Prediction of gradients in fibrous subaortic stenosis by continuous wave two-dimensional Doppler echocardiography: animal studies

Annuloaortic ectasia in a four-month-old male Newfoundland dog: long-term follow-up and immunofluorescent study

A 4 month-old, 14.8 kg, male Newfoundland dog was presented for cardiovascular evaluation following detection of a heart murmur. Echocardiography revealed enlargement of the sinuses of Valsalva and marked, diffuse dilation of the ascending aorta (annuloaortic ectasia, AAE), with mild/equivocal subaortic stenosis (SAS). The dog was monitored over the duration of its lifetime, with serial echocardiograms performed at 5, 6, and 8 months and 1, 2, 3, 4, 8, and 10 years demonstrating persistent, diffuse dilation of the ascending aorta. The dog lived until it was 10 years old and died of metastatic carcinoma. Postmortem examination confirmed AAE and mild SAS. Hematoxylin and eosin and Weigert van Gieson stains were used to compare the ascending aorta to the descending aorta and left subclavian artery, and to compare aortic samples to those of three control dogs. Histopathologic evaluation revealed mild medial degeneration in the ascending aorta of all four dogs. Immunofluorescent microscopy was used for determining the deposition of proteins known to play a role in aortic aneurysms in humans: fibrillin-1 (FBN1), latent transforming growth factor beta binding protein 4 (LTBP4) and fibronectin. The ascending aorta of the AAE case demonstrated reduced deposition of FBN1, indicating that its loss may have contributed to aortic dilation. Diffuse, primary ascending aortic dilation is uncommonly reported in dogs; when it is, it carries a poor prognosis. This case provides an important example of marked dilation of the ascending aorta in a dog that lived with no associated adverse effects for 10 years.

Echocardiographic follow-up of children with isolated discrete subaortic stenosis

This study evaluates the progression of stenosis, onset and progression of aortic regurgitation (AR), and the results of surgical outcomes in children with isolated discrete subaortic stenosis (SAS). The medical records of 108 patients (mean age, 5.5 +/- 3.8 years; range, 3 days to 18 years) with isolated discrete SAS were reviewed. Patients with lesions other than AR were excluded. Very mild stenosis was defined as Doppler peak systolic instantaneous gradient (PSIG) less than 25 mmHg, mild stenosis as 25-49 mmHg, moderate stenosis as 50-75 mmHg, and severe stenosis as more than 75 mmHg. Seventy-eight of 108 patients were followed for 2 months to 14 years (mean, 4.8 +/- 3.7 years; median, 5 years) with medical treatment alone. In these patients, the mean PSIG at last echocardiogram was higher than the mean PSIG at initial echocardiogram (39 +/- 19 vs 31 +/- 12 mmHg, respectively; p < 0.001). Among 24 patients with very mild stenosis at initial echocardiogram, 10 had mild and 2 had moderate stenosis after a mean period of 5.6 years. Among 46 patients with mild stenosis at initial echocardiogram, 11 had moderate and 5 had severe stenosis after a mean period of 4.1 years. Only 1 patient among the 8 patients with moderate stenosis at initial echocardiogram had severe stenosis after a mean period of 2.7 years. Thirty-nine patients (50%) had AR (13% trivial, 33% mild, and 4% moderate) at initial echocardiogram. After a mean period of 4.8 years, 77% of the patients had AR (10% trivial, 53% mild, 9% mild-moderate, and 5% moderate). Twenty-four patients underwent surgery. Preoperatively, mean Doppler PSIG and AR incidence were 64 +/- 17 mmHg and 91% (22/24), respectively. The mean Doppler PSIG was 30 +/- 19 mmHg and AR was present in all of the patients a mean period of 4.1 years after surgery. Two patients underwent reoperation for recurrent SAS and AR. Patients with very mild or mild stenosis may be followed noninvasively every year. One patient of the 8 patients with moderate stenosis progressed to severe stenosis, and moderate AR developed in 2 patients after a mean of 2.7 years. We recommend that patients with moderate stenosis undergo careful evaluation to determine whether surgery is necessary due to the severity of stenosis and AR.

