Noninvasive Temperature Estimation Using ... - Wiley Online Library

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Article

Noninvasive Temperature Estimation Using Sonographic Digital Images Mohammad D. Abolhassani, PhD, Ahmad Norouzy, MSc, Abbas Takavar, PhD, Hosein Ghanaati, PhD Objective. The purpose of this study was to develop and evaluate a speckle-tracking method for tissue temperature estimation due to heating fields using digital sonographic images. Methods. The temperature change estimation method is based on the thermal dependence of the ultrasound speed and the thermal expansion of the medium. Local changes in the speed of sound due to changes in the temperature produce apparent displacement of the scatterers, and the expansion introduces physical displacement. In our study, a new technique has been introduced in which the axial physical displacements were obtained from digital sonographic images. The axial speckle pattern displacement was determined with a cross-correlation algorithm. The displacement data were then used for computing the temperature changes. To monitor the temperature in real time, the computational time was decreased by restricting the search region in the cross-correlation algorithm and carrying out the cross-correlation function in the frequency domain via a fast Fourier transform algorithm. Results. Experiments were performed on tissue-mimicking phantoms. The imaging probe was a commercial linear array working at 10 MHz. In addition, the temperature changes during heating were measured invasively by negative temperature coefficient thermistors. There was good agreement between ultrasonic temperature estimations and invasive temperature measurements. Conclusions. The proposed method verifies the capability of the speckle-tracking algorithm for determining both the magnitude and direction of displacement. The average error was 0.2°C; the maximum error was 0.53°C; and the SD was 0.19°C. Therefore, the proposed algorithm is capable of extracting the temperature information from sonographic digital images. Key words: cross-correlation; speckle tracking; speed of sound; temperature monitoring; ultrasound.

Abbreviations RF, radio frequency; TM, tissue-mimicking; USAE, ultrasoundstimulated acoustic emission

Received June 26, 2006, from the Tehran University of Medical Sciences, Tehran, Iran (M.D.A., A.N., A.T., H.G.); and Research Center for Science and Technology in Medicine, Tehran, Iran (M.D.A.). Revision requested July 28, 2006. Revised manuscript accepted for publication September 13, 2006. We thank E. Mohammadi, for making phantoms, M. Alinaghizadeh for providing electronic circuits, and M. Hedjazi, PhD, for helpful advice. We also thank the staff of the Imaging Center of the Imam hospital, the members of the Research Center for Science and Technology in Medicine, and especially the members of the electronic laboratory. Address correspondence to Mohammad D. Abolhassani, PhD, Medical Physics and Biomedical Engineering Group, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran. E-mail: [email protected]

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inimally invasive thermal therapies such as high-intensity focused ultrasound,1 radio frequency (RF) ablation,2 microwave ablation,3 and laser-induced thermal therapy4 have gained increasing attention in the last decade as alternatives to standard surgical therapy. The efficacy of the thermotherapy depends on the accuracy of treatment monitoring. Treatment monitoring is generally performed in 2 different ways: real-time tissue damage monitoring and real-time temperature estimation of the heated region and surrounding normal tissue. Many researchers have been trying to develop new quantitative noninvasive techniques for tissue temperature measurement and treatment monitoring. These techniques are based on magnetic resonance imaging, impedance tomography, microwave radiometry, and sonography. Several studies of minimally invasive thermal therapies have been focused on the use of sonographic imaging to monitor thermal lesion size.5,6 One common factor in these studies was the observation of highly echogenic

© 2007 by the American Institute of Ultrasound in Medicine • J Ultrasound Med 2007; 26:215–222 • 0278-4297/07/$3.50


