Estimation of Acoustic Scatterer Parameters in an Object

Bjørn A.J. Angelsen, Tonni F. Johansen, Norwegian University of Science and Technology -NTNU, Trondheim, Norway.

Contents

ABSTRACT 1

1. FIELD OF THE INVENTION 1 2. BACKGROUND OF THE INVENTION 1

3. SUMMARY OF THE INVENTION 3

5. DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION 4

6. WE CLAIM: 9

Abstract

The invention presents methods and instrumentation for estimation of frequency dependent acoustic scatterer parameters in an object with elimination of the influence of the accumulative absorption in the object on these scatterers.

1. Field of the invention

The present invention, relates to characterization of acoustic scatterers in an object. The methods and instrumentation have applications to wide range of acoustic imaging situations, like geologic imaging of structures around oil wells, and SONAR imaging of fish and the sea bed, with particular reference to ultrasound imaging of scatterers in biological tissue. The method eliminates the effect of unknown acoustic absorption between the transducer and the scatterers, and produces local scattering parameters in the object and their frequency dependence.

2. Background of the invention

Acoustic back scatter imaging is a widely used imaging modality for diagnosis of many diseases of humans and animals, nondestructive testing of materials, acoustic imaging of geologic structures, and SONAR imaging offish and other objects and the sea bed. However, at present the method is used mainly to visualize object structures, object velocities, movements, and shear elasticity of the object, and there is a further need for improved characterization of the scattering oobject structures with dimensions below the resolution in the structural image.

Transmitting on one transducer with the direction of the beam incident on the scatterers defined by the angle θ _t and receiving on the same or another transducer so that the angle between the transmit and the receive beams is θ _tr , one can write the frequency dependency of the received power of the scattered signal from the cross over region of the transmit and receive beams (105 of Figure 1)

S _tr = κ(δβ - δγcosθ _t J V _s H(f ,θ _tr ;θ _t > ⁴ e- ^2a(s)f

(1) where K is an amplitude parameter, f is the acoustic frequency, and e ^~2a(s)f represents acoustic absorption where a(s) is the integral of the absorption coefficient for the whole propagation distance s of the signal along transmit and the receive beams. δβ is the relative deviation in the bulk compressibility and δγ is the relative deviation in the mass density between the scatterer and the surrounding medium, V _s is the scatterer volume, and H(f,θ _tr ;θ _t ) is a function that represents the scatterer size and shape and the dependency of the scattered intensity on the direction θ _t of the incident beam, and the angle θ _tr between the incident and receiving beams, for example θ _tr = θ ₁₂ as illustrated in Figure 1. For scatterers that are much smaller than the wavelength λ = c/f, where c ~ 1.54 mm/μsec is the acoustic propagation velocity in the tissue, we have H(f,θ _tr ;θ _t ) = 1. The scatterers are then referred to as point scatterers.

As the scatterer dimensions approaches or becomes larger than λ ( for example as λ is reduced with higher frequencies), one gets interference from waves scattered at different regions of the scatterer. Depending on the angles θ _t and θ _tr , one can get destructive interference that reduces the scattered power in certain directions, or constructive interference that increases the scattered power in other directions. The invention provides methods on how one can use this angular variation to characterize the scatterers.

We hence notice that information about the acoustic parameters of the scatterers, δβ and δγ, and the scatter size and shape are found in the magnitude of the scattered intensity, i.e. (δβ-δγcosθ _tr fV _s Hftθ _tr jθ _t ), the frequency variation of the intensity, H(f,θ _tr ;θ _t )fV ^2a(z)f , and the variation of the scattered intensity with the directions of the incident and receive beams

(δβ-δγcosθtr) ² H(f,θtr;θt).

