Ventricular Outflow Tract Fractional Shortening Research Articles

Assessment of regional and global right ventricular systolic function in children with repaired tetralogy of Fallot.

Echo assessment of right ventricular function is difficult due to its complex geometry and regional differences in wall motion. In patients with repaired tetralogy of Fallot, cardiac MRI is the gold standard for assessment of right ventricular function. There is scant data regarding the correlation of echo measures of right ventricular function with cardiac MRI right ventricular function in the paediatric population. Echocardiographic measures of regional and global right ventricular function were reviewed in 56 patients with repaired tetralogy of Fallot and 27 patients with structurally normal hearts. These measures were compared to global right ventricular ejection fraction by cardiac MRI. Despite having the same right ventricular ejection fraction by cardiac MRI as normal controls, patients with repaired tetralogy of Fallot had significantly worse global and regional echocardiographic measures of right ventricular function. Right ventricular fractional area change and fractional shortening of the right ventricular outflow tract correlated best with global right ventricular function by MRI. Incorporation of these measures into a regression model allowed accurate prediction of global right ventricular function by cardiac MRI. Children with repaired tetralogy of Fallot have abnormal regional and global right ventricular function compared to patients with normal hearts. Despite the presence of patch material, the right ventricular outflow tract significantly contributes to global right ventricular function by cardiac MRI. When incorporated into a model that includes regional and global echocardiographic measures of right ventricular function, right ventricular outflow tract fractional shortening helps predict global right ventricular function by MRI.

Prognostic Value of Tricuspid Annular Plane Systolic Excursion and Right Ventricular Outflow Tract Fractional Shortening in Mechanically Ventilated Septic Patients

The authors aimed to explore whether tricuspid annular plane systolic excursion (TAPSE) and right ventricular outflow fractional shortening (RVOT-FS) were associated with long-term prognosis in mechanically ventilated septic patients. A prospective observational study. A tertiary hospital intensive care unit (ICU). One hundred eighty-one septic patients who were on mechanical ventilation. Echocardiography was performed within 24 hours of ICU admission. Several echocardiographic parameters, including TAPSE and RVOT-FS, as well as prognostic information, were collected. A Cox regression survival analysis showed that TAPSE was independently associated with one-year all-cause mortality (hazard ratio [HR] 0.407, 95% confidence interval [CI]: 0.200-0.827, p = 0.013), but ROVT-FS was not (HR 0.997, 95% CI: 0.970-1.025, p = 0.828). ROC analysis showed that the optimal cutoff value for TAPSE and RVOT-FS to determine one-year mortality was TAPSE <18 mm and RVOT-FS <40%. The one-year mortality in patients with low TAPSE (n = 88) and in patients with both low TAPSE and low RVOT-FS (n = 60) was 45.5% and 48.3%, respectively; p = 0.724. In a multivariate analysis, RVOT-FS did not add significant prognostic information to that provided by TAPSE <18 mm (p = 0.197). TAPSE was an independent predictor of one-year all-cause mortality in mechanically ventilated septic patients. RVOT-FS was not associated with one-year mortality and added no prognostic value to TAPSE in these patients.

Association between left ventricular outflow tract opening and successful resuscitation after cardiac arrest

BackgroundSurvival after cardiac arrest depends on adequate cardiopulmonary resuscitation (CPR). Manual or mechanical external chest compression may be ineffective to restore circulation: structures subjected to external chest compression may differ in forces transfer to intrathoracic structures due to anatomic characteristics and physiological changes.This clinical study aims to assess the association of trans-oesophageal findings during CPR and successful resuscitation. MethodsRetrospective cohort study. Trans-oesophageal assessment of right ventricular fractional area change, right ventricular outflow tract fractional shortening, left ventricular volumes, ejection fraction, and aortic diameters were performed in refractory out-of-hospital cardiac arrest patients admitted to emergency department for extracorporeal CPR. Results19 patients were analyzed. 15 of 19 patients (79%) received venous-arterial extracorporeal membrane oxygenation support. Resuscitation was successful with return of spontaneous circulation or electromechanical activity in 7 patients (group-SUXX) and failed in 12 patients (group-FAIL). 6 patients (32%) were alive at 24 h from the cardiac arrest, one patient (5%) survived to hospital discharge. Left ventricular outflow tract (LVOT) was open during CPR in all patients in group-SUXX and in 1 patient in group-FAIL (p 0.0002). None of the patients with closed LVOT had successful resuscitation. Patients in group-SUXX had a higher ejection fraction (p 0.03), ascending aortic diameter (p 0.04), and survival rate than those in group-FAIL (p 0.015). In a multiple variable Cox’s proportional model LVOT opening was the only variable associated with successful resuscitation. ConclusionsTrans-oesophageal echocardiography can be useful in the emergency setting of cardiopulmonary arrest for discriminating between successful and failing resuscitation.

