Method and system for determining ultrasonic attenuation of a medium

Abstract

The present invention relates to the field of characterizing the acoustic and elastic properties of human tissue. More specifically, it is desired to obtain precise evaluation of attenuation coefficient in ultrasonic frequency range. Known methods implies the use of a complicated set-up. That's why the inventors worked on a method providing with the same accuracy with a simpler set-up. Thus, the present invention relates to a method for determining ultrasonic attenuation of a medium based on a unique ultrasound plane wave applied on the medium. This may notably be used to characterize the steatosis state of the liver, or its coagulation state during thermal treatment such as high-intensity focused ultrasound.

Description

[0001] METHOD AND SYSTEM FOR DETERMINING ULTRASONIC ATTENUATION OF A MEDIUM

[0002] FIELD OF THE INVENTION

[0003] The present invention concerns a method for determining ultrasonic attenuation of a medium. The present invention also relates to a system for determining such ultrasonic attenuation.

[0004] BACKGROUND OF THE INVENTION

[0005] The characterization of the acoustic and elastic properties of human tissue has been the subject of extensive research in recent years. The study of backscatter, sound velocity, elasticity and attenuation of compressional wave provides valuable information on the condition of organs in a non-invasive way.

[0006] Many experimental setups and signal processing methods were developped in the past to achieve precise evaluation of attenuation coefficient in ultrasonic frequency range. Measuring the attenuation coefficient can be problematic in the in-vivo situation, where only the backscattered signal is accessible. To date, only focused imaging probes have been used to measure attenuation coefficient in this context. This was recently used, for example, to characterize the steatosis state of the liver, or its coagulation state during thermal treatment such as high-intensity focused ultrasound (HIFU).

[0007] To date, the processing methods used to extract attenuation coefficient based on the backscattered intensity either used multiple acquisitions of radiofrequency (RF) signal when positioning the focus at different depth or the use of a reference medium or a planar reflector to normalize the backscattered spectrum and emancipate from beam focusing effects.

[0008] SUMMARY OF THE INVENTION

[0009] There is therefore a need for a method for determining attenuation of a medium, which is easier to implement, notably avoiding the need of a planar reflector, of a second receiving transducer or of a reference medium.

[0010] To this end, the specification describes a method for determining ultrasonic attenuation of a medium, the method for determining comprising the following steps:

[0011] - applying a unique ultrasound plane wave on the medium,

[0012] - collecting the backscattered plane waves from the medium excited by the ultrasound plane wave, and

[0013] - calculating an attenuation coefficient of the medium from the backscattered signal of the backscattered plane waves. Such method enables to use a single plane wave emission, without the need of a planar reflector, of a second receiving transducer or of a reference medium i.e. using only the backscattering signal. The strength of this method lies its simplicity and the fact that it could be used to help characterizing both in-vivo organs and ex-vivo samples without the need of a reference scattering medium often required to remove influence of beam focus.

[0014] As will appear from the experimental section, such method was first validated on two reference phantoms with different attenuations and with local echoneicity variations, and on in-vivo results obtained on several healthy volunteers. This in-vivo validation was made on the liver and kidneys. These are both accessible to clinical extracorporal probes and of growing interest in the context of HIFII.

[0015] The Applicant has also carried numerical simulations using the recently-developed computational code that accurately models the microstructure formed by scatterers in the heterogeneous medium, as well as multiple scattering effects.

[0016] According to further aspects, which are advantageous but not compulsory, the method for determining might incorporate one or several of the following features, taken in any technically admissible combination:

[0017] - the step of applying is carried out by an ultrasound probe having several transducers, the step of calculating comprises a sub-step of deducing the backscattered intensity of the backscattered plane waves based on each radiofrequency signal collected by the transducers.

[0018] - the step of applying is carried out by an ultrasound probe having several transducers, the step of calculating comprises a sub-step of deducing the backscattered amplitude of the backscattered plane waves based on each radiofrequency signal collected by the transducers.

[0019] - the ultrasound probe is an array of transducers.

[0020] - the ultrasound probe is a linear array of transducers.

[0021] - the step of calculating comprises a sub-step of fitting the spatial evolution of backscattered intensity by an exponential function whose one parameter is the value of attenuation and a sub-step of calculating the attenuation coefficient based on the value of absorption by using a relationship between the attenuation coefficient, the value of absorption and the frequency of the unique ultrasound plane wave.

[0022] - the step of calculating comprises a sub-step of fitting the spatial evolution of backscattered amplitude by an exponential function whose one parameter is the value of attenuation and a sub-step of calculating the attenuation coefficient based on the value of absorption by using a relationship between the attenuation coefficient, the value of absorption and the frequency of the unique ultrasound plane wave - the relationship is that the attenuation of the medium is equal to the product of the frequency of the ultrasound wave and the attenuation coefficient.

[0023] - the relationship is that attenuation of the medium is equal to the product of a power of the frequency of the ultrasound wave and the attenuation coefficient.

[0024] - the step of calculating comprises a sub-step of determining several areas in the medium, the sub-step of fitting and the sub-step of calculating being achieved for each area, to obtain an attenuation coefficient of the area.

[0025] - the step of calculating comprises a sub-step of obtaining an attenuation coefficient of the medium from the obtained attenuation coefficients.

[0026] - the sub-step of obtaining is carried out by applying a weighted average.

[0027] - for an intermediary area situated between two areas, a dimension being defined for said intermediary area, the step of calculating comprises deriving the attenuation coefficient of the intermediary area by using the coefficient attenuations of the two areas and the dimension of the intermediary area.

[0028] - for at least one area, the method further comprises a step of comparing the spectrum of the backscattered signal with a reference spectrum to deduce an attenuation coefficient of the area.

[0029] - the medium is a biological tissue.

[0030] - the biological tissue is a tissue chosen among the list constituted of a liver, a pancreas, a breast, a brain and a kidney.

[0031] The specification also describes a system for determining ultrasonic attenuation of a medium, the system for determining being configured to

[0032] - apply a unique ultrasound plane wave on the medium,

[0033] - collect the backscattered plane waves from the medium excited by the ultrasound plane wave, and

[0034] - calculate an attenuation coefficient of the medium from the backscattered signal of the backscattered plane waves.

[0035] The term “adapted to” used here should be understood as meaning “able to” or “configured to”.

[0036] BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The invention will be better understood on the basis of the following description which is given in correspondence with the annexed figures and as an illustrative example, without restricting the object of the invention. In the annexed figures: - figure 1 is a schematic representation of a medium and a system adapted to determine attenuation of the medium,

[0038] - figure 2 is a flowchart of an example of carrying out a method for determining attenuation of the medium, and

[0039] - figures 3 to 13 are figures showing results obtained with experiments carried out by the Applicant when using the method for determining of figure 2. More precisely:

[0040] - for figure 3:

[0041] (A), (B): Attenuation map and backscattered intensity / r(z) measured on the weakly attenuating part of the CIRS 040GSE phantom.

[0042] (C), (D): same quantities for the strongly attenuating part. Bmode images on the top right corner of (B) (respectively (D)) corresponds to the weakly (strongly) part.

[0043] - for figure 4:

[0044] (A) Bmode image of the phantom CIRS 040GSE (high attenuation part). Attenuation coefficient inside the three large inclusion : a0= 0.0789 Np / (cm.MHz),

[0045] Attenuation of the background medium : a0= 0.1071 Np / (cm.MHz).

[0046] (B) Backscattered intensity Ir(log. scale) average in the x direction between the two dotted lines shown in (A).

[0047] - for figure 5:

[0048] (A), (C), (E) : Bmode images obtained on three healthy volunteers, with respectively in (B), (D), (F) the corresponding attenuation map. Red dotted lines correspond to interfaces inside the medium. Liver and kidney average attenuation coefficients for the three cases are reported in Table II.

[0049] - for figure 6:

[0050] Numerical simulations of the real part of the scattered field obtained for a heterogeneous medium made of cylindrical fluid particles immersed in a fluid medium, for parameters (<|) = 9%, koa = 0.2) (A), (<|) = 45%, koa = 0.2) (B), (<|) = 45%, koa = 1) (C). Arrows indicate incident plane wave direction and black arrows indicate backscattering direction.