With direct back-scattering, i.e. the transmit and receive transducers are the same so that θ _tr = 0, we can often approximate the absorption integral as a(s) = 2az

(2) where z is the distance between the transducer and the scatterer so that s = 2z, and α is an absorption parameter with typical values of 0.035 - 0.058 Neper/cmMHz. These values correspond to an absorption attenuation of 0.3 - 0.5 dB/cmMHz.

From Eq.(l) we see that absorption plays an important role in the frequency dependency of the scattered intensity, except when a(s)f is so low that the frequency variation of e ^"2a ® ^f is negligible compared to the other terms. To get some more insight into this, we do as an initial exercise assume that we have point scatterers (H(f,θ _tr ;θ _t ) = 1), which gives the back scattered ( i.e. , θ _tr = 0)

S _back

(3) Differentiation with respect to f gives a maximum of this function, and also a maximum in

the frequency variation of fV ⁴ "^, for

CXZ

(4)

The absorption term will then have negligible effect on the frequency variation of the scattered intensity when f « f ₀ , while when f ~ f ₀ the absorption term has a strong influence on the frequency variation of the scattered intensity. From Eq. (4) we see that f ₀ is approximately inversely proportional to the depth, where we shall analyze three examples.

For intravascular imaging (IVUS) of coronary plaque we have typically z ~ 0.2 cm, for noninvasive imaging of carotid plaque we have typically z ~ 2.5 cm, and for noninvasive imaging of liver disorders we have typically z ~ 7cm. With the values of α given above, we get the following frequencies for peak of Eq. (3):

IVUS CoronaryPlaque: f ₀ = 85 - 145MHz

Noninvasive Carotid Plaque: f ₀ = 7 - 12MHz

Noninvasive Liver scatterers: f ₀ = 2.5 - 4MHz

(5) For the liver and carotid and liver imaging, fo = 2.5 - 4 MHz and 7 - 12 MHz covers the actual frequencies used for imaging, so that in these situations the absorption has a dominating effect on the frequency variation of the scattering. Hence, in these situations one should find methods for scatterer characterization, where the effect of frequency variation of absorption on the scattered intensity is reduced.

For rVUS imaging at 20 - 30MHz, the influence of absorption on the frequency variation of the scattered intensity can be neglected when the scatterer dimension approaches or gets larger than the wavelength, which is 50 - 80 μm for these frequencies. Hence, the frequency variation of the scattered intensity can contain some information for scatterers with dimensions approaching ~ 50 μm.

As the absorption is roughly proportional to the frequency, the image depth is inversely proportional to the frequency. For imaging of the carotid vessel and similar down to 40mm depth, one generally uses 10 MHz ultrasound. Hence, IVUS imaging of coronary artery wall down to 4 mm is hence very attractive at ~ 100 MHz. According to Eq.(5) the acoustic absorption will then play an important role in the frequency dependency of the back scattered intensity. The wave length at 100 MHz is ~ 15 μm, and by reducing the effect of absorption on the frequency variation of the scattered intensity, one is able to extract information on scatterers down to ~ 2 μm dimension. 3. Summary of the invention

The present invention provides methods for characterizing the scatterers in acoustic imaging that strongly reduces the effect of absorption attenuation of the waves in the characterization, and makes it possible to eliminate the effect of frequency dependent absorption in the transmit path of the acoustic pulse, and obtain frequency dependent scattering parameters from local regions in the tissue. It is furthermore possible to obtain

information of scattering anisotropy in such regions, that can provide information about fiber direction in fibrous and muscular tissue, as well as degree of fibroses. Moreover, by comparing acoustic angular scattering with back scattering, one is able to derive anisotropic properties of the scattering cross section from a local region, that can give information about fibrous structures in the tissue.

The method provides new acoustic parameters for characterization and contrast enhancement of tissue structures in acoustic imaging, like tumor structures, ischemia of a myocardial wall, and plaque composition in vascular atheroma. It can be used with many arrangements of acoustic transducers, particularly switched linear or curvilinear arrays.

