Basic concepts in
myocardial strain and strain rate
Department of Circulation and Medical Imaging,
Faculty of Medicine,
NTNU Norwegian University of Science and Technology
This section extends the basic concept of strain into the specific
geometry of the left ventricle. It is important to understand that
the effects seen by strain rate imaging has geometrical
explanations. This means that over all geometry governs the changes
and relations between strain components. This is true both of
transmural and circumferential as well as area strain. Also, the
strain gradient across the wall seen both in transmural and circumferential strain is mostly due to
geometry, not differential fibre action.
to website index
- Relations between tissue
velocities and strain rate
are the differences between strain rate and strain?
Basically, strain is the total systolic shortening,
equivalent to the isotonic shortening in experimental models,
and thus very afterload dependent. Peak systolic Strain rate,
on the other hand has been shown to be more closely related to
contractility, but the physiological limits of this
correlation is discussed.
volume It has been shown that strain relates best
to the stroke volume, and thus is both afterload and volume
Strain rate, being the temporal derivative of strain shows
more detectable shifts, especially in colour M-mode, making it
more useful for timing purposes.
left ventricular dimensions Left ventricular
dimensions and geometry is closely related to the geometry of
left ventricular strain. Thus, normal values and the relation to
body size, age and gender are included here. Normal values
provided from the HUNT study.
The data from the HUNT study suggests that
relative wall thickness are both body size and age
dependent, that while wall
thickness increases with age, LV length decreases, invalidating
previously findings of M-mode based LV mass increase with age.
Finally, the ratio
of LV length and external diameter is BSA
independent and (nearly) gender independent, but decreases
with age, being a measure of age related remodeling. Tables of
normal findings from the HUNT study are added.
- Geometry of myocardial strain
directions - normal strains
in the heart
- Transmural strain which some calls "radial strain". The
term "radial, however, is ambiguous, as in general
ultrasound terminology this means "in the direction of the
ultrasound beam".There is no such thing as "radial
function". Radial strain means wall thickening, but there
are no myocardial fibres going in the radial direction. Wall
thickening is a function of wall shortening, as the heart
muscle is incompressible.
strain Circumferential strain do NOT
reflect circumferential fibre contraction. There would have
been circumferential shortening even without circumferential
fibres. Circumferential strain is mainly
the circumferential shortening due to inward movement of
midwall or endocardial circumference as the wall thickens.
Also, the global circumferential strain is
the same as the negative value of fractional shortening as
As different vendors use different
definition of circumferential strain (midwall or endocardial),
there is no standard circumferential strain.
- Area strain Area
strain is neither the sum, nor the product of
circumferential strain. A slightly simplified modelling
will give the formula A = L * C + L + C . Thus, area
strain is a function of longitudinal and circumferential
strain, not a "new" parameter.As different vendors use
different definition of area strain (midwall or
endocardial), there is no standard circumferential strain.
there apex to base differences in strain and strain
there layer specific strain, and can we measure it?
- Even though analysis software will produce layer values at
request, layer strain separation depends on line density, line
width, direction in relation to the wall (in order to avoid
pericardial echoes), and focussing. Number of lines is again
dependent on frame rate. It is difficult to achieve a
sufficient line density as well as narrow enough lines.
and fibre direction
Relations between tissue
velocity and strain rate
Strain rate is calculated at the velocity difference
per length unit /velocity gradient) between two points in the
The velocity difference varies during the heart cycle,
and the distances are shaded red when the differences are
negative (v1<v2), and blue when they are positive
(v1>v2). The resulting strain rate curve is shown to the
left, with negative strain rate shown in red, positive shown
in blue. Mark also that the peak strain rate and peak
velocities are not simultaneous in this segment.
This is shown in more detail here. Peak velocity (left,
A) is earlier than peak strain rate (Middle, B), but from the
figurte to the right, it is shown that B is the point of
maximum ditansce between the curves.
Thus the distances between the two curves is an
indication of the strain rate:
Left: velocity curves. Middle: strain rate curves from
the two segments between the velocity curves. Right, the areas
between the velocity curves corresponding to, and shaded with
the corresponding strain rate curves. Peak strain rate is not
simultaneous in the two segments, peak velocity is more
simultaneous due to the tethering effects. This is described
in more detail here.
But this means that the global strain rate (of a wall or the whole
ventricle), equals the normalised, inverse value of the annular
If the two
points are at the apex and the mitral ring, the apical
velocity , apex being stationary, and is
annular velocity. then
equals wall length (WL),
thus and peak .
Thus, peak strain rate is peak annular velocity normalised for
Comparison between velocity and strain rate. Left, strain
rate of most of the length of the septum, right spectral Doppler
of the mitral annulus of the same wall. The two curves can be
seen to be very similar, although the strain rate curve is
inverted as explained above. Also, the values and units are
different, as strain rate is divided by the ventricular wall
length. The summed strainrate curve has peak strain rate very
close to the time of peak velocity, but tihis is due to the
averaging effect, as peak strain rates differ between segments.
Exactly the same is the case for basal displacement vs strain, of
course as shown in the basic concepts section.:
The difference in displacement varies during the heart
cycle, and the distances are shaded red, always being negative
(d1<d2). The resulting strain curve is shown to the left,
strain rate being negative during the whole heart cycle,
isshown in red. Mark that as opposed to peak strain rate and
peak velocities, peak displacement and peak strain are
simultaneous, being near end ejection.
Septal strain and strain rate (right) from (nearly) the
whole septum, and basal septal velocity and displacement
(left). As the apex is (nearly) stationary, the basal velocity
and displacement is a motion inscribing the whole of the
shortening of the wall, the deformation curves from of the
whole wall is very near the inverted motion curves from the
base as described elsewhere.
The negative deformation curves is from the original
Lagrangian definition where shortening is baseline
length + resulting length, becoming negative when there is
shortening. Motion measures are absolute, deformation
measures are relative. Peak shortening can be measured as
either peaks systolic annular displacement (MAPSE) and peak
systolic strain, and shortening rate as peak systolic basal
velocity, the S' or peak systolic strain rate, SR. All four
measures are in clinical use with ultrasound.
Thus, basal velocities are equivalent to wall
strain rate, and basal displacement, are equivalent to wall
The strain rate being the difference between the decreasing
velocities from base to apex, means that while velocities
decrease, strain rate is more or less constant ´from base to apex
as described below.
velocities from base to apex.
strain rate from base to apex, i.e. velocity fgradient
is constant (linear) as discussed below.
the differences between strain rate and strain?
Basically peak systolic strain rate is peak rate or velocity of
shortening. This occurs after ejection start. Thus, both peak rate
of shortening, and maximal shortening are afterload dependent, as
Peak rate of shortening occurs later, in the twitch model at the
transition from isometric (isovolumic) to isotonic work, and is a
function of the time from peak RFD to initial shortening, in the
intact ventricle a little later, probably due to inertia. Total
shortening, on the other hand, is also a function of the time where
tension is equals the total load. This means, it is an end
systolic measure, an expression of the total systolic work (at
least the ejection part). Thus, it will be load dependent to a great
degree. Peak strain rate, is peak systolic measure, the peak rate of
deformation during ejection. It is simultaneous with peak ejection
rate, thus early in ejection, closer to the time of peak dP/dt,
(which is during IVC), the peak rate of force development. Thus, it
is less afterload dependent, although shortening velocity is still
load dependent as shown already by Sonnenblick (209).
The relation of strain rate to contractility was shown
experimentally by Greenberg (80).
Greenberg found a 94% correlation of SR with LV elastance Emax, 82%
with preload recruitable stroke work PRSW and 78% with dP/dt, in a
study comparing baseline to low and high dose esmolol, baseline and
and low and high dose dobutamine. However, HR increased as well, and
inotropic stimulation increases.
|Left: Twitches in isolated
papillary muscle from (208).
Top, twitches with increasing afterload, showing the
isometric phases before tension equals load, and whan
tension equals load, further contraction is shortening
under constant tension (isotonic). Below are the
corresponding length diagrams of the same twitches.
From the diagram it is evident that:
- Peak rate of force development occurs during the
isometric phase, i.e. before onset of shortening,
except in the completely unloaded twitch
- Peak rate of shortening occurs at start of isotonic
shortening, i.e. later than peak rate of shortening
- With increasing afterload, onset of shortening is
delayed, peak rate of shortening as well as total
shortening is reduced
|Right: strain rate (top) and
strain curves from a healthy subject. The similarity
of the strain curve to the shortening curve to the
left. The differences are due to the interaction of
the ventricle with valves, blood and atria.
