Det medisinske fakultet

Strain rate imaging.

Cardiac deformation imaging by ultrasound / echocardiography

- Tissue Doppler and Speckle tracking

by Asbjørn Støylen, dr. med.

Contact address: asbjorn.stoylen@ntnu.no

Introduction for the novice researcher and curious clinician.


Website updated: February 2010.     This section updated: February 2010.
    


The website is formatted for a screen resolution of 1024 by 768 pixels (meaning that it shouldn't be less, as the pictures will then be cut off at the right side). Some of the animations may upload slowly or not at all by the first try, and remain motionless. Usually, just clicking the view reload /refresh button will correct this.

Recent updates:




January 2010: Happy new year.

Added a comparison between different methods for strain and strain rate measurement that was recently published. The pitfalls and limitations section have been slightly updated according to this.February 2010: Added a paragraph on the comparison of cavity measurements (Fractional shortening and Ejection fraction) and strains in three dimensions. Still harping on that, as there is a fundamental difference, as illustrated.

December 2009:

A paragraph comparing three main methods for deformation imaging; velocity gradient, speckle tracing in the form of 2D strain and segmental strain has been added, and the discussion on the speckle tracking application has been extended. The tree approaches are pricipally different, and may yield different measure values.  This keys into a new general paragraph on validity and reliability in the clinical utility section.
Perhaps the most important addition this time, is the table of normal values, based on the data from 1266 normal subjects in the HUNT study that is given below, and described in more detail in the clinical utility section.

Introduction

The website has existed for three and a half year, but even so, it remains unfinished. In fact, it probably will be developing all the time.  So far, much of the important fundamental experimental work is not yet mentioned as the section on physiology remains rudimentary. Other sections are also unfinished. Also, due to the increasing documentation and number of publications and the development of the technique, new sections will have to be added and others to be revised. New sub sections will also be added with irregular intervals.

For this website to become useful, we will depend on reactions from the readers. Please feel free to mail any suggestions, comments or questions. Don’t hesitate to complain if something is unclear or wrong, or if there are specific omissions. We also welcome discussion and disagreement.

The internet is free, so feel free to use the examples found on this website in demonstrations and lectures. However, ordinary ethics dictates that credit should be given to the author. Remember also that your audience may have visited this website too, or I might even have been at the same congress. As I was on the Euroecho in 2009, in the lecture #519 "How does deformation relate to contractility and myocardial function? " by J.E.S.Azevedo of Cascais-Portugal. I saw several of the pictures from this website, without acknowledgement. And I do not consider changing the colours to be sufficient to claim originality, as long as the source is not acknowledged. Although some of the figures have an embedded signature,  I don't think that is sufficient acknowledgement, the website should be acknowledged, preferably with the complete web address.
For publishing, I and the Norwegian University of Science and Technology retain the copyright to all material published here.



About the website:


The website is divided into sections, in order not to be too slow in downloading. In order to make it easier to navigate, this section is furnished with a complete index (website index) with links, of all sections including sub headings in each section . All other sections are furnished with the section index only, but at the end of each section index, as well as at the end of each section, there is a link back to the full website index in this section, as well as back to the section index of the same section.

This main section deals with history and basic terms. AS other sections are elaborated, this section may be seen as an introduction and overview. The section on parametric imaging focus on the methods for parametric imaging, and how this can be applied to strain rate imaging. How to use strain rate imaging is a section that will deal with the basic approach to how to interpret the curves, what is documented of clinical value and most important, the problems and pitfalls inherent in the method
and how to deal with them. Physiology will deal with with basic principles of left ventricular mechanics and new physiological and pathophysiological knowledge gained by the method, as well as experimental research. Mathematics of Strain Rate Imaging is intended to give a more in depth treatment of some of the concepts, for specially interested. However, still on a basic level intended for medical personnel, higher mathematical background is not required, and mathematicians and engineers will find it embarrassingly simple. There will also be a section on basic principles of ultrasound and scanner technology. Again not for technologists, but a basic understanding will give more insights in the limitations of the method and the basis for the pitfalls. Finally, all references are in a separate section.



It is important to note that at present there are several companies that are introducing velocity, displacement, strain rate and strain imaging based on grey scale information, using speckle tracking as well as other grey scale information in advanced mathematical treatments. And in addition experimental work is being done in using tracking in RF data as well.
Thus, the terms: - Velocity imaging, - Displacement imaging, - Strain rate imaging, - Strain Imaging, should not be taken synonymous with tissue Doppler, but should be used irrespectively of the method employed, and the term "by tissue Doppler",  "by speckle tracking" or whatever application is used should be added.
General principles of motion (velocity and displacement) vs. deformation (strain rate an\ad strain) apply, although each method may have different limitations and pitfalls, for tissue Doppler typically angle deviation and lateral resolution, for grey scale imaging typically frame rate. Thus some of what is said in this web site will be relevant only for tissue Doppler, but the new methods will be treated in more detail as the documentation is forthcoming.



Website index:

This section:

Other sections:


Normal values for strain and strain rate from the HUNT study



Female
Male

End systolic strain (%)
Peak systolic strain rate
End systolic strain Peak systolic strain rate
< 40 years
-17.9% (2.1)
-1.09s-1 (0.12)
-16.8% (2.0)
-1.06s-1 (0.13)
40 - 60 years
-17.6% (2.1)
-1.06s-1 (0.13) -18.8% (2.2)
-1.01s-1 (0.12)
> 60 years
-15.9% (2.4)
-0.97s-1 (0.14) -15.5% (2.4)
-0.97s-1 (0.14)
Over all
-17.4% (2.3)
-1.05s-1 (0.13) -15.9% (2.3)
-1.01s-1 (0.13)
 
The customary definition of normal values as mean ± 2SD, giving about 95% of the normal population, results in wider normal limits than previously shown as cut off values in small patient studies. The values were normally distributed, and with no clinically significant differences between levels or walls.

The table is based on 1266 healthy subject from the HUNT study by Dalen et al (153). The study is decribed in somewhat more detail in the clinical utility section.

Introduction

A detailed treatment of the field can be read in my thesis: Strain rate imaging of the left ventricle by ultrasound. Feasibility, clinical validation and physiological aspects. NTNU 2001, although it  may be somewhat out of date and the engineering thesis of Andreas Heimdal: Doppler based ultrasound imaging methods for non-invasive assessment of tissue viability. NTNU 1999. A detailed treatment of some of the problems from a mathematical engineering point of view, but with much information relevant for the clinician can be found in a recent doctoral thesis: Camilla Storaa. Reproducibility and Interpretation in Tissue Doppler Echocardiography. Doctoral thesis, Stockholm, 26th July 2004



First, a word of caution:
The method has severe limitations, resulting in problems and pitfalls that is treated in detail in a separate section. When reading the results of studies in strain rate imaging, it is important to know that  post  processing is operator (expert) dependent and may introduce a bias, when data are analysed unblinded. Feasibility and initial clinical studies are often unblinded, being pilots to assess the possibilities of a new method. Such studies should be confirmed by studies with blinded analysis, and with repeated measurements, and information should always include how much post processing necessary to achieve a high repeatability before the results to be transferred to clinical use. And in addition, data are often not processed unblinded to the grey scale images anyway, even if blinded to diagnosis or reference method. This means that operator dependent processing may bring out normal curves where function looks normal, abnormal curves where function looks abnormal. This means that most about strain rate imaging is about the added value of the method, compared to 2D echocardiography. On the other hand newer studies with automated analysis tells about the independent informational value of the method.






 Fig 1. Strain rate and strain of one heart cycle in the interventricular septum of a normal subject. To the left is a curved M-mode along the wall, apex on top, basis on the bottom. It is a parametric image, showing positive strain rate (lengthening in diastole) in cyan to blue, negative strain rate (shortening in systole in yellow to red). To the right are the curves from the apical, midwall and basal parts of the septum, levels on the M-mode roughly corresponding to the positions on the M-mode. Far left are the strain curves from the same points, obtained by integration of strain rate. The initial elongation occurs in the mid septum, resulting in initial negative velocities in mid and basal segments before aortic closure. This corresponds to the protodiastolic period, between end ejection and the final closure of the aortic valve, where a small backflow actually pulls the cusps together. ©A. Støylen.


History





Fig 2:  The two first strain rate images, left from a normal person, right from a patient with inferior infarction. The original term was “strain velocity imaging” (SVI), later changed to the more correct Strain Rate Imaging (SRI), as strain rate is not velocity. The original colour scale was inverted, positive strain rate in red, negative in blue. Both images show an M-mode along one wall, apex on top, base at the bottom. At that time only straight M-mode was used. ©A. Støylen.