The essence of the invention, is to use scattered signals either from multiple regions where one region is used as a reference, or multiple scattering directions, creating own reference signals from the same scattering region, so that the absorption attenuation of the acoustic wave is eliminated from the estimated parameters, and directional scattering information can be acheived.

4. Summary of the drawings Figure 1 shows an example embodiment according to the invention of two transducers arranged so that the scattering parameters of the tissue in the overlap region of the transducers beams can be investigated.

Figure 2 shows example embodiments according to the invention where a switched linear array is used to realize two transducer apertures, which are arranged so that the scattering parameters of the tissue in the overlap region of the apertures beams can be investigated.

Figure 3 illustrates how the scattering from a vessel atheroma with scatterers comparable to or larger than the wavelength can be investigated using a linear array.

Figure 4 shows imaging of anisotropic structures of a vascular plaque combined with two dimensional backscatter imaging.

5. Detailed description of example embodiments of the invention In the following we describe example embodiments of the invention with reference to the drawings. FIG. 1 shows two acoustic transducers 101 and 102 that are connected to an acoustic instrument 100 that allows selectable transmission of acoustic pulses on each transducer, with selectable reception of the scattered signal on each transducer, independent of the transducer selected for transmission. The transducers can be directed at an angle towards each other, where θ _t represents the direction of the transmit beam and θ _tr is the angle between the transmit beam and the receive beam. In the Figure we have θ _t = θu when transmitting on Transducer 1 101 and θ _t = θ _t2 when transmitting on Transducer 2 102. We denote the beam 103 from Transducer 1 as Beam 1, and the beam 104 from Transducer 2 as Beam 2. The beams intercept in a region labeled 105 in Figure 1. The angle between Beam 1 and Beam 2 is indicated as θ ₁₂ in Figure 1. When different beams are used to transmit and receive one gets θtr ⁼ θ ₁₂ , and when the same beam is used to transmit and receive one gets

θ _tr = 0.

A first method for reduction of the effect of frequency absorption according to the invention, is to combine the scattered signal from an observation region with the scattered signal from reference scatterers with known frequency variation of the scattering cross section, and located in a neighboring reference region with close to the same absorption attenuation of the signals as for the scatterers to be characterized in the observation region. This is obtained by using the same transmit and receive beams for the reference and the observation regions, where the reference region is so close to the observation region that the signals from the two regions have practically the same absorption attenuation. Such a situation can for example be obtained with backscatter imaging with the same beams, where the reference and observation regions have neighboring depths. Similar situations can also be obtained with angular scattering by adjusting the beam directions. Example reference scatterers can be the erythrocytes in blood, where for characterization of arterial wall plaque one would use the signal scattered from the blood close to the plaque as reference. For other situations (like the liver) one would find the blood vessels close to the area of interest as reference, or use other reference scatterers in the neighborhood of the region of interest. In such situations one can do back scatter imaging and use the same beam directions for the transmit and the receive beams. This will create a reference signal for back scatter imaging obtained from Eq.(l) as

(6) where σ _ref = (δβ-δγ) ² for the parameters of the reference scatterers with back scattered imaging, and H _ref represents the frequency variation of the back scatterers for the reference scatterers. For point scatterers, like erythrocytes up to f ~10MHz, H _re f = 1.

The backscattered signal from blood is often masked in close to stationary reverberation noise. As the blood is moving, the scatterers also move and the backscattered signal from blood can be retrieved from the stationary noise by collecting back scattered signal from several pulses in substantially the same beam direction and perform high pass filtering of the signal along the pulse number coordinate. A small variation of the beam direction between the pulses can be accepted, as for example with continuous, mechanical scanning of the beam direction.

Ultrasound contrast agent micro bubbles can also conveniently be used as reference scatterers, both in visible blood vessels, and within the capillary vessels. The reference signal from the contrast agent bubbles can be separated from the signal from surrounding tissue by several known methods, such as harmonic imaging, pulse inversion imaging, and manipulation of the scattering properties by a low frequency pulse. Other reference scatterers can be identifiable cells, like normal liver cells, or fat cells in atheroma.

The back scattered intensity from the scatterers in the observation region to be characterized can be approximated as

S _sca , ~

cs"scat ⁼ (δβ-δγ) for the scatterers in the actual observation region, and V _scat is the vo ⁽⁷ lu ⁾ me of these scatterers. H(f,O;θ _t ) then includes the frequency variation of the scattered signal due to the scatterer size and shape. The following ratio will then be independent of the absorption attenuation of the acoustic wave along the beams

^S scat ^σ scatKcat ^H _S cat(f' ⁰ A ^' )

S _ref σ _ref V _ref H _ref (f,0;θ _t )

(8)

A second method according to the invention, is to use angular scattering with two beams as illustrated in FIG. 1- 4. First transmitting on Transducer 1 101 and receiving the back scattered signal at a depth range along the beam corresponding to the cross over region 105 between the two beams, one receives a back scattered signal power on Transducer 1 and Transducer 2 102 as

S _{1 !} = A _x σ _{x x} H(j,0; θ _n ) Transmit Transd 1 and Receive Transd 1

(9)

S ₁₂ = A _x A ₂ G ₁₂ H[J, θ _X2 ; θ _n ) Transmit Transd 1 and Receive Transd 2

σ _n = (Aβ - A/) ² σ ₁₂ = (Aβ - AγcosθJ

where A ₁ contains the one-way power attenuation along Beam 1 103 from Transducer 1 101 to the scattering region 105, A ₂ contains the one-way power attenuation along the Beam 2 104 from Transducer 2 102 to the scattering region 105. Transmitting at Transducer 2 102 one gets scattered signal power from the overlap region 105 as

S ₂₂ = A%σ ₂₂ H(f,0; θ _t2 ) Transmit Transd 2 and Receive Transd 2

(10)

S ₂₁ = A ₂ A _x G _2x H[J ,θ _n ;θ _t2 ) Transmit Transd 2 and Receive Transd 1

σ ₂₂ - σ _u = (Aβ- A/) ² σ ₂₁ = σ _l2 = [Aβ- Aγ cos θ _u f

Direct calculation shows that the ratio

_ S ₁₂ S ₂₁ _ (Aβ- AγcosθJ H(J \θ _X2 ;θ _tX )H{f \θ _X2 ,θ _a ) σ _a = S _n S ₂₂ {Aβ -AγJ H(JmMfW _n )

(11) is independent of the cumulative power absorption along Beam 1 103 and Beam 2 104. The frequency variation of the ratios σ _a contains information on the scatterer size, and σ _a will

also contain information on the degree of anisotropy of the scatterers in the overlap region 103.

For scatterers that are much smaller than the wavelength, we have H = I (Rayleigh scattering). For ©i ₂ = π/2 we get

(12)

Typical values are |δβ| ~ 0.3 and |δγ| - 0.1, where δβ and δγ have opposite signs. This gives gives σ _a ~ 0.3. In the above situation, we can calculate

δ _r /δ/? = l-σ-; ^1M

(13)

As the scatterer dimensions become comparable to or larger than the wave length, the shape of the scatterers influences the scattering cross section so that the H's in Eq.(l 1) are different from unity. This influences the frequency variation of σ _a , and σ _a becomes dependent on the direction of the incident and the receive beams. For unidirectional fibrous scatterers, like collagene or muscle fibers, one can get large σ _a when the angle of Beam 1 to the fiber direction is similar to the angle of Beam 2 to the fiber direction. The value of σ _a then also increases above 0.3.

