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Description  |
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BACKGROUND OF THE INVENTION
1. Field of The Invention
This invention relates generally to a method and apparatus for performing
elastographic diagnosis of a target body. Elastography is a system for
measuring and imaging elastic modulus and compressibility distributions in
an elastic tissue. It also has application to strain profiling and
improved sonographic measurement and imaging. This system is typically
based on external compression of a target body, and utilizes one or more
transducers, acting as or with a compressor, to generate pre- and
post-compression sonic pulses and receive the resulting echo sequences
(A-lines) from within the target body. The pre- and post-compression echo
sequence pairs may then be cross-correlated or matched to determine the
strain along the path of the sonic pulses, and preferably to yield a
strain profile of the target body. This strain profile may then be
converted into a compressibility profile or elastogram by measuring the
stress imposed by the compressing device and calculating the elastic
moduli based on the stress and the strain profile.
An elastogram may be considered to be a special form of multi-trace
sonogram, wherein each trace is a record or display with depth within a
target body of an elastic modulus function of the body. A preferred
elastic modulus function for purposes of display is the inverse of the
bulk modulus, which provides a measure of compressibility. As explained
later in this description, the inverse of the Young's moduli may usually
be used instead of the bulk moduli. Less preferred but also helpful are
the Young's moduli themselves. Methods for making and using elastograms
are described at length in co-pending application Ser. No. 7/535,312.
While the methods described in application Ser. No. 7/535,312 produce
greatly improved records and understanding of structures of elastic
tissues, it has been observed that certain inaccuracies in the resulting
elastograms may arise. In particular, inaccuracies have been observed if
the transducer and compressor used to compress and insonify a tissue are
relatively small in size relative to the depth (or thickness) of the
target body, giving rise to decreasing stress in the target body as the
distance increases from the compressor. Likewise, inaccuracies have been
observed in elastograms and sonograms if the target body is not relatively
homogeneous with respect to sonic speed, giving rise to strata through
which sonic pulses travel at differing velocities. The improved methods
and apparatus for elastography disclosed herein, while generally enhancing
the accuracy of elastograms, have particular application in reducing the
effect of such inaccuracies in both elastograms and sonograms.
2. Related Art
Traditional ultrasonic diagnosis is achieved by transmitting ultrasonic
energy into a target body and generating an image from the resulting echo
signals. A transducer is used to both transmit the ultrasonic energy and
to receive the echo signals. During transmission, the transducer converts
electrical energy into mechanical vibrations. Acquired echo signals
produce mechanical oscillations in the transducer which are reconverted
into electrical signals for amplification and recognition.
A plot or display (e.g., on an oscilloscope, etc.) of the electrical signal
amplitude versus echo arrival time yields an amplitude line (A-line) or
echo sequence corresponding to a particular ultrasonic transmission. When
the A-line is displayed directly as a modulated sinusoidal pattern at
radio frequency ("RF"), it is typically referred to as an RF or
"undetected" signal. For imaging, the A-line is often demodulated to a
non-RF or "detected" signal.
Ultrasound techniques have been extensively used in the field of diagnostic
medicine as a non-invasive means of analyzing the properties of tissue in
vivo (i.e., living). A human or animal body represents a nonhomogeneous
medium for the propagation of ultrasound energy. Acoustic impedance
changes at boundaries of regions having varying densities and/or sound
speeds within such a target body. At such boundaries, a portion of the
incident ultrasonic beam is reflected. Inhomogeneities within the tissue
form lower level scatter sites that result in additional echo signals.
Images may be generated from this information by modulating the
intensities of pixels on a video display in proportion to the intensity of
echo sequence segments from corresponding points within the target body.
Conventional imaging techniques are widely used to evaluate various
diseases within organic tissue. Imaging provides information concerning
the size, shape, and position of soft tissue structures using the
assumption that sound velocity within the target is constant. Qualitative
tissue characterization is carried out by interpretation of the grey scale
appearance of the sonograms. Qualitative diagnosis largely depends on the
skill and experience of the examiner as well as characteristics of the
tissue. Images based only on relative tissue reflectivity, however, have
limited use for quantitative assessment of disease states.
Techniques for quantitative tissue characterization using ultrasound are
needed for more accurate diagnosis of disorders. In recent years many
significant developments have been achieved in the field of ultrasonic
tissue characterization. Some acoustic parameters, e.g., speed of sound
and attenuation, have been successfully used for tissue characterization.
