
 20−534.9 ± 0.99a−454.6 ± 0.70
 35−533.3 ± 0.48b−454.6 ± 0.84
 60−532.6 ± 0.52b−454.6 ± 0.70
2020−606.1 ± 0.57−538.6 ± 0.70
 35−606.1 ± 0.57−538.6 ± 0.70
 60−606.0 ± 0.67−538.6 ± 0.70
3535−663.0 ± 0.82−616.3 ± 0.67
 60−663.0 ± 0.82−616.0 ± 0.67
6060−699.0 ± 0.67−665.6 ± 0.52

Data are reported as mean ± SD values for 10 measurements at each negative suction volume for each size of syringe.

All values differ significantly (P < 0.001; 2-sample t test) from the corresponding values for the syringe alone.

Within a negative suction volume, values with different superscript letters differ significantly (P < 0.001; I-way ANOVA followed by Bonferroni pairwise multiple comparisons).

Phase 2

Mean and SD values for the amount of negative pressure generated by use of syringes attached to each of the four 20-cm-long 12F thoracostomy tubes were calculated (Table 2). Addition of the 12F red rubber catheter caused the amount of negative pressure generated for 1 mL of negative suction volume to be significantly (P < 0.001) less with each increase in size of syringe. For the other three 12F thoracostomy tubes, the amount of negative pressure generated for 1 mL of negative suction volume was not significantly different when comparing 1- and 3-mL syringes, when comparing 6- and 12-mL syringes, and when comparing 20-, 35-, and 60-mL syringes.

Table 2—

Negative pressure generated by application of various negative suction volumes with syringes of various size attached to various 20-cm-long thoracostomy tubes.

Negative suction volume (mL)Syringe size (mL)12F red rubber catheter (mm Hg)12F polyvinyl tube (mm Hg)12F silicone tube 1 (mm Hg)12F silicone tube 2 (mm Hg)
11−94.1 ± 0.57a,A−100.4 ± 0.52a,B−113.0 ± 0.67a,C−113.4 ± 0.52a,C
 3−93.9 ± 0.74a,A−100.4 ± 0.52a,B−113.0 ± 0.67a,C−113.4 ± 0.52a,C
 6−90.5 ± 0.85b,A−95.5 ± 0.53b,B−105.6 ± 0.52b,C−105.4 ± 0.52b,C
 12−89.3 ± 0.67b,A−95.5 ± 0.53b,B−105.6 ± 0.52b,C−105.4 ± 0.52b,C
 20−74.0 ± 0.67c,A−77.7 ± 0.67c,B−83.0 ± 0.82c,C−83.0 ± 0.67c,C
 35−74.0 ± 0.67c,A−77.7 ± 0.67c,B−83.0 ± 0.82c,C−83.0 ± 0.67c,C
 60−74.0 ± 0.67c,A−77.7 ± 0.67c,B−83.0 ± 0.67c,C−83.0 ± 0.67c,C
33−225.2 ± 0.42A−233.0 ± 0.67B−251.6 ± 0.52C−252.0 ± 0.82C
 6−225.2 ± 0.42A−233.0 ± 0.67B−251.6 ± 0.52C−252.0 ± 0.67C
 12−225.2 ± 0.42A−233.0 ± 0.67B−251.6 ± 0.52C−252.0 ± 0.67C
 20−225.2 ± 0.42A−233.0 ± 0.67B−251.6 ± 0.52C−252.0 ± 0.82C
 35−225.2 ± 0.42A−233.0 ± 0.67B−251.6 ± 0.52C−252.0 ± 0.67C
 60−225.2 ± 0.42A−233.0 ± 0.67B−251.6 ± 0.52C−252.0 ± 0.67C
66−344.0 ± 0.67A−352.4 ± 0.52B−376.8 ± 0.79C−376.9 ± 0.74C
 12−344.0 ± 0.67A−352.4 ± 0.52B−376.8 ± 0.79C−376.9 ± 0.74C
 20−344.0 ± 0.67A−352.4 ± 0.52B−376.8 ± 0.79C−376.9 ± 0.74C
 35−344.0 ± 0.67A−352.4 ± 0.52B−376.8 ± 0.79C−376.9 ± 0.74C
 60−344.0 ± 0.67A−352.4 ± 0.52B−376.8 ± 0.79C−376.9 ± 0.74C
1212−474.4 ± 0.70A−482.8 ± 0.79B−503.8 ± 0.63C−503.5 ± 0.53C
 20−474.4 ± 0.70A−482.8 ± 0.79B−503.8 ± 0.63C−503.5 ± 0.53C
 35−474.4 ± 0.70A−482.8 ± 0.79B−503.8 ± 0.63C−503.5 ± 0.53C
 60−474.4 ± 0.70A−482.8 ± 0.79B−503.8 ± 0.63C−503.5 ± 0.53C

Within a negative suction volume, values with different superscript letters differ significantly (P < 0.001; I-way ANOVA followed by Bonferroni pairwise multiple comparisons).

