A novel methodology for measuring global diaphragm thickness by ultrasonography in patients with critical illness: an exploratory pilot study

Abstract

Background

A global diaphragm thickness measurement technique was developed for the zone of apposition (ZOA) using an image edge identification approach. The method was assessed in terms of its repeatability and reliability when applied in patients with critical illness.

Methods

Diaphragm thickness measurements were conducted by experienced ultrasound examiners in 60 critically ill adult patients. The performance of continuous global diaphragm thickness measurements was compared to traditional localized diaphragm thickness measurements with regard to intra-observer and inter-observer consistency.

Results

End-expiratory diaphragm thickness was measured to assess consistency. For the traditional local diaphragm thickness measurements, the intraclass correlation coefficients (ICC) were 0.882 for intra-observer and 0.848 for inter-observer assessments (p < 0.001). The global diaphragm thickness measurements yielded ICC values of 0.968 and 0.955 for intra-observer and inter-observer assessments, respectively (p < 0.001). These findings indicated good reliability for the conventional method and excellent reliability for the global measurement method. The maximum observed variability was 16.5% with the traditional method and 3.9% with the continuous measurement approach. When using a 10% decrease in diaphragm thickness as the threshold for clinically relevant diaphragmatic atrophy, 16.7% of measurements obtained through the traditional method exceeded this error margin, whereas all measurements acquired through the continuous method remained within the acceptable range.

Conclusions

Compared to traditional localized diaphragm thickness ultrasonography, the continuous approach demonstrated superior repeatability and reliability. This newly developed methodology may enhance the precision of diaphragm thickness evaluations within the ZOA in patients with critical illness.

Background

Diaphragm dysfunction has gained increasing attention in recent years, with an estimated incidence of approximately 64% among mechanically ventilated patients in intensive care units (ICUs) [1]. Evidence from prior investigations has indicated a strong association between reduced diaphragm thickness or volume and the presence of diaphragm dysfunction in patients with critical illness [2, 3]. Among these manifestations, diaphragm atrophy, defined as a decrease in diaphragm thickness exceeding 10%, has been identified as the most prominent and has been associated with adverse clinical outcomes [4, 5]. As one of the core parameters in diaphragm ultrasound assessment, the common clinical scenario for diaphragm thickness assessment is evaluating diaphragm atrophy or calculating diaphragm thickening fraction, which can assess the patient’s diaphragm function or guide decisions regarding weaning or extubation in mechanically ventilated patients. More precise measurements of diaphragm thickness can enhance the clinical significance of diaphragm ultrasound indicators [5–7].

Over the past decade, diaphragm ultrasonography has emerged as a rapidly evolving technique, recognized for its feasibility and accuracy in evaluating diaphragm anatomy and respiratory physiology [8–11]. In current clinical settings, diaphragm thickness and the thickening fraction are typically measured at the zone of apposition (ZOA) [12]. However, challenges related to the repeatability and reproducibility of diaphragm thickness measurements and derived functional parameters, such as the thickening fraction, have been reported [13]. Variability in diaphragm thickness across different anatomical locations may further influence measurement outcomes [13]. Conventional measurement techniques primarily capture localized diaphragm thickness rather than reflecting its global characteristics [14, 15]. Furthermore, the diaphragm has an average thickness of approximately 2 to 3 mm, which limits the ability of current ultrasonographic modalities to detect small changes with sufficient precision [12, 16]. For instance, identifying a 0.2 to 0.3 mm reduction in diaphragm thickness, considered a potential marker of diaphragm atrophy, poses a significant challenge due to the inherent measurement error in existing ultrasonographic approaches.

In response to these limitations, a continuous diaphragm thickness measurement technique based on image machine learning principles has been developed. The current investigation aimed to compare this continuous approach with the conventional point-based method in terms of repeatability and reliability. It was hypothesized that this continuous measurement technique would enhance the accuracy of diaphragm thickness assessments and provide a more comprehensive representation of global diaphragm thickness.

Methods

Study design

An exploratory observational study was conducted in the Department of Critical Care Medicine at a research-affiliated university hospital in Nanjing, China, from January 2023 to December 2023. Ethical approval was granted by the Ethics Committee of Zhongda Hospital, Southeast University (approval number: 2021ZDSYLL342-P01). The study adhered to the principles outlined in the Declaration of Helsinki. Informed consent was obtained from all participating patients or their legal representatives prior to enrollment.

