Method for Performing Elastography

Abstract

A method for performing elastography is provided, comprising the following steps. First, emitting a first coded signal towards tissue and recording an echoed signal in response. Next, applying a strain on the tissue, such as a compression or an expansion. Then, emitting a second coded signal towards the tissue under strain, said second signal being a compressed (or stretched) version of the first emitted signal in the time domain, and recording an echoed signal in response. Then processing the second echoed signal by stretching (or compressing) it in the time domain by a factor matched to the compression (or stretching) factor that was applied to the second emitted signal. Finally, cross-correlating the first echoed signal and the processed second echoed signal to provide an elastographic image of said tissue. The method of the invention uses different emitted signals before and during strain applied to the tissue. The image quality in elastography can therefore be considerably improved.

Description

Other characteristics and advantages of the invention will appear on reading the following detailed description of some embodiments of the invention given solely as an example and taken in connection with the accompanying drawings in which:

FIG. 1 is a graph showing pre- and post-compression short pulse emitted signals;

FIG. 2 is a graph showing pre- and post-compression Barker coded emitted signals.

The invention concerns a method where the pre- and post-compression emitted signals have different characteristics, these characteristics being chosen depending on the strain to be measured.

According to the invention, a new elastography method is provided comprising the following steps. First, emitting a first coded signal towards tissue and recording a first echoed signal in response to said first signal. Next, applying a strain on the tissue, such as a compression or an expansion, preferably of a known value. The strain applied to the tissue could also alternate compression and expansion. Then, emitting a second coded signal towards the tissue under strain, said second signal being a compressed (or stretched) version of the first emitted signal in the time domain, and recording a second echoed signal in response to said second signal. Then processing the second echoed signal by stretching (or compressing) it in the time domain by a factor matched to the compression or stretching factor that was applied to the second emitted signal. Finally, cross-correlating the first echoed signal and the processed second echoed signal to provide an elastographic image of said tissue.

The time-domain stretching or compression of the second emitted signal depends on the strain applied to the tissue, i.e. if the tissue is compressed (respectively stretched by expansion), the second emitted signal will be a compressed version (respectively a stretched version) of the first emitted signal.

According to the invention, the elastography method uses different emitted signals before and after strain is applied to the tissue. In particular, the invention concerns a method for which the shape of the post-compression signal is a compressed (or stretched) version of the pre-strain signal. The compression (or stretching) factor a can be matched to an estimate of the applied strain ε. The pre- and post-compression signals are coded signals; it can be bursts coded signals.

The use of coded excitation allows further improvement in image quality in areas where the sonographic signal-to-noise ratio (SNRs) is low, without any loss in axial resolution.

According to the invention, an ultrasonic signal is emitted towards tissue, being firstly at rest. As well known from sonography, an echoed signal is returned from the tissue. Such echoed signal can be recorded and analyzed to provide information on the tissue condition.

The ultrasonic pulse p(t) emitted towards tissue can be modeled as follows:

p(t)=u(t)*h(t)

where t denotes time, and

with, u(t) being the electric pulse applied to the ultrasonic transducer

• • h(t) being the transducer impulse response
  • the symbol * being the convolution product

The echoed signal s(t) can be modeled as follows:

s(t)=p(t)*m(t)+η(t)

with, m(t) being the reflectivity function of the scatterer distribution that model the tissue, and η(t) being additive electronic noise.

If noise is neglected, the echoed signal recorded before strain is applied to the tissue is

s ₁(t)=p₁(t)*m(t);

and the echoed signal recorded while applying a strain to the tissue is

s ₂(t)=p₂(t)*m(αt);

with α=1/(1+ε) linked to the uniform strain s applied to the tissue. If ε is positive, the tissue is expanded and if ε is negative, the tissue is compressed. p₁(t) and p₂(t) are respectively the pre- and post-compression emitted ultrasonic pulses.

The cross-correlation in the frequency domain of said echoed signals before and during strain is formulated as such:

C(f)=S₁(f) S₂*(f)

with S₁(f) and S₂(f) being the Fourier Transform of the respective echoed signals s₁(t) and s₂(t), and * being the complex conjugation.

In conventional sonography, the emitted pre and post-compression pulses p₁(t) and p₂(t) are identical. The cross-correlation function can be expressed as follows:

C(f)=(1/|α|) ∥P₁(f)∥² M(f)M*(f/α)

with M(f) being the Fourier Transform of the reflectivity function m(t). Correlation degrades with increasing strain because the M(f)M*(f/α) product is lower that the autocorrelation function ∥M(f)∥² of the tissue.

Uniform or local stretching was proposed to recover the autocorrelation function of the tissue. It can be referred to the previously cited publications of T. Varghese, 1996; S K. Alam, 1998 and patents U.S. Pat. No. 6,514,204 and U.S. Pat. No. 6,277,074.