[0051] - for figure 7:

[0052] (A), (B) two dimensionnal heterogeneous media made with discrete cylinders randomly distributed in space. Surface fraction <|) = 9% (A) and <|) = 45% (B). Red arrows schematically illustrate the vector perpendicular to the interface of the media.

[0053] (C) Histological section (Hematoxylin and eosin stain) of a liver and

[0054] (D) binary version of (C), where cellular network is shown in black and extracellular network is shown in white. - for figure 8:

[0055] (A) Histological section of a liver sample (staining method : Red Sirius); (B) binarized version of (A) considering the cellular network as the scattering phase (in black); (C) monodisperse two-dimensional heterogeneous media made with discrete particles randomly distributed, with the idea to mimic (B). (D) Histological section of a kidney (staining method : H&E); ); (E) binarized version of (D) considering TS and CD structures as the scattering phase (in black); (F) bi-disperse two-dimensional heterogeneous media made with discrete particles randomly distributed, with the idea to mimic (E).

[0056] - for figure 9:

[0057] Real part of the acoustic field scattered by a ensemble of fluid particles immersed in a fluid medium, when excited by an incident plane wave. Long purple arrows indicate incident plane wave direction and short black arrows indicate backscattering direction. Source frequency, acoustic properties and particles concentration are reported in Table 2. The differential scattering cross-section of the particles are plotted in the insets on the right of each sub-figure. For bi-disperse media (D), (E), the purple dotted line corresponds to the differential scattering cross-section of the TS and the black continuous line corresponds to differential scattering cross-section of the CD.

[0058] - for figure 10:

[0059] (A), (B): Attenuation map superimposed on the conventional Bmode image and backscattered intensity I r(z) measured in the less attenuating part of the reference gelatin phantom. (C), (D): Attenuation map superimposed on the conventional Bmode image and backscattered intensity lr(z) measured in the more attenuating part of the reference gelatin phantom. Corresponding Bmode images are shown on the top right corner of (B) and (D). The near field distance is delimited by the vertical dotted lines at 1.25 cm in depth.

[0060] - for figure 11 :

[0061] (A) Bmode image of the reference phantom presenting an attenuation of 0.107 ± 0.006 Np / (cm.MHz) and containing three inclusions with different echogeneicities and lower attenuation (0.079 ± 0.006 Np / (cm.MHz)). (B) Backscattered intensity lr(log. scale) average in the part of the phantom highlighted by the two red dotted lines in (A). The attenuation coefficient measured inside the inclusion and in the surrounding background are reported in (B). The average attenuation slopes measured in the whole phantom are reported in Table 3.

[0062] - for figure 12: (A), (C), (E): Bmode images of livers and kidneys obtained on three healthy volunteers, with respectively in (B), (D), (F) the corresponding attenuation map computed from the backscattered pane waves. Red dotted lines correspond to interfaces of both organs. Liver and kidney average attenuation coefficients for all cases are reported in Table 4.

[0063] - for figure 13:

[0064] (A) Sparse (<p=9%) or (B) dense (cp=45%) heterogeneous media made of discrete particles. Red dotted lines delineate the interface of the medium, and the red arrows the normal of this interface.

[0065] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0066] A system 10 for determining is shown on figure 1.

[0067] The system 10 is adapted to determine ultrasonic attenuation of a medium.

[0068] Preferably, the medium 12 is a tissue of a subject.

[0069] According to an example, the tissue is the tissue of a liver.

[0070] However, the system 10 can also be used to any other biological tissue and mainly breast, pancreas, muscle, brain and kidney. The subject is, for instance, an animal, notably a rodent, a rabbit, a pig or a human.

[0071] The device for estimating 10 comprises an ultrasound probe 14 and a calculator 16.

[0072] The ultrasound probe 14 is adapted to send ultrasound waves to the area 12 and to collect the backscattered signal emitted by the area 12 in response to the ultrasound waves.

[0073] Said ultrasound waves may come from another apparatus, as is the case in the example of a therapy apparatus in figure 4.

[0074] More precisely, the ultrasound probe 14 is a set of transducers, each transducer being adapted to collect the radiofrequency backscattered signals from the ultrasound excitation.

[0075] The number of transducers and their spatial arrangement may vary according to the application.

[0076] As a specific example, the number of transducers is here set to 128 and the transducers are assumed to be arranged so as to form a rectangular array.

[0077] The ultrasound probe 14 is thus adapted to provide radiofrequency backscattered signals, which may be processed to obtain an ultrasound image of the medium 12 if desired.

[0078] The ultrasound probe 14 is adapted to apply ultrasound waves in a controlled manner to fulfill the requirement of health safety of the medium 12.

[0079] The ultrasound probe 14 is adapted to obtain such backscattered signals at several measuring times during a time measurement interval. the ultrasound probe is a linear array of transducers. The calculator 16 is adapted to collect the backscattered signals acquired by the ultrasound probe 14 and to process them to obtain an estimation of the attenuation of the medium 12.

[0080] The calculator 16 is an electronic circuit designed to manipulate and / or transform data represented by electronic or physical quantities in registers of the calculator 16 and / or memories into other similar data corresponding to physical data in the register or memory memories.

[0081] As specific examples, the calculator 16 is produced in the form of a programmable logic component, such as an FPGA (Field Programmable Gate Array), or even an integrated circuit, such as an ASIC (Specific Integrated Circuit).

[0082] Alternatively, the calculator 16 is carried out in the form of one or more software programs, that is to say in the form of a computer program, also called a computer program product, it is also capable of being recorded on a medium, not shown, readable by computer. The computer-readable medium is, for example, a medium capable of storing electronic instructions and of being coupled to a bus of a computer system. For example, the readable medium is an optical disk, a magneto-optical disk, a ROM memory, a RAM memory, any type of non-volatile memory (for example FLASH or NVRAM) or a magnetic card. A computer program comprising software instructions is then stored on the readable medium.

[0083] An example of the operating of the system 10 is now described in reference to figure 2, which is a flowchart showing an example of carrying out a method for determining.

[0084] The method for determining aims at determining attenuation of the medium 12.

[0085] More specifically, in this example, the aim is to obtain an attenuation coefficient of the medium 12.

[0086] According to this example, the method for determining comprises a step of applying S20, a step of collecting S30 and a step of deducing S40.

[0087] During the step of applying S20, the ultrasound probe 14 applies a unique ultrasound plane wave on the medium 12.

[0088] During the step of collecting S20, the ultrasound probe 14 collects the backscattered plane waves from the medium excited by the ultrasound plane wave.

[0089] This means that the ultrasound probe 14 obtains, for each transducer, a radiofrequency signal.

[0090] During the step of calculating S40, the calculator 16 calculates an attenuation coefficient of the medium 12 from the backscattered signal of the backscattered plane waves. In the present case, the intensity of the backscattered plane waves is used but the backscattered amplitude may be used in another embodiment.

[0091] For this, according to the case, the calculator 16 may apply one or several of the following sub-steps.

[0092] One sub-step is a sub-step of deducing the backscattered intensity of the backscattered plane waves based on each radiofrequency signal collected by the transducers.

[0093] In other words, the calculator 16 calculates the backscattered intensity of the ultrasound probe 14 by summing the contribution from each transducers of the ultrasound probe 14.

[0094] The backscattered intensity / r(z) is obtained based on all the N transducers of the ultrasound probe 14 as follows: where s;(z) is the RF signal acquired by the j-th element.

[0095] Other sub-steps are a sub-step of fitting and a sub-step of calculating the attenuation coefficient.

[0096] The sub-step of fitting consists in using equation 4 (see experimental and calculation section).

[0097] In the most simple case, the calculator 16 then extracts the argument of the signal according to the following equation:

[0098] Ir(z,f) = Ae ~4 atot(f zwhere:

[0099] •atot is the attenuation of the medium, and

[0100] • z is the depth (generally obtained by time-of-f light analysis).