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Noninvasive Temperature Estimation

regions caused by the production of microbubbles as a result of tissue heating. This intense signal was thought to result from the large reflection of ultrasonic energy from gas/tissue interfaces. In the field of ultrasonic thermometry, different approaches have been suggested: analysis of frequency-dependent attenuation,7 speed of sound and thermal expansion,1,8–11 and backscattered power.12 Recently, ultrasound-stimulated vibroacoustography, or ultrasound-stimulated acoustic emission (USAE), has been introduced as a potential method for measurement of the mechanical properties of tissue. Karajalainen et al13 showed that the amplitude of the USAE signal is temperature dependent. Konofagou et al14 applied USAE in both detection and monitoring of thermal lesion formation14 and temperature monitoring in thermal therapy.15,16 We have proposed a new method for noninvasive temperature estimation, which uses the envelope-detected signal (sonographic digital B-mode image). All previous methods of sonographic thermometry used an RF echo signal (RF raw data). The proposed method is based on the linear relationship between the temperature variation and the echo displacement (apparent and physical) as seen on A-lines acquired with pulseecho diagnostic sonography. Speckle tracking applied on high-quality digital sonographic images of a heated region determines the echo displacements and thus the temperature variation. With this technique, the need for access to the RF signal is eliminated, and it can be implemented on conventional digital sonography systems. The feasibility of this method was evaluated in vitro on a tissue-mimicking (TM) phantom.

shifts in the scatterer positions, and the thermal expansion of the medium introduces a physical shift in the scatterer positions. To estimate the displacements, first a physical model was introduced. This model was based on the following facts and assumptions. Facts 1. Biological tissue and media, as far as diagnostic ultrasound is concerned, can be thought of as consisting of a semiregular lattice of discrete scatterers. These scatterers are separated by an average distance, d, from each other over some region, which is called the average scatterer spacing.17 2. The average scatterer spacing, d, in tissue increases as the temperature of the tissue increases and decreases as the temperature decreases. This increase and decrease of d as a function of temperature is determined by the linear coefficient of thermal expansion (increase in displacement for 1°C temperature increase per unit length, α, of the tissue or medium in general). 3. The speed of sound, c, is a function temperature. In water and most tissue media, c increases with increasing temperature. In fatty tissue,18 c decreases with increasing temperature.19 Assumptions 1. The variation of speed of sound with respect to temperature,

is typically linear over the 5°C to 10°C temperature rises during hyperthermia treatment.20 2.

Materials and Methods Model The temperature change estimates were obtained by calculating axial displacement of the scatterers due to tissue heating. The displacements are caused primarily by changes in the speed of sound in tissue with temperature changes. A secondary cause for changes in the echo signals is the thermal expansion of tissue due to heating. The speed of sound variations with temperature introduce apparent or virtual 216

a medium-dependent parameter, is assumed to be invariant with respect to the temperature changes. This assumption is based on the increase of tissue temperature to not more than 50°C in hyperthermia applications. A 1-dimensional case of the tissue model is illustrated in Figure 1A. The distances between scatterers A, B, . . . F are the same and equal to d. The medium is initially at room temperature. An external heat source increases the temperature J Ultrasound Med 2007; 26:215–222


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between C and D by 2°C. The heat energy diffuses in the medium. The temperature elevation in the neighboring points is 1°C. For the sake of simplicity, we ignore the effect of the thermal expansion (the coefficient of thermal expansion of the biological tissue is very small). The speed of sound increases by 2 m/s for every degree Centigrade rise in the temperature around room temperature.9 To produce an image, the system determines the positions of scatterers by measuring the 2-way travel time of an ultrasonic pulse, from the transducer to the scatterers’ positions, and multiplying half of it by the preset speed of sound, c0. The 2-way travel time (measured by the system), the interpreted depth (position of the scatterer in the image), and apparent displacement for points B, C, and D are summarized in Table 1. The procedure is the same for the other points. As shown in Figure 1B, the scatterers A and B were constructed correctly in their actual positions. The temperature changes between points C and E alter the speed of sound. These changes are observed as displacements in the successive images (Figure 1C). The temperature estimates were obtained by calculating axial displacement in the image introduced because of the heating fields (Figure 1D). Simon et al10 derived an expression for the internal change in temperature at depth x, ΔT(x), corresponding to the speed of sound variations and thermal expansion of tissue. The relationship is given by (1)

Because the standard receiver beam-forming algorithms assume that the speed of sound is constant, the time shift (δt) leads to a displacement (Δd) in the scatterer location in the image Δd = δt × c0. Substituting this into Equation 1 and simplifying, we obtain (2)

Equation 2 shows a linear relationship between the displacement, Δd, and the sample temperature change, ΔΤ, at the location in the sample at which Δd was computed. The term J Ultrasound Med 2007; 26:215–222

Figure 1. A, An external heat source increases temperature between points C and D by 2°C, and the diffused heat energy increases the temperature between B and C and D and E by 1°C. B, Image of the medium after heating. The scatterers’ displacements have been exaggerated. C, Incremental displacement curve as a function of depth (axial direction). D, Derivative slope of the curve (C) along the axial direction. Equation 2 shows the relationship between temperature and the slope of the curve (C).