Echocardiographic follow-up of children with supravalvular aortic stenosis

This study evaluates the course of supravalvular aortic stenosis (SVAS)-associated right ventricular outflow tract (RVOT) obstruction and the results of surgery in children. We reviewed the medical records of 24 patients diagnosed with SVAS at initial echocardiographic examination or during the following period of RVOT obstruction. Very mild SVAS was defined as a transvalvular Doppler peak systolic instantanous gradient (PSIG) less than 25 mmHg, mild stenosis as 25-49 mmHg, moderate stenosis as 50-75 mmHg, and severe stenosis as more than 75 mmHg. The mean age of the patients was 3.1 +/- 2.9 years (range, 7 days to 12.7 years), and 18 of the patients (72%) were male. Fifteen patients had Williams' syndrome. Seventeen patients (71%) were followed for a mean of 5.2 +/- 3.8 years (range, 7 months to 13.5 years). Among 17 patients with complete follow-up records, 1 (6%) had very mild, 5 (29%) mild, 3 (18%) moderate, and 3 (18%) severe aortic stenosis at initial echocardiographic examination. In a newborn patient with mild pulmonary valvular stenosis. SVAS became evident after 2 months and progressed rapidly. Supravalvular aortic stenosis was very mild in 4 patients (23%), mild in 3 (18%), moderate in 3 (18%), and severe in 7 (41%) at last echocardiographic examination. Of 17 patients who were followed, 11 (65%) had RVOT obstruction at initial echocardiographic examination. RVOT obstruction disappeared in 5 patients, regressed in 1 patient, and appeared in 1 patient over the follow-up period. Four patients underwent operation. It appears reasonable that patients with very mild and mild stenosis should be followed medically every 1 or 2 years and patients with moderate stenosis once a year. Newborns with SVAS should be followed for rapid progression of SVAS. In some patients, RVOT obstruction may disappear, and SVAS may develop in others with RVOT obstruction. Patients with RVOT obstruction (at the valvular, supravalvular, or peripheral pulmonary arterial level) should be evaluated carefully for development of SVAS at follow-up.

Screening for aortic stenosis in the Boxer: Auscultatory, ECG, blood pressure and Doppler echocardiographic findings

OBJECTIVES

This study was conducted to estimate the incidence of aortic stenosis (AS) in a group of Boxers evaluated by auscultation, ECG, blood pressure measurement and Doppler-echocardiography.

BACKGROUND

The Boxer is a breed at significantly increased risk of AS. The prevalence of murmurs and Doppler-echocardiographic findings consistent with AS in this breed is reportedly high.

ANIMALS, MATERIALS AND METHODS

Eighty-nine Boxers were evaluated by auscultation, and final murmur grade recorded after stress testing. Doppler echocardiography was performed in fifty-five adult Boxers. Electrocardiograms (ECG, n=53), non-invasive blood pressure measurement (n=32), and Holter monitoring (n=24) were performed in selected dogs. Degree of AS was based on the aortic peak flow velocity (Ao PFV). Final Ao PFV was recorded as the highest value obtained after stress testing. AS was defined as an Ao PFV>2m/s on continuous wave Doppler, using the subcostal window. Pressure gradients (Deltap) were calculated using the modified Bernoulli equation (Deltap=4V(2)). Mild AS was defined as Deltap=16-40mmHg, moderate AS Deltap=40-75mmHg, and severe AS Deltap>75mmHg.

RESULTS

62% of adult Boxers evaluated by echocardiography had an Ao PFV>2m/s suggestive of AS. Systolic basilar ejection murmurs were diagnosed in 73%. Murmur intensity showed a statistically significant correlation with Ao PFV (p<0.05). ECG abnormalities were only detected in dogs with severe AS.

CONCLUSION

The study reports on systolic murmurs and Doppler-echocardiographic findings consistent with AS, as well as ECG and blood pressure measurements in a sample of pure-breed Boxers.

Discrete subaortic stenosis in adults: increased prevalence and slow rate of progression of the obstruction and aortic regurgitation

OBJECTIVES

We sought to determine the prevalence and rate of progression of left ventricular outflow tract obstruction (LVOTO) and aortic regurgitation (AR) in adults with discrete subaortic stenosis (DSS).

BACKGROUND

Discrete subaortic stenosis is an uncommon form of LVOTO, with rapid hemodynamic progression in children, but the prevalence and rate of progression in adults have not been studied so far.

