
==== Front
Ultrason Sonochem
Ultrason Sonochem
Ultrasonics Sonochemistry
1350-4177
1873-2828
Elsevier

S1350-4177(24)00250-5
10.1016/j.ultsonch.2024.107002
107002
Bioeffects of ultrasonic
Ultrasonic Nakagami imaging for automatically positioning and identifying the treated lesion induced by histotripsy
Han Meng 9906069@haust.edu.cn
a⁎
Song Weidong a
Lei Kun a
Cai Bianyun a
Qin Dui duiqin@cqupt.edu.cn
bc⁎
a School of Medical Technology and Engineering, Henan University of Science and Technology, Luoyang 471023, People’s Republic of China
b Department of Biomedical Engineering, School of Life Health Information Science and Engineering, Chongqing University of Posts and Telecommunications, Chongqing, People’s Republic of China
c Postdoctoral Workstation of Chongqing General Hospital, Chongqing, People’s Republic of China
⁎ Corresponding authors at: School of Medical Technology and Engineering, Henan University of Science and Technology, Luoyang 471023, People’s Republic of China (M. Han). 9906069@haust.edu.cnduiqin@cqupt.edu.cn
25 7 2024
10 2024
25 7 2024
109 10700228 9 2023
9 7 2024
23 7 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Histotripsy has been proposed as a non-invasive surgical procedure for clinical use that liquefies the tissue into acellular debris by utilizing the mechanical mechanism of bubbles. Accurate and reliable imaging guidance is essential for successful clinical histotripsy implementation. Nakagami imaging is a promising method to evaluate the microstructural change induced by high intensity focused ultrasound. However, practically, it is difficult for the Nakagami imaging to distinguish the treated lesion induced by histotripsy from the surrounding normal biological tissues. In this study, we introduce the use of noise-assisted correlation algorithm (NCA) in Nakagami images as a solution to suppress the background normal tissue and identify the treated lesion induced by histotripsy. Experiments are conducted on fresh porcine liver ex vivo by cavitation-cloud histotripsy. Results show that the contrast-to-noise ratio between the treated lesion and surrounding tissue corresponding to the Nakagami image after NCA and original Nakagami image is 3.434 and 0.505, respectively. The optimal artificial noise level is 1-fold of the background normal tissue amplitude, and the corresponding optimal threshold of correlation coefficient should be between 0.6 and 0.8 in the application of NCA. Therefore, the use of NCA in Nakagami image can suppress the background normal tissues without affecting the information of treated lesion for an appropriate artificial noise level and threshold used in the NCA. Moreover, the Nakagami images after the application of the NCA can also be used for automatically distinguishing and measuring the tissue fractionation accurately using binarization. The proposed Nakagami images overlaid on the B-mode images can provide a promising method for positioning and visualizing the treated lesion to achieve precise histotripsy treatment.

Keywords

Nakagami imaging
Histotripsy
Tissue fractionation detection
Noise-assisted analysis
==== Body
pmc1 Introduction

High intensity focused ultrasound (HIFU) is a promising modality for noninvasive treatment. It has been used in clinics for ablating localized solid tumors without damaging the surrounding vital structures. Thermal ablation is conventionally used for HIFU ablation in clinical applications, which converts the ultrasound energy into heat, causing targeted tissue coagulation necrosis [1]. In recent years, new therapeutic applications of histotripsy have been proposed and evaluated for clinical use [2].

Histotripsy is a therapeutic ultrasound procedure that liquefies the tissue into acellular slurry via the formation and collapse of microbubbles clouds, which exert a mechanical load on the soft tissues [3], [4]. Compared to the HIFU thermal ablation, histotripsy therapy does not generate the heat accumulation at the target sites and surrounding tissues, and is unaffected by heat-sink effects from blood perfusion. Moreover, the produced acellular slurry by mechanical mechanism can be reabsorbed by the body [5]. Histotripsy therapy is used for treating tumors [6], [7], thrombosis [8], [9] and stimulation of immune response [10] in preclinical and clinical trials.

In clinical implementation of histotripsy, real-time and accurate imaging techniques are essential to ensure the success of a treatment by monitoring and assessing its progress. At present, the HIFU treatment is guided by magnetic resonance (MR) imaging and diagnostic ultrasound in clinical practice. Unlike the conventional HIFU thermal therapy, the major mechanism of histotripsy is mechanical that does not create any temperature rise in tissues [11]. Therefore, the imaging methods that exploit the temperature sensitivity, such as the MR thermometry [12], cannot be used for visualizing the histotripsy. In the absence of any heat deposition and temperature buildup, the bubble cloud is the only observable mechanism that exerts an influence on localized tissue during histotripsy [13]. Therefore, only the bubble clouds and their effects on the localized tissue can be used for histotripsy guidance [14].

