Repeatability Assessment of the Wavelia#2 Microwave Breast Imaging Scan: Experimental Performance Analysis Prior to Clinical Investigation

Abstract

Microwave imaging is an emerging imaging modality with the potential to support the diagnosis of breast cancer. Over the last two decades, a notable number of MicroWave Breast Imaging (MWBI) prototype devices have been developed and experimentally tested in Europe, North America and Asia. A small number of prototypes are currently in large-scale clinical investigations towards the demonstration of clinical efficacy, as well as identification of the clinical cases for which MWBI could bring added value over the existing breast imaging modalities. In this chapter, the methodology employed for quantitative assessment of the Wavelia#2 MWBI system reliability based on experimental data is presented. The analysis includes an assembly of the most representative findings from the series of the MWBI experimental tests performed on breast phantoms after installation of the Wavelia#2 investigational device at Galway University Hospital (GUH) – Symptomatic Breast Unit for a Phase-II Pilot clinical investigation. To the authors’ knowledge, the notion of MWBI scan and reconstructed image repeatability assessment has never been addressed before in the MWBI state-of-the-art.

1. Introduction

MicroWave Breast Imaging (MWBI) is an emerging imaging modality with potential to support the diagnosis of breast cancer [1, 2, 3]. Microwave imaging uses the scattered wave, or reflected wave, that arises from the contrast in dielectric properties between the various breast tissues, in the microwave frequency range. The increased volume of water within the denser breast tissues is responsible for the detectable electromagnetic scattering associated with microwave imaging. The increase of sodium and water, particularly in-bound water within the tumour cells, is expected to lead to even greater conductivity and permittivity of the tumourous tissues [4, 5]. Due to the dielectric contrast, back-scattered radar signals are physically generated, when the breast is illuminated with electromagnetic waves in the microwave frequency range.

During the last two decades, MWBI has been extensively investigated as a novel modality for the detection of breast disease, offering a non-ionizing, non-compressive approach [6] and as a potential diagnostic management strategy in the monitoring of neoadjuvant chemotherapy [7]. The non-invasive and non-ionizing characteristics of microwaves are associated with the important advantage of allowing for frequent scans of the breast using microwave imaging, unlike mammography [8]. In addition to safety, microwave imaging has further potential advantages, as it does not require uncomfortable breast compression [9].

Numerous research groups have developed and optimized hardware prototypes for microwave breast imaging, however, most of these prototypes remained in pre-clinical stage [10, 11]. While each of these devices has a distinct approach to generating images of the breast, the underlying microwave technology and the device characteristics are similar. Based on recent reviews [12, 13, 14], a total of no more than 10 MWBI system prototypes have been employed in human subject tests, to investigate the clinical utility of the MWBI technology. Those trials differ significantly in their scale, ranging from few volunteers to hundreds of patients. While most of the studies have been too small to determine clinical efficacy, larger-scale trials have been conducted with three state-of-the-art MWBI system prototypes: MARIA [15], Mammowave [16, 17, 18] and SAFE [19, 20, 21]. It should be noted that there is a fourth MWBI system with a remarkable history of testing on hundreds of breast cancer patients; it is the MWBI system developed at Dartmouth College, USA [7, 22], to our knowledge though, there have been no recent publications reporting clinical trial results with this system.

Despite favourable clinical results being reported, several recurrent limitations remain unresolved across even the most recently published clinical studies with MWBI, likely hindering the migration of this modality to the clinical setting. These are detailed in Table 1.

Shortcomings of State-of-the-art Microwave Breast Imaging

A non-negligible false positive rate.

The challenges of managing a wide range of breast sizes with the same MWBI system.

The automated and repeatable/consistent detection of breast pathologies of various types in breasts of various levels of density.

Factor analysis (breast density, breast size, age, cancer type and stage) in the absence of consistent datasets from large-scale MWBI clinical trials.

The identification of clinical cases where the addition of MWBI would demonstrate to be a useful clinical adjunct to detect or characterize breast pathology.

The detectability of small, non-palpable, breast pathologies.

The achievable accuracy of lesion localization in the breast has not been quantified with MWBI by any group.

The standardization of the patient positioning and scan process.

Table 1.

Microwave breast imaging: Shortcomings of the state-of-the-art.

In addition, despite the extensive efforts to harness the potential of the MWBI modality, spanning over 40 years when considering all the preliminary experimental pre-clinical developments of the various groups, a pertinent clinical application for this modality has yet to be identified.

