Is quantitative interpretation likely to increase sensitivity of dobutamine stress echocardiography? A study of false-negative results

Background: False-negative interpretations of do-butamine stress echocardiography (DSE) may be associated with reduced wall stress. using measurements of contraction, we sought whether these segments were actually ischemic but unrecognized or showed normal contraction. Methods. We studied 48 patients (29 men; mean age 60 +/- 10 years) with normal regional function on the basis of standard qualitative interpretation of DSE. At coronary angiography within. 6 months of DSE, 32 were identified as having true-negative and 16 as having false-negative results of DSE. Three apical views were used to measure regional function with color Doppler tissue, integrated backscatter, and strain rate imaging. Cyclic variation of integrated backscatter was measured in 16 segments, and strain rate and peak systolic strain was calculated in 6 walls at rest and peak stress. Results. Segments with false-negative results of DSE were divided into 2 groups with and without low wall stress according to previously published cut-off values. Age, sex, left ventricular mass, left ventricular geometric pattern, and peak workload were not significantly different between patients with true and false-negative results of DSE. Importantly, no significant differences in cyclic variation and strain parameters at rest and peak stress were found among segments with true-and false-negative results of DSE with and without low wall stress. Stenosis severity had no influence on cyclic variation and strain parameters at peak stress. Conclusions: False-negative results of DSE reflect lack of ischemia rather than underinterpretation of regional left ventricular function. Quantitative markers are unlikely to increase the sensitivity of DSE.

Patients with a hypertensive response to exercise have impaired systolic function without diastolic dysfunction or left ventricular hypertrophy

OBJECTIVES We sought to determine if a hypertensive response to exercise (HRE) is associated with myocardial changes consistent with early hypertensive heart disease. BACKGROUND An HRE predicts the development of chronic hypertension (HT) and may reflect a preclinical stage of HT. METHODS Patients with a normal left ventricular (LV) ejection fraction and a negative stress test were recruited into three matched groups: 41 patients (age 56 +/- 10 years) with HRE (210/105 mm Hg in men; > 190/105 in women), comprising 22 patients with (HT+) and 19 without resting hypertension (HT-); and 17 matched control subjects without HRE. Long-axis function was determined by measurement of the strain rate (SR), peak systolic strain, and cyclic variation (CV) of integrated backscatter in three apical views. RESULTS An HRE was not associated with significant differences in LV mass index. Exercise performance and diastolic function were reduced in HRE(HT+) patients, but similar in HRE(HT-) patients and controls. Systolic dysfunction (peak systolic strain, SR, and CV) was significantly reduced in HRE patients (p < 0.001 for all). These reductions were equally apparent in patients with and without a history of resting HT (p = NS) and were independent of LV mass index and blood pressure (p < 0.01). CONCLUSIONS An HRE is associated with subtle systolic dysfunction, even in the absence of resting HT. These changes occur before the development of LV hypertrophy or detectable diastolic dysfunction and likely represent early hypertensive heart disease. (C) 2004 by the American College of Cardiology Foundation.

Postsystolic thickening detected by Doppler myocardial imaging: A marker of viability or ischemia in patients with myocardial infarction

Background: Postsystolic thickening (PST) of ischemic myocardial segments has been reported to account for the characteristic heterogeneity or regional asynchrony of myocardial wall motion during acute ischemia. Hypothesis: Postsystolic thickening detected by Doppler myocardial imaging (DMI) could be a useful clinical index of myocardial viability or peri-infarction viability in patients with myocardial infarction (MI). Methods: Doppler myocardial imaging was recorded at each stage of a standard dobutamine stress echocardiogram (DSE) in 20 patients (16 male, 60 +/- 13 years) with an NIT in the territory of the left anterior descending artery. Myocardial velocity data were measured in the interventricular septum and apical inferior segment of the MI territory. Postsystolic thickening was identified if the absolute velocity of PST was higher than peak systolic velocity in the presence of either a resting PST > 2.0 cm/s or if PST doubled at low-dose dobutamine infusion. Results: Doppler myocardial imaging data could be analyzed in 38 ischemic segments (95%), and PST was observed in 21 segments (55%), including 3 segments showing PST only at low-dose dobutamine infusion. There was no significant difference of baseline wall motion score index (2.1 +/- 0.3 vs. 2.1 +/- 0.6, p = 0.77) or peak systolic velocity (1.1 +/- 1.1 vs. 1.9 +/- 2.0 cm/s, p = 0.05) between segments with and without PST Peri-infarction ischemia or viability during DSE was more frequently observed in segments with PST than in those without (86 vs. 24%, p < 0.05). The sensitivity and specificity of PST for prediction of peri-infarction viability or ischemia was 82 and 81%, respectively. Conclusions: Postsystolic thickening in the infarct territory detected by DMI is closely related with peri-infarction ischemia or viability at DSE.