When Beam 1 103 and Beam 2 104 have the same shape and crosses through object material with similar absorption and scattering, we get A ₂ ~ A ₁ and we can calculate S ₁₂ /Sn or S ₁₂ /S ₂₂ as a measure of the object scattering anisotropy. The basic method is conveniently implemented with a linear array as illustrated in FIG. 2, where 206 shows the linear array that is connected to the acoustic instrument 200. The instrument is designed for free selection of the transmit apertures, where the Figure by way of example illustrates two transmit/receive apertures, Aperture 1 as 201 and Aperture 2 as 202, where one by time delay of the element signals steers the direction of the Beam 1 203 from Aperture 1 and the direction of Beam 2 204 from Aperture 2, so that we get an overlap region 205 between the beams. By transmitting and receiving from the two apertures in the same way as for the two transducers in FIG. 1, one can calculate the anisotropy scattering coefficient σ _a as defined in Eq.(ll). The linear array allows common lateral scanning of Beam 1 and Beam 2 that enables spatial imaging of σ _a , as illustrated in FIG. 3 for noninvasive imaging of a vascular plaque 301. It should also be clear that curving the array into a curvilinear array would also allow the same type of operation. Maintaining the distance between Aperture 1 and Aperture 2 and scanning the beams laterally with a fixed direction angle of the beams, one obtains a spatial image of σ _a at a fixed beam overlap depth. This overlap depth can be varied by varying the distance between Aperture 1 and Aperture 2, with constant direction angles of the beams. The angles between the beams can also be varied for more details of the anisotropic scattering. The two-dimensional back scatter image will indicate the location of the plaque, and one can hence use the back scatter image to limit the spatial region that is actual for

interrogation or observation of anisotropic scattering structures by the methods presented above, hence reducing the time of interrogation and the possibility of using multiple directions of the transmit beam with adequate frame rate of the anisotropic scattering imaging.

Variation of the direction angles of the beams will in principle also vary the scattering coefficients. FIG. 4 illustrates a method for at least semi-automatic observation of anisotropic scattering structures of unknown direction in relation to the transducer array. The Figure shows a linear array 404, and an anisotropic scattering structure 410. A pulsed beam 403 is emitted from the aperture 401 of the array, and the scattered wave is picked up by an array element or group of array elements 402, for several positions along the array. The received signal power as a function of receive element position is monitored at a time interval after the pulse transmission that selects a particular depth along the transmitted beam. An anisotropic scattering structure like 410 will back-scatter the main energy in a particular direction θ _tr indicated by the scattering diagram 411. The angle θ _tr between the transmit and the receive beam directions is determined by specular scattering. The middle direction between the incident beam direction and the peak scattered energy is then normal to the anisotropy direction of the scatterers. This scattering diagram produces a variation of the power in the received signal along the element position, indicated as 412 in FIG. 4, where the spread of this variation is determined by the correlation length of the scatterers in the anisotropy direction. Hence, a peaked variation of the scattering power along the element position like at 413 indicates an anisotropic scattering structure at the particular depth, the anisotropy direction of the scattering structures, and also scatterer dimensions in the anisotropy direction. By calculating the power of the received element signals for several time intervals, one can interrogate several depths along the transmitting beam for imaging possible anisotropic scatterers along the transmitted beam. Lateral scanning of the transmit beam then provides a two-dimensional image of anisotropic scattering structures in the tissue. Using several direction angles of the transmitted beam provides possibility of imaging a larger spread of the anisotropy directions.

Thus, while there have shown and described and pointed out fundamental novel features of the invention as applied to a preferred embodiment thereof, it will be understood that various omissions and substitutions and changes in the form and details of the devices illustrated, and in their operation, may be made by those skilled in the art without departing from the spirit of the invention. For example, it is expressly intended that all combinations of those elements and/or method steps which perform substantially the same function in substantially the same way to achieve the same results, are within the scope of the invention. Moreover, it should be recognized that structures and/or elements and/or method steps shown and/or described in connection with any disclosed form or embodiment of the invention, may be incorporated in any other disclosed or described or suggested form or embodiment as a general matter of design choice. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto.