Principles of Myocardial Mechanics and Strain Imaging

Velocities by Color Doppler

Myocardial velocity imaging was first introduced in the early 1990s. ^, Separation between velocities in the myocardium and in blood is possible because they have different signal amplitudes and Doppler frequencies, as illustrated in Fig. 2.1 .

Like color-flow imaging, TDI uses an autocorrelator technique to calculate and display multigated points of color-coded velocities along a series of ultrasound scan lines within a 2D sector. As illustrated in Fig. 2.2 , myocardial motion can be imaged as color-coded velocities superimposed on a 2D grayscale image in real time. The frame rate for 2D color Doppler imaging is typically 80 to 200 frames per second (fps), depending on the width of the ultrasound sector, and it is usually set higher than for the simultaneous grayscale images. Myocardial velocities are automatically decoded into numeric values, which can be stored digitally for later off-line analyses. By convention, velocities toward the transducer are color-coded red and velocities away from the transducer are coded blue. Fig. 2.3 shows recordings from a healthy person and from a patient with acute myocardial infarction (MI).

Assessment of LV function by TDI in parasternal short-axis views is possible, but only a very limited number of segments can be imaged ( Fig. 2.4 ). Therefore, apical views are usually preferred when assessing LV function by TDI.

Velocities by Pulsed Doppler

Another approach is to use spectral TDI with pulsed Doppler activation, which is applied mainly to measure mitral annular velocities ( Fig. 2.5 ). The velocity spectrum shows the distribution of velocities within the sample volume, and the myocardial velocity trace can easily be identified, even if clutter noise is present. It is important to be aware of spectral broadening (i.e., broadening of the velocity trace), which can lead to severe overestimation, depending on the gain setting (see Fig. 2.5B ). For color-mode TDI, mean velocities are used (see Fig. 2.5A ). The mean velocity trace is not affected by spectral broadening, but underestimation may result from clutter noise. This implies that velocities measured by the 2D color method described previously are lower than velocities measured by pulsed Doppler; a difference as high as 25% has been reported. To minimize overestimation in spectral TDI, it is recommended to adjust the gain as low as possible. In the example shown in Fig. 2.5B , the second beat is close to the optimal gain setting.

Peak early diastolic mitral annular velocity ( e ′) by pulsed Doppler is used in routine clinical practice as an index of myocardial relaxation and restoring forces. ^, Importantly, in adults, e ′ velocity decreases with age; therefore, age-based normal reference values should be used when applying these measures of LV diastolic function in clinical practice.

Basic Concepts

Strain means deformation. It is an excellent parameter for quantification of myocardial function. In principle, strain may also be used to assess diastolic function, but this application has not been well developed and is not yet recommended for routine diagnostics.

Quantification of myocardial function in terms of strain and strain rate has been available for a long time in cardiac physiology using implanted myocardial markers and for clinical research by magnetic resonance imaging with tissue tagging. Strain by echocardiography was first introduced as a TDI-based method ^, but was later replaced by 2-D strain using STE. Strain by STE is a more robust clinical method than strain by TDI, so the former has become the preferred modality in diagnostic routine.

In echocardiography, the term strain is used to describe local shortening, thickening, and lengthening of the myocardium. The term originates from the field of continuum mechanics and is used to describe a general three-dimensional (3D) deformation of a small cube during a short time interval. The strain tensor has six components: three numbers express the shortening along three orthogonal axes (x, y, and z), and three shared strain numbers give the skew in the x-y, x-z, and y-z planes. By dividing the myocardium into a large number of cubes, complex and detailed deformation can be described by one strain tensor for each small cube at each time during the cardiac cycle.

This description is, however, too detailed for practical use in echocardiography, where there is a need for a limited number of measurable parameters representing the average deformation within a segment of the myocardium. It is more convenient to use an internal coordinate system aligned with the three cardiac axes—longitudinal, circumferential, and radial—and to measure shortening and elongation in the three directions through the cardiac cycle, with reference to the size at the time of the QRS complex. If L(t) denotes the segment length along one of these directions at any time t in the cardiac cycle, one-dimensional strain ( ε ) is defined as the ratio between the change in length and the initial length (L ₀ ):

This is also called Lagrange strain . It is measured by the distance between two material points in the myocardium measured after contraction and relaxation. Fig. 2.6 illustrates schematically the principles for calculation of Lagrange strain. By convention, lengthening and thickening strains are assigned positive values, and shortening and thinning strains are given negative values, reported as a percentage. This implies that systolic shortening results in negative strains, and systolic thickening results in positive strains.