The method of strain rate imaging by tissue Doppler was developed here at the Norwegian University of Science and Technology in Trondheim, Norway. It was the subject of two doctoral theses, one in technology (1) and one in medicine (2), and was a result of a successful cooperation between technical research (in strain and velocity gradients) and medical research (in long axis function of the left ventricle). One of the important point of my work with long axis function, was that this lead to Strain Rate Imaging being applied to longitudinal velocity gradients, thus making the rough method more robust, as well as all segments of the ventricle available for analysis. The method was originally validated in a mechanical model, in cooperation with the university of Leuven, Belgium (3) and described in a method article from Trondheim in 1998 (4) and 2000 (5). The basic publications dealt with feasibility (1998) ( 4), clinical validation by comparison with echocardiography (6) and with coronary angiography (7). Validation of strain measurements (from integrated strain rate) was done at Rikshospitalet, Oslo, Norway by comparison with ultrasonomicrometry (8) although basically only for averages, with  wide limits of agreement ca. ± 10%.  The high correlation between the methods given in the paper does not agree with this, and is unrealistic, as the data are widely separated into two distinct situations of normal with and without volume loading with negative strain values and ischemia with positive strain, as discussed here. It is also validated against MR, in cooperation with Johns Hopkins Hospital (9). Early work on the feasibility of the method in myocardial infarction was also done at the university of Linköping and later at Leuven (10). An excellent early review paper was published by the Leuven group (11).

Technical improvements in strain rate imaging:

The first application shown above, was acquired blindly, and post processed into colour pictures. The numerical values could not be extracted, only estimated on the basis of colour images, and of course traces were unavailable. In addition, the colour scale was inverted, as shown above. As the method was intended for long axis use, we thought that the present colour scheme was better, as this lead to orange systole and cyan diastole similar to the red/blue of velocity imaging, although sufficiently different to distinguish the two modalities.

In the original post processing application  no smoothing was applied. That meant that the original studies were done by visually correcting for noise. Later temporal smoothing, and in the latest software (from about 2002), the Gaussian smoothing is implemented. In addition, the strain rate algorithm has moved from a simple subtraction algorithm back to the original (14) regression method, resulting in a more robust strain rate estimate. The tissue Doppler data can now also be acquired in the second harmonic mode, which may give an advantage in dealing with reverberations.

Now, it is important to emphasize that both motion and deformation imaging are no longer simply tissue Doppler derived modalities. Both can be derived by tracking the motion of the myocardium in grey scale pattern, speckle tracking. The basic concepts are the same, but the limitations may differ between the methods, for tissue Doppler typically angle deviation and lateral resolution, for grey scale imaging typically frame rate.

The terms: - Velocity imaging, - Displacement imaging, - Strain rate imaging, - Strain Imaging, should not be taken synonymous with tissue Doppler, but should be used irrespectively of the method employed, and the term "by tissue Doppler",  "by speckle tracking" or whatever application is used should be added.

Thus some of what is said in this web site will be relevant only for tissue Doppler, but the new methods will be treated in more detail as the documentation is forthcoming.


Finally, the two methods can be combined, used in an automated analysis, and the results are promising (127).

Basic concepts



Motion and deformation 
Strain
Incompressibility
Strain rate

Motion and deformation:

When considering the different modalities of echocardiography, the distinction between motion and deformation imaging is important. Displacement and velocity are motion, while strain and strain rate are deformation. A moving object does not undergo deformation so long as every part of the object moves with the same velocity. The object may then be said to have pure translational velocity, but the shape remains unchanged. Over time, the object will change position – displacement. On the other hand, if different parts of the object have different velocities, the object has to change shape. Then, the motion of the different parts can be described by their velocity and displacement, while the whole object can be described as undergoing deformation. This is illustrated below.



a.
The engine and the coaches all run with the same velocity. The engine permanently The engine keeps the connectors between the coaches stretched to a fixed length by pulling at constant speed, so the engine and coaches remain in the same position relative to each other. Over a defined period of time, the train will change position (displacement), but not shape. Thus, the train shows both velocity and displacement, i.e. motion, but no deformation. The coaches show only passive motion, being tethered to the engine. © A. Støylen.


b.  The engine and the last coach pull away from each other. This lead to the whole train having different velocities, both in magnitude and direction, as indicated by the arrows. Over a definite period of time, the engine and coaches will have moved away from each other. There are different velocities within the train, and the coaches change position in relation to each other. Thus each part of the train has different motion, and the whole train is stretched, i.e. deformed. The engines show intrinsic motion, different from the engine. © A. Støylen.



c.
Another instance of deformation. When the last coach and the locomotive push against each other, there is different velocities of each coach, but this time towards the middle of the train. This leads to compression of the whole train. Thus, motion of an object is different from deformation. When all parts of the object have the same motion, there is no deformation. When different parts of the object have different motion, there is overall deformation of the object.  Deformation is thus differential motion. See also Parametric imaging figs. 13 - 15.

Strain.

Strain, in daily language means, “stretching”. In scientific usage, the definition is extended to mean “deformation”. The concept of strain is complex, but linear strain can be defined by the Lagrangian formula:

Where e is strain, L0 = baseline length and L is the instantaneous length at the time of measurement as shown below (Fig 4).

An object undergoing strain. In this case there is a 25% elongation from the original length (L0), thus, according to the Lagrangian formula there is positive strain of 25% or 0.25. This strain can, however happen at different rates, as shown in fig. 4b.

Thus strain is deformation of an object, relative to its original length. By this definition, strain is a dimensionless ratio, and is often expressed in percent. From the formula, it is evident that positive strain is lengthening or stretching, in accordance with the everyday usage of the term, negative strain is shortening or compression, in relation to the original length. By using this definition, however, when an object is stretched from Lo, strain will remain positive during compression as long as the object remains longer than Lo, and vice versa after compression, strain will be positive during stretching so long as the object remains shorter than Lo.  (This is treated in more detail here).


Strain rate


The strain rate is the rate by which the deformation occurs, i.e. deformation or strain per time unit. This is equivalent to the instantaneous strain (or change in strain) per time unit.

The unit of strain rate is /s, or s-1. The strain rate is negative during shortening, positive during elongation, and is more suited  for diastolic deformation,  i.e.  the rate of  elongation or thinning will be positive during diastole. Thus, two objects can have the same amount of strain, but different strain rates as shown below:


Strain rate. Both objects show 25% positive strain, and both corresponds to the object in fig 4, but with different strain rates, the upper has twice the strain rate of the lower.  If the period is one second in the upper object, the strain rate is 25% or 0,25 per second, giving a strain rate of 0.25 s-1. The lower object has twice that period, i.e. half the strain rate, which then is 0.25 / 2 seconds = 0.125 s-1 . In these cases, the strain rate is constant.

Myocardial strain


The term strain was first used in relation to the heart by Mirsky and Parmley (12) to describe
to describe myocardial deformation.

Myocardial thickening during systole is thus positive strain. This is illustrated below.


M-mode of the left ventricle. Here the transmural  strain is wall thickening. © A. Støylen.

Thus,  transmural strain  is  nothing more than  wall thickening.  Transmural strain rate  is the same as the transmural velocity gradient.

It is extremely important that if longitudinal and radial function are comaperd, care should be taken that the measurements are comparable. To compare for instance fractional shortyenig of the LV diameter with longitudinal strain (wall shortening), is comparing two different measures, and may lead to completely erroneous conclusions as shown below.

As we see that the base of the ventricle has motion, and the apex is relatively stationary (fig 6a), it is evident that the myocardium also shows longitudinal strain, as shown in fig 6b.


a. This video shows how the apex is stationary, while the base moves. this means that the ventricle has to show differential motion, between zero at the apex and  maximum at the base. © A. Støylen. b. M-mode lines from an M-mode along the septum of a normal individual. These lines show regional motion. It is evident that there is most motion in the base, least in the apex. Thus, the lines converge in systole, diverge in diastole, showing differential motion, which equals deformation, see fig. 3b and c. © A. Støylen.





Diastolic and systolic images of the heart. Systolic shortening of the left ventricle relative to diastolic length, is the
systolic strain of the ventricle. However, it is also evident that as the wall shortens, it also thickens, to conserve the volume. Heart muscle is generally assumed to be incompressible. 
© A. Støylen.

Fig. 7b. Longitudinal shortening
can be measured by longitudinal M-mode of the mitral annulus.
© A. Støylen.


Longitudinal systolic strain of the left ventricle is shortening, normalised for diastolic length (similar to EF, which is volume decrease (stroke volume) normalised for end diastolic volume). As longitudinal shortening describes most of the actual pumping work (13), as described in long axis function, there is a strong relation between EF and longitudinal strain. It is evident that Lagrangian strain is well suited to describe systolic deformation. Diastolic thinning or elongation, however, is not so well described by Lagrangian strain as Lo is defined in end diastole.

As shown in the figures, deformation of a three dimensional object is in all three dimensions simultaneously. This is illustrated in fig. 8.




Strain in three dimensions. The cylinder shows strain, which can be described as Lagrangian strain from L0 to L. However, the figure also shows simultaneous thickening or expansion in the two transverse directions. If the cylinder is incompressible, the sum of the longitudinal and the two transverse strains will be zero.  All three-dimensional objects show strain in three dimensions. In the heart, the usual directions are longitudinal, transmural and circumferential as shown to the left. In systole, there is longitudinal shortening, transmural thickening and circumferential shortening. (This is an orthogonal coordinate system, but the directions of the axes are tangential to the myocardium, and thus changes from point to point.) As the heart muscle is generally considered incompressible, transmural thickening has to be balanced by longitudinal plus circumferential shortening.