Assessment of right ventricular outflow tract fractional shortening as a measure of right ventricular function in chronic heart failure patients

Background: assessment of RV function is a major component of the management and prognostication of heart failure (HF) patients. Its complexity makes this task difficult and therefore not appropriately considered. Right ventricular outflow tract fraction (RVOT FS) can serve that purpose if done. The functional capacity of a HF patient must always be assessed and decision made on that basis. Aim of the study: this study aimed to investigate the applicability of RVOT FS in assessment of RV function and also its relation to functional capacity. Patients and methods: seventy-one (71) patients with heart failure with reduce ejection fraction (HFrEF) were studied prospectively and nineteen (19) control healthy individuals (normal ECG, normal left and right ventricular function and no cardiac risk factors). A 2D guided M-mode was taken in the parasternal short axis view to determine RVOT FS and a six-minute walk test (6MWT) was done to determine their functional capacity. Results: there was a reduced RVOT FS reduced in the HFrEF group (p value =0.005), 6MWT D was reduced in the HFrEF group (p value <0.001), there was a positive correlation of RVOT FS with RVFAC (r=0.839, p value<0.001) TAPSE (r=0.830, p value<0.001), S’(r=0.830, p value<0.001) 6MWT D (r=0.953, p value<0.001) and a negative correlation with RIMP(r=-0.867, p value<0.001), RV FLS(r=-0.878, p value<0.001), SPAP(r=-0.633, p value<0.001). 6MWTD with RVFAC (r=0.851, p value<0.001) TAPSE (r=0.825, p value<0.001), S’ (r=0.837, p value<0.001), RVOT FS (r=0.953, p value<0.001) and a negative correlation with RIMP (r=-0.827, p value<0.001), RV FLS (r=-0.902, p value<0.001), SPAP (r=-0.621, p value<0.001). RVOT FS between HF subgroups significant (p value<0.001). Conclusion: RVOT FS is a simple and reliable parameter that can be used in assessment of RV function and has very positive correlation with functional capacity assessed by 6MWT.

Right Ventricular Outflow Tract Fractional Shortening (RVOT FS) As Echocardiography Parameter for Assessment Right Ventricular Function in Systolic Heart Failure

Right Ventricular Outflow Tract Fractional Shortening (RVOT FS) As Echocardiography Parameter for Assessment Right Ventricular Function in Systolic Heart Failure

Assessment of right ventricular outflow tract fractional shortening as a measure of right ventricular function in chronic heart failure patients

Background: assessment of RV function is a major component of the management and prognostication of heart failure (HF) patients. Its complexity makes this task difficult and therefore not appropriately considered. Right ventricular outflow tract fraction (RVOT FS) can serve that purpose if done. The functional capacity of a HF patient must always be assessed and decision made on that basis. Aim of the study: this study aimed to investigate the applicability of RVOT FS in assessment of RV function and also its relation to functional capacity. Patients and methods: seventy-one (71) patients with heart failure with reduce ejection fraction (HFrEF) were studied prospectively and nineteen (19) control healthy individuals (normal ECG, normal left and right ventricular function and no cardiac risk factors). A 2D guided M-mode was taken in the parasternal short axis view to determine RVOT FS and a six-minute walk test (6MWT) was done to determine their functional capacity. Results: there was a reduced RVOT FS reduced in the HFrEF group (p value =0.005), 6MWT D was reduced in the HFrEF group (p value <0.001), there was a positive correlation of RVOT FS with RVFAC (r=0.839, p value<0.001) TAPSE (r=0.830, p value<0.001), S’(r=0.830, p value<0.001) 6MWT D (r=0.953, p value<0.001) and a negative correlation with RIMP(r=-0.867, p value<0.001), RV FLS(r=-0.878, p value<0.001), SPAP(r=-0.633, p value<0.001). 6MWTD with RVFAC (r=0.851, p value<0.001) TAPSE (r=0.825, p value<0.001), S’ (r=0.837, p value<0.001), RVOT FS (r=0.953, p value<0.001) and a negative correlation with RIMP (r=-0.827, p value<0.001), RV FLS (r=-0.902, p value<0.001), SPAP (r=-0.621, p value<0.001). RVOT FS between HF subgroups significant (p value<0.001). Conclusion: RVOT FS is a simple and reliable parameter that can be used in assessment of RV function and has very positive correlation with functional capacity assessed by 6MWT.