Within a row, values with different superscript letters differ significantly (P < 0.001; I-way ANOVA followed by Bonferroni pairwise multiple comparisons).

See Table 1 for remainder of key.

Addition of the 12F red rubber catheter resulted in significantly (P < 0.001) less negative pressure, compared with results for the other three 12F thoracostomy tubes, for all syringe sizes regardless of the negative suction volume applied. Comparison of the other three 12F thoracostomy tubes revealed that addition of the polyvinyl tube resulted in significantly (P < 0.001) less negative pressure than addition of either of the silicone tubes for all syringe sizes regardless of the negative suction volume applied. However, there were no significant differences in negative pressure between the 2 silicone thoracostomy tubes for any syringe size or negative suction volume applied.

The amount of negative pressure generated increased significantly (P < 0.001) as the syringe size increased for each syringe-thoracostomy tube combination (Table 3). Within each syringe-thoracostomy tube combination, all pairwise comparisons between syringe sizes were significantly (P < 0.001) different.

Table 3—

Negative pressure generated by application of negative suction volumes with syringes of various sizes attached to each of four 20-cm-long thoracostomy tubes.

Syringe size (mL)Negative suction volume (mL)12F red rubber catheter (mm Hg)12F polyvinyl tube (mm Hg)12F silicone tube 1 (mm Hg)12F silicone tube 2 (mm Hg)
31−93.9 ± 0.74a−100.4 ± 0.52a−113.0 ± 0.67a−113.4 ± 0.52a
 3−225.2 ± 0.42b−233.0 ± 0.67b−251.6 ± 0.52b−252.0 ± 0.82b
61−90.5 ± 0.85a−95.5 ± 0.53a−105.6 ± 0.52a−105.4 ± 0.52a
 3−225.2 ± 0.42b−233.0 ± 0.67b−251.6 ± 0.52b−252.0 ± 0.67b
 6−344.0 ± 0.67c−352.4 ± 0.52c−376.8 ± 0.79c−376.9 ± 0.74c
121−89.3 ± 0.67a−95.5 ± 0.53a−105.6 ± 0.52a−105.4 ± 0.52a
 3−225.2 ± 0.42b−233.0 ± 0.67b−251.6 ± 0.52b−252.0 ± 0.67b
 6−344.0 ± 0.67c−352.4 ± 0.52c−376.8 ± 0.79c−376.9 ± 0.74c
 12−474.4 ± 0.70d−482.8 ± 0.79d−503.8 ± 0.63d−503.5 ± 0.53d
201−74.0 ± 0.67a−77.7 ± 0.67a−83.0 ± 0.82a−83.0 ± 0.67a
 3−225.2 ± 0.42b−233.0 ± 0.67b−251.6 ± 0.52b−252.0 ± 0.67b
 6−344.0 ± 0.67c−352.4 ± 0.52c−376.8 ± 0.79c−376.9 ± 0.74c
 12−474.4 ± 0.70d−482.8 ± 0.79d−503.8 ± 0.63d−503.5 ± 0.53d
351−74.0 ± 0.67a−77.7 ± 0.67a−83.0 ± 0.82a−83.0 ± 0.67a
 3−225.2 ± 0.42b−233.0 ± 0.67b−251.6 ± 0.52b−252.0 ± 0.67b
 6−344.0 ± 0.67c−352.4 ± 0.52c−376.8 ± 0.79c−376.9 ± 0.74c
 12−474.4 ± 0.70d−482.8 ± 0.79d−503.8 ± 0.63d−503.5 ± 0.53d
601−74.0 ± 0.67a−77.7 ± 0.67a−83.0 ± 0.82a−83.0 ± 0.67a
 3−225.2 ± 0.42b−233.0 ± 0.67b−251.6 ± 0.52b−252.0 ± 0.67b
 6−344.0 ± 0.67c−352.4 ± 0.52c−376.8 ± 0.79c−376.9 ± 0.74c
 12−474.4 ± 0.70d−482.8 ± 0.79d−503.8 ± 0.63d−503.5 ± 0.53d

Within a syringe size, values with different superscript letters differ significantly (P < 0.001; 1-way ANOVA followed by Bonferroni pairwise multiple comparisons).