(3)

is a medium-dependent parameter that can be experimentally determined for a homogeneous medium; α is the linear coefficient of the thermal expansion of the medium; and β is a constant related to the change in the speed of sound with the temperature changes. Although the model presented here is derived for a 1-dimensional case, it can be used to estimate temperatures on a 2-dimensional plane. The 2 dimensions considered in this study were axial (x) and lateral (y). The elevational direction was not considered because it was not possible to obtain information on the third spatial dimension with the imaging system used. However, an extension of the method presented herein is straightforward once a 3-dimensional sonographic imaging system is considered. To obtain meaningful temperature estimates, it is necessary to obtain accurate estimates of incremental displacement. Speckle tracking is an 217


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Table 1. Two-Way Travel Time, Interpreted Depth, and Apparent Displacement for Points B, C, and D Point

2-Way Travel Time

B

2×

C

D

2× ( 2× (

Position in the Image, Computed Depth

Displacement Real Depth — Computed Depth

d

0

d c0

d d + ) c 0 c0 + 2

d d d + + ) c0 c 0 + 2 c 0 + 4

c0 ( c0 (

d d + ) c 0 c0 + 2

2d − c 0 (

d d d + + ) c0 c0 + 2 c0 + 4

3d − c 0 (

d d d )= + c0 c0 + 2 771

d d d 3d + + )= c0 c0 + 2 c0 + 4 771

In this table, d is the spacing between scatterers in the model, and c0 is the initial speed of sound (1540 m/s).

efficient method to estimate tissue displacement or motion,21 as explained in detail in the following section. Once the displacement estimates are obtained, to reduce the data fluctuation, it is necessary to perform a smoothing filter on them. This filter removes any spikes that might be present in the displacement data. To perform smoothing, 3 to 5 point median filters are applied. The output of a median filter contains the median value in the m-by-n ([m, n] is the order of the filter; here, m = n) neighborhood around the corresponding pixel in the input image. The median filter pads the image with 0s on the edges, so the median values for the points within [m, n]/2 of the edges might appear distorted. Each filtered axial datum is then fit to a polynomial of order P (typically P is between 7 and 14). According to Equation 2, to obtain the temperature changes, the processed displacement values must be spatially differentiated. Differentiation is implemented through a linear 1-dimensional finite impulse response filter. The Remez algorithm can also be used to design the differentiator filter, where the weighted error is minimized in the mini-max sense.10 This filter is optimal in the sense that the maximum error between the desired frequency response and the actual frequency response is minimized. A filter designed this way exhibits an equiripple behavior in its frequency response and is sometimes called an equiripple filter. A ripple is observed behind the heated region in the temperature map, which is caused by a thermoacoustic lens effect. This means that behind 218

the heated region, the variation of temperature versus axial distance does not go down smoothly as expected. When a sharp lateral gradient in the temperature distribution is present, the correspondent local change in the speed of sound constitutes an aberration for the imaging system. To illustrate this, consider the acoustic paths between a scatterer location behind this lateral gradient and elements on opposite ends of the effective aperture of the imaging array. When the temperatures have no lateral gradients, the travel time along the 2 paths will be the same. However, when a lateral temperature gradient exists, the temperature along the 2 paths will be different from each other. Therefore, the signals received by the 2 elements will exhibit different shifts because of different local changes in the speed of sound. Because the receiver beam-forming algorithm of the imaging system assumes the speed of sound in the medium to be constant, it does not compensate for this aberration. Consequently, the echoes collected before and after heating exhibit decorrelation. This decorrelation is responsible for the ripple seen in the estimates of the temperatures. Several techniques have been proposed to compensate for the thermoacoustic lens effect.1,10 Speckle-Tracking Algorithm The speckle tracking involves dividing a 2dimensional digital image into subregions and tracking the backscattered echoes produced by the ultrasonic scatterers in tissue.22 This can be done because the speckle patterns, or “signaJ Ultrasound Med 2007; 26:215–222


