Value of 3D echocardiography in the diagnosis of arrhythmogenic right ventricular cardiomyopathy.

AIMS: The 2010 Task Force Criteria (TFC) require that both right ventricular (RV) regional wall-motion abnormalities (WMA) and specific RV size cut-offs be met in order to fulfil one of the major criterion for arrhythmogenic right ventricular cardiomyopathy (ARVC) diagnosis. Currently, 2D echocardiography (2DE) and cardiovascular magnetic resonance imaging (cMRI) are used to determine if these criteria are met. Little is known about the diagnostic value of 3D echocardiography (3DE) in ARVC. The aim of this study was to determine whether a combination of 2DE-3DE is non-inferior to the currently used 2DE-cMRI combination in the diagnosis of patients with ARVC. METHODS AND RESULTS: Thirty-nine individuals (47±15 years) with suspected ARVC underwent evaluation of the RV with cMRI, 2DE, and 3DE. 3DE and cMRI were independently used to obtain RV volumes, ejection fraction (EF) and determine the presence of segmental RV WMA. Studies were blindly classified as meeting criteria for ARVC in accordance with the 2010 TFC. Kappa statistics were used to test the concordance between 2DE-cMRI and 2DE-3DE approaches. Using the 2DE-cMRI approach, 3/39 were not affected, 5/39 possible, 8/39 borderline, and 23/39 definite ARVC. The proposed 2DE-3DE approach yielded 5/39 not affected, 7/39 possible, 8/39 borderline, and 19/39 definite diagnoses. The two approaches were highly concordant (k = 0.71; 95% confidence interval: 0.44-0.84). Although 3DE underestimated RV volumes in comparison with cMRI, interfering, in some instances with the fulfilment of a major criterion, it was able to identify more RV WMA (28/39) than 2DE (11/39), with a detection-rate comparable to cMRI (33/39) highlighting a unique advantage. CONCLUSION: The combination of 2DE-3DE for ARVC diagnosis is comparable to the conventional 2DE-cMRI approach. 3DE should be performed in all suspected ARVC patients to aide in the detection of WMA.

Three-Dimensional Echocardiographic Deconstruction: Feasibility of Clinical Evaluation from Two-Dimensional Views Derived from a Three-Dimensional Data Set.

BACKGROUND: Three-dimensional echocardiography (3DE) makes it possible to capture the entire heart in a single data set that theoretically could be used to extract any two-dimensional (2D) views and potentially replace the standard practice of serial 2D acquisitions. The aim of this study was to test the hypothesis that the quality of 3DE-derived 2D images is sufficient to allow the visualization of the left ventricular (LV), right ventricular (RV), and left atrial (LA) endocardium, on par with images from conventional two-dimensional echocardiography (2DE), and potentially more accurate quantification of chamber size and function. METHODS: First, the investigators prospectively studied 36 patients who underwent 2DE in 14 standard views, and full-volume data sets from 3DE, from which the same views were extracted offline. The ability to visualize the LV endocardium, RV free wall, and LA endocardium was scored. LV linear dimensions, LV volumes, and LV ejection fraction (LVEF), LA volume, and RV basal dimension were measured and compared between both types of images. Thereafter, 40 patients who underwent 2DE, 3DE, and cardiac magnetic resonance (CMR) imaging on the same day were retrospectively studied. LV volumes and LVEF derived from 2DE and 3DE were compared side by side against the CMR reference. RESULTS: Intertechnique agreement in visualization scores was 87% for LV segments, 86% for the RV free wall, and 83% for the LA endocardium. The correlations between 2DE- and 3DE-derived measurements were 0.95, 0.97, and 0.97 for LV volumes and LVEF, respectively, and 0.88 for RV basal dimension. Three-dimensional echocardiography-derived measurements of LV volumes and LVEF were more similar to those on CMR than those obtained on conventional 2DE. CONCLUSIONS: The feasibility of segmental assessment of cardiac chambers using 3DE-derived 2D views is similar to that using conventional 2DE. This approach provides similar quantitative information, including more accurate LV volumes and LVEF measurements compared with CMR, and thus promises to significantly shorten the duration of the echocardiographic examination.

Utility of transillumination and transparency renderings in 3D transthoracic imaging.

