Total Attenuation Compensation for Backscatter Coefficient Estimation Using Full Angular Spatial Compounding

Abstract

The backscatter coefficient (BSC) quantifies the frequency-dependent reflectivity of tissues. Accurate estimation of the BSC is only possible with the knowledge of the attenuation coefficient slope (ACS) of the tissues uncer examination. In this study, the use of attenuation maps constructed using full angular spatial compounding (FASC) is proposed for attenuation compensation when imaging integrated backscatter coefficients. Experimental validation of the proposed approach was obtained using two cylindrical physical phantoms with off-centered inclusions having different ACS and BSC values than the background, and in a phantom containing an ex vivo chicken breast sample embedded in an agar matrix. With the phantom data, three different ACS maps were employed for attenuation compensation: (1) a ground truth ACS map constructed using insertion loss techniques, (2) the estimated ACS map using FASC attenuation imaging, and (3) a uniform ACS map with a value of 0.5 dBcm⁻¹MHz⁻¹, which is commonly used to represent attenuation in soft tissues. Comparable results were obtained when using the ground truth and FASC-estimated ACS maps in term of inclusion detectability and estimation accuracy, with averaged fractional error below 2.8 dB in both phantoms. Conversely, the use of the homogeneous ACS map resulted in higher levels of fractional error (> 10 dB), which demonstrates the importance of an accurate attenuation compensation. The results with the ex vivo tissue sample were consistent with the observations using the physical phantoms, with the FASC-derived ACS map providing comparable BSC images to those formed using the ground truth ACS map and more accurate than those BSC images formed using a uniform ACS. These results suggest that BSCs can be reliably estimated using FASC when a self-consistent attenuation compensation stemming from prior estimation of an accurate ACS map is used.

1. Introduction

For a propagating wave in a scattering medium, such as soft tissues, the frequency-dependent backscatter coefficient (BSC) is a quantitative ultrasound (QUS) feature that describes how a medium reflects the incident ultrasonic energy [1]. Parameterizing the BSC enables the estimation of relevant properties such as the scatterer correlation length and acoustic concentration [2]. The feasibility of characterizing soft tissues from their estimated BSCs was reported in the late 1980s, and the derived scatterer properties have been correlated to histology in the cases of the myocardial muscle [3] and the renal cortex [4]. The BSC has shown promise for improving the diagnosis of pathologies in the liver [5], lymph nodes [6], thyroid [7], and breast [8].

Angular compounding extends the trade-off between estimation precision and spatial resolution in spectral-based QUS such as the BSC estimation. This effect was demonstrated theoretically and experimentally in [9] for the case of two scan lines with a variable angular separation (from 0° to 10°), and has been used for BSC imaging and attenuation coefficient imaging [10–14]. Only a few studies have reported the use of full angular spatial compounding (FASC) - i.e., collecting data at scanning angles ranging between 0° and 360° - when estimating attenuation coefficient slope (ACS) [15] and/or BSCs [16]. Also, the full angular coverage was evaluated in the estimation of a BSC-derived parameter, the effective scatter size [17], when attenuation compensation was negligible. Therefore, FASC has potential in tissues where full angular field of view is attainable, like in breast imaging. However, one of the limitations for BSC estimation in vivo is the inability to properly compensate for the ultrasonic attenuation losses from attenuation of the intervening tissue layers between the transducer and a region of interest, named the total attenuation.