In a three dimensional object, there is the possibility of deformation in three directions. Normal strain is the deformation components along the main axes of a coordinate system. To complicate matters further, there are also shear deformations, which means displacement of the surface borders relative to each other. In fact, 3-dimensional strain is a tensor with three normal and six shear components (11). This is further explained in a separate chapter. For present and clinical purposes, the present method is one dimensional. As all strain components are interrelated, one component may be representative of all of the regional function (7), but the 3-dimensional nature of the strain tensor is important to understand the specific problems of insonation angle in strain rate imaging compared to velocity imaging.

The basic direction in three dimensions are given by the coordinate system given. In a Cartesian coordinate system, the directions are x, y, z, somewhat randomly chosen. In relation to the heart, the directions are longitudinal, transmural and circumferential. In relation to the ultrasound beams, the directions are axial (along the beam), lateral (across the beam in the imaging plane) and elevation (out of the imaging plane), the coordinate systems are described here. Thus the terms "radial" should be avoided, as it can mean both axial in  relation to the ultrasound beam and transmural in relation to the heart, "lateral" can mean both transverse and transmural (although those may be the same in the apical views.)

Incompressibility.

If  the object is incompressible, the volume (not mass!) remains constant during deformation.This is the true definition of incompressibility. Thus, compression in one dimension has to be balanced by expansion in others as shown in fig. 8, i.e. strain in the three dimensions in a coordinate system cancel out, in way described in more detail here. This means that strain in three dimensions are interrelated, so strain in one direction is representative of regional deformation in more than one direction, as has been shown for heart muscle where wall thickening and wall shortening gives the same information about regional function (7).

Motion vs. deformation - velocity and displacement vs. strain and strain rate.

As the apical parts of the ventricle pulls on the basal, the displacement and velocity increases from apex to base, as shown in figs 6, 7 and 9. This means that some of the motion in the base is an effect of the apical contraction - tethering. In fact, completely passive segments can show motion due to tethering, but without deformation, as illustrated in fig3a. (4, 6, 7). This means that the velocity (and displacement) are position dependent, if not normalised while strain rate (and strain) are much more position independent, if the velocity gradient is evenly distributed.

The difference between motion and deformation as well as strain rate and velocity in the heart, is shown below.


Velocity, displacement, strain rate and strain from three different points, apex, midwall and base, in the septum of a normal person. Left, velocity curves. By temporal integration one obtains displacement. By spatial derivation of velocity, one obtains strain rate, and by temporal integration of strain rate one obtains strain. These curves all represent the same data set. It is evident that motion (velocity and deformation) increases from apex to base, showing a gradient, while deformation (strain rate and strain) is more constant, in fact a direct measure of the motion gradient. Notice also how the initial elongation of the mid septum occurs before the closure of the aortic valve, i.e. the initial negative velocities in the basal and mid septum are protodiastolic , as shown previously and illustrated below (16).



Parametric (colour) image from the septum of a normal subject. It is evident that there is an elongation in mid septum, resulting in
initial negative velocities in mid and basal septum before closure of the aortic valve.

We have seen that deformation of an object is present when there is differential motion within the object. As strain rate is equal to velocity gradient, in fact deformation can be described as motion gradient, strain rate being the velocity gradient (spatial derivative of of velocity), and strain the displacement gradient (spatial derivative of displacement) c fr. also "
How to use Strain rate imaging", Fig 2.
Velocity
Temporal integration

Displacement
Spatial derivation


Spatial derivation

Strain rate
Temporal integration

Strain

Basically, longitudinal strain and strain rate are methods to measure regional deformation, the basic algorithm subtracts the motion due to contraction of neighbouring segments (tethering effects). In principle, velocity and displacement measures the effect of contraction of the whole ventricle apical to the point of measurement. Thus, annular plane displacement and velocity measures the global function of the left ventricle (13). This has been demonstrated in several studies, both for systolic annular displacement (30 - 36) and velocity (37 - 40).

The term annular plane descent or mitral annular excursion (MAE) (31, 35, 37, 40) should be used. Atrioventricular plane descent (AVPD) (30, 32, 34, 36)is incorrect, as the term also comprises the tricuspid part, and while tricuspid displacement and velocity can be measured (and is higher than in the left ventricle) , it is usually measured only in one point, and the relative weights for the measurements is unclear.

In principle, one might measure annular motion in one point, and get information about the function of a sector of the myocardium. However, this is theoretically difficult, as different motion of various points of the mitral ring would mean that the ring would tilt, however, the ring is not an isolated structure, but an integral part of the annular plane, and tilting of the mitral part would mean deformation of the whole annular plane. In addition, global ventricular function by annular descent or velocity measured in four points of the mitral ring reduces variability by 25%. Limiting measurements to one point, will increase random variability, and drown out systematic variation ion regional dysfunction. Finally regional dyskinesia is seldom limited to one sector, and may be compensated by hyperkinesia in other areas. We demonstrated in a clinical study (40) that while annular measurements of motion or velocity could not demonstrate regional differences, segmental analysis of peak strain rate could. But taking average peak strain rate of a sector corresponding to a point on the mitral annulus, this "sector" index again failed to demonstrate regional differences.

Strain rate imaging is not the only method for regional analysis. Segmental velocities is another (25), the advantage is that the measurements are "cleaner", not being so processed, the disadvantage is that the values are level dependent. There are indications that segmental strain rate is the more sensitive method (41).

On the other hand, peak systolic strain rate and strain is an index of regional systolic function, but mean peak systolic strain rate measured in all segments of the left ventricle and averaged, is another global index (6, 7, 40). This index ought to be equivalent to annular plane velocity and displacement. In myocardial disease, however, where there is heterogeneous reduction in function,  segmental analysis may theoretically have higher sensitivity for small changes.


What does Strain and strain rate actually measure?

It is important to realise that  strain and strain rate measure only deformation. This is true also of 2D and M-mode measurements, fractional shortening, longitudinal shortening, myocardial velocities 2D volumes and EF are all related to myocardial motion. None are measurements of contractility, which involves myocardial tension (stress). Contractility is the stress / strain relation. One example, myocyte contraction is finished during the first half of ejection period, the rest of the emptying is inertial effects, but still, so long as volume is ejected, LV volume, LV length and diameter decreases, stroke volume, EF and absolute strain increases, and strain rate remains negative during the rest of EP while the myocytes relax. However, while systolic strain is more closely related to stroke volume, peak systolic strain rate, being an early systolic event, is more closely related to contractility (78).

Flow is pressure driven and the flow velocity measurements are the real indices of pressure differences.



What about strain rate imaging in the atria?

As the outer contour of the heart is relatively constant, as is the apex, and the atria is attached to the large veins, the atrioventricular plane has to be the piston of a reciprocating pump (see physiology, systolic function). expanding the atria while the ventricle shortens and shortening the atria while the ventricle expands.



Deformation in the atria is reciprocally related to the deformation of the ventricles. as both  apex and the atrial roof are relatively immobile, the ventricle shortens  (yellow) while atria elongates (cyan) during systole, ventricle elongates (cyan) and atria shortens (yellow) during the diastolic phases. In diastasis, there is no deformation, both are green. The curved M-mode to the left, going through both ventricular and atrial septum shows the reciprocal colours of the atria and ventricles.

Basically, the deformation of both chambers reflects the motion of the atrioventricular plane. In systole, the ventricle shortens while the atria expands. This is a function of ventricular contraction. In early diastole there is elongation of the ventricles and shortening of the atria, the active component of this is the ventricular relaxation. In late diastole, there is further elongation of the ventricles and shortening of the atria, but in this phase the active component is the atrial contraction. However, deformation of both chambers are reciprocating, both reflecting the atrioventricular function, and for instance the reservoir function of the atria during systole is not an independent parameter. Any added clinical value of this is uncertain. See also physiology, atrial deformation. In addition, because of its thin wall, strain rate imaging in the atria is extra prone to artefacts due to low lateral resolution.


Velocity gradient

The concept of velocity gradient was introduced by Fleming et al (14). The velocity gradient is defined as the slope of the linear regression of the myocardial velocities along the M-mode line across the myocardial wall. If velocities are linearly distributed through the wall, this is equal to the difference in endocardial and epicardial velocities divided by the instantaneous wall thickness (W).

The definition was extended by Uematsu et al (15) to include the transmural velocity gradient across the parts of the wall where the scan line is not perpendicular to the wall, by the cosine correction of the velocities. The velocity gradient measured in this way, was transmural (radial). As transmural strain rate is the rate of change in wall thickness, the strain rate is the


In other words, the velocity gradient is an estimator of the transmural strain rate, strain per time unit approximates velocity per length unit. The reason this is an approximation only, is that while strain rate is defined in relation to the initial (diastolic) wall thickness, the velocity gradient is a function of the instantaneous wall thickness as shown in the formula. The velocity gradient can also be applied to the longitudinal velocities. As the apex is stationary and the mitral plane moves (fig 6), there has to be increasing velocities as well as motion from apex to base, as shown below. In other word, there is a velocity gradient from apex to base. A general definition of the velocity gradient will then be:

which in the transverse direction will be equal to the original definition. A more detailed analysis of the velocity gradient here.

 


Pulsed Doppler recordings of longitudinal velocities from a normal left ventricle. Increasing velocities (i.e. velocity gradient) from the apex to the base is evident, as will be expected .

