2015 Volume 79 Issue 4 Pages 735-741
Although echocardiography is a noninvasive means of visualizing the heart, quantitative and reproducible assessment of myocardial motion remains to be established. Tissue Doppler imaging (TDI) emerged in the early 1990 s as a tool to measure tissue motion velocity. For the purpose of analyzing regional myocardial motion quantitatively, the myocardial velocity gradient (MVG) across the myocardial wall was first introduced by using TDI. MVG is mathematically equal to strain rate. Initially, strain was derived as the time integral of the TDI-derived strain rate, but it revealed substantial errors of measurement, which basically arose from the confusion of Eulerian coordinates with Lagrangian coordinates in fluid dynamics. Speckle tracking echocardiography (STE) has subsequently emerged as a technique that analyzes motion by tracking “speckles” on echocardiograms based on Lagrangian coordinates. Although STE-derived strain is a robust parameter of myocardial deformation, the stress-strain relationship has often been overlooked in the assessment of myocardial function. We should consider (1) blood pressure, (2) left ventricular size, and (3) left ventricular wall thickness, as well as strain. Practical means of normalizing strain by stress should be pursued in the quantitative assessment of myocardial function. Consideration of stress-strain relationships is mandatory when interpreting STE-derived strain. (Circ J 2015; 79: 735–741)
Over the past decade, speckle tracking echocardiography (STE) has emerged as a non-Doppler, and thereby angle-independent technique that analyzes the motion of the myocardium.1–4 STE is based on a pattern-matching technique that utilizes patterns on black and white echocardiographic images created by reflections and interference of the ultrasound.5,6 In contrast to tissue Doppler imaging (TDI), which is based on the Doppler shift of the submitted ultrasound, and thereby is dependent on the Doppler angle of incidence,7 STE is angle independent. Numerous publications on STE have appeared to date, but use of STE is still limited to “high-tech” echocardiographic laboratories.8 Current echocardiography guidelines have not yet incorporated STE-based measurements, but have adopted spectral Doppler velocity measurements such as E/E’ for the assessment of diastolic function.9,10 Even after thousands of publications on STE in clinical settings, we do not yet know where STE is going. In this review, I will recollect the concept that led to the development of STE, and review the current issues in STE, in the hope that we can foresee the future direction of STE in clinical practice.
By analyzing ultrasonic images, 2-dimensional (2D) echocardiography enables us to obtain information of the morphology of the heart and the vessels. From a real-time analysis of the morphology, it also enables us to appreciate the motion of the heart. The addition of a Doppler technique further provides accurate assessment of the velocity of the blood flow.11,12 By applying the simplified Bernoulli equation, the pressure gradient between chambers separated by a thin wall with a small orifice can be obtained with substantial accuracy.12 In spite of all these advantages, what we cannot measure with echocardiography is the absolute pressure. We can estimate the pressure gradient, but cannot measure the pressure itself.
Another unsolved issue with current echocardiography is quantification of myocardial motion. We can visualize how the myocardium is moving, but quantification of regional wall motion is problematic. Semi-quantitative scoring methods remain the standard for assessing left ventricular (LV) wall motion.13
TDI has emerged in early 1990 s as a tool to measure tissue motion velocity. The ultrasound system that enabled the measurement of tissue velocity by modification of a color flow Doppler technique was developed concurrently by a European group and a Japanese group.14–18 In brief, a moving target indicator (MTI) filter, which eliminates signals of low velocity from the myocardium, is removed or minimized from the color flow Doppler system, and Doppler signals of high amplitude are selected.19 Because TDI measures the velocity of the myocardium against the ultrasonic transducer based on the Doppler shift, the velocity measured is in principle influenced by the Doppler angle of incidence as well as by the translational motion of the tissue against the transducer. Thus, velocity measured by TDI hardly represents regional myocardial motion quantitatively.20
For the purpose of quantitatively analyzing regional myocardial motion, Uematsu et al proposed the concept of the myocardial velocity gradient (MVG) across the myocardial wall on the 2D TDI plane using the parasternal LV short-axis view.21 MVG was defined as the difference in velocity normalized to the distance between the sample points in the myocardium.21,22 Practically, the velocity gradient (ie, the slope of the velocity curve with reference to the distance between the sample points in the myocardium) was determined by linear regression using the least-square method to minimize the error of estimation. A hypothetical center of contraction was used to determine the direction of the myocardial motion, and for correction of the Doppler angle of incidence. Figure 1 is a schematic drawing of a LV short-axis slice demonstrating the concept of MVG, defined as the difference in velocity between the endocardium (Vend) and epicardium (Vepi) divided by the myocardial wall thickness (L). It reflects the rate of change in myocardial thickness, thereby expressing the degree of regional myocardial contraction, independent of the parallel motion of the heart (Vh). In this way, myocardial contraction was quantitatively differentiated in various heart diseases by using the peak MVG.19–21,23–25 Interestingly, unlike velocity, MVG was validated to be independent of the translational motion as demonstrated in patients with atrial septal defect, because patients with uncomplicated atrial septal defect are known to have normal LV contraction with exaggerated translational motion of the left ventricle.20