Transillumination (TI) is a new 3D rendering tool that uses a freely movable virtual light source to enhance depth, contours, and image detail. The TI model was recently modified to allow the operator adjust the degree of transparency of both cardiac and extra-cardiac structures. While the addition of transparency was shown to significantly improve quality in 3D transesophageal imaging, this has not yet been shown for transthoracic (TTE) imaging. We prospectively studied 35 patients who underwent clinically indicated TTE with standard 3D acquisition, as well as TI with and without transparency. Six experienced echocardiographers were shown images of all three display types in random order. Each image was scored independently using a Likert Scale while assessing each of the following aspects: ability to identify anatomy or pathology, depth perception, degree of anatomic detail, and border delineation. All experts perceived an incremental value of the transparency mode, compared to TI without transparency and standard 3D rendering, in terms of ability to identify anatomy or pathology (4.15 ± 0.97 vs. 3.88 ± 0.99 vs. 2.52 ± 1.41, p < 0.01), depth perception (4.33 ± 0.78 vs. 3.88 ± 0.82 vs. 2.29 ± 1.07, p < 0.01), degree of anatomic detail (4.08 ± 1.0 vs. 3.89 ± 0.79 vs. 2.31 ± 1.08, p < 0.01), and border delineation (4.44 ± 0.80 vs. 3.90 ± 0.78 vs. 2.42 ± 1.13, p < 0.01). Compared to standard 3D and TI renderings of TTE images, the addition of transparency significantly improves both image quality and diagnostic confidence.

Developing Insights Regarding Tricuspid Valve Regurgitation: Morphology, Assessment of Severity, and the Need for a Novel Grading Scheme.

Current understanding that progressive tricuspid regurgitation (TR) is associated with worse outcomes has highlighted the clinical need for a more accurate assessment of TR morphology and severity. This need has been further emphasized owing to the development of a myriad of percutaneous right-sided interventions, which may offer successful treatment of TR in selected patients. Understanding the etiology and quantification of the severity of TR has important implications in the selection of novel therapeutic strategies, i.e., medical vs. percutaneous vs. surgical approaches. Newer grading schemas that better reflect the TR lesion severity have been recently proposed and may facilitate monitoring of the evolution of TR following percutaneous and/or surgical treatment. In this review, we summarize contemporary concepts regarding tricuspid valve morphology, TR etiology, and associated mechanisms and echocardiographic approaches to grade TR severity.

Long-Term Postpartum Cardiac Function and Its Association With Preeclampsia.

Background Preeclampsia is a prominent risk factor for long-term development of cardiovascular disease. Although existing studies report a strong correlation between preeclampsia and heart failure, the underlying mechanisms are poorly understood. One possibility is the glycoprotein growth factor activin A. During pregnancy, elevated activin A levels are associated with impaired cardiac global longitudinal strain at 1 year, but whether these changes persist beyond 1 year is not known. We hypothesized that activin A levels would remain increased more than 1 year after a preeclamptic pregnancy and correlate with impaired cardiac function. Methods and Results To test our hypothesis, we performed echocardiograms and measured activin A levels in women approximately 10 years after an uncomplicated pregnancy (n=25) or a pregnancy complicated by preeclampsia (n=21). Compared with women with a previously normal pregnancy, women with preeclampsia had worse global longitudinal strain (-18.3% versus -21.3%, P=0.001), left ventricular posterior wall thickness (0.91 mm versus 0.80 mm, P=0.003), and interventricular septal thickness (0.96 mm versus 0.81 mm, P=0.0002). Women with preeclampsia also had higher levels of activin A (0.52 versus 0.37 ng/mL, P=0.02) and activin/follistatin-like 3 ratio (0.03 versus 0.02, P=0.04). In a multivariable model, the relationship between activin A levels and worsening global longitudinal strain persisted after adjusting for age at enrollment, mean arterial pressure, race, and body mass index (P=0.003). Conclusions Our findings suggest that both activin A levels and global longitudinal strain are elevated 10 years after a pregnancy complicated by preeclampsia. Future studies are needed to better understand the relationship between preeclampsia, activin A, and long-term cardiac function.

Improved Delineation of Cardiac Pathology Using a Novel Three-Dimensional Echocardiographic Tissue Transparency Tool.