Evaluation of Heart Functions With Detailed Echocardiogram in Patients With Septum Deviation.

One of the most important reasons for nasal congestion is septum deviation. Nasal septal deviation increases airway resistance and can cause systemic problems. In this study, echocardiographic findings were compared with the normal population to see how cardiac function was affected in patients with obstructive nasal septum deviation. This study included a young patient group with 44 obstructive septum deviation patients and 30 healthy individuals with no nasal-related problems. Echocardiography was performed by the same cardiologist and results were compared with normal patients. The authors got permission from the ethics committee of faculty for the study (E. 116795). In the patient group with septum deviation, pulmonary artery pressure was high. In addition, the size of the right heart chambers was also increased. TAPSE, pulmonary acceleration time, ejection fraction, and right ventricular outflow tract-fractional shortening were found to be lower than the normal group. Patients with obstructive septum deviations should be evaluated early for cardiologic functions.

Right ventricular outflow tract fractional shortening: an echocardiographic index of right ventricular systolic function in dogs with pulmonary hypertension

ObjectivesTo create reference intervals for right ventricular outflow tract fractional shortening (RVOT-FS) in healthy dogs and examine diagnostic performance of this index in dogs with pulmonary hypertension (PH). In addition, we examine the impact of myxomatous mitral valve disease (MMVD) without PH on RVOT-FS. Animals, materials and methodsThe study population included 52 healthy adult dogs, 51 dogs with MMVD but without PH, and 51 dogs with PH. This is a prospective study. Complete echocardiographic evaluations were performed on all dogs. Right ventricular outflow tract fractional shortening was obtained by two-dimensional guided M-mode recordings from the right parasternal short axis view. Right ventricular outflow tract fractional shortening was evaluated in healthy dogs of various breeds, and reference intervals were generated. We examined the effect of PH on RVOT-FS with receiver operating characteristic analysis and evaluated the effect of MMVD on RVOT-FS in dogs without PH. Intraobserver and interobserver reproducibility was calculated. ResultsHealthy dogs had RVOT-FS > 44%. Right ventricular outflow tract fractional shortening values of healthy dogs and MMVD dogs without PH did not differ (p=0.84). In dogs with PH, RVOT-FS decreased with increasing tricuspid regurgitation velocity (p<0.0001). Pimobendan use in dogs with PH increased RVOT-FS as PH worsened. Right ventricular outflow tract fractional shortening was acquired with clinically acceptable intraobserver and interobserver reproducibility. ConclusionsRight ventricular outflow tract fractional shortening is a novel, easy applicable, and repeatable index for evaluating RV systolic function. Studies comparing this index with common echocardiographic indices used to assess RV function in dogs are needed.

Regression equations for calculation of z scores for echocardiographic measurements of right heart structures in healthy Han Chinese children.

Clinical decision making in children with congenital and acquired heart disease relies on measurements of cardiac structures using two-dimensional echocardiography. We aimed to establish z-score regression equations for right heart structures in healthy Chinese Han children. Two-dimensional and M-mode echocardiography was performed in 515 patients. We measured the dimensions of the pulmonary valve annulus (PVA), main pulmonary artery (MPA), left pulmonary artery (LPA), right pulmonary artery (RPA), right ventricular outflow tract at end-diastole (RVOTd) and at end-systole (RVOTs), tricuspid valve annulus (TVA), right ventricular inflow tract at end-diastole (RVIDd) and at end-systole (RVIDs), and right atrium (RA). Regression analyses were conducted to relate the measurements of right heart structures to 4body surface area (BSA). Right ventricular outflow-tract fractional shortening (RVOTFS) was also calculated. Several models were used, and the best model was chosen to establish a z-score calculator. PVA, MPA, LPA, RPA, RVOTd, RVOTs, TVA, RVIDd, RVIDs, and RA (R2 = 0.786, 0.705, 0.728, 0.701, 0.706, 0.824, 0.804, 0.663, 0.626, and 0.793, respectively) had a cubic polynomial relationship with BSA; specifically, measurement (M) = β0 + β1 × BSA + β2 × BSA2 + β3 × BSA.3 RVOTFS (0.28 ± 0.02) fell within a narrow range (0.12-0.51). Our results provide reference values for z scores and regression equations for right heart structures in Han Chinese children. These data may help interpreting the routine clinical measurement of right heart structures in children with congenital or acquired heart disease. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:293-303, 2017.

