Radio Science

Evaluation of a hemi-spherical wideband antenna array for breast cancer imaging

Authors


Abstract

[1] Using similar techniques to ground penetrating radars, microwave detection of breast tumors is a potential nonionizing and noninvasive alternative to traditional body-imaging techniques. In order to develop an imaging system, the team at Bristol have been working on a number of antenna array prototypes, based around a stacked-patch element, starting with simple pairs of elements and progressing to fully populated planar arrays. As the system commences human subject trials, a curved breast phantom has been developed along with an approximately hemi-spherical conformal array. This contribution will present details of the conformal array design and initial results from this unique experimental imaging system as applied to an anatomically shaped breast phantom.

1. Introduction

[2] Breast cancer is the most common cancer in women. X-ray mammography is currently the most effective detection technique; however, it suffers from relatively high missed- and false-detection rates, involves uncomfortable compression of the breast and also entails exposure to ionizing radiation. Microwave detection of breast tumors is a potential nonionizing alternative being investigated by a number of groups [Hagness et al., 1998; Fear et al., 2003; Fear, 2005; Bialkowski and Wee, 2007]. In these microwave-based systems, in a similar fashion to ground penetrating radars, microwaves are transmitted from an antenna or antenna array, and the received signals, which contain reflections from tumors, are recorded and analyzed.

[3] This contribution presents details of the conformal radar-based breast cancer detection system. Unlike the other published work on the subject, the developed experimental radar system operates in a multistatic mode, originally proposed for breast cancer and land mine detection by [Benjamin, 1996]. Compared to the monostatic approaches, a multistatic approach with a fully populated antenna array enables far more data to be gathered.

[4] To date most of the work on the breast cancer detection have been based on the computer simulations [Kosmas et al., 2004; Abas et al., 2007]. There have been only a few experimental breast-imaging radar systems reported in the open literature [Craddock et al., 2005; Sill and Fear, 2005]. In this paper we present for the first time an assessment of techniques to de-embed the tumor response from real experimental data.

2. Development of an Experimental System

2.1. Antenna Design

[5] A prerequisite for all microwave imaging systems is a suitable antenna array. Initial work concentrated on developing a simple but low-profile and wide-band antenna that would cover the 4–10 GHz frequency range. An aperture stacked-patch antenna was designed for this purpose. The antenna used herein is a modified version of the antenna presented in [Nilavalan et al., 2007], where it was employed in a planar array for breast imaging.

[6] For the conformal array, the antenna was redesigned. The final antenna design in presented in Figure 1. The antenna cross-section, dielectric materials and size of individual patches were kept the same as in [Nilavalan et al., 2007]. Only the ground plane size (and hence a feeding line substrate) was substantially reduced to 28 × 17 mm2. Dimensions of two dielectric substrates where patches are printed are 17 × 17 mm2. Additionally, as we learned from the experience of using the planar array [Craddock et al., 2005] it is better to shield the antenna from the surrounding environment, therefore we added a cavity at the back of the antenna. The cavity has a planar inner dimensions of 18 × 11 mm2 and is 12 mm long. To absorb the back radiation of the antenna and avoid any resonances the cavity was lined with a broad-band absorbing material (Eccosorb FGM-40 from Emmerson & Cumming).

Figure 1.

Cavity backed aperture stacked-patch antenna for breast cancer detection.

[7] In Figure 2 we present the measured antenna input match (S11), which shows that the antenna is matched (S11 < −5 dB) between 4 and 10 GHz. The good transient performance in this frequency range is visible when looking at the simulated (FDTD) transmit transfer function of the antenna shown in Figure 3. The 10 dB bandwidth of the transmit transfer function is about 7 GHz (from 3.5 to 10.5 GHz).

Figure 2.

Measured S11 (input match) characteristic of the antenna.

Figure 3.

Simulated (FDTD) transmit transfer function (at boresite) of the antenna.