The ultrasound imaging guidance can allow the HIFU, particularly the histotripsy, to be applied to treat larger and multiple tumors over a longer time duration, and has distinct advantages over the MR guidance, such as low cost and good portability [15], [16]. Ultrasound imaging can be used to visualize the bubble clouds generated during the histotripsy for precise targeting. The hyperechoic region can be used to indicate the bubbles in B-mode images [15], and the bubble cloud can be mapped by passive cavitation detection [17]. The B-mode ultrasound can be also used to assess the change in tissue characteristics according to the reduction of backscatter amplitude during the histotripsy exposure. Histotripsy-induced tissue fractionation generally appears hypoechoic in ultrasound image, which is caused by the breakdown and mixing of tissue structure and the reduction of the backscattering cross-sectional area in the liquefied region [18], [19].

However, it is not sufficiently sensitive to detect the disrupted tissues caused by histotripsy during the early stage of the treatment [20]. This is because the bubble cloud generated during histotripsy is displaced as an echogenic region in the B-mode image [14]. At the early stage of the histotripsy treatment, the location of hyperechoic region in the B-mode image corresponds well to the location of the resulting lesion, but its size is overestimated [15]. The acoustic shadowing of bubbles generated during histotripsy may prevent the complete feedback of tissue fractionation in the B-mode imaging. Therefore, although the change in tissue characteristics can be visualized with B-mode imaging, it cannot be targeted precisely at the early stage of the treatment. Thus, the only use of changes in backscatter amplitude of B-mode image is frequently insufficient for reliable detection of histotripsy therapy [21]. It is necessary to develop more sensitive imaging techniques for accurate monitoring and evaluation of histotripsy treatments. Various quantitative ultrasound methods have been developed to supplement the diagnosis of B-mode images and provide the information relating to the tissue characteristics [20], [21], [22], [23].

Nakagami imaging is a promising imaging method for monitoring and evaluating tissue fractionation induced by histotripsy. Previous study has shown that Nakagami imaging is an effective method for enhancing the lesion-to-bubble ratio (LBR) during HIFU thermal ablation [24]. Moreover, the Nakagami parameter can be used to distinguish thermal coagulation induced by thermal ablation and tissue fractionation induced by histotripsy [22]. Nakagami imaging is the formation of Nakagami parameter map, which applies the Nakagami statistical distribution to model the probability density function of ultrasound backscattered echoes [25]. The Nakagami parameter is the shape parameter of Nakagami statistical distribution, which is determined by the scatter concentration and independent of echo intensity. It is related to the tissue microstructure and can be used for tissue characterization [26], [27].

The Nakagami imaging has been used for differentiating between various types of backscattered statistics in order to classify tissues, such as breast mass [28], [29], [30], liver fibrosis [31], [32], [33], carotid plaques [34] and thermal ablation [35], [36], [37]. The Nakagami parameter can be used for identifying the tissue structural changes. The histotripsy changes the tissue structure by liquefying cellular tissues into acellular homogenous slurry. Therefore, the Nakagami imaging may be a promising method for monitoring and assessing histotripsy treatment. However, it is difficult to practically use the Nakagami images for distinguishing the treated region from the surrounding soft tissues due to the inhomogeneous Nakagami values of biological tissues [22].

Normal soft tissues typically contain a large number of randomly distributed scatterers. The statistics of ultrasonic backscattered envelope signals from these tissues follow the Rayleigh distribution, behaving similar to the statistics of demodulated white noise [38], [39]. In this paper, we introduce the noise-assisted correlation algorithm (NCA) for suppressing the surrounding normal soft tissue. The use of this algorithm facilitates the detection of tissue fractionation and extends the use of Nakagami imaging for monitoring and evaluating histotripsy. We investigate the feasibility and practical performance of NCA for the suppression of the surrounding normal tissues in Nakagami images during the histotripsy treatment. Experiments are performed on fresh porcine liver ex vivo by cavitation-cloud histotripsy, and the radio frequency (RF) data are acquired immediately after histotripsy by the ultrasound imaging system. The effects of the added artificial noise level and the threshold value of correlation coefficient in the NCA on the tissue fractionation detection accuracy and sensitivity are discussed. The purpose of this work is to provide an ultrasonic Nakagami imaging method for positioning and evaluation of tissue fractionation sensitively and accurately at the early stage of histotripsy treatment.