See Table 1 for remainder of key.

Discussion

Results of phase 1 of the study reported here indicated that the amount of negative pressure generated for a designated negative suction volume significantly decreased as the size of the syringe increased. This finding did not support our first hypothesis that the amount of negative pressure would be consistent for a negative suction volume. We were unable to identify a reason for the variation in the amount of pressure generated for a constant negative suction volume. It is possible that there was error attributable to syringe design and measurement of such small volumes in the larger syringe sizes. Further studies are needed to verify the accuracy of the measurement of small volumes (1 mL) in large-volume (20, 35, and 60 mL) syringes.

The second hypothesis (ie, addition of a thoracostomy tube would decrease the amount of negative pressure generated) was supported by the data collected in phase 1. The change in the amount of negative pressure generated may have been attributable to the decrease in resistance on the basis of the Poiseuille law. Investigators of another study21 with a similar design claimed that the Poiseuille law had a mediating effect for the decrease in negative pressure when tubing was added. It has also been determined (Hagen-Poiseuille analysis) that the Poiseuille law is applicable to compressible fluids (gas and liquid) in addition to incompressible fluids.22 The addition of a thoracostomy tube with a constant diameter allows control of the flow rate to maintain laminar flow rather than turbulent flow, which can impact the pressure generated.

The final hypothesis (ie, various tubes would result in different amounts of negative pressure) was supported by results of phase 2. The interesting finding in phase 2 was that there were no significant differences between the 2 silicone thoracostomy tubes for any comparisons. This was presumably attributable to the fact that both silicone thoracostomy tubes were composed of the same base material, whereas the third commercially available thoracostomy tube was composed of polyvinyl, and the red rubber catheter was composed of natural rubber. Each material has a coefficient of friction that may have played a role in the amount of resistance encountered for each tube. Another, and more likely, variable that may have impacted the pressure is the deformation of a tube that can occur when the pressure differential reaches a point that can cause partial collapse of the tube.23,24 Further studies would be required to compare additional thoracostomy tubes composed of the same and different materials to determine whether this hypothesis would remain true.

The present study had multiple limitations. The most apparent limitation was the in vitro nature of the study design. It was possible that values could have differed if a portion of the thoracostomy tube were located within the thoracic cavity and exposed to an exterior pressure other than the atmospheric pressure that was present in the study reported here. Another limitation was collection of data for only 12F tubes. The 12F tubes were selected for the present study to provide consistency and reduce variables that could have contributed to errors in the results. Manufacturers of the thoracostomy tubes did not have a standard bore size for larger (> 12F) thoracostomy tubes. It was possible that a larger bore size could have further impacted the amount of negative pressure.

Data for the present study contradicted the recommendation of a negative suction volume of 5 to 10 mL for use in intermittent evacuation of the thoracic cavity.8,23 A negative suction volume of 5 to 10 mL would generate an amount of negative pressure substantially greater than the recommended −14.71 mm Hg (−20 cm H2O). On the basis of data for the study reported here, even for the least negative values recorded (−74 to −83 mm Hg [−100 to −112 cm H2O]), a syringe of ≥ 20 mL with a negative suction volume of 1 mL resulted in in vitro pressures much more negative than the current recommendation of −14.71 mm Hg (−20 cm H2O) for continuous suction. Additional in vitro or cadaveric studies are needed.

Acknowledgments

No third-party funding or support was received in connection with this study or the writing or publication of the man uscript. The authors declare that there were no conflicts of interest.

The authors thank Gary Clark for assistance with the statistical analysis.

Footnotes

a.

Monoject syringes, Covidien, Mansfield, Mass.

b.

DPM1B pneumatic transducer, Fluke Biomedical, Everett, Wash.

c.

Feeding tube and urethral catheter, Covidien, Mansfield, Mass.

d.

3-way stopcock, Braun, Bethlehem, Pa.

e.

Surgivet female Luer lock to tapered catheter, Smiths Medical ASD Inc, Saint Paul, Minn.

f.

Surgivet 12F thoracic drainage catheter, Smiths Medical ASD Inc, Saint Paul, Minn.

g.

12F silicone chest tube, Mila, Florence, Ky.

h.

Jorvet 12F silicone chest drainage tube, Jorgensen Labs, Loveland, Colo.

i.

Stata/IC, version 14.2, StataCorp LLC, College Station, Tex.

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Contributor Notes

Address correspondence to Dr. Mezzles (mjrm84@gmail.com).