The relationship between right ventricular outflow tract fractional shortening and Pulmonary Embolism Severity Index in acute pulmonary embolism.

Right ventricular (RV) functions are clinically important in acute pulmonary embolism (APE). Measurement of systolic function of the right ventricular outflow tract (RVOT) with echocardiography is a simple method to evaluate RV function. The aim of this study was to determine the relationship between RVOT systolic function and the Pulmonary Embolism Severity Index (PESI). A total of 151 patients diagnosed with APE by pulmonary computed tomography angiography or ventilation/perfusion scintigraphy were included. Patients were assigned to 2 groups based on the simplified PESI (sPESI): sPESI <1 (n=85) and sPESI ≥1 (n=66). RV conventional parameters, RVOT dimensions, and fractional shortening (RVOT-FS) were also measured. Mean age was similar between sPESI <1 and >1 patients (58.7±12.9 years vs. 61.1±12.7 years, respectively). Frequency of male gender was significantly higher in PESI <1 group (61.2% vs. 40.2%, p=0.013). No significant differences were found between the groups in fasting glucose, serum creatinine, hemoglobin, C-reactive protein, erythrocyte sedimentation rate, troponin, and D-dimer levels, and left ventricular ejection fraction. RVOT-FS was higher in patients with sPESI <1 than in patients with sPESI ≥1 (34.41±3.56 vs. 22.98±4.22), and this difference was significant (p<0.001). Tricuspid annular plane systolic excursion values were lower and pulmonary artery systolic pressure values were higher in the sPESI ≥1 group, which was also statistically significant (p<0.05). Mortality occurred in 7 patients with sPESI <1 and in 16 patients with sPESI ≥1. The mortality rate was higher in patients with lower RVOT-FS, and a RVOT-FS <0.22 predicted mortality with a sensitivity of 54.5% (AUC: 0.674, 95% CI 0.552-0.796; p=0.009). The RVOT-FS is a noninvasive measurement of RV systolic function, is well-correlated with the sPESI score, and associated with mortality in patients with APE. This easily applied measurement may be used to predict short-term mortality in patients with APE.

Right ventricular outflow tract systolic excursion: a useful method for determining right ventricular systolic function.

Assessment of right ventricular (RV) systolic function is not an easy task. Although RV fractional area change (FAC) and tricuspid annular plane systolic excursion (TAPSE) are useful in the assessment of RV function, their use can be sometimes limited. Right ventricular outflow tract systolic excursion (RVOT_SE) is a new way to evaluate RV systolic function. The aim of this study was to assess the correlation between RVOT_SE and other RV systolic function assessment methods. RVOT_SE was defined as the systolic excursion of the RV outflow tract anterior wall endocardium. A total of 104 patients with a wide range of RV systolic function, ejection fraction, and pulmonary artery systolic pressure were studied. We also measured another four ways to evaluate RV systolic function, FAC, TAPSE, right ventricular outflow tract fractional shortening (RVOT_FS), and tricuspid annular systolic excursion velocity S' (Tissue S'). There was a strong correlation between RVOT_SE and each one of the four studied ways to evaluate RV systolic function. Multivariate regression analysis showed that the independent variables correlated with RVOT_SE were RVOT_FS (p<0.0001), FAC (p=0.005) and TAPSE (p=0.023). RVOT_SE diagnosed patients with reduced RV systolic function with 98% sensitivity and 96% specificity. There was no correlation between RVOT_SE and ejection fraction, or between RVOT_SE and pulmonary artery systolic pressure in patients with reduced RV systolic function. Intra-observer and inter-observer reproducibility were favorable for RVOT_SE and all four studied ways. RVOT_SE is a simple, accurate, and promising method for evaluating RV systolic function.

