Patent Description:
Transmission of dual frequency pulse complexes composed of a high frequency (HF) and low frequency (LF) pulse for imaging of nonlinear propagation and scattering parameters of an object is described in <CIT>; <CIT>; <CIT> and <CIT>. The methods also provide suppression of multiple scattering noise (reverberation noise) and improved imaging of linear and nonlinear scatterers. Imaging with coherent acoustic pressure waves is shown as an example, but it is clear that the methods are also useful for imaging with all types of coherent wave imaging, such as shear elastic waves and electromagnetic waves. The cited methods require estimation of one or both of a nonlinear propagation delay (NPD) and a nonlinear propagation pulse form distortion (PFD) which both are challenging tasks. The present invention describes new methods and instrumentation for improved estimation of both the NPD and the PFD, and provides scatter images with reduced multiple scattering noise and images of nonlinear scatterers. Combined with measurements with zero LF pulse, the invention also provides estimates of linear propagation and scattering parameters, that combined with the estimates of nonlinear parameters is used to obtain a thermo-elastic description of the object.

<CIT> relates to a method for imaging of nonlinear interaction scattering by transmitting first and second pulsed waves along first and second transmit beams where at least one of the beams is broad in at least one direction and the transmitted timings between the first and second pulsed waves are selected so that the pulsed wave fronts overlap in an overlapping region, i.e. the first and second pulsed waves are transmitted in different directions for overlapping in the overlap region. This document does not disclose a pulse complex composed of overlapping high frequency and a low frequency pulses transmitted along at least one common transmit beam axis. This document does also not disclose to form cross-beam observation cells by directing at least one HF receive cross-beam to cross the common transmit beam axis at an angle > <NUM> deg.

<CIT> relates to methods and systems for imaging of spatial variation of ultrasound parameters of an object.

<NPL>, discloses nonlinear propagation delay and pulse distortion resulting from dual frequency band transmit pulse complexes.

This summary gives a brief overview of components of the invention and does not present any limitations as to the extent of the invention, where the invention is solely defined by the claims appended hereto.

The current invention provides methods and instrumentation for estimation and imaging of linear and nonlinear propagation and scattering parameters in a material object where the material parameters for wave propagation and scattering has a nonlinear dependence on the wave field amplitude. The methods have general application for both acoustic and shear elastic waves such as found in SONAR, seismography, medical ultrasound imaging, and ultrasound nondestructive testing, and also coherent electromagnetic waves such as found in RADAR and laser imaging. In the description below one uses acoustic waves as an example, but it is clear to anyone skilled in the art how to apply the methods to elastic shear waves and coherent electromagnetic waves.

In its broadest form, the methods comprises transmitting at least two pulse complexes composed of co-propagating high frequency (HF) and low frequency (LF) pulse along at least one LF and HF transmit beam axis, where said HF pulse propagates close to the crest or trough of the LF pulse along at least one HF transmit beam, and where one of the amplitude and polarity of the LF pulse varies between at least two transmitted pulse complexes, where the amplitude of the LF pulse can be zero for a pulse complex and the amplitude of at least one LF pulse of said at least two transmitted pulse complexes is non-zero.

Further, directing at least one HF receive cross-beam to cross said at least one HF transmit beam at an angle > <NUM> deg to form a cross-beam observation cell by the cross-over region between a HF transmit beam and said at least one HF receive cross-beam, and using said at least one HF receive cross-beam to record at least two HF cross-beam receive signals from the transmitted HF pulses scattered by object structures in said cross-beam observation cell for at least two transmitted pulse complexes with different LF pulses. The HF cross-beam receive signals are processed to estimate one or both of i) a nonlinear propagation delay (NPD), and ii) a nonlinear pulse form distortion (PFD) of the transmitted HF pulse for said cross-beam observation cell, where one or both of said NPD and PFD are used in the further processing to estimate one or more of i) a local nonlinear propagation parameter, and ii) a local quantitative nonlinear propagation parameter βp, and iii) a local value of the linear pulse propagation velocity c<NUM>, and iv) a linearly scattered HF signal, and v) a nonlinearly scattered HF signal, and vi) local changes in tissue structure during therapy, and vii) local changes in tissue temperature during HIFU therapy.

In general said at least one HF receive cross-beam is focused on the HF transmit beam axis forming a cross-beam observation cell as the cross-over region of the HF transmit and HF receive cross-beams.

A local nonlinear propagation parameter can be estimated through receiving scattered signals from the HF transmitted pulse for at least two HF receive cross-beams with close distance along the HF transmit beam, and estimating a nonlinear propagation delay (NPD) of the transmitted HF pulse at the at least two cross-beam observation cells determined by the cross-over between the HF transmit beam and each of the said at least two HF receive cross-beams. Said estimated NPDs from neighbouring cross-beam observation cells along a HF transmit beam are combined to form estimates of the local nonlinear propagation parameter. Scaling said estimated local nonlinear propagation parameter by an estimate of the LF pulse pressure at the location of the HF pulse gives a quantitative estimate of the nonlinear propagation parameter βp. The estimated βp gives rise to an estimate of the local linear propagation velocity c<NUM>, a change in tissue structure during therapy, and a change in the local tissue temperature during HIFU therapy. Both a local nonlinearly and a linearly scattered signal may be obtained through correcting said at least two HF receive signals with one or both of i) the NPD, and ii) the PFD to produce two corrected signals, and combining said at least two corrected signals.

The invention further devices to also use a HF back-scatter receive beam with the same beam axis as the HF transmit beam to record HF back-scatter receive signals. The estimated PFD and/or the NPD are processed to provide estimated multiple scattering PFD and NPD. The at least two HF back-scatter signals from at least two transmitted pulse complexes with different LF pulses are corrected with the estimated multiple scattering PFD and/or NPD to produce at least two corrected HF back-scatter signals. The at least two corrected HF back-scatter signals are combined to provide HF noise-suppressed back-scatter signals with suppression of multiple scattering noise, for example as described in <CIT>;<CIT>;<CIT>.

2D and 3D images of the estimated parameters and signals may be obtained by scanning the transmit beam and matched HF cross-beam and HF back-scatter beams across a 2D or a 3D region of the object, and recording HF back-scatter and/or cross-beam receive signals and back-scattered signals with further processing according to the invention to produce local estimates of said parameters.

The size of the cross-beam observation cell may then with 2D or 3D scanning be synthetically reduced through spatial filtering of the HF cross-beam receive signals from several neighbouring cross-beam observation cells.

The invention further devices to use HF back-scatter receive beams that are equal to the HF transmit beams, and for multiple depths carry through lateral filtering of one of i) the HF back-scatter receive signals, and ii) the HF noise-suppressed back-scatter signals to produce HF signals from combined HF transmit and receive beams that are synthetically focused for said multiple depths, for example as described in <CIT>.

The invention also describes instruments for carrying through the practical measurements and processing according to the invention, in particular to obtain local estimates of the PFD and/or the NPD, and one or more of the parameters:
i) a local nonlinear propagation parameter, and ii) a local quantitative nonlinear propagation parameter βp, and iii) a local value of the linear pulse propagation velocity c<NUM>, and iv) a linearly scattered HF signal, and v) a nonlinearly scattered HF signal, and vi) local changes in tissue structure during therapy, and vii) local changes in tissue temperature during HIFU therapy.

With one version of the instrument, HF back-scatter and/or cross beam receive signals are generated in dedicated beam forming HW according to known methods, and digital HF receive signals are transferred to the processing structure for storage and further processing in a general SW programmable processor structure of different, known types.

In another version of the instrument the individual receiver element signals are digitized and transferred to the memory of a general SW programmable processor structure where the receive beam forming and further processing is SW programmed.

The instrument comprises a display system for display of estimated parameters and images according to known technology, and user input to the instrument according to known methods. The transmit and receive of HF and LF pulses are obtained with known transducer arrays, for example as described in <CIT> and <CIT>.

Theory of nonlinear propagation and scattering.

For acoustic waves in fluids and solids, nonlinear bulk elasticity is commonly defined through a Taylor series expansion of the acoustic pressure to the <NUM>nd order in relation to the mass density as <MAT> <MAT> p(r,t) is the instantaneous, local acoustic pressure as a function of space vector, r , and time t, ρ(r, t) =ρ<NUM> (r, t) + ρ<NUM>(r,t) is the instantaneous mass density with ρ<NUM> as the equilibrium density for p = <NUM>, κ(r) is the isentropic compressibility, and B is a nonlinearity parameter. We use the Lagrange spatial description where the co-ordinate vector r refers to the location of the material point in the unstrained material (equilibrium), and ψ(r,t) describes the instantaneous, local displacement of a material point from its unstrained position r, produced by the particle vibrations in the wave.