Tissue compressibility is an important parameter which is used to detect
the presence of diffuse or localized disease. Measuring changes in
compressibility becomes important in the analysis of tissue for
pathological conditions. Many tumors are firmer than the surrounding
normal tissue, and many diffuse diseases result in firmer or more tender
pathology. Examples can be found in diffuse liver disease, prostate
cancer, uterine fibroids, muscle conditioning or disease, breast cancer
disease, and many other conditions.
Traditionally, physicians routinely palpate various regions of a patient's
body to get an impression of tissue firmness or tissue softness. This
technique is a form of remotely trying to sense what is going on in terms
of tissue compliance. For example, in a liver, if the compliance in an
area is sensed to be different from compliance in the surrounding area,
the physician concludes from the tactile sensations in his fingers that
something is wrong with the patient. The physician's fingers are used to
perform a qualitative measurement.
In the last several years, a number of articles have appeared in the
literature that explore various techniques for measurement and imaging of
soft tissue compliance and tissue motion using ultrasound. These
techniques rely on one of the following procedures: Doppler ultrasound
velocity measurements, cross-correlation techniques to quantify motion in
tissues, and visual inspection of M-mode and B-mode images. Additionally a
Fourier feature extraction technique has been proposed. Internal
mechanical excitation (motion of cardiac structures, arterial pulsation)
or external vibration sources of motion produce displacement of the
tissues under investigation. The displacements of different tissues are
then analyzed by one of these techniques.
The amplitude and velocity of motion induced by arterial pulsation is
generally too low for evaluation with Doppler velocity measurements.
However, a number of researchers have used pulsed Doppler and color flow
Doppler systems in conjunction with external mechanical harmonic
excitations to determine the elastic properties of tissue. Using a low
frequency external excitation source, the velocity of propagation of
mechanical waves has been measured and relates to the modulus of
elasticity of the tissues. The velocity of vibration of tissues under low
frequency vibration excitation has been used to determine their relative
compressibility. This technique has been termed "sonoelasticity" and
produces B-scans which are "stained" with color coded relative
compressibility information. Sophisticated Young's modulus measurements
have been applied to determine muscle elasticity as a function of
contractility state by measuring Doppler shifts due to very low frequency
excitations (10 Hz). A similar approach using vibrations in the 100-1000
Hz range has been proposed to study dynamic muscle elasticity in vivo.
Cross-correlation techniques allow the use of either internally or
externally generated sources of mechanical excitation due to their ability
to quantify minute motions of tissue. External harmonic excitation has
been used to assess motion of soft tissues with one dimensional and two
dimensional correlators. The displacement and/or velocity of internally
generated motion also have been measured using one dimensional and two
dimensional correlators. Tissue strain caused by arterial pulsation in the
liver and by transmitted cardiac motion in fetal lung have been proposed
for tissue characterization.
Visual inspection of ultrasound M-mode waveforms has been used to study
benign and malignant lesions in liver, pancreas and breast and to observe
the elasticity of fetal lung. In magnified B-scans of the fetal thorax
paracardiac lung movements have been measured to classify fetal lungs as
stiff, intermediate or compliant. The examination of fetal lung sonograms
has been used to evaluate compressibility as an indicator of lung tissue
maturity.
But, one of the main difficulties in these methods is the lack of
definition of the magnitude and direction of the driving force. This
difficulty applies to driving forces that are internally generated by the
pulsations of the heart and/or the aorta, as well as to those applied
externally at low frequency and limited directivity. Further, it is
difficult to measure the shape of an internal driving force, limiting the
ability to determine how stress resulting from the driving force decreases
as a function of distance from the driving force. The inability to define
the direction, magnitude and shape of the driving force limits the ability
of these methods to provide quantitative information about the elastic
properties of the tissue under investigation.
SUMMARY OF THE INVENTION
In constrast to these methods, elastography is not limited by a lack of
definition of the magnitude, direction or shape of a driving force.
Elastography preferably uses an external stimulus of known quantity, such
as compression of the target body by a known amount or known stress by a
compressor, preferably along with cross correlation or least-means-square
matching techniques to generate strain profiles of the tissue under
investigation. From these strain profiles and the measurement of the
stress applied by the compressor, an elastogram (or image of the inverse
elastic modulus profile) is determined. The inverse of the elastic modulus
profile is typically displayed on the elastogram because strain
measurements may be zero, yielding an elastogram with an infinite range of
elastic moduli.
Thus, elastography provides a pulse-echo system that has particular
application in estimating and imaging compressibility in a target body.