- Initial shortening occurs before
mitral valve closure (350,
351). This means that the initial contraction is
near unloaded, and thus show an initial shortening
- With MVC, the ventricle enters an isovolumic (i.e.)
isometric phase. Peak RFD occurs in this phase, and
corresponds to peak dP/dt.
- With AVO, the ventricle enters the ejection phase,
corresponding to the isometric phase, (although it is
not completely isometric, as seen from the pressure
curve). As seen from the strain rate curve, however,
there is a delay after AVO, before peak rate of
shortening (peak strain rate), which may be an
inertial effect as the blood pool being ejected is
Peak rate of force development is the peak
dP/dt, closely related to contractility (241) and afterload
although preload dependent (395
However, this occurs during during IVC (241), when ther
eis isometric contraction, and hence, no hsortening, i.e. no
strain or strain rate.
Thorstensen found that early (peak) systolic measures were more
responsive to changes in contractility (223)
than end systolic measures.
In an elaborate study using both esmolol and Dobutamine, but
controlling for heart rate by atrial pacing, Weidemann (79)
did show that while strain strain rate was a closer correlate of
contractility, as in the study by Greenberg, Strain was a correlate
of stroke volume. Thus, strain is both volume and afterload
sensitive. Peak strain rate is still preload sensitive (via the
Frank-Starling mechanism), and afterload sensitive, but to a lesser
degree. The same was found in animals exeriments by Ferferieva (408).
The close relation between strain and stroke volume seems evident,
when looking at the volume and strain curves below.
This has recently been supported by a work
showing changes in strain during chemotherapy may be due to
volume changes rather than contractility changes (396
Longitudinal strain is negative during systole, as the ventricle
shortens. Peak strain is in end systole, after this, the ventricle
lengthens again. But the strain remains negative until the ventricle
reaches baseline length. thus the values of the strain are less
sensitive to event timing. Strain rate on the other hand, is
negative when the ventricle shortens, shifting to positive when the
ventricle lengthens, irrespective of the relation to baseline
length. Thus events with changes in lengthening or shortening rate
are much more evident by the strain rate crossing over between
positive and negative. This is most evident in colour M-mode, which
also can differentiate timing of events at different depths.
Looking at the strain rate and strain curves from one
singe heart cycle to the left, it is evident that while strain
(bottom) remains negative throughout the heart cycle, strain
rate (top) shifts between positive and negative. It can be
seen that the shifts from positive to negative (zero
crossings), in strain rate, corresponds to the shifts from
increase to decrease, or vice versa in strain (i.e. the peaks
and troughs in the curve). The peaks of the strain rate curve
on the other hand, corresponds to the change in the rate of
increase in the strain curve (of course), seen as the shifts
from concave to convex (or vice versa). The correspondences
are not perfect, as the strain rate is Eulerian,
while the strain is recalculated to Lagrangian,
as is the common convention. To the left are colour M-modes.
Strain rate (top) can identify the events by the
positive-negative shifts (blue-orange), while the peaks are
not discernible. But the colour M-mode discerns the
differences between event shifts in different depths. Strain
colour M-mode is not very useful in timing events.
Dimensions of the ventricle is closely related to the functional
measures. While the motion
indices of displacement and velocity are dimension unrelated,
and strain rate are relative deformation measures,
and thus related to dimensions. Thus changes in dimensions will
relate to changes in strain and strain rate. The HUNT study, being
ta large study of normals has published normal values, related to
age and gender (386):
Conventional left ventricular cross sectional measures from
M-mode in the HUNT study by age and gender, raw and indexed for
BSA. SD in parentheses. From (386).
*p<0.001 compared to women. †p<0.01 compared to women.
‡Overall p<0.001 (ANOVA) for differences between age groups.
Wall thicknesses and LVIDD correlated with BSA (R from 0.41 - 0.48),
Thus, all values were consistently higher in men due to this. FS, of
course, did not correlate with BSA, and was thus gender
independent. Wall thicknesses increased with age (R=0.33),
while LVIDD and FS remained constant between age groups, in
accordance with other studies (387,
Normal range is generally considered the interval between the 2.5
and 97.5 percentiles, ie. more or less mean ± 2SD.
|Wall thicknesses and chamber
diameters. RWT = (IVSd + LVPWd)/LVIDd, but there was no
difference if we used LVPWd x 2 / LVIDd. FS = (LVIDd -
LVIDs)/LVIDd. Left ventricular external diameter; LVEDd
= IVSd + LVIDd + LVPWd.
|Left ventricular length. Wall
lengths were measured in a straight line (WL) in all six
walls from the apex to the mitral ring. This wil
underestimate true wall lengths (dotted, cirved lines),
but will be more reproducible, as the curvature may be
somewhat arbitrary. LVL was calculated as mean of all
four walls, thus overestmating true LVL (yellow line)
slightly, but again the arbitrary placement in the
middle of the ostium will result in lower
reproducibility, while taking the mean of six
measurements will increase it.
Relative wall thickness
Relative wall thickness is generally considered to be a body size
independent measure, as both wall thicknesses and LVIDD are body
size dependent, the RWT, supposedly, is normalised for heart size,
and hence, for body size. Interenstingly, in the HUNT study this was
not the case, although correlation with BSA was very modest
(R=0.18). This probably do not warrant normalising RWT for BSA. More
pronounced was correlation with age (R=0.34). The age dependency is
a logical consequence of the unchanged LVIDd and increasing wall
thickness, and has been shown also previously (391).
|Relation of RWT and BSA. This shows
that RWT is not perfectly aligned with body size.
|RWT and age. This shows a more
marked dependence of RWT and age, so age related normal
values is probably warranted.
Current guidelines recommend a cut off value of 0.42 between normal
and concentric geometry (146)
without taking age into consideration. In HUNT, however, the normal
upper limit is also closer to 0.52 over all.
The age relation is not taken into account either, as upper normal
limit is increases with age, from 0.41 to 0.54 in women and 0.44 -
0.54 in men, so age related values is warranted, unless one will
consider that all > 60 years have concentric geometry.
ventricular length and external diameter:
Left ventricular length and external diameter is also important in
an evaluation of the total strain images. We measured these in the
HUNT study as well:
Left ventricular length and external diameter by age and gender
from the HUNT study, raw and indexed for BSA. From (386).
Left ventricular external diameter, is simply the sum of the wall
thickensses and LVIDd, so it is logical that this increased both
with BSA (R=0.60) and modestly with age (R=0.11, the unchanged LVIDd
being part of it, dilutes the effect of wall thickness) (386).
Left ventricular length, on the other hand, increased with BSA
(R=0.29), but decreased with age (R = -0.12).
Fundamental findings are summarised below:
|Fundamental findings in the HUNT
study: With increasing BSA, both wall thickness,
internal diameter (and hence, external diameter) and
relative wall thickness increase, showing that neither
measure is independent of body size (or heart size). The
length / external diameter, however, remains body size
independent, being a true size independent measure.
Differences are exaggerated for illustration purposes.
|With increasing age, both wall
thickness (and hence, external diameter) increase, while
internal diameter is age independent. Left ventricular
length decreases, and hence length / external diameter
decreases, and i a measure of age dependent LV
remodeling. This has implication for LV mass
calculation. Dimension changes are exggerated for
LV length and external diameter
The ratio L/D did not correlate with BSA, was near gender
independent (although the difference was significant due to the high
numbers), but declined somewhat more steeply with age (R = -0.17).
This has some important corollaries:
The L/D ratio may be a new measure of LV hypertrophy.
- LV shape in healthy adults, is in itself a physiological
- Normalising cross sectional measures to LV length, corrects
better for heart size than normalising for BSA
- The ratio L/D is a measure of age dependent remodeling in
- LV mass calculations based on cross sectional (M.mode
measures), will over estimate LV mass increasingly with age, and
the assumption of age dependent mass increase with age may not
Wall lengths per wall
Different walls has different lengths. In the HUNT study, the wall
Diastolic lengths of different walls (Mean and SD) measured in a
straight line from apex to mitral ring, by age and gender. Only
over all values are published in (386):
All lengths in cm.
|Mean of two;
septal and lateral
|Mean of four;
|Mean of all six
The lateral and inferolateral walls were significantly longer than
all other walls (including each other). The septum and anteroseptal
walls were significantly shorter than all other walls. Means of two,
four and six walls were all significantly different from each other,
but the differences were negligible, considering that the limit for
measurement accuracy is 1 mm.
|Still preaching my
personal litany: Strain is geometry.