[0101] The calculator 16 then deduces the attenuation atot(f) by using a logarithmic regression and the previous relation.

[0102] This means that the sub-step of fitting is a step of fitting the spatial evolution of backscattered intensity by an exponential function whose one parameter is the value of attenuation atot(f).

[0103] During the sub-step of calculating, the calculator 16 calculates the attenuation coefficient based on the value of absorption by using a relationship between the attenuation coefficient, the value of absorption and the frequency of the unique ultrasound plane wave.

[0104] One example is equation 6. In this case, the relationship is that attenuation of the medium is equal to the product of the frequency of the ultrasound wave and the attenuation coefficient.

[0105] In other embodiments, the relationship is more complex. For instance, the relationship is that attenuation of the medium is equal to the product of a power of the frequency of the ultrasound wave and the attenuation coefficient.

[0106] One other sub-step is a sub-step of determining several areas in the medium.

[0107] This is illustrated by figure 3, wherein depths with a similar behaviour with regards to the variation of attenuation are put together to delimit the area.

[0108] In the case of figure 3, two of such areas can be found.

[0109] The sub-step of fitting and the sub-step of calculating are then achieved for each area, to obtain an attenuation coefficient of the area.

[0110] A sub-step of obtaining an attenuation coefficient of the medium from the obtained attenuation coefficients can then be carried out.

[0111] For this, the sub-step of obtaining is carried out by applying a weighted average.

[0112] The weights are, for instance, chosen in accordance with the dimension of each area (the extension in depth of the area).

[0113] For some intermediary areas, the behaviour may derive from the exponential fitting.

[0114] Alternatively or in complement, another technique providing access to attenuation of the intermediary area may be carried out.

[0115] For instance, this is achieved by comparing the spectrum of the backscattered signal with a reference spectrum to deduce an attenuation coefficient of the area.

[0116] Such technique may also be used for areas accessible to the exponential fitting, so as to obtain a more accurate value.

[0117] A new method for determining attenuation coefficient is thus proposed, based on the use of a linear ultrasound probe that emits a single plane wave. This method enables to achieve 2D mapping of ultrasonic attenuation in biological tissue using plane wave imaging.

[0118] The method is first validated with various reference phantoms, demonstrating the efficacy and high precision (error < 10%) of the estimation. Further measures show that this approach can also be used in media with local variations in attenuation and echogenicity. In-vivo, measurements on healthy volunteers allow to measure the attenuation coefficient in the liver and kidney with high accuracy (deviation < 10% from reference values). Finally, numerical simulations are performed using a numerical code based on multiple scattering equations. These simulations make it possible to study the propagation and impedance contrast conditions for which this method valid.

[0119] These results pave the way for very simple quantification of the attenuation coefficient both in laboratory conditions or for clinical use. It can help to improve tissue characterization, make diagnosis more accurate and make treatment planning with focused ultrasound more precise.

[0120] EXPERIMENTAL AND CALCULATION SECTION

[0121] I. INTRODUCTION

[0122] The aim of this section is to demonstrate the feasibility of measuring the attenuation coefficient using a single plane wave emission, without the need of a planar reflector, i.e. using only the backscattering signal. The strength of this approach lies its simplicity and the fact that it could be used to help characterizing both in-vivo organs and ex-vivo samples without the need of a reference scattering medium often required to remove influence of beam focus.

[0123] We first validate this method on two reference phantoms with different attenuations and with local echoneicity variations, then present in-vivo results obtained on several healthy volunteers. We focus on characterizing the liver and kidneys. These are both accessible to clinical extracorporal probes and of growing interest in the context of HIFU. Next, we carry out numerical simulations using the recently-developed computational code that accurately models the microstructure formed by scatterers in the heterogeneous medium, as well as multiple scattering effects.

[0124] II. METHODS

[0125] A. Computation of the attenuation coefficient based on plane wave propagation

[0126] Let us consider an incident plane wave propagating inside a medium made of a ) collection of scatterers randomly distributed inside a host matrix. Let us denote k0= — the ) wavenumber inside the host medium and k = — + jatotthe wavenumber inside this ^0 heterogeneous medium accounting for dispersion, scattering and absorption effects, with co the angular frequency, the wavespeed and atotthe total attenuation that is the sum of scattering (a ) and absorption (cra) effects: atot= as+ aa(equation 1)

[0127] With f the frequency, fa and fs respectively the absorption and the scattering mean free paths.

[0128] Using this notation, the plane wave can be written inside the medium a : (equation 2) With:

[0129] • z the direction of propagation and

[0130] • A the amplitude of the wave at location z = 0.

[0131] From equation 2, it is clear that incident wave pi decreases during propagation because of attenuation effects.

[0132] The incident intensity / ;(z) = \pi(x,ke') |2can therefore be written as : (equation 3)

[0133] At all depth z, the wavefront is backscattered by all the particles located around depth z.

[0134] Under several assumptions that will be detailed in the Discussion part, the backscattered intensity at this depth can be written as: lr(z,f) = Ae ”4'“tot^-)z(equation 4)

[0135] From there, we can use equation 4 to measure attenuation inside the medium, only based on the reflected intensity.

[0136] From there one can express the attenuation a(f) as: (equation 5)

[0137] In many biological tissue, attenuation a(f) variates almost linearly with frequency atot(f) =ao-f, which leads to writing the attenuation coefficient a0as: (equation 6)

[0138] It is important to point the fact that this development is only valid when no or weak physical interfaces exist inside the heterogeneous medium. That is to say that the effective homogeneized medium is continuous (atotand constant in space) or that the interfaces do not impact the propagation.

[0139] Otherwise, equation 3 and all the more equation 4 are wrong. Further comments on this important point will be given in the next parts of this paper.

[0140] B. Radio-frequency signals acquisitions

[0141] In this section, a Verasonic ultrasound scanner was used to measure / r(z). A L7-4 linear probe is used that is made of 128 piezo-electric elements of width 250 pm and separated by a distance of 298 pm.

[0142] The Verasonics system provided the raw radio frequency (RF) signals at a sampling frequency of 20 MHz, which is 4 times larger than the center frequency of the probe.

[0143] The imaging sequence is composed of a single plane wave. Total backscattered intensity is obtained based on radiofrequency signals of all the N = 128 elements as equation 7: where s,(z) is the RF signal acquired by the ithelement.

[0144] III. RESULTS

[0145] A. Attenuation of a homogeneous reference phantom

[0146] The first result presented is a validation test of the method proposed in section ll-A. To this end, we chose to characterize the attenuation of a reference medium. We selected the CIRS 040GSE phantom that contains inclusions of varying echogenicity, as well as a tissue mimicking background with known attenuation properties : one part of the phantom background has an attenuation coefficient of 0.079 ± 0.006 Np / (cm.MHz) and the other is more attenuating, with a coefficient of 0.107± 0.006 Np / (cm.MHz).

[0147] Figures 3(A) and (C) show the attenuation coefficient maps measured on each part of the phantom, away from the inclusions. The value for each pixel is obtained from a linear regression on the windowed temporal signal around the pixel (window width following z: Co

[0148] 10A = ^ « 3 mm10 (see continous line in Figures 3(B) and (D)). The width of the moving average window along x is 2.5mm (covering a distance of approximately 8 piezoelectric elements).

[0149] Manufacturer values and average values obtained with the proposed method are reported in Table I.

[0150] Table I: Attenuation coefficients of the cirs 040g se phantom. Values given by the manufacturer and values measured based on the plane wave imaging method

[0151] For the weakly attenuating part, the average value obtained is exactly the value given by the manufacturer. In the case of the strongly attenuating part, only 7% difference are observed between average values and the manufacturer value is inside the confidence interval of the measurement. This comparison provides a quantitative validation of the proposed characterization method.

[0152] B. Attenuation of a reference phantom containing inclusions

[0153] In order to validate the method on a medium in which echogenicity and attenuation change locally, a second acquisition is carried out on the most attenuating part of the reference phantom, where the inclusions are visible. These inclusions have an attenuation coefficient of 0.079 Np / (cm.MHz), i.e. slightly lower than the background.