The target body may be any animal or human tissue, or any organic or
inorganic substance that is compressible or compliant. The term "animal
tissue" includes "human tissue". An ultrasonic source is used to
interrogate the target body. The detection of echo sequences may be at the
ultrasonic source. Thus, elastography allows for accurate, localized
determination and imaging of an important parameter, compressibility,
which has been used qualitatively in medicine for a very long time.
Compressibility of a material is normally defined as the inverse of the
bulk modulus of the material. The bulk modulus of a volume may be
determined by the following formula:
BM=P/(.DELTA.V/V) where Equation 1
BM=Bulk modulus
P=the pressure or stress on a tissue segment of interest
(.DELTA.V/V)=the volumetric strain of a tissue segment of interest, where
.DELTA.V=a change in the volume of the segment, and
V=the original volume of the segment.
In a preferred method of elastography where an external source of
compression is applied to stress the target body, it may be generally
assumed that the volumetric strain (or differential displacement) along
the axis of compression may be determined by the formula:
strain=(.DELTA.L/L), where Equation 2
.DELTA.L=a change in the length of the segment along the axis of
compression, and
L=the original length of the segment,
Further, it may be generally assumed that the stress on the tissue segment
of interest caused by the external source of compression may be determined
by the formula:
stress=(F/a), where Equation 3
F=compressive force applied to the segment, and
a=area across which the force is applied.
Therefore, applying these assumptions to Equation 1, the elastic modulus
(E) of a tissue segment of interest may be estimated by the formula for
determination of a Young's modulus:
E=(F/a)/(.DELTA.L/L). Equation 4
Further, compressibility (K), the inverse of E, may be estimated by the
formula:
K=(.DELTA.L/L)/(F/a). Equation 5
Thus, the compressibility of any given segment or layer within a material
relative to another segment or layer may be further estimated from the
relationship
K.sub.1 =K.sub.2 (.DELTA.L.sub.1 /L.sub.1)/(.DELTA.L.sub.2 /L.sub.2),
whereEquation 6
K.sub.1 =compressibility of a first segment or layer;
.DELTA.L.sub.1 =change in length of the first segment or layer along an
axis of compression in response to a given force;
L.sub.1 =original length of the first segment;
.DELTA.L.sub.2 =corresponding change in length of a second segment or
layer;
L.sub.2 =original length of the second segment or layer; and
K.sub.2 =compressibility of the second segment or layer.
In elastography, the velocities of sound in different segments or layers
may be employed, together with time measurements, to calculate distances
within the segments or layers. The ultrasonic signals also provide a
precise measuring tool. The velocities of sound may be determined using
the apparatus and procedures disclosed in application Ser. No. 7/438,695.
However, in the techniques previously disclosed for elastography in
applications Ser. Nos. 7/438,695 and 7/535,312, the method for estimating
compressibility in targets having multiple layers may lead to some
inaccuracies. These inaccuracies may similarly arise in sonography. Such
inaccuracies generally result from one of two conditions, or both. Thus, a
first group of such inaccuracies may arise due to substantial variations
in the speed of sound in the different layers. Expressed otherwise, the
techniques estimate compressibility in each layer from two echo sequences
along the axis of radiation without consideration for variations in the
speed of sound.
Some regions in a target body of interest may contain multiple layers
having substantially different velocities of sound. For example, the human
body wall may include regions of interspersed fat and muscle tissue, and
sound may typically travel at about 1450 m/s in a fatty region, while it
will typically travel faster in muscle tissue, around 1580 m/s. The
variation in the speed of sound through different layers can cause sonic
pulses traveling on different sonic paths, but through the same distance
relative to the transducer, to take different amounts of time. This time
difference may in turn lead to a distortion, and possibly a shift, in the
elastograms and sonograms of the target body.
A second condition that may cause a significant inaccuracy in the
previously disclosed techniques for elastography lies in the assumption
that stress will be relatively uniform throughout the tissue of interest,
and may be calculated for all layers based on measurements proximal to the
compressor. However, inaccuracies have been observed if the transducer and
compressor used to compress and sound a tissue are relatively small in
area relative to the depth (or thickness) of the target body, giving rise
to decreasing stress in the target body as the distance increases from the
compressor. If this decreasing stress is substantial and unaccounted for,
levels of decreasing compressibility may appear on the elastograms as a
function of increasing distance from the compressor.