One approach used to compute the total attenuation for BSC estimation consists of using attenuation coefficient values reported in the literature ([18, 19]) for the tissue intervening layers [20, 21]. A second approach is the joint estimation of total attenuation and BSC where the calibrated spectrum is fit to a model that assumes all intervening tissues have attenuation coefficients with linear dependencies on frequency [22, 23]. A third approach is to utilize attenuation maps from an ultrasound tomography system where the attenuation is estimated from the transmitted signal rather than the backscatter [24, 25]. These approaches typically use sources of around 1 MHz in order to ensure sufficient signal-to-noise ratio (SNR) for parameter estimation. However, it is often desired to quantify the BSC at higher frequencies. A fourth approach is based on creating maps from local ACS estimates [26] and computing the total attenuation coefficient as the cumulative sum of the local attenuation map values. The latter method has the potential to be the most robust, provided a local attenuation map with sufficient precision and accuracy can be generated. Moreover, in cases where FASC approaches might not be feasible to improve the quality of ACS maps, further optimization approaches, based on piece-wise homogeneity assumptions of acoustic properties within the media, have been developed to improve significantly the precision of ACS estimates by factors between 2 to 5 [27, 28].

Therefore, the present study explores a potential strategy for BSC tissue characterization where the ACS map required for total attenuation, similar to [26], was estimated using the FASC approach and subsequently used for the total attenuation required in the BSC estimation. Moreover, the BSC is computed using the FASC configuration. The method was tested using two calibrated cylindrical physical phantoms with an embedded low-contrast inclusion and one ex vivo chicken breast sample embedded in an agar/graphite matrix. The results using FASC and a reconstructed total attenuation map for compensation of the BSC were compared to the cases when the actual spatial map of attenuation was known and when a uniform attenuation map was used having an assigned attenuation value that was characteristic of soft tissue.

2. Spectral-based estimation formalism

In this study, the methods were tested using data acquired with a single-element transducer and therefore all methods for QUS parameter estimation employ the substitution method with a planar reference of known reflectivity. This study is a proof-of-concept of the proposed methods, whereas potential usage in clinical applications would require using array transducers as in [16].

2.1. Backscatter coefficient estimation

The BSC curve from a data block at depth z, denoted by η(z, f), can be estimated using [1]

$$\eta (z,f)=\frac{\langle |S(z,f){|}^2\rangle }{{\left|S_{\text{ref}}(F,f)\right|}^2}\frac{D_{\text{ref}}(2F,f)}{A(z,f)L{D}_s(z,f)},$$ (1)

where f is the ultrasonic frequency, $\langle |S(z,f){|}^2\rangle$ is the averaged power spectrum of the gated scan lines within the data block, |S_ref(F, f)|² is the reference power spectrum acquired from the planar reflector at the focal length, F. A(z, f) is the total attenuation, L is the axial length of the gated window, and D_ref(2F, f) is the acoustic coupling function defined as

$$D_{\text{ref}}(2F,f)={\left|1-e^{-i{G}_p(f)}\left[J_0\left(G_p(f)\right)+i{J}_1\left(G_p(f)\right)\right]\right|}^2,$$ (2)

where J_m is the m-th order Bessel function of the first kind. The effects of diffraction are corrected using

$$D_s(z,f)\cong \{\begin{array}{l}0.46\frac{\pi a^2}{z^2}\exp \left[\frac{-0.46}{\pi }{G}_p^2(f){\left(\frac{F}{z}-1\right)}^2\right],\\ {\left(1+\frac{\pi }{G_p(f)}\right)}^{-1}<\frac{z}{F}<{\left(1-\frac{\pi }{G_p(f)}\right)}^{-1}\\ \frac{\pi a^2}{z^2}1.07{\left[G_p(f)\left(\frac{F}{z}-1\right)\right]}^{-2},\\ \text{otherwise,}\end{array}$$ (3)

$$G_p(f)=\frac{\pi a^2}{\left(c_0/f\right)F},$$ (4)

The total attenuation compensation function used is given by

$$A(z,f)=\exp \left[-4\sum _q{\alpha }_{q}f\text{Δ}z\right]{\left(\frac{1-e^{-\alpha FL}}{\alpha FL}\right)}^2,$$ (5)

where Δz is the axial step employed for space discretization in the axial direction and a_q is the ACS of the medium at location z_q = qΔz, with q = 1, 2,... representing the corresponding numerical position in the discretized ACS map. Each a is the frequency-dependent attenuation coefficient over a window obtained from the available ACS map.