(Cormorant, Galway, Ireland).
longitudinal, transmural, circumferential.
Myocardial directions -
Asa describe in "basic
concepts"section, the strain tensor has three normal strains (11)
in the x, y and z directions in a Cartesian coordinate system. Also,
in an incompressible object, meaning that deformation doesn't affect
volume, the three strains have to balance by the incompressibility
Strain in the heart also has three main components, but the
directions are customary related to the most common coordinate
system used in the heart: Longitudinal, circumferential and
transmural. (The term "radial" is often used to describe transmural
direction, but as this in ultrasound terms also means in the
direction of the ultrasound beam in the ultrasound
coordinate system, "radial" strain is ambiguous and should be
avoided. Transmural strain is unambiguous).
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.)
||This long axis video shows
how the apex is stationary, while the base moves toward
the apex in systole, away from the apex in diastole.
This means the ventricle shows strain between apex and
base. Longitudinal strain will be negative (shortening)
during systole and positive (lengthening) during
diastole (if calculated from end systole).
||This short axis video shows
both transmural and circumferential strain. Systolic
transmural strain equals wall thickening. Systolic
circumferential strain is the systolic shortening of any
of the countours; outer, midwall or endocardial, The
change in outer contour is least, while the endocardial
contour shortens most, thus, there is a gradient of
circumferential strain across the wall. This is
Thus, systolic deformation in the heart occurs in all three
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.
- Longitudinal systolic strain
- Transmural systolic strain
= relative shortening of one of the
circumferences (external, midwall or endocardial).
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.
In addition, as the myocardium is (basically) incompressible, the
volume do not change (much) during systole, so the strains are inter
in the heart:
If an 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, i.e. strain in the three dimensions
in a coordinate system cancel out as described in the basic
concepts section. This means that cartesian strains balance:
Although there may be some diminishing of volume due to collapse of
small intramural vessels, and crypts, but this is limited, and
still, there has to be substantial inter relation between the strain
components as illustrated below.
In the heart, this is equivalent with:
, the myocardium is expanding,
, the myocardium is shrinking
In two larger studies of strain by speckle tracking in three
the strain product values were 0.87 and 0.91, respectively. Due to
inherent limitations in speckle tracking, however, there may be
systematic over estimations of longitudinal strain, or under
estimation of transmural strain, or both, so this is not resolved.
Longitudinal strain, being relative longitudinal systolic
shortening, is, from the Lagrangian
definition of strain, it follows that longitudinal strain is:
. It follows from the formula, that as
there is systolic shortening, systolic longitudinal strain is
negative (systolic length smaller than diastolic).
Longitudinal shortening of the left ventricle. The
absolute shortening is the MAPSE, while the relative
shortening is the normalised MAPSE = MAPSE / L0.
However, this is not ambiguous. Over all ventricular strain
should be as illustrated above. However, wall strain would be
measured along the walls, and the mean wall strain would be a
measure of global LV strain. As shown above, wall strain
length can be measured in different ways, which has consequences
for strain measuremnt.
|Left ventricular length, is
LVL, ,easured from the apex to the mid-annulus. Wall
length is either measured in a straight line from
apex to the mitral ring, or in a curved along the
wall. The mean of the straight line
leasures, will over estimate LV length, but under
estimate the true wall length. The curved line will
further over estimate the LVL, thus being further
from the LV strain, and will also be less robust, as
the curvature may be somewhat arbitrary.
being (L - L0) / L0
will thus relate to
the length used. Both the strain length, L0
and the shortening (L - L0) will be different when
measured along the LV length (Black/grey), a skewed
line (red) and even longer along a line following the
wall curvature (blue). This will be especially
evident depending on how shortening is used.
It's important to realise that different
applications may measure strain in different ways as indicated
in the above right figure, and as shown
measures along the curved line following the wall,
as well as Tissue Doppler will measure along the
ultrasound beam, being a straight line, while segmental
will measure along a straight line in each segment,
thus being somewhat in between, as shown by this
figure. Also, there is a slight difference between longitudinal
stain measured in the midwall compared to endocardial
measurement, due to the inward shift being more pronounced in
the endocardium as discussed below
as well as due to the fact that the midwall line is slightly
longer than the endocardial, thus giving a larger denominator in
the strain expression.
Thus, global longitudinal strain will vary with processing
Now, the EACVI?EAE task force
has recommended that for speckle tracking, the denominator
should be the line following the myocardial wall, whether it is
is the endocardial or midwall, and also that the level should
always be reported by the software (287
- However, this is for the speckle tracking
applications only, as it is not feasible (or
indeed possible) for tissue Doppler, nor for normalised
MAPSE. And some of the comments are not valid for segmental
strain by speckle
tracking either. (The recommendations explicitly are
for 2D speckle tracking only).
- Secondly, some ambiguity remains, as applications where
the ROI has the same width in the base and apex, despite the
differences in thickness of the myocardium. In this case, at
least one side of the ROI will not follow the wall, and the
mid line of the ROI will not follow the midline of the wall
(or, if the ROI are suited to the midline, the endocardial
side of the ROI will not follow the endocardium). If so, the
results may vary as shown in the figure below:
This is discussed further in the pitfalls
Transmural strain is simply relative wall thickening. There is no
such thing as "transmural myocardial function", as there are no
transmural fibres. Wall thickening is solely due to incompressibility; as
the wall shortens, in the longitudinal, and eventually also in the
circumferential direction, it must thicken in the transverse
direction to conserve volume.
|Wall thickening. Systolic wall
thickening equals systolic transmural strain: WT = (WS
- WD)/WD =
|Wall thickening, illustrated from
the loop shown to the left. The outer (red) and
endocardial (yellow) contours and wall thicknesses are
shown in the diastolic image to the left, and
transferred to the systolic image on the right, shown as
dotted lines of the same colour. The systolic contours
are shown as solid lines. The systolic wall thickness is
then (more or less) the dotted plus the solid blue
lines, and the wall thickening the solid blue lines.
Thus, transmural strain
is a purely segmental measure. Global transmural strain either has
to be measured in all 16 segments, (three parasternal short axis
planes), or inferred from assumptions of symmetry.
What is very evident here, is that transmural strain in fact is a
quantitative equivalent to the semi quantitative wall
Transmural strain can be measured by speckle tracking as shown
below. It has to be measured from short axis images, as the decreasing
lateral resolution with depth precludes transmural measurements
from apical images. In fact, that option was removed after we
pointed it out.
|Short axis cine
|Speckle tracking in
the same cine loop
strain values and strain curves from the tracking.
The basics of this method is given in detail in basic
strain ultrasound section, and the limitations of the speckle
tracking method is discussed in the pitfalls
Speckle tracking, however, is not necessary for transmural
strain. Wall thickening can be measured by simple caliper
measurements of wall thickness in systole and diastole. It is still
segmental, but can be generalised from fewer measurements under
assumptions of symmetry, as has been done from M-mode. The
transmural strain can be measured in M-mode from systolic and
diastolic wall thickness, which will give wall thickening in only
two segments, but may be taken as representative as the mean wall
thickening in this plane where there is no segmental dysfunction.
However, in this case, generalizing from M-mode measurements, the
sepal and inferiolateral wall should be averaged, as septal
thickening is less than inferiolateral wall thickening (392):
strain by M-mode. The M-mode measurement is more accurate
than 2D measurements, but are only feasible in the septum
and inferolateral (posterior) wall. Thus, the transmural
strain can only be extrapolated in symmetric ventricles. Strain by tissue
Doppler is also only feasible in the two walls
perpendicular to the ultrasound beam as indicated by the
||If using M-mode, however, the
average of septal and inferolateral wall should be used,
as septal thickening is less than inferiolateral wall
However, it is very
evident that longitudinal and transmural strain are not independent.
Longitudinal shortening can easily be demonstrated in apical echo
images as shown above, as well as measured as shown below.