Thus, the present invention in one aspect provides a method and apparatus
to determine the strain and compressibility of a target body regardless of
whether the target body has multiple layers with different sonic
velocities. In another aspect, the invention provides a method and
apparatus to determine the compressibility of a target body even where the
stress in the target body resulting from compression by the compressor
decreases with distance from the compressor. In yet another aspect, the
invention generally provides an ultrasound method and apparatus for
accurately measuring and imaging strain and elastic modulus distributions
in an elastic tissue. The ability of the invention to quantitatively
measure the compressibility or compliance of tissue in localized regions
provides help with (1) objective quantification of commonly used clinical
signs, (2) localizing these measures, (3) making the measurements deep in
tissue with simple equipment, (4) observing new tissue properties, which
may be related to pathology, not seen by other known means; and (5)
constructing images of a compressibility or compliance parameter in vivo,
which may be used alone or in conjunction with ordinary sonograms.
Diseased tissue, such as tumors, may be harder or softer than normal
tissue, and thus have a different amount of compressibility. In this
regard, elastography gives promise of a distinct advantage over prior art
methods in the accurate detection of diseases such as breast cancer and
prostate cancer and localization of tumors at an early stage. Another
advantage of elastography is that its sensitivity may be greater than
sonography, because of its measurement and imaging of compressibility and
not just echo amplitudes, allowing for better visualization of target
bodies. Still another advantage of elastography is the accurate imaging of
sub-surface tissue while avoiding the use of ionizing radiation from
x-rays.
It will be noted at this point that elastography is contemplated to have
significant applications other than in medicine. One such application, for
example, is in the quality grading of beef. Elastography may be used to
quantitate both the tenderness of beef and the fat content (marbeling)
before and after slaughter. This ability is economically important in
determining when to slaughter cattle. Other applications may include, for
example, interrogation of materials and products such as cheese or crude
oil that are physically displaceable by the movement of a transducer.
Other objects and advantages of elastography will become readily apparent
from the ensuing description.
In a broad sense the present invention comprises an ultrasonic system for
producing improved elastograms and sonograms of elastic target bodies, and
notably animal and human tissue. In one broad aspect, elastography
comprises sonically coupling a sonic device to a target body to determine
its compressibility. The sonic device is used to emit an ultrasonic signal
and receive returning echo sequences from along a sonic path in the target
body. The sonic device is then moved a known amount along the axis of the
sonic path, and the target body is interrogated again along the sonic
path. Congruent segments in echo sequences from the different sonic
signals are then preferably cross correlated or matched, and the temporal
displacements are used to calculate the strain along the sonic path. This
procedure is repeated for a plurality of sonic paths, either sequentially
or by means of a sonic array, to produce strain profiles for the target
body.
To obtain a compressibility profile, a second body having a known,
preferably uniform, elastic modulus may be first sonically joined to and
between the target body and the sonic device. The strain profiles of both
bodies may then be determined using the steps described above. The stress
caused by the movement of the sonic device may then be determined from the
strain profiles and elastic modulus of the second body. Compressibility
profiles for the target body may be obtained by dividing the values for
the strain profiles in the target body by the stress. The resulting
compressibilities may be further arranged as an elastogram, a positional
multi-dimensional plot or picture of the relative magnitudes of
compressibility of a tissue or other target body.
In another aspect, the invention resides in using the above method of
elastography, but further correcting for variations in stress along the
sonic path. These variations may occur in instances where a sonic device,
which is employed to stress and compress the target body, has a small
cross-sectional area relative to the depth or thickness of the target
body. These variations in stress may be determined by first measuring the
dimensions of the surface of the sonic device (which may include a
transducer in combination with a compressor) which contacts the second
body. These measured dimensions may then be applied to analytically derive
the variations in stress within the target body as a function of position
relative to the sonic device. The result is, in effect, a stress profile.
Once derived, these variations in stress may be applied to correct the
values for the stress profiles, as well as the resulting compressibility
profiles and elastograms for the target body, previously determined by use
of the above-described preceding embodiment.
In another aspect, the above variations in stress may be experimentally
derived. Thus, a body of known elasticity may be compressed by the sonic
device and the resulting strains along varying sonic paths inside the body
may be measured. The variations in stress may then be calculated as a
function of position relative to the sonic device. From these known
variations the corrected values for the stress and compressibility
profiles and elastograms may then be determined.
In yet another aspect of the invention, appropriate time delays, necessary
to correct for variations in echo sequence travel time through regions of
the target body having different speeds of sound, may be determined and
applied to each echo sequence. The resulting time shifts in echo sequences
correct for distortions that might otherwise occur when there are
different regions within a target body, e.g., fat and muscle tissue, that
have differing sonic velocities.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention, together with further advantages and features
thereof, may be more readily understood by reference to the following
detailed description taken in connection with the accompanying drawings in
which:
FIG. 1a shows an embodiment of an elastographic apparatus where a
transducer and compressor are sonically coupled to a target body to
interrogate a distal tissue region within the target body.
