Expiratory time constant for determinations of plateau pressure, respiratory system compliance, and total resistance
© Al Rawas et al.; licensee BioMed Central Ltd. 2013
Received: 10 October 2012
Accepted: 29 January 2013
Published: 5 February 2013
We hypothesized the expiratory time constant (ƬE) may be used to provide real time determinations of inspiratory plateau pressure (Pplt), respiratory system compliance (Crs), and total resistance (respiratory system resistance plus series resistance of endotracheal tube) (Rtot) of patients with respiratory failure using various modes of ventilatory support.
Adults (n = 92) with acute respiratory failure were categorized into four groups depending on the mode of ventilatory support ordered by attending physicians, i.e., volume controlled-continuous mandatory ventilation (VC-CMV), volume controlled-synchronized intermittent mandatory ventilation (VC-SIMV), volume control plus (VC+), and pressure support ventilation (PSV). Positive end expiratory pressure as ordered was combined with all aforementioned modes. Pplt, determined by the traditional end inspiratory pause (EIP) method, was combined in equations to determine Crs and Rtot. Following that, the ƬE method was employed, ƬE was estimated from point-by-point measurements of exhaled tidal volume and flow rate, it was then combined in equations to determine Pplt, Crs, and Rtot. Both methods were compared using regression analysis.
ƬE, ranging from mean values of 0.54 sec to 0.66 sec, was not significantly different among ventilatory modes. The ƬE method was an excellent predictor of Pplt, Crs, and Rtot for various ventilatory modes; r2 values for the relationships of ƬE and EIP methods ranged from 0.94 to 0.99 for Pplt, 0.90 to 0.99 for Crs, and 0.88 to 0.94 for Rtot (P <0.001). Bias and precision values were negligible.
We found the ƬE method was just as good as the EIP method for determining Pplt, Crs, and Rtot for various modes of ventilatory support for patients with acute respiratory failure. It is unclear if the ƬE method can be generalized to patients with chronic obstructive lung disease. ƬE is determined during passive deflation of the lungs without the need for changing the ventilatory mode and disrupting a patient's breathing. The ƬE method obviates the need to apply an EIP, allows for continuous and automatic surveillance of inspiratory Pplt so it can be maintained ≤ 30 cm H2O for lung protection and patient safety, and permits real time assessments of pulmonary mechanics.
An automatic and continuous method of determining Pplt, Crs and Rtot, that is not dependent on an EIP is desirable. We propose using the expiratory time constant (ƬE) for determinations of Pplt, Crs, and Rtot. ƬE contains information about the mechanical properties of the respiratory system, namely, elastance and resistance . It is hypothesized that real-time determinations of inspiratory Pplt, Crs, and Rtot may be estimated from the passive deflation of the lungs by using ƬE, and combined with appropriate equations. Another purpose of the study was to demonstrate that the ƬE method can be used with various modes of ventilatory support.
Materials and methods
Patient group data (total number of patients = 92)
49 ± 19
52 ± 18
50 ± 20
53 ± 20
69 ± 30
68 ± 40
81 ± 30
78 ± 27
Breathing frequency, breaths/minute,
13 ± 8
32 ± 9†
16 ± 5
20 ± 6
VT, ml/kg IBW
8 ± 4
9 ± 4
6 ± 4
7 ± 4
Paw, cm H2O
PEEP (cm H2O)
32 ± 6
7.7 ± 4.4
34 ± 7
9.9 ± 3.6
29 ± 8
7.9 ± 4
28 ± 8
7.9 ± 3
0.43 ± 0.14
0.45 ± 0.10
0.45 ± 0.12
0.44 ± 0.09
0.58 ± 0.20
0.54 ± 0.27
0.66 ± 0.27
0.58 ± 0.18
Although ƬE applies to the exhalation phase of breathing, it is a required mathematical term in equations for determining inspiratory Pplt, Crs, and Rtot. After ƬE was estimated, Pplt, Crs, and Rtot were determined using the following equations (derivations of equations are stated in Additional File 1):
It was necessary to apply multiple EIP breaths to obtain an appropriate Pplt for some patients breathing spontaneously, for example, those receiving PSV. Many of these patients attempted to inhale and exhale during the pause (Figure 1, third breath), these breaths were not used. Those EIP breaths where patients did not inhale and exhale during the pause and in whom airway pressure decreased passively, generating a smooth plateau, (Figure 1, second breath) were used for determinations of Pplt. On average, EIP breaths were applied 5 to 10 times over a 15-minute period. A computer software code (Matlab) was developed to automatically verify valid pressure plateau segments. The software was programmed to find segments of the EIP with the following criteria: maximum tidal volume value, zero flow, and a horizontal or flat pressure plateau for a length equal to approximately 0.5 seconds. Manual visual inspection of every patient's pressure, flow, and volume waveforms were performed to verify the values garnered by the software.