Distribution of strain rate / Strain

If systolic displacement and velocity decreases evenly from base to apex, the systolic deformation (strain) and velocity gradient (strain rate) is evenly distributed throughout the myocardium. Some of the earliest studies seem to indicate this (10, 19), although later studies seem to find differences (74). However, with the high possibility of  systematic errors (see problems and pitfalls), this question must be considered unresolved, some of the findings of inequalities are obviously artefacts (46, 47). Theoretical volume considerations may indicate a relatively even distribution, while considerations of fibre architecture may not.

Strain rate by tissue Doppler

Thus, longitudinal velocity gradient, is a measure of longitudinal strain rate. However, it can be shown that this is equal to the velocity gradient over a fixed distance. Strain rate by tissue Doppler measures the velocity gradient of two points over a segment with a fixed distance (In the latest scanner software, the velocity gradient is in fact calculated by linear regression of all pixel velocities within the delta x, to reduce noise.):

This is a different algorithm from the velocity gradient, but it can be proved (here) that the two formulas result in the same ratio. The distance  is called the offset distance or strain length.


a


b
a, longitudinal velocity gradient, where v1 and v2 are two different velocities measured at points 1 and 2, and L the instantaneous length of the segment between those points. The velocity gradient is given in the formula.  b, strain rate measured by tissue Doppler, as the velocities of a segment with fixed length as shown by the formula. It can be proven that these two approaches yield the same result.

Thus:        

This is explained in more detail here. The velocity gradient and SR are equal to the Eulerian strain rate, which normalises the velocity difference to the instantaneous length, while it is customary to use the Lagrangian strain, which normalises the change of length to the initial length,which is explained in more detail here.

The difference in shape between strain rate and velocity curves

It is obvious that strain rate and velocity curves are different. Apart from being inverted, which is due to the subtraction algorithm, the systolic strain rate curves are much more rounded, while velocity curves show a sharper peak. If strain rate is equal to normalised velocity, why is the shape different as illustrated below?





Above left velocity curves. It can be seen that the two velocity curves have an early maximum, showing that the myocardial acceleration occurs early, and is an early event. Above right, the strain rate curve from the segment between the two ROI's in the left picture. It can be seen that peak strain rate is a much later event. This is due to the fact that the velocity difference is normalised for the instantaneous distance (although indirectly, see below), i.e.  Eulerian strain rate.  This can be demonstrated by the simulation in the lower row. Left: two systolic velocity curves with velocities somewhat arbitrarily chosen, but within normal range, and with a fairly normal shape.  The values on the cyan curve is two thirds of the red one, and both have peak velocity at 0.05 sec.  Left: strain rate curves calculated from the velocity curves on the right side.  Assuming an initial distance between the points of the two velocity curves of 2.5 cm, again a realistic distance for the velocity difference.  Lagrangian strain (yellow) is derived by dividing the velocity difference at each time point by the initial distance.  This results in a simple inversion of the velocity difference, in a different scale, and with minimum value (maximum absolute) at 0.05 sec. Eulerian strain (green curve) is obtained by dividing with a strain length that decreases by the time interval times the velocity difference. In this case the differences between the curves is evident, and the minimum value (maximum absolute) is reached at 0.25 seconds.

This is due to the difference between Lagrangian and Eulerian strain rate, which is explained here. As we use Lagrangian strain, this is displacement normalised for end diastolic length. However, it has become customary to use Eulerian strain, which is a normalization for instantaneous length. This means that as velocities increase, the length decreases,  (or, in reality, the absolute velocity difference increases relatively), thus blunting the absolute increase in the velocity difference (i.e. the decrease in the negative difference) in the first incremental phase, while the phase where velocities are relatively constant, strain rate will continue to increase as the strain length decreases. Thus, peak strain rate is a later event than peak velocity, which means that it may be more load dependent than peak systolic velocity. In addition to giving a higher and later value for peak strain, it will have consequences in resulting in a higher peak strain value as shown below.


Strain measured by integration of the strain rate curves in the figure above. It is evident
that the total systolic strain is about 6% higher (absolute values) by Eulerian strain rate.

Strain rate by linear regression

Instead of measuring just the velocities at the ends of the offset distance;  or  respectively, the velocity gradient / strain rate can be calculated as the slope of the regression line of all velocities along the offset distance as described originally (14). With perfect data, the values will be identical, both formulas defining the slope. With imperfect data, this method will tend to make the method less sensitive to errors in velocity measurements, as the value is an average of more measurements.


Fig. 15. Strain rate calculated over an offset  (strain length) of  12 mm (L). "True" strain rate at the end points are v1 = 0 and v2 = 1.2 cm s-1 giving a strain rate of -1.0 s-1 (blue squares), the strain rate is actually the slope of the line between the points, being equal to (v2 - v1)/L. Due to random variability of the measurements, the measured values deviate from the slope. Here velocities are sampled for each 0.5 mm along the strain length (red points), and are seen to be dispersed around the true strain rate line. The regression line through the points (red line) is fairly close to the true strain line, and results in a strain rate measurement of -1.14 s-1. This makes the measurement far less vulnerable to measurement variability than simply measuring the two velocities at the end of the strain length (points in the green open squares), and compute SR = (v2 - v1)/L shown by the green line, yielding a strain rate of -1.63 s-1.




Fig. 16a. In short axis view,  the septum and inferior wall can be imagined in cross section. Here displacement and velocity can be measured across the wall, meaning that deformation imaging with tissue Doppler can be done in only those two areas in real time.

Fig. 16b.  Wall thickening . The relatively constant outer contour and inward moving endocardium, shows clearly a displacement gradient (strain) and hence, a velocity gradient across the wall.

In the transmural direction, strain and strain rate can be measured where the ultrasound beam crosses the wall at an angle. This means in the septum and inferior wall, just as the M-mode. As the outer contour of the left ventricle is relatively stationary, while the endocardium moves inwardly, there is a gradient of displacement and velocity across the wall.

Thus, the concepts transmural displacement and transmural velocity are in reality meaningless in a physiological sense. The displacement and velocity in the transmural direction is dependent on where across the wall it is measured, i.e. the transmural depth of the ROI placement. Different data sets from tissue Doppler in the transmural direction is thus not comparable, and the measurements have little clinical value. Some applications like 2D strain will give the segmental average value for transmural velocity and displacement. They may have a clinical meaning, in that they may separate normal from reduced function, but the use of clinical measurements that are physiologically unsound, is doubtful.

The velocity gradient can be measured by the strain rate imaging method, which is quicker than tracing the endo- and epicardial borders. Measuring the transmural systolic strain by integrating strain rate, however, is a roundabout way of arriving at the relative wall thickening, which can be measured with equal temporal resolution and much higher reliability with M-mode. In addition, anatomical M-mode can imagine wall thickening in other directions as well, although with only 2D grey scale frame rate.

 

Segmental strain and strain rate.

Segmental strain and strain rate is takjen to mean the deformatioon measured over a complete segment, giving the average value for the segment, as shown in figs. 19 and 20. Also the application 2D strain does in practice give segmental values, althoug in some versions local values can be extracted. Segmental strain has several advantages: As measuremnts are fairly noisy, the average of a whole segment will tend to be more robust. The segments are the basic unit for evaluating regional wall mnotion score (WMS) in the recommendations of the ASE/EAE (146), and so far the clinical usefullness of a higher resolution has not been demonstrated.

Tissue Doppler measures the velocity gradient along the ulotrasound beam. Increasing the strain length will reduce noise, but the strain length will follow the direction of the ultrasound beam, and this will give problems where the alignment is not perfect, as discussed in the pitfalls chpter, under the discussion on lateral resolution. However, the size and shape of the ROI, averaging gradients from more than one beam may be made to follow the segment contour fairly well.

Instead of calculating strain rate along one ultrasound beam as shown in figs 10 a and b, it has been proposed (44) to calculate strain rate from the velocity differences at the segmental interfaces and segment length along the wall. (Any points will do actually), as shown in fig. 10c. This will make the method less angle sensitive, as well as more similar to the other methods as the measurements are related to kernels at the segmental borders. However, this may be a more noisy solution, compared to averaging measuremkents over a whole segment.

Fig. 17. Segmental strain rate, measured by tissue Doppler, but by segmental velocities that do not lie on one ultrasound beam, while strain length is measured along the wall, between the velocity points. 

The advantage of this is that there may be less insonation angle dependency. The disadvantage is that this method will give slightly different values. This is due to the fact that the velocities will not be parallel to the segments,  so there is a smaller,  but less variable insonation angle error. Thus findings will not be directly comparable to existing reference values, and it will be more sensitive to errors in velocity measurement than a regression along the ultrasound line.




Strain rate by speckle tracking in grey scale images.

The basic principle of speckle tracking is based on the interference of the reflected ultrasound giving rise to an irregular - random - speckled pattern. The random distribution of the speckles ensures that each region of the myocardium has an unique pattern, a fingerprint (fig. 18a).  The speckles follow the motion of the myocardium so when the myocardium moves from one frame to the next, the position of this fingerprint will shift slightly, remaining fairly constant (fig 18b). Thus, if a region (kernel) is defined in one frame, a search algorithm will be able to recognise the lie sized and -shaped area with the most similar speckle pattern in the next frame, within a defined search area (fig. 18c), and hence, to find the new position of the kernel (26). This has been shown to be feasible in flow (94) and strain rate imaging (95).