Participants

Eligibility criteria included invasive mechanical ventilated patients aged ≥ 18 years who had started to receive spontaneous breathing trial (SBT) and able to cooperate during ultrasonographic examination. The SBT mode was uniformly selected as pressure support (PS), and PS level was set to 6 cmH₂O, and positive end-expiratory pressure (PEEP) was set to 0. Exclusion criteria were: (1) presence of preexisting neuromuscular disorders; (2) severe obesity, defined as a body mass index (BMI) greater than 35; (3) medical conditions likely to interfere with diaphragm ultrasonography, such as thoracic trauma, recent thoracic surgery, or severe pneumothorax; (4) current pregnancy; (5) advanced malignancy; and (6) a clinical prognosis deemed futile, with documented decisions to forgo life-sustaining treatments.

Procedures of diaphragm thickness ultrasonography

Diaphragm local thickness ultrasonography

All diaphragm ultrasound images were obtained using a Philips CX50 ultrasound system (Philips Healthcare, Bothell, WA, USA). Patients were positioned in a 30° semi-recumbent posture. A 10 MHz high-frequency linear transducer was placed near the right anterior or mid-axillary line at the eighth or ninth intercostal space, corresponding to the ZOA. The transducer was oriented parallel to the intercostal space and perpendicular to the chest wall. Gain settings were adjusted to optimize contrast with surrounding anatomical structures. An optimal acoustic window was defined as one in which the diaphragm appeared as a clear three-layered structure, consisting of the pleura, diaphragm, and peritoneum (Fig. 1). The examination site was marked to maintain consistency in subsequent measurements. Diaphragm thickness was measured in B-mode, with end-expiratory diaphragm thickness (Tdi^Exp) used as the reference parameter (Fig. 1). All ultrasound examinations were performed by trained and certified operators with a minimum of two years of experience in diaphragm ultrasonography.

Fig. 1.

Schematic presentation of diaphragm thickness ultrasonography in the ZOA

Diaphragm global thickness ultrasonography

A semi-automated method for global diaphragm thickness measurement was developed based on image analysis and anatomical priors involving the parietal pleura and peritoneum. This method incorporated phase symmetry feature analysis to enhance boundary detection accuracy. Initially, the region of interest (ROI) containing the diaphragm was manually identified on the ultrasound images. A Gaussian filter was applied to the ROI to reduce speckle noise. Given the diaphragm’s anatomical adjacency to the pleura and peritoneum, the measurement approach focused on detecting these surrounding structures rather than attempting direct diaphragm segmentation. Local phase congruency was employed to highlight symmetric features suitable for identifying the pleura and peritoneum [17]. A set of Log-Gabor filters was used to conduct local phase analysis, chosen for their ability to localize features effectively while minimizing the influence of noise [18]. For each point (x, y) in the image, the horizontal-oriented symmetric phase measure () was calculated using the following expression [17]:

where and represent the even and odd symmetric components of the filter response at scale and orientation , respectively. denotes the response amplitude at a given scale and orientation . is the noise compensation threshold, and is a small constant to prevent division by zero. The operator indicates: ; otherwise .

Following phase analysis, the OTSU thresholding algorithm was applied to the ROI [19]. The two connected components with the largest and second-largest major axis lengths were identified as the parietal pleura and peritoneum. Detected edge points were fitted using polynomial curve fitting to derive equations representing the diaphragm’s upper and lower boundaries. The global diaphragm thickness was then computed as the average vertical distance between these two fitted boundaries. A schematic flowchart illustrating the complete measurement framework and the accompanying software interface is presented in Fig. 2.

Fig. 2.