METHODS

The prevalence of DSS was determined in 2,057 consecutive adults diagnosed with congenital heart disease (CHD). The relationship between LVOTO on Doppler echocardiography and patient age was analyzed. Sequential changes in LVOTO and AR were determined for patients with two or more Doppler echocardiograms obtained with at least a two-year interval.

RESULTS

A total of 134 adults (mean age 31 +/- 17 years) were diagnosed with DSS. The prevalence was 6.5% for all adults with CHD. Sixty patients (44%) had other associated CHD. The mean age of 29 patients who had undergone an operation for DSS during their adult life (56 +/- 15 years) was significantly higher than that of 64 patients (27 +/- 13 years) who had not required a surgical intervention (p < 0.0001). A significant relationship between LVOTO and patient age (r = 0.61, p < 0.0001) was found: 21 +/- 16 mm Hg in patients <25 years old, 51 +/- 47 mm Hg for those between 25 and 50 years old, and 78 +/- 36 mm Hg for those >50 years old. The LVOTO increased from 39.2 +/- 28 to 46.8 +/- 34 mm Hg (p = 0.01) during a mean follow-up of 4.8 +/- 1.8 years in 25 patients. The slope of the change in LVOTO was 2.25 +/- 4.7 mm Hg per year of follow-up. Aortic regurgitation was detected by color Doppler imaging in 109 patients (81%), but it was hemodynamically significant in <20%. An increase in the mean degree of AR over time was not significant (baseline: 1.3 +/- 0.8; follow-up: 1.5 +/- 0.9; p = 0.096).

CONCLUSIONS

The prevalence of DSS is increasing in adults due to the greater number of repaired CHDs that develop into evolutive DSS. In contrast to infants and children, adults with DSS show a slow rate of LVOTO progression. Aortic regurgitation is a common but usually mild and nonprogressive consequence. The current indications for surgical intervention should be revised.

Progression of aortic stenosis in the boxer

Thirty-five boxers that had been referred to the Royal (Dick) School of Veterinary Studies between 1989 and 1994 with left heart base murmurs and aortic velocities greater than 1.5 m/second on Doppler echocardiography were recalled for clinical examination and Doppler echocardiography between 1995 and 1996. Five dogs (14 per cent) showed an increase in murmur grade on repeat visit. Six dogs (17 per cent) showed an increase in aortic velocity of greater than 20 per cent. Eight dogs (23 per cent) had developed aortic valvular or subvalvular two-dimensional echocardiographic changes that had not been present at the initial visit. Seven dogs (20 per cent) had developed aortic regurgitation, and three dogs (8 per cent) mitral regurgitation.

Prevalence of murmurs consistent with aortic stenosis among boxer dogs in Norway and Sweden

The prevalence and severity of cardiac murmurs consistent with subclinical or clinically detectable aortic stenosis among purebred boxer dogs in Norway and Sweden were evaluated. Two hundred and thirty-one boxers, randomly selected or investigated at dog shows, were examined by phonocardiography by two veterinarians and classified on the basis of the characteristics of their murmurs into categories 0 to 4. No murmur was detected in 23 per cent of the dogs, murmurs classified as category 1 were diagnosed in 25 per cent of the dogs, as category 2 in 46 per cent, as category 3 in 7 per cent cent, and two dogs had category 4 murmurs. In 55 per cent of the dogs, primarily those with very soft murmurs, there was some variation in the intensity of the murmur from beat to beat. The prevalence of cardiac murmurs among Norwegian and Swedish boxers was high and similar to the prevalence reported in Great Britain.

[Echocardiographic evaluation in unoperated congenital heart disease in adults]