2 Materials and methods

2.1 Experimental setup

Experiments were performed in a transparent tank (50 cm × 30 cm × 28 cm) filled with degassed and deionized water. The experimental setup for histotripsy ablation of porcine liver ex vivo primarily consisted of three main parts: histotripsy system, ultrasound imaging system, and the tissue samples preparation.1) Histotripsy system

An arbitrary waveform generator (AWG2021, Tektronix, Beaverton, OR, USA) and a power amplifier (AG1017, T&G Power Conversion, Rochester, NY, USA) were used to generate and amplify the exposure pulses, respectively. The amplified signals were used by a single-element concave HIFU transducer (Imasonic, Besancon, France) to induce lesion in the treated samples, where the central frequency, outer diameter and focal length of the transducer were equal to 1.6 MHz, 140 mm and 75 mm, respectively. The histotripsy was performed using a pulse sequence of 10 µs pulse duration and 2 % duty cycle at the electric power levels of 200 W and 240 W. The entire treatment duration took 60 s.2) Ultrasound imaging system

A SonixRP ultrasound imaging system (Ultrasonix Medical Corp., Richmond, BC, Canada) was used for the B-mode imaging and acquiring the ultrasonic RF data. A linear array probe (L14-5/38 probe, 7.5 MHz center frequency, 65 % bandwidth) was fixed along the HIFU axis, which ensured the imaging plane all along the HIFU focus for visualizing the treatment region. It worked at a frequency of 10 MHz. Finally, the RF data were acquired immediately after the HIFU transducer was switched off to avoid any disturbance from the HIFU excitation. The RF data were stored in a computer for the B-mode imaging and off-line Nakagami imaging.3) Tissue samples preparation

The fresh porcine liver was obtained from a local abattoir on the same day as the experiments and kept in a physiological saline solution (0.9 %) before the experiments. This tissue preservation method could maintain the tissue functionality for up to 72 h [40]. The porcine livers were cut into samples of equal size (approximately 50 mm × 50 mm × 60 mm), and placed in a vacuum chamber and degassed for 30 min. The tissue samples were fixed at the focus of HIFU transducer during the experiments.

2.2 Nakagami distribution and parametric imaging

Various statistical distributions have been proposed in the literature for modeling the probability density function (pdf) of the ultrasound backscattered echo envelope to provide the biological tissue information. The Nakagami distribution covers the pre-Rayleigh, Rayleigh and post-Rayleigh distributions, has a comparatively lower computational complexity and can be used to describe most medical ultrasonic envelopes. Therefore, it is widely used to model of the ultrasound backscattered signals statistically for tissue characterization.

The pdf of the ultrasonic backscattered envelope r based on the Nakagami distribution is given by [25](1) f(r)=2mmr2m-1Γ(m)Ωmexp-mΩr2U(r)

where Γ(·) and U(·) are the gamma function and the unit step function, respectively, m is the shape parameter and Ω is the scaling parameter.

The shape parameter m, also known as the Nakagami parameter, can be used to classify the tissues with different scatterer densities. It was demonstrated in [28], [41] that the shape parameter of Nakagami distribution depended only on the size, shape and concentration of scatterers. Denoting E(·) as the statistical mean, the Nakagami parameter m can be obtained as follows:(2) m=[E(r2)]2E[r2-E(r2)]2

The Nakagami imaging using the sliding window method is a typical technique that has been described in earlier research [26]. The backscattered envelopes are collected with each window and used for estimating the local Nakagami parameter m, which is the pixel of Nakagami image located in the center of the window. The window is moved by one-pixel in each step, and the above process is repeated until all the ultrasonic enveloped data have been collected. Finally, the Nakagami image can be constructed using the Nakagami parameter map. The Nakagami parameter is generally obtained using estimators, such as the moment or maximum likelihood estimators. The estimation method used in this study is the inverse normalized variance (INV) estimator, which is one of the most basic and widely used moment estimators [42].

2.3 Nakagami imaging after NCA

Previous study has demonstrated that the Nakagami imaging has an outstanding ability to distinguish between various scatterer properties for tissue characterization [41]. Therefore, Nakagami imaging is a promising tool to complement the B-mode imaging for visualizing histotripsy treatment. However, in practical scenarios, the Nakagami imaging cannot properly identify the area treated by histotripsy from the surrounding normal tissues. Note that the statistics of biological tissues that generally contain homogeneous scatterers with similar echogenicity follow the Rayleigh distribution, which is similar to the demodulated white noise statistics [38], [39]. Therefore, the background tissues in the Nakagami images is an impediment to monitor and evaluate histotripsy in practical biological tissue treatment.