[0154] Figure 4(A) shows the Bmode image in this phantom. The inclusion on the left has a much higher echogenicity than the background. As a result, the Ir intensity decay is not continuous with depth. Figure 4(B) shows the evolution of lrwith depth z, averaged between the two dotted lines drawn in figure (A). This figure clearly shows the different echogenicity appearing at the inclusions (2.5 cm < z < 3.3 cm) and the well-localized spot around z » 3.9 cm.

[0155] Figure 4(B) shows that, in this situation, the calculation of the attenuation coefficient must be limited to regions at a distance from the interfaces separating zones of different echogenicity in order to avoid misestimating the attenuation coefficient. From the figure, one can unambiguously see that the decay of lris exponential inside the large inclusion, endorsing the fact that the method can be applied in this area of less than a centimer in diameter for the frequency range used in this section ([4 - 7] MHz) that is close to clinical reality. On the other hand, the spot downstream of this first inclusion is too small to allow precise calculation of the attenuation coefficient, which illustrates the limit of the method.

[0156] C. Computation of attenuation maps in various in-vivo conditions

[0157] This section is dedicated to validating the method on several examples of attenuation measurements. These measures were performed on three healthy volunteers. The target areas chosen are the liver and the kidney. Liver is an advantageous zone because it is not located deeply inside the human body and homogeneous from a tissue microstructure point of view. Kidney is more located deeper below the liver. If less studied than the liver, kidney is also at the heart of many current therapeutic challenges.

[0158] Measuring attenuation coefficient in liver and kidney is therefore of great interest. The attenuation coefficient maps obtained with the plane wave imaging method are reported in figure 5(B), (D) and (F) and the average and standard deviation values in table II.

[0159] Table II: Average value of attenuation coefficient in liver and kidney for three healthy volunteers, and reference attenuation coefficient values from the literature

[0160] Firstly, important local variations are observed within the liver, particularly in the mapping (F). These variations are related to the strong variations in fat inclusions distribution in liver tissue. Indeed, the density of fat inclusions is strongly correlated with the ultrasound attenuation of the tissue.

[0161] Secondly, a large area in the center of the kidneys appears to return no attenuation measurements in cases (B) and (D): these areas contain urine, whose attenuation coefficient is around 0.0053 Np / cm at 1 MHz, i.e. 13 times less attenuating than liver. This value is too low to be extracted from background noise at certain locations. Nevertheless, the values measured all around are very close to the reference value.

[0162] These results support the efficiency of the plane wave imaging method for locally measuring attenuation coefficient in-vivo.

[0163] D. Numerical simulation of backscattering in various heterogeneous media

[0164] In order to catch the physical properties of the biological tissue that allow to write the backscattered intensity as a plane wave, Numerical simulations were carried out using the recently developed calculation code. Results of these simulations are presented in Figures 6(A-C). This code allows to compute the field scattered by a ensemble of particles when excited by an incident plane wave at a given frequency. It takes into account particle size, position and multiple scattering effects at all orders.

[0165] For the sake of simplicity, these simulations were carried out in two dimensions (the scatterers are infinitely long cylinders) and no shear effects are accounted for in the surrounding medium. In order to get as close as possible to an ensemble of cells, the radius of the diffusers is a = 12.5 pm. Scatterers are considered to be fluid particles, with density is pp= 1150 kg / m3and the sound velocity inside is c0= 1500 m / s, Zo= 1.50 Mray). These

[0166] (.ZP-ZO) properties lead to a contrast of — « 0.22.

[0167] Three numerical simulations were performed. In the first, the particle concentration (surface fraction) is <p = 9% and the frequency is 2nfa koa = -^- = 0.2 (f = 3.9 MHz). In this situation, the backscattered wavefront is not planar, probably due to the disordered positions of the scatterers.

[0168] The second simulation is at the same frequency, but at five times the density (<p = 45% ). In this situation, the line formed by the scatterers, which forms the boundary between the water and the heterogeneous medium, is clearly visible. In this situation, backscattering, which is more important due to the increase in density, becomes also flatter.

[0169] In a third simulation, the density <p = 45% is maintained and the frequency is increased to / coa=1 (f = 19 MHz). In this situation, the wavelength becomes comparable to the particle size, and the roughness of the planes formed by the scatterers at each depth z becomes visible to the incident wave. Moreover, particles scatter less backward at this frequency regime.

[0170] Further detailed comments on these simulations are provided in the Discussion section.

[0171] IV. DISCUSSION

[0172] A. Ultrasonic backscattering by dense media with low impedance contrast

[0173] The validity of equation 2 is based on the assumption that the backscattered intensity takes the form of a plane wave. This assumption is very strong and is generally not verified. Let’s analyze the elements on which it is based.

[0174] In a sparse medium, particles are distributed randomly. The scattered waves are rarely located on the same phase plane (plane (x,y) in the case where the incident wave propagates along z), so they usually scatter waves with very different phases. As a result, the reflection coefficient of such media is usually negligible (around 0). This is the situation described by the Independent Scattering Approximation (ISA). This is in great agreement with the scattered field presented in Figure 6(A). In this situation, concentration <p = 9% is low enough to let the particles be sparsely distributed in space, preventing a plane backscattered wavefront from appearing (see Figure 7(A)).

[0175] For a more dense medium, second order model are needed to properly describe propagation of in the forward direction (coherent wave) or in the backward direction (backscattering). The reflection coefficient is then written as equation 8: where F(n) is the form function of a single spherical scatterer evaluated in the backward direction 6 = n (0 = 0 corresponding to the incident plane wave). From a physical point of view, in a dense medium, the position of one particle is constrained by the presence of others (assuming that they cannot overlap). This creates short-range spatial correlations and leads to the fact that on each phase plane (i.e. each depth z), the scatterers are all relatively well aligned. The waves scattered by this ensemble are more in phase, making it possible to measure and interpret the backscattered signal (see Figure 7(B)). This is visible in equation 8 : the reflection coefficient is on one hand built with the contribution of a given particle (the term F(TT)) times the concentration of particles

[0176] Simulation presented in Figure 6(B) helps supporting this idea : the concentration of the heterogeneous medium is of = 45% in this case, and particles are strongly short range correlated. From there, a planar wavefront appears in the backscattered direction.

[0177] Propagation in a dense medium also depends on the scattering strength of each particle. In the case of a highly scattering medium (the resonant regime of elastic particles immersed in water for example), localization phenomena can occur. In the weak localization situation, the backscattered signal becomes coherent not only at 6 = n but also over an angular range around this value, creating a cone of coherent backscattering. This effect, in our situation, would be detrimental and would make it impossible to consider equation 4 valid, as the reflection coefficient would in this case be constructed with much more complex paths within the medium than simple round trips.

[0178] For these reasons, another condition needs to be fulfilled in order to use equation 4 as a manner to calculate. The medium must be composed of weak scatterers. In the case of a biological tissue, the question of the nature of scatters remain unclear, but it is likely that cells are involved in the scattering response. In figure 7 (C) is shown a histological section of an excised liver. In (D), this section is made binary in order to distinguish only two phases : the hepatocyte network is shown in black and the extra-cellular network in white. The comparison of (D) and (B) unambiguously endorses the fact that the cellular matrix can be seen as a dense medium. Furthermore, the center frequency of the ultrasonic probe used for imaging was 5.2 MHz, which leads to a wavelength of 0.3 mm. This value is ten times larger than hepatocyte diameter (dceN» 24 pm). Scattering being weak in this frequency regime for this non-resonnant particles. Therefore, biological tissue such as liver is a very favorable situation for measuring a flat backscattering front. It is likely that this result can be extended to any other biological tissue with similar characteristics.

[0179] To highlight the importance to have small scatterers in the tissue, a last simulation is reported in Figure 6(C), with a medium similar to (B) (same scatterers, same concentration) but for a frequency five times higher, leading to / coa=1 . At this frequency, the characteristic size of the “roughness” of the successive particles planes inside the medium at each depth z become important. This roughness becomes of the same order of magnitude than the wavelength, so the wavefront is backscattered in multiple directions.