When evaluating LV systolic function, strain can be measured as peak systolic strain (positive or negative), as peak strain at end-systole (at the time of aortic valve closure), or as peak strain regardless of timing (in systole or early diastole). When using data from multiple segments to estimate global strain, end-systolic strain is the preferred measure, because this is what determines stroke volume.

The slope of the strain curve, called the strain rate (SR) also carries important information. Because strain is dimensionless, SR has units of 1 per second. Of special interest is the maximum slope in systole, as well as in early and late diastole. SR can be calculated from the time derivative of strain, which is given by the velocity difference ( v ₂ [ t ] − v ₁ [ t ]) between the end points of the segment L ( t ) :

This definition of strain rate is quite similar to the myocardial velocity gradient, also known as the Euler strain rate:

The only difference is in the denominator; in the first formulation, the velocity difference is compared with the initial segment length, whereas the velocity gradient uses the segment length at the same time instant as the velocity difference is measured. Myocardial velocity gradient was first measured by M-mode TDI to determine the rate of wall thickening. Later, velocity gradient measurement was combined with 2D TDI to image the longitudinal strain rate in the myocardium from apical views.

Starting with the Euler strain rate, strain can be calculated by time integration of SR from end diastole ( t = 0) to any time t in the cardiac cycle:

This version of strain, ε _N , is usually called natural strain, probably because of its relation with Langrange strain, ε, given by the natural logarithm function, ln, and τ is the variable of integration. In echocardiography, Euler strain rate is preferred over Lagrange strain rate because it is easier to calculate as a direct spatial derivative of myocardial velocity, without the need to track segment end points through the cardiac cycle. For strain measurements, Lagrange strain is the preferred method because it can be directly interpreted as shortening or elongation, as opposed to natural strain, for which the conversion formula ( Eq. 2.4 ) is needed.

Strain and Strain Rate by Tissue Doppler Imaging

In TDI, the velocity component along the ultrasound beam is measured at several spatial points simultaneously. By picking two velocity values, v ₁ and v ₂ , along the beam with a spatial distance L , the Euler strain rate SR( t ), or velocity gradient, can be calculated according to Eq. 2.3 for each TDI frame. The accuracy can be further improved by using several adjacent spatial points followed by linear regression. Using this concept, Heimdal et al. introduced real-time strain rate imaging based on myocardial Doppler velocities. Temporal integration of the velocity gradient gives the logarithmic strain estimate denoted natural strain (ε _N ) in Eq. 2.4 . Lagrange strain (ε) can be derived from natural strain using the mathematical conversion in Eq. 2.4 . To accurately determine strain, it is necessary to track and follow the motion of the material points (fixed particles) within the myocardium through time. This is not feasible with TDI, and therefore a small error is introduced, especially in the basal segments, where the motion relative to the ultrasound probe is highest.

The rationale for using spatial velocity gradient as a marker of myocardial function is that a velocity difference between two adjacent regions implies either compression or lengthening of the tissue in between, and the spatial velocity gradient equals the strain rate. When LV systolic function is studied in the LV long axis, strain rate measures the regional shortening rate, and strain measures the regional shortening fraction. In the LV short axis, strain rate measures the systolic thickening rate. During diastole, strain rate measures myocardial lengthening rate.

In principle, SR is not influenced by overall motion of the heart (translation) and only to a limited degree by motion caused by contraction in adjacent segments. This is in contrast to velocity within a myocardial segment, which is the net result of motion caused by contractions in that segment, motion due to tethering to other segments, and cardiac translation. ^, The effect of tethering explains why LV longitudinal velocities measured from an apical window increase progressively from the apex toward the base, whereas strains and strain rates are more similar.

Physical Principles of Speckle Tracking Echocardiography

STE measures local myocardial displacement in echocardiographic images and may be used to quantify myocardial function in terms of velocity and strain. Furthermore, STE may be used to assess LV rotation and twist. The speckles are created by interference of ultrasound beams in the myocardium and are seen in grayscale B-mode images as a characteristic speckle pattern. The speckles are the result of constructive and destructive interference of ultrasound waves, which are back-scattered from structures smaller than a wavelength of ultrasound. Random noise is filtered out by the computer algorithm, yielding small segments of myocardium with temporarily stable and unique speckle patterns. These segments, or kernels , serve as acoustic markers that can be tracked from frame to frame within an image plane using block matching.