Echo and Doppler echocardiographic procedures have gained special importance in the diagnostics of congenital diseases in adults. These procedures permit detailed visualization of the pathomorphology of the heart as well as reliable evaluation of the hemodynamic changes. There are differentiated indications for the various procedures, such as transthoracic and transesophageal echocardiography, Doppler and color-Doppler echocardiography, contrast echocardiography and 3-dimensional echocardiography. This article discusses the opposition of the various echo and Doppler echocardiographic procedures with respect to the diagnostics of the most frequent non-operated congenital diseases in adults. The pathomorphology of the various congenital diseases will be summarized and then the important echocardiographic criteria presented which are decisive for the diagnostic procedure. In simple congenital malformation of cardiac valves, such as bicuspid aortic valve (Figure 1: aortic ring abscess), pulmonary valve stenosis (Figure 2), Ebstein's anomaly (Figure 3) or malformations of the mitral valve (Figure 4: cleft in the anterior mitral cusp), the diagnosis can often be made using transthoracic echo and Doppler echocardiography, and the severity of the defect determined. However, the sonographic conditions, especially in adults, are frequently too limited to permit recognition of detailed smaller changes, so that transesophageal examination is required to finally confirm the diagnosis in these patients. In the diagnostics of diseases of the left ventricular outflow tract and the thoracic aorta, such as subvalvular aortic valve stenosis (Figure 5), the sinus of Valsalva aneurysm or the coarctation of the aorta (Figure 6), the left ventricular outflow tract can be evaluated morphologically from a transthoracic procedure and the accelerations of flow can be recorded by continuous wave Doppler. If there is no sclerosis of the fibrous membrane, these can often not be depicted by transthoracic procedures, so that a supplementary transesophageal examination is meaningful. This is required in any case for diseases of the descending thoracic aorta. In the case of congenital lesions, such as atrial septal defects (Figure 7: anomalous pulmonary venous return, Figure 8: 3-dimensional visualization of an atrial septal defect, Figure 9: sinus venosus defect), ventricular septal defect or a patent ductus arteriosus Botalli (Figure 10), color-Doppler and contrast echocardiography have become especially important. Transesophageal examination is also indicated for these congenital diseases for direct depiction of the defect as well as for precise evaluation of the shunt. Moreover, in atrial septal defects, it has been shown that a 3-dimensional echocardiography provides additional advantage with respect to spatial relationship of the defect to the other cardiac structures, as well as presenting dynamic changes during a heart cycle. Extensive knowledge of complex congenital heart disease, such as tetralogy of Fallot (Figure 11), complete transposition of the great arteries, congenitally corrected transposition of the great arteries (Figure 12), the double-outlet right ventricle, truncus arteriosus communis, the cor triatriatum, tricuspid atresia (Figure 13) or the univentricular heart (Figure 14) usually requires performance of a transthoracic echo- and Doppler echocardiographic examination to assess the pathomorphological changes and to examine hemodynamics. In the majority of patients, supplementary transesophageal echocardiography and an echo contrast examination are important. Initial examinations using 3-dimensional echocardiography are very promising in this connection and with respect to the exact spatial presentation of pathoanatomical structures.

Comparison of catheterization and Doppler-derived pressure gradients in a canine model of subaortic stenosis

The relationship between Doppler-estimated and catheterization-measured pressure gradients was examined by repeated-measures linear regression analysis and difference plots in 15 dogs with naturally occurring subvalvular aortic stenosis. Thirty left ventricular outflow tract gradients were compared during sinus rhythm and 142 gradients during premature or postextrasystolic beats for the following pairs of data: (1) mean catheterization gradient versus mean Doppler gradient, (2) maximal instantaneous catheterization gradient versus maximal Doppler gradient, and (3) peak-to-peak catheterization gradient versus maximal Doppler gradient. The correlation between Doppler-derived and catheterization-derived pressure gradients was excellent (r = 0.99; p < 0.001) for the maximal instantaneous (sinus rhythm: standard error of the estimate [SEE] = 5.7 mm Hg; premature and postextrasystolic beats: SEE = 6.7 mm Hg) and mean gradients (sinus rhythm: SEE = 3.6 mm Hg; premature and postextrasystolic beats: SEE = 4.5 mm Hg). There was also a strong correlation between the peak-to-peak catheterization gradient and the maximal Doppler gradient (sinus rhythm: r = 0.99, p < 0.001, SEE = 5.3 mm Hg; premature and postextrasystolic beats: r = 0.97, p < 0.001, SEE = 7.2 mm Hg). Agreement between the two techniques was best for mean gradients and most disparate for the comparisons of maximal Doppler gradients and peak-to-peak catheterization gradients.