Schematic drawing of a left ventricular short-axis slice demonstrating the concept of myocardial velocity gradient, defined as the difference in velocity between the endocardium (Vend) and epicardium (Vepi) divided by the myocardial wall thickness (L). It reflects the rate of change in myocardial thickness, thereby expressing the degree of regional myocardial contraction, independent of the parallel motion of the heart (Vh). Dashed lines denote ultrasound beam directions. Reproduced with permission from Uematsu M, et al.21
MVG is a spatial difference in velocity between 2 points in the myocardium normalized to the distance. Hence, MVG is equal to the rate of deformation between those points at a given time. Mathematically, MVG equals strain rate, which is a derivative of strain with respect to time. When it was introduced, MVG was limited to analysis on the LV short-axis view. Edvardsen et al developed a TDI technique that utilized the apical approaches to measure the LV longitudinal strain rate (ie, longitudinal MVG).26–29 They subsequently calculated strain as a time integral of strain rate. Numerous publications have appeared since the introduction of TDI-derived strain rate and strain.30–40
Strain refers to the deformation of an object, normalized to its original shape. Tensile strain ε is expressed as a fractional or percent change from an object’s original dimension: ε=∆l/l (Figure 2). Strain rate is a time derivative of strain. It is the speed at which the deformation occurs. Strain is a dimensionless parameter, whereas the strain rate has the dimension of s−1. Because a Doppler technique enables accurate measurement of velocity, dx/dt, with high temporal resolution, the instantaneous strain rate can be simply calculated as ∆V/L, where ∆V is the difference in velocity and L is the distance between the sample points. In order to calculate strain, the strain rate was integrated with respect to time. Strain was calculated by these 2 steps in the early years of development in TDI.41
Tensile strain refers to the deformation of an object (∆l), normalized to its original length “l”. It is expressed as a fractional or percent change from an object’s original dimension: ε=∆l/l. F, tensile force imposed on the object.
Investigators, however, soon noticed that TDI-derived strain curve did not return to the baseline after the cardiac cycle.41 There seemed to be an inherent error in the TDI-derived strain. At first, the error was attributed to a poor signal to noise ratio, as well as to Doppler angle dependence, but these were theoretically incorrect. Sugawara proposed a theory that elegantly explained why TDI-derived strain without a tracking technique was inaccurate (Scientific Meeting of the Japan Society of Ultrasonics in Medicine, Tochigi, 2004, personal communications).
Engineers, even undergraduate students of engineering, will be familiar with the Lagrangian and Eulerian coordinates in fluid dynamics,42 but these may sound alien to the medical community. In the Lagrangian coordinates (Figure 3A), we assume an infinite number of particles in the fluid. When an arbitrary particle is defined as x=a, t=0, it will be described as x=x(a, t) at any given time t. Velocity of the particle is given as ∂x/∂t; acceleration as ∂2x/∂t2. An example of Lagrangian coordinates seen in daily life is a satellite picture of the typhoons in the Pacific Ocean. We can track the motion of each typhoon at a glance from a satellite. It is an application of the Newtonian mechanics of a particle to flow dynamics. From the engineering point of view, however, it would take days or even weeks for a supercomputer of high specifications to calculate the motion of a large number of particles, and thus, mathematical application of the Lagrangian description to flow analysis is often impractical.
Comparison of Lagrangian and Eulerian coordinates in fluid dynamics. In the Lagrangian coordinates (A), when an arbitrary particle is defined as x=a, t=0, it will be described as x= x(a, t) at any given time t. In the Eulerian coordinates (B), flow velocity v is measured at fixed sample points: v=v(x, t), where, x1, x2, and x3 are the sample points, and t refers to time. Flow is described by giving the velocity of an arbitrary point at any given time. See text for details.
On the other hand, in the Eulerian coordinates, flow velocity v is measured at fixed sample points: v=v(x, t), where, x refers to the sample points, and t refers to time (Figure 3B). Flow is described by giving the velocity of an arbitrary point at any given time. In the Eulerian coordinates, multiple particles pass through the sample point, but we never track a particular particle. Eulerian coordinates are easily handled with mathematics. A good example includes a classic weather chart, on which data from many meteorological stations are displayed.