The term A·(ρ<NUM>/ρ<NUM>) describes linear bulk elasticity, and hence does the last term (B/<NUM>A)(ρ<NUM>/ρ<NUM>) in the parenthesis represent deviation from linear elasticity. The parameter B/2A is therefore commonly used to describe the magnitude of nonlinear bulk elasticity.

The continuity equation in Lagrange coordinates takes the form <MAT>.

To the <NUM>nd order in ∇ψ we then get isentropic state equation as <MAT>.

(<NUM>, <NUM>) describes isentropic compression, where there is no transformation of elastic energy to heat, i.e. no absorption of acoustic energy in the wave propagation. Linear absorption can be introduced by adding a temporal convolution term hab ⊗ ∇ψ, where hab (r,t) is a convolution kernel that represents absorption of wave energy to heat due to deviation from fully isentropic compression.

For the analysis of wave propagation and scattering it is convenient to invert Eq.(<NUM>) to the <NUM>nd order in p and add the absorption term that gives a material equation for bulk elasticity to the <NUM>nd order in p <MAT> <MAT> where the absorption term is small and we include only <NUM>st order in p. Attenuation of a propagating wave is given by both the extinction coefficient of the incident wave, which is the sum of absorption to heat given by hab, and scattering of the wave.

The <NUM>nd order approximation of Eqs. (<NUM>, <NUM>, <NUM>) holds for soft tissues in medical imaging, fluids and polymers in non-destructive testing, and also rocks in seismography that show special high nonlinear bulk elasticity due to their granular micro-structure. Gases generally show stronger nonlinear elasticity, where higher order terms in the pressure often might be included. Micro gas-bubbles with diameter much lower than the acoustic wavelength in fluids, show in addition a resonant compression response to an oscillating pressure which gives a differential equation (frequency dependent) form of the nonlinear elasticity, as described by the Rayleigh-Plesset equation.

To develop a full wave equation, we must include Newtons law of acceleration, that for waves with limited curvature of the wave-fronts can be described in the Lagrange description as <MAT>.

Both the mass density, the compressibility, and the absorption have spatial variation in many practical materials, like soft tissue and geologic materials. We separate the spatial variation into a slow variation that mainly influences the forward propagation of the wave (subscript a), and a rapid variation that produces scattering of the wave (subscript f), as <MAT>.

Combining Eqs. (<NUM> - <NUM>) ), using <NUM>/ρ<NUM> = ρa/ρaρ<NUM> = (ρ<NUM> - ρf)/ρaρ<NUM> =<NUM>/ρa -γ/ρa, γ = ρf/ρ<NUM>, produces a wave equation of a form that includes nonlinear forward propagation and scattering phenomena as <MAT> <MAT> where we have neglected ∇(<NUM>/ρa), the low amplitude terms ββpf of σn, and the <NUM>nd order p<NUM> term in the absorption. c<NUM> (r) is the linear wave propagation velocity for low field amplitudes. The left side terms determine the spatial propagation of the wave from the slowly varying components of the material parameters c<NUM> (r), βpa (r), and hab (r, t). The right side terms represent scattering sources that originate from the rapid spatial variation of the material parameters, β(r), γ(r), and σn(r). β(r) represents the rapid, relative variation of the isentropic compressibility, γ(r) represents the rapid, relative variation of the mass density, while σn (r) represents the rapid, relative variation of the nonlinear parameters βp (r)κ(r) of Eqs. (<NUM>,<NUM>).

The linear propagation terms (<NUM>) of Eq.(<NUM>) guide the linear forward spatial propagation of the incident wave with propagation velocity c<NUM> (r) and absorption given by term (<NUM>), without addition of new frequency components. The linear scattering source terms (<NUM>) produce local linear scattering of the incident wave that has the same frequency components as the incident wave, with an amplitude modification of the components <MAT> produced by the <NUM>nd order differentiation in the scattering terms, where ω is the angular frequency of the incident wave.

The slow variation of the nonlinear parameters give a value to βpa (r) that provides a nonlinear forward propagation distortion of the incident wave that accumulates in magnitude with propagation distance through term (<NUM>) of Eq.(<NUM>). A rapid variation of the nonlinear material parameters gives a value to σn (r) that produces a local nonlinear distorted scattering of the incident wave through term (<NUM>) of Eq.(<NUM>).

Similar equations for elastic shear waves and electromagnetic waves can be formulated that represents similar propagation and local scattering phenomena, linear and nonlinear, for the shear and EM waves.

For estimation of non-linear material parameters, we transmit dual frequency pulse complexes where two examples are shown in <FIG> shows a high frequency (HF) transmit pulse <NUM> propagating at the crest of a low frequency (LF) pulse <NUM>, where <FIG> shows the same transmitted HF pulse <NUM> propagating at the through of the LF pulse <NUM>, where the example is obtained by inversing the polarity of <NUM>. For estimation of nonlinear parameters, we typically transmit at least two pulse complexes for each transmit beam direction, where the LF pulse varies in amplitude and/or polarity between at least two transmitted pulse complexes, where the LF pulse can be zero (i.e. no transmitted LF pulse) for a pulse complex, and the LF pulse is non-zero for at least one pulse complex. The HF:LF ratio is typically > <NUM>:<NUM>. For estimation of linear parameters we would preferably transmit only a HF pulse, i.e. the LF pulse is zero, or one could use the sum of the received HF signal from a positive and a negative LF pulse.

We study the situation where the total incident wave is the sum of the LF and HF pulses, i.e. p(r,t) = pL(r, t) + pH (r, t). The nonlinear propagation and scattering are in this <NUM>nd order approximation both given by <MAT>.

Inserting Eq.(<NUM>) into Eq.(<NUM>) we can separate Eq.(<NUM>) into one equation for the LF and a second equation for the HF pulses as <MAT>.

where the material parameters c<NUM> (r), βpa(r), β(r), γ(r), σn(r) all have spatial variation, and the wave fields and absorption kernel pL(r,t), pH (r,t), hab(r,t) depend on space and time. We note that with zero LF pulse, the HF pulse propagates according to Eq.(9b) with term (2b) and (5b) as zero. The low amplitude, linear propagation velocity is c<NUM> (r) of Eq.(<NUM>) that produces linear propagation, term (<NUM>), modified by a self-distortion propagation term (2b), that is responsible for the harmonic propagation distortion utilized in harmonic imaging. The scattering is dominated by the linear term (<NUM>) where the self-distortion scattering term (5b) is important for scattering from micro-bubbles in a more complex form.

As shown in <FIG> we use a temporal HF pulse length TpH that is much shorter than half the period of the LF pulse, TL/<NUM>, i.e. the bandwidth of the HF pulse BH > ωL/<NUM>, where ωL = <NUM>π/TL is the centre angular frequency of the LF wave. For the further analysis we assume that |<NUM>βp (r) pL(r, t)| = |x| << <NUM> which allows the approximation <NUM>-x ≈ <NUM>/(<NUM>+x). The propagation terms (<NUM>) and (<NUM>a) of the left side of Eq.(9b) can for the manipulation of the HF pulse by the co-propagating LF pulse be approximated as <MAT>.

The numerator in front of the temporal derivative in this propagation operator is the square propagation velocity, and we hence see that the LF pulse pressure pL modifies the propagation velocity for the co-propagating HF pulse pH as <MAT> where pL (r,t) is the actual LF field variable along the co-propagating HF pulse. Solving Eqs. (<NUM>a,b) for LF and HF transmit apertures with transmit pulse complexes as shown in <FIG>, gives co-propagating LF and HF pulses along beams, where schematic examples of transmitted HF beams according to the invention are shown as beams <NUM>, <NUM>, <NUM>, and <NUM> in <FIG>, <FIG>, <FIG>. As the HF:LF ratio is typically > <NUM>:<NUM>, often ~ <NUM>:<NUM>, the LF wavelength is > <NUM> - <NUM> times the HF wave length. To minimize diffraction and keep the LF beam adequately collimated, the transmit aperture and beam for the LF pulse is typically much wider than for the HF pulse.

The HF pulse propagates close to the crest or trough of the LF pulses. The orthogonal trajectories of the HF pulse wave-fronts are paths of energy flow in the HF pulse propagation. We define the curves Γ(r)as the orthogonal trajectories of the HF pulse wave-fronts that ends at r. Let pc(s) = p · pLc (s) and c<NUM>(s) be the LF pressure and linear propagation velocity at the centre of gravity of the HF pulse at the distance coordinate s along Γ(r), and p is a scaling factor for polarity and amplitude of the LF pulse. The propagation time-lag of the HF pulse at depth r along the orthogonal trajectories to the HF pulse wave-fronts, can then be approximated as <MAT>.