In this paper, we introduce the NCA to suppress the background normal tissues in the Nakagami images, where the artificial white noise is added to the original ultrasound RF data to produce two noisy RF datasets. The correlation coefficients between these two datasets are calculated using a sliding window. The normalized correlation profile along the ultrasound beam is given by [43](3) ρ1,2[n]=∑k=1+(n-1)ΔLo+nΔ(S1[k]-S¯1n)·(S2[k]-S¯2n)∗∑k=1+(n-1)ΔLo+nΔ(S1[k]-S¯1n)2·∑k=1+(n-1)ΔLo+nΔ(S2[k]-S¯2n)2;n=1...N-LwΔ+1

where n denotes the number of the sliding windows, and S1[k] and S2[k] denote the two noisy RF datasets, respectively, and k represents the sample number along the beam. Furthermore, S¯1n and S¯2n are the means of the S1[k] and S2[k] in the sliding window n, respectively, Δ=Lw-Lo, where Lw is the number of samples per window, and Lo is the number of overlapping samples (Lo<Lw). The symbol ∗ denotes the complex conjugate.

Fig. 1 illustrates the NCA processing method proposed in this paper. It is based on the noise randomness and noise-assisted analysis. The Nakagami imaging process after the application of NCA involves seven steps: 1) First, ultrasonic RF data are acquired by the ultrasound imaging system and demodulated using the Hilbert transform to obtain the envelope data. Subsequently, the B-mode image is constructed through log-compression and median filter; 2) A rectangular region of the background normal tissue is manually chosen from the B-mode image, and the corresponding region of the RF data is used to calculate the signal power value of the background normal tissue; 3) White Gaussian noise with a given power is generated and added to the original RF data to produce the first noisy RF data, and the step is repeated to produce the second noisy RF data; 4) The correlation coefficients of the two noisy RF data are calculated using a sliding window to establish their correlation coefficients map; 5) A threshold value is chosen, and the amplitude of the corresponding RF data is set to zero when the correlation coefficient is less than the threshold. The NCA is applied to the RF data; 6) The RF data after the application of the NCA are demodulated into the envelope data using the Hilbert transform, and the envelope data are used for the Nakagami imaging. Subsequently, the Nakagami image is constructed using the sliding window method; 7) The Nakagami image of the tissue fractionation region is overlaid on the B-mode image with a certain degree of transparency for positioning the tissue fractionation more directly.Fig. 1 Illustration of the NCA process, B-mode image and Nakagami image reconstruction.

2.4 Performance evaluation

1) Contrast-to-noise ratio

The degree of background normal tissues suppression by the NCA is evaluated using contrast-to-noise ratio (CNR), which indicates the contrast between the tissue fractionation (F) and background region (B). The CNR is obtained as follows [44], [45]:(4) CNR=μF-μBσF+σB

where μ and σ represent the mean and standard deviation of the Nakagami parameters in the corresponding region, respectively.2) Lesion-to-bubble ratio

The LBR is used to evaluate the contrast between the tissue fractionation (F) and bubbles as follows [24]:(5) LBR=20log10IFIbubble

where IF and Ibubble represent the average amplitudes in the tissue fractionation and bubble regions, respectively, corresponding to the B-mode and Nakagami images.3) Treated area comparison

Tissue fractionation areas measured from the B-mode images, Nakagami images and Nakagami images after the NCA application are compared with the actual treated area. The specified threshold is used to transform the Nakagami images into binary images, which can then be used to automatically extract tissue fractionations from the background. The treated area is automatically measured in mm2 units using the ImageJ software (National Institutes of Health, USA, http://imagej.nih.gov/ij). The treated area is marked manually in both the photos of tissue sections and B-mode images, where the area in the photos is considered as the actual treated area. The lesion area in the B-mode images and the photos are also measured using the ImageJ software.