The above-reported aspects justify further clinical research with alternative MWBI systems, such as Wavelia™ [23, 24]. In the First-in-Human (FiH) clinical study (NCT03475992), which has been conducted in a small cohort of 24 patients, the Wavelia#1 prototype system demonstrated the potential to detect and discriminate between palpable benign and malignant breast lumps, while the imaging procedure had no safety issues and patients reported a favourable experience of the test. The promising findings from this study, which provided initial data to support a valid clinical association for the Wavelia™ breast imaging technology, have warranted the preparation of further clinical investigations with an upgraded prototype version of the Wavelia™ system (Wavelia#2). The clinical data that will be further collected with Wavelia#2 is intended to build upon the outcomes of the FiH study of Wavelia#1 in larger and more diverse patient populations, as well as further address the current limitations of the state-of-the-art MWBI technology applied to clinical trials by now, as reported in Table 1. In this chapter, an evaluation of the Wavelia#2 MWBI system performance based on realistically complex experimental anthropomorphic breast phantoms is presented.

Even though several breast phantom studies, performed in a purely experimental setup within engineering laboratories, have been published so far [25, 26, 27], no systematic experimental evaluation performed on a MWBI prototype after installation for testing in the clinical setting, has ever been published before, to our knowledge. Among the three above-referenced MWBI prototypes, which have been employed in large-scale clinical investigations in the recent years, an experimental evaluation study has been very recently published only for the Mammowave system [28]. In this study, a simplistic phantom structure and experimental setup have been implemented though. A cylindrical plastic container filled with a low-permittivity liquid was used to mimic the adipose tissue of the breast. A glass tube, filled with a very high-permittivity liquid, was inserted in the plastic cylinder to mimic a tumourous inclusion. The whole structure was held in the prototype using a cylindrical holder, which is different from the cup that is used to hold the real breast in the clinical setting.

To our knowledge, realistically anthropomorphic, MRI-derived, 3D-printed breast phantoms [29], heterogeneously filled with adipose and fibro-glandular tissue-mimicking liquids as per [30] and including malignant and benign solid tumour phantoms with breast tumour-like irregular shapes as per [25, 31] and a realistic permittivity profile, have only been employed for the Wavelia™ system [32] so far. A series of achieved tumour detectability and imaging results on tests performed in Galway University Hospital after installation of the Wavelia#1 prototype for its FiH study were earlier published in [33].

The methodology and metrics employed for the evaluation of the Wavelia#2 MWBI system reliability are presented in the sequel of this chapter. The demonstration includes an assembly of some of the most representative findings from the series of imaging tests that were performed in a systematic manner, on the same complex anthropomorphic breast phantoms as earlier developed for Wavelia#1 [32], after installation of the Wavelia#2 investigational device at Galway University Hospital (GUH) – Symptomatic Breast Unit for a clinical investigation. To this end, the achievable level of repeatability of the Wavelia#2 scan and reported imaging findings is a key element and has thus been prioritized in the experimental evaluation of the system, towards acceptance at the clinical investigation site.

To the authors’ knowledge, this is the first time that the notion of MWBI scan repeatability/reliability is ever being conceived and quantitatively assessed. A quite extensive review on the qualitative and quantitative assessment methods earlier employed on MWBI system prototypes has been recently published by Porter et al. [34] and confirms the previous statement.

2. Wavelia™ microwave breast imaging

2.1 The principles

The Wavelia#2 MWBI system operates using an array of 21 wideband probes in a horizontal circular configuration. The probes are located outside of a cylindrical container that hosts a creamy liquid, serving as a transition medium between the scanner and the breast. The liquid has dielectric properties akin to the ones of the human skin, such that it favours the penetration of the Electro-Magnetic (EM) waves in the breast. With the patient lying in a prone position, one breast is submerged at a time into the cylinder, which is filled with the liquid. The probe array is piloted to perform a vertical motion, such that the full vertical extent of the breast is included in a cylindrical scan of the imaging scene. At each 2 mm vertical scan position, each antenna illuminates individually the breast using EM waves in the frequency range [0.8–4] GHz, while the remaining antennas receive the electromagnetic scattering at various angles around the circle in a multi-static radar imaging system configuration. This data is used to form a 3D image of the dielectrically contrasted interior breast tissues.