FIG. 1b shows a plot of an RF echo signal originating from the distal
tissue region interrogated in FIG. 1a.
FIG. 2a shows the transducer and compressor of FIG. 1a imparting a small
compression to a proximal region of the target body.
FIG. 2b shows a plot of a typical pre- and post-compression RF echo signal
pair originating from the distal tissue region as interrogated in FIG. 2a.
FIG. 2c shows a plot of a cross correlation of the echo signal pair shown
in FIG. 2b.
FIG. 3a shows the axial strain in foam as a function of depth using a 127
mm circular compressor.
FIG. 3b shows the normalized stress in foam as a function of depth using
various sizes of circular compressors.
FIG. 3c shows the normalized stress in dB as a function of z/a, the depth
divided by the area of a circular compressor.
FIG. 4a shows a cross sectional view of an apparatus for determining stress
distribution under a given compressor.
FIG. 4b shows a cross sectional view of a stress distribution under a
compressor as a function of position relative to the compressor.
FIG. 5a shows a photograph of a phantom consisting of two triangular foam
pieces joined along a diagonal seam.
FIG. 5b shows a B-scan of the phantom pictured in FIG. 5a.
FIG. 5c shows the elastogram corresponding to the B-scan shown in FIG. 5b.
FIG. 5d shows the depth-corrected elastogram corresponding to the B-scan
shown in FIG. 5b.
FIG. 6 shows an embodiment of an apparatus in which a compressor is coupled
to a target body for purposes of experimentally determining the variations
of stress with depth in the target body.
DETAILED DESCRIPTION
FIG. 1a shows the transducer 10 and compressor 10a sonically coupled to a
target body 15. An ultrasonic pulse 18 is shown propagating within sonic
beam 20 toward an echo source 25 on beam axis 12. As the pulse 18
propagates through the target 15, corresponding echoes are generated and
arrival times noted at the transducer aperture 11. The combination of all
echoes generated from reflections within the beam 20 is the echo sequence
or A-line corresponding to pulse 18.
A radio frequency ("RF") signal plot of the A-line acquired from pulse 18
is shown in FIG. 1b. The amplitude of the signal in volts is plotted
against echo arrival times in microseconds (.mu.s). Later arrival times
correspond to progressively deeper regions within the target body 15. An
echo segment or echo wavelet 30, within a chosen arrival time window, is
selected as a reference. The time window may be selected based on
anatomical data from ultrasound imaging, or may be arbitrary, e.g., every
x micro seconds. The echo segment or wavelet 30 originates from the echo
source 25.
FIG. 2a shows the transducer 10 and compressor 10a being translated along
axis 12 to impart a small compression (.DELTA.y.sub.1) to the tissue.
After the transducer 10 and compressor 10a compress the target body 15, a
second pulse 22 is emitted and the corresponding A-line segment is
acquired from a desired depth within the tissue.
FIG. 2b shows an RF plot pairing a typical pre-compression A-line,
corresponding to pulse 18, and a post-compression A-line, corresponding to
pulse 22. The echo segment or wavelet 32 associated with a given echo
source and pulse 22 is time shifted with respect to the same segment of
wavelet 30 associated with the same echo source and pre-compression pulse
18. The time shifted wavelet 32 may be tracked within the selected time
window using standard pattern matching techniques. The window selected
must be such that the wavelet of interest will not be shifted out of the
window. This selection may involve the size of the window or the
positioning of the window. The window selected should reveal both wavelets
or echo segments. The arrival time of echo segment or wavelet 32 is prior
to that of echo segment or wavelet 30 above, since the distance between
aperture 11 and feature 25 was shortened by the compression
.DELTA.y.sub.1.
FIG. 2c shows the cross-correlation function between the pre- and
post-compression A-lines shown in FIG. 2b.
In a preferred method of elastography, a transducer and compressor are
positioned on or otherwise coupled to a target tissue and advanced axially
toward the target to compress the target. Alternatively, elastography may
be practiced by retracting a transducer and compressor from a previously
compressed position. Further, in both methods the transducer may alone
serve as the compressor. Since the relatively large size of the compressor
precludes penetration of the tissue, small tissue displacements occur
instead. A pulse is emitted from the transducer prior to the displacement,
and a first echo sequence received in response to the pulse is recorded.
