METHOD FOR OBTAINING ELASTIC PROPERTIES OF A SOFT SOLID, WHICH USES ACOUSTIC VORTICES

Abstract

The present invention relates to a method for obtaining elastic properties of a soft solid by means of quasi-omnidirectional transverse waves generated by a focused ultrasound beam, with a helical phase profile that produces an acoustic vortex that generates a transverse wave front, not only in the direction perpendicular to the ultrasound beam but also in the same direction as the ultrasound beam. The invention also allows control of the transverse wave front generated, which facilitates the carrying out of elastography studies at different frequencies and increases the amplitude of the transverse waves produced, thereby improving the signal-to-noise ratio.

Claims

1. A method for obtaining elastic properties of a soft solid on which an acoustic radiation force is exerted which causes deformations in said soft solid, wherein the method comprises the steps of: applying a pulsed or amplitude-modulated signal to an ultrasound transducer, generating, in the ultrasound transducer, a focused vortex ultrasound beam, which generates a quasi-omnidirectional transverse wave front, characterized by a speed, which is transmitted through the soft solid, acquiring images of the soft solid while the wave front is propagated, making use of a second ultrasound transducer in contact with the soft solid, calculating the deformations produced in the soft solid by cross-correlation or Doppler techniques from the images, calculating the propagation speed of the wave front from the deformations, using standard tracking techniques, calculating the transverse modulus of elasticity (G) of the soft solid from the equation: $v=\sqrt{\frac{G}{\rho }}$  wherein v is the propagation speed of the wave front and ρ the density of the soft solid, and obtaining elastography images from the transverse modulus of elasticity at different points of the soft solid.

2. The method of claim 1, wherein the acoustic radiation force is given by a force field that is defined by: $F\left(x,y,z\right)=i\frac{\alpha \left(\omega \right)}{2{\mathrm{\omega \rho }}_0{c}_0}\left(P\nabla P^{*}-P^{*}\nabla P\right)$ F being the force vector field, α(ω) the absorption of the soft solid, ω the angular frequency, ρ.sub.0 the density of the soft solid, c.sub.0 the speed of the wave front, P the pressure field produced, and P* the complex conjugate thereof.

3. The method of claim 1, wherein the ultrasound transducer is a single element transducer, comprising a holographic lens, positioned on the surface of the ultrasound transducer, the holographic lens modifying the phase of the wave front so that it is adjusted to that of a focused acoustic vortex, given by:
A(x.sub.0,y.sub.0)=exp(−ik.sub.0√{square root over (x.sub.0.sup.2+y.sub.0.sup.2+F.sup.2)})exp(−im tan.sup.−1(y.sub.0,x.sub.0)) A(x.sub.0,y.sub.0) being the phase along the surface of the ultrasound transducer given by x.sub.0, y.sub.0, k.sub.0=2πf/c.sub.0 the wave number, wherein f is the frequency and c.sub.0 is the speed of sound in the soft solid, F is the focal length of the lens and m the topological charge of the vortex.

4. The method of claim 1, wherein the ultrasound transducer is a flat multi-element transducer, comprising elements that are adjusted to an amplitude given by |A| and a phase given by tan.sup.−1(Im(A)/Re(A)), being:
A(x.sub.0,y.sub.0)=exp(−ik.sub.0√{square root over (x.sub.0.sup.2+y.sub.0.sup.2+F.sup.2)})exp(−im tan.sup.−1(y.sub.0,x.sub.0)) A(x.sub.0,y.sub.0) being the phase along the surface of the ultrasound transducer given by x.sub.0, y.sub.0 which represent the spatial position in Cartesian coordinates of each element of the primary transducer, k.sub.0=2πf/c.sub.0 the wave number, wherein f is the frequency and c.sub.0 is the speed of sound in the soft solid, F is the focal length of the lens and m the topological charge of the vortex.

5. The method of claim 1, wherein the ultrasound transducer is a geometric focusing multi-element transducer, wherein each element of the ultrasound transducer is adjusted to an amplitude given by |A| and a phase given by tan.sup.−1(Im(A)/Re(A)), being:
A(x.sub.0,y.sub.0)=exp(—im tan.sup.−1(x.sub.0,y.sub.0)) wherein A(x.sub.0,y.sub.0) is the phase along the surface of the ultrasound transducer given by x.sub.0, y.sub.0 which represent the spatial position in Cartesian coordinates of each element of the primary transducer, and m the topological charge of the vortex.

6. The method of claim 3, wherein the sign of the topological charge m is varied by modifying the phase of the wave front at the output of the primary transducer using the lens, which works with a positive topological charge m at a first frequency and with a negative topological charge m at a second frequency.

7. The method of claim 3, wherein the sign of the topological charge m is varied by using two ultrasound transducers positioned in the form of concentric rings wherein each one comprises a different lens with a different topological charge m, one being positive and the other negative, and alternating the emission between one ultrasound transducer and another.

8. The method of claim 4, wherein the sign of the topological charge m is varied by angularly reversing the phase of the elements of the ultrasound transducer.

9. The method of claim 5, wherein the sign of the topological charge m is varied by angularly reversing the phase of the elements of the ultrasound transducer.