2.2. Attenuation coefficient slope estimation

ACS maps were constructed from regions of uniform scattering properties. Each attenuation coefficient slope from these spatial locations can be computed using the spectral log difference technique that requires he division of a range gate of length L into two sub-windows of equal length called proximal window (notation with subscript p) and distal window (notation with subscript d). This technique is based on the comparison of the averaged power spectrum from the sub-windows [29], i.e.,

$$\frac{\langle {\left|S\left(z_d,f\right)\right|}^2\rangle }{\langle {\left|S\left(z_p,f\right)\right|}^2\rangle }=\frac{A\left(z_d,f\right)\eta \left(z_d,f\right)D_s\left(z_d,f\right)}{A\left(z_p,f\right)\eta \left(z_p,f\right)D_s\left(z_p,f\right)}.$$ (6)

If the condition of homogeneity in the scatterer size distribution is satisfied within the data block, $\eta \left(z_p,f\right)=C\eta \left(z_d,f\right)$ where C is a multiplicative constant and therefore

$$C\frac{A\left(z_p,f\right)}{A\left(z_d,f\right)}=\frac{\langle {\left|S\left(z_p,f\right)\right|}^2\rangle D_s\left(z_d,f\right)}{\langle {\left|S\left(z_d,f\right)\right|}^2\rangle D_s\left(z_p,f\right)}.$$ (7)

The ratio of cumulative attenuations in (7) can be simplified as

$$\frac{A\left(z_p,f\right)}{A\left(z_d,f\right)}=e^{4\alpha (f)\left(z_d-z_p\right)}.$$ (8)

Applying the natural logarithm to (7) results in

$$\frac{1}{4\left(z_d-z_p\right)}\ln \left[\frac{\langle {\left|S\left(z_p,f\right)\right|}^2\rangle D_s\left(z_d,f\right)}{\langle {\left|S\left(z_d,f\right)\right|}^2\rangle D_s\left(z_p,f\right)}\right]=\alpha (f)+\ln C.$$ (9)

The effects of the diffraction can be calculated using (3) and (4). Therefore, the attenuation coefficient can be estimated from (9). The frequency dependence of attenuation coefficients in soft tissues is often modeled as a power law. However, when dealing with an experimentally bounded bandwidth, a linear model is sufficient to describe the frequency-dependent attenuation coefficient [30] (i.e., $\alpha (f)={\alpha }_{0}f$, with ${\alpha }_0$ the ACS).

3. Materials and methods

3.1. Soft tissue-mimicking phantoms

Two agar-based tissue-mimicking phantoms were employed and designed with the same cylindrical shape consisting of a 70-mm diameter background with an off-centered 25-mm inclusion (see Fig. 1). Attenuation and backscatter coefficients for each region were varied by using different concentrations of graphite powder (for the inclusion and background of the first phantom, P1, the concentrations were 0.12 and 0.04 gr/mL, respectively, whereas these values were 0.08 and 0.02 gr/mL for the second phantom, P2).

Figure 1:

Schematic representation of the tomographic acquisition. A single-element transducer was moved laterally along the x-axis from −43 to +43 mm. This procedure was repeated at N=30 orientation angles (θ) with a 12° angular step (Δθ).

The ground truth values for the speed of sound and attenuation coefficient of background and inclusion regions of the phantoms were estimated using insertion-loss techniques [31] by measuring the arrival times from the echo from a Plexiglas planar reflector located at the transducer focal length in the case of the speed of sound and the exponential loss (dB) of the spectral content for attenuation, when a piece of the sample is located between the transducer and reflector. A 7.5-MHz, f/4 single-element transducer (Olympus Corporation, Waltham, MA, USA) was employed together with a 5900PR pulser/receiver unit (Panametrics Olympus, USA). The diameter of the transducer active surface was 18 mm and its focal length was 72 mm. RF signals were recorded using a UF3–4121 14-bit digitizer PCI-X card with a 250-MHz sampling frequency (Strategic Test Corporation, Woburn, MA, USA). For all regions, the speed of sound was measured at 1482 m/s and did not change with graphite concentration [32]. The ACS values for P1 and P2 are summarized in Table 1. The ground truth curves for the BSCs from each region were estimated over the frequency range of 4 to 9 MHz using the methods in [1] by placing the center of each phantom region sample at the transducer focal length [33]. The procedure is the same as described in section 2.1 but because just a small piece of sample is used during data acquisition, we can compensate accurately the cumulative attenuation with the known ACS value of such sample. The estimated BSC curves are presented in Fig. 2. The estimated values of ACS and BSC obtained here were used for the purpose of quantitative assessments and referred to as ground truth values for the remainder of this study.