The basics of speckle formation and speckle tracking is given in more details here.









Fig 18 a. Typical speckle pattern in the myocardium. The two enlarged areas show completely different speckle patterns, which is due to the randomness of the interference. This creates an unique pattern for any selected region that can identify this region and hence, the displacement of the region in the next  frame.  b. When the speckle pattern is followed by an M-mode in the wall, the alternating bright and dark points are seen as alternating bright and dark lines. The lines remaining to a large degree unbroken, shows the pattern to be relatively stable, the speckles moving along with the true myocardial motion, and thus myocardial motion can be tracked by the speckles. Fig c. Speckle tracking. Defining a kernel in the myocardium will define a speckle pattern within (red). Within a defined search area ( blue), the new position of the kernel in the next frame (green) can be recognised by finding the same speckle pattern in a new position. The movement of the kernel  (thick blue arrow) can then be measured.

In principle, pure speckle tracking  is direction independent, and can track crosswise. However, lateral resolution is important in delineating the speckles in the lateral direction. If the lateral resolution is low,  the interpolation will result in a "smeared" picture, with speckles that are nor so easily tracked in the lateral direction. In addition the lateral resolution decreases in depth with sector probes.

However, the speckle pattern will not repeat perfectly. This is due to both true out of plane motion (rotation and torsion relative to apical planes and longitudinal deformation relative to short axis planes) and to small changes in the interference pattern. But the frame to frame change is small, and the approach to recognition is statistical, the basic algorithms are shown here. This means, however, that the with lower frame rate, the changes from frame to frame are greater, resulting in poorer tracking.

Fig. 19a. The resulting tracking of the kernels shown in motion. As can be seen, with a drop out apicolateral, this ROI tracks less than perfect, giving too low strain both in LA and MA segments. b. Speckle tracking can be applied crosswise. In this parasternal long axis view, the myocardial motion is tracked both in axial and transverse (longitudinal) direction. It is evident that the tracking is far poorer in the inferior wall, due to the poor lateral resolution at greater depth.

Motion of one kernel can thus be measured throughout one heart cycle. Velocity can be derived from the motion curve or calculated by the motion divided by the frame interval (fig 20a). With two kernels, the relative displacement per distance can be derived. This is equal to strain (fig. 20b). Likewise the relative velocity per distance (velocity gradient / strain rate) can be calculated or derived from the strain curve.

Strain by speckle tracking has been validated experimentally by ultrasonomicrometry (124, 125).

 One way of using this approach, is to place defined ROI in the myocardium at the segmental borders and measure segmental strain and strain rate directly by changes in segment length. This is true segmental strain rate, and angle independent measures, eliminating the insonation angle problems discussed elsewhere..


20a.  Kernel displacement  Displacement curve obtained by tracking through a whole heart cycle shown to the right, derived velocity curve shown below.

b. From two different kernels, the relative displacement and hence, strain as well as strain rate can be derived.

c. With kernels at all segmental borders, segmental motion and deformation can be tracked, as shown in b.

The application also uses automatic segmentation, reducing the variability compared to manual placement of the ROI.

 The advantage of this method is that it tracks in two dimensions, along the direction of the wall, not along the ultrasound beam, and thus is angle independent. This means true longitudinal strain. The disadvantage is that if the algorithm does not track one kernel correctly, the strain values will be wrong for the segments on both sides of the kernel. This is evident in areas of drop outs or reverberations as shown here. This can be overcome by increasing the number of kernels, or manually avoiding placing a kernel in an area of drop out or reverberation.


It is important to be aware that strain measured by speckle tracking  is Lagrangian strain directly. Derivation yields Lagrangian strain rate, while tissue Doppler yields Eulerian strain rate. Commercially, it has been customary to display the Eulerian or natural strain rate (velocity gradient) derived directly from tissue velocity data, but to apply a correction when integrating to strain rate and display Lagrangian strain. For Strain rate from speckle tracking, a reverse correction has to be applied, either calculating velocity from displacement and then strain rate from velocity, or calculate strain rate from strain and then apply a conversion. If not, the values are not comparable. Even so, the values are not absolutely identical, speckle tracking measuring along the wall, tissue Doppler along the ultrasound beam, and that may affect the relation to previously published normal values. The method described above, is robust, due to the large kernel size.

This method is also relatively angle independent, giving true longitudinal strain. In addition, it gives very much improved lateral resolution, using the line density of grey scale rather than tissue Doppler imaging. Finally, the lateral resolution is better, as the grey scale images has much higher number of scan lines (typically 64) as compared to tissue Doppler (typically 16).

However, as the lateral resolution is far less than tha axial, the two directions are not equal. This means that tracking in the longitudinal direction is better than tha lateral, so the method is angle depentden to some degree. And increasing the frame rate (for instance to compensate for high heart rate) reduces the lateral resolution even more, reducing the angle independency of the speckle tracking method even further. The clinical value of the angle independency remains to be demonstrated.

The method is dependent on frame rate. Too low frame rate will result in too great changes from frame to frame, resulting in poor tracking. This may also limit the use in high heart rates, as the motion and thus frame to frame change increases relative to the frame rate. On the other hand, too high frame rate is obtained by reducing lateral resolution, and thus resulting in poorer tracking at least in the transverse direction. At present, the optimal frame rate for speckle tracking seems to be 50-70 FPS. Thus, speckle tracking has limitations in sampling rate. Shorter events like the isovolumic phases may disappear all together, and peak values may be reduced due to under sampling, especially isovolumic and diastolic velocities and strain rate. This is most important for measuring peak values in diastole and isovolumic phases, not so much in systolic strain rate, and systolic strain has least frame rate sensitivity of all.

2D Strain by speckle tracking.

With a greater number of kernels, distributed both along and across the wall, each can be tracked individually, and displacement and velocity can be measured in two dimensions, both longitudinally and transversally for each (73). From this, differential motion - i.e. deformation - can in principle be measured, both in the longitudinal and transverse direction. The smaller the kernel, the less certain will the tracking be, but this can be compensated by selection of kernels on the basis of a stable pattern from one frame to next.  One method of insuring stable tracking is to discard kernels that are not present in a sufficient number of frames. In the same way, kernels that does not move can be discarded, reducing the influence of reverberations.However, the dependence on recognising stable kernels from one frame to next, makes the method even more frame rate sensitive.

Averaging a large number of kernels may make tracking more robust, although this reduces the number of useful speckles in each kernel. This can be done in various ways and combinations. With more than one layer of kernels across the wall, the longitudinal measurements can be averaged from all layers, giving a transmural average. Longitudinal averaging can be done along one segment, giving the segmental average. This can also be done in a more sophisticated way, by spatial interpolation along the wall. This will result in a gradual effect of spatial smoothing, although the extent of the smoothing is less easily discerned. It will reduce the effect of artefacts such as drop outs and reverberations. But it may also mask abrupt changes in deformation pattern, e.g. at infarct borders. In addition, this kind of interpolation will reduce temporal resolution as well, in the case of regional timing differences.

The 2D strain method uses stable speckles, and measures the displacement

On top of this, smoothing in post processing may be applied in the same way as for tissue Doppler based methods.



Fig. 21 a. 2-dimensional strain by speckle tracking.  Each red point represents a kernel for speckle tracking. Velocity and displacement decreases from base to apex, and the differential motion along the segment gives longitudinal strain and strain rate. As the true direction of the motion is tracked in this instance, the transverse component can also be tracked, and the differential motion from epi- to endocardium can also be tracked., giving transmural strain and strain rate.

b. 2D strain in practice. The midwall line is used for the longitudinal strain, being an average of all points in the wall. The ROI follows the wall, the limits can be seen diverging in systole, converging i n diastole, giving the transmural strain and strain rate at the same time. The colours show longitudinal strain rate, green is shortening and red is lengthening.

c.  In order to make the speckle tracking more robust, values are averaged over a whole segment.

This method can the calculate segmental longitudinal velocity and displacement:



Fig. 22.  Longitudinal displacement and velocity, derived from speckle tracking. Each curve represents the average of a segment. The curves are very smooth, due to a specific smoothing by curve fitting from segment to segment as well as temporal averaging.

We did an initial evaluation of an earlier version of this application in February 2004, comparing the longitudinal motion and deformation measurements by this application with those obtained by tissue Doppler, in separate images. The study consisted of 20 patients with a wide range of function.



Fig. 23. Strain rate and strain, comparison of 2D strain and Tissue Doppler. There is a considerable spread between methods, but most probable due to variability of both methods. There 2D strain gives lower values than DTI, and this tendency increases with increasing strain rate/strain. The term "CEB" meaning "computerized eye balling" was an early term to describe the application.

When measurements was sorted in quartiles, Concordance was only between 27 and 34%. Feasibility was the same with 2D strain and TVI. Further investigation was not undertaken at that time, as the application was modified in later versions.