3 Results

Fig. 2 shows the B-mode image and Nakagami image of treated lesion in the porcine liver ex vivo obtained immediately after the histotripsy treatment. In the B-mode image (Fig. 2(a)), the bright hyperechoic area is identified as the treated area [15] and delineated by a red line. In the Nakagami image (Fig. 2(b)), the treated area is indicated by a solid white line. However, it is difficult to distinguish the treated region from the background normal tissue in the Nakagami image. A further quantitative comparison between the Nakagami parameters in the treated lesion and normal tissue is carried out. A square region with a size of 8 mm is randomly chosen in the normal tissue as the region of interest (ROI), shown in Fig. 2(b) by the white dotted line. Fig. 2(c) and (d) show the corresponding histograms of the Nakagami parameters for the normal tissue and the treated lesion, respectively. The Nakagami parameters of the normal liver tissue and the treated lesion are concentrated between 0.5 and 1.5 with the average values of 0.986 ± 0.368 and 1.117 ± 0.238, respectively. The range of Nakagami parameters in the treated lesion is similar to that of the background normal tissue, which increases the difficulty of lesion identification.Fig. 2 Performance of imaging evaluation of histotripsy in porcine liver ex vivo. (a) B-mode image, (b) Nakagami image, the histograms of Nakagami parameter in region of (c) background (ROI), (d) treated lesion (solid white line).

We analyze the use of NCA for suppressing the background normal tissues to enable effective identification of the treated region. The power of RF signal from the normal tissue corresponding to the ROI in Fig. 2(b) is estimated. The estimated power is used to generate artificial white Gaussian noise, which is added to the original RF data twice to produce two noisy RF data. The original RF data corresponding to the white dotted line in Fig. 2(a) and the noisy RF data are shown in Fig. 3(a) and (b), respectively. The correlation profile of the two noisy RF data is depicted in Fig. 3(c). The correlation coefficients of the backscattered signals corresponding to the treated lesion are higher than 0.8, while those from the normal tissue are obviously less than 0.8. Therefore, the RF data with correlation coefficients less than 0.8 [46] are replaced by a zero amplitude, and the obtained result is shown in Fig. 3(d). The RF data processed by the NCA show that the backscattered echoes corresponding to the normal tissue are replaced by an ideal dc baseline, and the echoes corresponding to the treated lesion exhibit no deformation after the application of the NCA.Fig. 3 A typical illustration of the backscattered signal processed by NCA. (a) original RF data, (b) one of the two noisy RF data, (c) correlation profile for two noisy RF data, (d) RF data after NCA.

Next, we further compare the potential of using the original Nakagami images and those obtained after the application of NCA for identifying the region treated by histotripsy. Porcine liver samples are treated by histotripsy using different electric power levels, and Fig. 4 shows the corresponding B-mode image, original Nakagami image and the Nakagami image obtained after the NCA application. It can be observed that the background normal tissue is almost completely suppressed after the application of NCA and it is easy to recognize the treated region. A further quantitative analysis of the effect of NCA on the Nakagami parameters in the treated region is performed by extracting and comparing the Nakagami parameters curves corresponding to the white dotted line in the original Nakagami image and that obtained after the application of NCA. The treated lesions can be hardly distinguished from the background normal tissue in the original Nakagami image, while the Nakagami parameter of background normal tissue is replaced by a dc baseline after the application of the NCA. Moreover, the Nakagami parameters associated with the treated region remain unchanged. Therefore, the NCA can effectively suppress the background normal tissues from the Nakagami images and accurately identify the lesion treated by histotripsy.Fig. 4 B-mode image, original Nakagami image and Nakagami image after NCA of porcine livers ex vivo treated by histotripsy at electric power of 240 W (a, b) and 200 W (c, d). The Nakagami parameter profile corresponding to the white dotted line in Nakagami image (original and after NCA) was extracted.

The threshold setting of correlation coefficients is important for background suppression. Fig. 5 shows the original Nakagami image (Fig. 5(a)) and those obtained after the NCA processing with different threshold values (Fig. 5(b)). When the threshold is smaller, the background normal soft tissues are not completely suppressed. As the threshold value increases, the background tissues are gradually suppressed without any changes in the texture of the treated region. However, the area of the treated region is smaller when the threshold value is higher than 0.8. To quantitatively evaluate the effect of the threshold value on the Nakagami images after the application of the NCA, the average values of the Nakagami parameters are calculated in the treated and background regions. Furthermore, the CNR of the Nakagami image is estimated to evaluate the performance of the proposed method and analyze the influence of threshold selection.Fig. 5 Performance comparison among Nakagami images (a) original, (b) after NCA application using different correlation threshold values when the added noise level equal to the power of background tissue.

Fig. 6 shows the curves of the average Nakagami values for the treated and background regions (Fig. 6(a)) and the corresponding CNR of the Nakagami image (Fig. 6(b)) as a function of threshold value, when the added noise amplitude is equal to the background amplitude. The average and standard deviation values of the Nakagami parameters of the background normal tissue generally decrease with the increasing threshold, indicating that a higher proportion of background normal tissues is suppressed as the threshold increases. However, the Nakagami parameter of the target lesion decreases when the threshold is higher than 0.8. Fig. 6(b) shows that the CNR of the Nakagami image processed by the NCA increases with the increasing threshold, and reaches the maximum value of 3.434 when the threshold is equal to 0.6. Therefore, the optimal threshold is between 0.6 and 0.8 when the added noise amplitude is equal to that of the background normal tissues.Fig. 6 Quantitative evaluation of threshold values on Nakagami images after NCA. (a) the mean and standard deviation of Nakagami parameters in lesion region and background as a function of threshold, (b) CNR of Nakagami image as a function of threshold.