Table 1:

ACS in dBcm⁻¹MHz⁻¹ for the background and the inclusion in the two cylindrical phantoms P1 and P2 using through transmission technique. The standard deviation of these values was approximately 0.01 dBcm⁻¹MHz⁻¹ out of 10 values.

	P1	P2
Background	0.41 dBcm−1MHz−1	0.54 dBcm−1MHz−1
Inclusion	0.75 dBcm−1MHz−1	1.04 dBcm−1MHz−1

Figure 2:

BSC curves of background and inclusion regions for both physical phantoms used in this study (see Section 3.1).

3.2. Ex vivo soft tissue

An additional experiment was conducted using a chicken breast sample embedded in an agar matrix mixed with graphite (with concentration 0.008 gr/mL) to increase ultrasonic attenuating properties. The tissue sample was placed to have the muscle fibers oriented perpendicular to the ultrasound beam. The ground truth values corresponding to the ACS of the chicken breast sample and the agar matrix, obtained with the same method described in the previous subsection, were 1.21 and 0.25 dBcm⁻¹MHz⁻¹, respectively. Similar to the procedure from the earlier phantoms, the BSC curves obtained as ground truth are shown in Fig. 3. Noisier BSC curves with respect to the phantoms are due to less spectral averaging of the power spectra used in (1).

Figure 3:

BSC curves of background and ex vivo sample used in the chicken breast phantom (see Section 3.2).

3.3. Full angular spatial compounding

3.3.1. Acquisition procedure

Data acquisition was performed with the same equipment used for FASC data acquisition described in section 3.1. Each phantom was immersed in a water tank and scanned using a micro-positioning system controlled by custom LabVIEW software (National Instruments, Austin, TX) as depicted in Fig. 1.

In this work, a total of N=30 angular views with a 12° angular step (Δθ) was used. This configuration provided the best trade-off between variance reduction and acquisition time in previous studies using an f/4, 10 MHz transducer [17]. Although some differences in performance are expected due to the use of a different center frequency and focal length, the configuration was considered suitable for the current proof-of-concept study. For each view, 173 RF lines were obtained by translating the transducer from −43 to +43 mm with a 0.5-mm step along the x-axis. B-mode representations of each phantom are provided in Fig. 4 for the first angular position (θ=0°) of the acquired data set.

Figure 4:

B-mode images corresponding to the first angular view at θ=0°. The phantom P1 and the phantom P2 are the two top figures. Regions of same area as the inclusions were chosen in the background for computation of metrics. The agar-embedded breast chicken phantom is represented below. The dynamic range in the B-mode images is 60 dB.

3.3.2. Full angular spatial reconstructions

3.3.2.1. Window rejection criteria.

Because of acoustic attenuation, the signal-to-noise ratio (SNR) becomes too low for QUS estimation as the data block depth increases. Both the ACS and BSC were estimated over a frequency range of 4 to 9 MHz for the phantoms P1 and P2, and a frequency range of 5 to 9 MHz for the chicken phantom (due to the less attenuating values of the background used for ex vivo) following a −15 dB bandwidth criterion, which enabled QUS analysis down to the center of all phantoms. Estimates from a data block were considered in the FASC process only if SNR>20 dB within the analysis bandwidth.