Other authors have found a much better correspondence between TDI and 2D strain (73), with correlations of 0.94 and 0.96 for strain rate and strain, respectively. However, as seen by the curves in the figure below, both data sets are analysed by the 2Dstrain software, and thus subject to the same high degree of smoothing, so the results do not reflect independent analysis.


From a validation study where tissue Doppler and 2D strain derived strainrate (left) and strain (right) values were compared. However, as can be seen
from these curves, both curves are very smoothed and concordant. Thus, much of the concordance must be assumed to be due to smoothing, as both
methods were processed by the 2D strain software, and not by independent analysis software. Adapted from Modesto 2006 (73).

Another study by Cho et al (148) finds only correlations of longitudinal strain by 2DS and TVI with MR tagging of 0.51 and 0.40, respectively. This may reflect the real precision of both methods (and of MR tagging as well?) but then the correlation between the methods cannot be higher.


Transverse displacement an velocity can also be derived, but as this will be the segmental average, this value has little meaning, the velocity and displacement increased from outer to inner contour (c fr. fig. 16b). It is the displacement and velocity gradient that is of interest, i.e. transverse strain and strain rate. However, this can also be calculated by this method:


Longitudinal Transverse




Strain
rate




Strain

Fig 23. Longitudinal and transverse strain derived from speckle tracking.  It can be seen that in this case the differential tracking in the transverse direction is poor in the basal segments, thus underestimating transverse thickening in this healthy subject.

Whether this adds clinical information, remains to be seen, as longitudinal and transverse strain are interrelated.


As speckle tracking is angle independent, it may be applied to the short axis as well:




Fig. 24a.  2D strain applied to short axis image. Again this can be seen to track in two dimensions, the thickness following the wall thickening, and the mid line in the ROI Showing midwall circumferential shortening.
b. Transmural strain. In this image the application only measures between 10 and 15% transmural strain, while the true values in a normal person as this may be as high as 40 - 50%.
c. Midwall circumferential shortening.  In this image about 15%, which may be closer to the actual values.

The transmural strain measurement needs to be validated, while the physiological meaning of midwall circumferential shortening may be discussed in terms of the circumferential strain tensor.  However, subject to validation, midwall circumferential shortening may be established as a separate measurement with its own reference values. Whether this adds information remains to be shown, as the different strain components are interrelated.

The application will also give transmural velocity and displacement as an average of the whole segment. These values have no physiological meaning, as there is a transmural gradient of both displacement and velocity as described before. However, in a clinical setting, the measurements may separate normal from reduced wall function, and thus have a meaning in a clinical setting. It is rather doubtful, however, if this adds anything to transmural strain and strain rate, and the use of these values is physiologically unsound.

The lines looking smoother, is a function of the averaging function used in the algorithm, the application will do the same to tissue Doppler data.


Fig. 25. Strain rate curves from speckle tracking and tissue Doppler from the same cine - loop.  The same smoothing is applied to both, showing that smoothing of the curves is not the result of the robustness of the algorithm, but of specific temporal and spatial smoothing applied by the application. The curves differ somewhat (but not too much), as strain rate is calculated with different angle and lateral resolution.

Smoothing in 2D strain

There is a liberal amount of temporal smoothing. In addition there is built in a spline or polynomial smoothing along the whole region of interest (ROI). The AV plane is the heaviest feature that is tracked, and contributes the most to the motion. Then there is a curve fitting along the mid ROI curve, resulting in a smoother transition from segment to segment, distributing the deformation along the ROI. This diminishes the effect of poor tracking of single kernels, but may result in diminishing the differences between normal an hypokinetic segments, and reduced sensitivity for hypokinesia as seen below.

2D strain (left) vs. tissue Doppler (right) in an inferior infarct, analysed from the same cine loop recording. In this case, tissue Doppler derived strain shows systolic akinesia ( or slight dyskinesia) in the basal segment (yellow curve), hypokinesia in the midwall segment (systolic strain of -8%) And near normokinesia of the apical segment (-11%). 2D strain, on the other hand, shows normokinesia in the whole of the inferior wall. In this case, the drop out of the entire anterior wall may be part of the problem, as all anterior wall segments are excluded, and the values obtained are ditributed over three segments only. On the other hand, tissue Doppler analyses each segment without interdependence.



In the case of asynchrony, this may be reduced as well by the same function. Thus the diagnostic accuracy of this application is so far not very well documented. For global strain, however, this is of no importance, and the idea of measuring shortening normalised for LV length appears to be sound (150).

The same limitations apply to this application as to speckle tracking in general, concerning frame rate, heart rate and under sampling. The amount of smoothing may increase the undersampling even more.

Both methods have been compared for longitudinal strain, and compared to tissue Doppler (126). Both seem to agree fairly well. In addition variability is lower by both methods than by tissue Doppler. However, as both methods use automatic segmentation, this may be the main cause for better repeatability, not speckle tracking vs. tissue Doppler per se. Feasibility of both methods is reported to be between 70 and 80% of segments.

Segmental strain by combined use of tissue Doppler and Speckle tracking.

Modern ultrasound equipment has the capability of acquiring second harmonic grey scale images with an acceptable frame rate of 40 - 50 FPS and good lateral resolution, simultaneously with tissue Doppler data. This opens the possibility of tracking along the ultrasound beam by tissue Doppler,  while tracking transverse to the ultrasound beam by speckle tracking (124) in the grey scale data.


Combined search by tissue Doppler and speckle tracking. The kernels are shown as the small, round, yellow circles.  The longitudinal search area along the ultrasound beam by tissue Doppler is shown in red. The lateral search area by speckle tracking is shown in white.

This simplifies the search algorithm, limiting the search area to a sector extending in the radial direction and thus reducing the time for the speckle search.  In addition, if the method is used to compute longitudinal velocities or strain rate, the longitudinal tracking is done with the high sampling frequency of tissue Doppler.  Finally, it utilises the full dataset inherent in the combined image. In fact, it seems rather absurd that having access to high quality grey scale tissue data as well as high frame rate tissue Doppler data in the same image, the quality of measurements will improve by discarding one of the data sets.

Thus it seems probable that in the future, some combined approach will be the state of the art. The combined method can be used in different ways to analyse strain rate imaging (127).

  1. Segmental strain and strain rate can be calculated directly from segment length, in the same way as by speckle tracking alone as described above.
  2. Velocity, displacement, strain rate and strain can be calculated by tissue Doppler, placing an ROI in the middle of the segment, and letting the ROI follow the segment as it moves longitudinally and transversally by the combined tracking method, ensuring that the ROI stays in the same position relative to the myocardium, instead of in space as in the original application and in standard tissue Doppler, we have called it dynamic TVI.
  3. The automated segmentation can be used to place the ROI in mid segment in the first frame, without tracking. This results in a stationary  ROI as in traditional tissue Doppler, but the reproducibility will improve compared to manual ROI placement.
Feasibility was reported to be between 75 and 80% of segments, compared to 92% with manual analysis. There may, however be reasons why the latter number may be too high.

This method  has already been shown clinically useful in stress echo (128), giving a sensitivity of peak systolic strain rate for ischemia of 84% and an AUC of 0.9, compared to coronary angiography, and with a feasibility at peak stress of 80% of segments.


Differences and limitations of different methods.

It is important to be aware of the limitations of each method. It should also be emphasized that different methods are not necessarily directly comparable, and may yield different normal values and cut offs. Some of these are discussed in more details in the chapter on problems and pitfalls. One of the fundamental differences stem from the different geometrical assumptions that are present as shown below:


Differences in geometry between methods. The fairly invariable outer LV contour is shown in heavy black. The diastolic inner contour, segmental borders, kernel positions and measurement lines are shown in light black. Systolic inner contour,
segmental borders, kernel positions and measurement lines are shown in red. Left: Segmental strain by tracking of kernels at segmental borders. It can be seen that the main deformation is measured along the longitudinal axis of each segment. As the wall thickens, the longitudinal mid line of the segments moves inwards, but in the basal and mid wall segments this does not add to the shortening as the angle does not change much. In the apex, however,  the angle of the center line changes,  contributing to the segmental shortening when it is measured by this method, however, the effect is slight.  To the right is shown the geometric assumptions of the 2D strain method.  The ROI uses an assumption of equal thickness from base to apex, and the mid line moves with the thickening of the contour.  The segment length is measured along the curved line, and both the curvature and the angle contributes to the shortening of the segment mid line as it moves inward. Thus, the shortening (strain)  might be expected to be higher in the apical segments by this method, as well as being dependent on the curvature, especially in the apex.  (However, this effect may be masked by the high degree of smoothing inherent in the application, which may distribute the differences between segments.  Ultrasound beams are shown in blue, illustrating the alignment problem of this method,  thus resulting in lower values in segments that are poorly aligned.