[0180] All these elements of thought lead to the conclusion that, in our situation, the conditions required for a relevant use ofequation are fulfilled. The combination of the density of the cellular network (which is suspected to play a predominant role in scattering) and the low impedance contrast between the cells and the extra-cellular matrix are important elements to understand the relevance and effectiveness of equation 4 for measuring the attenuation coefficient.

[0181] B. Propagation in subcutaneous tissue and wavefront distortion

[0182] The intermediate subcutaneous layers between the probe and the organs are made up of diverse structures (mainly the skin, fat and muscles) and are anatomically very heterogeneous (see Figures 5(A, C, E)). In these areas, backscattering intensity cannot simply be expressed as a plane wave (equation 4) because scattering events are much stronger and the microstructure more complex.

[0183] But what about the incident wave that travels forward? The wave passing through the tissue can be deflected by the successive interfaces of the different layers. Nevertheless, the density of these layers is always close to that of water, and the velocities of the compressional waves do not vary by more than 10% compared with water. As a result, acoustic impedance differences remain small (typically < 20%). Interface angles are also always quite small (< 20 deg), so the wavefront can be considered as approximately flat when entering the liver.

[0184] C. Usefulness of the method and possible refinements

[0185] Now that several physical explanations of what makes the method presented in this section possible have been proposed, important points have to be drawn from our results. Also, several refinements and uses can be described.

[0186] In this study, no frequency filtering was performed. The attenuation coefficient a0estimated using equation 6 is therefore an average attenuation coefficient obtained for frequencies around f = fc= 5.2 MHz.

[0187] In tissues where the frequency behavior is highly nonlinear, this procedure needs to be adjusted, by adding a filter to characterize atot(f) for narrower frequency window. To this end, the linear approximation used to write equation 6 can also be improved by modeling attenuation using a power law.

[0188] To manage thermal ablation of tumors, it is crucial to know the attenuation contrast between the tumor and its environment. Figure 4 presented in section (B) of the Result section reports also that it is possible to evaluate the attenuation coefficient inside a small area characterized by strong variation of echogeneicity and variation of attenuation. On one hand, this endorses the fact that this method could be used for attenuation estimation inside closed areas like tumors.

[0189] On the other hand, it would be also possible to argue that tumor’s echogeneicity is very heterogeneous and therefore very different from the reference phantom used in this section. For this reason, using equation 2 to estimate tumor’s attenuation could be more challenging. Even if this might be true, tumors are very often immersed in the tissue of a single organ. Therefore, measuring the variation in backscattered intensity between downstream and upstream of the tumor enables to, at least, arrive at an average attenuation coefficient that accounts for all absorption and scattering losses within the tumour.

[0190] Lastly, it is important to place this section in perspective with the important challenge of estimating the attenuation inside subcutaneous tissues. These tissues are both very heterogeneous from a structural point of view, and are obviously never surrounded by two tissues of the same type. The conditions detailed in the previous section are therefore not fulfilled for these tissues, this is a limitation of the current procedure.

[0191] Nevertheless, it would be possible to calculate the attenuation coefficient of these layers by comparing the spectrum of the backscattered signal with that obtained on a reference reflector placed in the water at the distance at which the attenuation coefficient needs to be evaluated.

[0192] Other methods using focused transducers can also be used to obtain in-vivo attenuation in these subcutaneous tissues [that are important for focusing efficacy during HIFU procedure.

[0193] The combination of plane wave imaging method (for deep organs) to one of these methods (for subcutaneous layers) will provide an efficient procedure for a complete 2D map of attenuation coefficient in-vivo.

[0194] MATERIALS AND METHODS

[0195] Ultrasound equipment

[0196] Acquisitions were performed using a 5.2 MHz linear probe of 128 elements (L7-4 probe, Verasonics, Kirkland WA, USA) connected to a Vantage 256 system (Verasonics, Kirkland WA, USA). The ultrasound imaging probe is made of 128 piezo-electric elements. Each element has a width of 250 pm and is separated by a distance of 298 pm. The Verasonics Vantage system provided the raw radio frequency (RF) signals at a sampling frequency of 20.8 MHz. The imaging sequence is composed of a single plane wave. The backscattered intensity received by the ultrasound imaging probe was obtained based on radiofrequency signals measured by each element k among the 128 elements as described by Eq 7.

[0197] / W(Z) = |sfc(z)|2Eq. 7 where sk(z,t) is the RF signal acquired by the kthelement.

[0198] Computation of the attenuation coefficient based on plane wave propagation

[0199] The local attenuation of an incident plane wave propagating inside a medium made of scatterers randomly distributed inside a host matrix is the sum of attenuation by scattering (as) and by absorption (aa) can be described by Eq. 8:

[0200] «( / ) = «s( / ) + aa( / ) Eq. 8 where a is the local attenuation and f the frequency of the plane wave.

[0201] The amplitude of this plane wave can be described by Eq. 9: where ptis the pressure of the incident plane wave, z is the direction of propagation, A is the amplitude of the wave at location z = 0, co is the angular frequency and is the phase velocity.

[0202] The incident intensity can therefore be described by Eq. 11 :

[0203] Iiz,f) = Ae -'Za^zEq. 11

[0204] At all depth z, the wavefront is backscattered by all the particles located around depth z.

[0205] The backscattered intensity (Zr) at this depth can be described by Eq. 12 under the assumption that there are small scatterers in the medium and a low impedance contrast between the scatterers and the surrounding medium. Together, these two conditions limit the influence of multiple scattering.

[0206] Furthermore, Eq. 12 is only valid when no or weak physical interfaces are encountered inside the heterogeneous medium, apart from the scatterers. In other words, the effective homogenized medium is continuous (atotand c^ are constant in space) or that the interfaces do not impact the ultrasound wave propagation. Further comments on the validity of these important assumptions will be given in the discussion section.

[0207] Ir(z,n = Ae~4a^zEq. 12

[0208] According to Eq. 11 , it is possible to calculate the attenuation inside the medium, only based on the reflected intensity as described by Eq. 13: In many biological tissues, the attenuation a(f) varies almost linearly with frequency such as a(f) = a , allowing to write Eq 14:

[0209] Experiments in a reference gelatin phantom and in human volunteers

[0210] Attenuation measurements using ultrasound plane waves were first performed in gelatin reference phantom. The phantom (Cl RS 040GSE) contains inclusions with different echogenicity, as well as a tissue mimicking background with known attenuation properties. One part of the phantom background has an attenuation coefficient of 0.079 ± 0.006 Np / (cm.MHz) and the other is more attenuating, with a coefficient of 0.107± 0.006 Np / (cm.MHz). The ultrasound imaging probe was placed at the top of the phantom with a thin layer of ultrasound coupling gel. Plane wave images were acquired in the homogenous parts of the phantom as well as along inclusions were both echogenicity and attenuation change locally.

[0211] Experiments were then performed on twelve healthy volunteers. The volunteers were seated and scanned by a trained radiologist. The ultrasound imaging probe was positioned on right side so that the liver and the kidney could be viewed using conventional Bmode imaging. Once the organs were visible, plane wave imaging was used and radiofrequencies signals were acquired for post-processing as described previously. These two organs were chosen because they are easily accessible for ultrasound imaging and they are also the target for many ultrasound-guided HIFII treatments. Moreover, the ultrasound attenuation of both organs is well documented in ex vivo or in vitro studies for comparisons purposes.

[0212] In all cases, the value of each pixel of the image was obtained from a exponential regression on the windowed temporal signal around the pixel. The window width along the acoustic axis was 5 mm in both directions, which corresponds to approximately 17 wavelengths. In the horizontal direction, the width covers a distance of approximately 15 piezoelectric elements. All measured data are given as average values ± standard deviations.