3.3.2.2. Attenuation coefficient slope map.

Attenuation coefficient slopes for each incidence angle were estimated using 6.5-by-6.5 mm data blocks with an 87.5% overlap in both axial and lateral directions. Given the high standard deviation of the ACS values in the single-angle ACS images of around 0.6 dB/cm/MFz for this data block size, the FASC ACS values were calculated as the median of all single-angle estimates corresponding to a given data block.

3.3.2.3. Backscatter coefficient map.

Backscatter coefficients were estimated using 2.3-by-2.3 mm data blocks with a 75% overlap in both axial and lateral directions. The compensation of the total attenuation along the ultrasonic path was conducted using (5), with the path between transducer and data block being water or the cylindrical phantom. For the water path we used an attenuation of 0.002/² dB/cm, with f the frequency in MHz, whereas for the cylindrical phantom part we used the ACS map pixel values in the path. The FASC BSC vaiues were calculated as the average of all single-angle estimates corresponding to a given data block located at position (x,z). The integrated backscatter coefficient (iBSC) [34] was then derived from the BSC curves using

$$iBSC(x,z)=\frac{1}{f_2-f_1}\underset{f_2}{\overset{f_1}{\int }}\eta (x,z,f)df,$$ (10)

where f₁ and f₂ are the lower and upper bounds of the analysis bandwidth.

3.3.2.4. Assessment of the estimated maps on phantoms.

To evaluate the ability to perform quantitative characterization, the error in the iBSC parameter was determined in each data block using the local fractional error (LFE) in decibels between the estimated and ground truth iBSC values (iBSCo),

$$\text{LFE}(x,z)=\left|10{\log }_{10}\left(\frac{\text{iBSC}(x,z)}{{\text{iBSC}}_0(x,z)}\right)\right|.$$ (11)

In addition, the ability to differentiate the inclusion and the background in the QUS maps was evaluated using the contrast-to-noise ratio (CNR) [35]

$$\text{CNR}=\frac{\left|{\mu }_I-{\mu }_B\right|}{\sqrt{{\sigma }_I^2+{\sigma }_B^2}},$$ (12)

where μ and σ are the average and standard deviation of the parameter, respectively. The subscripts I and B correspond to the values in the inclusion and the background regions, respectively.

For comparison, two other approaches for attenuation compensation were employed. In the first approach, ground truth ACS maps were constructed using knowledge of the geometry and ground truth ACS values of the phantoms. In the second approach, the ACS was assumed to be constant throughout the phantoms and equal to 0.5 dBcm⁻¹MHz⁻¹, i.e., a common ACS value for soft tissues [19]. A value of 2×10⁻³ dBcm⁻¹MHz⁻² [36] was used to compensate for attenuation in the water path.

3.4. Results

3.4.1. Soft tissue mimicking phantoms

The estimated FASC ACS maps for phantoms P1 and P2 are presented in Fig. 5. The average, standard deviation and the relative error of the estimated ACS values for the inclusion and background are summarized in Table 2. The relative error was less than 5% with respect to the through transmission measurements in every case. The CNR was 1.27 and 1.91 for P1 and P2, respectively.

Figure 5:

Estimated map of the ACS using FASC for agar phantoms P1 (top) and P2 (bottom). Thirty angular views were compounded to form the presented images. Note: Median filter with window 3×3 used for better visualization.

Table 2:

Estimated ACS in dBcm⁻¹MHz⁻¹ for the background and the inclusion using FASC. The average, the standard deviation (first line) and the relative error in percent (second line) are provided for the two phantoms.