[8] Additionally, we performed a transmission measurement between two antennas (face to face, 10 cm separation) immersed in a lossy matching liquid (described in the following paragraph). As an input pulse we chose the waveform presented in Figure 4, which covers a frequency range between 4 and 9 GHz on a −3 dB level. As described by Hines and Stinehelfer [1974], this type of pulse is suitable for time domain analysis of microwave systems when performing measurements in the frequency-domain. The resulting pulse transmitted between our antennas and its spectrum is shown in Figure 5. The transmitted pulse is clearly longer than the input pulse, due to the antenna's response but also due to a lossy and dispersive immersion medium. Comparing the simulated transfer function of the single antenna (see Figure 4) with the measured two-antenna transfer function (see Figure 5), we can clearly see the effect of the lossy medium. The 10 dB bandwidth of the measured transfer function was reduced to 3 GHz (3.5–6.5 GHz), for the 10 cm distance between antennas. Obviously, as the distance between antennas with change, also the transfer function will have different 10 dB bandwidth and also its maximum value will be at slightly different frequency. From these transmission experiments it is apparent that dispersive losses of the normal breast tissue will have a biggest impact on limiting the achievable temporal resolution.

Figure 4.

Synthetic pulse used as an antenna excitation: (left) time domain waveform and (right) spectrum.

Figure 5.

Two antenna transfer function (along boreside direction). Antennas were immersed in the lossy matching liquid, 10 cm distance.

2.2. Conformal Symmetrical Antenna Array Design

[9] Given the effort in designing and constructing a conformal hemi-spherical array, the intention from the outset was to design not only an array for laboratory use on a realistic, curved phantom, but also one that would serve as an initial clinical prototype. Approximately 20 female volunteers came forward from the University and the fit between their breasts and various plastic spherical sections was assessed with them lying in a prone position - the prone (face-down) position being felt to offer the best chance of the breast forming a gently and uniformly curved shape. Following this assessment, the dimensions of the array were input into a 3-D CAD model, along with the antenna elements and all supporting metalwork.

[10] The resulting antenna array is formed around lower part of a 78 mm-radius sphere, in four rows of four antennas. The side view of the array and breast model is shown in Figure 6. The arrangement of antenna elements (top view) seen in Figure 7 gives enough clearance for the cables and connectors, which pass between the elements of adjacent rows. The partly constructed array is shown in Figure 8.

Figure 6.

Hemi-spherical antenna array and breast phantom configuration: side view.

Figure 7.

Positions of antenna elements in the array, looking from the top.

Figure 8.

Partly constructed real antenna array.

[11] The clear advantage of the designed curved array is its conformity to the breast's shape, providing a good breast coverage by antennas radiation patterns. The real aperture array, together with the switching network, give a fast data acquisition. In a single scan there is no mechanical scanning involved, saving a lot of measurement time (it is important for measurement with real patients). Another benefit of this radar system is the fact that it operates in a multistatic mode, what gives a far greater spatial diversity compared with the monostatic operation. The main disadvantage of the presented real aperture radar system is the antenna coupling, as well as additional reflection from mechanical parts of the array. We will describe later in the paper how to deal with these undesired signals.

2.3. Three-Dimensional Physical Breast Phantom

[12] For experimental testing we developed appropriate materials and a 3-D breast phantom. As shown in Figure 6, during the measurements the antennas are immersed in a matching liquid, to reduce reflections from the skin and for a more compact antenna design. We decided that this matching liquid would be the same as the material simulating properties of a normal breast-fat, mainly for practical reasons (only one liquid required in manufacturing). The developed matching and normal breast tissue equivalent liquid [Leendertz et al., 2003] has a relative dielectric constant of about 9.5 and attenuation of 1.2 dB/cm at 6 GHz. This material is also dispersive (see Craddock et al. [2005] for its frequency-dependent characteristics).

[13] Next, a curved skin phantom was developed. The skin layer is 2 mm thick, it is a part of a 58 mm-radius hemi-sphere. When the skin phantom is fitted into the array, as shown in Figure 9, it lies 20 mm above the antenna elements. This standoff between antennas and breast provides a reasonable coverage of a breast by an antenna radiation pattern. The electrical parameters of the skin layer were chosen again according to the previously published data: the material is dispersive and at 6 GHz it has a relative dielectric constant of 30 and attenuation of 16 dB/cm.

Figure 9.

Skin phantom fitted into the antenna array.

[14] After fitting the skin phantom into antenna array, a plastic tank is connected to the array as presented in Figure 10. The tank is then filled with the normal breast-fat equivalent liquid (the same as matching liquid).

Figure 10.

Antenna array together with the tank.