Following displacement, a second pulse is emitted and a second echo
sequence is recorded in response to transmission. Next, a comparison of
the waveforms is made to reveal a decreasing displacement of the tissue
structure with depth. The decrease will generally be asymptotic in
character.
In the foregoing method, a single compression of a homogenous target body
has been described. It will be apparent, however, that other conditions
may be employed. Thus, multiple compressions, repetitive or real time
compressions, varying waveforms and other signal sources, such as array
transducers, may be used. These signal sources, for example may be
non-repetitive and may generate spike-like signals.
Further, an internal source of compression, alone or in conjunction with an
external compressor, may be used. In the case of an internal source of
compression, such as the heart or arteries, the tissue of interest should
preferably be located sufficiently distant from the internal source of
compression such that stress caused by the internal source of compression,
even while changing as a function of time, remains substantially uniform
throughout the tissue of interest. A transducer may then be sonically
coupled to the target body, preferably with a compliant body of known
uniform elasticity sonically coupled between the transducer and the target
body, such that the tissue adjacent to the transducer compresses against
the compliant body and transducer as the tissue is compressed by the
internal source of compression, and decreases in stress against the
transducer and compliant body as the stress caused by internal source of
compression decreases in the tissue of interest. The strain in the
compliant body and tissue of interest may then be sonically measured using
the method described herein, and the stress against the compliant body
determined from elasticity and strain measurements for the compliant body.
Finally, this stress may be assumed to be the level of stress throughout
the tissue of interest, and used with the measured strains to determine
the compressibility profile in the tissue of interest.
In tissue that is not homogeneous, the shifting of tissue in various
segments will differ. For example, if a segment of tissue is less
compressible than the overall tissue containing the segment, the tissue in
the segment will compress or strain less than if the segment of tissue
were of the same compressibility as the tissue as a whole. Alternatively,
when a segment is more compressible than the tissue as a whole, the
segment will compress or strain more than if the segment were of the same
compressibility as other segments. The presence of a strain "defect," or
segment of different compressibility, along the compression axis in a
target body influences all other strains along that axis, increasing or
decreasing the otherwise proportional change in strain with depth along
the axis. In this way a strain "defect" is said to be "smeared" along the
axis. For this reason, it may be preferable to convert the strain profiles
into elastic modulus profiles. Since the elastic modulus is a basic tissue
property, it may be ultimately a more reliable parameter. In any event, it
is possible to obtain useful images from strain or elastic modulus data.
In order to illustrate these principles, it is convenient to consider a
simple onedimensional cascaded spring system, where the spring constants
represent the elastic moduli of tissue regions. We assume that all three
springs are equal and are of length l, and that each spring represents the
behavior of a cylindrical tissue element with unit cross section. If the
top of the first tissue element is compressed by an axial downward force
such that the overall length of the system is reduced by (2.DELTA.y), then
a simple statics calculation shows that each and every spring will shrink
by .DELTA.l=2.DELTA.y/3. If we define the strain of each spring
=.DELTA.l/l, it is clear then that the strain is constant for all springs,
and is equal to 2.DELTA.y/3l.
Where the center spring has been replaced by an infinitely stiff spring,
i.e. E=.infin., the total displacement is taken up by two outer springs
only. Thus, the strain in the two outer springs will increase to
.DELTA.y/l.
It is evident from this example that a strain profile is dependent on the
initial compression and on the number and stiffness of all springs. A
given local measured value of the strain is influenced by the elastic
properties of elements located elsewhere along the axis of compression.
For these reasons, it appears that while strain profiling may be useful
for imaging, it may be of limited use for quantitative estimation of local
tissue elasticity.
If instead of imparting a known displacement a known stress is applied, it
becomes possible to estimate the elastic modulus of each component in this
system of springs, since the stress remains constant with depth in this
one dimensional system. In this case, the measurable strain in each spring
and the known stress on each spring may be used to construct an elastic
modulus profile along the compression axis. Such a profile would be
independent of the initial compression, and the interdependence among the
component springs would disappear.
Further, the stress applied to the target body may be measured
ultrasonically by interposing an anterior compliant standoff layer which
has a known value of E, and which allows the free passage of ultrasonic
waves. The simultaneous measurement of the strain in this layer allows the
computation of the stress acting on the target. This layer may consist of
compressible or compliant material such as rubber, sponge, gels, etc. The
material should be compressible and provide for an ultrasonic transmission
path to the tissue. The material may be echogenic, but it is not
necessary.