Bedside assessment of central venous pressure by sonographic measurement of right ventricular outflow-tract fractional shortening

We aimed to assess the suitability of right ventricular outflow tract (RVOT) fractional shortening for estimating low central venous pressure (CVP). To the best of our knowledge, there have been no similar studies in the English language literature. In this cross-sectional study, the emergency physicians measured the RVOT fractional shortening on parasternal short-axis view. A receiver operating characteristic curve analysis was conducted to identify the threshold that maximized the sensitivity and specificity for discriminating normal and low CVPs by the RVOT fractional shortening value. The sensitivity, specificity, and the positive and the negative likelihood ratios of RVOT fractional shortening to truly estimate CVP were calculated. Fifty-eight consecutive patients had invasive CVP monitoring. Nine patients with high CVP and eight for other reasons were excluded. Forty-one patients were enrolled in the study, of whom 21 were in low CVP group and 20 were in normal CVP group. RVOT diastolic diameters, RVOT systolic diameters, and RVOT fractional shortening were lower in low CVP group and this difference was statistically significant (P<0.001). The cutoff value for RVOT fractional shortening to differentiate the low and normal CVPs using the highest sensitivity and specificity was 26.44%. Area under the receiver operating characteristic curve was 0.933 (0.810-0.987) with a P value of less than 0.001. The sensitivity and specificity of RVOT fractional shortening to truly estimate CVP were 95 (75-99) and 80% (58-94), respectively. In the hands of emergency physicians, a RVOT fractional shortening measurement is a good predictor of low CVP.

Inter- and Intra-Observer Variability in the Echocardiographic Evaluation of Right Ventricular Function

Echocardiographic evaluation of right ventricular systolic function remains subject to debate because of the anatomic peculiarities of the right ventricle. Several methods have been developed for quantifying right ventricular systolic function. The aim of this study was to determine the reliability and reproducibility of a number of echocardiographic parameters by evaluating their inter-observer and intra-observer variability. The study included 30 patients with isolated mitral valvulopathy scheduled for heart surgery. All underwent echocardiography, which was performed independently by two echocardiographers within 24 hours. The intra-observer analysis was carried out using the recorded images at least 1 month after they had been obtained. The parameters studied were the tricuspid annular plane systolic excursion (TAPSE), the tricuspid annular peak systolic velocity on tissue Doppler imaging, right ventricular outflow tract fractional shortening, fractional shortening of right ventricular diameters, and fractional shortening of right ventricular areas. Variability was analyzed using the intraclass correlation coefficient. The degree of concordance on TAPSE and tricuspid annular peak systolic velocity measurement was good in the inter-observer analysis and excellent in the intra-observer analysis. However, concordance was poor on measurements of the fractional shortening of the right ventricular outflow tract, areas and diameters on both inter-observer and intra-observer analyses. The most reliable and reproducible echocardiographic parameters for evaluating right ventricular systolic function in patients with isolated mitral valvulopathy were the TAPSE and the tricuspid annular peak systolic velocity.

Evaluation of Right Ventricular Systolic and Diastolic Function in Patients with Newly Diagnosed Obstructive Sleep Apnea Syndrome without Hypertension

Objectives: We investigated right ventricular (RV) structural and functional cardiac alterations in obstructive sleep apnea (OSA) independent of systemic hypertension and their correlation to the severity of OSA. Methods: Forty-one moderate-to-severe OSA but otherwise healthy patients and 30 body mass index-matched control subjects were included. All subjects underwent 24-hour ambulatory blood pressure monitoring, standard and tissue Doppler imaging of the RV. Results: The OSA group had increased RV wall thickness, impaired right ventricular outflow tract fractional shortening (RVOT fs), tricuspid annular plane systolic excursion (TAPSE), RV myocardial performance index (MPI) and RV myocardial acceleration during isovolumic contraction (IVA) (p < 0.001). Apnea hypopnea index (AHI) and mean pulmonary artery (PA) pressure were correlated with all these indices (p < 0.01 for all). RV free wall thickness (p < 0.001) and IVA (p = 0.006) remained significant predictors of AHI after adjusting for age, body mass index, mean PA pressure, RVOT fs, TAPSE and MPI in a multiple stepwise linear regression model. Conclusions: OSA is associated with impaired RV function despite normal systemic blood pressures. The level of RV dysfunction has a direct relationship with the severity of OSA. RV free wall thickness and IVA are independent predictors of AHI in uncomplicated OSA patients.