The principle of these methods is to stretch the post-compression echoed signal s₂(t) by a factor a in the time domain, i.e. to define s₂′(t) as follows:

s ₂′(t)=s₂(t/α)=p₂(t/α)*m(t)/α

Then the cross-correlation between the pre-compression signal s₁(t) and the stretched post-compression signal s₂′(t) is, in the frequency domain:

C(f)=(1/|α|) P₁(f) P₁*(αf) ∥M(f)∥²

This method recovers the autocorrelation function of the tissues but at the cost of degrading the autocorrelation function of the transmitted pulse ∥P₁(f)∥². This is because the point-spread function (PSF) is also stretched with this method.

However, according to the invention, the pre- and post-strain signals are not identical, i.e. the duration of the second emitted pulse is stretched or compressed compared to the duration of the first emitted pulse.

The post-compression pulse p₂(t) is compressed in the time domain compared to the pre-compression pulse p₁(t) and can be expressed as follows:

p ₂(t)=p₁(αt).

This is achieved using different excitation voltage waveforms u₁(t) and u₂(t) that are related by: u₂(t)*h(t)=α u₁(αt)*h(αt).

Knowledge of the impulse response h(t) is necessary to apply this equation. In practice, a difficulty arises because the spectrum H(f) of the impulse response h(t) can be measured accurately only within a limited frequency range. A solution is to fit a theoretical model, for example a Gaussian distribution, to the experimental impulse response. Alternatively, a combination of experimental data (inside the frequency range in which the impulse response can be measured accurately) and of theoretical data (outside of the range) can also be used.

Moreover, because the shortest PSF will always be achieved with a spike voltage, it is not possible to achieve compression of the post-compression PSF p₂(t) if the pre-compression PSF p₁(t) was obtained with spike excitation. However this is still possible if care was taken to pre-stretch the pre-compression PSF p₁(t) so that the post-compression PSF p₂(t)=p₁(αt) has duration greater or equal to the duration of the impulse response h(t).

FIG. 1 shows an example of emitted signals p₁(t) and p₂(t) with a factor α=1.02, corresponding to an applied compression strain ε of 2% on the tissue of the target body. The method according to the invention makes it possible to improve greatly the signal to noise ratio through an improvement in the correlation between the pre- and post-compression echoed signals.

In the example of FIG. 1, an ultrasonic transducer was used to provide pulsed excitations with a central frequency of 5 MHz. It can be seen that the signal p₂(t) is a compressed version in the time domain of p₁(t).

The method creates a time-domain compression (or expansion) of the PSF (Point Spread Function) of the imaging system, which is then restored by numerical stretching (or compression) of the echoed signal, as shown below.

The post-compression signal becomes: s₂(t)=α p₁(αt)*M(αt);

Then global or adaptive stretching of the post-compression signal is used to obtain a stretched version s₂″ of the post-compression echoed signal:

s ₂″(t)=s₂(t/α)=p₁(t)*m(t)=s₁(t)

Then the cross-correlation between the pre-compression signal s₁(t) and the stretched post-compression signal s₂″(t) can be expressed as:

C(f)=S₁(f)S₂″*(f)=∥S₁(f)∥²=∥P₁(f)∥² ∥M(f)∥²

It can be noted that the cross-correlation function is equal to auto-correlation function of the pre-compression pulse. Therefore, the decorrelation noise due to the strain applied to the tissue is totally eliminated. The image quality in elastography can therefore be considerably improved by such method according to the invention.

The calculation applies regardless of the shape of the emitted signals, which can be either short pulses, burst signals, or coded waveforms.

The strain applied to the tissue may be a compression or an expansion, without impacting on the method according to the invention. The terms pre-compression, post-compression, global stretching and others, can be changed into pre-stretching, post-stretching and global compressing without changing the previous equations, as the value of the factor α depends on the type of strain applied to the tissue.

According to an embodiment of the invention, the image quality can be improved by adjusting the value α to a value as close as possible to the real strain ε applied. First, the method according to the invention is conducted by emitting a second signal p₂(t) with a predetermined value of α, as illustrated on FIG. 1. A first elastographic image is provided and the local strain ε applied on tissue can be calculated from said first elastographic image. The value of α can therefore be adjusted to the calculated strain E and further second signals p₂(t) can be emitted with an adjusted values of α to generate a new elastogram. The emitting of a post-compression signal p₂(t) can be repeated iteratively until the calculated adjusted value of α is substantially equal to the value applied to the second emitted signal p₂(t).

According to the invention, the use of coded excitation allows further improvement in image quality in areas where the sonographic signal-to-noise ratio (SNRs) is low, without any loss in axial resolution.