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tures,” are relatively stable between frames as the tissue or blood moves. An effective technique is to find the displacement for each speckle pattern that gives the maximum normalized cross-correlation between consecutive images.23,24 Given a digital image pair of the same size m × n, the discrete cross-correlation function is defined as (3)

where i = 0, 1, 2, . . . m – 1; j = 0, 1, 2, . . . n – 1; and SP1 and SP2 are kernel and search regions in the first and second images, respectively. SP stands for the speckle pattern. The maximum peak location in C (m, n) indicates the speckle displacement. Equation 3 can be computed either directly in the spatial domain or in the frequency domain via a fast Fourier transform algorithm.24 The fast Fourier transform algorithm is used because it provides a fast implementation of Equation 3, especially when the sizes of SP1 and SP2 are the same. The cross-correlation function given in Equation 3, although simple in nature, has the drawback that it is sensitive to intensity changes in SP1 and SP2. A method frequently used to overcome this difficulty is to normalize Equation 3 as follows24: (4)

where SP1 and SP2 are the means of SP1 and SP2, respectively. The spatial resolution and accuracy of the noninvasive temperature estimation method depend considerably on the size of the kernel. The window size (area) must be large enough to enclose at least 1 dominant scattering center for the speckle-tracking technique to provide meaningful estimates of the displacements. To find an optimum kernel size, the normalized correlation coefficient of SP1 and SP2 for different dimensions, 1 × 1, 1.5 × 1.5, 2 × 2, 2.5 × 2.5, 3 × 3, 3.5 × 3.5, 4 × 4, 4.5 × 4.5, and 5 × 5 mm2, were computed. The maximum correlation coefficient indicates the optimum window size of the kernel.

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Experimental Setups To simulate the local heating by any hyperthermia modalities, such as laser and high-intensity focused ultrasound, a setup shown in Figure 2 was used. As a heat source, a 4-mm-long cylindrical resistor was implanted in the center of a TM phantom. The TM phantom was composed of 82.3% distilled water, 2% agar gelatin, 4.1% graphite powder, and 11.6% glycerin. The graphite powder acted as ultrasonic scattering elements, and glycerin was added to reach the speed of sound in biological tissue (ie, 1540 m/s). The thermal and acoustical properties of the TM phantom are very similar to those of soft tissue; the attenuation coefficient and speed of sound were 0.5 ± 0.03 dB/(cm ⋅ MHz) and 1540 ± 5 m/s, respectively. Those were determined by using an A-mode system applied on a block of phantom material 5 cm thick. Seven tiny (0.5 mm in diameter) thermistors were inserted into the phantom at different radial distances from the heating resistor on the same plane as the heat source (3, 4, 6, 8, 10, 11, and 13 mm). The imaging system was a commercial machine (Siemens AG, Erlangen, Germany) with a linear array transducer set at 10 MHz. The field of view was 35 (lateral) × 25 (axial) mm. Before any heating, the reference frame l(t0, x, y) was acquired at time t0 = 0. Then the switch of the resistor circuit was closed. At time tj, a total energy (I2Rtj) was dissipated in the resistor as a result of Joule heating. The image l(tj, x, y) was acquired at this time (tj). This procedure continued until the temperature reached 45°C. These images were transferred to a noninvasive temperature estimator program. The speckle displacements during heating were estimated by

Figure 2. Experimental setup.

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cross-correlating the reference image and the images acquired during the heating. The displacement data were substituted in Equation 1 to estimate temperature changes. Then the results were compared with the invasive measurements of the thermistors, which were calibrated with a digital thermometer with 0.1°C accuracy. The idea behind this experiment was to illustrate the capability of the proposed model, shown above in “Model,” to estimate the temperature changes in nonuniform heating fields.

Results The speckle images from the phantom before and during the heating are shown in Figure 3. The effect of different window sizes on the correlation coefficients for a 10-MHz transducer was analyzed. The correlation coefficients were computed for different dimensions, 1 × 1, 1.5 × 1.5, 2 × 2, 2.5 × 2.5, 3 × 3, 3.5 × 3.5, 4 × 4, 4.5 × 4.5, and 5 × 5 mm2, over the entire image including both heated and nonheated regions. The results were averaged for each window size. The averages of the correlation coefficients were plotted versus window sizes in Figure 4 for the images taken from the phantom at 30, 150, 300, and 420 seconds after the heating. The maximum temperature reached was 45°C. For the images at different temperatures, there were similar trends for the correlation coefficients. Figure 3. Gray scale B-mode images obtained on the TM phantom before (A) and 20 (B) and 40 (C) seconds after heating.