BACKGROUND: Accurate visualization of cardiac valves and lesions by three-dimensional (3D) echocardiography is integral for optimal guidance of structural procedures and appropriate selection of closure devices. A new 3D rendering tool known as transillumination (TI), which integrates a virtual light source into the data set, was recently reported to effectively enhance depth perception and orifice definition. We hypothesized that adding the ability to adjust transparency to this tool would result in improved visualization and delineation of anatomy and pathology and improved localization of regurgitant jets compared with TI without transparency and standard 3D rendering. METHODS: We prospectively studied 30 patients with a spectrum of structural heart disease who underwent 3D transesophageal imaging (EPIQ system, Philips) with standard acquisition and TI with and without the transparency feature. Six experienced cardiologists and sonographers were shown randomized images of all three display types in a blinded fashion. Each image was scored independently by all experts using a Likert scale from 1 to 5, while assessing each of the following aspects: (1) ability to recognize anatomy, (2) ability to identify pathology, including regurgitant jet origin, (3) depth perception, and (4) quality of border delineation. RESULTS: TI images with transparency were successfully obtained in all cases. All experts perceived an incremental value of the transparency mode, compared with TI without transparency and standard 3D rendering, in terms of ability to recognize anatomy (respective scores: 4.5 ± 1.1 vs 4.1 ± 1.1 vs 3.6 ± 1.1, P < .05), ability to identify pathology (4.1 ± 1.1 vs 3.9 ± 1.2 vs 3.3 ± 1, P < .05), depth perception (4.6 ± 0.7 vs 4.1 ± 0.8 vs 3.2 ± 1.0, P < .05), and border delineation (4.6 ± 0.8 vs 4.1 ± 1.0 vs 3.1 ± 1.1, P < .05). CONCLUSIONS: The addition of the transparency mode to TI rendering significantly improves the diagnostic and clinical utility of 3D echocardiography and has the potential to markedly enhance echocardiographic guidance of cardiac structural interventions.

Refining Severe Tricuspid Regurgitation Definition by Echocardiography with a New Outcomes-Based "Massive" Grade.

BACKGROUND: Current echocardiographic guidelines recommend that tricuspid regurgitation (TR) severity be graded in three categories, following assessment of specific parameters. Findings from recent trials have shown that the severity of TR frequently far exceeds the current definition of severe. We postulated that a grading approach that emphasizes outcomes could be useful to identify patients with severe TR at increased risk of mortality. METHODS: We identified 284 patients with echocardiograms demonstrating severe functional TR, defined as vena contracta (VC) ≥ 0.7 cm. Demographics and mortality data were obtained from the medical records. Patients were divided into study (n = 122 patients with three-dimensional images) and validation (n = 162) cohorts. The VC was measured in both the right ventricular (RV) inflow and apical four-chamber views and averaged. For the study cohort, tricuspid annular, RV end-diastolic (basal, mid, long axis) dimensions, tricuspid leaflet tenting height and area, RV free-wall longitudinal strain, and RV volumes were measured from two- and three-dimensional data sets. A K-partition algorithm was used in the study cohort to derive a mortality-related cutoff VC value, above which TR was termed "massive." The ability of this VC cutoff to identify patients at greater mortality risk was then tested in the validation cohort using Kaplan-Meier survival analysis. RESULTS: In the study cohort, VC > 0.92 cm (massive TR) was optimally associated with worse survival. Tricuspid annular and RV size were larger in the massive group (P < .05), while there were no significant differences in demographics between the TR groups. Importantly, in the independent validation cohort, the above VC cutoff also correlated with increased mortality in the massive group (log-rank P < .05). CONCLUSIONS: Among patients traditionally defined as having severe TR, a subset exists with massive TR, resulting in greater adverse RV remodeling and increased mortality. These patients may derive the greatest benefit from emerging percutaneous therapies.

Three-dimensional echocardiography investigation of the mechanisms of tricuspid annular dilatation.