  • The main limitations of the tissue Doppler method are:
    • Noise, reducing radial and temporal resolution due to the need for smoothing
    • Problems arising from alignment of the ultrasound beam, resulting in angle artifacts and problems with lateral resolution
    • Reverberations resulting in systematic measurement errors that may invert, reduce or increase measurement values, depending on position. In general, it may be assumed that segments more basal to reverberations will tend to increased absolute values, and thus mean values in the basal segments may be overestimated. This may be the explanation of an apparent skewness in the strain values seen in a recent population study (152) using tissue Doppler in the basal segments only.
  • The main limitation of speckle tracking in general is a lower frame rate at the outset, resulting in possible under sampling of peak values. This is mainly a problem in peak systolic and diastolic values, less in systolic strain measurement. It may also be a problem in tracking in high heart rate, as the tracking may be poor due to greater changes from frame to frame.
  • The 2D strain has the same limitation in frame rate. Increasing frame rate will reduce the lateral resolution, thus making the method more angle dependent.
    • In addition. segmental values may be curvature dependent, as discussed in the figure above.
    • The method is also affected by reverberations. The smoothing inherent in the method may eliminate this, but may in itself create new problems:
    • The main problem may be the smoothing. As deformation imaging is mainly a method for diagnosing regional function, any method that uses global measurements as a basis for smoothing (as 2D strain uses annular displacement), may reduce sensitivity for regional dysfunction. Whether this has clinical impact is not so far clarified. Smoothing also effectively reduces the radial resolution.
  • The main problem in segmental strain is the poor radial resolution. Sub segmental values cannot be extracted (although they could be interpolated).
    • The method may avoid reverberations without smoothing as shown, but in the case of poor tracking anyway, both the segemnt above and below the affected kernel must be discarded, thus reducing the feasibility of the method.
    • Another problem is that the combined method is not commercially available, at present it is a research tool at the Norwegian University of Science and technology. It has been criticized by some, that the results are not useful, as they are not transferable. I consider this criticism only partially valid.
      • Firstly, the research tool can be used as described above, for both stationary velocity gradient (thus being in principle the same method as any tissue Doppler based method, differences being no greater than between manufacturers), dynamic velocity gradient, showing the measurements if the ROI for the velocity gradient is tracked through the cycle, as well as for segmental strain and strain rate, both using tissue Doppler for longitudinal tracking as well as using only speckle tracking in both directions. Thus the application makes it possible to compare tissue Doppler, speckle tracking and the combination directly (151), without the confounders that are inherent in each manufacturer's secret adaptions.
      • Secondly a recent study comparing methods (153) has compared the methods in normals, and thus the bias between normal values from  different methods may be taken into account.
In this study (153), it was shown that mean values by segmental strain from combined speckle tracking and TDI and 2D strain gave very comparable results for both strain rate and strain, although there was some statistically differences, these were small and of little clinical importance. Standard deviations, as a measure of variability were also comparable, in the combined method probably due to low noise because of low spatial resolution, in the 2DS probably due to smoothing. There were no tendency to higher values in the apex as discussed as a possibility above, but this again may be smoothed away.

In a reproducibility study (154) the two methods also had similar inter observer reproducibility (different recordings and analysers).

The comparison did show that the velocity gradient gave lower values for strain and strain rate in the apical segments, but this effect disappeared in the dynamic mode, where the ROI for the velocity gradient followed the myocardium.

The main finding of the velocity gradient was that average peak strain rate values were close to 30% higher than with segmental strain and 2D strain. This might be either an effect of under sampling in the latter methods, or noise spikes in the tissue Doppler methods, but as standard deviations were more than twice as wide by tissue Doppler than by segmental and 2DS, it appears that the main cause is noise. Thus the tissue Doppler is more sensitive to noise than other methods. However,systolic strain values were very similar with all methods (except in the apex for TDI with fixed ROI), showing that the smoothing that is a function of temporal integration eliminates this problem, and basically in strain measurements tissue Doppler is as reliable as other methods, although still with somewhat higher standard deviations.

Comparison between methods in a population study (HUNT)

In a recent study of normal values (153) we have compared the different methods for deformation measurement in a subset of 57 patients :
  1. The combined tissue Doppler - speckle tracking method described above
  2. Longitudinal velocity gradient from tissue Doppler without tracking of the ROI,
  3. Longitudinal velocity gradient with tracking ogf the ROI and
  4. Speckle tracking with the 2D strain application.

The velocity gradient is analysed by customised software, but the basic principle is exactly the same as in commercial software (EchoPAC), except allowing for automated analysis and automated tracking. The results were as follows:


Method 1 Method 2
Method 3
Method 4

Peak Strain rate
End systolic Strain
Peak Strain rate End systolic Strain Peak Strain rate End systolic Strain Peak Strain rate End systolic Strain
Apical -1.12 (0.27)
-18.0 (3.6)
-1.46 (0.85)
-14.6 (9.0)
-1.31 (0.73)
-17.2 (9.1)
-1.12 (0.37)
-18.7 (6.6)
Midwall
-1.08 (0.22)
-17.2 (3.2)
-1.29 (0.56)
-18.2 (7.4)
-16.9 (7.1)
-16.9 (7.1)
-0.99 (0.23)
-18.3 (4.7)
Basal
-1.03 (0.24)
-17.2 (3.5)
-1.71 (0.94)
-19.6 (9.3)
-1.59 (0.74)
-17.1 (8.6)
-1.12 (0.36)
-18.0 (6.2)
Mean
-1.08 (0.25
-17.4 (3.4)
-1.45 (0.79)
-17.7 (8.5)
-1.43 (0.67)
-16.7 (8.1)
-1.07 (0.33)
-18.4 (5.9)
Comparison between methods. Standard deviations in parentheses.
Looking at the findings, it is evident that the tissue Doppler methods gives far higher peak strain rate velues that the two other methods. This is probably due to a higher random noise component in tissue Doppler, rather than the opposite, too low peak values due to under sampling in the two other methods. This is evdent from two reasons:

  1. Tissue Doppler derived strain rate shows a far wider standard deviations
  2. Integrated stran from strain rate eliminates the differences, showing that the noise is random.
Another thing is also evident: Tracking the ROI in tissue Doppler results in equal strain values in apex, midwall and base, as in the other two applications, while no tracking yields lower values in the apex, so there is an advantage in tracking, but only in the apical segments.

Finally it seems that the combined method and 2D strain gives almost the same results, however probably due to different causes, low resolution in the combined method, smooting in 2D strain. But it seems that the normal values are transferrable, and for strain between all methods. .


Tracking in RF data:

AS the reflected ultrasound signal really consists of not only information about the amplitude and wavelength, but about the actual waveform being reflected, this information can be extracted. From these data, both grey scale information and Doppler data can be calculated. (In fact this is what is done by the scanner, before giving what is known as "raw data".) Extracting the RF data themselves requires far more storage, and thus computational power in post processing, and has so far been slow. However, the RF data can also be used for tracking, in a matter similar to speckle tracking. Both cross correlation, normalised cross correlation, sum of absolute differences and sum of squared differences has been shown feasible (129). The method has been validated in both phantom (130) and animal experiments (131). This method has the advantage of being angle independent, as well as having the raw material for bot tissue Doppler and grey scale image formation. Theoretical considerations indicates that this is advantageous in dealing with reverberation artefacts as well, compared to clutter filtering, but this remains to be shown. The clinical feasibility is so far not clear, as the method is time consuming and demanding in computational power.



Global left ventricular systolic function

With the appearance of new methodology, a number of new methods for measuring left ventricular global function has emerged. Older measures has traditionally been measurements of the cavity function: Stroke volume, ejection fraction (and the M-mode equivalent shortening fraction). Newer methods include annular displacement and velocity, as well as mean strain/strain rate, either based on segmental measurements, or a global averaging (as global strain form speckle tracking 2D strain). It should be of general interest to comment on the relationship between the methods.

Cavity measurements

Based on Nuclear or X-ray contrast studies, the first measures was measurements of cavity reduction in systole, i.e. the stroke volume. While this may be the most important result of cardiac pumping, it confers little information about the state of the heart itself. A dilated ventricle can maintain stroke volume, but it is reduced in terms of the left ventricle volume, and may have a severely reduced contractility. Thus stroke volume should be normalised for end diastolic volume, to obtain Ejection fraction:

Ejection fraction is still the most widely used measure of systolic left ventricular function today. This is mainly due to the vast amount of prognostic information from earlier studies, and the prognostic interventions that are geared to a cut off point in EF. Thus it will remain in use for an foreseeable future. In assessing EF, it should be emphasized, however, that EF is not a direct measure of myocardial function, as it measures the cavity, not the myocardial deformation. At best, it could be characterised as an indirect measure. Does this matter? Yes. If we look at a few examples:

1: A person with an EDV of 125 ml, a stroke volume of 70 ml has an EF of 56%, which is fairly normal values for a grown man.
2: A dilated ventricle to 250 ml, with maintained stroke volume of 70 ml, gives an EF of 28%, which is reduced. This is in accordance with reduced systolic function.
3: Concentric hypertrophy reduced the cavity volume. A little old lady of 80 years with concentric hypertrophy may have a cavity of 75 ml, a stroke volume of 40 ml and an EF of 53%. Thus EF is normal, but in terms of stroke volume, the systolic function is not!

The same erroneous results will be obtained by the fractional shortening of the left ventricular cavity by M-mode, as shown by the example below.

Thus, the EF or FS is a measure that actually only works with dilation of the ventricles, and becomes erroneous in the cases of reduced EDV. Because this has been poorly  recognised, it has lead to some fairly bisaqrre results. As systolic function has been measured by EF, and diastolic function with mitral flow parameters, the hypothesis of "isolated diastolic heart failure" has been proposed. At the outset, measuring systolic and diastolic function by different measures with different sensitivity, is methodological nonsense in any case.