Flowchart of the diaphragm global thickness measurement framework and the associated measurement software

Evaluation metrics

Reproducibility of the two diaphragm thickness measurement methods

For each patient, end-expiratory diaphragm thickness was measured twice by a single examiner at the same time point. These two measurements were used to assess intra-observer reproducibility. During the same time period (i.e., the SBT phase), two additional measurements were performed by a different examiner. The average of the two measurements from each examiner was used to evaluate inter-observer reproducibility. Different ultrasound measurers were mutual blinded and completely uninformed of each other’s measurement information, and the order of measurements between measurers was randomized. The ultrasound measurers in this study all have completed the official training course of the Chinese Critical Ultrasound Study Group (CCUSG) and they have already had at least 1 year of experience in critical care ultrasonography and have acquired sufficient proficiency in muscle ultrasound measurements. Ultrasound images obtained by both examiners were exported, and global diaphragm thickness was measured using the proposed semi-automated method. Repeatability and reproducibility were compared between the traditional local thickness and the global thickness measurement methods.

Stability of diaphragm edge identification

Diaphragm ultrasound images were acquired and frozen for each patient. Using the traditional local diaphragm thickness ultrasonography, three examiners—blinded to each other’s results—independently measured diaphragm thickness, resulting in three local thickness values per image. The same images were also assessed using the global thickness method, with three repeated measurements performed to obtain three global thickness values. A test-retest reliability analysis was conducted to evaluate the stability of edge identification for both methods. The maximum and minimum values among the three measurements obtained by each method were compared using Bland–Altman plots. To assess clinical relevance, a 10% threshold was defined as the maximum acceptable measurement error, based on the criterion for diaphragmatic atrophy (a reduction in diaphragm thickness of ≥ 10%) [5, 13]. Measurement variation distributions were evaluated for both methods under this criterion.

Sample size

Previous literature has reported intraclass correlation coefficients (ICCs) for traditional diaphragm thickness measurements ranging from 0.8 to 0.9 [20–22]. The aim of the present exploratory study was to validate the measurement precision of the global diaphragm thickness ultrasonography. Assuming an ICC of 0.9 for the traditional method and an expected ICC greater than 0.95 for the global method, a sample size calculation was conducted using a two-sided α level of 0.05, 90% statistical power, and two measurements per participant. This yielded a required sample size of 50 individuals.

Statistical analysis

The Kolmogorov-Smirnov test was employed to assess the normality of continuous data, which were reported as mean ± standard deviation (SD) for normally distributed data or as median and interquartile range (IQR) for non-normally distributed data. Categorical variables were reported as percentages. Agreement and reliability were evaluated using Bland–Altman plots and ICCs. The type of ICC was absolute agreement, and ICC values were interpreted according to published reliability guidelines: < 0.5 indicating poor reliability, 0.5 to 0.75 moderate, 0.75 to 0.9 good, and > 0.9 excellent reliability [23]. All statistical analyses were performed using SPSS version 23.0 (IBM, Armonk, NY, USA) and MedCalc (MedCalc Software, Ostend, Belgium). A p-value of < 0.05 was considered statistically significant.

Results

Patient characteristics

A total of 60 patients were enrolled, and diaphragm thickness measurements were successfully obtained for all participants. The demographic and clinical characteristics are presented in Table 1. Among the participants, 36 (60%) were male, and the mean age was 62.4 years. The most common indications for ICU admission included sepsis, respiratory disease, and postoperative monitoring. Among these postoperative patients, 8 (66.7%) received volume-controlled ventilation (VCV), while 4 (33.3%) received pressure-controlled ventilation (PCV); the median tidal volume was 434 (48) ml, and the PEEP level was 8 (3) cm H₂O.

Table 1.

Patient demographics and clinical characteristics

Characteristics	N = 60 mean(SD)/median(IQR)/n(%)
Age (years)	62.4(19.7)
Sex (male)	36(60%)
Weight (kg)	66.1(11.1)
Height (mm)	166.6(8.2)
BMI (Kg/m2)	23.8(3.2)
APACHE II	17.8(7.6)
SOFA	5.6(4.0)
Reason of ICU Admission
Central nervous system	5(8.3%)
Cardiovascular system	7(11.6%)
Post-operation	12(20.0%)
Respiratory system	13(21.7%)
Sepsis	16(26.7%)
Trauma	4(6.7%)
Others	3(5.0%)
Initial ventilation mode
CMV	14(23.3%)
SIMV	38(63.3%)
Others	8(13.3%)
Respiration parameter pre-SBT
FiO2 (%)	40(5)
P/F (mmHg)	274.9(35.9)
Vte (ml)	415.4(40.3)
RR (breaths/min)	17.9(2.7)
P0.1 (cmH₂O)	2.9(0.9)
Cdyn (ml/cmH₂O)	54.2(12.1)
Respiratory support mode post-SBT
COT	22(36.7%)
HFO	27(45.0%)
NIV	11(18.3%)
Need for steroid therapy	13(21.7%)
History of muscle relaxants use	5(8.3%)
Average cumulative fluid balance(ml)	1014.9(612.4)