As earlier introduced in [33, 35], due to the lossy profile of both the breast tissues and the employed transition medium, but also due to the distinct physical meaning of the forward and backward scattering mechanisms, sectorization of the imaging scene is performed in Wavelia™, to more efficiently illuminate and reconstruct the imaging scene. A subset of 8 out of the 21 probes of the Wavelia#2 system is used each time to numerically form a sub-array, the full multi-static data matrix of which is used to form a partial image of the breast per azimuthal sector of illumination. The process is repeated 21 times; at each repetition, the centre of the sub-array is numerically moved to the next, adjacent, probe. This way, a total of 21 partially overlapping sub-images of the breast are formed and subsequently stitched to reconstruct a coronal slice of the pendulous breast, at each vertical position of the probe array.

Wavelia™ employs the Time-Reversal MUltiple SIgnal Classification (TR-MUSIC) algorithm [36] to form the aforementioned partial images (“sub-images”) of the breast. For the formation of a single TR-MUSIC sub-image of the breast at each sector and each frequency, the noise eigenvectors of the Time-Reversal Operator (TRO) are projected on the illumination vector of the sectorized probe sub-array. The scalar electric field approximation is employed, considering the co-polar component of the electric field, as radiated by the antennas of the system, to be dominant. The Hankel function of 1st kind and 0th order is then used as a basic propagation model to define each element of the illumination vector on each pixel of the imaging scene that lies within the transmitting (Tx) sensor fidelity zone, as introduced in [37].

The breast tissues are associated with high levels of power loss of the propagating electromagnetic waves, in the microwave frequency range. This is why, prior to radar imaging of the interior of the breast, pre-processing of the backscattered signals is required, to remove artefacts and unwanted interference signals, and enhance the useful radar echoes of weak-power level, originating from the interior of the breast. The strong received signals mainly consist of direct coupling between the antennas, skin reflections, and antenna reverberation.

The speed of propagation of electromagnetic waves through the breast tissues is determined by the dielectric properties (permittivity) of these tissues. In turn, the wave speed determines the time delay for reception of the waves, which were scattered by the tissues. The time delay (or phase shift of the EM waves) is mapped to a physical distance between the transmitting/receiving antennas and the scatterer. The distance information drives the image formation, i.e. spatial mapping of any scattered radar echoes in the patient’s breast. A large variability exists in the dielectric properties of each breast tissue type, over the population, as demonstrated by multiple studies involving ex-vivo dielectric measurements of a large sample of excised breast tissues [38, 39]. Considering the lack of a priori information on the dielectric consistency of each patient’s breast (full dielectric map of the breast), data-driven techniques are employed in Wavelia™ to deduce the speed of the EM waves for MWBI imaging (a parameter called pc_fib is employed for image formation, as introduced in [23, 35]).

2.2 The second generation prototype

The second generation prototype of the Wavelia™ MWBI system (Wavelia#2), depicted in Figure 1, is a significantly upgraded version of the first generation prototype (Wavelia#1), in terms of enhanced measurement stability, better control on the patient positioning, potential to reliably scan larger volumes of breasts and an improved ergonomic design.

Figure 1.

The Wavelia#2 microwave breast imaging prototype.

The technical upgrade of the Wavelia™ prototype has been designed based on the experience gained from the FiH clinical investigation. It is intended to ensure enhanced performance, mainly in terms of better repeatability of the MWBI scan, and thus a higher confidence level for the information content of the reconstructed breast images and their diagnostic value. Enhanced sensitivity to weaker signals, to ultimately support detection of smaller lesions and a better accuracy of the lesion localization is also targeted with the Wavelia™ technical upgrades.

The following are the main adaptations which have been implemented in the transition from the Wavelia#1 to the Wavelia#2 prototype:

1. Adjustment in the size of the container of the scanner to facilitate better scan quality for larger breasts. To be noted though that breast volumes larger than >1000 mL have been scanned with Wavelia#1 during the FiH study already. An upper size limit of ∼500 ml has been earlier reported for the MARIA M5 prototype [15]. No information on the breast size limits of the subsequent prototypes of MARIA (M6 and M7), nor of the Mammowave and the SAFE systems, have been more recently published. The range of breast volumes and thus the portion of the women population for whom MWBI is appropriate with each implementation of the technology remains yet open to be specified.

2. Design and integration of smaller antennas to improve imaging of the posterior part of the breast, i.e., reduce the distance between the uppermost scanning position and the examination table.

3. Use of upgraded Radio-Frequency (RF) components, cabling, and mechanical support of the probe array.

4. Chemical stabilization of the transition liquid, as well as automation of its injection and suction from the cylindrical container of the scanner.

5. Better control on the environmental conditions, in the examination room and within the scanner itself, during the breast scan.