Tricuspid annular (TA) size, assessed by 2D transthoracic echocardiography (TTE), has a well-established prognostic value in patients undergoing mitral valve surgery, with TA dilatation triggering simultaneous tricuspid annuloplasty. While TA dilatation is common in patients with dilated atria secondary to atrial fibrillation, little is known about the mechanisms of TA dilatation in patients with sinus rhythm (SR). This study aimed to identify echocardiographic parameters most closely related to the TA size as a potential tool for identification of patients prone to developing TA enlargement. 120 patients with SR underwent clinically indicated TTE, including 30 patients with normal hearts and 90 patients diagnosed with at least one right heart abnormality, defined as: right ventricular (RV) or right atrial (RA) dilatation, ≥ moderate tricuspid regurgitation (TR) and elevated systolic pulmonary artery pressure (sPAP). RA and RV end-diastolic and end-systolic volumes (EDV, ESV) and function were measured using commercial 3D software (TomTec). 3D RV long and short axes were used as surrogate indices of RV shape. Degrees of TR and sPAP were estimated by 2D TTE. 3D TA sizing was performed at end-diastole using 3D custom software. Linear regression analysis was used to identify variables best correlated with TA size, followed by multivariate analysis to identify independent associations. The highest correlations were found between TA area and: RA ESV (r = 0.73; p < 0.01), RV EDV (r = 0.58; p < 0.01), RV end-diastolic long and short axes (r = 0.53, 0.42; both p < 0.01), TR degree (r = 0.40; p < 0.01) and sPAP (r = 0.32; p < 0.01). Multivariate analysis revealed that RA ESV was the only parameter independently associated with TA area (p < 0.05, r = 0.85). In conclusion, RA volume plays an important role in TA dilatation even in patients with normal SR. Understanding of annular remodeling mechanisms could aid in identifying patients at higher risk for TA dilatation, especially those scheduled for mitral valve surgery.

Echocardiographic evaluation of the effects of sacubitril-valsartan on vascular properties in heart failure patients.

Increased vascular stiffness is known to be an independent predictor of mortality in patients with heart failure with reduced ejection fraction (HFrEF). The effects of sacubitril-valsartan on vascular structure and function have not been systematically studied in this patient population. We hypothesized that aortic distensibility (AD) and fractional area change (AFAC), as assessed by 2D transthoracic echocardiography (TTE), would improve over time in HFrEF patients on sacubitril-valsartan therapy, due to the vasodilatory properties of the medication. We prospectively studied 30 patients with HFrEF (25 < EF < 40%) on optimal guideline-directed medical therapy who were subsequently started on sacubitril-valsartan. Patients underwent serial 2D TTE imaging at baseline, 3 and 6 months following therapy initiation. Ascending aortic diameters were measured 3 cm above the aortic valve in the parasternal long-axis view and used to calculate AD and AFAC, two markers of vascular compliance. For reference, we also measured AD and AFAC in 30 healthy, age and gender-matched controls at a single time point. Normal controls had significantly higher values of AD and AFAC than HFrEF patients at baseline (AD: 4.0 ± 1.1 vs. 2.2 ± 0.9 cm2dyne-110-3, p < 0.0001 and AFAC: 18.8 ± 3.7% vs. 10.3 ± 4.3%, p < 0.0001). In HFrEF patients on sacubitril-valsartan, both indices of aortic compliance progressively improved towards normal from baseline to 6 months: AD from 2.2 ± 0.9 to 3.6 ± 1.5 cm2dyne-110-3 (p < 0.0001) and AFAC from 10.3 ± 4.3 to 13.7 ± 4.1% (p < 0.0001). In conclusion, AD and AFAC are decreased in patients with HFrEF and gradually improve with sacubitril-valsartan treatment. The echocardiographic markers used in this study may become a useful tool to assess the effectiveness of sacubitril-valsartan therapy in HFrEF patients.

Comparison Between Four-Chamber and Right Ventricular-Focused Views for the Quantitative Evaluation of Right Ventricular Size and Function.