Relationship between longitudinal and radial contractility in subclinical diabetic heart disease

Subclinical left ventricular (W) dysfunction may be identified by reduced longitudinal contraction. We sought to define the effects of subclinical LV dysfunction on radial contractility in 53 patients with diabetes mellitus with no LV hypertrophy, normal ejection fraction and no ischaemia as assessed by dobutamine echocardiography, in comparison with age-matched controls. Radial peak myocardial systolic velocity (S-m) and early diastolic velocity (E-m), strain and strain rate were measured in the mid-posterior and mid-anteroseptal walls in parasternal views and each variable was averaged for individual patients (radial contractility). These variables were also measured in the mid-posterior and mid-anteroseptal walls in the apical long-axis view and each variable was averaged for individual patients (longitudinal contractility). Mean radial S-m, strain and strain rate were significantly increased in diabetic patients (2.9+/-0.6 cm/s, 28+/-5% and 1.8+/-0.4 s(-1) respectively) compared with controls (2.4+/-0.7 cm/s, 23+/-4% and 1.6+/-0.3 s(-1) respectively; all P<0.001), but there was no difference in E-m (3.3&PLUSMN;1.2 compared with 3.1&PLUSMN;1.1 cm/s, P=not significant). In contrast, longitudinal S-m, E-m, strain and strain rate were significantly lower in diabetic patients (3.6&PLUSMN;1.1 cm/s, 4.3&PLUSMN;1.6 cm/s, 21&PLUSMN;4% and 1.6&PLUSMN;0.3 s(-1) respectively) than in controls (4.3&PLUSMN;1.0 cm/s, 5.7&PLUSMN;2.3 cm/s, 26&PLUSMN;4% and 1.9&PLUSMN;0.3 s(-1) respectively; all P<0.00 1). Thus radial contractility appears to compensate for reduced longitudinal contractility in subclinical LV dysfunction occurring in the absence of ischaemia or LV hypertrophy.

Tissue Doppler imaging for evaluation of myocardial function in patients with diabetes mellitus

Purpose of review Heart failure and diabetes mellitus are frequently associated, and diabetes appears to potentiate the clinical presentation of heart failure related to other causes. The purpose of this review is to examine recent advances in the application of tissue Doppler imaging for the assessment of diabetic heart disease. Recent findings Recent studies have documented that both myocardial systolic and diastolic abnormalities can be identified in apparently healthy patients with diabetes and no overt cardiac dysfunction. Interestingly, these are disturbances of longitudinal function, with compensatory increases of radial function-suggesting primary involvement of the subendocardium, which is a hallmark of myocardial ischemia. Despite this, there is limited evidence that diabetic microangiopathy is responsible-with reduced myocardial blood volume rather than reduced resting flow, and at least some evidence suggesting a normal increment of tissue velocity with stress. Finally, a few correlative studies have shown association of diabetic myocardial disease with poor glycemic control, while angiotensin converting enzyme inhibition may be protective. Summary Tissue Doppler imaging (and the related technique of strain rate imaging) appears to be extremely effective for the identification of subclinical LV dysfunction in diabetic patients It is hoped that the recognition of this condition will prompt specific therapy to prevent the development of overt LV dysfunction.

Determinants of exercise capacity in patients with type 2 diabetes

OBJECTIVE - Type 2 diabetes is associated with reduced exercise capacity, but the cause of this association is unclear. We sought the associations of impaired exercise capacity in type 2 diabetes. RESEARCH DESIGN AND METHODS - Subclinical left ventricular (LV) dysfunction was sought from myocardial strain rate and the basal segmental diastolic velocity (Em) of each wall in 170 patients with type 2 diabetes (aged 56 +/- 10 years, 91 men), good quality echocardiographic images, and negative exercise echocardiograms. The same measurements were made in 56 control subjects (aged 53 +/- 10 years, 29 men). Exercise capacity was calculated in metabolic equivalents, and heart rate recovery (HRR) was measured as the heart rate difference between peak and 1 min after exercise. In subjects with type 2 diabetes, exercise capacity was correlated with clinical, therapeutic, biochemical, and echocardiographic variables, and significant independent associations were sought using a multiple linear regression model. RESULTS - Exercise capacity, strain rate, Em, and HRR were significantly reduced in type 2 diabetes. Exercise capacity was associated with age (r- = -0.37, P < 0.001), male sex (r = 0.26, P = 0.001), BMI (r = -0.19, P = 0.012), HbA(1c) (AlC; r = -0.22, P = 0.009), Em (r = 0.43, P < 0.001), HRR (r = 0.42, P < 0.001), diabetes duration (r = -0.18, P = 0.021), and hypertension history (r = -0.28, P < 0.001). Age (P < 0.001), male sex (P = 0.007), BMI (P = 0.001), Em (P = 0.032), HRR (P = 0.013), and AlC (P = 0.0007) were independent predictors of exercise capacity. CONCLUSIONS - Reduced exercise capacity in patients with type 2 diabetes is associated with diabetes control, subclinical LV dysfunction, and impaired HRR.