Transmural thickening is equivalent to wall thickening, but from the
images below, it is evident that the wall has to thicken as it
shortens in order to conserve volume (NOT MASS!!!).
ventricle shortens, the wall has to thicken in order to
maintain the wall volume, as the myocardium is more or
And as the outer contour of the ventricle
either do not change (13,
or changes very little (158),
this means that the wall thickening has to be inwards.
|Ventricular strain. Diastolic
and systolic images of the heart. Systolic shortening of
the left ventricle relative to diastolic length, is the
systolic strain of
the ventricle. From the Lagrangian definition of
linear strain; , it follows that systolic
longitudinal strain is:
it is also evident from this image, that as the wall
shortens, it also thickens, to conserve the volume.
Heart muscle is generally assumed to be incompressible.
of the left ventricle, showing the relation between
shortening and wall thickening (exaggerated for
illustration purposes), with a model of unchanging outer
contour in an incompressible myocardium.
Thus, one source of the wall thickening is simply that the volume
has to be conserved when the walls shorten. Circumferential fibre
shortening would also cause the wall to thicken, because moving the
outer contour inwards would cause the wall to thicken, as there is
less room for the myocardium within a smaller outer circumference,
thus circumferential shortening will also contribute to wall
thickening. So even inward motion of the outer circumference would
cause the wall to thicken, even without longitudinal shortening:
Wall thickening as a function of longitudinal
shortening. Calculated from a symmetric half ellipsoid model
with a diastolic mid wall thickness of 0.9 mm (decreasing
towards apex), an outer diastolic diameter of 60 mm, a
diastolic length of 95 mm. Wall thickening is calculated from
longitudinal shortening and conservation of wall volume, given
different degrees of outer contour change (outer
circumferential strain or shortening). Longitudinal
strain given in negative values; i.e. wall thickening
increases as THE VALUE of longitudinal strain increases. As
seen here, if there is no outer diameter reduction, the wall
thickening is solely a function of wall shortening.
There is no such thing as transmural function. Transmural
strain is thus in itself not a function measure. This is hardly
surprising, as there are no transmurally directed fibres. Wall
thickening reflects the thickening of the individual muscle fibers
inn all directions as they shorten.
Depending on how much or little change there is in outer contour,
the transmural strain will mainly be a function of longitudinal
shortening. Wall thickness and cavity diameter are also geometric
determinants of wall thickening. However, in any given ventricle
with a given cavity diameter and end diastolic wall thickness, the
transmural (radial) strain is a function of longitudinal strain, not
an independent measure.
If there is no outer circumferential shortening, meaning that there
is no change in outer diameter (and circumference), transmural
strain will be solely a function of longitudinal shortening, and
both globally and regionally those two parameters give the same
information. Then, the only source of wall thickening will be
the wall shortening. As the outer contour changes little during
systole, this means that as the ventricle shortens, the wall has to
thicken inwards. This has been shown in semi quantitative assessment
of regional function (7),
which supports this.
Circumferential strain means shortening of a circumference in the
|As transmural strain,
circumferential strain must be measured in short axis
|External circumference is shown in
red, midwall circumference in blue, and endocardial
circumference in orange. The circumferences from the
diastolic left frame are shown as dotted lines of the
same colour in the systolic frame to the right, to
compare with the systolic contours in unbroken lines.
The inward motion is evident, and there is a gradient
from outer to inner contour.
strain is an ambiguous term.
The circumferential strain has no meaning except as a shortening of
a defined circumference.
And this is dependent on which
circumference, as circumferential shortening increases from
the epicardium to the endocardium. Thus, there is a gradient
of circumferential strain from the outer to the inner contour, (due
to geometry NOT to layer specific function).
Thus, in order to talk about circumferential strain, first, the
question has to be answered: Which circumference?
(external, midwall or endocardial) as illustrated below.
Different software today use different definitions, some
measuring endocardial, others midwall circumferential shortening.
Thus, there is no standard circumferential strain, it is is method dependent.
When considering circumferential shortening, three points is
This means that there is fairly little relation between
circumferential fibre action and circumferential strain, except for
the outer contour. The main function of the circumferential vectors
seems to be balancing of the intracavitary pressure, but this is
isometric, and do not necessarily cause shortening.
- Circumferential shortening is to a large degree due to the
inward shift of the circumferences as the wall thickens. thus:
- Even without any change in outer contour, the endocardium will
shift inwards as the wall thickens, and there will be both
endocardial and midwall circumferential shortening
- There would have been circumferential shortening even if there
had been no circumferential fibres, as the wall thickening due
to shortening would give this inward shift.
The circumferential strain in a normal ventricle is the shortening
of a circumference due to the inward shift caused by the wall
thickening. Even if there had been no circumferential fibres,
there would have been wall thickening and thus circumferential
strain as shown in the figures below.
|Illustration of the geometric
mechanism for circumferential shortening. Outer contour
is shown in black, midwall contour in blue and
endcardium in orange. Even without presupposing
circumferential fibre shortening as shown by the
invariant outer contour, there is inward shift of
midwall and endocardial contours as the wall thickens.
This is geometry, not fibre shortening. Also as the
endocardial circumference is pushed further inwardss,
being on the inside of the whole wall, while the midwall
contour is only pushed inwards by half the wall
thickening, there is a gradient of circumferential
shortening, and thus the two are different.
|Schematic diagram of
the left ventricle, showing the relation between
shortening and wall thickening (exaggerated for
illustration purposes), with a model of unchanging
outer contour in an incompressible myocardium.
Wall thickening again
relates to circumferential shortening. Also, relative
diameter shortening (fractional shortening) equals
relative circumferential shortening.
The circumferential fibre shortening contribute
to circumferential strain, depending on how much reduction there
is in outer diameter. This will increase not only the shortening
of the midwall and endocardial surfaces, but also the gradient
of shortening from outer to inner surface. If the outer
circumference shortens, there is less room for the myocardium
which has no alternative than expanding inwards.
But again: If transmural strain is mainly a function of longitudinal
shortening, and circumferential shortening mainly a function of
transmural thickening, this means the three are inter related:
This means: Circumferential strain is partly a function of wall
thickening (and outer circ shortening)
Wall thickening is a function of longitudinal shortening (and outer
from a symmetric half ellipsoid model with a diastolic
mid wall thickness of 0.9 mm (decreasing towards apex),
an outer diastolic diameter of 60 mm, a diastolic length
of 95 mm. Wall thickening is calculated from
longitudinal shortening and conservation of wall volume,
given different degrees of outer contour change (outer
circumferential strain or shortening). Longitudinal
and circumferential strains are given in negative
values; i.e. wall thickening increases as THE VALUE of
longitudinal strain increases.
|Midwall and endocardial strain as
functions of wall thickening, for 0%, 5% and 10% outer
|As wall thickening also is a
function of longitudinal strain, midwall and endocardial
strain as functions of longitudinal strain, for 0%, 5%
and 10% outer diameter reduction.
Finally, as the circumference is simply a
function of the diameter (C = * D), circumferential strain can be
computed directly from the diameter fractional shortening
(i.e. midwall or endocardial, respectively):
= (C - C0
= ( * D - * D0
) / * D0
= (D - D0
) / D0
= ÷ FS
Thus, circumferential strain equals
(I.e. either endocardial or midwall)
strain again is available by speckle tracking in short axis images:
|Short axis cine
|Speckle tracking in
the same cine loop
circumferential strain strain values and strain curves
from the tracking. There is abnormal swtrain curves in
the inferior segments due to imperfect lateral tracking
in the remote region (reduced lateral resolution with
depth) as discussed int the pitfalls
However, again, speckle tracking is not necessary for measuring
circumferential strain. As circumferential strain equals the
negative value of fractional shortening, it can be generalised from
fewer measurements from assumptions of symmetry, as has been done
from M-mode. If the cross section of the LV is assumed circular, the
CS equals - FS. Angulation of the M-mode line wil not matter, as
this is the relative shoirtening, which will remain constant.
Illustration of the circumferential shortening from
diameter measurement, and how these can be derived from
Strain area. The Thingvellir Rift Valley in Iceland is
the rift between the North American and the Eurasian
continental plates. The plates are diverging, so the rift is
expanding and the area undergoes positive strain.