The amplitude level of artificial noise added to the RF data is another factor affecting the suppression of background tissue. Fig. 7 shows the correlation profiles of the two noisy RF data processed using the NCA (Fig. 7(b)). These RF data correspond to the white dotted line in Fig. 7(a) and are added noise with different levels. When the added noise level is less than 0.4, the coefficient values in the lesion and background regions are hardly distinguishable. When the added noise level increases, the lesion region can be distinguished from the background. However, it should be noted that when the noise level is higher than twice the background tissue amplitudes, the correlation coefficients of some part of the treated lesion area is lower than 0.5, which may be recognized as possible noise. Therefore, the added noise level range should be between 0.4 to twice the background normal tissue amplitude.Fig. 7 Performance evaluation of the added noise level on the correlation coefficient. (a) B-mode image, (b) the correlation profile of the noisy RF data corresponding to the scan line (white dotted line in (a)) using different noise levels.

Next, the effect of the added noise level on the capability to distinguish between the background normal tissue and lesion region is quantitatively analyzed. Fig. 8(a) shows the correlation coefficients map corresponding to Fig. 7(a) when the added noise level is equal to the power of the background normal tissues. The mean and standard deviation values of correlation coefficients in the normal tissue (ROI1) and treated lesion (ROI2) are calculated at different added noise levels and shown in Fig. 8(b). The correlation coefficients of the treated lesion and the background decrease as the added noise level increases. A higher difference between these coefficient values is helpful for distinguishing the lesion region from the background region. This difference at first increases and then decreases with the increase of the added noise level, and reaches the maximum value when the added noise level is equal to the power of background normal tissue.Fig. 8 Comparison of correlation coefficient between background region and treated region. (a) correlation coefficient map when the added noise level equal to the power of background, (b) correlation coefficient as a function of added noise level for background region (ROI1) and treated region (ROI2). Error bars present mean ± standard deviations.

Fig. 7 shows that the optimal threshold should change according to the added noise level. To conveniently implement the proposed method, the relationship between various added noise levels and the corresponding optimal threshold is evaluated and shown in Fig. 9. The optimal threshold decreases as the added noise level increases. Curve fitting using linear regression shows that the correlation coefficient is equal to 0.997. The results show that the added noise level and the corresponding optimal threshold are linearly related when the added noise level is between 0.2 and 1.8 times the background normal tissue amplitude.Fig. 9 The optimal threshold as a function of the added noise level. The expression between the added noise level and the optimal threshold are given at the top right.

The background can be suppressed and the backscattered signals from the treated region remain unaffected after NCA processing. However, it is difficult to position the treated region in the Nakagami image obtained after the NCA processing because there is no normal tissue information. Therefore, the processed Nakagami image is added to the B-mode image, which is shown in Fig. 10(c), while Fig. 10(a) and 10(b) depict the actual B-mode image and the Nakagami image after the NCA processing, respectively. Fig. 10(c) is helpful for simultaneous identification and positioning of the treated lesion. Fig. 10(d) shows the magnified local region at the edge of the treated area in the B-mode and Nakagami images. The average amplitudes of ROI1 and ROI2 in the B-mode images are 84.939 and 86.756, respectively. The results show that the average the grayscale values of the bubbles and lesion area are similar, and the LBR in the B-mode image is 0.184. The average Nakagami values of ROI1 and ROI2 are 0.652 and 1.676, respectively. The results further show that the Nakagami values of bubbles and lesion are obviously different, and the LBR is 8.201. Moreover, the average Nakagami value of ROI1 is lower than 0.70, which indicates that the ROI1 actually corresponds to the bubbles [47]. Therefore, the Nakagami image after the NCA processing is also helpful for identifying the tissue erosion caused by the bubbles in the treated region.Fig. 10 The ultrasonic image for positioning and detecting tissue fractionation. (a) B-mode image, (b) Nakagami image after NCA, (c) ultrasonic image superposition, (d) the boundary of the treated region were zoomed in to emphasis the different performance between bubbles and tissue fractionation in B-mode image and Nakagami image.

