Performance of Noninvasive Airway Occlusion Maneuvers to Assess Lung Stress and Diaphragm Effort in Mechanically Ventilated Critically Ill Patients

This diagnostic study is a secondary analysis on data from two clinical trials: a randomized controlled trial conducted in The Netherlands (NCT 03527797)²⁰  and a physiologic trial conducted in China (NCT 01663480).²¹  This analysis was not registered a priori. The article is reported according to the STARD guidelines.²² 

The primary cohort was recruited at the mixed medical-surgical intensive care unit (ICU) of a tertiary university hospital (Amsterdam UMC, location VUmc, Amsterdam, The Netherlands), and consisted of patients (n = 39) with acute respiratory failure ventilated with a spontaneous mode of mechanical ventilation (either pressure support or neurally adjusted ventilatory assist) with an expected duration of ventilation of at least 48 h.²⁰  The external validation cohort was recruited at another academic hospital (South East University, Nanjing, China) and consisted of patients (n = 13) ventilated in neurally adjusted ventilatory assist mode at different neurally adjusted ventilatory assist levels.²¹  Both cohorts were convenience samples.

In the primary cohort flow, volume (time-integral of flow), airway opening pressure, esophageal pressure, gastric pressure, transdiaphragmatic pressure (gastric pressure minus esophageal pressure), and transpulmonary pressure (airway opening pressure minus esophageal pressure) were recorded continuously for 24 h with a flow sensor and a double-balloon nasogastric catheter (Nutrivent, Sidam, Italy) connected to a dedicated signal acquisition system (MP160, BIOPAC Systems Inc, USA) as described previously.²³ Airway occlusions lasting 2 to 3 s were performed at baseline and were repeated every 1 to 3 h (fig. 1) to assess correct positioning and filling of the esophageal balloons and to calculate Pocc and P0.1. End-inspiratory occlusions lasting 2 to 3 s were performed at baseline and were repeated every 4 to 6 h to calculate the elastance of the chest wall and lungs in semistatic conditions. Patients in the external validation cohort had a nasogastric catheter (NeuroVent Research, Toronto, Canada) to record esophageal, gastric, transdiaphragmatic, and transpulmonary pressure and the electrical activity of the diaphragm. The patients received multiple expiratory occlusions at baseline, after which the neurally adjusted ventilatory assist level (i.e., cm H₂O of inspiratory support above positive end-expiratory pressure per microvolt of electrical activity of the diaphragm) was increased gradually to induce a wide range of diaphragm effort in the subjects. Airway occlusion maneuvers lasting 2 to 3 s were repeated at each neurally adjusted ventilatory assist level.²¹ All recordings with airway occlusion maneuvers with a ratio of the change in airway opening pressure–to–change in esophageal pressure less than 0.8 or more than 1.2 were discarded because the esophageal pressure–based measurements were deemed unreliable due to inadequate balloon filling or positioning.^14,24 In this article, the term “diaphragm effort” refers to diaphragm pressure output (transdiaphragmatic pressure), and respiratory drive to the intensity of respiratory center output to the diaphragm.

Signal analyses for the current study were performed with a custom software (Matlab 2021a, MathWorks, USA) as described previously,²⁰  and are shown in figure 1 and figure E1 (https://links.lww.com/ALN/C991). Comprehensive description of the signal analysis including calculation of mechanical power is available in the Supplemental Digital Content (https://links.lww.com/ALN/C989). In this study, we have adopted the term “occluded inspiratory airway pressure” for Pocc instead of “expiratory occlusion pressure” to reflect that the measurement is obtained during inspiration.

Descriptive statistics are expressed as mean ± SD, median [interquartile range], or count (percentages), as appropriate. The reference parameters were averaged per hour before each occlusion in each subject. Normality of distributions was assessed visually on normal-probability plots. Log transformations were used to transform distributions to normal if required. Sample size calculations were not performed. Biologic variability of change in transdiaphragmatic pressure, change in total respiratory muscle pressure, and the ratio of the two was estimated by calculating the coefficient of variation (SD/mean) of the respective parameters in each hour of the recordings, averaged for each subject.