In this case, the pre-compression emitted signal p₁(t) can be any of the coded signals that can be used for sonography, such as a frequency-modulated chirp, a Barker code, a Golay complementary series or any pseudo-random sequences whose auto-correlation function is a Dirac function. The post-compression emitted signal p₂(t) is derived from the coded pre-compression emitted signal p₁(t) using equation p₂(t)=p₁(αt).

FIG. 2 shows an example of pre-compression emitted coded signal p₁(t) and matched post-compression emitted signal p₂(t) designed for an estimated compression strain of 2% (α=1.02) and an ultrasonic transducer with a central frequency of 5 MHz, using a Barker code of length 7. The signal p₂(t) is a compressed version in the time domain of p₁(t).

Combining coded excitation with the invention has great potential because two of the major causes of noise in displacement estimates in elastography, namely strain-induced decorrelation and SNRs-induced decorrelation, are significantly decreased.

Moreover, using coded excitation in elastography can be very simple as no matched filtering is mandatory on echoed signals before the cross-correlation of the echoed signals is estimated. Cross-correlation of the first echoed signal s₁(t) and the processed second echoed signal s″₂(t) can be conducted on coded signal without impacting the results of the elastographic image

The invention also relates to a computer system able to implement the method according to the invention. The computer system thereof comprises computer-implemented software to link the second signal to be emitted to the first emitted signal, and computer-implemented software to cross-correlate the echoed signals.

The computer system of the invention is adapted to handle the signal processing in order to define the parameters of the post-compression signal p₂(t) to be emitted responding to the criteria of the first or second embodiment of the method of the invention. In particular, the computer comprises hardware or computer-implemented software to stretch or compress the second signal pulse compared to the first signal pulse.

The computer system may also include computer-implemented software to calculate a local strain ε applied on tissue and adjust the value of α accordingly.

The computer system may also include computer-implemented software to code the emitted signals. The computer system may include software code generator or controlled hardware code generator.

Conventional equipment may be use to implement the elastography method according to the invention. The equipment may comprise a computer, a transmitter emitting signals according to the invention towards tissue and a receiver of echoed signals from the tissue, means for applying a strain on tissue, such as a hand-held compressor or a compressor activated by a motor controlled by the computer. The computer may be linked to a cross-correlator receiving digitalized signal of the emitted and echoed signals towards and from the tissue. A monitor may display the elastographic image. Such an equipment is described in U.S. Pat. No. 5,474,070.

Claims

1. A method for performing elastography, the method comprising the steps of: a) applying a first coded voltage waveform u1(t) to a transducer to emit a first ultrasonic signal p1(t) towards tissue, with p1(t)=u1(t)*h(t) being the point spread function (PSF) generated by the waveform u1, where t denotes the time and symbol * denotes a convolution product, h(t) being the impulse response of the transducer;b) recording a first echoed signal s1(t) in response to said first emitted signal;c) applying a strain on the tissue;d) applying a second coded voltage waveform u2(t) to the transducer to emit a second ultrasonic signal p2(t) towards the tissue under strain with p2(t)=u2(t)*h(t) being the point spread function (PSF) generated by the waveform u2,said second emitted signal being linked to said first emitted signal with the following relation: p2(t)=p1(αt),with a =1/(1 +), F being an initial estimate of the strain applied to the tissue;e) recording a second echoed signal s2(t) in response to said second emitted signal;f) processing said second echoed signal according to the following relation: s2″(t)=s2(t/α);g) cross-correlating the first echoed signal s1(t) and the processed second echoed signal s″2(t) to provide an elastographic image of said tissue.

2. The method according to claim 1, wherein the strain applied to the tissue in step c) is negative, providing a compression of said tissue.

3. The method according to claim 1, wherein the strain applied to the tissue in step c) is positive, providing an expansion of said tissue.

4. The method according claim 1, wherein the first and second emitted signals are burst signals.

5. The method according claim 1, wherein the first emitted signal p1(t) is pre-stretched so that its point spread function (PSF) duration is increased.

6. The method according claim 1, wherein the second signal p2(t) is emitted with a predetermined value of α in step d), providing an elastographic image in step g); the method further comprising the steps of:h) calculating a local strain ε applied on tissue from the results of said elastographic image;i) adjusting the value of α according to the calculated local strain ε;j) repeating steps d) to g) with an adjusted value of α.

7. The method according to claim 6, wherein steps h) to j) are repeated iteratively until the adjusted value of a is substantially equal to the value applied to the second emitted signal p2(t).

8. A system for performing the elastography method according to any claim 1, comprising: hardware or computer-implemented software to link the second signal to be emitted to the first emitted signal;hardware or computer-implemented software to cross-correlate the echoed signals.

9. The system according to claim 8, further comprising: hardware or computer-implemented software to calculate a local strain ε applied on tissue and adjust the value of α accordingly.

10. The system according to claim 8, further comprising: hardware or computer-implemented software to code the emitted signals.