Mammography is the gold standard technology for mammographic screening, which has been demonstrated through different randomized controlled trials (RCTs) [1–3] to reduce breast cancer mortality. However, it has some limitations and potential harms, such as the use of ionizing radiation, breast compression and performance restrictions due to the intrinsic nature of x-rays. In particular, breast density is a restrictive property that can prevent breast cancer detection in mammograms of women with radiographically dense breasts [4,5]. In general, women are eligible for biannual screening after the age of 49 in order to minimize the impact of ionizing radiation. Nevertheless, recent studies estimate that breast cancer is diagnosed in 6.6% of women below the age of 40 [4], and an average of 20% of breast cancer cases in Europe occur in women when they are younger than 50 years old [6].

Many efforts are being done to develop non-ionizing technologies which could allow to carry out screening with neither age nor follow-up examination interval restrictions. In this context, microwave imaging appears as a promising technology for breast lesions detection [7]. Microwave imaging methods are developed to discriminate between healthy tissues and tissues with lesions by exploiting their contrast in dielectric properties, i.e. permittivity and conductivity, within the spectrum of microwave frequencies. A high contrast (up to 5) has been reported [7] between healthy breast tissue and malignant tissue, while newer studies confirm a high contrast only between fatty and malignant breast tissues, while it decreases between healthy fibro glandular and malignant tissues [8,9].

Microwave imaging techniques may be classified into two main groups: microwave tomography and ultra-wideband (UWB) radar methods [10]. Microwave tomography is based on inverse scattering algorithms that create maps of permittivity and conductivity; however, inverse scattering approaches could suffer from mathematical instability, which may not converge to a meaningful solution. UWB radar methods instead perform a linear reconstruction of the image, which is a scattering map in arbitrary units.

The exploitation of both microwave imaging techniques has led to the construction of different prototypes, which may differ in hardware and imaging algorithm, i.e., software. Some prototypes are being tested at clinical level: a quite complete review of prototypes at clinical level can be found in [11].

One of these prototypes, Maria system, uses an array of 60 antennas and a matching liquid to carry out radar approach [12] with a sensitivity of 76% [13].

Among prototypes at clinical level, MammoWave requires to operate just two (azimuthally rotating) antennas without any matching liquid, i.e. antennas and breast are in free space. MammoWave has an innovative frequency domain imaging algorithm which is based on Huygens Principle (HP) [14]. This device has been presented, tested and clinically validated [15–17]. Images obtained using the proposed apparatus are intensity maps, given in linear arbitrary units, representing the homogeneity of tissues’ dielectric properties. In this paper, we propose to generate, for each breast, a set of microwave images by using different values of conductivity in the HP imaging algorithm, i.e. conductivity weighted microwave images. Next, microwave images’ parameters, i.e. features, are calculated to quantify and measure the non-homogenous behaviour of the image. We show that an appropriate selection of image features may allow distinction between breasts with no radiological finding (NF), and breasts with radiological findings (WF), i.e. with lesions which may be benign or malignant. In addition, we show that an appropriate combination and use of image features may allow performance enhancement. The procedure has been empirically verified on 103 breasts, each one with the correspondent output of the radiologist study review obtained using echography and/or mammography and/or MRI.

According to the radiologist study review, a total number of 52 NF (19 dense, i.e. ACR density C and D) and 51 WF (22 dense, i.e. ACR density C and D) breasts were analyzed. The summary of the patient population used in this study is shown in Table 1, while the summary of the radiological study review is given in Table 2. In Table 3, some details of the radiologist study review are given for the 51 WF breasts. Lesions’ final assessment, performed using pathology and/or at least one year of clinical follow-up as reference standards, leads to 30 benign and 17 malignant lesions, while in 4 cases the final assessment is not available.

The selected features for the selected conductivity weighed images are listed in Table 4. For each feature, we indicate: the mean and standard deviation for the NF breasts; the mean and standard deviation for the WF breasts; the decision offset corresponding to TN = 0.55; Welch’s t-test score and p-value; the AUC. ROC curves of the selected features are shown in Fig 2.

Six breasts are shown here in more details as six test cases, each one with three of the selected conductivity weighed microwave images (obtained for conductivities equal to 0.3 S/m, 0.4 S/m and 0.5 S/m, respectively). Figs 3 and 4 refer to NF breasts, while Figs 5–8 refer to WF breasts. Microwave images, normalized to unitary average of the intensity, are given here as 2D images in the azimuthal, i.e. coronal, plane; the images are divided into four quadrants corresponding to breast Upper-Outer (UO) quadrant; Upper-Inner (UI) quadrant; Lower-Outer (LO) quadrant; Lower-Inner (LI) quadrant. Moreover, 1D intensity projection on X and Y is displayed in the inserts. X and Y are given in meters; intensity is in arbitrary units. In each figure, the tables given as inserts of microwave images show the values of the correspondent selected features; in the same tables, for each feature we also report the binary score S in brackets, calculated from Eq (3).

For each one of the six test cases, the output and main findings of the radiologist study review, with the correspondent conventional images, is also given. BI-RADS categories are also given for WF breasts. In more details, Figs 5 and 6 refer to breasts with microcalcifications and for both cases the final assessment is benign lesion; Fig 7 refers to breast with suspected carcinoma and the final assessment is malignant lesion; Fig 8 refers to breast with a macro-calcification and focal contrast enhancement (the final assessment is not available).

Performances of the rule-of-thumb introduced above are evaluated empirically, after setting M = 2 and N = 3. We obtain a sensitivity of 38/51 ~ 74% (which increases to 18/22 ~ 82% when considering dense breasts only, i.e. ACR C and ACR D), with a specificity of 32/52 ~ 62%. Sensitivity performances of the rule-of-thumb are summarized in Table 5, while the performance details for each one of the 51 WF breasts can be found in the last column of Table 3. In Table 5, MammoWave rule-of-thumb sensitivity is given also for benign and malignant findings, separately; specifically, for benign findings we obtain a sensitivity of 21/30 ~ 70% (which increases to 11/14 ~ 78% when considering dense breasts only) while for malignant findings we obtain a sensitivity of 12/17 ~ 71% (which increases to 6/7 ~ 85% when considering dense breasts only).

Microwave images obtained using the proposed apparatus are intensity maps, given in linear arbitrary units, representing the homogeneity of breast’s dielectric properties. MammoWave does not use any patient-specific estimation, which means that breast images are generated without any prior knowledge of patient-specific breast dielectric properties. In more details, the images have been obtained using free space dielectric constant in Eq (1). Concerning the conductivity, for each breast we produced ten different microwave images by varying the conductivity from 0 to 0.9 S/m (in agreement with the breast conductivity average values reported in [10]).

From visual inspection of microwave images, it can be pointed out that microwave images of WF breasts have a more non-homogenous behaviour with respect to NF breast. This confirms what was previously highlighted in [15,16], also through the use of phantom measurements, i.e. the contrast in dielectric properties between breast lesions and the surrounding tissues generates a peak in microwave images. Interestingly, small microcalcifications (1.6 mm) also lead to non-homogenous behaviour which can be visually appreciated.

With the aim of discriminating between WF and NF breasts, some dedicated features have been introduced and selected. Such features allow a quantification of the non-homogeneity of the microwave images: some of them describe the entire image [15,16], while others describe the peak region [23]. From Table 4, it is possible to verify that p-values of all the selected features are <0.001; thus, it follows that selected features are statistically robust in discriminating between WF and NF breasts. False Discovery Rate (FDR) correction for multiple comparisons may also be applied to the statistical tests: we verified that this leads to a slight increase of the p-values for the selected features, which remain statistically robust in discriminating between WF and NF breasts. Yet, from Table 4 it is clear that overlap exists among WF and NF breasts features. AUC of selected features span from 0.65 to 0.69. In addition, we also calculated AUCs of the selected features when considering dense breasts only, noting an increase up to 0.77.

The binary score S operating on the combination of features may be used for establishing an empirical rule-of-thumb allowing breast assessment; the underlying idea is that a “large number of occurrences of 1” may indicate a WF breast, while a “large number of occurrences of 0” may indicate a NF breast. From the examples given here, it can be noted that microcalcifications in an ACR C breast may have a “large number of occurrences of 1” in microwave images with lower conductivity weighting. Conversely, a carcinoma in an ACR C breast have a “large number of occurrences of 1” also in microwave images with higher conductivity weighting. Indeed, also from visual inspection it can be seen that a carcinoma in an ACR C may be better highlighted in microwave images with higher conductivity weighting. It follows that the use of a range of conductivity weighting when generating microwave images may be beneficial in detecting different kinds of lesions.

Performances of the proposed rule-of-thumb have been evaluated by empirically calculating the sensitivity (after setting M = 2 and N = 3), obtaining an overall value of 74%, with a specificity of 62%. Sensitivity increases to an overall value of 82% when considering dense breasts only. From the results obtained when considering benign and malignant findings, separately, it appears that MammoWave sensitivity is similar for both benign and malignant lesions, i.e. 70% and 71%, respectively (it should be noted that such values are lower than the overall value, since in 4 cases the final assessment is not available). Higher breast density has a positive impact in detection, increasing MammoWave sensitivity for both benign and malignant lesions to 78% and 85%, respectively. These values are in agreement with [12,13], where symptomatic patients only have been recruited; specifically, it is reported that sensitivity is 74% and 76% for benign and malignant lesions, respectively, and it increases to 79% (in both benign and malignant lesions) when considering dense breasts [13].

A patient-specific knowledge of dielectric properties may lead to a further improvement in sensitivity/specificity [23,24], By comparing the performances of the proposed rule-of-thumb (which combines many features) with respect to single features ROC curves (given in Fig 2), we can appreciate an increase in sensitivity; this is in agreement with [25], where a multi-feature analysis of Magnetic Resonance breast images has been performed.

A limitation of this investigation is that we did not consider pre-menstrual information of the subjects, due to such information not being available. A further limitation of this investigation is that, concerning rule-of-thumb modality for breast assessment, the impact on detection capabilities of the features/methods selection procedure, number of selected features/methods as well as of features’ correlation has not been investigated. Specifically, the number of selected features, i.e. 4, and methods, i.e. 5, has been selected arbitrarily. Moreover, ROC curves have been empirically calculated. However, it should be emphasized that the main aims of this paper are: i) to verify if a selection of features obtained from a range of conductivity weighted microwave images may allow discriminating between NF and WF breasts; ii) to verify if an appropriate combination and use of microwave image features may achieve performance enhancement versus single feature. Finally, it should be pointed out that, for this study, each breast has its own correspondent output of the radiologist study review, which has been used here as gold standard for classification of the breast into two categories: NF and WF breast. Some details of the detected or suspected lesions (such as BI-RADS categories, sizes and notes) have been collected throughout the study and, thus, they are shown here, but they are not used in statistical analysis.

Further work on MammoWave, which has recently received CE Mark (Conformité Européenne) approval, is ongoing and more clinical trials are planned with the aim of improving clinical evidence on the use of microwave imaging in the breast screening pathway. In addition, while our main current goal is discriminating between NF and WF breasts, dedicated clinical trials are also planned for quantifying capability in distinguishing malignant lesions.