Sound speed imaging of small animal organs by ultrasound computed tomography

■ An ultrasound computed tomography system with a 256-element ring array transducer was developed for sound speed imaging and evaluation of small animal organs. ■ Sound speeds of five excised rat organs were imaged and measured and the results are consistent to published data. ■ This work demonstrates a new method for sound speed imaging and holds potential for in vivo applications. Abstract: Sound speed is an important acoustic parameter for tissue characterization. Herein we developed an ultrasound computed tomography (USCT) system for ex vivo sound speed imaging and evaluation of small animal organs. The proposed USCT system employs a 256-element ring array transducer and allows simultaneous signal transmission and reception for all channels. The method does not require complicated sample preparation procedures and can yield accurate measurement results. Experimental results show that sound speeds of excised rat brain, heart, liver, spleen, and kidney measured by the method are close to published data. This work demonstrates a new method for sound speed imaging and holds potential for in vivo applications.


Introduction
Sound speed (c) is an important acoustic parameter of biological tissues. It relates to two fundamental tissue properties, the elasticity (K) and the density (ρ) through the formula c = (K/ρ) 1/2 . Since elasticity and density usually change with tissue state, the value of sound speed is helpful to reflect the pathophysiological condition of tissues and can be used as an important measure for disease diagnosis [1−5] . In particular, tissues with a high protein content usually have a higher sound speed while tissues (e.g. fat) with a high lipid content have a lower sound speed. Bamber and Hill showed that normal human livers have an average sound speed of 1577 m·s −1 while fatty livers have an average value of 1553 m·s −1 [6] . It is also clear that cancerous breast tissue has an average sound speed of 1559 m·s −1 and is different from that in surrounding fat (≈ 1470 m·s −1 ) and glandular tissues (≈ 1515 m·s −1 ) [7] . Based on these facts, there are several groups worldwide working to map the sound speed distribution of breast tissues for noninvasive early cancer diagnosis [7−9] .
In addition to probing the pathophysiological state of tissues, sound speed information is also important for image formation. In conventional ultrasound and photoacoustic imaging, soft tissue is usually assumed to be homogeneous and a constant sound speed is used for image reconstruction. However, actual biological tissues are heterogeneous and the sound speed in soft tissues varies significantly, which may yield substantial image distortion and artifacts and lead to degraded image contrast and resolution [10−13] . Accurate mapping of the sound speed of biological tissues is important for highquality ultrasound and photoacoustic imaging.
Current sound speed measurement methods can be mainly divided into two groups, i.e., average sound speed estimation and local sound speed estimation. The average methods, such as beam tracking [14] , transaxial compression [15] and phase variance [16] , estimate the average sound speed between a transducer and its focal depth. These methods can produce accurate measurement results for homogenous media but may yield significant errors for in vivo measurements due to tissue heterogeneity [17] . The local sound speed estimation methods, such as the model-based method [17] , the crossed-beam method [18] and the registered virtual detector method [19] are based on the pulse-echo principle and estimate sound speed in a localized target area [20] . These methods can provide improved sound speed measurement accuracy in a local area when tissue heterogeneities are present but they are not able to visualize entire sound speed maps of biological tissues. Compared with these methods, scanning acoustic microscopy can realize sound speed map imaging but needs special sample preparation procedures [21] , which is not suitable for in vivo measurements.
Ultrasound computed tomography (USCT), first proposed by Greenleaf et al. [22] is a technique that works similarly as Xray computed tomography and can produce accurate sound speed maps of soft tissues. USCT typically employs an array transducer, which consists of hundreds to thousands of elements. During imaging, one element of the array emits ultrasonic signals while the facing elements receive the signals. By repeating this process for each element and extracting the travel time of the signals from the emitters to the receivers, a sound speed tomogram can be reconstructed using geometrical acoustics or full-wave inversion based methods [7,23] . Based on this principle, Rajagopalan et al studied the dependence of sound speed with temperature in various excised human tissues in 1979 [24] . However, limited by transducer technology, electronics, and computing power, they only used a pair of transducers to perform the measurements. The imaging process was slow and the image quality needs improvement.
The objective of this study is to perform ex vivo imaging of the sound speed distribution of different organs and tissues of small animals using state-of-the-art USCT technology and provide reference data of sound speed for the medical ultrasound community. Towards this goal, we developed an advanced USCT system using a full ring array transducer and imaged the sound speed maps of different types of organs of normal rats, including the brain, heart, liver, spleen, and kidney. Average sound speed values were calculated and compared with published data.

Method
The USCT system developed to image the sound speed map of isolated organs and tissues is shown in Fig.1a. The system consists of the following parts: A water bath, a custom ring array ultrasound transducer, a research ultrasound platform, and a host computer. The water bath is filled with an ultrasound coupling medium and is equipped with a temperature controller, which can maintain the temperature of the coupling medium at 37 ± 0.2 ℃ for tissue imaging. The coupling medium used in this study is either water for gelatin phantom imaging or phosphate-buffered saline (PBS) for tissue imaging, whose acoustic properties have been well studied [25,26] . The ring transducer array (diameter: 50 mm; center frequency: 3 MHz; element number: 256; Guangzhou Doppler Ltd., Guangzhou, China) is immersed in the water bath and is connected with the research ultrasound platform (Vantage 256, Verasonics Inc., WA, USA). The research ultrasound platform can perform real-time multichannel ultrasound transmission and reception through the ring array transducer and transfers received radiofrequency data to the host computer for image reconstruction.
The height h and width w of each transducer element are 10 mm and 0.5 mm, respectively. The near field distance d is thus estimated to be 50 mm in the elevational plane according to the near field distance formula d = h 2 /4λ, where λ is the ultrasound wavelength. This indicates that the entire imaging region enclosed by the ring transducer array is within the near field region. Since the acoustic field in the near field region depends on the size of the transducer element, the elevational thickness of ultrasound beam used for sound speed imaging is approximately 10 mm. This value determines the elevational size of the tissue that is considered in the sound speed measurement.
The image reconstruction process works as follows. The travel time of ultrasound signals from the emitters to the receivers are first calculated by extracting the first arrival time of the received radiofrequency data using the Akaike information criterion (AIC) [27] . Based on the estimated travel time data, sound speed maps are reconstructed using the algebraic iterative algorithm with Laplacian regularization [28] . In this reconstruction algorithm, ultrasound is modeled as bent rays and the ROI is divided into discrete grids, as shown in Fig.1 b. As such, the bent rays traveling through the ROI can be mathematically represented by a series of linear equations as a 11 s 1 + a 12 s 2 + · · · + a 1m s m = p 1 a 21 s 1 + a 22 s 2 + · · · + a 2m s m = p 2 . . .
where a and s denote the weight of the ray in the grid and the slowness (the reciprocal of sound speed) of sound in the grid, respectively; p denotes the travel time of the ray from the emitter to the receiver; m and n represent the total number of grids and rays, respectively. Eq. (1) can be written in the matrix form as where A is the coefficient matrix; s and p are the slowness vector and the projection vector, respectively. The matrix A and the vectors s and p can be written as Based on this matrix equation, an objective function can be constructed as where L is the Laplacian matrix and μ is a regularization coefficient. The second term in Eq. (4) denotes the Laplacian regularization to avoid possible numerical instability. Solving Eq. (2) is equivalent to minimize the functional U(s) in Eq.
(4) with respect to the slowness s, which can be computed using the conjugate gradient least squares algorithm [29] . The final sound speed is calculated by averaging segmented sound speed images. It is worth noting that to eliminate possible system errors, the travel time of background media is first measured and then subtracted from the travel time data when test samples are present.
All animal experiments were performed in accordance with the NIH Guide for the Care and Use of Laboratory Animals, after approval of the laboratory animal protocol by the Institutional Animal Care and Use Committee (IACUC) of the University of Science and Technology of China (Protocol Number USTCACUC1803065). Twelve adult Sprague-Dawley rats (age: 8~9 weeks, body weight: ~200 g) were used in this study.The rats were euthanized by CO 2 inhalation before organs were excised.

System characterization
The accuracy of the USCT imaging system was calibrated by comparing measurement results of the same samples with those measured by the pulse-echo method proposed by Kuo et al. [30] . In this calibration experiment, gelatin cylinders (Fig.2  a) with mass concentrations varying from 14% to 30% were used as phantoms. Fig.2 b and c show the sound speed image of a 22% gelatin phantom using water at 22 ℃ as the coupling medium and the average sound speed values of the gelatin phantoms at different concentrations by USCT, respectively. The results indicate that the sound speed of the phantom increases with the increase of gelatin concentration. As a comparison, the sound speeds of the gelatin phantoms were also measured by the pulse-echo method. The method employs the same system as USCT but operates the ring array transducer in pulse-echo mode instead of the transmission mode in USCT. Measurement data are presented in Fig.2c in the form of a box plot and tabulated in Table 1 as mean ± standard deviation (SD) for comparison. The results suggest that USCT and the pulse-echo method have comparable measurement accuracy. All samples were measured five times independently in this comparison experiment.

Animal experiments
After the calibration experiment, sound speed imaging and estimation of ex vivo organs using USCT were performed. Five types of organs including the brain, heart, liver, spleen, and kidney (the first column of Fig.3) were excised from twelve recently euthanized rats and positioned in the center of the ring array transducer. The freshly excised organs were allowed to stand for two minutes before the imaging procedure starts to ensure temperature equalization between the samples and background PBS buffer. All samples were measured within 20 minutes after excision and the temperature of the PBS buffer was kept at 37 ± 0.2 ℃. The second column of Fig.3 presents the sound speed imaging results, demonstrating that USCT can delineate the shape of the organs based on the sound speed information. To estimate the average sound speed of each organ, masks for the ROIs were generated by thresholding the sound speed maps based on their histograms (Fig.4) and are shown in the third column of Fig.3. Corresponding ROIs within the masks are presented in the last column of Fig.3.
The average sound speed of each type of organ is statistically evaluated within the ROIs and is tabulated in Table 2. The results suggest that the sound speeds measured in this study for the brain, heart, liver, spleen, and kidney are 1560.2 ± 1.8 m·s −1 , 1579.4 ± 2.1 m·s −1 , 1591.2 ± 3.3 m·s −1 , 1574.3 ± 1.2 m·s −1 , 1575.0 ± 3.5 m·s −1 , respectively. The liver has the highest sound speed among all five types of organs. The estimated sound speed values were also compared with published data, as shown in Table 3. The measured sound speeds of some organs, e.g., brain and heart, in this study are close to results reported in the literature while the sound speeds of  others, such as liver and spleen, slightly deviate from previously published results. This is probably due to the differences in measurement procedures of different methods. The USCT method proposed in this study can measure the sound speeds of animal whole organs immediately after excision. Moreover, it is a global measurement method, which indicates that the estimated sound speed is an average representation of the sound speed of a whole organ. In contrast, most measurement methods used in the literature require complicated sample preparation procedures and can only reflect the local sound speed property of an organ. Therefore, measured sound speed may vary at different organ locations due to tissue heterogeneity.

Conclusions
In conclusion, we developed a USCT technique based on a ring array transducer for sound speed imaging and evaluation of small animal organs ex vivo. The proposed technique can Third column: masks used to segment the regions of interest (ROIs). Fourth column: segmented images used to calculate the average sound speeds. First row to the fifth row: brain, heart, liver, spleen, kidney.  not only measure average sound speed values of soft tissues but also provide two-dimensional cross-sectional sound speed images. It does not need complicated sample preparation procedures and can yield accurate measurement results. The measured sound speeds of the brain, heart, liver, spleen, and kidney are close to published data and can be used as a reference for disease diagnosis and image quality optimization in photoacoustic tomography. This work demonstrates a new method for sound speed imaging and evaluation of soft tissues and can potentially be extended to in vivo applications.