	P1	P2
Bkgnd.	0.40±0.19 dBcm−1MHz−1	0.53±0.16 dBcm−1MHz−1
	(−2.4%)	(−1.9%)
Inclusion	0.74±0.19 dBcm−1MHz−1	0.99±0.18 dBcm−1 MHz−1
	(−1.3%)	(−4.8%)

The average BSC curves in the background (plain line) and the inclusion (dashed line) are plotted in Fig. 6 along with the ground truth BSC curves (black color) for both phantoms P1 and P2. The BSC estimates obtained with total attenuation derived from FASC ACS maps provide similar performance to the BSC estimates obtained with total attenuation derived from ground truth ACS maps. In contrast, the uniform map resulted in the largest mismatch of the BSC curve of the inclusion for phantom P2 although for P1 the BSC was relatively close to ground truth BSC curves.

Figure 6:

Average BSC curves in phantoms P1 (a, b, c) and P2 (d, e, f) calculated in the background and inclusion regions. The standard deviation of the BSC at particular frequencies is given using an error bar representation. The BSCs were obtained by employing the ground truth ACS map (a, d), the FASC ACS map (b, e), and a uniform ACS map (c, f). The dashed lines correspond to the inclusion region, and plain lines to the background region; black lines are the ground truth BSC curves (see Fig. 2), and colored curves are for the estimated BSC curves.

Figures 7 and 8 present the iBSC maps for phantoms P1 and P2, respectively, together with the corresponding fractional error images in decibels. Visually, using the FASC ACS map for total attenuation compensation generated iBSC maps with better contrast. The CNR improved a factor of 2.3 and 17 for P1 and P2, respectively, when comparing the FASC-based attenuation map versus the uniform attenuation (see Table 4). The mean LFE values of reconstructed iBSC maps when using the FASC ACS map for compensation were generally worse than using the ground truth ACS map (which was expected) but this difference was less than 1.6 dB. However, the use of the uniform ACS map for total attenuation compensation resulted in the largest differences of LFE compared to the use of the ground truth ACS map, e.g., LFE was 2.2 dB larger for the background of P1 and 8.9 dB larger for the inclusion of P2 (see Table 3). The use of FASC ACS maps for attenuation compensation also resulted in an appropriate depiction of the iBSC profiles passing through the center of the inclusion (close to the ground truth ACS case) and more accurate than using merely uniform ACS maps, as evidenced in Fig. 9

Figure 7:

Phantom P1 - The iBSC maps (top) and the LFE expressed in dB (bottom) are presented when the ultrasonic attenuation compensation was performed using (a, d) the ground truth ACS map, (b, e) the FASC ACS map and (c, f) a uniform ACS map.

Figure 8:

Phantom P2 - The iBSC maps (top) and the LFE expressed in dB (bottom) are presented when the ultrasonic attenuation compensation was performed using (a, d) the ground truth ACS map, (b, e) the FASC ACS map and (c, f) a uniform ACS map.

Table 4:

CNR of the iBSC maps (Figs. 7 and 8) when employing different ACS maps to compensate for attenuation during the BSC estimation process.

	P1	P2
Ground truth ACS map	4.42	2.86
FASC ACS map	3.05	2.29
Uniform ACS map	1.32	0.13

Table 3:

LFE (11) in decibels of the iBSC when employing different ACS maps to compensate for the attenuation in the BSC estimation process.

	P1		P2
	Inclusion	Bkgnd.	Inclusion	Bkgnd.
Ground truth ACS map	0.8 dB	0.7 dB	1.3 dB	1.2 dB
FASC ACS map	1.6 dB	1.6 dB	2.0 dB	2.8 dB
Uniform ACS map	0.8 dB	2.9 dB	10.2 dB	2.5 dB

Figure 9:

Representation of the iBSC profile passing through the center of the inclusion in the case of the (a) P1 and (b) P2. The ground truth value iBSC₀ is represented in thick black line and indicates the actual location of the inclusion in the background. The local iBSC estimations were performed by employing three methods of attenuation compensation, namely the ground truth ACS map, the FASC ACS estimated map and the uniform ACS map represented in green, blue and orange lines, respectively.

3.4.2. Ex vivo soft tissue sample

The resulting FASC ACS image of the chicken breast sample is presented in Fig. 10. The average and standard deviation was 0.22±0.32 dBcm⁻¹1MHz⁻¹ and 0.83±0.43 dB cm⁻¹MHz⁻¹ in the background and in the chicken breast tissue. Based on preliminary characterization, the corresponding relative error in the background and chicken breast tissue are −12% and −31.4%, respectively, with CNR of 1.15.

Figure 10:

Estimated map of the ACS in the embedded chicken breast in an agar-based matrix. Note: Median filter with window 7×7 used for better visualization.

Following the previous approach, the frequency dependent BSC curves were estimated for a segmented region of the chicken breast and the image plane using the ground truth ACS map and the estimated map presented in Fig. 10. The average BSC curves for background and chicken breast are presented in Fig. 11 when using the ground truth ACS map, the FASC ACS map and the uniform ACS map for total attenuation compensation. From Fig. 11(c) the largest mismatch with respect to the ground truth BSC curves were observed.

Figure 11:

Average BSC curves calculated in the chicken breast and background regions. The standard deviation of the BSC at particular frequencies is given using an error bar representation. The BSCs were obtained by employing the ground truth ACS map (a), the FASC ACS map (b), and a uniform ACS map (c). The dashed lines correspond to the chicken breast, and plain lines to the background region; black lines are the ground truth BSC curves (see Fig. 3), and colored curves are for the estimated BSC curves.

The iBSC maps and fractional error maps are presented in Fig. 12. In spite of the moderate variance in the estimated FASC ACS map, its usage resulted in iBSC images that resembled the iBSC map using the ground truth ACS map. The largest fractional error 9.8 dB was observed using a uniform ACS map (see values from Table 5), which is 8.1 dB larger than in the ground truth ACS case and 8.4 dB larger than the FASC ACS map case. On the other hand, the CNR of the iBSC maps were 2.54, 1.07, and 2.41 for the ground truth, FASC, and uniform ACS maps, respectively. Hence, the FASC ACS map did not improve the CNR possibly due to large variance of the iBSC maps within the segmented ex vivo sample.

Figure 12:

Ex vivo - The iBSC maps (top) and the LFE expressed in dB (bottom) are presented when the ultrasonic attenuation compensation was performed using (a, d) the ground truth ACS map, (b, e) the FASC ACS map and (c, f) a uniform ACS map.

Table 5:

LFE (11) in decibels of the ex vivo iBSC maps when employing different ACS maps to compensate for the attenuation in the BSC estimation process.

	Ex vivo
	Inclusion	Background
Ground truth ACS map	1.9 dB	1.7 dB
FASC ACS map	4.1 dB	1.4 dB
Uniform ACS map	2.0 dB	9.8 dB

4. Discussion

The accurate estimation of the BSC requires knowledge of the attenuation coefficient of the interrogated medium in order to compensate for attenuation effects. It has been reported that compounding decreases the variance in both the estimation of local attenuation [9–15] and BSC-based parameters [17]. The present study explored the estimation of compounded ACS maps and their use for attenuation correction when estimating iBSC images when full angular compounding was available.

As expected, the use of ground truth ACS maps resulted in the overall best performance when compared to using the FASC and uniform ACS maps in terms of CNR and in LFE, except in the background of breast chicken sample, by a marginal difference of 0.3 dB (see Table 5). The use of ground truth ACS maps for attenuation compensation also resulted in an appropriate depiction of the iBSC profiles, as evidenced for phantoms P1 and P2 in Fig. 9, with the spatial resolution limited by the size of the data blocks [26].

The performance of iBSC imaging using the FASC ACS images for attenuation compensation resulted in a similar performance when compared to using the ground truth ACS maps. The images in Figs. 7(b), 8(b), and 10 as well as the profiles in Fig. 9, demonstrate that the visual appearance of the reconstructed iBSC images had comparable quality to their ground truth compensated counterparts. The maximum difference in iBSC LFE was 2.2 dB in the inclusion of the chicken breast sample. These results are significant because in practice the ground truth ACS maps will not be available for attenuation compensation. Therefore, the use of FASC ACS maps appears to be a more suitable alternative than the uniform ACS map.