6. Better control of the breast positioning in the scanner.

Wavelia#2 is currently being tested in a Phase-II pilot clinical investigation, at Galway University Hospital, Ireland, targeting to include approximately 70 patients. (NCT05757427).

2.3 The Wavelia™ breast imaging methodology revisited

The principles of the multi-static radar imaging methodology that is employed for the generation of the Wavelia#2 MWBI images are the same as earlier conceived for Wavelia#1 [35, 40], yet adapted to the Wavelia#2 geometry (i.e. an increase of the internal radius of the system by 11 mm, combined with an increase of the number of probes from 18 to 21). The Wavelia#2 data processing flow is revisited in Figure 2. The blocks in which methodological evolutions have been recently integrated for Wavelia#2, are highlighted in the block diagram and discussed in the sequel of this section. Only the MWBI image formation part of the Wavelia™ breast imaging methodology and not the image post-processing for automated Region-Of-Interest (ROI) detection [40], is part of the experimental analysis on the breast phantom MWBI scans, presented in the following sections.

Figure 2.

Wavelia#2 data processing flow: Blocks evolved since Wavelia#1 are highlighted.

As highlighted in Figure 2, the key evolutions that have been performed as part of the adaptation of the data processing flow for Wavelia#2 are the following:

1. The normalization of the amplitude pattern of each Tx/Rx channel with respect to a reference channel, thus eliminating the impact of the evolution of the conducted RF paths over the frequency band.

2. The estimation of the antenna coupling as the first principal component, while performing Principal Component Analysis (PCA), per imaging sector. In Wavelia#1, PCA was performed on data from the full probe array having a fixed distance between Transmitter and Receiver (Tx/Rx separation) [35].

3. The employment of the Empirical Model Decomposition (EMD) method [41] to define the signal components to be further filtered or retained based on distance and/or amplitude pattern criteria.

4. The integration of the notion of the sensor fidelity zone [37] in the TR-MUSIC imaging algorithm implementation [35, 36] for the Wavelia#2 prototype. The sensor fidelity zone is specified as a binary indicator of the pixels in the imaging scene, which are compliant with two constraints: (i) the propagation loss on the pixel does not exceed a certain Maximum Attenuation Level (MAL), (ii) the co-polar component of the radiated electric field dominates the other two field components at least by a ratio Minimum Polarization Ratio (MPR), such that the scalar field approximation can be considered relevant for the TR-MUSIC algorithm. The sensor fidelity zone has been re-defined for Wavelia#2 based on simulations of the radiated EM field in the CST simulation environment.

In addition to the aforementioned methodological evolutions, robustification, numerical stabilization, as well as significant acceleration of the computation have been achieved as part of the adaptation of the MWBI imaging algorithm to the Wavelia#2 prototype. This upgraded implementation is a step ahead towards standardization of the Wavelia™ breast images and more efficient processing of the data during the ongoing clinical investigation, as compared to the FiH study.

3. The experimental validation campaign

The anthropomorphic breast phantoms that have been used for the experimental testing and validation of the Wavelia#2 prototype are the same as the ones earlier developed for Wavelia#1 and presented in detail in [32, 33]. Despite the limitations and complexities introduced to the repeatability analysis by the hybrid (liquid/solid) consistency of these phantoms, to our knowledge, these phantoms represent the current state-of-the-art for experimental Microwave Breast Imaging.

The Wavelia#2 MWBI scan repeatability analysis has been structured as follows:

1. Employ two breast phantoms, Breast#1 and Breast#2, of distinct size and interior tissue heterogeneity pattern: evaluate the imaging system performance in cases of significantly different distances between the skin and the probes, which is a critical factor for the calibration of the mutual coupling between probes, before the scan data can be exploitable by the imaging algorithm. The two breast phantoms are depicted in Figures 3 and 4.

2. Employ azimuthal rotation of each phantom placement in the scanner and repeat the measurement: identify potential asymmetries of the MWBI scanner. Two azimuthal rotational positions of 0° and 180°, of both phantoms, have been systematically employed in the tests. In addition, all phantom configurations were rotated by 90° and 270° in a series of 16 MWBI scans, performed on a single day of the test campaign, to provide more experimental data on any potential asymmetries of the system.