BMI: body mass index; APACHE II: Acute Physiology and Chronic Health Score; SOFA: Sequential Organ Failure Assessment; CMV: continuous mandatory ventilation; SIMV: synchronized intermittent mechanical ventilation; SBT: spontaneous breathing trial; FiO₂: inspiratory fraction of oxygen; P/F: PaO₂/FiO₂ ratio; Vte: expiratory tidal volume; RR: respiratory rate; P0.1: airway occlusion pressure at 0.1s; Cdyn: dynamic compliance; COT: conventional oxygen therapy; HFO: high-flow oxygen therapy; NIV: noninvasive ventilation

Reproducibility of the two diaphragm thickness measurements methodology

The ICC values for intra-observer and inter-observer variability of diaphragm local thickness ultrasonography were 0.882 and 0.848, respectively. In contrast, the ICC values for intra-observer and inter-observer variability of diaphragm global thickness ultrasonography were 0.968 and 0.955, respectively. Based on reliability research guidelines, local diaphragm thickness ultrasonography demonstrated good intra- and inter-observer agreement, while global diaphragm thickness ultrasonography demonstrated excellent reproducibility (Table 2) [23].

Table 2.

Comparison of repeatability of the two measurement methods in diaphragm thickness measurement

Measurement method	Intra-observer consistency				Inter-observer consistency
	ICC	95%CI	Reliability level	P-value	ICC	95%CI	Reliability level	P-value
Local measurement	0.882	0.810–0.928	good	< 0.001	0.848	0.757–0.906	good	< 0.001
Continuous measurement	0.968	0.947–0.981	excellent	< 0.001	0.955	0.925–0.973	excellent	< 0.001

ICC: intraclass correlation coefficient; CI: confidence interval

Stability of diaphragm edge identification

Using identical diaphragm ultrasound images, three separate measurements were performed using each method. The ICC values obtained for local and global thickness methods were 0.893 and 0.992, respectively (p < 0.001), as presented in Table 3. Bland–Altman analyses were conducted to assess the maximum and minimum values of the three measurements from each method. For the local thickness method, the maximum measurement variation was 16.5%, and the mean variation was 1.8%. For the global thickness method, the maximum variation was 3.9%, with a mean variation of 0.5%. When applying a 10% threshold as the clinically acceptable range of measurement error—based on the diagnostic criterion for diaphragm atrophy (≥ 10% reduction in thickness)—16.7% (10 out of 60) of the measurements obtained via the local thickness method exceeded this threshold [5, 13]. In contrast, all measurements acquired using the global thickness method remained within the acceptable error range (Fig. 3). The global diaphragm thickness method demonstrated high stability in diaphragm edge identification, as presented in Fig. 4.

Table 3.

Comparison of stability of the two measurement methods in diaphragm edge identification

	Mean (SD)	Coefficient of Variation	ICC	95%CI	Reliability level	P-value
Local diaphragm thickness (1st)	2.19(0.54)	24.7%	0.893	0.842–0.931	good	< 0.001
Local diaphragm thickness (2nd)	2.16(0.50)	23.1%
Local diaphragm thickness (3rd)	2.21(0.49)	22.2%
Continuous diaphragm thickness (1st)	2.289(0.53)	23.2%	0.992	0.988–0.995	excellent	< 0.001
Continuous diaphragm thickness (2nd)	2.292(0.51)	22.3%
Continuous diaphragm thickness (3rd)	2.300(0.54)	23.5%

Fig. 3.

Agreement between the two diaphragm thickness measurement methods in edge identification. (Green line indicates maximum allowable measurement error: 10% variability of diaphragm thickness)

Fig. 4.