Data were analyzed using regression analyses to evaluate relationships of the ƬE method for determining Pplt, Crs, and Rtot with the EIP method for determining Pplt, Crs, and Rtot, using analysis of variance (ANOVA), Fisher's exact test, and Bland and Altman analyses . Data are mean ± SD; alpha was set at 0.05 for statistical significance.
There were no significant differences in ƬE among groups. ƬE was 0.58 ± 0.20 sec for the VC-CMV group, 0.54 ± 0.27 sec for the VC-SIMV group, 0.66 ± 0.27 sec for the VC+ group, and 0.58 ± 0.18 sec for the PSV group.
Pplt values ranged from 11 to 38 cm H2O, 13 to 38 cm H2O, 11 to 38 cm H2O, and 12 to 33 cm H2O for the VC-CMV, VC-SIMV, VC+, and PSV groups, respectively. The r2 values for the relationships of ƬE and EIP methods were 0.99, 0.99, 0.98, and 0.94 (P <0.001) for the VC-CMV, VC-SIMV, VC+, and PSV groups, respectively.
Crs values ranged from 0.02 to 0.095 L/cm H2O, 0.015 to 0.09 L/cm H2O, 0.022 to 0.092 L/cm H2O, and 0.022 to 0.068 L/cm H2O for the VC-CMV, VC-SIMV, VC+, and PSV groups, respectively. The r2 values for the relationships of ƬE and EIP methods were 0.99, 0.98, 0.97, and 0.90 (P <0.001) for VC-CMV, VC-SIMV, VC+, and PSV groups, respectively.
Rtot values ranged from 8 to 21 cm H2O/L/sec, 8 to 15.5 cm H2O/L/sec, 5 to 23 cm H2O/L/sec, and 5 to 17 cm H2O/L/sec for the VC-CMV, VC-SIMV, VC+, and PSV groups respectively. The r2 values for the relationships of the ƬE and EIP methods were 0.92, 0.94, 0.88, and 0.91 (P <0.001) for the VC-CMV, VC-SIMV, VC+, and PSV groups, respectively.
The ƬE method provided appropriate determinations and was an excellent predictor of Pplt, Crs, and Rtot for patients with acute respiratory failure receiving various modes of ventilatory support. It predicted or explained 94 to 99% of the variance in determining Pplt, 90 to 99% of the variance in determining Crs, and 88 to 94% of the variance in determining Rtot for patients receiving VC-CMV, VC-SIMV, VC+, and PSV. Bias and precision values were negligible for all measurements.
Crs ranged from near normal values at 0.095 L/cm H20 to much lower values at 0.022 L/cm H2O, indicative of patients with stiff non-compliant lungs. Rtot for some patients was higher than normal and in the range of 15 to 23 cm H2O/L/sec, although most did not have COPD. We speculate that the increased Rtot values may have been due to increased physiologic airways resistance and/or increased imposed resistance of the ETT as a result of internal narrowing of the tube due to secretions. The values for Crs and Rtot obtained in this study span ranges from moderate to more compromised forms of impaired pulmonary mechanics of patients with respiratory failure.
For healthy, non-intubated adults, ƬE was reported in the range of 0.38 to 0.51 seconds . The mean values of ƬE determined in this study for patients with acute respiratory failure were larger and comparable to other studies of non-COPD patients with acute respiratory failure at similar levels of PEEP. Guttmann et al.  reported an average ƬE of 0.60 seconds and Kondili et al.  reported ƬE to be in the range of 0.70 seconds. In another study of COPD patients, ƬE varied inversely with PEEP; at end exhalation ƬE ranged up to 3.75 seconds on zero PEEP and up to 1.58 seconds on 10 cm H20 PEEP .