Hypothetically, with the advent of 3D
echocardiography, it would also be possible to measure
simultaneously in all direction, enabling the measurement of
composite measures. One candidate for such composite measures
is area strain
. However, as discussed elsewhere
there are serious shortcomings in 3D speckle tracking, due to
low frame rate and line density.
Both area strain as well as
transmural and circumferential strain can in principle be
assessed by 2D acquisitions, if they are processed into a 3/4D
This, however, requires tracking in both longitudinal and
transverse directions, ans thus has to be done with either speckle
alone , or
combined tissue Doppler and speckle tracking
, as shown
below. It also includes some assumptions about the angle between
the planes and simultaneity of events in the loops that are
acquired sequentially, but processed into a simultaneous image.
|3D strain rate mapping.
Reconstructed 3/4D image with longitudinal tracking
from tissue Doppler. (This is described in detail below).
Yellow represents shortening, blue elongation
and green no strain. In this case only longitudinal
strain is tracked and displayed, as can be seen from
the diameter circumference of the grid, it doesnt
change during the heart cycle.
|Apical four chamber view with
B-mode and tissue Doppler data. Longitudinal
shortening is tracked by tissue Doppler. In this
image both sides of the LV wall are marked and
the wall thickening is tracked as well, by
speckle tracking. In this
analysis both longitudinal and transmural strains
are available, but for circumferential strain 3/4D
reconstruction is necessary, and requires three
|3/4D reconstruction from three
sequential planes to a thick walled model
analysed as shown in the image in the middle.
In this case, the endocardial and midwall
circumferences are given in the grid, and
circumferential and area strains can be calculated.
(The colours in this image, however, are
tissue Doppler derived strain rate, i. e.
longitudinal strain rate).
Giving the present sorry state of 3D speckle tracking, this may
still be an option, especially as B-mode has improved
substantially with new computing
, giving both higher line density and frame
However, as area strain is not part of the original Lagangian
definition, the concept needs a definition, one reasonable
candidate is simply the systolic relative reduction in area,
giving an analogous definition to the one concerning one
Area strain. As the one dimensional
strain is relative change in length, the area strain should
have the same definition: relative change in area.
However, just as circumferential
strain, the area strain is dependent on which level of the
wall it is measured. Epicardially, there is very little
circumferential shortening at all, and the area strain would be
equal to the longitudinal strain, as the area will shorten by length
Simple geometry will then show that the area strain is a function of
longitudinal circumferential strain, and that the relation is: A = L * C + L + C
One dimensional strain is defined as
= (L - L0
equivalent for the change in area is thus A
= (A - A0
Then, in an approximately cylindrical segment: A0
and A = L * C
= (L - L0
= (C - C0
L - L0
and C - C0
L = L
+ 1) and C = C
A = L0
+ 1) * C0
A = (L0
+ 1) * C0
+ 1)) - (C0
) / C0
= ( L
+ 1) * (C
+ 1) - 1 = A
Thus the area strain is:
As area strain is a function of circumferential and longitudinal
strain, and in the "eggshell
model" circumferential strain again is solely a function of
longitudinal strain, area strain itself can be seen as solely a
function of longitudinal strain. But even if there is dependency on
both variables, this is stillnot added information, just a
Thus, for global function, area strain does
not seem to add new information. Also, for area strain, the 3D
speckle tracking technique may render it inferior to single measures
from 2D or tissue Doppler.
Where there is regionally reduced function,
however, the situation may be different. The circumferential
shortening may be reduced in a sector, and the area strain would
then be a compound of reduced longitudinal and circumferential
shortening. However, it could still be computed to certain
degree, as endocardial circumferential shortening can be computed
from the fractional shortening through the hypokinetic area. The
limitations in area strain, however, will still persist.
However, in a recent study (279)
of myocardial infarcts, 3D strain did not show incremental
diagnostic value to the other modalities. 3D longitudinal strain was
inferior to 2D longitudinal strain, and 3D Circumferential,
longitudinal and area strain did not add information, as opposed to
infarct area by tissue Doppler (243).
In order to see which consequences the incompressibility of
myocardium has for cardiac mechanics, it is important to look at the
eggshell model of left ventricular function.
The concept that the heart functions as
a double pump, with the atrioventricular
plane as a piston, rather than pumping by squeezing, is indeed a
concept dating back to Leonardo da
Vinci (57).In 1951 Rushmere was able to show by means of implanted
iron filings in dog hearts inserted in the wall of the
ventricles, that the pumping action of the right ventricle was
predominantly in the long axis direction, while the left
ventricle apparently pumped by an inward squeezing action (58).
The inward motion of the markers, however, is
dependent on how deep into the myocardium (close to the endocardium) the markers are placed.
The concept of inward squeezing motion has been confirmed by
innumerable ventriculographies (59),
the viewers to what happens the outer contour of the heart
Already in 1932, Hamilton and Rompf (59)
argued from experimental studies that the heart worked mainly by the
movement of the atrioventricular plane toward apex in systole, away
from apex in diastole, while the apex remained stationary and the
outer contour of the heart relatively constant. The heart will the
work by the principle of a reciprocating pump, alternately expanding
the atria and the ventricles, without moving the surrounding
tissue. Their hypothesis was confirmed by Hoffman and Ritmann
in CT studies in dogs in 1985 (60),
a stationary apex, constant outer contour and motion of the
AV-plane. They also stressed that this mode of action minimised the
energy expenditure as the ventricular volume rediction in systole
moves blood into the heart, rather than moving the surrounding
tissue during systole. If the heart should be pumping by inward
squeezing, reducing the outer contour of the heart this would be
unfavourable energetics, as this means moving the surrounding tissue
(lungs and mediastinum) inward by each heartbeat, without regaining
this energy in diastole. Mitral ring movement was first demonstrated
by echocardiography from the apical position by Zacky in 1967
before the time of MR and second harmonic 2D echo, Stig Lundbäck, in
a series of elegant human studies using both gated
myocardial scintigraphy, echocardiography and coronary angiography
(Demonstrating the outer heart contour by tangential cine angiograms
of the LAD), documented the invariant outer contour and the AV-plane
mode of working (13).
It has been established that the longitudinal shortening of the left
ventricle, and thus the longitudinal measures is closest related to
the stroke volume and EF, i.e. to the total left ventricular volume
- 35, 56,
This is seems to be the case when looking at modern imaging such as
MR or high quality echocardiography as f.i. above.
The radial motion
of the septum in diastole is determined by the differences in
filling pressure of the left and right ventricles. In systole, If
the filling pressures are reasonably similar, as in the normal
situation, the septum has little radial displacement in
diastole. In systole, the pressure induces a circular cross
section, as the most energetically feasible shape. Thus, during
systole, the left ventricle operates without much change in the
Given an invariant
outer contour, the whole of the stroke volume is described by the
longitudinal shortening, as wall thickening is simply a function
of wall shortening. The total volume in diastole is the sum of the
blood inside, and the muscle wall. When the left ventricle
shortens in systole, the total volume is reduced by the volume of
the cylinder shown in grey: . But the
myocardium, comprising a part of this volume is incompressible,
thus maintaining a constant volume. Thus, the whole
volume reduction is the reduction in blood volume, in
other words the stroke volume: . Thus, the
stroke volume is given by the outer diameter and the systolic
longitudinal ventricular shortening (56).
as the myocardium is incompressible, the wall shortening and
thickening, and thus the internal diameter reduction have to be interrelated
thus both would be valid measures of stroke volume. In a newer
study, the correlation between MAE and stroke volume in healthy
adults was seen to be about 90%, corresponding to an explained 82%
of the stroke volume compared to the reference (Simpson). Thus, an
outer contour systolic reduction of about 3% should be present to
explain the rest of the stroke volume (158),
and may be more in real situations. This is little compared to
wall thickening, showing that the main inner contour diameter
reduction is due to longitudinal shortening and incompressibility,
as discussed above.
Thus, the eggshell model is fairly accurate, and the long
axis function describes most of the pumping action of the
M-mode as well as short axis cross sections, may sometimes show
greater inward motion of the outer contour, due to the out of plane
motion of the base of the heart.
|As can be seen, the base of the
heart moves through the M-mode line during the heart
|This means that measurements in
fact are taken from different part of the ventricle in
end diastolie and end systole. It seems to indicate that
systolic measurements are done in a part of the
ventricle withsmaller diameter, thus over
estimating inward motion of the outer contour.
model and atrial filling.