The Nakagami images before and after the NCA processing are binarized using the optimal threshold of 0.7, as shown in Fig. 11. The tissue erosion induced by the histotripsy can be automatically identified, and the lesion area measured by the ImageJ software is equal to 5.421 mm2. The lesion region in the original Nakagami image is delineated manually, and the measured lesion area is 5.613 mm2. Comparing the measured lesion areas obtained from different images with the actual area (measured from the tissue section), the area values measured from the Nakagami images are closer to the actual area (5.367 mm2), while that in the B-mode image is considerably different (11.429 mm2). The Nakagami image can also be used for automatic identification and measurement of the tissue fractionation area accurately.Fig. 11 Measurement of the treated lesion area using different imaging methods. The measured area by photo of tissue section is considered as a criterion.

4 Discussion

4.1 Performance of the proposed method

The Nakagami parameter can be used to evaluate the formation of thermal lesion caused by the HIFU in the presence of strong shadowing effect of bubbles [37]. Therefore, the Nakagami imaging may also be used for monitoring and evaluating the histotripsy to identify tissue fractionation from the bubbles. However, it is difficult to identify the treated region from the Nakagami images due to the influence of background normal tissue (Fig. 2(b)). Considering the earlier analysis, we introduce the NCA to suppress the background normal tissue in the Nakagami images to enable their use in accurate visualization of the tissue fractionation caused by histotripsy.

The objective of the NCA is to establish the correlation profile for removing the background normal tissue without any change in the information of treated lesion. The normal soft tissues typically contain homogeneous scatters with similar echogenicity, while the statistics of soft tissues follow the Rayleigh distribution [48]. Moreover, the echogenicity of the treated lesion is higher than that of the background tissues at the early stage of histotripsy [15]. Thus, an appropriate level of white noise added to the backscattered signals may cause the background normal tissue to have a low degree of correlation. Based on the difference of correlation between the background tissue and treated lesion, we can remove the corresponding signals from the background normal tissue by choosing the correlation threshold.

Fig. 3 shows the addition of white Gaussian noise to the original RF data, where the amplitude of noise is similar to that of the normal tissues. Fig. 3(c) shows the correlation profile of the two noisy RF data. The added noise amplitude is relatively small for the lesion region and, therefore, the corresponding signals of the treated region in the noisy RF data (Fig. 3(b)) are almost identical to that in the original RF data (Fig. 3(a)). Consequently, the correlation coefficients are high and almost equal to 1. On the other hand, the correlation coefficients of the normal tissues are less than 0.8. The normal tissue can be removed from the original RF signals by choosing the threshold values (Fig. 3(d)). Therefore, the NCA allows suppressing the background normal tissue without changing the information of the treated region.

The results in Fig. 4 confirm that the Nakagami image obtained after the NCA processing can suppress the background normal tissue without changing the Nakagami parameter of the treated region. The processed Nakagami image is helpful for identifying the lesion treated by histotripsy. Fig. 6(b) shows that the CNR of the original Nakagami image is 0.505, while the maximum CNR of the Nakagami image after the NCA application is 3.412. This comparison highlights that the contrast between the treated lesion and normal tissue improves significantly after the NCA processing.

Threshold selection and the white Gaussian noise level added to the RF data are two crucial factors that affect the success of the background tissues suppression by the NCA. Therefore, we further explore the influence of these two factors on the Nakagami images. It can be observed that the threshold should neither be too small nor too large (Fig. 5). The background normal tissue cannot be suppressed completely for a low threshold. However, when the threshold is excessively high, some information in the treated region is also suppressed. Based on the quantitative results depicted in Fig. 6, the optimal threshold should be between 0.6 and 0.8 when the added noise level is equal to the amplitude of the normal tissues.

Next, the noise level added to the RF data is investigated. Fig. 7 shows that the added noise level affects the performance of the proposed method as well as the choice of threshold. When the added noise level is lower than 0.4 times the normal tissue amplitude, the lesion cannot be identified because the difference between the background and treated lesion is very small. When the added noise level is larger than twice the normal tissue amplitude, some parts of the signals backscattered from the lesion are obscured by noise. Furthermore, the correlation coefficients in the lesion region also decrease as the added noise level increases(Fig. 8). A larger difference between the correlation coefficients of normal tissues and lesion is more helpful for distinguishing the lesion from the background. However, when the noise level is exceed twice the amplitude of normal tissues, the correlation coefficients of normal tissues remain relatively constant. Therefore, the appropriate noise level added in the NCA processing should be between 0.4 to twice the amplitude of normal tissues. Meanwhile, the optimal threshold should change with the added noise level, and the relationship between both is linear. According to the trend shown in Fig. 9, the initial threshold can be chosen based on the amplitude of the added noise level in the practical applications.

4.2 Application and significance

The proposed Nakagami imaging method has been shown to be helpful in identifying the lesion treated by histotripsy. However, it is difficult to find the lesion location by only using the processed Nakagami image (Fig. 10(b)), because the NCA suppresses the background normal tissues. Therefore, the Nakagami image (Fig. 10(b)) is added to the B-mode image (Fig. 10(a)), and the result is shown in Fig. 10(c). The ultrasonic image superposition is helpful for identifying the treated lesion as well as for directly positioning the treated region using pseudo-color coded display. The bubbles and the treated lesion are both hyperechoic during the histotripsy [15], [49]. Some studies have demonstrated that the Nakagami parameter of bubbles induced by the HIFU is less than 0.7 even for high bubbles concentration [47]. The region, whose Nakagami value is lower than 0.7 in the treated region, can be considered as the bubble cloud. Moreover, the LBR in the Nakagami image is apparently higher than that in the B-mode image (Fig. 10(d)), indicating that the Nakagami imaging helps in increasing the contrast between tissue fractionation and bubbles. The results show that the Nakagami image after the application of NCA is also helpful for distinguishing the treated lesion from surrounding bubbles during histotripsy.

A comparison of lesion area measured from the original Nakagami image and that processed by the NCA (Fig. 11) shows that the measured areas from both images are approximately identical, indicating that the NCA does not cause any change in the treated lesion area. Moreover, the area measured from the Nakagami image after processing by the NCA is closer to the actual area than that measured from the B-mode image, indicating the potential of Nakagami imaging for accurate detection of lesion induced by histotripsy. The binarization of the processed Nakagami image using a suitable threshold can also be utilized for automatic identification and measurement of the tissue fractionation area. The threshold for identifying the tissue fractionation from bubbles is determined by the window size for Nakagami imaging.

4.3 Limitations of the study

In the experiments of this study, the imaging plane and the tissue slice plane are maintained at the same position as much as possible to achieve a precise comparison. However, the slicing and imaging planes in an actual operation may still be different, resulting in the inconsistency of lesion shape and size between the ultrasound images and the tissue section. In the future, further experimental setup and other measurement details should be considered. Moreover, in vivo animal experiments will be conducted to further investigate the performance of the proposed ultrasonic Nakagami imaging technique for evaluating and monitoring the histotripsy treatment.

5 Conclusion

This study proposed the use of NCA on the Nakagami images to improve the identification of the treated region from the background normal soft tissue at the early stage of histotripsy treatment. Based on the noise randomness and the amplitude difference between the normal tissue and treated lesion during histotripsy, white Gaussian noise with amplitude level similar to the background normal tissue was added to the RF data, and the correlation coefficients were calculated for suppressing the background normal tissues using threshold filtering. The application of the NCA to the Nakagami images could suppress the background normal tissue without changing the Nakagami parameter of the treated lesion. The amplitude level of the added white noise and the threshold for suppressing the background normal tissues were explored to enable successful suppression of the background without changing the information of treated region. Results showed that the optimal threshold was related to the added white noise amplitude level. Moreover, it was also shown that the added white noise amplitude level should be chosen between 0.4 to twice the background normal tissue amplitudes. The ex vivo experiments demonstrated that the Nakagami images after the use of NCA could be used for accurate visualization of the treated lesion from the background normal tissue. The ultrasonic image superposition of the B-mode and processed Nakagami images could be useful in positioning and monitoring the histotripsy treatment. The processed Nakagami image may be a supplementary ultrasound imaging method for identifying and visualizing the tissue fractionation accurately to improve the precision of histotripsy treatment.

CRediT authorship contribution statement

Meng Han: Conceptualization, Data curation, Funding acquisition, Methodology, Visualization, Writing – original draft, Writing – review & editing. Weidong Song: Methodology, Software, Validation. Kun Lei: Supervision, Validation. Bianyun Cai: Supervision, Validation. Dui Qin: Conceptualization, Funding acquisition, Resources, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgements

This work was supported by the 10.13039/501100017700 Henan Provincial Science and Technology Research Project (No. 222102310314 and No. 212102310234 ), the Henan Province Natural Science Foundation (No. 242300420423 ), the 10.13039/501100002858 China Postdoctoral Science Foundation (2022MD723728 ) and the Natural Science Foundation Project of Chongqing (CSTB2023NSCQ-MSX0861 ).
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