3. Evaluation using three tumour phantoms: use of a macro-lobulated tumour phantom (Tumour#4) and two tumour phantoms of the same micro-lobulated shape model, however one tumour phantom being new and used for the first time in this test campaign (Tumour#3), while the other tumour phantom (Tumour#1) being used in numerous experimental tests before, resulting in progressive degradation of its shape sharpness and potentially its dielectric properties. It is reminded that the tumour phantoms are immersed in a chemically aggressive liquid mixture mimicking the fibro-glandular tissue of the Wavelia™ breast phantoms [32]. The immersion of the tumour in this liquid is performed each time manually using a thin string to hold it in position (additional source of variability). Photos of the three tumour phantoms, taken on the first day of the use of each, as part of the hereby reported test campaign, are shown in Figure 3.

4. Repetition of each MWBI scan twice, while the breast phantom remains idle at the exact same position: the comparison of the achieved imaging results in each set of two tests is intended to demonstrate the expected level of reproducibility of the MWBI scan, for various experimental setups. The main sources of variability being evaluated here, necessarily as an aggregate, for the Wavelia#2 MWBI imaging system are the following:

   1. the noise level in the RF measurement itself;

   2. the imperfect mechanical stability of the scanner;

   3. the uncertainty introduced by the imaging algorithm on its own, i.e. residual numerical instabilities and/or estimation uncertainties.

Figure 3.

(a) The Wavelia#2 examination table—schematic top view and imaging coordinate system, (b) the Tumour#1, (c) the Tumour#3, (d) the Tumour#4, (e) the Breast#2, and (f) the Breast#1 phantom.

Figure 4.

The breast phantoms, with tumourous inclusion, in the Wavelia#2 imaging coordinate system: (a) Breast#2, (b) Breast#1 at the 0° rotational position.

A sequence of 40 experimental setups defined in total the on-site testing and validation campaign of the Wavelia#2 prototype at the GUH clinical investigation site. This resulted in a total number of 80 MWBI scans, given that every experimental setup was measured twice, without touching the breast phantom, and with main objective the ultimate evaluation of the repeatability of the imaging result, in various experimental conditions. The 80-MWBI scan dataset was collected during a period of 5 consecutive days (30 January – 3 February, 2023) and also on a single day approximately 1 month earlier (22 December 2022).

Each breast phantom was partially scanned in a 44 mm vertical extent around the theoretical centroid of the tumourous inclusion, at each repetition. This adds-up to 23 vertical scan positions, with a moving step of 2 mm of the probe array. That is the scan data contributing to the reconstructed breast images being part of the analysis.

4. Representative subset of imaging results for Wavelia#2 scan repeatability assessment

Imaging results for a representative subset of 34 MWBI scans are presented in Figures 5–11. The presented images are the ones that have also been included in the quantitative assessment of the imaging system repeatability, which is presented in the following section.

Figure 5.

Breast#2, rotation 180°: Sequence of MWBI scan results. 14 scans performed on four different days.

Figure 6.

Breast#2, rotation 180°: Full imaging scene reconstructions for the 4 MWBI scans of 2 days: (a)-(d) 30 January (e)-(h) 3 February.

Figure 7.

Breast#2, rotation 0°: Sequence of MWBI scan results for repeatability assessment.

Figure 8.

Breast#2, rotation 270°: Sequence of MWBI scan results for repeatability assessment.

Figure 9.

Breast#2, rotation 90°: Sequence of MWBI scan results for repeatability assessment.

Figure 10.

Breast#1, rotation 270°: Sequence of MWBI scan results for repeatability assessment.

Figure 11.

Breast#1, rotation 90°: Sequence of MWBI scan results for repeatability assessment.

According to the methodology in [37], breast images were systematically generated for a set of four combinations for the (MAL, MPR) set of parameters defining the sensor fidelity zone, i.e. MAL = [−40–35] dB and MPR = [5 10] dB. Averaging of the images that have been generated for the multiple sensor fidelity zone settings was further performed, to cancel out ambiguities. The averaged images are presented in Figures 5–11 and considered by default in the quantitative assessment of repeatability.

Systematic generation of the breast images for a pre-defined set of narrow and wide search ranges for the pc_fib parameter was performed, in accordance with the methodology defined in [40], towards lesion detectability assessment based on persistence. Imaging results for a fixed pc_fib search range, the best-fitting to the tumour location in each given experimental setup, i.e.

• Breast#2 phantom results – pc_fib search range = [50–70]%

• Breast#1 phantom results – pc_fib search range = [20–50]%

are presented in the following. It has been verified though and confirmed that all the presented imaging results are persistent in varying pc_fib search range and would clearly declare detectability of the visible, tumour phantom-associated, ROI.