A

B

The maximum correlation coefficient occurred at 3 × 3 mm2. The correlation coefficients decreased at very large window sizes, as well as very small ones. The reason for the correlation coefficient reduction at very large kernels is that a larger window contains a greater temperature gradient than a smaller window. The temperature gradient distorts the speckle patterns; therefore, the correlation coefficients of large windows decrease. That means that the temperatures are poorly estimated with large kernel sizes. As the kernel size decreases, speckle patterns lose their uniqueness. Therefore, cross-correlation algorithms find incorrect matches, resulting in low correlation coefficients. Although the maximum of the correlation coefficient occurred at 3 × 3 mm2, the correlation coefficients from 2 × 2 up to 4 × 4 mm2 were close. A kernel size of 2 × 2 mm2 was chosen for the calculations in this study, because a smaller kernel size improves the spatial resolution and also decreases the computational time. The noninvasively estimated temperatures corresponding to the thermistors’ locations were computed and compared with the thermistors’ measurements (Figure 5). There was good agreement between estimated temperatures and sensor measurements. These findings verify the capability of the speckle-tracking method for determining both the magnitude and direction of displacement and, thus, the temperature. The average error was 0.2°C; the maximum error was 0.53°C; and the SD was 0.19°C.

C Figure 4. Optimum kernel width: correlation coefficients between kernel and search region versus kernel size.

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The correlation coefficients fall to 0.67 behind the heated region because of thermoacoustic noise.

Discussion

Figure 5. Noninvasively estimated (points) and measured (lines) temperatures at 3 sensor locations.

The temperature images at different times after heating are presented in Figure 6. Note the progressive increase in the maximum temperature, starting at a room temperature of 25.7°C and increasing to 27.1°C (Figure 6A), 31.2°C (Figure 6B), 37°C (Figure 6C), and 42.2°C (Figure 6D). The spread in the heating distribution can also be observed in Figure 6, A–D. Figure 7A shows the temperature estimates of the local heating experiment. The ripple resulting from the thermoacoustic lens effect is seen behind the heated region. Figure 7B shows the corresponding correlation coefficients versus depth (axial direction). Figure 6. Images of the temperature distribution 30 (A), 150 (B), 300 (C), and 420 (D) seconds after heating. The unit of the right bar is degrees Centigrade.

The experimental results show the feasibility of the speckle-tracking method for estimating the displacement in 2 dimensions in a TM phantom. In general, good agreement existed between estimated temperatures and the thermistor measurements. The speckle-tracking technique for the temperature estimation used here assumes that the thermal dependence of the speed of sound is linear for small temperature elevations (up to ≈10°C), which has been verified for biological soft tissues.10,23 For higher temperature elevations but below the necrosis threshold, it has been reported that the relationship between the speed of sound and the change in temperature is nonlinear.23 The experiments in TM phantoms showed that accuracy better than 0.5°C can be obtained. It should be noted that the accuracy of the noninvasive temperature estimation technique is material dependent. The tissue proportionality coefficient, k, and homogeneity of the tissue sample influence the accuracy. The kernel size, the imaging frequency, and the type of data used (RF echo signal or envelope detected) are the other parameters contributing to the accuracy of the technique. Figure 7. A, Temperature versus depth: axial line through the center of the heated region. B, Corresponding correlation coefficients.


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Furthermore, the calibration curves of the variation of the speed of sound and tissue expansion with temperature have to be generated before an accurate estimate of the temperature distribution with this method. Knowledge of these parameters can be used to calibrate ultrasoundbased thermal imaging systems. The major limitations of noninvasive thermometry are the thermoacoustic lens and patient motion. The speckle-tracking algorithm is sensitive to body motion because it is based on an echo-tracking approach. It must be mentioned that motion may cause additional difficulties when use of the proposed method is attempted in vivo.

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