A potential limitation of our study is that only two patients had COPD. For COPD patients with increased airways resistance and Crs, ƬE may be longer than in our patients with acute respiratory failure. This does not imply the ƬE method for determining Pplt, Crs, and Rtot cannot be employed for COPD patients; we speculate it may be effective for these patients. It is unclear if our method can be generalized to patients with COPD with abnormally long expiratory time constants. A follow up study of COPD patients would offer additional insight.
In normal, non-intubated adults, McIlroy et al. initially described using exhaled VT and flow rate to construct a line, and the slope of the line reflected ƬE . This was done using an X-Y plotter and a complicated process of determining angular tangents of the slope. Using a test lung and dogs, Brunner et al. modified this method by applying multiple correction factors, equations, and mathematical modeling to determine ƬE . In adults with acute respiratory failure, Guttmann et al. discarded the initial portion of the exhaled flow rate tracing just after the inflection point (point of greatest flow rate at the onset of exhalation) and then divided the exhaled VT curve into five slices to determine representative expiratory time constant components for each slice . The slope of straight lines fitted to the exhaled VT and flow rate curve within each slice was then used to determine an average value for ƬE. The aforementioned methods were done by hand, and were unwieldy, complicated, and time-consuming processes. They are impractical for clinical use, in contrast to our method. Our approach simplifies these methods by using only the 0.10 to 0.50 seconds portion of the exhaled VT and flow rate curves to derive a slope for determination of ƬE, and then use ƬE in equations for determinations of Pplt, Crs, and Rtot. Additionally, the approach is automated by using the rapid processing speed of a laptop computer with appropriate software at the bedside to generate real time determinations of Pplt, Crs, and Rtot; a practical easy-to-use clinical method (Figure 3).
ƬE as determined in this study may be considered as the total expiratory time constant, it includes physiologic and breathing apparatus components. Crs and bronchial airways resistance reflect the physiologic expiratory time constant component, and the series flow resistance of the ETT and PEEP/exhalation breathing valve constitute the breathing apparatus expiratory time constant component. The expiratory time constants for these various components were quantified in intubated adults with acute respiratory failure (non-COPD patients) . The physiologic expiratory time constant was lowest at 0.30 seconds (average), the physiologic expiratory time constant plus flow resistive time constant of the ETT was higher at 0.50 seconds (average), and the physiologic expiratory time constant, plus the combined flow resistive time constants of the ETT, ventilator circuit, and PEEP/exhalation valve, that is, the total ƬE, was highest at 0.65 seconds, similar to values we determined (Table 1). It was not a purpose of our study to differentiate and quantify physiologic and expiratory time constant components for intubated patients with respiratory failure connected to a ventilator. A purpose was to demonstrate an automatic method for determining the total expiratory time constant, which is of practical concern because it reflects the rate of lung emptying for intubated patients receiving ventilatory support, and because ƬE can be used for determinations of Pplt, Crs, and Rtot.
Another purpose of the study was to demonstrate that the ƬE method for determining Pplt, Crs, and Rtot was valid for representative forms of ventilatory support. Figures 4, 5, 6 and 7 illustrate comparable values for Pplt, Crs, and Rtot using the ƬE and traditional EIP methods for various ventilatory modes. To add additional patient groups receiving other forms of positive pressure ventilation, we believe is unnecessary because the ƬE method is predicated on passive deflation of the lungs using exhaled tidal volume and flow waveforms.
The ƬE method obviates the need to temporarily change modes and apply a VC-SIMV breath with an EIP. At times, the EIP method may be impractical. Consider a spontaneously breathing patient treated with PSV and PEEP, for example, in whom applying an EIP is uncomfortable and disrupts the breathing pattern. During the pause, the patient may not remain passive and attempt to breathe, precluding accurate estimates of Pplt, and thus, Crs and Rtot. As a result, the clinician may become frustrated and forego continued attempts to apply an EIP. Consequently, vital information about the patient's pulmonary elastance and resistance is denied. It is important to assess and follow changes in pulmonary mechanics due to effects of disease and/or therapeutic maneuvers applied to the lungs. For example, the before and after effects of PEEP on Crs, as well as the before and after effects of bronchodilator therapy on Rtot can be assessed.