[0213] Histological analysis of liver and renal tissue

[0214] In order to question the validity of the method proposed in this paper, numerical simulation of wave propagation in various soft heterogenous were carried out. To build the heterogeneous medium, histological analysis of kidney and liver tissue was performed, as presented in Figure 8A, 8D. In the case of the liver, the cellular network is isolated from the other structures and considered as the principal scattering source, which is supported by recent findings (Figure 8B). In the case of the kidney, we made the assumption that the thick segments of Henle’s loop (TS) and the collecting ducts (CD) were involved in scattering, due to the important size compared to other structures (Figure 8E). Based on these two binarized maps representing the scattering phase, heterogeneous media were built to mimic this media (Figure 8C, 8F). These heterogeneous media were simplify and made of discrete non-overlapping particles of circular section, in order use a recent multiple scattering numerical model that allows to compute the scattered field in a semi-analytical manner.

[0215] Numerical simulations of backscattered waves in various heterogeneous media

[0216] Numerical simulations were used to verify that the wave backscattered by a plane wave propagating in biological media is also a plane wave. Simulations were carried out using the MuScat calculation code allowing to compute the field scattered by an ensemble of non-overlapping particles excited by an incident harmonic plane wave. It considers particle size, position and multiple scattering effects at all orders. Simulations were carried out in two dimensions (i.e. the scatterers are infinitely long cylinders) and no shear effects are accounted for in the surrounding medium. Scatterers were considered to be fluid particles. The size and acoustic properties of the particles used for the numerical simulations are reported in Table 1. For the sake of simplicity, the host medium properties are assimilated to those of water, with impedance z0= 1.5 MRay. The impedance contrast is defined as yz= (z - z0) / z0.

[0217] Radius a (pm) Impedance Impedance contrast yz(Ray)

[0218] Hepatocytes 12.5 1.83 x 1060.22

[0219] Thick segment of Henle’s 12.0 1.59 x 1060.058 loop (TS)

[0220] Collecting ducts (CD) 22.5 1.59 x 1060.058

[0221] Air filled scatterers 12.5 340 -0.99

[0222] Table 1. Properties of the particles used to simulate the propagation of a plane wave inside a biological tissue. These values closely matched values reported in the literature (see references). Six different conditions were considered in this paper to observe and describe the conditions for which the backscattered wavefront is planar.

[0223] The distributions of scatterers were created based on dense random packings of particles. In order to mimick the tissue of the liver, the liver and renal cortex were analyzed using histological sections of human samples, obtained from a previous study. In the case of the liver, it was assumed that cells and nuclei are strongly involved in scattering. Therefore, histological images were binarized to obtain a continuous two phase medium separating hepatocytes from extracellular matrix. In the case of the renal cortex, CD and TS were assumed to be involved in scattering. These two types of structure being of different size, bi-disperse distributions of particles were built. This is a crucial step to account for the different scattering strength between them.

[0224] Apart from the particle properties, different particle concentration (surface fraction) and source frequency were considered, as reported in Table 2.

[0225] The numerical tool used to perform the simulations accounts for the size of each particle, which leads to an exact description of the scattered field, using a modal decomposition of the fields. Based on that, the differential scattering cross section were evaluated for each type of particles at each frequency.

[0226] Simulation Scatterers Particles

[0227] (organ) concentration

[0228] Frequency (MHz)

[0229] (surface fraction)

[0230] A Hepatocytes (liver) (p = 9% 3.9 (koa = 0.20)

[0231] B Hepatocytes (liver) (p = 45% 3.9 (koa = 0.20)

[0232] C Hepatocytes (liver) (p = 45% 19 (koa = 1.0)

[0233] D CD + TS 3.9 koaCD= 0.37, rp = 34%

[0234] (renal cortex) koaTS= 0.19)

[0235] E CD + TS 19 (koaCD= 1.8, cp = 34%

[0236] (renal cortex) koaTS= 0.96)

[0237] F Air filled scatterers (p = 45% 3.9 (koa = 0.2)

[0238] Table 2. Parameters used to simulate the backscattered waves due to the propagation of an ultrasound plane wave in a medium containing fluid particles. Particles properties are reported in Table 1.

[0239] RESULTS Numerical simulations of backscatte red waves in various heterogeneous media

[0240] Figures 8A-C show the scattered fields from the six different configurations considered in this paper. For the medium made of hepatocytes sparsely distributed (Figure 8A) the backscattered wavefront is divergent. This is due to the lack of spatial correlation between scatterers. Considering the second simulated case at the same frequency but with a particle concentration five times higher (Figure 8B), the backscattering wavefront becomes unambiguously closer to a plane wave, probably because of the relatively well aligned arrangement of scatterers at all depths for this concentration. In this case the waves emitted by all the particles around a given depth are approximately in phase.

[0241] In the third simulation (Figure 8C) the particle concentration is the same than the previous case, and the frequency is higher, such as kGa = -a = 1. In this case the wavelength (A ~ 80 m becomes comparable to the particle size (radius a = 12.5 pm) creating more directional scattering and less in the backward direction. Even if the distribution is the same as (B) and that each particle radiate mostly in the backward direction, the surface is more “rough” at this smaller wavelength : an axial shift in the positions of two particles leads to a stronger phase shift. This result highlights the importance to have relatively small scatterers in the tissue compared to the wavelength. As a result, the wavefront is backscattered in multiple directions. Therefore, a large wavelength compared to the scattering source diameter is favorable to consider the backscattered wave as plane. In the case of the liver, such a wavelength corresponds to the typical frequencies used in ultrasound imaging (3 - 10 MHz).

[0242] In the two next simulations (Figure 9D, 9E), distributions are made of particles of two different size, corresponding to the size of CD and TS (see Table 1) and the impedance contrast is weaker than in the case of the liver. From (D) to (E), the same conclusions as between (B) and (C) can be made : an increase in the frequency leads to a strongly disordered backscattering. It is interesting to note that scattered field (B) and (D) are qualitatively relatively close, despite the fact that in (D) the impedance contrast as the concentration are weaker. Lastly, in Figure 9F is shown the field scattered by an ensemble of air-filled particles. Such particles radiate almost isotropically, as shown by the differential scattering cross-section reported in the inset of the subfigure. Their scattering amplitude is 30 to 60 times greater than the scattering amplitude of the other structures considered in this paper. As a result, this is the only situation for which the backscattered wavefront is higher than the wavefront travelling forward. Lastly, the conclusion regarding the shape of the backscattered wavefront remains the same compared to Figure 9B and 9D.

[0243] These simulations offer a way to assess the physical conditions for which a planar backscattered wavefront appears while a plane wave propagates through a heterogeneous medium. From these results, one can argue that the spatial organization of the particles and the frequency of the source are likely to have a greater influence than the impedance contrast between the particles and the host medium. Further elements of discussions on this will be given in the Discussion section.

[0244] Attenuation measurements in a reference gelatin phantom

[0245] Figures 10A and 10C show the attenuation coefficient maps measured in the homogeneous parts of the reference phantom (i.e. away from the inclusions) presenting two different attenuations. Figures 10B and 10D show a typical line along the 2D maps of Figures 10A and 10C along with the corresponding conventional Bmode image. Attenuation can be calculated only in the far field region by fitting Eq. 12 along the curve.

[0246] A close agreement was observed between average measured values and those provided by the manufacturer of the reference phantom as reported in Table 3.

[0247] Weakly attenuating Strongly attenuating part of the reference part of the reference Inclusions phantom phantom

[0248] 0.079 ± 0.030 0.10 ± 0.030 0.078 ± 0.020

[0249] (Np / cm / MHz))

[0250] Manufacturer

[0251] 0 081 ± 0 008 0.11 ± 0.011 0.081 ± 0.008 specifications (Np / cm / MHz))

[0252] Table 3. Comparison of attenuation values obtained using the method presented in this study and the ones provided by the manufacturer of the reference phantom in two homogenous parts with different attenuation values.