STE has emerged as a technique that analyzes motion by tracking “speckles” on 2D or 3-dimensional (3D) black and white echocardiograms. State-of-the-art review articles on STE are available.5,6,8,43 Speckles are produced by reflection and scattering of the ultrasound, but they do not exist as real structures. The image-processing algorithm tracks user-defined regions of interest that comprise blocks of approximately 20–40 pixels containing stable patterns described as “speckles”, “markers”, “patterns”, “features”, or “fingerprints”.1–4 Speckles are tracked consecutively frame to frame using a sum-of-absolute differences algorithm.5 The accuracy, validity and clinical applications of STE have rapidly been accumulating since its introduction.43–50
STE vs. TDIReaders may have already noticed from the preceding discussion that STE applies the Lagrangian coordinates, whereas TDI uses the Eulerian. In this regard, it is not surprising that the TDI-derived strain curve does not return to baseline after the cardiac cycle if there is no tracking technique involved. Thus, from the theoretical considerations, strain should be calculated by using STE, which is based on the Lagrangian coordinates. Nonetheless, TDI accurately measures instantaneous velocity with a high temporal resolution, and thereby the TDI-derived instantaneous strain rate is correct, apart from the angle-dependency issues. In order to calculate strain by TDI, which is based on the Eulerian coordinates, we must use a tracking technique to move the sample points before the time integration of strain rates, because the target object is moving at the measured speed (Figure 4). Displacement can be calculated as the time integral of the velocity, and subsequently the sample point can be moved toward the apex in the apical window (toward the hypothetical center of myocardial contraction) based on the displacement calculated. However, rather than applying such a cumbersome tracking technique with TDI, STE has made it simple to calculate correct strain based on the Lagrangian coordinates.
Source of error in strain measurement by tissue Doppler imaging (TDI). Although the instantaneous strain rate derived from TDI is correct, the time integral of TDI-derived strain rates does not yield strain. Strain rate is initially determined from v1 and v2 (Left), but after time=∆t, the strain rate is determined from the different particles, V2 and V3 (Right), because of the fixed sample points. A tracking technique is necessary for calculating strain from TDI-derived instantaneous strain rates. Blue squares denote the fixed sample points. L denotes the distance between the fixed sample points.
STE is thus superior to TDI in terms of the assessment of strain because STE is based on the Lagrangian coordinates as opposed to TDI, which uses the Eulerian coordinates. Nonetheless, STE has several limitations. (1) The accuracy of STE is dependent on the quality of the 2D image being analyzed. Images must have high-quality resolution to accurately track the region of interest. (2) The accuracy of STE is also dependent on the frame rate. Low frame rates result in unstable speckle patterns, whereas high frame rates reduce scan line density and reduce image resolution.5 (3) Unlike TDI, which is based on a principle in physics (ie, Doppler shift), STE depends on a 2D-tracking technique that uses a sum-of-absolute differences algorithm. The statistical nature of the algorithm comprises inherent errors, particularly when the images are of inadequate quality. (4) Another source of error in STE is the “through-the-plane” phenomenon (Figure 5), which arises from the discrepancy between the 3D nature of motion and the 2D nature of measurement. The motion of an object is expressed as a 3D vector, whereas 2D echocardiographic techniques, including STE, measure a vector projected on the 2D plane. Values obtained by the 2D techniques are different from those of real 3D vectors. Care should be taken to compare the values measured. If the echocardiographic slice is different, values measured are also different. The through-the-plane phenomenon affects all 2D echocardiographic techniques, including conventional 2D echocardiography, TDI and STE. (5) Speckles are lost to follow-up when they move out of the plane, particularly when a low frame rate is used. 3D STE should be a solution, but it has its own disadvantages, such as poor spatial resolution, low frame rate, and a heavy burden of calculations compared with 2D STE. (6) Speckles are not real structures, but are “artifacts” produced by ultrasound. The markers that STE depends on may not be stable, but are affected by the condition of the ultrasound used. Anyhow, we should be aware of these limitations, and should not interpret STE beyond its limitations.
“Though-the-plane” phenomenon. Green arrow represents a true velocity vector, which has a 3D nature. 2D echocardiographic techniques, including speckle tracking echocardiography (STE), tissue Doppler imaging, and conventional 2D echocardiography, merely measure 2D vectors projected on the image plane as indicated by the red arrow. Although STE is not Doppler angle dependent, we should be cautious when interpreting STE data quantitatively.
When we measure deformation of an object (ie, strain), we must also think of stress (ie, force per unit area imposed on the object). Considering strain alone without thinking of stress does not clarify the nature of the object because stress-strain relationships are not linear in biological materials, including the myocardium.51 In other words, the myocardium does not obey Hooke’s law. When we compare strain, we must concomitantly consider stress. Regrettably, the stress-strain relationship is often overlooked in many clinical STE studies, despite its importance, partly because of the inability of echocardiography to estimate absolute pressure.