The date on which each MWBI scan was performed is indicated in the 1st column of each set of tabulated imaging results in Figures 5–11. The imaging results of two scan repetitions of each experimental setup appear in the 2nd column, between which the phantom and tumour have not been moved. The experimental setup is indicated below for each couple of repeated MWBI scan results. The dynamic range of the image intensity is indicated on the colour bar at the upper part of each image. The partial transparency profile of the MWBI image colour map remains fixed in all illustrations. The contour of the mould containing the fibro-glandular tissue-mimicking liquid and the tumour phantom structure (centered at (X,Y,Z) = (20,0,77) mm in the case of the Breast#2, Rotation 180° setup in Figure 5 and visible in purple colour) are overlaid with the MWBI images as reference.

A qualitative assessment of the results presented in Figure 5 indicates very good levels of repeatability of the images reported by the Wavelia#2 prototype when the experimental setup remains idle (i.e. comparison of the two images per row).

For the scans performed on the same day, using two different tumour models, the main source of variability is associated with the replacement and repositioning of the tumour phantom, which is performed manually using a flexible string. The following phenomena may occur during the tumour replacement, in an uncontrolled manner: (a) rotation of the tumour during/after insertion in the phantom, (b) tendency of the tumour phantom to adhere to the interior wall of the fibro-glandular tissue-mimicking mould, (c) varying immersion depth of the tumour in the breast. The breast phantom is not repositioned between two tumour exchanges on the same day.

For the scans performed on different days, aside from the aforementioned, tumour-related sources of variability, the principal source of variability is associated with the potential non-optimal immersion of the phantom itself in the transition liquid of the scanner, resulting in the presence of air bubbles or other local inhomogeneities on the coverage of the skin phantom with transition liquid.

In Figure 6, the reconstruction of the full imaging scene within the cylindrical container (not only the image within the breast) is depicted for the four MWBI scans that were performed on the 30th January and the four scans of the 3rd of February with the Breast#2 phantom at Rotation 180°. The first two scans of each day (Figure 6a, b, e and f) were performed using Tumour#3, while the latter (Figure 6c, d, g and h) using Tumour#4.

The out-of-the-breast portion of the presented images in Figure 6 provides a clear explanation for the visibly decreased Signal-to-Clutter Ratio (SCR) [34] on the breast phantom images of the 3rd of February (particularly the ones including the Tumour#4 phantom), when compared to the images of the 30th of January. A strong artefact radar echo appears systematically in the liquid, mostly dominant in the vicinity of the interface with the breast skin on all the four images of the 3rd of February. This is expected to be related with sub-optimal phantom placement and/or liquid consistency after mechanical injection in the scanner. The level of repeatability of the reconstructed images, both within and out-of-the breast, is remarkable, in the below 8 MWBI scans demonstration.

In Figures 7–9, indicative imaging results for repeatability assessment are presented at three distinct rotational positions of the Breast#2 phantom: 0°, 270° and 90° respectively. In Figures 10–11, a subset of indicative imaging results is presented for two rotational positions (270° and 90°) of the Breast#1 phantom.

The clarity/focusing of the image, as well as the SCR and the tumour localization accuracy, may vary from one setup to the other. This is not a surprise and can be acceptable, given the numerous sources of experimental variability. In addition, the breast phantoms are very heterogeneous, and the weak echo of the tumour phantom (low dielectric contrast against the surrounding fibro-glandular tissue) is highly sensitive to slight changes in the geometry. The tested experimental setups are of unrealistically high complexity and much discretized, compared to the real human breast.

5. Quantitative assessment of repeatability: methodology and results

Overall, it is important for the imaging system to demonstrate repeatability in its results, so that it can be trusted with confidence to deliver similar results under slight adjustments to patient position, temperature, operational process etc. during actual patient scans. Thus, in this section, the repeatability is being quantitatively assessed for the set of 34 MWBI scan imaging results that were qualitatively assessed in the previous section. Quantitative assessment is achieved by measuring the similarity between the final 3D-images obtained using the MWBI imaging software.

To measure the similarity, the sum of squared differences has been used as a metric [42], which is defined in the following way:

$$S_{\mathit{sq}}=\sum _{n,m,l}{\left(J_{n,m,l}-I_{n,m,l}\right)}^2$$E1

where N x M x L are the dimensions of the 3D images J and I. This has been divided by the term:

$$\sqrt{{\sum }_{n,m,l}{J}_{n,m,l}^2\times {\sum }_{n,m,l}{I}_{n,m,l}^2}$$E2

to provide a more appropriate scale to the [0, 1] range. More sophisticated similarity metrics can be derived using e.g. feature extractors. However, at this stage of development, it was desired to use a simple metric which directly measures pixel-to-pixel difference. This way, we would have a more primitive, raw, estimation of the similarity between repeated measurements, without having the benefit of rotation- or scale-invariant features being used to measure similarity.