A patient safety/lung protection implication involves continuous surveillance of Pplt by using the ƬE method. Lung protective strategies for patients with acute lung injury call for limiting Pplt to ≤30 cm H2O and preventing lung stretch to protect the lungs from physical trauma to lung tissue [2, 3]. Increased Pplt associated with VT should be avoided; it is associated with ventilator-induced lung injury [17, 18]. Because real-time Pplt values are generated using the ƬE method, if Pplt acutely increased to 45 cm H2O, for example, the clinician would be alerted to this potentially injurious pressure and intervene to lower Pplt (open-loop approach). Contrast the ƬE method to the current traditional practice of applying an EIP once every four or eight hours, for example, where acute increases in Pplt may go undetected for long periods. Pplt values >30 cm H20 occurred at times for some patients in our study. When made aware of these pressures using the traditional EIP method, VT was decreased in 1-ml/kg steps (minimal VT 4 ml/kg) [2, 4] to maintain Pplt at ≤30 cm H2O. Had Pplt been monitored continuously using the ƬE method, Pplt >30 cm H2O for long periods could have been avoided. If a ventilator's operating software employed the ƬE method for determining Pplt, then as Pplt increased to inappropriately high levels, the ventilator would immediately alert the clinician and automatically intervene to limit Pplt to ≤30 cm H2O by decreasing VT as stated above (closed-loop approach).
In conclusion, Pplt, Crs, and Rtot may be derived automatically and continuously by using ƬE from passive deflation of the lungs for various modes of ventilatory support. The ƬE method was just as good as the traditional EIP method for determining Pplt, Crs, and Rtot for patients with acute respiratory failure. The ƬE method obviates the need to apply a volume-controlled breath with an EIP, which may be impractical for many intubated, spontaneously breathing patients. Real-time monitoring of pulmonary mechanics during ventilatory support are facilitated using the ƬE method.
The expiratory time constant (ƬE) may be determined in real-time for patients receiving ventilatory support using point-by-point analyses of exhaled tidal volume and flow waveform data.
ƬE is combined in equations allowing for real-time determinations of Pplt, Crs, and Rtot (respiratory system resistance, plus series resistance of endotracheal tube and ventilator breathing apparatus) for ventilator-dependent patients.
The ƬE method for determining Pplt, Crs, and Rtot was compared with the traditional EIP method for determining Pplt, Crs, and Rtot for four forms of ventilatory support, namely, volume controlled-continuous mandatory ventilation, volume controlled-synchronized intermittent mandatory ventilation, pressure control plus, and pressure support ventilation. The r2 values for the relationships of ƬE and EIP methods ranged from 0.94 to 0.99 for Pplt, 0.90 to 0.99 for Crs, and 0.88 to 0.94 for Rtot (P <0.001). Bias and precision values were negligible.
The ƬE method obviates the need to disrupt the breathing pattern with an EIP, a requirement for determination of Pplt, Crs, and Rtot.
For patient safety/lung protection, continuous surveillance of Pplt is achieved using the ƬE method. Lung protective strategies for patients with acute lung injury call for limiting Pplt to ≤30 cm H2O and preventing lung stretch to protect the lungs from physical trauma to lung tissue.
Sources of funding: Dr. Banner: State of Florida and Convergent Engineering; Dr. Al-Rawas: University of Florida, College of Medicine; Dr. Euliano: Convergent Engineering; Dr. Tams: Convergent Engineering; Mr. Brown: Shands Hospital at the University of Florida; Dr. Gabrielli: University of Florida, College of Medicine and Convergent Engineering.
analysis of variance
chronic obstructive pulmonary disease
respiratory system compliance
end inspiratory pause
fractional inhaled oxygen concentration
internal review board
peak airway pressure during inhalation
positive end expiratory pressure
partial pressure end-tidal carbon dioxide
peak inflation pressure
inspiratory plateau pressure
pressure support ventilation
- SAS score:
Riker sedation-agitation scale score
pulse oximeter oxygen saturation
expiratory time constant
volume control plus
volume controlled-continuous mandatory ventilation
volume controlled-synchronized intermittent mandatory ventilation
- Kirby RR, Banner MJ, Downs JB, eds: Clinical Applications of Ventilatory Support. New York, Churchill Livingstone Inc; 1990:415.