The natural clinical history of canine congenital subaortic stenosis

The demographics and natural clinical history of canine congenital subaortic stenosis (SAS) were evaluated by retrospective analysis of 195 confirmed cases (1967 to 1991), 96 of which were untreated and available for follow-up evaluation. Of these, 58 dogs had left ventricular outflow systolic pressure gradients available for assessment of severity. All 195 dogs were used for demographic analysis. Breeds found to be at increased relative risk included the Newfoundland (odds ratio, 88.1; P < .001), Rottweiler (odds ratio, 19.3; P < .001), Boxer (odds ratio, 8.6; P < .001), and Golden Retriever (odds ratio, 5.5; P < .001). Dogs with mild gradients (16 to 35 mm Hg) and those that developed infective endocarditis or left heart failure were diagnosed at older ages than those with moderate (36 to 80 mm Hg) and severe (> 80 mm Hg) gradients. Of 96 untreated dogs, 32 (33.3%) had signs of illness varying from fatigue to syncope; 11 dogs (11.3%) developed infective endocarditis or left heart failure. Exercise intolerance or fatigue was reported in 22 dogs, syncope in 11 dogs, and respiratory signs (cough, dyspnea, tachypnea) in 9 dogs. In addition, 21 dogs (21.9%) died suddenly. Sudden death occurred mainly in the first 3 years of life, primarily but not exclusively, in dogs with severe obstructions (gradient, > 80 mm Hg; odds ratio, 16.0; P < .001). Infective endocarditis (6.3%) and left heart failure (7.3%) tended to occur later in life and in dogs with mild to moderate obstructions.(ABSTRACT TRUNCATED AT 250 WORDS)

Intraoperative echocardiography for surgical repair of the aortic valve and left ventricular outflow tract

Valve conservation surgery represents an exciting advance in the evolution of valve surgery. Recent studies have shown the significant advantages of mitral valve repair over valve replacement. While there are significant advantages for valve repair, the surgeon requires a greater understanding of the mechanism of valvular dysfunction prior to repair and requires an accurate means to assess the adequacy of the repair in the operating room immediately following the repair. Intraoperative echocardiography with color flow Doppler mapping provides immediate and accurate assessment of cardiac anatomy, hemodynamics, and valve integrity. These data are vital for optimal intraoperative surgical decision making. Intraoperative echocardiography has an important role in the evaluation in patients undergoing surgery to the aortic valve and left ventricular outflow tract by the delineation of presence and mechanism of left ventricular outflow tract obstruction, the quantification of severity of the left ventricular outflow tract gradient, the severity and mechanism of aortic regurgitation, the distribution and severity of left ventricular hypertrophy, and identification of associated lesions such as mitral regurgitation. Aortic valve conservation surgery is more complex than mitral valve surgery. The surgical techniques for aortic valve repair have been slower to evolve than mitral repair with a much smaller percentage of patients currently suitable for valve repair. However, with the aid of intraoperative echocardiography, the future shows similar promise that has already been fulfilled with mitral valve repair. Even in its infancy, intraoperative echocardiography has become indispensable to the innovative cardiac surgeon. However, without consideration of adequate echocardiographic training, incorrect echocardiography diagnoses can lead to inappropriate surgical decisions.

Use of Doppler echocardiography and amyl nitrite inhalation to characterize left ventricular outflow obstruction in hypertrophic cardiomyopathy

The presence of left ventricular outflow tract obstruction (LVOTO) of either a resting or dynamic nature may have important therapeutic and prognostic implications in patients with hypertrophic cardiomyopathy (HCM). Doppler echocardiograms combined with amyl nitrite (Amyl) inhalation were performed in 333 consecutive patients referred for suspected HCM to diagnose and categorize the nature and severity of LVOTO. Hypertrophic cardiomyopathy was present by 2-D and M-mode criteria in 145/333 (44 percent) patients. Normal limits of resting and post-Amyl continuous wave Doppler peak left ventricular outflow tract velocities were established in 15 subjects with completely normal 2-D and Doppler echocardiograms. Based on these criteria, of the 145 patients with HCM, 63 (43 percent) were classified as having resting LVOTO, peak velocity 4.2 +/- 1.3 m/s. Among 82 patients with HCM without resting LVOTO, 47 (57 percent) received Amyl. Latent LVOTO was provoked in 25/47 (53 percent), peak post-Amyl velocity 4.5 +/- 1.2 m/s. The remaining 22 (47 percent) had nonobstructive HCM, as indicated by no significant increase in post-Amyl velocity. Among a total 62 subjects receiving Amyl, none experienced serious morbidity or mortality. Doppler echocardiography, in conjunction with Amyl inhalation in selected patients, is a useful noninvasive method to diagnose and categorize patients with HCM according to the nature and severity of LVOTO.