In the eggshell model, the atrioventricular plane has to be the
piston of a reciprocating pump as discussed ), expanding the atria
while the ventricle shortens and shortening the atria while the
ventricle expands. This is energetically feasiblel, as the work used
to decrease the volume, in additon to ejection, also moves the blood
from the veins into the atria. If the heart had worked by squeezing
changing outer contour to a high degree, the work would have been
used to shift the rest of the thoracic contents especially lungs
inwards in each systole, work that would have been wasted. Thus,
most of the filling volume to the ventricles, is a function of the
AV-plane pumping, as also discussed it the section of strain
in the atria.
The eggshell mechanism
But how is this possible, even if energetically favorable, the
pericardium is not stiff, and the surrounding lung tissue is highly
compliant. The muscle forces would tend to reduce both inner and
outer contour, as the circumferential fibres contract. If the
pericardium had been stiff, this would generate a pressure drop, and
the vacuum would hold the myocardium against the pericardium. But as
the pericardium is pliable, this would not work. And Smiseth et al
has shown that pericardial pressure actually increases during
systole, if measured by proper techniques (63).
Allso, the apex beat is a clinical empirical fact, meaning that the
apex moves towards the chest wall in systole, thus not creating a
suction at the apical location:
The answer may lie in the recoil forces. The pericardium is soft,
but non-compliant. During ejection, the ventricle impels a momentum
to the blood volume being ejected, generating a momentum of similar
magnitude, but opposite direction according top Newton's third law (mv
- mv where m is mass and v is velocity). The
recoil, pressing the heart toward the chest wall as can be felt by
the apex beat and demonstrated by apexcardiography and has been
demonstrated by echocardiography as well (33).
the pericardium, although pliant, is not elastic, and pressing the
heart into the pericardial sac will give a constraint and pressure
increase as previously shown (63).
momentum away from the apex is ejection of the stroke
displacement of the ejected volume is equal to the stroke
velocity integral (measured by Doppler flow in the left
ventricular outflow), which is about 15 to 20 cm. The motion of the opposite
momentum is displacement of the annular plane,
which is between 1 and 1,5 cm (30) at the same time, and the
mass being displaced also equals the (mass of the)
stroke volume. The mass is the same. The
mean velocity, and thus, the momentum, being mv, being
generated by ejection is at least ten times the momentum
pushing in the other direction, thus generating the
forces pushing the heart into the pericardium, which is
can be felt as the apex beat, shown here in an
apexcardiogram taken with a pressure transducer,
demonstrating that the beat is a systolic event. (Image
modified from Hurst: The Heart).
beat can also be demonstrated by M-mode echocardiography
and tissue Doppler.
A recent study demonstrates the importance of the pericardium in
accordance with the above arguments in an elegant way (122).
the velocity and strain rate by TEE during an operation, they show
that when the apex was dislodged from the pericardium, the basal
velocities changed direction, so the base and apex moved toward each
other in systole, without any change in strain, i.e. the myocardium
still shortening at the same rate. The motion of all basal regions
toward the apex was reestablished after the heart was repositioned
within the pericardium.
The volume (and
mass) being ejected, is equal to the volume being moved
towards the apex as shown here.
However, the septum is not contained in the pericardial sac. But the
motion of the septum is small compared to the wall thickening, and
some of the motion may be apparent as shown above.
Thus, the pumping action of the left ventricle can be described by
the long axis changes, and is a measure of the systolic
pumping function. Even so, much of the ventricular work is not taken
into account by this, namely the work that is used for increasing
the pressure from low filling pressure to high ejection (aortic)
pressure. However, this is true whether measures of cavity size such
as stroke volume, ejection fraction, shortening fraction. or
measures of longitudinal shortening such as mitral annulus
displacement, systolic annulus velocity, longitudinal strain or
longitudinal strain rate is used.
As stated above, transmural strain is a measure of deformation, not
of function, due to the incompressibility.
strain in three dimensions. Relation of long axis
shortening and wall thickening. As the heart muscle is
generally considered incompressible, longitudinal
shortening must give transmural thickening.. Thus as the ventricle
shortens, the wall has to thicken correspondingly in order
to preserve wall volume, the thickening shown in blue. In
this case, the outer contour of the left ventricle is
assumed fairly constant, as described below.
However, transmural strain will be very much influenced by
processing, especially ROI size (276),
as discussed here.
There will be a gradient of transmural strain from the epi- to the
endocardium. As the wall thickens, the endocardial layers expand in
a space with a smaller circumference, and thus they have to thicken
more for the same volume increase. But this is due to geometry,
not to any gradient in layer function, as discussed below.
This so-called "eggshell" model of the left ventricle has been
supported by other studies (13,
as discussed below.
If there is a component of
circumferential fibre shortening, this must mean that there will be
a decrease in outer diameter, which then also contributes to wall
Speckle tracking in short axis image. The thickness
follows the wall thickening,
and the mid line in the ROI shows midwall circumferential
This means that the measure of circumferential strain is
- either segmental, measuring strain in separate segments,
- or regional, the average circumferential strain in a short
axis plane is representative for that plane only,
- and that the FS of that plane as measured by M-mode, is equal
to the average circumferential strain in the same plane.
|Midwall (blue) and endocardial
(orange) circumferential strain is equalt o the negative
value of fractional shortening, and thus, the mean
circumferential shortening of the short axis plane can
be measured from M-mode.
is incompressible, and the incompressibility equation then
works out to:
all normal strains are interrelated.
In the "eggshell" model of the left
ventricle, if there is no outer diameter change, circumferential
strain is solely a function of wall thickening, which again is
solely a function of longitudinal shortening. Then, all information
about LV deformation is given by the longitudinal strain, the other
principal strains are simply derivatives. The function of the
circumferential fibres are mainly to balance pressure, thus
circumferential function is mainly given by the peak pressure (and
diameter - wall stress), and without sortening, this is tension
without deformation, i.e. isometric muscle work.
Looking at the ventricular
volume curve shown below left, it is evident how much the volume
curve reflects a longitudinal strain curve, showing the close
relation between longitudinal deformation and pumping volume.
|Left ventricular volume curve
from MUGA scan (gated blood pool imaging by 99Tc
labelled albumin. The total volume is proportional to
tne number of counts, thus making MUGA a true volumetric
method, but averaged from several hundred beats.) It is
evident that there is volume reduction corresponding to
ejection, then there is early and late filling. Thus
this might seem to correspond to contraction -
relaxation. The temporal resolution of MUGA is low, and
the isovolumic phases are poorly defined.
(shortening) curve from left ventricle. Note the close
correspondence to the volume curve on the left, but due
to higher temporal resolution, the isovolumic phases are
visible. It is evident that the longitudinal
shortening describes most of the volume changes. Again
the shortening might seem to be contraction, and the
(early) elongation relaxation.
Thus, the pumping action of the
heart, i.e. the ejection
volume can be described mainly by the long
If myocardium is incompressible the three strains anyway must
If myocardium is partly compressible;
if the object expands, (i.e. volume increase, )
if it compresses (i.e. volume decrease)
Thus, neither transmural nor circumferential strain are
independent measures of ventricular function. However, the
relations will change not only with longitudinal strain, but also
with ventricular size and wall thickness, still dependent on the
geometry of the ventricle.
As strain measurements are software dependent, inter vendor
consistency is low, although best for global longitudinal strain (277,
as might be expected as the sources of differences are smaller.
apex to base differences in strain and strain rate?
As apex is stationary and the base of the ventricle moves, there
has to be a gradient in velocity and motion from base to apex. As
strain rate actually is that velocity gradient, the
presence of a gradient in strain rate depends on whether the
velocity gradient is constant or not.
Looking at the V-plot,
the curve seems fairly straight, i.e. the velocity gradient
seems fairly constant along the wall:
|Good quality V-plot shows
velocities as near straight lines, and
thus, a constant velocity gradient. This seems
to exclude that there is a strain rate gradient from
base to apex.
|A nearly straight line. Blue eyed
shags (cormorants) at Cabo de Hornos (Cape Horn), Chile.
...Indicating that there is no gradient in strain rate, and
thus not in strain.
|Motion (velocity and
displacement - left) and deformation (strain rate and
strain - right) traces from the base, midwall and apex
of the septum in the same heart cycle. It is evident
that there is highest motion in the base (yellow
traces), and least near the apex (red trace), and this
is seen both in velocity (top - actually both in
systolic and diastolic velocity) and systolic
displacement (bottom). The distance between the curves
are a direct visualization of strain rate and strain, showing fairly
equal width of the intervals. Strain rate (top and
strain (bottom) curves are shown to the left, showing no
difference in systolic strain rate or strain between the
Some of the earliest strain rate studies found no base - to apex
although later studies seem to find differences with lowest values in the apex (124). However,
the angle error is also greatest in the apex (206).
In the comparative
study between methods in HUNT (153),
using tissue Doppler velocity gradient, there was
lower values in the apex, but only only when the ROI did
not track the myocardial motion through the heart cycle.
Tracking the ROI eliminated this gradient:
Comparison between standard
tissue Doppler velocity gradient and tracked ROI. Standard
deviations in parentheses.
gradient (tracked ROI)
|Peak Strain rate
||End systolic Strain
||Peak Strain rate
||End systolic Strain
Thus, it seems fairly reasonable to conclude that
this finding is artificial.
strain, some authors have found a reverse gradient of
systolic strain as well, highest in the apex, lower in the base
However, in that application, measurements are curvature
dependent, the apparent curvature being highest in the
apex and lowest in the base, and the discrepancy between ROI
width and myocardial thickness being greatest:
Curvature dependency of strain in 2D strain by speckle
tracking. The two images are processed from the same loop, to the
right, care was taken to straighten out the ROI before
processing, while the left was using the default ROI. In both
analyses the application accepted all segments. It can be seen
that the apical strain values are far higher in the right than
in the left image (27 and 21% vs 19 and 17%). However,
the curvature of the ROI even affects the global
strain, as also discussed above in the basic
The large HUNT study (153)
found no such gradient either way with the combined
tracking -TDI method:
Results from the HUNT study
with normal values based on 1266 healthy individuals. Values are
mean values (SD in parentheses). Differences between walls
are small, and may be due to tracking or angular problems.
No systematic gradient from apex to base was found.
In the subset of 50 analysed for comparison
of the methods, taking care to avoid both foreshortened
images and excessive curvature, there were no level differences
in 2D strain either:
Comparison between methods.
Standard deviations in parentheses.
|Segment length by
TDI and ST
|2D strain (AFI)
|Peak Strain rate
|End systolic Strain
|Peak Strain rate
||End systolic Strain
In addition, in the comparative study, there was no gradient using the 2D strain application,
in this case care was taken to align ROI shapes as much as
MR studies have also found various results. Bogaert and Rademakers (171)
in a study of healthy subjects (N=87) found lowest longitudinal
strain in the midwall segments, higher in both base and apex,
but no systematic gradient from base to apex. Moore et al (384)
in a study of healthy volunteers (N= 31) found a systematic
gradient, but with the lowest strain in the apex, highest in
the base. Venkatesh
et al in a healthy subset from the MESA study (N= 129) (385)
examined only transmural and circumferential strains in cross
sectional planes, and found decreasing transmural strains from
base to apex in all layers. As segmental shortening and
thickening are very closely
related through incompressibility,
this should amount to a decreasing strain from base to apex too.
Circumferential strains, on the other hand, seemed to be less
systematic, and the apex to base gradient varied between both
layers and walls. This, however, is counterintuitive, as wall
thickening causes inwards displacement of the circumference,
wall thickening is equivalent to shortening, as the findings
should show the same gradient.
MR measurements have processing issues as well. Using short axis
planes, the planes will show an increasing deviation from the
90° angle with the wall, towards apex, causing an over
estimation of wall thickness in the apical planes. Using
magnetic tagging, this is usually done in a grid with 90°
angles, at least in the transcverse/longitudinal direction,
while the radial might vary, although usually at 90° with the
horisontal plane. This might cause angle deviations as shown
Diagram illustrating MR planes and magnetig tagging
grids and relation to myocardial directions. Horizontal planes
and grud lines (red) are usually cross sectional, causing
increasing angulation with the transverse direction of the
wall (green) towards the apex. Longitudinal grid lines deviate
increasingly from the longitudinal direction of the wall
toward the apex as well (orange).
MR tagging may include algortihms for calculation of the local
coordinates, but this again will introduce new uncertainties in
the angle calculations, causing both over- and under corrections
depending on the calculation. Shear
strain may affect the motion of tags, and attempts to
calculate shear strains and separate them from the normal strains,
will again increase the complexity of calculations and possible
presence of a base to apex gradient in deformation
parameters has so far not been established.
there layer specific strain, and can we measure it?
The advance of speckle
tracking have enabled analysis of deformation in all
directions, although with severe
ultrasound itself as well as due to the
specific applications for analysis. Speckle
tracking also gives the possibility of measuring smaller regions of
the myocardium. This may be subject to severe restrictions, however.
Also, measurements are related to geometry, which do not necessarily
relate to differences in fibre function.
transmural and circumferential strain gradients
There is a normal gradient of strain from outer to inner contour.
This has been confirmed emprically (255).
This, however, has got
nothing to do with differences in fibre function, but is
simply due to geometric factors,and is already discussed inder the
paragraph on circumferential
transmural gradient of strain. The thickening of the
outer layer displaces the inner layer inwards. This alobe will
cause the inner layer to thicken, due to being pushed into a
region where the circumference is smaller, and thus thickening
has to compensate in order to preserve layer volume. The
thickening of the inner layer comes in addition to this, and
thus the inner layer has to thicken more than the outer layer.
Thus, there is a gradient of ttransmural strain across the
wall, increasing towards the endocardium. But this also is the
case for circumferential strain. The mid circumference of the
outer layer moves inwards (and hence, shortens) according to
the thickening of the outer layer. The midwall line of the
inner layer moves inwards (and hence, shortens) both due to
the inward shift of the inner alyer, and due to the increased
thickening of the inner layer. Thus there is a gradient of
circumferential strain increasing towards the endocardium as
The gradients of transmural and circumferential
strains are thus a function of geometry alone in the normal
ventricle, simply as the myocardium nearest the inner wall is
pushed more inwards, and thus have to both thicken and shorten
more due to reduction in available space.
gradient of longitudinal strain.
A transmural gradient of longitudinal strain has likewise been
This again, is solely a function of the geometry of myocardial
thickening, and the way strain is measured, and the fact that the
endocardial parts have to thicken more, due to the decreasing space
analoguous with the circumferential strain. If there had been an
additional increase in endocardial longitudinal strain, this would
have resulted in systolic torsion of the mitral ring, which, being
part of the larger fibrous AV-plane, is inconceivable.
|Longitudinal layer strain. The mid
layer lines in diastole (unbroken lines), move inwards
in systole (dotted lines), both using straight lines and
curved lines, and the endocardial moves most, due to the
inner layer thickening most as there is less room.
Colurs are for differentation only, and have nothing to
do with the colours seen in parametric
|Proposed geometry if there should
have been more absolute shortening in the inner layer,
this would mean a torsion of the mitral plane in systole
as illustrated here by the rise of the inner part, but
this is inconceivable, the mitral plane is part of the
larger fibrous annular plane.
|Wall layers in relation to beams.
Even though the beam width is exaggerated for
illustration purposes, it show that one beam may cross
different layers at different depths, and that at some
depths the beam may overlap more than one layer, which
will cause "smearing" of speckles, which may be
allocated to the wrong layer, While focusing may
increase lateral resolution in some level, this is only
if line density is adequate, if not the interpolation
described elsewhere will take over. .
The layer structure is well established (62,
Due to different fibre direction (62,
may have different longitudinal tension also in the natural
situation. As fibre directions vary across the wall, the
longitudinal tension has to be unequally distributed; specifically
it will probably be lowest in the middle layer, where the fibre
direction is mostly circular.So, again from anatomy, it is evident
that layer strain do not measure layer function.
Finally, measurement of layer strains depend on an
adequate beam width to separate the layers, This is not the case
all over the field, as the lines broadens with depth, and have
different widths depending on the focussing. this is discussed in
more detail elsewhere
This might mean wrongly allocating deformation to different
layers, as well as picking up stationary echoes from the
pericardium on the outside. (The beam problem may change with
newer generations where increased processing enables both higher MLA
and focusing along the whole beam. Beam broadening
with increasing depth, however, remains a fact of geometry).