[15] A tumor phantom material with a relative dielectric constant close to 50 and conductivity 7 S/m (at 6 GHz) was also developed. This gives a contrast between dielectric properties of breast fat and tumor phantom materials of around 1:5. Recently published data in Lazebnik et al. [2007], based on a large clinical study, however suggest that the contrast between healthy and malignant breast tissues might be lower, at least in some women.

3. Focusing Algorithms

[16] To obtain the 3-D image of the scattered energy, we employ postreception synthetic focusing. We employ a modified version of a classical delay-and-sum (DAS) beamforming [Benjamin et al., 2001], briefly described below.

3.1. Preprocessing: Equalization

[17] Before applying the focusing algorithm we have to perform a preprocessing step. This process aims at equalization of scattered tumor responses for different antenna pairs. Ideal preprocessing would result in all received pulses being of the same shape, amplitude and perfectly time-aligned. In our preprocessing the following steps are performed: (1) extraction of the tumor response from measured data, (2) equalization of tissue losses, and (3) equalization of radial spread of the spherical wavefront.

[18] In the work reported herein there will be frequency-dependence both of the tissue losses and of the radiation patterns of the antennas, however for simplicity we do not attempt to correct for these frequency-dependencies in our processing.

3.2. Modified Delay-and-Sum Algorithm

[19] The modified DAS algorithm uses an additional weighting factor QF (quality factor), compared to the standard DAS. QF can be interpreted as a quality factor of the coherent focusing algorithm.

[20] The characteristic equation of the improved DAS algorithm is expressed as:

equation image

where M = N(N-1)/2 (N is the number of antennas in the array), wi is the location dependent weight calculated during preprocessing (steps 2 and 3 of the preprocessing), yi is the measured radar signal and Ti is the time delay. The time delay Ti for a given transmitting and receiving antenna is calculated based on the antenna's position, position of the focal point r = (x, y, z) as well as an estimate of average wave propagation speed, which in our processing is simply assumed to be constant across the band (though in our experiments it will not be). As we recently presented in Klemm et al. [2008], by using this additional weighting factor QF, quality of images is significantly improved due to the clutter reduction capability of the new algorithm.

4. Array Evaluation Results and Imaging Results

4.1. Tumor Response De-embedding Techniques

[21] Before applying the preprocessing step and the focusing algorithm, the tumor response must be extracted from measured data. Measured data contain the tumor response, as well as additional undesired signals (antenna coupling, reflections from the skin, reflections from mechanical parts of the array). To subtract all the unwanted signals, we employ two techniques: either (1) background subtraction, or (2) rotation subtraction.

[22] In the background subtraction method the tumor response is extracted using two measurements, with and without the tumor present in the breast. This method is effective and useful in evaluating the array imaging properties, as well as in array calibration, but cannot possibly be used with real patients.

[23] The second method, rotation subtraction, also employs two measurements, but with the tumor present in the breast in both cases. The first measurement is performed with the array in a given position, then the array is rotated (in a horizontal plane, around its central vertical axis) and a second measurement is recorded. Because the rotation subtraction method does not require a background measurement, it can potentially be used in realistic scenarios with breast cancer patients.

[24] To obtain the relevant measured data for background and rotation subtraction methods, the following measurement steps were performed:

[25] 1. First, in a given array position (AP1), a background measurement BAP1 is taken. There is no tumor present in the breast phantom.

[26] Then, as the array stays in the same position AP1, we introduce a tumor into the breast phantom at a certain location and a measurement TAP1 is recorded.

[27] 3. Next, keeping the breast phantom with tumor fixed we rotate the array to a second position AP2. After rotation we perform a second measurement of the breast with tumor (TAP2).

[28] 4. Finally, while the array is in position AP2, the tumor is removed from the breast phantom and the second background measurement BAP2 is obtained.

[29] These four data sets provide a basis for obtaining three focused images of the phantom: two images using the impractical but ideal background subtraction method and one using the more practical rotation subtraction method. The tumor responses TR for respective images are obtained using the following operations on the recorded time domain signals (not on the images): (1) Image 1: TRI1 = TAP1BAP1; (2) Image 2: TRI2 = TAP2TAP1; (3) Image 3: TRI3 =TAP2BAP2.

4.2. Comparison of Tumor Response Extraction Methods: Evaluation of Experimental Radar Signals

[30] In this paragraph we compare the tumor response extraction techniques described above, by investigating individual multistatic radar signals. Additionally, we show how we minimize effects of antenna mutual couplings.