The propagation lag with zero LF pulse is t<NUM>(r) given by the propagation velocity c<NUM>(r) that is found with no LF manipulation of the tissue bulk elasticity. τp (r) is the added nonlinear propagation delay (NPD) of the centre of gravity of the HF pulse, produced by the nonlinear manipulation of the propagation velocity for the HF pulse by the LF pressure pc(s) at the centre of gravity of the HF pulse.

Variations of the LF pressure along the co-propagating HF pulse, outside the centre of gravity of the HF pulse, produces a variation of the propagation velocity along the HF pulse, that in addition to the NPD produces a nonlinear pulse form distortion (PFD) of the HF pulse that accumulates with propagation distance. For HF pulses much shorter than the LF half period, as shown in <FIG>, the PFD can be described by a filter. Defining Ptp (r,ω) as the temporal Fourier transform of the transmitted HF pulse field that co-propagates with a LF pulse, and Pt<NUM>(r,ω) as the HF pulse for zero LF pulse, the PFD filter is defined as <MAT> <MAT> and the subscript p designates the amplitude/polarity/phase of the LF pulse. Ptp(r,ω) is obtained from the temporal Fourier transform of pH in Eq.(9b). Vp includes all nonlinear forward propagation distortion, where the linear phase component of Vp is separated out as the nonlinear propagation delay (NPD) τp (r) up to the point r as described in Eq.(<NUM>). The filter Ṽp hence represents the nonlinear pulse form distortion (PFD) of the HF pulse by the co-propagating LF pulse, and also the nonlinear attenuation produced by the nonlinear self-distortion of the HF pulse.

We note that when the <NUM>st scattering/reflection occurs, the scattered LF pressure amplitude drops so much that after the scattering the LF modification of the propagation velocity is negligible for the scattered HF wave. This means that we only get essential contribution of the LF pulse to the NPD, τp(r) of Eq.(<NUM>), and the PFD, Ṽp, of Eq.(<NUM>), up to the <NUM>st scattering, an effect that we will use to estimate the spatial variation of the nonlinear propagation parameter βpa (r), and the nonlinear scattering given by σn (r), and suppress multiple scattered waves (noise) in the received signal to enhance the <NUM>st order linear and nonlinear scattering parameters.

In summary, the nonlinear terms (<NUM>a, b) in Eq.(<NUM>b) produces a propagation distortion of the HF pulse as:.

The HF scattering cross section given in the right side of Eq.(9b) is composed of a linear component. term (<NUM>), and a nonlinear component, term (<NUM>), where term (<NUM>a) takes care of the variation of the HF fundamental band scattering produced by the LF pulse, while term (<NUM>b) represents self distortion scattering that produces scattered signal in the harmonic and sub-harmonic components of the HF-band. This scattering term is however so low that it can be neglected, except for micro-bubbles at adequately low frequency, where the scattering process is described by a differential equation, i.e. highly frequency dependent scattering with a resonance frequency, producing a well known, more complex Rayleigh-Plesset term for HF self distortion scattering.

Because the temporal pulse length of the HF pulse TpH << TL/<NUM>, we can approximate pL (r) ≈ pc (r) also in the interaction scattering term (5a) of Eq.(9b) <MAT> where pc(r) is the LF pressure at the centre of gravity of the co-propagating HF pulse as for the NPD propagation term in Eq.(<NUM>).

The scattering from the rapid, relative fluctuations in the compressibility, β(r), is a monopole term that from small scatterers (dim < ~ ¼ HF wave length) give the same scattering in all directions, while the scattering from the rapid, relative fluctuations in the mass density, γ(r), is a dipole term where the scattering from small scatterers depends on cosine to the angle between the transmit and receive beams [<NUM>]. For a given angle between the transmit and receive beams one can hence for the fundamental HF band write the scattering coefficient as a sum of a linear scattering coefficient and a nonlinear scattering coefficient as <MAT> σl(r) represents the sum of the linear scattering from fluctuations in compressibility and mass density. For larger structures of scatterers (dim > ~ HF wave length), like for example layers of fat, muscle, connective tissue, or a vessel wall, the total scattered wave will be the sum of contributions from local parts of the structures which gives a directional scattering also influenced by the detailed shape of the structures [<NUM>].

The effect of the low frequency (LF) pulse on the received HF signal, can hence be split into three groups with reference to Eq.(9b):.

Example embodiments of the invention will now be described in relation to the drawings. The methods and structure of the instrumentation are applicable to both electromagnetic (EM) and elastic (EL) waves, and to a wide range of frequencies with a wide range of applications. For EL waves one can apply the methods and instrumentation to both shear waves and compression waves, both in the subsonic, sonic, and ultrasonic frequency ranges. We do in the embodiments describe by example ultrasonic measurements or imaging, both for technical and medical applications. This presentation is meant for illustration purposes only, and by no means represents limitations of the invention, which in its broadest aspect is defined by the claims appended hereto.

<FIG> shows by example an instrument setup according to the invention for measurement and estimation of local linear, and nonlinear propagation and scattering parameters in the object <NUM>. <NUM> shows a transmit array system for transmission of pulses into the object. Acoustic contact between the transmit and receive (<NUM>) arrays can for example be obtained by immersing the object in a fluid (<NUM>), e.g. water, which for example is common with breast tomography, (<FIG>), or other types of acoustic stand-off between the receive probe and the object, or direct contact between the probes and the object. With EM waves vacuum forms a good contact between the transmitters and the object, while fluids or soft tissue can provide contact for adequately small dimensions.

For estimation of nonlinear parameters the methods comprises transmitting at least two pulse complexes composed of co-propagating high frequency (HF) and low frequency (LF) pulses, where said HF pulse propagates close to the crest or trough of the LF pulse along at least one HF transmit beam, and where at least one of the amplitude and polarity of the LF pulse varies between at least two transmitted pulse complexes, where the amplitude of the LF pulse can be zero for a pulse complex and the amplitude of at least one LF pulse of said at least two transmitted pulse complexes is non-zero, as described in relation to <FIG> above. A preferred embodiment would be arranged to estimate both linear and nonlinear parameters, where <NUM> would be arranged to be able to transmit dual band pulse complexes, also including a zero LF pulse.

An example HF beam in the object is indicated as <NUM>, with the HF pulse propagating to the right along the beam indicated as <NUM> at a particular time in the propagation. A LF pulse is, at the same time point, indicated as <NUM> with the positive swings as grey, co-propagating with the HF pulse to the right to manipulate both the propagation velocity and the scattering of the HF pulse, as discussed in Section <NUM>. The HF pulse is indicated to be located at the crest of the LF pulse as indicated in <FIG>. The HF pulse is scattered both linearly and nonlinearly, Eqs. (9b,<NUM>,<NUM>) as it propagates along the beam, and generates a scattered HF wave field propagating as a Mach-cone indicated by the front waves <NUM> and <NUM>.

Element <NUM> shows a HF receive array and processing system, where the Figure shows by example one HF receive cross-beam <NUM>, where the HF receive cross-beam axis <NUM> crosses the HF transmit beam axis <NUM> at <NUM>. An x-y-z Cartesian coordinate system shows the HF transmit beam axis along the z-direction and the HF receive cross-beam in the x-direction, where the x-axis is in the paper plane, and the y-axis is vertical to the paper plane. In this example, the coordinate system is defined so that the HF transmit aperture has the centre rti = (xi,yi,<NUM>), and the HF receive cross-beam aperture has the centre at rrj = (-xr, yj, zj), preferably with focus at the crossing of the HF transmit and receive beam axes. The overlap of the HF transmit and receive beams define a cross-beam observation cell Rij of scatterers, centered at <NUM> with the position rij = (xi,yi,zj) that defines an image measurement point r.

With single HF transmit and receive cross-beams one will observe a scattered signal from a single cross-beam observation cell R(r) centered at r. However, scanning the HF receive cross-beam axis along the HF transmit beam axis as indicated by the dots <NUM>, allows measurement of scattered HF cross-beam receive signals from cross-beam observation cells centered at a set of crossing positions rij between the HF transmit axis starting at rti, and receive beam axes starting at rrj, , j = <NUM>,. This can be done in time series by transmitting a LF-HF pulse complex for each HF receive cross-beam position, or with time parallel HF receive beam forming with focus at several locations along the HF transmit beam, for measurements of the scattered HF cross-beam receive signal at these locations along the HF transmit beam. The array <NUM> can for example be a linear array, or a phased array, receiving in parallel on all elements where the element signals are coupled to a parallel receive beam former, producing in parallel individual receive signals for a set of receive cross-beams, all focused at different locations on the HF transmit beam axis.