Thus, studies of longitudinal layer strain from apical
full sectors older than about 2016 may be dubious, and if focus
and line density is not reported, actually valueless.
Myocardial shear strains
As explained in the basics
section, there may, at least theoretically be shear
strains in the myocardium as well. In the myocardium the
principal deformations should be as for the principal strains,
longitudinal, circumferential and transmural. (this is evident,
force being a vector can only have three spatial components). But
as measured relatively, there will be six different shear strains.
If shear strains will be available for measurements, some may have
more practical implications than others. Measuring shear strains
means that one will be able to measure differential strain across
a cross section of the image. This is related to measurement of layer strains as
With some degree of layer independence, and differential tension both across as well as along
the wall, there may be differential layer strain. The difference
in longitudinal strain across the wall is will then be
longitudinal shear deformation, and measured relatively to wall
thickness, it will be longitudinal/transmural shear strain.
The shear strain has been demonstrated experimentally by applying
differential stress to isolated tissue (i. e;. passive strain),
showing that the tissue strains most easily in the direction
l the myocardial layers (258).
Differential tension restricted to regions in the myocardial wall
is what is expected from non transmural ischemia. Thus, shear
strain might be demonstrable in these situations, and has been
demonstrated experimentally (259)
to the normal tension distribution of the tension, with
least longitudinal tension in the middle layer. With a
deformable mitral ring and independent layers, the
deformation would be unequal as well (orange, high
longitudinal deformation, yellow less longitudinal
deformation), causing the mitral ring to buckle in the
middle (A). As discussed above, this is undocumented as
well as improbable, the more probable model being
homogeneous deformation across the wall, as a resultant
of the different forces.
||Hypothetical model of shear strains
with non transmural loss of force. In both cases, the
weakened layer in the affecte dsegment(s) will shorten
less (yellow), but this must be compensated by more
shortening of the non affected segment in the same layer
(red), as the mitral ring doesn't torque. This must mean
that there has to be inverse shear strains in hte
affected vs non affected segments in the same wall.
If there are non transmural infarcts, this might in principle
cause shear strains especially in the longitudinal-transmural
direction. However, as discussed in the section on regional
function, this must happen within the framework of the
AV-plane. This means, that the different segments must interact,
without deforming the mitral ring, and will result in differential
shear strains between the different segments of the same wall. .
Hypothetically, measuring sub endocardial longitudinal strain
selectively, if possible, might increase sensitivity for non
transmural infarcts / ischemia, as the endocardial layer will be the
most affected. However, this remains to be proven. Also it may
hypothetically be a method for differentiating transmural and non
transmural akinesia, in the acute situation demonstrating transmural
ischemia. Transmural ischemia in the acute situation may be an
indication of coronary occlusion as opposed to non transmural
Strain and fibre
It has been a popular misconception that
strain in the different directions have to do with the actions of
different muscle fibers, i.e. circumferential and transmural
(radial) strain reflects the action of circular fibers, while
longitudinal shortening reflects the function of the longitudinal
fibers. It seems to be something almost "everybody knew". While the
latter is partially true, the first is not. There would have been circumferential
shortening even if there had been no circumferential fibres. Mean
circumferential strain must be taken to mean midwall circumferential
shortening. As shown above,
the midwall circumferential shortening is almost entirely the
function of diameter shortening, which again is a function of wall
thickening. This is due to the finding that the LV outer contour is
nearly invariant from diastole to systole (13,
as shown in the example above, the
diameter reduction being a function of wall thickening inside a
virtual "eggshell". The reduction in outer
contour contributes only to a small part of the circumferential
fibre directions are diverse, and varies throughout
the thickness of the heart, the middle layer being
more circular, while the endo- and epicardial layers
being more longitudinal, although helically ordered (62, 257). In dealing
with the principal strains, the wall is treated as
isotropic, which it is not. Thus, there may be
differential strain as well as shear strain.
three principal strains are totally interrelated and does not
convey separate information about different fibre function. The
information is about the myocardial volume deformation in
The longitudinal fibers are responsible for the
longitudinal shortening, and any process that mainly affect
longitudinal shortening (f.i. sub endocardial ischemia), will
result in reduced longitudinal shortening. It is also true that
the ejection work (stroke volume and ejection fraction) is closely
correlated with longitudinal strain as discussed in long
axis function. In fact, the longitudinal shortening can
explain most (but not absolutely all (158))
of the stroke volume. This is mainly the work of the longitudinal
fibers (or the longitudinal component of the spiral fibers) both
in the endo- and epicardium and represents mainly isotonic work.
This is what we measure by longitudinal displacement, velocity and
longitudinal deformation measures.
Thus, circumferential shortening is related to wall thickening,
which is due to the thickening of the individual muscle fibres. In addition, as the inner circumference
decreases, the longitudinal fibers gets less room,
especially in the endocardial parts, and thus the
longitudinal fibers have to shift inwards during
systole. This also contributes to the wall
thickening as illustrated below. Wall thickening is thus greater than the sum of the
individual fibre thickenings.
is not only due to wall thickening, but also
of inward displacement of the inner layers.
Simplified and exaggerated diagram showing the
relation between fiber thickening and wall
thickening. As the fibers shorten, they
thicken. Thus, the sub epicardial
longitudinal fibers will thicken, displacing
the circular fibers in the mid wall inwards.
In addition, as the fibre become thicker, they
will need more room, thus necessitating some
rearrangement of the fibres, making the layer
thickening even more than the individual
fibres. They will also displace the circular
fibres inwards, thus making the shorten and
also thicken as they contract. Finally the sub
endocardial longitudinal fibers will be
displaced inward. The sub endocardial fibers
will also, thicken. But the circumference has
been decreased at the same time due to the
thickening of the outer fibers, and thus
there has to be an extra inward shift of
longitudinal fibers for them to have room.
Assuming a systolic reduction in outer
diameter will only enhance this effect. By
this, it's evident that wall thickening is not
equivalent to the sum of fibre thickening
alone. The circumferential strain is thus
mainly the shift of the midwall line inwards
due to wall thickening.
fibers, mainly contributes to the pressure increase, i.e.
isometric work, which takes place mainly during the isovolumic
contraction phase. Isometric contraction cannot be measured by
deformation along the fibers, and thus by no imaging modality at
all. As they contract, however, there will also be a slight inward
shift, due to the displacement of the fibres, which also results in
a shortening and thickening of the fibres. In addition, the
circumferential fibers may be responsible for whatever there is of
outer contour diameter reduction . If so, they contribute to the
ejection work, and in addition slightly to wall thickening, as the
wall has to thicken even more in order to retain wall volume with a
reduced outer diameter. If there is loss of longitudinal contractile
function, either regionally (typical ischemia) or globally as in
cardiomyopathia with sub endocardial affection (e.g. Fabry), there
may be a shift toward circumferential pumping, with an increase in
the variations of outer circumference. Then there will be true
radial compensation for loss of longitudinal function. But in
hypertrophic states, there is usually loss of longitudinal function
and circumferential function both, but due to the increased wall
thickness the fractional shortening may be increased. This has been
called "radial compensation", but as explained below,
this is a total misunderstanding of geometry.
It is also extremely important that if longitudinal and "radial
function" are compared, care should be taken that the measurements
are comparable. To compare for instance fractional shortening of
the LV diameter with longitudinal strain (wall shortening), is
comparing two different measures, and may lead to completely
erroneous conclusions as shown below,
where fractional shortening increases but wall thickening
In terms of energetics, the ejection work may be described as the
kinetic energy in the blood being ejected is 1/2 m v2,
which is less than 20% of the potential energy (P*V). Thus, almost
80% of the work is pressure buildup, and this is done by tension
increase, before onset of shortening (deformation).
Thus, deformation analysis, whether it is factional shortening, EF,
shortening, or deformation, all measure myocardial deformation
in one way or other, and thus only a fraction of the work done by
the heart. The greatest
great part of the ventricular work - the isometric work, cannot be
described by deformation analysis (or any imaging modality) at all
as all functional analysis by cardiac imaging is about deformation.
The full description of LV work need to incorporate a measure of load,
either by invasive measures, or by externally measured pressure
(eventually pressure traces) in combination with mathematical
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