Quantitative applications of Doppler cardiography in congenital heart disease

Doppler ultrasound has rapidly become a valuable tool in the noninvasive investigation of cardiac hemodynamics. Although based on secure principles, accurate application of this methodology to quantitative measurements necessitates a thorough understanding of both Doppler physics and instrumentation. Over the past several years a large body of clinical and animal data verifying the accuracy of Doppler determination of pressure and flow data at various sites in the cardiovascular system, as well as the potential sources of error in acquisition and interpretation of blood velocity recordings, has been published. Quantitative use of Doppler in congenital heart disease, with emphasis on limitations of existing studies and issues particular to this patient population, is reviewed.

Continuous-wave Doppler velocities and gradients across fixed tunnel obstructions: studies in vitro and in vivo

The simplified Bernoulli relationship appears to be quite accurate for predicting gradients across discrete valvular obstructions. Controversy exists about how accurately it predicts the severity of disease in longer segment obstructions. In this study we constructed a pulsatile model of subvalvular pulmonary stensosis in vitro to study nine custom-made subvalvular tunnels 2, 4, and 7 mm in length with flow cross sections of 0.5 to 1.5 cm2 and with the stenotic segment proximal to a nonstenotic bioprosthetic valve, and a pulsatile model in vitro of a 16 mm long tunnel-like ventricular septal defect (VSD) of varying cross-sectional area (0.20 to 0.64 cm2). We also compared the observations in vitro with those in an open-chest dog preparation with a tunnel-like interventricular communication. In the subpulmonic stenosis model, for each individual tunnel, 10 instantaneous peak gradients between 15 to 105 mm Hg were available. The pressure gradients across the tunnel alone, measured in the subvalvular area, were consistently higher than the measured gradients across the tunnel plus valve, suggesting some relaminarization of flow (i.e., a decrease in velocity) and pressure recovery (i.e., an increase in pressure) distal to the obstruction. Continuous-wave Doppler velocities across the 4 and 7 mm tunnels for the highest gradients were slightly lower than for the 2 mm tunnel at the same gradients, and it was only for the 0.5 cm2 cross section, 4 and 7 mm tunnels that there was a suggestion of minor viscous energy loss. For all the subvalvular tunnels studied, the Bernoulli relationship accurately predicted the results of the pressure drop across the tunnel only, while the gradient across tunnel plus valve was consistently lower. For the VSD tunnel model in vitro, the Doppler-derived gradients were approximately 40% higher than the measured gradients. The findings for the subvalvular and VSD tunnels in vitro and similar findings in the open-chest dogs with VSD suggest that relaminarization of flow and recovery of pressure occurred distal to the tunnel orifice, whereas continuous-wave Doppler findings correlate with the highest instantaneous gradients measured in the lowest pressure areas at the vena contracta of the tunnel.

Intraoperative Doppler echocardiography in hypertrophic cardiomyopathy: correlations with the obstructive gradient

Although significant pressure gradients can be recorded across the left ventricular outflow tract in patients with hypertrophic cardiomyopathy, controversy exists regarding the presence or absence of true obstruction. Ten patients with hypertrophic cardiomyopathy were studied at the time of septal myectomy. A sterile continuous wave Doppler transducer was placed on the ascending aorta and directed toward the left ventricular outflow tract to measure velocity simultaneously with invasive gradient measured using solid-state hub transducers by direct puncture of the left ventricle and aorta. Simultaneous Doppler velocity and invasive gradient measurements (n = 33) were made at rest, before and after myectomy and during interventions with isoproterenol, volume loading and phenylephrine. High velocity flow with a characteristic contour was recorded in patients with a significant gradient. Using the modified Bernoulli equation (gradient = 4 X velocity), a good correlation was found between the Doppler-derived gradient and the peak instantaneous gradient measured invasively (r = 0.93, y = 0.89X + 12, p = 0.0001). Changes in gradient and velocity due to interventions also correlated well (r = 0.96, y = 0.91X - 3, p = 0.0001). Continuous wave Doppler echocardiography can accurately estimate the outflow tract gradient. The magnitude, timing and contour of these high velocity flow signals support the hypothesis that true obstruction is present in patients with hypertrophic cardiomyopathy who have a significant gradient.