Determinants of subclinical diabetic heart disease

Aims/hypothesis: Subclinical left ventricular (LV) dysfunction has been shown by tissue Doppler and strain imaging in diabetic patients in the absence of coronary disease or LV hypertrophy, but the prevalence and aetiology of this finding remain unclear. This study sought to identify the prevalence and the determinants of subclinical diabetic heart disease. Methods: A group of 219 unselected patients with type 2 diabetes without known cardiac disease underwent resting and stress echocardiography. After exclusion of coronary artery disease or LV hypertrophy, the remaining 120 patients ( age 57 +/- 10 years, 73 male) were studied with tissue Doppler imaging. Peak systolic strain of each wall and systolic (Sm) and diastolic ( Em) velocity of each basal segment were measured from the three apical views and averaged for each patient. Significant subclinical LV dysfunction was identified according to Sm and Em normal ranges adjusted by age and sex. Strain and Em were correlated with clinical, therapeutic, echocardiographic and biochemical variables, and significant independent associations were sought using a multiple linear regressionmodel. Results: Significant subclinical LV dysfunction was present in 27% diabetic patients. Myocardial systolic dysfunction by peak strain was independently associated with glycosylated haemoglobin level ( p< 0.001) and lack of angiotensin- converting enzyme inhibitor treatment ( p= 0.003). Myocardial diastolic function ( Em) was independently predicted by age ( p= 0.013), hypertension ( p= 0.001), insulin ( p= 0.008) and metformin ( p= 0.01) treatment. Conclusions/ interpretation: In patients with diabetes mellitus, subclinical LV dysfunction is common and associated with poor diabetic control, advancing age, hypertension and metformin treatment; ACE inhibitor and insulin therapies appear to be protective.

Myocardial and vascular dysfunction and exercise capacity in the metabolic syndrome

The metabolic syndrome (MS) is associated with cardiovascular risk exceeding that expected from atherosclerotic risk factors, but the mechanism of this association is unclear. We sought to determine the effects of the MS on myocardial and vascular function and cardiorespiratory fitness in 393 subjects with significant risk factors but no cardiovascular disease and negative stress echocardiographic findings. Myocardial function was assessed by global strain rate, strain, and regional systolic velocity (s(m)) and diastolic velocity (e(m)) using tissue Doppler imaging. Arterial compliance was assessed using the pulse pressure method, involving simultaneous radial applanation tonometry and echocardiographic measurement of stroke volume. Exercise capacity was measured by expired gas analysis. Significant and incremental variations in left ventricular systolic (s(m), global strain, and strain rate) and diastolic (e(m)) function were found according to the number of components of MS (p <0.001). MS contributed to reduced systolic and diastolic function even in those without left ventricular hypertrophy (p <0.01). A similar dose-response association was present between the number of components of the MS and exercise capacity (p <0.001) and arterial compliance. The global strain rate and em were independent predictors of exercise capacity. In conclusion, subclinical left ventricular dysfunction corresponded to the degree of metabolic burden, and these myocardial changes were associated with reduced cardiorespiratory fitness.' Subjects with MS who also have subclinical myocardial abnormalities and reduced cardiorespiratory fitness may have a higher risk of cardiovascular disease events and heart failure. (C) 2005 Elsevier Inc. All rights reserved.

Effect of exfoliation and dispersion on the yield behavior of melt-compounded polyethylene-montmorillonite nanocomposites

The yield behavior of melt-mixed nanocomposites containing 5 wt % organically modified montmorillonite in matrices of a linear low-density polyethylene (LLDPE) or a modified polyethylene was studied as a function of the temperature. and strain rate. In the melt-mixed LLDPE nanocomposite, the montmorillonite showed a slight increase in the clay spacing, which suggested that the clay was at best intercalated. Transmission electron microscopy (TEM) images showed that the dispersion in this nanocomposite was poor. The use of the modified polyethylene promoted exfoliation of the clay tactoids in the nanocomposite, as assessed by X-ray diffraction and TEM. In both nanocomposites, the yield mechanisms were insensitive to the addition of the organoclay, even though modest increases in the modulus were produced. (c) 2006 Wiley Periodicals, Inc.