Strain and Strain Rate by Speckle Tracking Echocardiography

In contrast to TDI-based strain, which measures velocities from a fixed point in space with reference to an external probe, STE measures the instantaneous distance between two kernels. Therefore STE can measure strain in different directions in the same image. The ability of STE to measure strain had been documented in studies using both sonomicrometry and magnetic resonance imaging as reference methods. Strain rate by STE can be calculated as the time derivative of the strain curve, followed by application of the conversion formula in Eq. 2.4 to obtain the Euler strain rate.

When applying STE, it is important to optimize the image quality of the grayscale image. This includes keeping the focus position at intermediate depth and adjusting the sector depth and width to include little but the region of interest. Assessment of 2D strain by STE is a semiautomatic method that requires a brief manual definition of a few points along the endocardial border. Furthermore, the sampling region of interest needs to be adjusted to ensure that most of the wall thickness is incorporated in the analysis and to avoid the pericardium. When automated tracking does not fit with the visual impression of wall motion, regions of interest need to be adjusted manually. End-systole is defined by aortic valve closure in the apical long-axis view, and this view should always be analyzed first.

Assessment of 2D strain by STE can be done successfully in multiple LV segments in most patients. Strain values are calculated for each segment (segmental strain) and as the average value of all segmental strains (global strain). Feasibility is best for longitudinal and circumferential strain; it is more challenging for radial strain because fewer speckles are present in this direction and the measured values in a normal ventricle differ substantially between inner and outer layers of the wall, reflecting a geometric effect. GLS is calculated as the average of the peak systolic longitudinal strain values from all LV segments in apical 4-, 3-, and 2-chamber views. Because longitudinal strain is normally negative, reporting of values can be confusing. Therefore, it is recommended to report changes in strain in absolute values.

In spite of different software in ultrasound machines from different vendors, GLS values are relatively similar. However, there are small differences in strain values among vendors and among different software packages from the same vendor. Therefore, when doing serial studies, such as observing effects of chemotherapy on LV function, this limitation needs to be taken into account, and one should preferably use a machine from the same vendor and with similar software when repeating studies in an individual patient. In normal hearts, typical absolute values for GLS are about 20%. The lower limit for normal GLS was found to be 15.9% in a large meta-analysis and 17.2% in a large multicenter study of healthy individuals. Therefore, in clinical practice, absolute values of GLS less than 16% to 17% indicate reduced LV systolic function.

It is also feasible to measure right ventricular (RV) strain by STE ( Fig. 2.7 ), but in some cases, speckle tracking of the thin RV lateral wall can be challenging. The same applies for the left atrium (LA), but here the signal quality is poorer due to low spatial resolution. A small structure in the image will blur out, with the amount of blurring given by the formula, (λ × depth)/probe aperture, where λ is the ultrasonic wavelength. Typical values for a 3-MHz cardiac probe are λ = 0.5 mm and aperture = 2 cm; this can result in a blurring of 3 mm in a 12-cm depth, and 4 mm in a 16-cm depth.

LA reservoir function (reservoir strain) by STE is measured from LV end-diastole (onset of QRS) to peak LA strain. LA reservoir strain is related to LA mean pressure and has been proposed as a supplementary index for estimating LV filling pressure ( Fig. 2.8 ). The cutoff for LA reservoir strain as a marker of elevated LV filling pressure has so far not been defined in appropriately designed studies.

In contrast to 2D STE, which cannot track motion occurring out of plane, 3D STE can track motion of speckles within the scan volume, regardless of its direction ( Figs. 2.9 and 2.10 ). One limitation of the 3D STE technique is its dependency on image quality and, in particular, its ability to define the endocardial border. Furthermore, 3D STE is limited by relatively low temporal and spatial resolution. Currently, technology for 3D STE strain imaging is developing rapidly, and it is expected to become an increasingly important modality.

LV Rotation and Twist

LV twist is the relative rotation of the apex around the LV long axis with respect to the base during the cardiac cycle; it can be measured by STE. ^, When viewed from apex to base, the apex rotates counterclockwise during systole, and the base rotates in the opposite direction. This is demonstrated in Fig. 2.11 , which shows LV rotation by STE in a healthy individual.

The rotation is expressed in degrees, and the apex-to-base difference in rotation is referred to as the LV twist angle (degrees). The term torsion is a normalized value and refers to the base-to-apex gradient in rotation angle, expressed in degrees per centimeter (°/cm) (see Fig. 2.11 ).