Right ventricular outflow-tract fractional shortening: an applicable measure of right ventricular systolic function.

Assessment of right ventricular function is important. However, this is not easy to achieve due to the complex anatomy and geometry of the right ventricle, making the evaluation of its function limited. Therefore, a simple reliable and easy method is needed. This study was performed (1) to evaluate the use of right ventricular outflow tract fractional shortening obtained by M-mode echocardiography as a measure of right ventricular systolic function and (2) to determine the relationship between this parameter and other established measurements of right ventricular function such as long axis excursion. Ninety-two consecutive patients referred for echocardiographic assessment of left and right ventricular function, age mean+/-SD was 68+/-14 years, were investigated. Twenty healthy controls, age 46+/-12 years were also studied. M-mode echocardiography was used to measure right ventricular outflow tract fractional shortening and right ventricular long axis excursion. Doppler echocardiography was used for the estimation of right ventricular-right atrial pressure drop and pulmonary artery acceleration time. Right ventricular outflow tract fractional shortening (P<0.0001), right ventricular long axis excursion (P<0.0001) and pulmonary acceleration time (P<0.0001) were reduced in patients compared to controls. Right ventricular outflow tract fractional shortening correlated with long axis excursion (r=0.66 P<0.0001), pulmonary artery acceleration time (r=0.80 P<0.0001) and right ventricular-right atrial pressure drop (r=-0.53 P<0.0001). Right ventricular long axis excursion correlated with right ventricular-right atrial pressure drop though to a lesser significance (r=-0.27 P <0.001). Furthermore, right ventricular outflow tract fractional shortening was reduced in patients with pulmonary hypertension compared to patients without, this difference was not observed in the right ventricular systolic long axis excursion. Right ventricular outflow tract fractional shortening provides a simple and non-invasive measure of right ventricular systolic function. In combination with long axis excursion and Doppler velocities they should provide comprehensive assessment of right ventricular function.

Right Ventricular Outflow-Tract Fractional Shortening: An Applicable Measure of Right Ventricular Systolic Function

Aims: Assessment of right ventricular function is important. However, this is not easy to achieve due to the complex anatomy and geometry of the right ventricle, making the evaluation of its function limited. Therefore, a simple reliable and easy method is needed. This study was performed (1) to evaluate the use of right ventricular outflow tract fractional shortening obtained by M-mode echocardiography as a measure of right ventricular systolic function and (2) to determine the relationship between this parameter and other established measurements of right ventricular function such as long axis excursion. Methods and Results: Ninety-two consecutive patients referred for echocardiographic assessment of left and right ventricular function, age mean±SD was 68±14 years, were investigated. Twenty healthy controls, age 46±12 years were also studied. M-mode echocardiography was used to measure right ventricular outflow tract fractional shortening and right ventricular long axis excursion. Doppler echocardiography was used for the estimation of right ventricular–right atrial pressure drop and pulmonary artery acceleration time. Right ventricular outflow tract fractional shortening ( P <0·0001), right ventricular long axis excursion ( P <0·0001) and pulmonary acceleration time ( P <0·0001) were reduced in patients compared to controls. Right ventricular outflow tract fractional shortening correlated with long axis excursion (r=0·66 P <0·0001), pulmonary artery acceleration time (r=0·80 P <0·0001) and right ventricular–right atrial pressure drop (r=−0·53 P <0·0001). Right ventricular long axis excursion correlated with right ventricular–right atrial pressure drop though to a lesser significance (r=−0·27 P <0·001). Furthermore, right ventricular outflow tract fractional shortening was reduced in patients with pulmonary hypertension compared to patients without, this difference was not observed in the right ventricular systolic long axis excursion. Conclusion: Right ventricular outflow tract fractional shortening provides a simple and non-invasive measure of right ventricular systolic function. In combination with long axis excursion and Doppler velocities they should provide comprehensive assessment of right ventricular function. Copyright 2002 The European Society of Cardiology. Published by Elsevier Science Ltd. All rights reserved .