What does the animal model teach us about the effects of physical activity on growing bone?

Experiments to design physical activity programs that optimize their osteogenic potential are difficult to accomplish in humans. The aim of this article is to review the contributions that animal studies have made to knowledge of the loading conditions that are osteogenic to the skeleton during growth, as well as to consider to what extent animal studies fail to provide valid models of physical activity and skeletal maturation. Controlled loading studies demonstrate that static loads are ineffective, and that bone formation is threshold driven and dependent on strain rate, amplitude, and duration of loading. Only a few loading cycles per session are required, and distributed bouts are more osteogenic than sessions of long duration. Finally, animal models fail to inform us of the most appropriate ways to account for the variations in biological maturation that occur in our studies of children and adolescents, requiring the use of techniques for studying human growth and development.

Association of subclinical right ventricular dysfunction with obesity

OBJECTIVES The purpose of this research was to identify the determinants of right ventricular (RV) dysfunction in overweight and obese subjects. BACKGROUND Right ventricular dysfunction in obese subjects is usually ascribed to comorbid diseases, especially obstructive sleep apnea. We used tissue Doppler imaging to identify the determinants of RV dysfunction in overweight and obese subjects. METHODS Standard and tissue Doppler echocardiography was performed in 112 overweight (body mass index [BMI] 25 to 29.9 kg/m(2)) or obese (BMI >30 kg/m(1)) subjects and 36 referents (BMI 35 kg/m(2) had reduced RV function compared with referent subjects, evidenced by reduced s(m) (6.5 +/- 2.4 cm/s vs. 10.2 +/- 1.5 cm/s, p < 0.001), peak strain (-21 +/- 4% vs. -28 +/- 4%, p < 0.001), peak strain rate (-1.4 +/- 0.4 s(-1) vs. -2.0 +/- 0.5 s(-1), p < 0.001), and e(m) (6.8 +/- 2.4 cm/s vs. -10.3 +/- 2.5 cm/s, p < 0.001), irrespective of the presence of sleep apnea. Similar but lesser degrees of reduced systolic function (p < 0.05) were present in overweight (BMI 25 to 29.9 kg/m(2)) and mildly obese (BMI 30 to 35 kg/m(2)) groups. Differences in RV e(m), s(m), and strain indexes were demonstrated between the severely versus overweight and mildly obese groups (p < 0.05). Body mass index remained independently related to RV changes after adjusting for age, log insulin, and mean arterial pressures. In obese patients, these changes were associated with reduced exercise capacity but not the duration of obesity and presence of sleep apnea or its severity. CONCLUSIONS Increasing BMI is associated with increasing severity of RV dysfunction in overweight and obese subjects without overt heart disease, independent of sleep apnea.

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

Radial artery pulse upstroke is not a good marker of left ventricular dysfunction: A comparison of radial tonometry, angiographic and echocardiographic measures of dP/dt

The first derivative of pressure over time (dP/dt) is a marker of left ventricular (LV) systolic function that can be assessed during cardiac catheterization and echocardiography. Radial artery dP/dt (Radial-dP/dt) has been proposed as a possible marker of LV systolic function (Nichols & O’Rourke, McDonald’s Blood Flow in Arteries) and we sought to test this hypothesis. Methods:We compared simultaneously recorded RadialdP/ dt (by high-fidelity tonometry) with LV-dP/dt (by highfidelity catheter and echocardiography parameters analogous to LV-dP/dt) in patients without aortic valve disease. In study 1, beat to beat Radial-dP/dt and LV-dP/dt were recorded at rest and during supine exercise in 12 males (aged 61±12 years) undergoing cardiac catheterization. In study 2, 2D-echocardiography and Radial-dP/dt were recorded in 59 patients (43 men; aged 64±10 years) at baseline and peak dobutamine-induced stress. Three measures at the basal septum were taken as being analogous to LV-dP/dt: (1) peak systolic strain rate, (2) strain rate (SR-dP/dt), and (3) tissue velocity during isovolumic contraction. Results: Study 1; there was a significant difference between resting LV-dP/dt (1461±383 mmHg/s) and Radial-dP/dt (1182±319 mmHg/s; P < 0.001), and a poor, but statistically significant, correlation between the variables (R2 = 0.006; P < 0.001) due to the high number of data points compared (n = 681). Similar results were observed during exercise. Study 2; there was a moderate association between baseline Radial-dP/dt and SRdP/ dt (R2 =−0.17; P < 0.01), but no significant relationship between Radial-dP/dt and all other echocardiographic measures analogous to LV-dP/dt at rest or peak stress (P > 0.05). Conclusion: The radial pressurewaveform is not a reliable marker of LV contractility.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.

Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.