The results obtained with the uniform ACS map (i.e., constant ACS of 0.5 dBcm⁻¹MHz⁻¹) did not follow a trend. In phantom P1 the chosen uniform ACS value was higher than in the background region (i.e., 0.41 dBcm⁻¹ MHz⁻¹). Thus, the BSC magnitude in the background region was overcompensated (see profile in Fig. 9, top). In the case of phantom P2, the uniform ACS value of 0.5 dBcm⁻¹ MHz⁻¹ was close to the true attenuation in the background (i.e., 0.54 dBcm⁻¹ MHz⁻¹). As a result, the BSC estimates in the background region were not distant from the ground truth ACS or FASC ACS cases. On the other hand, an important mismatch occurred for the inclusion of phantom P2 $(\langle \text{LFE}\rangle =10.2\text{dB})$ because of the corresponding under compensation of attenuation in this region. This resulted in a poor inclusion detectability in phantom P2. These observations demonstrate the importance of correctly compensating for frequency-dependent attenuation losses in BSC estimation and the potential limitations of non-subject-specific attenuation compensation.

For the chicken breast phantom, the FASC ACS maps presented larger variance (see Fig. 10) than the tissue-mimicking phantoms P1 or P2. Hence, although the reconstructed iBSC map (Fig. 12(b)) resembled the reconstruction with the ground truth ACS map, and outperformed those LFE maps obtained using a uniform ACS map, there is still room for improvement. For example, using compounding with more views (than the 30 used in this study) could improve the performance of the ACS map reconstruction. Large variances of the ACS maps from the chicken breast phantom (0.43 dBcm⁻¹ MHz⁻¹ in the sample and 0.32 dBcm⁻¹ MHz⁻¹ in the background) may be due to the limited uniformity of scattering properties in the data blocks of the ex vivo sample and could have played a role in the underestimated BSC curves results obtained in the inclusion region of Fig. 11. On the other hand, better reconstructed iBSC maps were obtained using the ground truth ACS map because the insertion loss value 1.21 dBcm⁻¹ MHz⁻¹ was closer to literature values for this type of soft tissues 1.24 ± 0.10 in the range 5 to 9 MHz [37]. In order to further reduce the variance of the FASC ACS map, spatial filtering or slightly larger data block sizes for ACS maps might be used.

In this study we chose the spectral log difference technique for the estimation of the ACS. The compounding principle can be applied with other attenuation estimation techniques as long as they allow estimating ACS values in sufficiently small data blocks to get a spatially resolved parametric image. Similarly, alternative geometries of transducers could be used whereas beam diffraction corrections could be performed with a reference phantom [38] instead of a single-element theoretical diffraction function. In this way, one could imagine the transfer of the ACS and BSC procedures developed in this study to an ultrasound computed tomography system for breast imaging using a rotating transducer array [39], or circular antenna with a full or partial angular coverage [40–43]. Application of the proposed technique could provide improved attenuation imaging for ultrasound computed tomography and provide additional diagnostic information with accurate frequency-dependent BSC estimation.

5. Conclusion

The usefulness of the full angular spatial compounding for improved spectral-based tissue characterization was explored in this study. The experimental results from two tissue-mimicking phantoms and one chicken breast phantom suggest that the use of ACS maps derived using full angular spatial compounding allowed compensating total attenuation effects when estimating BSCs. The performance obtained with this approach was comparable to the results obtained with the knowledge of the ground truth ACS maps and outperformed the case where the iBSC was obtained using pre-selected uniform attenuation coefficient slope maps.

Highlights:

• Full angular spatial compounding (FASC) for ultrasonic tissue characterization

• FASC attenuation maps can be used to calculate the total attenuation compensation

• FASC attenuation compensation produce accurate backscatter coefficient estimates

• Uniform attenuation maps can produce biased backscatter coefficient estimates