BACKGROUND: Right ventricular (RV) function plays a pivotal prognostic role in multiple cardiac diseases. Echocardiography guidelines recommend that RV quantification be performed in the RV-focused view, which is theoretically more reproducible than the four-chamber (4Ch) view. However, differences between views in RV size and function measurements have never been systematically studied. Accordingly, the aim of this study was to compare (1) RV size and function parameters obtained from the RV-focused and 4Ch views and (2) test-retest variability between these two views. METHODS: Fifty patients (26 men; mean age, 63 ± 18 years) undergoing clinically indicated transthoracic echocardiography were prospectively enrolled. Each patient underwent three repeated acquisitions of the 4Ch and RV-focused views by two sonographers. The first operator performed two acquisitions at the beginning and the end of the clinical transthoracic echocardiographic study, and the second operator performed the third acquisition afterward. RV size and function measurements were obtained from the two views and compared using paired t-test analysis and Bland-Altman analysis. Intra- and interoperator test-retest and intra- and interreader variability for both views were assessed using intraclass correlations and coefficients of variation. RESULTS: All RV size parameters were significantly larger when measured in the RV-focused view compared with the 4Ch view. Also, all RV function parameters, including RV free wall and global longitudinal strain, were larger in magnitude when measured in the RV-focused view. Measurements variability was consistently better for the RV-focused view. CONCLUSIONS: RV size and function measurements obtained from the RV-focused and 4Ch views are not interchangeable. RV size and function parameters measured from the RV-focused view are more reproducible than from 4Ch acquisitions. Therefore, only the RV-focused view should be used for quantitative assessment of the right ventricle.

Echocardiographic Assessment of the Tricuspid Annulus: The Effects of the Third Dimension and Measurement Methodology.

BACKGROUND: Evaluation of the tricuspid annulus is crucial for the decision making at the time of left heart surgery. Current recommendations for tricuspid valve repair are based on two-dimensional (2D) transthoracic echocardiography (TTE), despite the known underestimation compared with three-dimensional (3D) echocardiography. However, little is known about the differences in 3D tricuspid annular (TA) sizing using TTE versus transesophageal echocardiography (TEE). The aims of this study were to (1) compare 2D and 3D TA measurements performed with both TTE and TEE and (2) compare two 3D methods for TA measurements: multiplanar reconstruction (MPR) and dedicated software (DS) designed to take into account TA nonplanarity. METHODS: Seventy patients underwent 2D and 3D TTE and TEE. Two-dimensional images were used to measure TA diameter from apical four-chamber, right ventricular-focused (TTE), and midesophageal four-chamber (TEE) views. Three-dimensional full-volume data sets were analyzed using both MPR and DS, to obtain major and minor axes, perimeter, and area. Intertechnique agreement was assessed using Bland-Altman analysis. RESULTS: Measurements on 2D TTE and TEE, which were view dependent, underestimated TA major dimensions in all views compared with 3D values, irrespective of the 3D method. MPR and DS measurements were significantly different, with DS resulting in larger values for all parameters, irrespective of approach. No differences were found between 3D TTE and 3D TEE for both MPR and DS. CONCLUSIONS: Our findings highlight the need for methodology that respects the 3D geometry of the tricuspid annulus, including its nonplanarity, which cannot be accurately assessed from 2D images and is not equally taken into account by different 3D measurement methodologies. Accordingly, a 3D cutoff value for TA enlargement needs to be established and is likely to be larger than the guideline-recommended 2D-based 40-mm cutoff. Importantly, noninvasive 3D TTE can be used instead of 3D TEE because TA measurements are not different.

Load Dependency of Left Atrial Strain in Normal Subjects.

BACKGROUND: Left atrial (LA) longitudinal strain is a novel parameter used for the evaluation of LA function, with demonstrated prognostic value in several cardiac diseases. However, the extent of load dependency of LA strain is not well known. The aim of this study was to evaluate the impact of acute changes in preload on LA strain, side by side with LA volume, in normal subjects. METHODS: Twenty-five healthy volunteers (13 men; mean age, 31 ± 2 years) were prospectively enrolled, who underwent two-dimensional and three-dimensional echocardiographic imaging during acute stepwise reductions in preload using a tilt maneuver: baseline at 0°, followed by 40° and 80°. Left ventricular and LA size and function parameters were measured using standard methodology, and LA strain-time curves were obtained using speckle-tracking software (TomTec), resulting in reservoir, conduit, and contractile strain components. All parameters were compared among the three loading conditions using one-way analysis of variance for repeated measurements. RESULTS: Although there were no significant changes in blood pressure, heart rate increased significantly with tilt. As expected, LA volumes, left ventricular volumes, and left ventricular ejection fraction, as well as E wave, A wave, and e' significantly decreased with progressive inclination. In parallel, LA reservoir, conduit, and contractile strain values decreased with reduction in preload (reservoir: 42.9 ± 3.9% to 27.5 ± 3.8%, P < .001; conduit: 29.3 ± 2.7% to 20.2 ± 5.0%, P < .001; contractile: 13.6 ± 2.9% to 7.3 ± 3.5%, P < .001). Paired post hoc analysis showed that all LA strain values were significantly different among all three tilt phases. Of note, percentage change in LA reservoir strain was significantly smaller than that in LA maximum volume. CONCLUSIONS: In normal subjects, LA strain is preload dependent but to a lesser degree than LA volume. This difference underscores the relative advantage of LA strain over maximum volume, when LA assessment is used as part of the diagnostic paradigm.