The steps shown in figure 2 were taken consecutively to assess the diagnostic accuracy of Pocc and P0.1 to assess lung stress and diaphragm effort. First, the conversion factors to estimate change in transpulmonary pressure, transpulmonary mechanical power, and change in transdiaphragmatic pressure from Pocc and P0.1 were obtained with internal bootstrap procedures as described previously in the primary cohort.¹⁷  The bootstrap procedure randomly selected half of the patients in each loop, after which repeated-measures mixed models were used to obtain the optimal coefficient to convert Pocc and P0.1 into the reference parameters (change in transpulmonary pressure, transpulmonary mechanical power, or change in transdiaphragmatic pressure). The mean coefficient factor after 1,000 loops was selected as the final conversion factor for each respective measure; the CI is reported to show variability of this factor in the different loops of the bootstrap.

Next, correlations between the observed and predicted lung stress and diaphragm effort (based on Pocc and P0.1) were calculated using the obtained conversion factors and were compared with the reference standards with the methods of Bland and Altman in the primary cohort.²⁵  Within-subject limits of agreement were calculated with repeated-measure mixed models as described previously.¹⁷  The within-subject explained variance (R²) was calculated with the methods described by Nakagawa and Schielzeth.²⁶  Correlations with R² less than 0.30 were defined as poor, 0.31 to 0.50 as moderate, 0.51 to 0.80 as fair, 0.81 to 0.90 as strong, and greater than 0.90 as very strong.

Additionally, the discriminative power of Pocc and P0.1 to detect extremes of lung stress and diaphragm effort were calculated using standard formulas and by constructing the receiver operating characteristic curves in the primary and external cohort.²⁷  The limits for high lung stress were set at change in transpulmonary pressure > 20 cm H₂O^5,14  and transpulmonary mechanical power > 12 J/min²⁸  based on recent consensus statements. The limits for low and high diaphragm effort were set at less than 3 cm H₂O and greater than 12 cm H₂O, respectively, also based on consensus statements.^5,6,20  Because no interventional studies have shown that these limits are not injurious in critically ill patients as of yet, additional limits for potentially injurious lung stress and diaphragm effort were analyzed as well (table E1, https://links.lww.com/ALN/C990). Areas under the receiver operating characteristic curves between 0.5 and 0.7 were defined as poor, between 0.7 and 0.8 as acceptable, between 0.8 and 0.9 as excellent, and 0.9 or more as outstanding discrimination.²⁹  The cutoffs with the highest Youden J-statistic (sensitivity + specificity – 1) were selected from the ROC curves.³⁰  The CI of the areas under the receiver operating characteristic curves was constructed with the standard error of the Wilcoxon statistic as described previously.³¹ 

Next, the overall diagnostic accuracy of Pocc and P0.1 to identify patients with extremes in lung stress and diaphragm effort was calculated as the proportion of cases that were correctly identified by these cutoffs (i.e., [true positives + true negatives]/all cases) in the primary cohort and in the external validation cohort. Accuracy of different tests was compared with the “N-1” chi-square test.³² 

A two-tailed significance level of 5% was used for all statistical analyses. All the statistical analyses were performed in R version 4.0.1 (R Foundation for Statistical Programming, Vienna, Austria). Additional details are available in the Supplemental Digital Content (https://links.lww.com/ALN/C989) and figure E2 (https://links.lww.com/ALN/C992).

Patient characteristics are summarized in table 1, and patient flow is shown in figure 2. In total, 840,817 breaths obtained in 38 patients during a 24-h period were analyzed from the primary cohort, including 341 occluded inspiration maneuvers from which 282 met the criteria for adequate filling and positioning of the esophageal and gastric balloon that were used for further analysis. Number of recordings with low and high lung stress and diaphragm effort are shown in table 2. The average hourly within-subject coefficients of variation of change in esophageal pressure, transdiaphragmatic pressure, and total respiratory muscle pressure were 32 ± 5%, 33 ± 6%, and 25 ± 4%, respectively. The average ratio between change in transdiaphragmatic pressure and change in total respiratory muscle pressure was 0.93 ± 0.15, with a within-subject breath-by-breath coefficient of variation of 48 ± 12%.