[31] We compare effectiveness of two extraction techniques by looking at respective raw measured multistatic radar signals. As an example, we chose a pulse transmitted between antennas 1 and 2 (see Figure 8 for antenna positions), where we can also observe the effect of mutual coupling between antennas. In Figure 11 we can see two radar signals, without and with the tumor inside the breast phantom, used in background subtraction method. As described in the previous paragraph, by subtracting these two signals we can easily extract tumor response from measured signals. This method however is not clinically useful, because the background measurement (without tumor inside a breast) will not be available with real cancer patient. In the figure we indicated a different parts of the radar signal. As this is a signal transmitted between two adjacent antennas in the array, a first signal received in a direct signal coupled from the transmitting antenna. Next, we can identify a signal reflected from the skin and then the tumor response. As we can see, the tumor response is very small and hidden within the late-time portion of the received signal. The tumor response can only be extracted by subtracting the background signal (shown later in a paper in Figure 13). Other parts of the signal (antenna coupling and skin reflection) are almost identical for cases with and without the tumor.

Figure 11.

Comparison of two radar signals (raw measured data) used in background subtraction technique. Both signals are for the same multistatic path (transmission between antennas 1 and 2, as shown in Figure 8), with and without the tumor inside breast phantom.

[32] Next, in Figure 12 we can see radar signals used in the second tumor extraction technique: rotation subtraction. Signals are shown for the same multistatic channel as used in background subtraction. Both signals from Figure 12 contain tumor response, they were obtained when array was in two different positions due to array rotation (AP1 and AP2, as described in previous paragraph). Again we can distinguish signals originating from antenna coupling, skin reflection and the tumor.

Figure 12.

Comparison of two radar signals (raw measured data) used in rotation subtraction technique. Both signals are for the same multistatic path (transmission between antennas 1 and 2, as shown in Figure 8), but at two array positions: AP1 and AP2.

[33] In Figure 13 we present signals obtained from background and rotation subtraction methods. We can see that the ‘ideal’ background subtraction method (solid line) provides a good tumor response, with very small distortions. The antenna coupling and skin reflection signals were nicely canceled. Significantly more distortions can be seen in the rotation subtraction signal (dashed line). The tumor response was reasonably recovered from measured data. However, signals at other ranges also appeared. Especially the skin reflection signal is visible. It has actually higher magnitude that the tumor response. The remaining of the sin reflection signal is due to measurement imperfections during array rotation. Because in raw measured data the skin reflection signal is few orders of magnitude stronger than tumor backscattered response, even small changes in distance between antennas and the skin layer, or changes in a skin thickness will result in skin reflection signal at two array positions not being the same. This can be observed in Figure 12 on raw signals (before applying subtraction; only small difference in amplitudes for both skin reflection signals, hardly visible). It is worth adding, that the antenna coupling signal was also well canceled using rotation subtraction technique.

Figure 13.

Comparison of extracted tumor response when using background subtraction and rotation subtraction methods.

[34] The problem of remaining signals when using rotation subtraction although clearly visible on individual multistatic radar signals, is not very critical overall. These clutter signals will usually add incoherently during focusing processing. But the tumor response will be combined coherently, as presented in a next section. In conclusion, we can clearly see the difference between ideal (not practically useful) background subtraction and the practically useful rotation subtraction method.

4.3. Comparison of Tumor Response Extraction Methods: Experimental Imaging Results

[35] In this section we compare the techniques presented above for tumor response extraction and their impact on imaging quality. Using the system described in section 2, we performed a number of measurements of tumors in different locations within the breast phantom.

[36] We present an example of a 8 mm (diameter) spherical tumor phantom at two different locations in the breast phantom. For each location, we compared the three focused images obtained using the tumor response extraction methods described above. Additionally, we evaluated the quality of coherent radar operation by examining the radar signals obtained after focusing at the focal location where the tumor was detected.

4.3.1. Results for Tumor Location P1: x = 10, y = 0, z = −20 mm

[37] Below we present experimental tumor detection results for a 8 mm spherical tumor phantom located in the breast at a position P1: x = 10, y = 0, z = −20 (all positions quoted in mm). Following the measurement procedure described in section 4.1, three focused images of the detected tumor were created, two using background subtraction method and one using rotation subtraction.