In the more realistic three-dimensional case, one would expect that the
applied stress would not be constant along the axis of compression. The
reason for this lies in the fact that stresses along transverse springs
become important, and since their vertical force components are a function
of the displacement which in turn is a function of depth, the resultant
forces along the compression axis vary with depth. On the other hand,
enlarging the area of the compressor, the transverse springs that are
actually stretched, and hence contribute to the depth dependent stress
field, become less important and the applied stress field becomes more
uniform. Experiments have confirmed that larger compressors cause more
uniform axial stress fields.
In elastography, however, the velocities of sound in different segments or
layers are used, together with time measurements, to calculate distances
within the target body. More specifically, elastograms are based on time
shift differences among segments of ultrasound A-lines and preferably,
when based on more than about 64 data points, rely heavily on
cross-correlation computations. The use of cross-correlation analysis for
time shift estimation derives from Fourier theory, and is well known in
the art. In recent years a number of industrial and medical applications
have utilized cross-correlation analysis for time shift measurements. The
application of ultrasonic correlation techniques to the measurement of
flow velocity of coal slurries has been described. Similarly, an
ultrasonic correlation flowmeter for pulp suspension has been proposed. In
the medical field, a number of publications describe the measurement of
blood velocity profiles using one-dimensional and two-dimensional
correlators, as well as applications of cross-correlation measurements for
tissue motion evaluations, described above.
The generation of an elastogram involves a pairwise evaluation of the time
shift between congruent segments in an A-line pair, preferably by means of
cross-correlation techniques. The linear cross-correlation of segment
pairs may be computed using FFTs (fast Fourier transforms). The temporal
location of the maximum peak of the cross-correlation function may be used
to estimate the time shift between the data in the two segments.
However, the time shift differences among segments of an ultrasound A-line
may also be evaluated by using a least-means-square match analysis, which
is also well known in the art, or by manually measuring the differences
between A-lines on a display or picture, instead of by cross-correlation.
When there are less than about 64 data points being analyzed, a time
domain computation, such as a least-means-square match, may often take
less time than a fourier domain cross-correlation computation will take to
determine the time shifts. Further, a least-means-square match analysis
may be computed for a limited number of time-lags, where the approximate
time shift is known, while cross-correlation using an FFT computation must
analyze the entire data sequence. Thus, a least-means-square match may be
faster than cross-correlation where the approximate time-shift is known,
allowing a time-shift determination to be made by matching only a portion
of the echo sequences.
By way of illustration only, one approach to elastography could involve the
derivation of an elastogram from a strain image created from 40-60 A-line
pairs obtained with a 1-2 mm lateral translation of the transducer between
pairs. An A-line pair consists of the original A-line which is obtained
with the transducer slightly precompressing the target in order to assure
good contact, and a compressed A-line which is obtained after axially
compressing the target an additional .DELTA.z. The compressed A-line would
be shorter than the original A-line by 2.DELTA.z/c, where c is the speed
of sound in the target. The length of the A-line pair is taken to be that
of the original A-line; zeros are appended to the compressed A-line. These
A-lines would be obtained from a 12 cm total depth in the target, and
divided into 40-60 overlapping 4 mm segments obtained every one or two mm.
The data acquisition, and therefore the time scale, is relative to the face
of the transducer. Thus one can observe that the relative shift of the
signal at the beginning of an A-line pair is very small, whereas towards
the end it is significant. In general, the time shift of the compressed
A-line relative to the uncompressed A-line would increase from 0 to a
maximum of 2.DELTA.z/C.
In general, the precision of the time shift estimate improves with
increasing segment size. However, it is typically better to keep the
segment size small to improve the axial resolution of the estimate.
Additionally, because of the relative compression and the resultant
progressive distortion of the data within a segment pair, the
cross-correlation estimate may deteriorate with increasing segment size.
This, in turn may degrade the precision of the estimate. Thus, there are
two competing mechanisms that affect the precision of a time shift
estimate as a function of the segment size. Although this trade-off has
not been studied in depth, it has been observed that a segment size of
about 4 mm with about 3 mm overlap between segments leads to strain data
which may result in reasonable images with about 1 mm axial resolution.
The resolution of a measured time shift may be bounded by the sampling
period at which the data is digitized. To improve the resolution, some
interpolation algorithms have been proposed. For example, a quadratic
interpolation algorithm has been shown to be effective and it is simple to
implement. See, Foster et al., "Flow Velocity Profile Via Time-Domain
Correlation," IEEE Trans. Ultrason. Ferroel. Freq. Control, Vol. 37, No.