Change in total respiratory muscle pressure and change in transdiaphragmatic pressure of individual breaths were strongly correlated (change in transdiaphragmatic pressure = 0.85 × change in total respiratory muscle pressure, R² = 0.87, P < 0.001; fig. E3, https://links.lww.com/ALN/C993). Converting change in total respiratory muscle pressure into change in transdiaphragmatic pressure with this formula resulted in a bias of less than 0.1 cm H₂O and 95% limits-of-agreement from –4.5 to 4.3 cm H₂O. Change in esophageal pressure and change in transdiaphragmatic pressure of individual breaths were very strongly correlated (change in transdiaphragmatic pressure = 1.08 × change in esophageal pressure, R² = 0.92, P < 0.001; fig. E3, https://links.lww.com/ALN/C993). Converting change in esophageal pressure into change in transdiaphragmatic pressure with this formula resulted in a bias of 1.1 cm H₂O with 95% limits-of-agreement from –1.9 to 3.8 cm H₂O.

Change in esophageal pressure correlated fairly with diaphragm effort (change in transdiaphragmatic pressure) in the preceding hour (average change in transdiaphragmatic pressure = 1.04 × change in esophageal pressure, R² = 0.79, P < 0.001; fig. 3). Converting change in esophageal pressure into change in transdiaphragmatic pressure with this formula, bias was 0.4 cm H₂O and 95% limits-of-agreement ranged from –3.5 to +3.7 cm H₂O. Averaging three consecutive change in esophageal pressure measurements improved the correlation slightly (R² = 0.84, P < 0.001; fig. E4, https://links.lww.com/ALN/C994). Diagnostic metrics to identify patients with extremes in lung stress and diaphragm effort are shown in table 2. Diagnostic metrics for additional parameters and cutoffs are reported in table E1 (https://links.lww.com/ALN/C990).

The mean conversion factor to predict change in transpulmonary pressure with Pocc was 0.67 (0.64 to 0.71). The predicted lung stress (change in transpulmonary pressure = inspiratory support provided by the ventilator – 0.67 × Pocc) correlated fairly well with the observed lung stress in the preceding hour (R² = 0.62, P < 0.001; fig. 4). Bias was –1.6 cm H₂O, 95% limits-of-agreement ranged from –10.0 to +6.6 cm H₂O.

The conversion factor to predict transpulmonary mechanical power with Pocc was on average 0.93 (0.90 to 0.95). The predicted mechanical power (predicted transpulmonary mechanical power = 0.5 × (inspiratory support – 0.93 × Pocc) × tidal volume [Vt] × respiratory rate [RR] × 0.098, with Vt in liters) correlated moderately well with the observed mechanical power (R² = 0.47, P < 0.001; fig. 4); bias was 0.4 J/min, 95% limits-of-agreement ranged from –6.4 to 7.6 J/min.

The conversion factor to predict change in transdiaphragmatic pressure with Pocc was on average 0.71 (0.65 to 0.76). The predicted diaphragm effort (change in transdiaphragmatic pressure = 0.71 × –Pocc) correlated fairly well with observed diaphragm effort (R² = 0.53, P < 0.001; fig. 4). Bias was 1.2 cm H₂O and 95% limits-of-agreement from –6.4 to +7.6 cm H₂O. Cutoffs and diagnostic metrics are shown in table 2.

The conversion factor to predict change in transpulmonary pressure with P0.1 was on average 3.3 (2.4 to 4.1). The predicted lung stress (change in transpulmonary pressure = 3.3 × P0.1 + inspiratory support) correlated fairly well with the observed lung stress in the preceding hour (R² = 0.51, P < 0.001; fig. 5). Bias was –0.6 cm H₂O; 95% limits-of-agreement ranged from –10.2 to +10.1 cm H₂O.

The conversion factor to predict MP_L with P0.1 was on average 4.7 (4.2 to 5.3). The predicted mechanical power (predicted transpulmonary mechanical power = 0.5 × (inspiratory support + 4.7 × P0.1) × RR × Vt × 0.098, with Vt in liters) correlated moderately with the observed mechanical power (R² = 0.35, P < 0.001; fig. 5). Bias was 1.4 J/min, 95% limits-of-agreement ranged from –6.7 to 8.2 J/min.

The conversion factor to predict change in transdiaphragmatic pressure with P0.1 was on average 3.5 (2.0 to 4.9). The predicted diaphragm effort (change in transdiaphragmatic pressure = 3.5 × P0.1) correlated poorly with observed diaphragm effort (R² = 0.22, P < 0.001; fig. 5). Bias was –0.6 cm H₂O; 95% limits-of-agreement ranged from –7.3 to 6.2 cm H₂O. Cutoffs and diagnostic metrics are shown in table 2.