This has been realised, ad the term is now substituted with the term "Heart failure with normal ejection fraction" (HFNEF).

But as EF as a measure of systolic function in the case of small, hypertrophic ventricles is meaningless, the whole concept is still utter nonsense.

In all cases of pathological hypertrophy, the long axis measurements of displacement and velocity (ref), as well as strain (ref), will be reduced, demonstrating a reduced systolic function. In fact there is a close link between diastolic and systolic function when the same measures (e.g. tissue Doppler) are used for both (ref).


 The erroneous comparison between longitudinal strain and fractional shortening:

The incompressibility principle tells us that as the wall shortens in the longitudinal and circumferential direction, it has to thicken in the transverse direction, and the relation is geometrically determined. Thus the longitudinal and transverse function as measured by strain should be interrelated. Reports about radial compensation of reduced longitudinal function is in direct opposition to the incompressibility principle.  The problem arises if we do not measure the same values for longitudinal and radial function. It is quite common to measure longitudinal strain, i.e. wall or segment shortening as a measure of longitudinal function. On the other hand the fractional shortening of the chamber diameter is a well established measure of global and radial function. But in the case of hypertrophy, this may lead to completely erroneous conclusions about the changes in radial versus global function, as shown in the theoretical treatment below.


In this theoretical M-mode of the LV, a normal ventricle has a wall thickness of 1 cm, an internal end diastolic chamber diameter (EDD) of 4 cm, resulting in an external diameter of 6 cm. As most of the wall thickening is inward, with little change in outward diameter (except in the case of differing filling pressures on the two sides), an end systolic wall thickness of 1.5 cm will result in a diameter shortening of 1 cm and an end systolic chamber diameter of 3 cm. Thus, wall thickening (WT, transmural strain) is (1.5 cm - 1 cm) / 1 cm = 50%, chamber diameter reduction is 1 cm, fractional shortening (FS) is (4 cm - 3 cm) / 4 cm = 25%.  In the case of concentric hypertrophy, the chamber diameter is reduced due to increased wall thickness.  A hypertrophy leading to a wall thickness of 1.5 cm, will give an EDD of 3 cm. A systolic wall thickening of  0.5 cm will then be (2 cm - 1.5 cm) / 1.5 cm = 33%; i.e. a clear reduction in radial function. But 1 cm diameter shortening  is FS = (3 cm - 2 cm) / 3 cm = 33%, an apparent  increase in radial function, due to geometrical misconception!

From the reasoning above, any conclusions about radial function based on fractional shortening in the presence of hypertrophy may be erroneous, and the term radial function needs to be defined. The conclusion that there is radial compensation for reduced longitudinal function should be reserved to the cases where WT is increased.

This can be extended to three dimensions, and in an ellipsoid model of the heart, there is possible to have

Comparison of cavity measurements and strains in three dimensions.

The lack of absolute relations can be illustrated by the following theoretical example (the calculation of the values are described in the mathemathics section here):


Normal
Hypertrophic

Diastole
Systole
Diastole
Systole
Outer diameter (cm)
6.5
5.85
7
6.6
Wall thickness base (cm)
0.9
1.35
2
2.3
Wall thickening (%)
50

15
Midwall diameter (cm) 5.6
4.5
5
4
Midwall circumference (cm) 17.6
14.1
15.7
12.6
Circumferential strain (%)

20

20
Inner diameter (cm) 4.7
3.15
3
1.7
Fractional shortening (FS %)

33

43
Outer length (cm)
10
8.7
10
>10
Longitudinal strain (%)

-13%

>0
Total volume (ml)
221
155
256
230
Cavity volume (ml) 110
45
42
17
Wall volume (ml) 111
111
214
214
Stroke volume (ml)
65

25
EF (%)

59

60
Theoretical comparison of a normal versus a hypertrophioc ventricle, with the end diastolic length, diameter,  wall thickness and wall thickening chosen as shown above. Then Circumferential strain and fractional shortening can be calculated. The total volume and wall volume can likewise be calculated from an ellipsoid model. Assuming an unchanged wall volume (incompressibility), the length can be calculated, giving longitudinal strain and systolic total volume, and the cavity volume is given as the difference between systolic total volume and (unchaged) wall volume. Although the values are arbitrarily chosen, it goes to illustrate that in the case of hyopertrophy, there may be an increase in all cavity measurements, despite no increase in any strain values (absolute).

Peak systolic versus end systolic measures of ventricular function.

Peak systolic measures are the measures of peak ventricular performance, and can be measured as peak ejection velocity in the LVOT, peak annular systolic velocity, and global ventricular strain rate. These occur early in systole, and are fairly load independent, as maximum afterload is reached later in systole. Peak velocity is related to accelleration, which is a direct measure of force, and thus to contractility. However, they are not completely load independent, as increased load will result in a delayed and blunted development of force and velocity, as opposed to the pressure/volume relation.

End systolic measures on the other side, are measures of the total work performed by the left ventricle during ejection. This is influenced not only by force, but also by load (resistance), and the ejection time (HR). They are stroke volume, annular displacement and global strain, in addition to EF. Whether this influences the sensitivity of the measures, is not clear so far.


Global strain and strain rate

Global strain and strain rate, may be taken as global measures of ventricular function. This can be achieved simply by measuring and averaging the strain/strain rate in all segments of the ventricle.  However, there is one caveat:
Commercial software may give segmental values for six segments in each  imaging plane, resulting in a total of 18 segmental values. However, this results in equal weight given to all myocardial levels, despite there being much less myocadium in the apical level. In order to ensure that the average value gives similar weight to all parts of the myocardium, only four segemnts in the apical level should be included, as recommended by ASE/EAE (146). Thus, the global measures may be misleading.

It is common to normalise levt ventricular volumes, stroke volume and cardiac output for body size, f.i. body surface area (BSA). Mitral annular displacement and systolic velocity are also related to heart size, and might be normalised for body size. However, this is so far not customary, and further investigation into normal variation should be undertaken.

Strain and strain rate, however should not be normalised for body size. Both measures are deformation per length, i.e. in fact normalised already for the size of the ventricle. Further normalisation for body size (which in fact is a correlate of healthy heart size), will then be erroneous. This is analogous to the fact that EF, which is stroke volume normalised to end diastolic volume, is never normalised again for BSA.

Global strain by speckle tracking has been introduced as a new measure of global left ventricular function (147). This compensates for the shortcomings of ejection fraction, being both more correct in the case of small or hypertrophic ventricles, and more sensitive (149). In the 2D strain application, it should be noted that the application relies heavily on the AV plane motion, and then distributes the motion along the wall as explained and shown above. By this method, regional artefacts as drop outs and reverberations will have less impact, which is an advantage in measuring global function. (As it may be a disadvantage in regional function, as the same smothing may reduce the sensitivity to regional reduced function). Global longitudinal strain by this method has been shown to be more sensitive to infarct size and correlate better with infarct mass than bot EF (poor performance) and annulus displacement (fair performance) (150). Global longitudinal strain is thus a measure of wall shortening, normalised for the length of the wall, as length is measured along the curvature. Whether this allows sufficiently for the reduced amount of myocardium in the apex, seems unclear, as the referred study included 33 anterior and only 7 inferior infarcts. Annulus displacement had a slightly less accuracy than global strain, but wether this was significant is less clear. Normalising the annular displacement for LV length (see below), improved the accuracy, bringing it closer to global strain (150). In fact, annular displacement normalised for LV length IS a measure of longitudinal strain.

Normalised displacement and velocity.

As described above, the annular displacement divided by the length of the ventricle is a measure of global strain. Similarly, the annular velocity divided by the ventricular length is a measure of global strain rate. In fact, both displacement and velocity can be normalised for (divided by) the distance from the apex to the point of measurement as shown below.  


Normalised velocity/ displacement.  The velocity and displacement in each point along the wall from apex to base is the resultant (sum) of the contraction of all the segments apical to the measuring point. Thus dividing the velocity or displacement at a certain point along the wall by the distance of the point from the apex, will normalise the velocity and displacement for the distance, resulting in values that are similar to strain rate and strain.

Mainly, this approach will be a compensation for the velocity / motion differences between apex and base, making the evaluation of these measures position independent (54). For displacement, being maximal at end systole, this will be similar to the strain of  the whole myocardial segment between the apex and the measurement point. The normalised velocity may also be taken as a global strain rate. For this to be similar to regional strain rate, however, the systolic curves has to be parallel in all segments. This means that peak strain rate must be simultaneous in all segments, and simultaneous with peak velocity. It has been clearly demonstrated that this is not the case in diastole (19). In systole, it seems probable that the peak velocity of contraction is simultaneous. With the present high variability of strain rate measurement, however, this cannot be demonstrated, there is wide range of time intervals to peak systolic strain rate (55). However, this variation is random (55), not systematic as it is in diastole (19), so the variability may be method dependent.


 

Back to website index.

References:



Editor: Asbjørn Støylen Contact address: isb-post@medisin.ntnu.no, Updated: 2008    Hits so far: