Hyperthermia is proved to be beneficial to treating chest wall recurrences of breast cancer.^[1–4] Researches have proved that the combination of hyperthermia and other medical treatments, especially radiotherapy in local control^[5,6] and chemotherapy,^[7,8] can yield better medical effects. In order to achieve the best treatment effect in hyperthermia, temperature ranges in the target area are typically tuned close to 42 °C or 43 °C ± 1 °C. Therefore, precisely monitoring temperature is of great importance to assure safe medical treatment.

Invasive temperature measurement methods have been used primarily by embedding heat-sensitive sensors in the tissues. These methods give accurate local results, low cost, and easy operation. However, spatial sampling is too limited to make corrections for most of the tissue heterogeneities in a complex tissue like breast and it brings pain and risk of infection to the patient.^[9] Common medical measurement methods with non-invasive attributes have previously been studied including: magnetic resonance (MR),^[10,11] ultrasound,^[12,13] and microwave^[14] technologies. The three-dimensional (3D) temperature imaging with MR methods based on the diffusion coefficient,^[15] the relaxation time, or proton resonance frequency (PRF)^[16] of tissue has also been well reported. A hybrid PRF approach to simultaneously measuring time variations of PRF shift temperatures in water-based tissue and in fat-based tissues is proposed,^[17] which makes temperature changes accurately monitored in both water-based and fat-based tissues. However, it costs quite a lot in the cycle of multiple treatments when the MR method is reused. While a temperature measurement method based on microwaves has proved that the microwave can penetrate into tissue in only a limited depth and can be easily influenced by the environment.^[18] Ultrasound is a convenient, non-ionizing, and inexpensive method with less calculation requirements for temperature monitoring. The methods of using ultrasound as a temperature monitor involve measuring the sound attenuation coefficient,^[19,20] measuring echo-shift deviation in tissue thermal expansion,^[21,22] and measuring the backscattered energy difference of tissue in homogeneities.^[23] Several research centers in the world are working on constructing a prototype of ultrasonic transmission tomography for women's breast examination. In our experiment, a clinical ultrasound ring array scanner for breast cancer diagnosis was built to record both reflected ultrasound energy and transmitted ultrasound energy.^[24,25] However, the prior information about propagation speed of ultrasound and coefficient of thermal expansion are necessary for the echo-shift method.^[26]

Maintaining uniform temperature over one or more large target regions requires the compensation for a number of factors. The Pennes bioheat equation^[27,28] allows fairly good calculation provided that each of these variables is reasonably a function of time, but it is not so easy to determine the values of these factors for hyperthermia treatments and measurements as required. Some of these factors, particularly perfusion and absorption coefficients are substantially different in different tissues. Therefore, temperature often changes rapidly near tissue boundaries. This phenomenon will inevitably be wrongly reflected as overshoot artifacts around tissue boundaries, such as the greatly different thermal coefficients of speed of ultrasound between fat and muscle or connective tissues, when building temperature images with ultrasonic transmission tomography.

Researches on reducing overshoot artifacts normally consider the root cause of the artifacts and then perform an inverse operation.^[29,30] Our previous contribution^[31] proposed a method based on a physical mode. When applying our previous method, we solve a differential equation based on heat conduction rules with boundary conditions. Although the result is satisfactory for future biomedical treatment, it is characterized with a heavy computation burden and lack of the adaptive property.

In this paper, an alternative method of combining de-convolution, continuity constraint and empirical mode decomposition (EMD)^[32,33] is proposed to build a temperature image based on ultrasonic transmission speed tomography, which can yield better border information adaptively with less calculation. The proposed method can provide accurate and fast measurements for assistant medical treatment control by effectively alleviating the negative effect from overshoot artifacts in temperature images. The rest of this paper is organized as follows. In Section 2, both the direct method and the proposed method of optimally rebuilding the temperature image are presented. In Section 3, the experimental result and the analysis are given for subjective evaluation. Finally, conclusions are given in Section 4.

Application of our proposed method to the abnormal data (marked by the red curve in Fig. 1) yields a satisfactory result as shown in Fig. 1 (marked by the green curve in Fig. 1). It can be clearly noticed that the overshoot artifacts in the mixture area significantly decreased. The mean variation between the rebuilt temperature and ground truth in the overshoot area is 0.2908 °C, while the mean variation is 1.9284 °C before applying our proposed method. In our phantom experiment, we use a cylindrical gelatin with a flow tube at the center to mimic the cancerous and benign masses embedded in glandular tissue.^[36] To record both reflected ultrasound energy and transmitted ultrasound energy, a clinical ultrasound ring array scanner for breast cancer diagnosis was built (Karmanos Cancer Institute, Detroit, MI, USA).^[37,38] During the experiment, all ultrasound transducer elements emit signals with the fan beam toward the opposite side of the ultrasound ring sequentially. The reflection ultrasound signals and the transmission ultrasound signals of each element are recorded to build images with acoustic propagation properties.^[36]

Fig. 2.

Figure Option ViewDownloadNew Window

Fig. 2. (color online) Speed of sound imaging by a prototype SoftVue ® breast imaging system. (a) Cylindrical phantom of gelatin immersed in water, with 15% gelatin (light cylinder with dark central hole from cooled water in thin walled latex tube) and with a very attenuating thick walled silicone flow return tube outside the gelatin at the 8 o’clock position; (b) speed of sound image; (c) reflection mode ultrasound image; (d) profiles of speed of ultrasound versus temperature for water and gelatin.

Reflection mode ultrasound image (Fig. 2(c)) and speed of sound images (Fig. 2(b)) of a cylindrical gelatin with a flow tube in the center immersed in water (Fig. 2(a)) are calculated by a prototype SoftVue® breast imaging system (Delphinus Medical Technologies, Inc., Plymouth, MI). The different sections of the image are segmented from reflection images. Curves of speed of sound vs. temperature of water and 15% gelatin are drafted from corresponding data in the literature^[39,40] to yield the profiles (Fig. 2(d)).

From the original un-optimized three-dimensional (3D) temperature (Fig. 3(a)) it follows that in the boundary between water and gelatin, there exist non-physical overshoot artifacts. Since the overshoot artifacts are not physically existing, the temperature profiles after optimization will apparently differ from the un-optimized temperature profiles. The result from the method based on our previous physical model is shown in Fig. 3(b). With our proposed method in this paper, the optimized 3D temperature image is shown in Fig. 3(c). The artifacts are obviously depressed and temperature in the mixture area is effectively optimized by both methods. The profiles of temperature and mean temperature variations of all image rows are compared in Figs. 3(d) and 3(e), respectively, showing almost the same optimization results and quality. The reduction of mean variation of temperature indicates that the overshoot artifacts are effectively eliminated and the smoothness of the mixture area is recovered. The mean temperature variations in all rows and all columns decrease from 0.6845 °C to 0.2760 °C and 0.6893 °C to 0.2685 °C respectively after applying our optimized method. Since precisely monitoring the temperature is of great importance for insuring safe medical treatment, like the result in the numerical simulation, the absolute mean variation also effectively decreases, which increases the precision of the rebuilt temperature image. When calculating at six other angles (results are shown in Table 1), the image optimization results are close. Thus, we need not use BEMD (Bi-dimensional Empirical Mode Decomposition) to optimize the image.

Table 1.

Table 1.

Table 1. Mean temperature variation in different angles. . Angle/(°) 30 45 60 120 135 150 0.372 0.3773 0.3729 0.3860 0.3988 0.3795 0.922 0.879 0.8866 0.8880 0.8996 0.8981 0.491 0.322 0.394 0.478 0.480 0.440

Table 1. Mean temperature variation in different angles. .

When our previous method is applied, the temperature distribution of the mixture area is calculated by the finite element method with using Comsol® Multi-Physics 3.5a with 25 repeated iterations and temperature of the other area is also calculated. The total calculation time is over 5 minutes when using an 8-core Intel ® X5570 HP XW8600 workstation with 64-GB memory. In addition, for comparison, the temperature field of the whole area optimized with the current method is also computed using an nVidia ® Quadro K5200 GPU card since it contains no iteration. The total calculation time is less than 400 mil-seconds, which proves the advantages in reducing the computation burden with our proposed method in this paper. Furthermore, the whole optimization and reconstruction procedure is characterized with an adaptive property, which does not need any prior information or assumption.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. (color online) Temperature images and comparisons. (a) Original 3D map of temperature from the segmentation of the speed of sound image using the reflection image; (b) temperature image from our previous method; (c) temperature image from our proposed method; (d) comparison among temperature profiles; (e) comparison among temperature mean variations.

Empirical mode decomposition is an excellent data analysis method for non-stationary signals with adaptive property. Signals reconstructed from IMFs with different weights can prevail favorably over those from a complicated filter. Here in this paper, our adopted EMD approach combined with similarity constraint and continuity constraint, can yield better optimization temperature images adaptively with less computation time than our previously proposed method. The phantom in this study mimics the cancerous and benign masses embedded in glandular tissue of human breast. In future human clinical study, temperature imaging through ultrasound transmission tomography for localized feedback of hyperthermia can present the more precise details to enhance the feasibility with acceptable computation time when stable ultrasound transmission tomography is applied.