For 2D or 3D imaging, one can use as system set up to scan the LF-HF transmit beam laterally (x-direction) or vertically (y-direction) as indicated by the arrows <NUM>, in order to irradiate a 2D or 3D section of at least a region of the object. With a matched scanning of the HF receive cross-beam focus along each HF transmit beam axes, gives a 2D/3D set of HF cross-beam receive signals scattered from cross-beam observation cells Rij defined by the crossings of the HF transmit and receive beams and centered at the crossing of the HF transmit and receive cross-beam axes at rij. We label the positions of the array origin of the HF transmit beam axes by the coordinate vectors rti, i = <NUM>,. , I , and the positions of the array origin of the receive beam axes by the coordinate vectors rrj, j = <NUM>,. The distance between transmit beam axes is Δrt, and between the receive beam axes the distance is Δrr. Note that to minimize the dimension of Rij one would adjust the aperture and focus of the HF receive cross-beams for narrow receive focus at the actual HF transmit beam axis.

The HF cross-beam receive signals are processed in the receive unit <NUM> to provide linear and nonlinear propagation and scattering parameters for each measurement point rij in the scanned region with spatial resolution given by the dimension of the cross-beam observation cells Rij, as described below. The unit <NUM> also contains a display system for the images. To give an impression of a continuous image in the display, one typically introduces interpolated image display values between the image measurement points rij.

To simplify notation in the equations below, we label rij = r. The HF cross-beam receive signals are composed of three components: i) a linear scattering component ylp (t,r) , and ii) a nonlinear scattering component 2pc (r)ynp (t,r) where pc is the LF pulse amplitude defined in Eq.(<NUM>,<NUM>), and iii) followed by a multiple scattering component np (t,r), illustrated in <FIG>. The receive signal for each measurement point r can hence be modeled as <MAT> <MAT> where we have defined p as a scaling and polarity factor of the LF pressure as in Eq.(<NUM>), i.e. pc (r) = p · pLc (r). r<NUM> = (x<NUM>, y<NUM>, z<NUM>) is the scatterer source point, and σl (r<NUM>) and σn (r<NUM> )are the linear and nonlinear HF scattering densities from Eqs. (<NUM>b,<NUM>,<NUM>). The combined HF receive, Ar, and HF transmit beam, At, amplitude weighting around the image measurement point r = (x, y, z) defines the cross-beam observation cells A(r - r<NUM>,r) = Ar(y - y<NUM>, z - z<NUM>,x)At(x - x<NUM>, y - y<NUM>,z). up (· , r) is the received HF pulse from a point scatterer within the cross-beam observation cell R(r) centered around the image point r, that observes a nonlinear propagation delay (NPD) τp (r) according to Eq.(<NUM>), and a nonlinear pulse form distortion (PFD) according to Eq.(<NUM>) for the transmit pulse propagation up to depth r. The NPD and PFD vary so slowly with position that we approximate it as constant within each observation cell.

τf (r - r<NUM>, r) = τt (r - r<NUM>, z) + τr (r - r<NUM>, x) is the sum of the HF transmit beam focusing phase delay τt and the HF receive beam focusing phase delay τr, and |r<NUM> - rt| + |r<NUM> - rr| is the total propagation distance of the pulse from the transmit aperture centered at rt to the scatterer at r<NUM> and to the receiver aperture centered at rr. Close to the focus of a HF receive or transmit beam we can approximate τr or τt ≈ <NUM>. A preferred system allows for adjustment of the HF receive cross-beam focus onto the HF transmit beam axis, which allows the approximation τr ≈ <NUM> in the observation cell, while for a fixed transmit focus τt ≠ <NUM> for r outside the HF transmit focus. Lateral filtering of the HF cross-beam receive signal provides a synthetic focusing in the actual image range, as discussed in relation to Eqs. (<NUM>, <NUM>) below. This allows the approximation of both τt, τr ≈ <NUM>.

Schematic example received scattered signals from HF receive cross-beam <NUM> are shown in <FIG> at a given image point r = (x,y,z). The upper signal <NUM> shows the situation when the HF pulse propagates close to the positive crest of the LF pulse as in <FIG>, the middle signal <NUM> shows the situation when the LF pulse is zero, and the lowest signal <NUM> shows the situation when the LF pulse is inverted so that the HF pulse propagates close to the trough of the LF pulse as in <FIG>. All signals comprises a first part <NUM> generated by <NUM>st order scattering from the cross-beam observation cell R(r) around r = (x,y,z) with a propagation time lag given by the distance |r<NUM> - rt| +|r<NUM> - rr| in the models of Eqs. (<NUM>-<NUM>). After this <NUM>st part of the scattered signal follows a tail of weaker signals <NUM> that is the multiple scattered signal np (t, r) within the HF transmit beam before the last scattering in the overlap between the receive beam and the multiple scattered beam.

(<NUM>, <NUM>) we see that p > <NUM> provides a nonlinear increase in the HF propagation velocity that advances the arrival time (negative delay) of the scattered signal compared to for p = <NUM>, and p < <NUM> provides a nonlinear decrease in the HF propagation velocity that delays the arrival time (positive delay) of the scattered signal compared to that for p = <NUM>. The <NUM> part of <NUM> is an advancement of the <NUM> part of <NUM>, i.e. a negative NPD τ+ (r) < 0according to Eq.(<NUM>). The <NUM> part of <NUM> is in the same way a delay of <NUM>, i.e. a positive NPD τ_ (r) > <NUM>, where the subscript + and - and <NUM> indicates with reference to <FIG>, measurements with a positive (<NUM>), negative (<NUM>) and zero transmitted LF pulse. The amplitude of the LF pulse drops so much in the <NUM>st scattering that the advancement/delay of the multiple scattered signal np (t,r) (<NUM>) is much less than for the <NUM>st part <NUM>. Crossing side lobes, grating lobes and edge waves of the transmit and receive beams can add noise components that arrives before the <NUM>st order scattered component <NUM> from the cross-beam observation cell. These noise components are suppressed by proper apodization of transmit and receive beam apertures. Temporal Fourier transform of the front part <NUM> of the received signal in Eq.(<NUM>) gives <MAT> <MAT> where Xl (ω, r) and Xn (ω, r) are the temporal Fourier transforms of the linear and nonlinear scattering components from the cross-beam observation cell centered at r. The exponential function arises from the delay components in the temporal argument of up in Eq.(<NUM>).

One will ideally set a narrow focus of the HF receive cross-beam essentially on the transmit beam axis. In the y- and z-directions the observation region is therefore generally limited by a narrow receive beam, but in the x-direction the observation region is limited by the x-width of the transmit beam. As the transmit beam operates with a fixed transmit focus, the transmit beam width varies with depth z outside the focus. For z outside the focal region, the HF transmit beam can therefore be wide both in the azimuth (x-) and elevation (y-) direction.

When 3D scanning of a stationary object is available, one can obtain synthetically focused transmit and receive beams through spatial filtering of measurement signals as <MAT> <MAT> where B is a weighting function to reduce spatial side-lobes of the filter. The filter kernel can be obtained from simulation of the transmit and receive beams to obtain τt (r - r<NUM>, r) and τr (r - r<NUM>, r). (<NUM>-<NUM>) below also present methods of estimating τt (r - r<NUM>, r) and τr (r - r<NUM>, r) that corrects for wave front aberrations due to spatial variations in the propagation velocity within the object. The filter amplitude weighting B, can conveniently be proportional to the amplitude of the simulated beams, potentially with added windowing. When the receive beam is focused onto the transmit beam axis, we can approximate τr ≈ <NUM> within in the observation region. The integration is then done over the transversal coordinate to the transmit beam axis, r⊥ = (x, y), as <MAT>.

When the y-width of the receive beam focus is sufficiently narrow, the integration over r⊥ can be approximated by an integration in the x-direction (azimuth) only, with a filter adapted for use with 2D scanning of the transmit beam in the x-direction.

One advantage of the synthetic focusing is that the cross beam observation cell is reduced, and the approximation that the NPD and PFD are constant in the observation cell becomes more accurate, i.e. improves the approximation of taking τp (r) and Up (ω, r) outside the integral in Eq.(<NUM>). The synthetic focus filtering also provides images with improved spatial resolution. From the models in Eqs. (<NUM>,<NUM>,<NUM>), we can determine τp (r) from the delay between the front parts <NUM> of two of the signals <NUM> - <NUM>, or all three signals in combination. This can for example be done through correlation between the <NUM>st order scattered front part <NUM> of the HF cross-beam receive signals from pulse complexes with different LF pulses, or by measuring the arrival time difference between the front edge of the signals, or a combination of both. An advantage of the method as described is that we have first intervals of the measured signals that comprises mainly <NUM>st order scattering, which gives a clear definition of τp (rt, z) in Eq.(<NUM>) at depth z along the transmit beam axis starting at rt. A schematic example of τ_ (rt, z) is shown as <NUM> in <FIG>.

Having measured τp (rt, zj) at a set of points zi with distance Δz we can from Eq.(<NUM>) estimate the nonlinear propagation parameter <MAT> where <NUM> in <FIG> shows by example the z-differential of τ_. From the description of Eq.(<NUM>), pc (rt, zj) is the LF pressure approximately at the centre of gravity of the HF pulse, and c<NUM> (rt, zj) is the linear propagation velocity at the same position, i.e. zj along the transmit beam axis starting at rt. The spatial variation of c<NUM> (rt, zj) in soft tissue is ~ ± <NUM>%, and is for image reconstruction approximated by a constant <NUM>/s, which is also a useful approximation in Eq.(<NUM>-<NUM>). As described in relation to Eqs. (<NUM>,<NUM>) below, one can obtain local estimates of c<NUM>(r) from a first estimate of βpa(rt,z) with constant c<NUM>, and then modify the first estimate of βpa(rt,z) with the new estimate c<NUM>(r), for example in an iterative procedure. With a ring array as in <FIG> one can estimate locally varying c<NUM>(r) with tomographic methods [<NUM>-<NUM>], and use this estimate in Eqs. (<NUM>-<NUM>). This opens for a combination of βp and c<NUM> for the tissue characterization, as discussed below. Low-pass filtered differentiation can be obtained by combining more samples of the NPD at different depths along the HF transmit beam, for example as <MAT> where an are filtering coefficients and N describes an interval of terms. Allowing for reduced spatial resolution in the estimate of βpa, one can also in Eq.(<NUM>) include weighted sums along neighbouring transmit beams (i.e. along rt) to reduce noise in the estimate, according to known methods. One can also use nonlinear differentiation, for example through minimizing a functional of the form <MAT> where βpa(rt,z)z denotes the gradient with respect to z, and Wβ and Wn are weights to be chosen to balance between rapid response to spatial changes in βp( ) for high values of Wβ /Wn, and noise reduction for low values of Wβ/Wn. We can also include integration/summation for neighbouring transmit beams, i.e. along rt to reduce noise at the cost of lower spatial resolution, as for the linear estimation in Eq.(<NUM>).

With a 2D or 3D scanning of the transmit and receive beams, we note that Eqs. (<NUM>-<NUM>) presents a quantitative spatial imaging of the nonlinear elastic tissue parameter, where <FIG> shows by example typical values of βpa = βnaκa for connective (<NUM>) , glandular (<NUM>), and fat (<NUM>) tissues in breast. We note that the difference of βp between the different tissues is so large that it makes estimation of the βp parameter very interesting for tissue characterization, for example detection and characterization of cancer tumors and atherosclerotic arterial plaque.

The nonlinear scattering is found at highly local points from micro-bubbles and hard particles like micro-calcifications, and the nonlinear pulse form distortion (PFD) can hence from Eqs. (<NUM>,<NUM>-<NUM>) be estimated as <MAT>.

We define a Wiener form of inversion of Ṽp (z,ω;rt ) as <MAT> where the parameter µ is adjusted to maximize the signal to noise ratio in the filtered signal.

Ŷp (ω, ri) as given in Eqs. (<NUM>-<NUM>) for image points rij is subject to absorption of the HF pulse both along the HF transmit and the HF receive cross-beams. When estimates of the tissue absorption exist, for example from ultrasound tomography imaging [<NUM>-<NUM>], the absorption can be compensated for. When such estimates do not exist, it is in ultrasound imaging common to use a depth varying gain control, either set manually or through some automatic estimation. Assuming that the receive signal in Eqs. (<NUM>-<NUM>) has undergone some depth gain adjustment to compensate for absorption, we can from Eqs. (<NUM>-<NUM>) obtain absorption compensated estimates of the linear and nonlinear scattering components as <MAT><MAT>.

We could then for example display |X̂l(ω,ri)| and |X̂n(ω,ri )| at a typical frequency, say the centre frequency ω<NUM> of the HF band, or an average of |X̂l| and |X̂n| across a band B of strong frequency components within the HF band, for example <MAT>.

Other alternatives are to show the average of the square |X̂l/n(ω,ri)|<NUM>.

When pc is unknown, we still get an interesting visualization of the spatial variation of the nonlinear scattering without the scaling of <NUM>/pc in Eqs. (<NUM>-<NUM>) for example to detect and visualize micro-bubbles or micro-calcifications in the tissue. When estimates of local absorption are available, these can be combined with Eq.(<NUM>) by anyone skilled in the art to obtain quantitative estimates of both linear and nonlinear scattering, that is useful for tissue characterization, for example of cancer tumors and atherosclerotic plaques.

We notice from Eqs. (<NUM> -<NUM>) that several scatterers within the cross-beam observation cell can participate to the front signal <NUM> in <FIG>, which produces an interference pattern (speckle) in this part of the signal that depends on the relative position between the participating scatterers and the directions of the HF transmit and receive cross-beams. Using several HF receive cross-beams crossing the HF transmit beam with different directions at the same image position r, as shown by the examples <NUM>, <NUM> in <FIG> and <NUM>, <NUM> in <FIG>, then provides several HF receive signals with different speckle (interference patterns) that can be used for statistical averaging in the signal processing to reduce random errors in the estimation of the nonlinear propagation and scattering parameters. In the example system shown in <FIG> we could for example within this frame of thinking also use HF receive cross-beams with different directions, and also have HF receive beams crossing the HF transmit beam in the opposite direction of <NUM> at the image point r at <NUM>.

This would require a HF receive array at the opposite side of the object that still could be operated by the same parallel HF receive beam former as <NUM>.

The separate transmit and receive array systems in <FIG> can conveniently be substituted with a dual frequency ring array used for combined transmit and receive, shown as <NUM> in <FIG>. The ring array surrounds an object <NUM> that is in acoustic contact with the ring array through a substance <NUM>, typically a fluid like water or an oil. The ring array structure allows through-transmission of the ultrasound, typically used for ultrasound tomography imaging of objects, such as the breast and the male testicles.

Element <NUM> of <FIG> shows a set of HF transmit/receive elements and <NUM> shows a set of LF transmit elements of ring array <NUM>, for example described in more detail in [<NUM>-<NUM>]. The HF and LF elements are connected to a transmit switching system <NUM>, that selectively connects a group of HF and LF elements to a HF and LF transmit system <NUM> comprising a HF and LF transmit beam former to generate selectable and/or steerable HF and LF transmit beams, where <NUM> shows an example HF transmit beam through the object <NUM>. The HF array elements are also connected to a HF receive switching system <NUM>, that selectively connects a group of HF elements to a HF receive system <NUM> comprising a HF receive beam former, that generates selectable and/or steerable HF receive cross-beams, where <NUM> shows an example crossing the transmit beam <NUM> at the observation cell <NUM>, and a receive processing system <NUM> as described in relation to FIG. 2a to present estimates of linear and nonlinear object parameters.

Element <NUM> shows a further example HF receive cross-beam that crosses the HF transmit beam at the same cross-beam observation cell <NUM> as the HF receive cross-beam <NUM> with a different direction, and hence obtains a different speckle pattern of the front part <NUM> HF cross-beam receive signal, than for the HF receive cross-beam <NUM>, as discussed in relation to <FIG>, above. To obtain several HF receive cross-beams at different directions for each image point, indicated by the dots <NUM>, the HF receive switching system connects selectable groups of HF array elements to the HF receive system <NUM> that produces a selectable number of HF cross-beam receive signals with different speckle of the front part <NUM>, from selectable HF receive cross-beams in parallel. The variation in speckle in these different HF cross-beam receive signals from the same image point r allows for statistical averaging in the signal processing to reduce random errors in the estimates of the nonlinear propagation and scattering parameters. The subunits <NUM>, <NUM>, <NUM>, <NUM> are connected to a processor and display system <NUM> via the bus <NUM> for set up, transmission, processing, and display of image data, according to known methods.

Because the modification of the bulk elasticity elasticity of the tissue by the LF pulse severely drops at the first scattering, as discussed following Eq.(<NUM>), the methods according to the invention as described above, do not require through-transmission through the object. A full ring array is therefore not necessary for these methods, where one for example could operate with a "horseshoe" array extraction of the ring array <NUM> to emulate the functional essence of the array system in <FIG>. A <NUM> deg ring array would however open for more measurements, such as direct transmission through the object, that can be used to improve spatial resolution and estimation accuracy of the NPD and PFD, using tomographic techniques. Such a ring array can also be used for tomographic estimation of local tissue absorption and linear propagation velocity according to known methods that can be combined with methods according to this invention for improved detection and characterization of disease in tissue, as discussed in relation to Eqs. (<NUM>-<NUM>) below.

We further notice that measurement of through transmission of the HF pulses with a ring array can also be used to improve accuracy of estimates of the nonlinear propagation and scattering parameters with tomographic methods, where for example the values obtained according to the methods described above could be used as starting values in an iterative tomographic procedure, e.g. the "bent ray" method described in the following citations to obtain more accurate values.

An example structure for assessment of nonlinear propagation and scattering parameters using a limited access area of the object, is shown in <FIG>, where <NUM> shows an array probe arrangement that is in direct contact with only one side of the object <NUM>, for example the surface of a body. The probe front comprises a combined LF and HF array, <NUM>, where selectable elements are used to transmit LF and HF pulse complexes, where <NUM> shows an example, schematic HF transmit beam. HF receive elements are selected from the array elements to define HF receive cross-beams, where an example, schematic HF receive cross-beam is shown as <NUM>. <NUM> shows another example, schematic HF receive cross-beam crossing the HF transmit beam at the same cross-beam observation cell <NUM> as <NUM> at a different angle, to obtain a HF receive signals with different speckle, for the same purpose as described for the beam <NUM> in <FIG>. Through selection of one or both of i) transmit and receive array elements, and ii) transmit and receive delays, both the HF transmit and receive beams can according to known methods be scanned one or both of i) laterally along the probe surface, and ii) angularly from a given selection of elements, to generate crossing HF transmit and receive beams and move the cross-beam observation cell <NUM> within a region of the object, for estimation of linear and nonlinear object parameters using methods as described in relation to <FIG>.

The strong angular steering of the HF transmit and receive beams in <FIG> requires down to λHF/<NUM> pitch of the HF array, which increases the required number of elements. <FIG> shows a modification that allows the use of wider pitch of the elements, and also the use of annular arrays and even fixed focus transducers, to estimate linear and nonlinear wave propagation and scattering parameters in a cross-beam observation cell <NUM> of the object <NUM>. <NUM> shows a combined transmit and receive system that comprises a LF and HF transmit array <NUM> and a HF receive array <NUM>, embedded in a fluid filled region <NUM> to provide wave propagation contact to the object. Embedment in the fluid allows mechanical rotation of the arrays around the axes <NUM> and <NUM>, or other mechanical movement of the arrays, potentially in combination with electronic scanning of the beam directions according to known methods. The LF-HF transmit array is connected to a transmit beam former inside the system <NUM> where the resulting HF transmit beam is shown schematically as <NUM>. The HF receive array <NUM> is connected to a HF receive beam former inside <NUM> that is used to define HF receive beams, for example schematically as <NUM>, and further connected to a receive processing system according to the methods described in relation to <FIG>. The beam formers and processing structures operates and are implemented according to known methods, and details are therefore not shown in the Figure. The system allows crossing HF transmit and receive beams with an overlap <NUM> that defines the transmit-receive cross-beam observation cell <NUM> that can be scanned within a region of the object, exemplified with <NUM>, by scanning the receive and/or the transmit beams as described for <NUM> in relation to <FIG> and to Eqs. (<NUM>-<NUM>).

The coupling medium <NUM> between the transmit and receive (<NUM>, <NUM>) arrays and the object allows the transmit and receive arrays to have an angle to the object surface, which hence allows for larger pitch of the array elements. With linear arrays one can scan the transmit and receive beams side-ways for imaging of linear and nonlinear propagation and scattering parameters as presented in relation to <FIG>. Mounting the transmit and receive arrays <NUM> and <NUM> to rotating shafts <NUM> and <NUM>, respectively, allows mechanical scanning of the transmit and receive beams that enlarges the number of measurement observation regions that can be obtained. The arrays <NUM> and <NUM> can then be reduced to annular arrays with sharp symmetric focusing, and even fixed focused transducers for a limited number of cross beam observation regions. Mechanical scanning of the beams in an elevation direction (normal to the paper plane) also opens for 3D imaging of regions of the object with methods according to this invention. These solutions also allow for low cost systems for estimation of linear and nonlinear propagation and scattering parameters in selected regions of an object.

The system according <FIG> can conveniently be simplified for objects that are approximately homogenous, such as the muscle of a fish or even a human, to measure for example uniform fat content in the muscle. One then can use fixed directions of fixed focused annular transmit and HF receive arrays (<NUM>, <NUM>) that provides a fixed cross-beam observation region. From the measured NPD one can estimate the nonlinear propagation factor as <MAT> <MAT> where τ(cell) is the measured NPD at the cross-beam observation cell <NUM>, τ(<NUM>) is a previously measured NPD from the transmit array <NUM> through the acoustic contact medium <NUM> to the surface of the object, and T(tissue) is the propagation time from the probe surface to the centre of the cross-beam observation cell. The composition of the homogeneous tissue can then be obtained from a table of prior data.

We note that the direct measurement of the effect of nonlinear elasticity parameter β̂pa as in Eqs. (<NUM>-<NUM>) produces a result that according to Eqs. (<NUM>- <NUM>) depend on both the direct nonlinear elasticity parameter B(r) and the compressibility κ = <NUM>/A. When we have an estimate of κ(r) we note from Eq.(<NUM>-<NUM>) that we can estimate the pure nonlinear elasticity term B(r) from the estimate β̂pa (r) in Eqs,(<NUM>-<NUM>, <NUM>) as <MAT> where the hat denotes estimates. This introduces a pure nonlinear elasticity parameter with less correlation to the linear parameter A(r) = <NUM>/κ(r) and c<NUM>(r). However, the effect of B on the nonlinear elasticity is also determined by how much the material compresses from a given pressure, that makes B/A = Bκ a better description of the relative effect of nonlinear elasticity on wave propagation, as described following Eq.(<NUM>). With the further development to the wave equation, Eqs. (<NUM>,<NUM>), we note that it is the slowly varying component βpa = (<NUM> + Baκa /<NUM>) κa that affects the forward wave propagation and determines the NPD and the PFD. This is one reason that Ballou found a high correlation between B/A and c<NUM> (See.

When estimates of c<NUM>(r) exist, for example from ultrasound tomography or other, one can also obtain estimates of the nonlinear elasticity parameters B/A and B defined in Eqs. (<NUM>-<NUM>). One can for example use an empirical relation κ = κ(c<NUM>), or for example an approximate linear correlation between the mass density and the isentropic compressibility as <MAT> <MAT>.

Within this approximation one can hence obtain estimates of both the local mass density and the local compressibility of the tissue from c<NUM>(r). One could also use more complex parametric models of the relationship between mass density and isentropic compressibility.

The high correlation between βpa and κa can also be used to generate estimates ĉ<NUM> (r), for example as <MAT> where κ̂(β̂pa) is an empirical relation between β̂pa and κ̂. Eq.(<NUM>) then implies that ĉ<NUM> itself could be directly obtained from an empirical relation between β̂pa and ĉ<NUM>.

Such estimates for ĉ<NUM> could be used as initial values for iterative improvement procedures of estimates of c<NUM> (r), for example to form start parameters in iterative "bent ray" estimation procedures to estimate the spatially varying linear wave propagation velocity and absorption, for example according to tomographic methods disclosed in<NPL>; <NPL>; <NPL>); and <NPL>.

When a first image of c<NUM>(rij) is estimated, one can use these values to estimate corrections for wave front aberrations in the heterogeneous medium for both the transmit and the receive beams. We describe two methods for estimation of corrections for wave front aberrations for focusing the transmit and/or receive beams from an array aperture Srf onto the focal point rf. We assume Srf comprises a set of K elements out of the total number of elements in the array, where rk is the centre of array element #k. We first do spatial interpolation of c<NUM>(rij) to c<NUM>(r) with an adequately low spatial sampling distance.

In the first method we start by numerical simulation of the wave propagation from a point source in the focal point at rf to the actual array aperture, through the heterogeneous object with spatially varying propagation velocity c<NUM>(r). We write the simulated wave function at the centre rk of array element #k as g(rk,rf,ω), where ω is the angular frequency of the point source at the focal point rf. We note that g(rk,rf,ω) is the Greens function for the point source at rf. We then filter the transmit pulse for each element by the filter <MAT> where A(rk,rf) is the standard amplitude apodization of the transmit pulse across the actual aperture Srf. The phase of g represents both the standard focusing delay for beam forming in a homogeneous medium, and together with the amplitude of g an optimal correction for the wave front aberrations due to the spatially varying propagation velocity. The major component of this filter is however the linear component of the phase that represents a delay correction for the wave front aberrations.

This first method requires a large numerical simulation capacity, which has a practical solution using Graphics Processing Units (GPUs). A less computer intensive approach can be obtained with ray acoustics techniques. We define c as the spatial average of c<NUM>(r) over the actual region in front of the array. The well-known differential equation for an acoustic ray r(s) that passes normal to the acoustic wave fronts, is given as <MAT> where s is the arc-length along the ray (i.e. r(s) is a taxameter representation of the ray) and n(r) is the spatially varying refractive index of the material. To focus the transmit or receive beams onto the focal point rf, we simulate numerically Eq.(<NUM>) for the acoustic ray rfk(s) from the focal point rf to the centre rk of array element #k. The beam steering delay for element #k is then calculated as <MAT> where al(rk,rf) is the acoustic length of the acoustic ray rfk(s) from rf to rk.

For best results one should do 3D scanning of the beams to obtain 3D images of c<NUM>(rij) as described above. For corrections of wave front aberrations, the array should with mechanical elevation scanning be of the <NUM>. 75D type with larger elements in the elevation direction used for beam focusing and aberration corrections. With a full matrix array, one obtains electronic focusing and beam steering both in the azimuth and elevation directions. For stationary objects the aberration corrections can be included in the filter functions W(w,r - r<NUM>, r) for synthetic focusing of the observed beams. Hence with mechanical scanning in the elevation direction, we can avoid deviding of the arrays in the elevation direction, as focusing in the elevation direction can be done in the synthetic focusing.

We note that the NPD and the PFD estimated with the crossing transmit and receive beams can also be used in the processing of back-scattered HF signals obtained with a HF receive beam axis along or close to the HF transmit beam axis, as for example described in <CIT>; <CIT>; <CIT>; <CIT> to suppress multiple scattering noise and estimate nonlinear scattering for received HF back-scatter signals. The back scatter images have better spatial resolution in range, and is also the type of images currently in general use, while the cross beam method provides more accurate estimation of the spatial variation of the NPD and PFD with less influence from multiple scattering noise.

It is shown in <CIT> that Class I and II multiple scattering noise are equal for equal transmit and receive beams, which is a great advantage for combined suppression of both noise classes, as described in the cited US patents. For back-scatter imaging it is hence an advantage to form receive beams that are equal to the transmit beams, i.e. same focus, aperture, and apodization. This, however, gives fixed focused beams, but synthetic depth focusing of the combined transmit/receive beam can be obtained by lateral filtering of the received HF back-scatter receive signals as in Eq.(<NUM>).

A useful method is therefore to couple the array elements to a receive beam former that in parallel produces receive cross beams that crosses the transmit beams like in <FIG>, <FIG>, <FIG>, and back-scatter HF receive beams close to equal to the HF transmit beams. For further processing both the cross beam and back-scatter receive HF signals from the transmitted pulse complexes for each HF transmit beam are stored. The HF cross-beam receive signals are used for estimation of at least the spatially varying NPD, τp (r), as described above, and potentially also the Ṽp (r,ω), the βpa (r), the ĉ<NUM> (r) , the H(rk, rf), and the τf (rk, rf) as described in Eqs. (<NUM>-<NUM>) above.

The HF back-scatter receive beam signals are then for each HF receive beam axis filtered laterally as given in Eq.(<NUM>) at a selected set of depths zi to form synthetically focused HF back-scatter receive signals at said selected depths as described in <CIT>. These filtered back-scattered HF receive signals are then corrected for propagation delay and potentially also pulse form and speckle distortion, and combined for suppression of multiple scattering noise and also for estimation of nonlinear scattering, as described in said patent.

Estimation of H(rk,rf), and the τf(rk,rf) from the cross beam signals as described in Eqs. (<NUM>-<NUM>) above, also allows for correction of the wave front aberrations in the synthetic focusing filtering of Eq.(<NUM>), according to known methods.

With the advances in compact computer storage and processing performance, the invention also devices a method for combined HF cross-beam and back-scatter imaging where the HF receive signals for the individual HF array elements are digitized and stored for each transmit pulse complex and each transmit beam. The stored receive element signals are then first processed to i) generate focused HF receive beams crossing the HF transmit beams for example as shown in <FIG>, <FIG>, <FIG>, according to known methods. The receive HF cross-beam signals are then used for estimation of at least the spatially varying NPD, τp(r), and potentially also the Ṽp(r,ω), as described above, and further βpa (r), the ĉ<NUM> (r), the H(rk,rf), and the τf(rk,rf) as described in Eqs. (<NUM> - <NUM>) and Eqs. (<NUM>-<NUM>) above.

In further steps, the method applies further processing on the stored element signals to ii) form a set of HF back-scatter receive signals from HF receive back-scatter beams with axis along or close to the HF transmit beam axis and aperture, focus, and apodization that are equal to that of the HF transmit beams, and iii) The HF back-scatter receive signal contains multiple scattering noise that can be strongly suppressed by delay corrections and potentially also speckle and pulse form corrections of the HF back-scatter receive signals, and combining the corrected HF back-scatter signals from transmitted pulse complexes with different LF pulses as described in <CIT>; <CIT>; <CIT>, to produce noise suppressed HF back scatter receive signals; and iv) perform synthetic dynamic focusing of the noise suppressed HF back-scatter receive signals by lateral filtering of the HF back-scatter receive signals at selected depths according to Eq.(<NUM>). Estimated H(rk,rf) or τf(rk,rf) according to Eqs. (<NUM>,<NUM>) under point i) then allows for correction of the wave front aberrations in the lateral filtering.

With such scanning of the HF transmit and receive beams in a 2D or 3D manner, the methods hence allow formation of 2D and 3D back-scatter images with suppression of multiple scattering noise and also focus corrections of the wave front aberration effect of spatial variations in ultrasound propagation velocity.

<FIG> shows a block diagram of an example instrument for carrying out imaging according to this method. Element <NUM> shows a 3D ultrasound probe comprising a dual frequency linear array <NUM> with a set of M LF elements and N HF elements in an azimuth direction indicated by the arrows <NUM>. The dual frequency band linear array can be made according to known methods, for example as described in <CIT>. The LF and HF elements of the array are via a cable <NUM> connected to a transmit/receive unit <NUM> that connects each LF array element to LF transmit amplifiers, and each HF element to HF transmit/receive circuits comprising a HF transmit amplifier and a HF receive amplifier where the output of the HF receive amplifier is further connected to an analog to digital converter (A/D) presenting a digital representation of the HF received signals from all HF receive elements, according to known methods. The AD converter can in a modified embodiment present digital representations of the I-Q components of the HF receive signals from each HF element that represents the same information as the radio frequency (RF) HF signal, according to known methods.

For 3D scanning of the ultrasound beams, the linear array <NUM> can in this example embodiment be rotated around the long axis <NUM> that provides a mechanical scanning of the LF/HF beam in an elevation direction, indicated by the arrows <NUM>. For each elevation position of the array, one does electronic scanning of a combined LF/HF transmit beam in an azimuth direction indicated by the arrows <NUM>, through electronic selection of transmitting LF and HF elements, and transmitting combined LF/HF pulse complexes similar to what is shown in <FIG>, with selected beam directions and focus. An example HF transmit beam is illustrated schematically as <NUM> within a 2D azimuth plane <NUM> with given elevation position within a total 3D scan volume <NUM>. Alternative elevation movements of the array, like side-ways movement can equivalently be done according to known methods, depending on the space available for such movement, and the shape of the object.

At least two pulse complexes with different LF pulses, for example as illustrated in <FIG>, are transmitted for each transmit beam direction. The LF pulse might be zero in one pulse complex per HF transmit beam, but must be non/zero in at least one pulse complex for each HF transmit beam.

Two versions of the instrument are useful, where in the first version <NUM> comprises beam former for HF receive cross-beams, illustrated as element <NUM> in the 2D scan plane <NUM>, and HF back scatter receive beams with the same axis as the HF transmit beam <NUM>. In a preferred embodiment the HF back-scatter receive beam is equal to the HF transmit beam as this improves suppression of multiple scattering noise in the HF back-scatter receive signal, as discussed in <CIT>. During the scan, the HF cross-beam and back-scatter receive signals are via the high speed bus <NUM> transferred to the processor <NUM> for storage and further processing.

The processor <NUM> comprises a multicore central processing unit (CPU) and a graphics processor unit (GPU) that are SW programmable. The processor receives user inputs from a user/operator input unit <NUM> that operates according to known methods, and displays image data and other information necessary for communication with the user/operator through a combined display and audio unit <NUM>, according to known methods.

In the second version, the digital HF receive signals from each HF receive elements and each transmitted pulse complex are via the high speed bus <NUM> transferred to the processor <NUM> for storage and further processing. For 2D imaging in the second version, a SW program in the processor <NUM> combines HF receive signals from multiple HF receive elements and produces a set of HF receive cross-beams crossing each HF transmit beam in the 2D set, for example as described in relation to <FIG>. A SW program also produces a set of HF back-scatter receive signals from HF back-scatter receive beams with the same axis as the HF transmit beams, and preferably also equal to the HF transmit beams.

Example transmit and receive beams are shown in <FIG>, where <NUM> shows by example a combined HF transmit beam, Ht, and HF back-scatter receive beam, Hbr. The spatial frequency responses of the HF transmit n'beam and the HF back-scatter receive beam are Ht(r - rt,ω) and Hbr(r - rt,ω). The position vector rt(i,j) defines the origin of the HF transmit and receive beam axes, where i defines the azimuth aperture centre element position, and j defines the 2D scan plane elevation position in a 3D scan. <NUM> shows an example HF receive cross-beam focused at the HF transmit beam axis at depth zk, Hcr(r - rr,ω), where rr(i,j,k) defines the origin of the HF receive cross-beam axes, where i, j defines the azimuth and elevation position, and k defines the depth of the cross-over image point zk that is also the focus point of Hcr. <NUM> shows a cross-beam observation cell by the cross-over region between a HF transmit beam and the HF receive cross-beam, and <NUM> shows an indication of a HF cross beam receive signal from the whole cross-over region. By selecting a limited interval of this HF receive signal, the effective range of the observation cell is reduced along the cross-beam axis to the hatched region <NUM>. A schematic form of the HF back-scatter observation cell is shown as the hatched region <NUM>, along the HF combined transmit and back-scatter receive beams <NUM>.

The dimensions of the observation cells can be reduced by filtering of the received signals, as shown in Eqs. (<NUM>,<NUM>). Estimates of the NPD and PFD can then be obtained from the HF cross-beam receive signals at several observation cells along each transmit beam direction, f. as described in relation to <FIG> and Eq.(<NUM>). Estimates of the nonlinear propagation parameter and β̂pa (r)pc(r) and the quantitative propagation parameter β̂pa (r) along the same HF transmit beam directions f. according to Eqs. (<NUM>-<NUM>) or similar. This gives a 2D image of an estimate β̂pa (r) within a 2D scan plane, indicated as <NUM>. (<NUM>-<NUM>) one can obtain a 2D cross-beam image of the linear and nonlinear scattering within the 2D scan plane. Display of the 2D image data are shown on the display unit <NUM>.

When we have an estimate of the linear compressibility across the 2D scan plane, κ̂(r) = <NUM>/A(r) for example from other sources, we obtain a 2D image estimate of the nonlinear parameter B(r) or B(r)/A(r) from Eq.(<NUM>). When spatial estimates of the linear propagation velocity c<NUM>(r) exists, we can produce spatial estimates of the linear compressibility according to Eq.(<NUM>). Other estimates of the compressibility can be obtained from empirical correlation with the linear compressibility and β̂pa (r), for example obtained by machine learning, which then could give estimates of c<NUM>(r) as in Eq.(<NUM>). This equation also gives direct empirical correlation between β̂pa (r) and the linear propagation velocity c<NUM>(r).

From estimates of the linear propagation velocity, the processor can calculate corrections for wave front aberrations produced by the spatial variations in c<NUM>(r), for example according to Eqs. (<NUM>-<NUM>). These aberration correction estimates can then be included in the filter kernels of Eqs. (<NUM>,<NUM>) to provide improved beam focusing with corrections for these aberrations, that reduces the dimension of the observation range cells. The processing on the element signals can then be carried through in several steps, where first a synthetic focusing of the HF receive beam and the HF transmit beam for the HF cross-beam receive signal according to Eqs. (<NUM>,<NUM>) are obtained with a spatially constant propagation velocity estimate, for example c<NUM> = <NUM> m/s. This leads to a first estimate of a spatially varying c<NUM>(r) that opens for corrections for wave front aberrations in a second step, producing improved image estimates with lower dimension of the cross-beam observation cells. This leads to improved estimates of c<NUM>(r) that is used for improved corrections for wave front aberrations in a next step, leading to further improved image estimates with lower dimension of the cross-beam observation cells, and so on.

With the final estimate of c<NUM>(r), one can from Eqs. (<NUM>-<NUM>) calculate wave front aberration corrections for the combined HF transmit beam and the HF back-scatter receive beam. These corrections are then included in a lateral filtering of the HF back-scatter receive signals at selected depths, to provide synthetic focusing of the combined HF transmit and backscatter receive beams at said selected depths.

With 3D scanning of the beams we get 2D data from several neighbouring 2D scan planes. Filters as in Eqs. (<NUM>,<NUM>) can now produce a 2D synthetic focusing of both the transmit and receive beams both in the azimuth and the elevation directions to minimize the observation cells at all depths along the transmit beams. The estimation of material data and images proceeds otherwise in the same manner as above for each 2D scan plane, to produce 3D images of material parameter estimates. The 3D synthetic focusing will produce smaller image cells with more accurate spatial estimates of the parameters, and improved corrections for wave front aberrations.

For good suppression of multiple scattering noise in the HF back-scatter receive signals, it is advantageous to use equal HF transmit and back-scatter receive beams, as described in <CIT>. The HF back-scatter receive signal for an image pixel depth zk = ctk/<NUM>, where tk is the arrival time for the signal for that pixel, can be modeled as <MAT> where HtHbr = Ht<NUM> because the HF back-scatter receive beam and transmit beams are equal. The back-scatter observation cell is defined by the HF pulse length in the z direction, and is hence short. A very useful synthetic focusing of the HF back-scatter receive signal can then be obtained by only transversal filtering of the HF back-scatter receive signal at fixed depth as <MAT> <MAT>.

To minimize the width of Hf in the transversal direction rt we chose the filter kernel Wrt so that the phase gradient of the Fourier transform Hf in the transversal direction is zero. Denoting the Fourier transform in the transversal coordinates by Frt { } the convolution gives <MAT> <MAT> where kt is the Fourier coordinates in the transversal plane, and Art is an apodization function to reduce sidelobes. In particular is the so-called matched filter <MAT> useful, which includes both phase correction and apodization. Wave front aberrations can be included in our model of the HF transmit beam frequency response Ht according to known methods, and the focus filtering in Eqs. (<NUM>-<NUM>) then also corrects for wave front aberrations.

For special versions of the processing one might also use all LF/HF array elements to transmit LF/HF beams that are approximately plane in the azimuth direction. Transmitting azimuth plane waves in several directions one can combine the received signals from the different directions to produce synthetic transmit beams focused at different locations within the 2D plane, according to known methods. With a single azimuth direction azimuth plane wave, one can obtain spatial resolution with regular back-scatter registration of several parallel, dynamically focused receive beams, where time of arrival of scattered pulses produces spatial resolution along the depth of each receive beam, while the receive beam focusing produces lateral spatial resolution, all according to known methods. This method is however more sensitive to multiple scattering noise than the cross beam method described in relation to <FIG>, <FIG>, and <FIG>, b.

The methods and instrumentation described above provides quantitative tissue images that opens for improved detection of tissue diseases, such as cancer and atherosclerotic plaques. It also opens for artificial intelligence (AI) detection and characterization of such diseases, when 3D data of the diseased tissue and some surrounding tissue is available.

Claim 1:
A method for estimation of propagation and scattering parameters in an object (<NUM>, <NUM>,<NUM>), comprising transmitting at least two pulse complexes, each composed of an overlapping high frequency HF and a low frequency LF pulse (<NUM>, <NUM>) along at least one common HF transmit beam axis (<NUM>),
where said HF pulse (<NUM>) propagates close to the crest or trough of the LF pulse (<NUM>), and where one of the amplitude and polarity of the LF pulse (<NUM>) varies between the at least two transmitted pulse complexes, where the amplitude of the LF pulse (<NUM>) can be zero for a pulse complex and the amplitude of the LF pulse (<NUM>) for at least one pulse complex of said at least two transmitted pulse complexes is non-zero, and
directing at least one HF receive cross-beam (<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>) to cross said at least one HF transmit beam axis (<NUM>) at an angle > <NUM> deg to form cross-beam observation cells (Rij) by the cross-over regions defined by the product between each of said at least one HF receive cross-beam (<NUM>) and each of said at least one HF transmit beam (<NUM>, <NUM>, <NUM>), and
recording at least two HF cross-beam receive signals scattered from object structures in each cross-beam observation cell (Rij) from said at least two transmitted pulse complexes with different LF pulses, and
processing said HF cross-beam receive signals for each said at least one HF receive cross-beams (<NUM>) to provide at least one of
i) an estimated nonlinear propagation delay NPD and
ii) an estimated nonlinear pulse form distortion PFD
of the transmitted HF pulse (<NUM>) at image points along said at least one HF transmit beam axis where said HF transmit beam axis (<NUM>) and said at least one HF receive cross-beam axis (<NUM>) have shortest distance within each of said cross-beam observation cells (Rij), and using said estimated PFD and/or NPD for further processing to form measurements of object propagation and scattering parameters at said image points.