2, 164-174 (1990); See also, Boucher et al., "A Method of Discrete
Implementation of Generalized Cross-Correlator," IEEE Transactions:
Acoustics, Speech and Signal Processing, Vol. ASSP-29, No. 3 (June 1981).
This algorithm first fits a second-order polynomial which passes through
the peak sample value of the cross correlation and its two neighbors using
the Lagrange polynomial interpolation. Then it analytically locates the
peak of the fitted polynomial, assigning that temporal value to the
improved time shift estimate.
Returning to the illustration, after processing one A-line pair a set of
time shifts, t1 through t60, may be obtained. The corresponding strain
profile may then be defined by the relationship
##EQU1##
where s.sub.i is the strain estimate for segment pair i, and where
.DELTA.x is an axial increment.
The process may then be repeated for all A-line pairs, resulting in an
array of strain data. These values may then be scaled and assigned to an
intensity for display, e.g., an intensity varying within 256 grey scale
levels. Due to the large dynamic range of some strain data, contrast
stretching may be applied in order to observe variation in particular
strain ranges. For example, 256 grey scale levels may be assigned to a
user specified strain range, thus stretching the contrast in that region.
In general, elastography contemplates sonically coupling an ultrasonic
source to a target body; energizing the ultrasonic source to emit a first
ultrasonic signal or pulse of ultrasonic energy from the source along an
axis into the target body; detecting from a region within the target body
a first echo sequence including a plurality of echo segments resulting
from the first transmitted signal; displacing the target body along the
axis while maintaining coupling between the ultrasonic source and the
target body; energizing the ultrasonic source to emit a second ultrasonic
signal along the axis into the target body; and detecting from the region
within the target body a second echo sequence including a plurality of
echo segments resulting from the second transmitted signal; and measuring
the differential displacement of the echo segments. A plurality of first
ultrasonic signals or pulses of ultrasonic energy may be emitted and a
plurality of first echo sequences detected before compressing the target
body. Then a plurality of second signals and pulses are emitted along a
plurality of parallel paths and a plurality of second echo sequences are
detected.
In one embodiment of elastography, a transducer is the ultrasonic source
and is sonically coupled to direct an ultrasonic signal or pulse of
ultrasonic energy into the tissue along a radiation axis such that
movement of the transducer along the axis effects a change in compression
of the tissue.
In a preferred embodiment of elastography, the ultrasonic source is a
transducer sonically coupled to a tissue of interest. A first pulse of
ultrasonic energy is emitted along a path into the target body and the
arrival of a first echo sequence (A-line) including one or more echo
segments is detected from regions within the tissue along the path
resulting from the first pulse of ultrasonic energy. Thereafter,
compression is changed within the tissue along the path. The compression
change may be accomplished by transaxially moving the transducer along the
path to compress or displace a proximal region of the tissue. A second
pulse is emitted, and the arrival of a second echo sequence including one
or more echo segments common to the first echo sequence is detected in
response to the second pulse. The differential displacements of at least
one echo segment are measured. The echo sequences detected are from common
regions within the tissue.
A comparison of the first and second echo sequences or waveforms with
intervening compression reveals a generally decreasing displacement of
tissue structures with depth. In a homogeneous medium, the rate of
decrease will tend to be asymptotic. Of particular interest is the
differential displacement per unit length--i.e., strain. In a homogeneous
compressible medium, the strain will tend to be constant along the axis of
compression. In a non-homogeneous medium, the strain varies along the axis
of compression.
The strain of a tissue may be calculated using the arrival times of first
and second echo sequences from proximal and distal features in a target
body--i.e., tissue--using the following equation:
##EQU2##
t.sub.1A =arrival time of a first echo sequence from a proximal feature;
t.sub.1B =arrival time of a first echo sequence from a distal feature;
t.sub.2A =arrival time of a second echo sequence from a proximal feature;
and
t.sub.2B =arrival time of a second echo sequence from a distal feature.
The arrival times of the echo segments from a common point detected in
response to a first and second pulse of ultrasonic energy are compared.
The common points may be found in features occurring within the echo
signal. The time shifting of the two echo segments is used to determine
compressibility.
Thus, if no change in arrival time has occurred with an intervening
compressive force, it follows that a target body has not been compressed
along the travel path leading to the source of the echo segments. On the
other hand, if the arrival time of the second echo segment is smaller than
the arrival time of the first echo segment, it is clear that compression
has occurred and that the target body is compressible. Moreover, the
difference in arrival times, taken together with other available data,
makes it possible to quantify th | | |