Diagnosis of Isolated Cleft Mitral Valve Using Three-Dimensional Echocardiography.

BACKGROUND: The prevalence of isolated cleft mitral valve (MV; no concomitant congenital heart disease or degenerative MV disease) with significant mitral regurgitation (MR) diagnosed using two-dimensional echocardiography (2DE) has been reported to be very low. Three-dimensional echocardiography (3DE) has enabled a more comprehensive visualization of the MV and detailed understanding of the mechanisms of MR and can potentially reveal isolated cleft MV that is not recognized with 2DE. The aim of this study was to determine, using 3DE, the prevalence, location, and associated MV annular and left ventricular characteristics of isolated cleft MV, in the absence of associated congenital heart disease, in patients with significant MR. METHODS: A total of 1,092 patients with unexplained moderate or greater MR on two-dimensional transthoracic echocardiography who were referred for three-dimensional transesophageal echocardiography between 2005 and 2017 (n = 626) were retrospectively studied. Left ventricular dimensions and function were determined, and quantitative MR assessment and three-dimensional analysis of the MV annulus was performed. RESULTS: Twenty-one patients (prevalence 3.3%) were diagnosed with isolated cleft MV using three-dimensional transesophageal echocardiography but not 2DE. The majority of these patients (n = 16) were noted to have anterior cleft MVs, with most located in the mid-A1 (n = 10) or mid-A3 (n = 5) scallops. Posterior clefts were less common (n = 5) and occurred at the site of the natural scallop indentations (three between P1 and P2 and two between P2 and P3). Among patients with either anterior or posterior MV cleft, there were no differences in left ventricular ejection fraction or three-dimensional MV geometry (annular distance, height, circumference, and area). There was a trend toward worse MR severity in patients with anterior cleft MV. CONCLUSIONS: In patients with otherwise unexplained significant MR referred for transesophageal echocardiography, 3DE uncovered a considerably higher prevalence of isolated cleft MV than previously reported by 2DE, with the majority located in the anterior MV. Although the annular geometry was similar between patients with anterior and posterior cleft MVs, a trend toward more severe MR in anterior clefts may reflect underlying abnormalities in the embryologic development of the anterior MV leaflet. Evaluation of MV pathology is improved by 3DE, which should be used routinely in the setting significant MR.

Residual native left ventricular function optimization using quantitative 3D echocardiographic assessment of rotational mechanics in patients with left ventricular assist devices.

Preservation of native left ventricular (LV) function in patients supported with LV assist device (LVAD) may be beneficial to attain optimal hemodynamics and enhance potential recovery. Currently, LVAD speed optimization is based on hemodynamic parameters, without considering residual native LV function. We hypothesized that alternatively, LV rotational mechanics can be quantified by 3D echocardiography (3DE), and may help preserve native LV function while optimizing LVAD speed. The goal of this study was to test the feasibility of quantifying the effects of LVAD implantation on LV rotational mechanics and to determine whether conventional speed optimization maximally preserves native LV function. We studied 55 patients with LVADs, who underwent 3DE imaging and quantitative analysis of LV twist. Thirty patients were studied before and after LVAD implantation. The remaining 25 patients were studied during hemodynamic ramp studies. The pump speed at which LV twist was maximal was compared with the hemodynamics-based optimal speed. LV twist decreased following LVAD implantation from 4.2 ± 2.7 to 2.3 ± 1.9° (P < 0.01), reflecting the constricting effects on native function. With lower pump speeds, no significant changes were noted in LV twist, which peaked at a higher speed. In 11/25 (44%) patients, the conventional hemodynamic/2DE methodology and 3DE assessment of maximal residual function did not indicate the same optimal conditions, suggesting that a higher pump speed would have better preserved native function. In conclusion, quantitative 3DE analysis of LV rotational mechanics provides information, which together with hemodynamics may help select optimal pump speed, while maximally preserving native LV function.