[38] In Figure 14 we present results for the background subtraction method with an array in position AP1 (as described in section 4.1). Figure 14a shows a three-dimensional (3-D) focused energy image (−3 dB energy contour), with the tumor detected at position: x = 9, y = −3, z = −15. The skin is also shown in the image (in gray). There is a slight shift in the location of the detected tumor, but otherwise the image is clear and of good quality (there is no clutter present in the image). The small spatial offset is most likely due to nonideally coherent summation of received pulse (which differ slightly in shape and duration).

Figure 14.

Experimental imaging and antenna array evaluation results for 8 mm spherical tumor located at position P1: x = 10, y = 0, z = −20: (a) 3-D focused image, (b) 2-D image through the horizontal plane z = −15, (c) channel data at the location of the detected tumor (x = 9, y = −3, z = −15), (d) as Figure 14c but normalized. Images were obtained using background subtraction for array position AP1. Two-dimensional contour plot shows signal energy on a linear scale, normalized to maximum in the 3-D volume, values below 0.1 rendered as white.

[39] When looking at the horizontal plane where tumor was detected (z = −15), shown in Figure 14b, we can easily identify the tumor. Moreover, there is no visible clutter in this 2-D image, demonstrating the good quality of our imaging process. Two-dimensional contour plots show signal energy on a linear scale, normalized to maximum in the 3-D volume, values below 0.1 rendered as white.

[40] To further evaluate the quality of our results, we investigated the coherence quality of our radar system. As described in section 3.2, using a synthetic postreception focusing algorithm, by proper time-shift and alignment of received signals, coherent operation of the radar should be achieved. Therefore, at the focal location where tumor is located, after ideal focusing and preprocessing of all radar channels the received pulses should have the same amplitude and be time-aligned. In reality we cannot expect all pulses to be the same, because we do not account for frequency-dependent factors (e.g. antenna characteristics, losses). Also, the tumor scattering is angle-dependent, resulting in slightly different pulse shapes received by different antennas. However, we do expect the pulses to be well time-aligned.

[41] In Figures 14c and 14d we can see the array channel data at the focal point where the tumor was detected (x = 9, y = −3, z = −15). Figure 14c shows the signal with absolute amplitude values, to investigate time-alignment but also the amplitude spread of the signals after preprocessing. The figure shows about 800 time samples (x axis) of the received channel data (with 16 antennas we record 120 channels, each displayed as a line parallel to the x axis). The black lines on the figure represent the extent of the integration window τ used in our modified DAS algorithm. We can observe that pulses have a similar amplitude across all channels, demonstrating their good equalization. In Figure 14d the same data are presented but with the amplitudes normalized to the maximum in each channel, we can see more easily the good time-alignment of the received pulses. The slight differences in time-shifts at individual channels are most likely due to the effects discussed above.

[42] In Figure 15 we present imaging results and channel data for the second background measurement, after the array was rotated by 10 degrees to position AP2. We can observe in the focused images (3-D in Figure 15a and 2-D in Figure 15b), that the tumor phantom is again successfully detected. However, due to the array rotation it is now seen at a slightly different location (x = 9, y = 0, z = −15) by the array. The channel data presented in Figures 15c and 15d show again that good coherent radar operation is achieved.

Figure 15.

Experimental imaging and antenna array evaluation results for 8 mm spherical tumor located at position P1: x = 10, y = 0, z = −20: (a) 3-D focused image, (b) 2-D image through the horizontal plane z = −15, (c and d) channel data at the location of the detected tumor (x = 9, y = 0, z = −15). Images obtained using background subtraction for array position AP2.

[43] Finally, in Figure 16, results are shown for the case when rotation subtraction method was used to de-embed the tumor response from raw measured data. Focused energy images (Figures 16a and 16b for 3-D and 2-D results, respectively) show that although tumor was again detected without any problems, detection quality is slightly degraded. Beside the tumor response, there is also some clutter present in images. The reason for this can be seen by looking at channel data in Figures 16c and 16d. Here the received channel data have a much larger amplitude spread, compared with results for background subtraction. Moreover, the coherence of pulses is also not as good.

Figure 16.

Experimental imaging and antenna array evaluation results for 8 mm spherical tumor located at position P1: x = 10, y = 0, z = −20: (a) 3-D focused image, (b) 2-D image through the horizontal plane z = −15, (c) channel data at the location of the detected tumor (x = 9, y = −3, z = −21), (d) as Figure 16c but normalized. Images obtained using rotation subtraction for array positions AP1 and AP2.

[44] The degraded performance can be explained by differences in time-shifts for different array channels, due to the difference in the physical displacement of each antenna during rotation: when rotating the array around its center, antennas close to the center of rotation experience smaller displacement than antennas located further away. Nevertheless, this rotation subtraction still provides performance sufficient to detect small tumors in the phantom.

4.3.2. Results for Tumor Location P2: x = 0, y = 30, z = −20 mm

[45] We present here results similar to those shown in the previous subsection, but for a tumor located at a different position: P2: x = 0, y = 30, z = −20. An 8 mm spherical tumor was again used in the measurements.

[46] In Figures 17 and 18 we present results for two background subtraction measurements, with the array in position AP1 and AP2. The array was rotated by 10 degrees, as before. By looking at focused images in Figures 17a and 17b for position AP1, and Figures 18a and 18b for position AP2, we can observe that tumor was in both cases easily detected. However, the difference in the location of the detected tumor is larger than for the first tumor location, as would be expected (due to larger physical displacement for the same angle of rotation). The tumor was detected at position: x = 6, y = 24, z = −12 for AP1, and position: x = −3, y = 24, z = −12 for AP2. Focused images are clear with no clutter visible. This good performance is again confirmed by the channel data (Figures 17c and 17d and Figures 18c and 18d) at the focal points where the tumor was detected: signals are relatively well-aligned and with comparable amplitudes.

Figure 17.

Experimental imaging and antenna array evaluation results for 8 mm spherical tumor located at position P2: x = 0, y = 30, z = −20: (a) 3-D focused image, (b) 2-D image through the horizontal plane z = −15, (c) channel data at the location of the detected tumor (x = 6, y = 24, z = −12), (d) as Figure 17c but normalized. Images obtained using background subtraction for array position AP1.

Figure 18.

Experimental imaging and antenna array evaluation results for 8 mm spherical tumor located at position P2: x = 0, y = 30, z = −20: (a) 3-D focused image, (b) 2-D image through the horizontal plane z = −15, (c) channel data at the location of the detected tumor (x = −3, y = 24, z = −12), (d) as Figure 18c but normalized. Images obtained using background subtraction for array position AP2.

[47] When using rotation subtraction, the tumor was also detected, as seen in the focused images Figures 19a and 19b. Although a small amount of clutter exists in these images, their overall quality is more than satisfactory. The channel data in Figures 19c and 19d show again that the signals vary more in amplitude after rotation subtraction, compared to the ideal background subtraction, and they are also less aligned. But the good quality of focused images shows that this effect of smaller coherence is equally translated onto the entire focusing domain. This is an encouraging conclusion of our evaluations, since possibly only the rotation subtraction method could be used in realistic breast cancer detection scenarios.

Figure 19.

Experimental imaging and antenna array evaluation results for 8 mm spherical tumor located at position P2: x = 0, y = 30, z = −20: (a) 3-D focused image, (b) 2-D image through the horizontal plane z = −15, (c) channel data at the location of the detected tumor (x = −3, y = 27, z = −12), (d) as Figure 19c but normalized. Images obtained using rotation subtraction for array positions AP1 and AP2.

5. Conclusions and Future Work

[48] In this contribution we presented a microwave system for breast cancer detection, employing a conformal antenna array. The antenna elements populate the inside of a section of a hemisphere, this being a suitable geometry for clinical application. A 3-D physical breast phantom was also presented including a geometrically and electrically realistic skin (this being the dominant source of clutter).

[49] The new investigations presented herein have focused on the evaluation of two methods of de-embedding tumor response from raw measured data. We compared quality of detection as well as coherence quality of these methods. Results show that both de-embedding techniques provide good quality images and there is no difficulty in detecting 8 mm spherical tumor at different locations within the breast phantom. However using a rotational subtraction the coherent radar operation is degraded, compared to the ideal (but unachievable) case of background subtraction.

[50] This effect is due to the different physical displacement of each antennas after array rotation arising from the different antenna locations in the array. We believe that this effect can be lessened to a certain degree and this is the subject of ongoing research.

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