Description

DESCRIPTION OF THE DRAWINGS

[0055] To complement the description that is being made and for the purpose of helping to better understand the features of the invention according to a preferred practical exemplary embodiment thereof, a set of drawings is attached as an integral part of said description in which the following is depicted in an illustrative and non-limiting manner:

[0056] FIG. 1 shows a diagram of the primary and secondary ultrasound transducers used by the method.

[0057] FIG. 2 shows a block diagram of the process wherein a possible sequence to follow is shown.

[0058] FIG. 3 shows the acoustic field generated by the ultrasound transducer.

[0059] FIG. 4 shows the radiation acoustic force field generated on the soft solid.

[0060] FIG. 5 shows the movement of the soft solid in the direction z at different instants in time.

PREFERRED EMBODIMENT OF THE INVENTION

[0061] In view of the figures described above, a non-limiting exemplary embodiment of the method for obtaining elastic properties of a soft solid, object of this invention, can be observed.

[0062] The first step of the method, a block diagram of which is shown in FIG. 2, consists of applying a pulsed or modulated frequency signal, with a carrier frequency of around 1 MHz, comprised in the ultrasound range, and a modulator frequency in the range from 1 Hz to 1000 Hz, to an ultrasound transducer (1), like the one in FIG. 1, comprising a surface intended to make contact with a soft solid.

[0063] Once the signal is applied to the ultrasound transducer (1), a focused ultrasound beam (5) is generated, with a helical phase profile, i.e., an acoustic vortex, and which generates a quasi-omnidirectional transverse wave front (6) that is transmitted through the soft solid. The frequency of the wave front (6) is equal to the modulation frequency of the pulsed signal applied to the ultrasound transducer (1).

[0064] The focused vortex ultrasound beam (5) is generated by means of the ultrasound transducer (1) which is multi-element (or phased-array), the array being a geometric focusing array. To do this, each element of the ultrasound transducer (1) is adjusted to an amplitude given by:

|A(x.sub.0,y.sub.0)|=exp(−im tan.sup.−1(x.sub.0,y.sub.0)),  (Equation 6)

i.e., a phase profile that linearly depends on the polar angle occupied by each element of the ultrasound transducer (1).

[0065] Therefore, the emitted ultrasound beam (5) has an acoustic intensity that rotates with respect to the angular coordinate, which transfers to the soft solid both an amount of linear momentum in the direction of the ultrasound beam and an angular momentum in the form of a torus around the ultrasound beam (5).

[0066] FIG. 3 shows the acoustic field generated by the ultrasound transducer (1). Image a) represents the magnitude of the field in the sagittal plane in the direction of propagation y=0. Image b) represents the magnitude of the field in the transverse plane, over the focal length z=F. Image c) represents the phase of the field in the transverse plane, over the focal length z=F.

[0067] FIG. 3 shows how a phase singularity is produced on the axis that gives rise to an acoustic vortex. The phase also rotates around the focus an integer number of times.

[0068] The transfer of linear momentum generates a force field in the soft solid that can be calculated as:

[00004]$\begin{array}{cc}F\left(x,y,z\right)=i\frac{\alpha \left(\omega \right)}{2{\mathrm{\omega \rho }}_0{c}_0}\left(P\nabla P^{*}-P^{*}\nabla P\right),& \left(\mathrm{Equation}7\right)\end{array}$

F being the force vector field, α(ω) the absorption of the soft solid, ω the angular frequency, ρ.sub.0 the density, c.sub.0 the speed of front transverse waves, P the pressure field produced, and P* the complex conjugate thereof.

[0069] This force field is shown in FIG. 4. Graph a) shows a representation in the transverse plane of the force component in the direction x, calculated at z=F. Graph b) is the representation in the transverse plane of the force component in the direction y, calculated at z=F. Graph c) is a representation in the sagittal plane of the force component in the direction z, calculated at y=0. Graph d) is the representation in the transverse plane of the force torque component, calculated at z=F. Subgraph e) is the representation of the vector field.

[0070] From the previous force field, a force is produced in the soft solid that is of the torque type, with a small axial component. Since the soft solid absorbs a large part of the energy of the ultrasound beam (5), the transfer of angular momentum in the form of torque to the soft solid causes a transient deformation thereof, curling it.

[0071] The next step of the method consists of acquiring radiofrequency signals that are reflected by the soft solid at different instants in time, a process that is repeated while the transverse wave front (6) is propagated. To do this, a second ultrasound medical imaging transducer (2) is used, in pulse-echo mode.

[0072] Once the signals have been obtained, the deformations produced are calculated as a function of time, based on the amplitude of the transverse movements suffered by the soft solid, using cross-correlation or Doppler techniques. These deformations can be observed in the graphs of FIG. 5, wherein the movement of the tissue in the direction z is reflected, at different instants in time, from t=0.6 ms to t=2.4 ms.

[0073] From these deformations, using standard tracking techniques, the propagation speed of the transverse wave front (6) is calculated.

[0074] From the speeds, the transverse or shear modulus of elasticity is obtained from the equation:

[00005]$\begin{array}{cc}v=\sqrt{\frac{G}{\rho }}& \left(\mathrm{Equation}8\right)\end{array}$

G being the transverse or shear modulus of elasticity and p the density of the soft solid.

[0075] Finally, from the transverse elastic modulus obtained at different points of the soft solid, elastography images can be obtained that are used to make a medical diagnosis.