Theory of PlasticityGoing back to basics is what we should do when we face difficulties. In order to fully describe the deformation of non-Hookean biological materials, we must consider 3 elements: (1) stress, (2) strain, and (3) motion, according to the theory of plasticity. We must thereby clarify the 3 relationships among them: (1) the stress-strain relationship, (2) the stress and motion relationship (the equation of motion), and (3) the motion and strain relationship (strain definition by motion) as shown in Figure 6. When the materials are not in motion, however, we only need to describe the stress-strain relationship. Such a condition is observed in the heart exclusively in both end-diastole and end-systole. During the ejection phase and the filling phase, we must consider all the elements, including stress, strain, motion and the relationships among them. This is why the analyses of the ejection phase, and in particular, of the diastolic filling phase, remain extremely difficult to perform even to date. Anyhow, it is important to emphasize that we must consider stress when we measure strain, even in resting states such as end-systole and end-diastole, but stress is often ignored when we measure strain in the clinical setting. This may be in part because of the complicated nature of stress imposed on the LV wall,52,53 in addition to the inability of echocardiography to measure absolute pressure.
Theory of plasticity. In order to fully describe the deformation of non-Hookean biological materials, we must consider 3 elements: (1) stress, (2) strain, and (3) motion, according to the theory of plasticity. We must thereby clarify the 3 relationships among them: (1) the stress-strain relationship, (2) the stress and motion relationship (the equation of motion), and (3) the motion and strain relationship (strain definition by motion). Considering strain alone is far from perfect in understanding the properties of materials.
From these theoretical considerations, the stress-strain relationship is indispensable for the assessment of myocardial function. However, stress imposed on the left ventricle is influenced not only by intraventricular pressure, but also by multiple factors such as the size, shape, and thickness of the left ventricle. LV wall stress is different from region to region even under the same intracardiac pressure. Hence, it is extremely difficult to exactly determine the distribution of LV wall stresses, and consequently the stress-strain relationships in the left ventricle. Nevertheless, an approximation based on the law of Laplace is a practical approach to estimating wall stress imposed on the myocardium, although limitations apply.53
According to the law of Laplace, wall tension T is expressed as T=(1/2)rP, where the left ventricle is simplified to be a sphere of the radius r, and the pressure is given by P. The equation is derived by considering the total force F imposed on the equatorial plane: F=πr2P, where F=2πrT. Therefore, πr2P=2πrT. Then, T=(1/2)rP.
Wall stress is expressed as S=T/Th, where Th is the thickness of the myocardial wall. Therefore, S is proportional to the size of the heart and the pressure, and is inversely proportional to the myocardial thickness. In this regard, when we compare strains, we must also compare the size and shape of the chamber, pressure, and the wall thickness of the particular region of the myocardium. Regrettably, these were often ignored in many clinical investigations where STE-derived strains are compared. Consideration of the size of the left ventricle, blood pressure, and the myocardial wall thickness is at least mandatory in evaluating strain by STE.
Currently, projects for obtaining normal values of strain by using STE are in progress.54–59 Normal values of strain, however, are of little use when the wall stress is different. Small hearts should have larger strains than large hearts. Thicker myocardium should demonstrate a larger strain than thinner myocardium. Those presenting with uncontrolled high blood pressure should have lower strain than the normotensive subjects. Those presenting with severe aortic stenosis should show improved strain after the aortic valve replacement even though the myocardial function does not differ significantly. Simply referring to the normal range is incomplete, if not useless.
Although innumerable publications on strain and strain rate have appeared to date, STE has not yet gained popularity in real-world cardiology practice. STE by itself is a robust technique that enables assessment of the deformation of the myocardium noninvasively and quantitatively. However, whether intentionally or inadvertently, many of the current publications on STE have overlooked the differences in stress imposed on the myocardium, concentrating merely on the strain, whereas consideration of the stress-strain relationship is the correct direction to proceed. According to the law of Laplace, we should consider (1) blood pressure, (2) LV size, and (3) LV wall thickness, as well as strain. Let us at least begin with considering these qualitatively. Care should be taken, for example, when we compare the strain from extremely large ventricles with that from small ventricles; when we compare strain with and without aortic stenosis; with and without hypertension; with and without LV hypertrophy. It may be difficult to evaluate LV stress concomitantly, but if strain could be quantitatively normalized to the wall stress, strain would become by far the clinically relevant pathophysiologic parameter to access myocardial function. I encourage all echocardiographic investigators to participate in research toward this direction.
STE is a robust non-Doppler, and thereby angle-independent technique, for the assessment of regional and global deformation of the myocardium. However, STE-derived strain and strain rate measurements have several limitations. Consideration of the stress-strain relationship is mandatory when interpreting STE-derived strain or strain rate in various clinical settings.
Names of Grants: None.