- The Acute Respiratory Distress Syndrome Network: Ventilation with lower tidal volumes and compared to traditional tidal volumes for acute lung injury and acute respiratory distress syndrome. NEJM 2000, 342: 1301-1308.View ArticleGoogle Scholar
- The National Heart, Lung, and Blood Institute ARDS Clinical Trials Network: Higher versus lower positive end expiratory pressures in patients with the acute respiratory distress syndrome. NEJM 2004, 351: 327-336.View ArticleGoogle Scholar
- Ventilation protocol card.pdf - ARDS Net. National Institutes of Health, National Heart, Lung and Blood Institute Clinical Network mechanical ventilation protocol summary2012. [http://www.ardsnet.org/node/77791]
- Milic-Emili J, Zin WA: Relationship between neuromuscular drive and ventilatory output. In Handbook of Physiology Section 3. The Respiratory System. Vol III. Mechanics of Breathing. Part 2. Edited by: Macklem PT, Mead J. Washington DC: American Physiological Society; 1986:640.Google Scholar
- Riker RR, Fraser GL, Simmons LE, Wilkins ML: Validating the sedation-agitation scale with the bispectral index and visual analog scale in adult ICU patients after cardiac surgery. Intensive Care Med 2001, 27: 853-858. 10.1007/s001340100912View ArticlePubMedGoogle Scholar
- Engel LA: Dynamic distribution of gas flow. In Handbook of Physiology. The respiratory system. Section 3, volume 3. Edited by: Macklem PT, Mead J. Washington DC: American Physiologic Society; 1986:575.Google Scholar
- Banner MJ, Lampotang S: Clinical use of inspiratory and expiratory waveforms. In Current Respiratory Care. Edited by: Kacmarek R M, Stoller J K. Toronto: BC Decker; 1988:137.Google Scholar
- McIlroy MB, Tierney DF, Nadel JA: A new method of measurement of compliance and resistance of the lungs and thorax. J Appl Physiol 1963, 18: 424-427.Google Scholar
- Guttmann J, Eberhard L, Fabry B, Bertschmann W, Zeravik J, Adolph M, Eckart J, Wolff G: Time constant/volume relationship of passive expiration in mechanically ventilated ARDS patients. Eur Respir J 1995, 8: 114-120. 10.1183/09031936.95.08010114View ArticlePubMedGoogle Scholar
- Otis AB, McKerrow RA, Bartlett RA: Mechanical factors in distribution of pulmonary ventilation. J App Physiol 1956, 8: 427-443.Google Scholar
- Hogg JC: Pathophysiology of airflow limitation in chronic obstructive pulmonary disease. Lancet 2004, 364: 709-721. 10.1016/S0140-6736(04)16900-6View ArticlePubMedGoogle Scholar
- Bland JM, Altman DG: Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986, 1: 307-310.View ArticlePubMedGoogle Scholar
- Kondilli E, Prinianakis H, Athanasakis D, Georgopoulos D: Lung emptying in patients with acute respiratory distress syndrome: Effect of positive end expiratory pressure. Eur Respir J 2002, 19: 811-819. 10.1183/09031936.02.00255102View ArticleGoogle Scholar
- Kondilli E, Alexopoulou C, Prinianakis G, Xirouchaki N, Georgopoulos D: Pattern of lung emptying and expiratory resistance in mechanically ventilated patients with chronic obstructive pulmonary disease. Intensive Care Med 2004, 30: 1311-1318.Google Scholar
- Brunner JX, Laubscher TP, Banner MJ, Iotti G, Braschi A: Simple method to measure total expiratory time constant based on the passive expiratory flow-volume curve. Crit Care Med 1995, 23: 1117-1122. 10.1097/00003246-199506000-00019View ArticlePubMedGoogle Scholar
- MacIntyre NR: Current issues in mechanical ventilation for respiratory failure. Chest 2005, 128: 561S-567S. 10.1378/chest.128.5_suppl_2.561SView ArticlePubMedGoogle Scholar
- Villar J, Kacmarek RM, Perez-Mendez L, Aguirre-Jamie A: ARIES Network. A high PEEP-low tidal volume ventilatory strategy improves outcome in persistent ARDS. A randomized controlled trial. Crit Care Med 2006, 34: 1311-1318. 10.1097/01.CCM.0000215598.84885.01View ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.