In Figure 12, the similarity matrix of Breast #2 with Rotation = 180° is shown, for the 14 images depicted in Figure 5 (averaging over multiple sensor fidelity zones applied). Each element of the matrix corresponds to the similarity obtained using the sum-squared difference metric between the final 3D-images of the two respective MWBI scans. This similarity was computed from the volume inside the breast, i.e., not including the image reconstruction in the transition liquid of the cylindrical container, out-of-the breast. The following three similarity zones can be interestingly spotted in Figure 12.

• L0: this is the similarity level observed between consecutive MWBI scans performed on the same day, without moving the breast phantom or the tumour in-between the two scans (e.g. 3-Feb-T#3-R1 to 3-Feb-T#3-R2, where T# and R# stand for Tumour # and Repetition #, respectively). L0 is meant to quantify the expected level of variability that is introduced by the imaging system itself (measurement variability + uncertainty of the imaging algorithm). L0 is systematically associated with the smallest values of difference i.e., the best similarity in Figure 12, as expected.

• L1: This zone corresponds to scans performed on the same day but involving replacement and repositioning of the tumour model in the breast phantom, for instance 30-Jan-T#3-R1 to 30-Jan-T#4-R1. The values are generally higher, thus the similarity level degraded, for the L1 zone, when compared to the L0-zone.

• L2: Measurements of the same experimental setup from different dates fall into this category. These values are typically higher than those of L1 but can be close.

Figure 12.

In-breast similarity matrix for repeated measurements of breast #2 with rotation = 180°.

Furthermore, it is apparent from Figure 12, that the scans of the 22nd of December, and T#3-R2 in particular, which appears as an outlier, are substantially more different, compared to the rest of the scans. To the contrary, the 30th of January appears to be the date with the most stable measurements, with the L1-similarity values approaching the respective L0-values.

In Figure 13, side views of the 3D images (XZ plane) are depicted for four MWBI scans of the same experimental setup (Breast#2 phantom, Rotation 180°, Tumour#3) performed on four distinct days. It is apparent that the reason for the decreased similarity of the 22nd December scans versus the measurements that were performed post the 30th of January is that the tumour response is detected at a slightly higher position and with a visibly increased intensity on the 22nd of December. The latter phenomenon could have to do with the sensitivity on the MWBI imaging software part, but does not affect the final image’s quality, related to the tumour’s detection and localization, in a negative way. The same observation holds when comparing the images in Figure 14 as well, which involve the Tumour#1 or Tumour#4 (instead of the Tumour#3) and otherwise the same configuration as for Figure 13. It is clearly visible in Figures 5,13 and 14 that the SCR level and the overall image quality is very good for the 22-December scans, however the implementation of the experimental setup is slightly different when compared to the posterior scans of January and February.

Figure 13.

Effective vertical position of the tumour phantom: Scans with Breast#2, Rotation180° and Tumour#3 inclusion: (a) 22-Dec-T#3-R2 (b) 30-Jan-T#3-R1 (c) 31-Jan-T#3-R1 (d) 03-Feb-T#3-R1.

Figure 14.

Effective vertical position of the tumour phantom: Scans with Breast#2, Rotation180° and Tumour#1 or Tumour4 inclusion: (a) 22-Dec-T#1-R1 (b) 30-Jan-T#4-R1 (c) 03-Feb-T#4-R1.

In addition, the increased L0 levels for the repetitions of the 22-December scans, as indicated in Figure 12, suggest potentially not sufficient waiting time for stabilization/immobilization of the tumour, after manual insertion in the breast phantom and before starting the 1st scan. This experimental factor was learnt from numerous preliminary tests with these breast phantoms and its handling got progressively optimized towards the end of the test campaign, when a more systematic series of MWBI scans was possible.

In Figure 15, the evolution of the L0-Similarity level over the full set of 34 MWBI images being considered in this analysis and shown in Figures 5–11 is depicted. Four curves are present in the figure, for either the full volume or only the volume inside the breast and the average or a single sensor fidelity zone.

Figure 15.

L0-similarity for different dates, breast phantoms, rotations and tumours.

The following observations can be made about these curves:

• The full volumes follow the same tendency as the in-breast volumes and appear to have slightly degraded similarity (higher values), barring the 22-Dec-B#2-Rot180 outlier scans.

• Averaging the sensor fidelity zones does not have a significant effect on similarity.

• Looking at the in-breast similarity curves, the L0-similarity is relatively stable around the 0.04 mark, again except for the 22-Dec-B#2-Rot180 scans. This is an important outcome of this analysis, concerning the stability and repeatability of the Wavelia#2 MWBI scan and image reconstruction in the case of repetition of a fixed experimental setup.

Figure 16 depicts the respective L1-Similarity curves. It can be observed that multiple values correspond to the same date, breast and rotation, as the L1 similarity compares measurements from the same date and the same breast phantom, after replacement and repositioning of the tumour phantom only. What can be inferred from this figure is that:

• Again, the full volumes vs. in-breast volumes, as well as single vs. average fidelity zones present the same trends as in L0.

• The values for the in-breast volume range from 0.04 (close to L0), up to 0.15. Human error is a deciding contributing factor when replacing the tumour, which can lead to similarity values 3 times as high as those of L0.

Figure 16.

L1-similarity for different date, breast phantoms and rotations.

Concerning the L2-similarity levels, it can directly be observed in Figure 12 that the L2-Similarity values can be close to L1 but are in general higher. Repeating the scan of the same experimental setup on different dates (L2) requires complete repositioning of the phantom, as well as tumour placement, which provides a margin for even greater human error. In addition, the variation and potential impact of the environmental conditions on which the MWBI scan is performed (i.e. temperature within the room and the scanner, a distinct batch of transition liquid being injected in the scanner, distinct operator preparing the setup/performing the scan) are part of the L2 evaluation. The mean and standard deviation values for all similarity zones are depicted in Table 2, for different configurations, as well as for the concatenated data of all of them (Total).

Configuration	L0		L1		L2
	Mean	Std	Mean	Std	Mean	Std
Breast#2 Rot 180° (excl. 22-Dec)	0.033	0.005	0.057	0.02	0.104	0.01
Breast#2 Rot 180° (incl. 22-Dec)	0.069	0.064	0.092	0.067	0.2	0.119
Breast#2 Rot 0°	0.034	0.006	—	—	0.132	0.013
Total	0.061	0.058	0.092	0.067	0.196	0.117

Table 2.

In-breast volume mean and std. of different levels of similarity for different configurations.

According to the table, the expected tendency for progressive degradation of the achieved level of repeatability when passing from L0 to L1 and L2 are indeed followed, such that L0 < L1 < L2. The similarity levels are clearly degraded (higher values of the metric defined in Eqs. (1) and (2)) when including the scans of the 22nd December, Breast#2 phantom, Rotation 180° in the analysis, as earlier discussed and experimentally justified. When these datasets are excluded from the analysis, it is interesting to confirm that comparable levels of the L0 similarity (as depicted and analysed in more detail in Figure 15), but also of the L2 similarity, are achievable on both Breast#2 Rotation 180° and Breast#2 Rotation 0° experimental setups.

6. Conclusions

Imaging results for 34 MWBI scans, being part of the on-site evaluation for acceptance of the Wavelia#2 MWBI system at the GUH clinical investigation site for a Phase-II Pilot#1 clinical investigation, have been presented. The experimental testing and validation of Wavelia#2 was performed on highly heterogeneous and complex breast phantoms, and in diverse experimental setups. Significant variability of each experimental setup itself was inherent in the MWBI scans being part of this analysis. All the experimental setups were systematically scanned twice, all along the test campaign, without moving the breast phantom or tumour in-between the two consecutive MWBI scans. The main objective of this test campaign was to understand and assess the sources of variability, in an attempt to isolate and quantify the impact of the imaging system itself (measurement variability and imaging algorithm uncertainty) on the repeatability of the MWBI imaging results.

The similarity between the images of repeated scans under different conditions of repetition was quantitatively assessed using the sum-squared difference metric. It was observed both qualitatively/visually and quantitatively that repeating a measurement without changing anything in the experimental setup (L0 level) yields very similar imaging results. A quite stable level of image similarity was demonstrated to be achievable for the L0 level, on multiple tests with highly diverse experimental setups. The inherent variability introduced by each distinct implementation of the experiment was demonstrated to be mapped to L1 and L2 similarity levels higher than the L0 levels, however consistently reproduced on multiple days of testing and with diverse experimental setups being employed. The reported results are promising, in terms of the expected performance of the Wavelia#2 prototype in the ongoing clinical investigation, the reliability of the reported images, as well as towards suitability of the prototype for a repeatability study on patients.