In total, 14,651 breaths obtained in 13 patients were analyzed in the external validation cohort. The recordings included 61 expiratory occlusions, of which 43 had a Pocc/change in esophageal pressure_occ ratio between 0.8 and 1.2 which were used for further analysis (fig. 2). Correlations are shown in figure E5 (https://links.lww.com/ALN/C995) and figure E6 (https://links.lww.com/ALN/C996). Lung stress was high in 7 of 43 (16%) of the recordings. Diaphragm effort was low in 4 of 43 (10%) and high in 3 of 43 (7%) of the recordings. Accuracy of Pocc and P0.1 to identify patients with extremes in lung stress and diaphragm effort was not significantly different in the external cohort compared with the primary cohort (fig. E5, https://links.lww.com/ALN/C995, and fig. E6, https://links.lww.com/ALN/C996).

In the current study we tested the validity of noninvasive airway occlusion maneuvers to quantify lung stress and diaphragm effort in ventilated critically ill patients. Our findings can be summarized as follows: First, Pocc and P0.1 cannot be used to calculate the exact values of diaphragm effort and lung stress in the preceding hour, due to wide limits of agreement between occlusions pressures and the reference standard (esophageal pressure). Second, if the goal is to obtain lung stress and diaphragm effort in purported safe ranges,^5,6  Pocc and P0.1 have good to excellent diagnostic performance in identifying extremes of lung stress and diaphragm effort. Third, Pocc is at least as reliable as P0.1 in all instances but outperforms P0.1 in detecting patients with high diaphragm effort.

The predicted lung stress based on Pocc and P0.1 correlates with change in transpulmonary pressure in the preceding hour (R² = 0.62 and 0.51, respectively), albeit with wide limits of agreement ranging from 5 to 10 cm H₂O in either direction (figs. 4 and 5). Likewise, Pocc and P0.1 correlate with change in transdiaphragmatic pressure (R² = 0.53 and 0.22, respectively) with equally wide limits of agreement. The limits of agreement are likely wide because of variations in breathing effort within subjects over time, and because a single breath is extrapolated to diaphragm effort and/or lung stress over a longer period of time. Pocc and P0.1 can therefore not replace esophageal pressure when precise values are required such as in physiologic studies.

The area under receiver operating characteristic curves of Pocc and P0.1 to identify patients with extremes in lung stress and diaphragm effort are high (table 2). The predicted lung stress and diaphragm effort show considerable heteroscedasticity (fanning out) compared with observed change in transpulmonary pressure and transdiaphragmatic pressure (figs. 4 and 5), meaning that errors are lower at low lung stress and diaphragm effort and greater at higher levels. This provides an explanation for the discrepancy between the wide limits of agreement and the high accuracy; most of the errors are made at higher levels of lung stress and diaphragm effort, where differences of 5 cm H₂O might be less important than at lower levels (e.g., a change in transpulmonary pressure of either 30 or 35 cm H₂O are both far beyond proposed safe values, so precision is less important at this level).

Pocc has higher discriminative power than P0.1 in detecting patients with high transdiaphragmatic pressure in our cohort (area under receiver operating characteristic curves 0.86 vs. 0.73, respectively), which might be explained be several factors. First, P0.1 is based on a shorter measurement interval and thus suffers more from high-frequency noise such as cardiac artefacts. Second, factors that cause a time delay in the transmission of pressures between the patient and measurement setup might have more effect on dynamic measurements such as P0.1. Third, properties of the respiratory system and control center might influence the convexity of airway pressure curves, distorting the relation between P0.1 and total respiratory muscle pressure in the same breath.³³ 

Our data show that Pocc together with tidal volume and respiratory rate may be used to estimate mechanical power, which correlates moderately well to observed mechanical power (R² = 0.47) as shown in figure 4. Area under receiver operating characteristic curves to detect high mechanical power are acceptable to excellent (table 2).³⁴  Mechanical power has been theorized to better reflect the risk of lung injury than pressure alone in animal studies²⁸  and retrospective cohorts of ICU patients.³⁵  However, the superiority of mechanical power to predict lung injury requires further validation in prospective clinical studies.

Lung- and diaphragm-protective mechanical ventilation is an emerging concept for ventilatory management in critically ill patients. The hypothesis is that monitoring and controlling breathing effort and lung stress in critically ill patients could have several benefits: limiting lung stress might hamper development of lung injury, whereas targeting moderate diaphragm effort has been theorized to protect against disuse atrophy while limiting the probability of developing load-induced diaphragm injury.^5,6  The evidence that absence of diaphragm effort leads to atrophy and weakness is compelling,^7,8  and maintaining some diaphragm effort reduces diaphragm atrophy in animal studies.^9,10  Evidence that high diaphragm effort leads to injury is currently based on small sets of experimental human and animal data.^36–38  Apart from potentially preventing diaphragm injury, limiting excessive diaphragm effort might improve patient comfort by reducing dyspnea,³⁹  and is proposed to reduce regional lung stress by limiting pendelluft.¹²  The proposed pathophysiology of diaphragm protective ventilation, including current knowledge gaps, has been covered in depth recently.^5,40 

State-of-the-art monitoring of lung stress and diaphragm effort requires esophageal (and gastric) pressure measurement, which is not routine performed in clinical practice.¹  Our data show that the Pocc and P0.1 cannot replace esophageal and gastric manometry when precise values are desired. At best, Pocc and P0.1 give an indication of a range of the true lung stress and diaphragm effort. This range can allow a clinician to identify patients that are most likely to benefit from advanced respiratory monitoring: a patient with a predicted transdiaphragmatic pressure of 20 cm H₂O based on Pocc has an actual change in transdiaphragmatic pressure between 13 and 27 cm H₂O with 95% certainty and could thus benefit from additional monitoring. Additionally, a clinician can use Pocc and P0.1 to estimate whether lung stress and diaphragm effort are likely within proposed safe limits when esophageal manometry is not available by using the cutoffs provided in table 2: 86% of patients with an estimated change in transpulmonary pressure < 22 cm H₂O are expected to have actual lung stress in the proposed safe range (less than 20 cm H₂O), and 89% of patients with a Pocc between –7 and –15 cm H₂O will have diaphragm effort in the proposed safe range (transdiaphragmatic pressure of 3 to 12 cm H₂O). An example of a bedside monitoring protocol based on Pocc and these cutoffs is presented in figure E7 (https://links.lww.com/ALN/C997), but prospective studies are required to assess whether using this protocol results in more lung stress and effort in purported safe ranges.

Transdiaphragmatic pressure, the pressure output of the diaphragm, is the current reference standard to assess diaphragm effort.^6,14–16,23  Several factors influence a patient’s capacity to generate pressure, such as diaphragm weakness before ICU admission⁴¹  and changes in diaphragm geometry due to lung collapse and positive end-expiratory pressure.⁴²  Consequently, a certain transdiaphragmatic pressure may require more myofiber recruitment in critically ill patients compared with healthy subjects. Thus, the precise “safe transdiaphragmatic pressure interval” may be patient specific. Furthermore, diaphragm weakness was found to associate strongly to ICU outcomes such as weaning failure in several studies,^41,43,44  but the correlation was absent in others.^45,46  Prospective trials are thus required to assess whether diaphragm effort during mechanical ventilation is indeed causally related to ICU outcomes, and not merely a confounder for disease severity.^47,48  Additionally, further research must assess the optimal cutoffs to prevent lung and diaphragm injury, because the current cutoffs are based only on consensus.

The conversion factor to predict lung stress from Pocc in our cohort (0.67) closely matches the conversion factor reported in an earlier study (0.66),¹⁷  suggesting that this factor is generalizable to external populations. Likewise, the conversion factor to predict change in total respiratory muscle pressure with Pocc found in our cohort (0.73, fig. E8, https://links.lww.com/ALN/C998) was very close to value reported previously (0.75).¹⁷  The high accuracy of P0.1 to identify patients with purported insufficient respiratory muscle effort is in agreement with recent studies.^19,49  Accurately detecting insufficient effort is a novel observation for Pocc, because an earlier study lacked recordings with low effort.¹⁷ 

This study has several strengths. We included a heterogeneous group of patients with acute respiratory failure, displaying a wide range of lung stress and diaphragm effort. In contrast to previous studies, we used the reference methods to assess lung stress and diaphragm effort, recorded patients for prolonged periods of time (24 h), included more patients (38 vs. 16) and conducted much more occlusion measurements (282 vs. 52). We also confirmed the robustness of Pocc and P0.1 in an external cohort. Earlier studies validated the Pocc and P0.1 with total respiratory muscle pressure, which reflects total pressure generation resulting from activation of the diaphragm, accessory muscles and relaxation of the expiratory muscles.^17,18,50  Transdiaphragmatic pressure may be more linked to studies on diaphragm injury during mechanical ventilation which have demonstrated an association (but not necessarily causation⁴⁷ ) between diaphragm function and clinical outcome.^41,43  Whether monitoring transdiaphragmatic pressure leads to better outcomes than monitoring total respiratory muscle pressure requires further study. Last, we have estimated the potential magnitude of measurement errors in our study, and found that these likely do not influence our conclusions (Supplemental Digital Content, https://links.lww.com/ALN/C989).

Several limitations should be acknowledged. First, the optimal ranges for lung stress and diaphragm effort to prevent both lung injury and diaphragm weakness are unknown and were based on expert consensus. Second, although we used data from two independent centers, performance of Pocc and P0.1 needs to be evaluated in larger cohorts from multiple international centers. Third, earlier reports averaged three consecutive P0.1 measurements to improve reliability.¹⁹  We could not conduct the same analysis as single occlusions were performed in our protocol. We have, however, estimated to which degree averaging multiple consecutive change in esophageal pressure measurements would improve correlations and diagnostic accuracy with change in transdiaphragmatic pressure (fig. 3 and fig. E4, https://links.lww.com/ALN/C994), and found the benefit to be relatively minor: averaging three measurements improved R² from 0.79 to 0.84, but had little effect on diagnostic performance. Fourth, we used the same external validation cohort as an earlier report validating Pocc.¹⁷  This external cohort had few recordings with low diaphragm effort, underlining the importance of further validation in larger cohorts. Fifth, the external validation cohort ventilated patients exclusively in neurally adjusted ventilatory assist, which is a proportional mode of ventilation, whereas the primary cohort used mostly pressure support. This likely had little effect on the validity of the Pocc and P0.1, however, because single airway occlusions were found not to affect respiratory drive¹⁷  and the correlations and diagnostic performance were not different in primary cohort and the external cohort (fig. E5, https://links.lww.com/ALN/C995, and fig. E6, https://links.lww.com/ALN/C996). Finally, 20 to 30% of all recordings in the main cohort and external data set had to be discarded due to our strict quality control for adequate calibration of the esophageal pressure balloons.

This study shows that Pocc and P0.1 cannot predict exact values for lung stress and diaphragm effort in ventilated critically ill patients. Both maneuvers can reliably identify patients with purported low diaphragm effort and high lung stress in the preceding hour. Pocc is more accurate than P0.1 in identifying patients with high diaphragm effort.

The authors thank R. H. Driessen, B.Sc., from the Department of Intensive Care Medicine, Amsterdam UMC, location VUmc (Amsterdam, The Netherlands), for database management support.

This study was funded by a Ph.D.-research grant to Dr. de Vries from the Amsterdam Cardiovascular Sciences research institute (Amsterdam, The Netherlands). No commercial support was received.

Dr. Heunks has received research support from Liberate Medical (Crestwood, Kentucky) and speakers fee from Getinge (Göteborg, Sweden). Dr. de Vries has received travel and speaker fees from the Chinese Association of Rehabilitation Medicine (Beijing, China). Dr. Jonkman has received personal fees from Liberate Medical. The other authors declare no competing interests.

Supplemental methods and results, https://links.lww.com/ALN/C989

Table E1 Additional diagnostic performance, https://links.lww.com/ALN/C990

Figure E1 Pressure-volume loopst, https://links.lww.com/ALN/C991

Figure E2 Example delayed cycling, https://links.lww.com/ALN/C992

Figure E3 Correlations of Pes, Pmus and Pdi, https://links.lww.com/ALN/C993

Figure E4 Performance of averaging Pes, https://links.lww.com/ALN/C994

Figure E5 Pocc in external cohort2, https://links.lww.com/ALN/C995

Figure E6 P0.1 in external cohort, https://links.lww.com/ALN/C996

Figure E7 Proposed monitoring protocol, https://links.lww.com/ALN/C997

Figure E8 Performance of Pocc for Pmus, https://links.lww.com/ALN/C998