[0253] Figure 11A shows the Bmode image acquired in the part of the reference phantom containing an inclusion with lower attenuation and higher echogeneicity than the background. The attenuation of the three inclusions was 0.081 ± 0.008 Np / (cm.MHz) whereas the attenuation of the background was 0.11 ± 0.011 Np / (cm.MHz). As a result, Figure 11 B shows the decay of the reflected intensity I r discontinuous as a function of depth. Moreover, the different echogenicity appearing at the inclusions (2.5 cm < z < 3.3 cm) and the well-localized spot around z » 3.9 cm are also clearly visible. In this case, the calculation of the attenuation coefficient must be limited to regions at a distance from the interfaces separating zones of different echogenicity in order to avoid misestimating the attenuation coefficient. Although the three inclusions measured less than 1 cm (8 mm in diameter), the exponential decay of Ir allowed to estimate the attenuation in all inclusions. On average the estimated attenuation in the inclusions was 0.078 ± 0.020 Np / (cm.MHz), very close to the one provided by the manufacturer. On the other hand, the spot downstream of this first inclusion is too small to allow precise calculation of the attenuation coefficient, which illustrates one of the limits of the method. Indeed, the spatial resolution can never be smaller than a characteristic length, that is proportional to the extinction mean free path inside the medium and therefore depends on microstructural properties and frequency. In the background the average estimated attenuation was 0.10 ± 0.03 Np / (cm.MHz) which is also very close to the value provided by the manufacturer (0.11 ± 0.011 Np / (cm.MHz)). In vivo attenuation measurements in the liver and the kidney of human volunteers

[0254] The attenuation coefficient maps obtained with the plane wave imaging method in healthy volunteers are described in Figure 12. The corresponding average and standard deviation values are reported in Table 4. Acquisitions were feasible in all volunteers and attenuation maps were created in all cases.

[0255] Attenuation in the liver Attenuation in the cortex

[0256] Volunteer # (Np / (cm / MHz)) part of the kidney

[0257] (n=12) (Np / (cm / MHz)) (n=12)

[0258] 1 0.069 ± 0.035 0.071 ± 0.023

[0259] 2 0.11 ± 0.008 0.074 ± 0.047

[0260] 3 0.091± 0.019 0.045 ± 0.026

[0261] 4 0.097 ± 0.021 0.047 ± 0.023

[0262] 5 0.085 ± 0.022 0.067 ± 0.028

[0263] 6 0.093 ± 0.020 0.076 ± 0.033

[0264] 7 0.097 ± 0.020 0.075 ± 0.020

[0265] 8 0.076 ± 0.030 0.052 ± 0.025

[0266] 9 0.072 ± 0.033 0.059 ± 0.037

[0267] 10 0.064 ± 0.017 0.071 ± 0.016

[0268] 11 0.072 ± 0.015 0.072 ± 0.020

[0269] 12 0.098 ± 0.034 0.075 ± 0.035

[0270] Average measured 0.085 ± 0.023 0.065 ± 0.028 value

[0271] Value sourced from 0.082 + 0.044 0.051 - 0.064 literature Table 4. Average attenuation coefficients measured in the livers and kidneys of three volunteers in comparison with average reported attenuation value sourced from relevant references.

[0272] The intermediate tissues between the skin and the liver are composed of thin layers (between 2 and 10 mm) of different tissues, mainly skin, fat and muscles. In these regions, backscattering intensity cannot be expressed as a plane wave mainly due to stronger scattering events. Therefore, attenuation was not estimated in these tissues. Intermediate tissues between the liver and the kidney were also excluded for the same reasons.

[0273] The average attenuation measured in liver tissues 0.085 ± 0.023 Np / (cm.MHz). This value was relatively homogeneous between volunteers who presented almost the same BMI (in the interval 20-25) with no known pathology. This value is also in agreement with to the ones that can be found in the literature. The average reported attenuation value coming from litterature was calculated to be 0.082 ± 0.044 Np / cm at 1 MHz. In the kidney a large area corresponding to the medulla can be observed in most cases. In this region the attenuation was, as expected, close to 0 due to the presence of urine. It was, however, difficult to quantify precisely this value due to noisy signal in the background. Nevertheless, this is in close agreement with the attenuation values (0.0053 Np / cm at 1 MHz) reported in the literature. In the area corresponding to the cortex, the average attenuation was measured to be 0.065 ± 0.028 Np / (cm.MHz), also close to values from the literature. Moreover, the anisotropy of this tissue explains the strong variations from one measure to another: the uncontrol orientation of the organ during the acquisition leads to variations in the scattering response of the tissue and therefore different attenuation coefficients. This can be explained by the fact that scattering phase of this tissue is composed of cylindrical particles whose scattering properties depend on insonification angle.

[0274] Preliminary results on tumoral tissue:

[0275] Attenuation maps using the plane wave technique were generated in four healthy volunteers. The average attenuation value was 0.10 ± 0.03 Np / (cm MHz), demonstrating the feasibility of real-time attenuation mapping using a conventional ultrasound imaging probe.

[0276] Additionally, attenuation maps were acquired from human breast tissue samples containing tumors. In these cases, attenuation values obtained using the plane wave technique were compared with those measured using the conventional pulse-echo method. In normal tissues, the average attenuation measured with plane waves was 0.17 ± 0.02 Np / (cm MHz), identical to the value obtained with the pulse-echo method, indicating excellent agreement between the two techniques.

[0277] In tumoral tissues, the average attenuation measured with plane waves was 0.31 ± 0.02 Np / (cm MHz), compared to 0.30 ± 0.02 Np / (cm MHz) using the pulse-echo method, also demonstrating excellent concordance between both methods."

[0278] DISCUSSION

[0279] The results presented above demonstrate that, at typical frequencies used for ultrasound imaging (around 5 MHz), a plane wave propagation creates a backscattered plane wave in vivo for specific soft tissues that are structurally homogeneous. For such tissues, like the liver and the kidney, measurement of these backscattered signals is a simple, reliable and efficient technique to estimate ultrasound attenuation in vivo. In vitro experiments in reference phantoms have shown excellent agreements between measured and references attenuation in different regions of different size, echogenicity and attenuation. Our method has also been validated in healthy volunteers by measuring the attenuation of the liver and the kidney with good agreement with previous referenced values. Of particular interest is the simplicity and straightforward implementation of this attenuation measurement. A single round of plane wave imaging is sufficient to obtain backscattered signals and compute the attenuation of the medium whereas existing methods often imply iterative processes, reference medium to consider the diffraction of the emitter. In our method, this single round of measurement allows to obtain a 2D map of attenuation. A synthetic comparison of our method specificities compared to others’ is proposed in Table 5.

[0280] Pulse Spectral (Log) Spectral Shift Plane Wave echo Diff. Method Algorithms Imaging

[0281] Reference medium free Yes No Yes Yes

[0282] Accessible in-vivo No Yes Yes Yes

[0283] Local estimation No Yes Yes Yes

[0284] One acquisition measurement No No No Yes

[0285] Beam compensation required Yes Yes Yes No

[0286] Table 5. characteristics of classical attenuation measurement methods. It is important to point out the conditions for which the method is efficient. To achieve this, let us shortly recall the different propagation regimes inside a heterogeneous scattering medium.

[0287] First, the propagation in a heterogeneous medium depends on the scattering strength of each particle. In the case of a highly scattering medium like the resonant regime of elastic particles immersed in water, localization phenomena can occur. In the weak localization situation, the backscattered signal becomes coherent over an angular range around 0 = TT, creating a cone of coherent backscattering. This effect, would be detrimental for our method since it would make it impossible to consider equation Eq. 11 valid, because the reflection coefficient would in this case be constructed with much more complex paths within the medium than simple round trips. In such systems multiple scattering effects are predominant. The media for which the method can be used are those that are composed of weak scatterers. In the case of a biological tissue, the question of the nature of scatterers remains unclear, but it is likely that cells are highly involved in the scattering response

[0020] , The experimental results presented in this paper support this assumption. In our study, the center frequency of the ultrasonic probe used for imaging was 5.2 MHz, which leads to koa = 0.26 assuming hepatocyte diameter to be in the order of 25 pm. Scattering is weak in this frequency regime for these non-resonant particles that closely match the contrast of the host medium. Therefore, biological tissue such as liver or renal cortex is a very favorable situation for measuring a plane backscattered wavefront. It is likely that this result can be extended to other biological tissues with similar characteristics. This will motivate future work.