Illustration of the diaphragm global thickness ultrasonography method. (a) B-mode diaphragm ultrasound image with the red box indicating the ROI in the ZOA. (b) Three repeated continuous thickness measurements within the ROI: 2.860, 2.856, and 2.858 mm. (c) Non-uniform diaphragm thickness in the ROI, with midpoint thickness at 2.927 mm, mean thickness at tertiary points 2.794 mm, and mean thickness at quintile points 2.824 mm. (Red lines indicate diaphragm edge tracing by the continuous measurement method; green crosses mark equal division points)

Discussion

A novel continuous diaphragm thickness measurement technique within the ZOA, employing phase congruency edge detection was introduced in this study. Findings indicated that this method demonstrated superior stability in delineating diaphragm boundaries. In comparison to conventional local diaphragm thickness measurement, this new approach yielded excellent intra-observer and inter-observer reproducibility. The continuous methodology may provide a more objective assessment of absolute diaphragm thickness and subtle morphological changes.

Alterations in diaphragm thickness are frequently observed among individuals admitted to the ICU, particularly diaphragm atrophy, which has been reported in approximately 40% of mechanically ventilated individuals [5, 24]. In pediatric populations undergoing mechanical ventilation, diaphragm thickness has been demonstrated to decrease by an average of 3.4% per day, with reductions reaching up to 13.8% [25]. In adults, daily reductions of up to 6% in diaphragm thickness have been documented [26]. Diaphragm atrophy is typically defined as a reduction in diaphragm thickness greater than 10% [5, 13]. This condition is closely associated with impaired diaphragm function, prolonged durations of mechanical ventilation, and increased mortality, all of which significantly influence clinical outcomes [2, 5, 27]. Therefore, regular monitoring of diaphragm thickness is essential for the timely detection and intervention of diaphragm atrophy.

Ultrasonography is currently a widely utilized bedside modality for assessing diaphragm thickness. Within the ZOA, diaphragm visualization and measurement can be readily performed using ultrasound [28]. Nonetheless, measurement accuracy remains a key challenge. Given that the diaphragm is a dome-shaped, broad, and relatively flat muscle, its thickness can vary across different anatomical locations [29]. Although the ZOA is generally the most accessible site for ultrasound evaluation of diaphragm morphology, regional thickness may change continuously along this zone. Moreover, diaphragm thickness measurements can be influenced by anatomical positioning and patient posture. Even minimal variations in measurement site or body position may alter thickness readings and derivative parameters, such as the diaphragm thickening fraction [13]. Current diaphragm ultrasound protocols typically assess localized rather than global thickness across the ZOA, and there is limited literature supporting the use of continuous thickness measurement in this context [14, 15, 30].

Additionally, the diaphragm is considerably thinner than most appendicular skeletal muscles. Previous studies have reported an average diaphragm thickness of approximately 2 mm [15, 20, 31]. Although ultrasonography has proven reliable in detecting changes in large muscles, such as the quadriceps, it poses greater difficulty when evaluating the relatively smaller changes in diaphragm thickness [22]. Prior studies have demonstrated measurement variability in diaphragm thickness on the order of 0.2 to 0.4 mm, and reported inter-observer limits of agreement ranging from − 2 mm to 0.7 mm [9, 32]. Given that a variation of 0.2 mm represents approximately 10% of a 2 mm diaphragm, such variability verges on the diagnostic threshold for diaphragm atrophy and is therefore clinically unacceptable.

To address these limitations, the present study proposed a semi-automatic global thickness measurement approach, incorporating local phase analysis for diaphragm assessment within the ZOA. Accurate detection of diaphragm boundaries is critical to the success of such semi-automated measurements. However, this task is complicated by the poorly defined interfaces among the parietal pleura, peritoneum, and diaphragm. To overcome this challenge, phase congruency—a contrast- and illumination-invariant feature detection method—was employed instead of traditional gradient-based detectors [17, 33]. This strategy leveraged prior anatomical knowledge of the pleura and peritoneum, in conjunction with symmetric phase features, to facilitate precise segmentation of the diaphragm’s superior and inferior margins [33–35].

A custom measurement software application was also developed based on this algorithm to enable efficient extraction of global diaphragm thickness from ultrasound images. The study’s results indicated that the global thickness method produced superior intra- and inter-observer reproducibility when compared to the conventional local thickness approach: based on reliability research guidelines [23], local diaphragm thickness approach demonstrated good reliability, while global diaphragm thickness method demonstrated excellent reliability. Implementation of this technique is anticipated to reduce measurement variability and enhance the accuracy of diaphragm thickness assessments in clinical ultrasonography.