[0288] Secondly, the volume fraction (concentration) of scatterers plays also a major role in wave propagation. On one hand, a larger concentration leads to stronger multiple scattering effects, on the other hand it leads to a strong spatial correlation, because the particles cannot overlap. In the low frequency regime, these structural constraints lead to a decrease of attenuation due to scattering, because of destructive interferences between scattered waves. To qualitatively support this interpretation, Figure 13 shows two-dimensional heterogeneous media simulated in this study. In the case of sparse medium, the waves are time shifted and scattered with very different phases, as it is schematically described in Figure 13A. As a result, the reflection coefficient is usually negligible. In this case, the Independent Scattering Approximation (ISA) is valid. This is confirmed by simulation reported in Figure 9A where the particles are sparsely distributed in space (concentration cp=9%), preventing a plane backscattered wavefront from appearing. Furthermore, in a random sparse medium, local density variations are much more important, making ineffective the average process performed between RF signals. Recently published experimental results endorse this interpretation, for a 2D systems made of steel elastic particles immersed in water. Authors show that for cp<10%, measurement of reflection coefficient is hardly achievable because the time signals strongly variate from one position to another.

[0289] As opposed to that, for a denser medium, more sophisticated models are required to properly describe the propagation in the forward direction (coherent wave) or in the backward direction (backscattering). The reflection coefficient can then be written as Eq. (15) where F( ) is the form function of a single spherical scatterer evaluated in the backward direction 0 = TT (0 = 0 corresponding to the incident plane wave). In such dense medium, the position of one particle is constrained by the presence of others (assuming that they cannot overlap). This creates short-range spatial correlations (Figure 13B) and thus a relative low phase shift between all scattered waves at a given depth. This can also be deduced from Eq. 15 since the reflection coefficient varies according to the product of the contribution of a given particle (F(n)) with the concentration of particles cp. This is also shown by the simulations presented in Figure 9(B-F) where the particles are strongly short range correlated, leading to a plane backscattered wavefront.

[0290] Now that several physical explanations of what makes the method presented in this work possible have been proposed, important points have to be drawn from our results. Also, several refinements and uses can be described that will be the subject of future work.

[0291] In this study, no frequency filtering was performed. The attenuation coefficient a0estimated using Eq. 14 is therefore an average attenuation coefficient obtained for frequencies around 5.2 MHz. In tissues where the frequency behavior is highly nonlinear, this procedure needs to be adjusted, by adding a filter to characterize a(f) for narrower frequency window. To this end, the linear approximation used to write Eq. 14 can also be improved by modeling attenuation using a power law, as is frequently done.

[0292] To manage efficient thermal ablation of tumors, it is crucial to know the attenuation contrast between the tumor and its environment. Figure 10 presented in Results section reports also that it is possible to evaluate the attenuation coefficient inside a small area characterized by strong variation of echogenicity and variation of attenuation. On one hand, this endorses the fact that this method could be used for attenuation estimation inside closed areas like tumors.

[0293] On the other hand, it would be also possible to argue that tumor's echogenicity is very heterogeneous and therefore very different from the reference phantom used in this work. For this reason, using Eq. 12 to estimate tumor's attenuation could be much more challenging, if not impossible. It is noteworthy that other studies deal with this problematic, proposing promising new alternative methods. Usually, tumors are immersed in the tissue of a single organ. Therefore, measuring the variation in backscattered intensity between downstream and upstream of the tumor enables to, at least, estimate an average attenuation coefficient that accounts for all absorption and scattering losses within the tumor.

[0294] Lastly, it is important to place this work in perspective with the important challenge of estimating the attenuation inside subcutaneous tissues. These tissues are both very heterogeneous from a structural point of view, and are obviously never surrounded by two tissues of the same type. The conditions detailed in the previous section are therefore not fulfilled for these tissues, this is a limitation of the current procedure. Nevertheless, it would be possible to calculate the attenuation coefficient of these layers by comparing the spectrum of the backscattered signal with that obtained on a reference reflector placed in the water at the distance at which the attenuation coefficient needs to be evaluated. Other methods using focused transducers can also be used to obtain in-vivo attenuation in these subcutaneous tissues that are important for focusing efficacy during HIFU procedure. The combination of plane wave imaging method (for deep organs) to one of these methods (for subcutaneous layers) will provide an efficient procedure for a complete 2D map of attenuation coefficient in-vivo. This is out of the scope of this study and will motivate future work.

[0295] CONCLUSION

[0296] In conclusion, this study demonstrates the feasibility of measuring ultrasonic attenuation in biological tissue using a single plane wave emission. The method was validated on calibrated gels with an accuracy higher than 90%, and images acquired on twelve healthy volunteers support its efficacy for in-vivo characterization of the attenuation in the liver and the renal cortex. In both cases, results were in quantitative agreement with values reported in the literature, which demonstrate the efficacy of the method for these two organs.

[0297] Numerical simulations were presented to support and validate the relevance of the method. If future work will be dedicated to the characterization of other biological tissues, such as breast or pancreas, important elements of thought were given on the conditions for which the method is efficient. Specific tests are now to be conducted in order to characterize complex microstructures such as tumors, with the global objective to improve non-invasive diagnosis and planification of high intensity focused ultrasound treatments.

Claims

CLAIMS1.- Method for determining ultrasonic attenuation of a medium, the method for determining comprising the following steps:- applying a unique ultrasound plane wave on the medium,- collecting the backscattered plane waves from the medium excited by the ultrasound plane wave, and- calculating an attenuation coefficient of the medium from the backscattered signal of the backscattered plane waves.2.- Method for determining according to claim 1 , wherein the step of applying is carried out by an ultrasound probe having several transducers, the step of calculating comprises a sub-step of deducing the backscattered intensity or the backscattered amplitude of the backscattered plane waves based on each radiofrequency signal collected by the transducers.3.- Method for determining according to claim 1 or 2, wherein the ultrasound probe is an array of transducers.4.- Method for determining according to claims 1 to 3, wherein the step of calculating comprises a sub-step of fitting the spatial evolution of backscattered intensity or backscattered amplitude by an exponential function whose one parameter is the value of attenuation and a sub-step of calculating the attenuation coefficient based on the value of absorption by using a relationship between the attenuation coefficient, the value of absorption and the frequency of the unique ultrasound plane wave.5.- Method for determining according to claim 4, wherein the relationship is that the attenuation of the medium is equal to the product of the frequency of the ultrasound wave and the attenuation coefficient.6.- Method for determining according to claim 4, wherein the relationship is that attenuation of the medium is equal to the product of a power of the frequency of the ultrasound wave and the attenuation coefficient.7.- Method for determining according to any one of the claims 4 to 6, wherein the step of calculating comprises a sub-step of determining several areas in the medium, the sub-step of fitting and the sub-step of calculating being achieved for each area, to obtain an attenuation coefficient of the area.8.- Method for determining according to claim 7, wherein the step of calculating comprises a sub-step of obtaining an attenuation coefficient of the medium from the obtained attenuation coefficients.9.- Method for determining according to claim 8, wherein the sub-step of obtaining is carried out by applying a weighted average.10.- Method for determining according to any one of the claims 7 to 9, wherein, for at least one area, the method further comprises a step of comparing the spectrum of the backscattered signal with a reference spectrum to deduce an attenuation coefficient of the area.11.- Method for determining according to any one of the claims 1 to 10, wherein the medium is a biological tissue.12.- Method for determining according to claim 11 , wherein the biological tissue is a tissue chosen among the list constituted of a liver, a pancreas, a breast, a brain and a kidney.13.- System for determining ultrasonic attenuation of a medium, the system for determining comprising :- an ultrasound probe (14) configured to apply a unique ultrasound plane wave on the medium, and- a calculator (16) configured to:- collect the backscattered plane waves from the medium excited by the ultrasound plane wave, and- calculate an attenuation coefficient of the medium from the backscattered signal of the backscattered plane waves.

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