Furthermore, given the heterogeneity in diaphragm thickness, continuous diaphragm thickness measurements offer a methodological advantage by mitigating the influence of relative changes in probe placement. This is achieved through the replacement of point-based measurements with area-based (face) measurements. In contrast, conventional point-based local diaphragm thickness measurements are susceptible to positional and postural variations [36, 37]. To address this issue, the present study adopted optimized methodologies from existing literature, including marking the sonographic site to ensure consistency in measurement location, thereby minimizing the effect of changes in body position on repeated diaphragm thickness assessments [22].

This study had several limitations. First, although continuous diaphragm thickness measurement was successfully implemented, the measurement range remained constrained by the physical width of the ultrasound probe. The proposed diaphragm global thickness measurement approach was developed using a standard ultrasound probe with a width of 38 mm. Utilization or development of wider probes may allow for a more comprehensive assessment of diaphragm morphology within the ZOA. Second, current ultrasound technology enables diaphragm thickness measurement only within the ZOA. Obtaining clear structural images of other diaphragm regions, such as the dome or the crural diaphragm, remains challenging. Further investigation is required to develop ultrasonographic techniques capable of evaluating the diaphragm in its entirety. Third, this study was conducted as an exploratory pilot study in a critically ill population. To further validate the relationship between diaphragm thickness measurements derived from both methods and actual diaphragm morphology, confirmatory studies involving anatomical specimens at the animal level are necessary. Fourth, in present study the diaphragm ultrasound image was acquired in frozen state on B-mode. Analyzing frozen images probably does not fully reflect real-life clinical conditions, and the results of this study may not fully generalize to live, bedside assessments. However, the methodology of automatically detecting and identifying diaphragm boundaries of this study may provide valuable idea for the “automation of image acquisition” proposed by the EXODUS consensus [13].

Conclusions

The application of phase congruency edge detection to ultrasound imaging enables the measurement of global diaphragm thickness within the ZOA. Compared to conventional local diaphragm thickness measurement methods, the continuous measurement approach demonstrated superior repeatability and stability. This methodology holds potential for minimizing measurement variability in diaphragm thickness assessments conducted via ultrasonography.

Abbreviations

APACHE II

Acute Physiology and Chronic Health Evaluation II score

BMI

Body Mass Index

Cdyn

Dynamic compliance

CMV

Continuous mandatory ventilation

COT

Conventional oxygen therapy

FiO₂

Inspiratory fraction of oxygen

HFO

High-flow oxygen therapy

ICC

Intraclass correlation coefficients

ICU

Intensive care unit

IQR

Interquartile range

NIV

Noninvasive ventilation

P0.1

Airway occlusion pressure at 0.1s

PEEP

Positive end-expiratory pressure

P/F

PaO₂/FiO₂ ratio

PS

Pressure support

ROI

Region of interest

RR

Respiratory rate

SBT

Spontaneous breathing trial

SD

Standard deviation

SIMV

Synchronized intermittent mandatory ventilation

SOFA

Sequential Organ Failure Assessment

Vte

Expiratory tidal volume

ZOA

Zone of apposition

Author contributions

Chen-Liang Sun: Conceptualization, Funding acquisition, Writing – original draft. Si-Ping Zhou: Formal Analysis, Writing – original draft. Li-Sha Hou: Data curation, Investigation, Resources. Meng-Jie Zhan: Data curation, Software. Yi-Ping Wang: Data curation, Software. Hong-Sheng Zhao: Funding acquisition, Writing – review & editing. Feng-Mei Guo: Conceptualization, Funding acquisition, Writing – review & editing. Guang-Quan Zhou: Conceptualization, Formal Analysis. All authors read and approved the final draft.

Funding

This study was funded by the National Science and Technology Major Project of China (Grant No. 2022YFC2504505) and the Scientific Research Project Foundation of Nantong Municipal Health Commission (Grant No. MS2024015). The funding bodies had no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

This study was conducted with approval from the Ethics Committee of Zhongda Hospital, Southeast University (Approval No. 2021ZDSYLL342-P01). This study was conducted in accordance with the declaration of Helsinki. Written informed consent was obtained from all participants.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.