Isabelle Thomassin-Naggara

Nicolas Perrot

Sophie Dechoux

Carine Ribeiro

Jocelyne Chopier

Cedric De Bazelaire

Added value of one-view breast tomosynthesis combined with digital mammography according to reader experience

Added value of one-view breast tomosynthesis combined with digital mammography according to reader experience

Highlights for review

Breast tomosynthesis improves diagnostic performance especially for radiologists with lower experience in mammography Adding only one-view digital breast tomosynthesis to mammography improves the cancer detection rate Breast tomosynthesis is mainly useful for helping radiologists to detect architectural distortion Abstract Purpose: To retrospectively evaluate the added value of one-view breast tomosynthesis in adjunct with mammography to characterize breast lesions.

Materials and methods: Our institutional ethics committees approved the study and granted a waiver of informed consent. One hundred fifty-five women (mean age, 51.3 years, range: 24-92 years) who systematically underwent mammography and breast tomosynthesis with subsequent percutaneous biopsy were analyzed. Four radiologists (two seniors, R1 and R2, and two juniors, R3 and R4 with 30, 10, 3 and 1 years of experience in breast imaging, respectively) independently reviewed exams in 2 steps: mammography alone and tomosynthesis in adjunct with mammography. The lesions in the cohort included 39.3% (61/155) cancers, 2.5% (4/155) high-risk lesions and 58.1% (90/155) benign lesions. A receiver operating characteristic (ROC) curve analysis was performed to compare the results of the two readings.

Results: There was almost perfect agreement irrespective of reader experience for the reading of the mammography in adjunct with tomosynthesis, whereas agreement was poor between junior and senior readers for the reading of mammography alone. Area under the ROC (Az) values for the tomosynthesis in adjunct with mammography were significantly better than Az values for mammography alone for all readers except the most experienced, for whom only a tendency was noted. The proportion of cancers undiagnosed by mammography alone that were well diagnosed by tomosynthesis in adjunct with mammography was 6.5% (4/61), 13.1% (8/61), 27.8% (17/61) and 26.2% (16/61) for Readers 1, 2, 3 and 4, respectively. The proportion of false positive cases induced by the addition of breast tomosynthesis to mammography was 2.1% (2/94), 2.1% (2/94), 9.5% (9/94) and 12.7% (12/94) for Readers 1, 2, 3 and 4, respectively.

While this technique is highly sensitive (80-90%) for less dense breasts (types 1 and 2), its sensitivity is only 50-60% for dense breasts (types 3 and 4) [START_REF] Leconte | Mammography and subsequent whole-breast sonography of nonpalpable breast cancers: the importance of radiologic breast density[END_REF]. This phenomenon is due to the superimposition of breast tissue, because mammography is a 2D projection technique and, similarly to "anatomical noise", normal gland limits the visibility of breast abnormalities.

Another factor influencing cancer visibility is the tumor pattern, such as lobular cancer, which in some patients may not produce any mass and may be difficult to detect on 2D imaging [START_REF] Andersson | Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings[END_REF].

Recently, with the development of digital mammography, a new technique named breast tomosynthesis has been developed, offering 3D mammographic acquisition. This technique is derived from tomography and consists in a series of exposures made on the same film while the tube moves in definite angulations . This imaging technique allows visualization of the breast in three dimensions and lowers the impact of tissue overlap. Thus, theory suggests that this technique could be useful in a routine setting by potentially increasing both the sensitivity and specificity for the detection and characterization of breast lesions. As tomosynthesis is a new technique, the majority of initial studies published on the technique deal with optimizing the physical and geometric parameters for tomosynthesis, [START_REF] Zhou | A computer simulation platform for the optimization of a breast tomosynthesis system[END_REF][START_REF] Wu | A comparison of reconstruction algorithms for breast tomosynthesis[END_REF] improving the reconstruction algorithms, [START_REF] Wu | Voting strategy for artifact reduction in digital breast tomosynthesis[END_REF][START_REF] Zhang | A comparative study of limited-angle cone-beam reconstruction methods for breast tomosynthesis[END_REF] and developing CAD for tomosynthesis [START_REF] Reiser | Computerized mass detection for digital breast tomosynthesis directly from the projection images[END_REF][START_REF] Chan | Computer-aided detection system for breast masses on digital tomosynthesis mammograms: preliminary experience[END_REF][START_REF] Chan | Computer-aided detection of masses in digital tomosynthesis mammography: comparison of three approaches[END_REF][START_REF] Reiser | Automated detection of microcalcification clusters for digital breast tomosynthesis using projection data only: a preliminary study[END_REF]. In addition, most of these studies were performed on a small number of patients.

Recently, breast tomosynthesis was proven to be better than mammography [START_REF] Rafferty | Digital mammography: novel applications[END_REF], including for use in a population-based screening program [START_REF] Skaane | Comparison of Digital Mammography Alone and Digital Mammography Plus Tomosynthesis in a Population-based Screening Program[END_REF][START_REF] Bernardi | Application of breast tomosynthesis in screening: incremental effect on mammography acquisition and reading time[END_REF], and it could possibly be implemented in our screening program in the future. However, one of the primary uses of digital breast tomosynthesis is likely to be in diagnosis, to optimize lesion characterization and improve positive predictive values of percutaneous biopsies, which, in a large majority of A c c e p t e d M a n u s c r i p t 6 cases, reveal benign entities. Few papers have proposed any guidelines on how to use this technique in daily practice [START_REF] Teertstra | Breast tomosynthesis in clinical practice: initial results[END_REF].

The aim of our study was therefore to report our experience in a clinical routine use of tomosynthesis, with an evaluation of the added value of this technique by comparing the diagnostic accuracy of breast tomosynthesis combined with mammography with the accuracy of mammography alone. Our purpose was not to compare the accuracy of the two techniques but to evaluate if tomosynthesis in adjunct with mammography is better than mammography alone

Materials and methods

Our institutional ethics committee (Comité de Protection des Personnes Ile de France V) approved the study and granted a waiver of informed consent.

Population

Between December 1 2009 and July 31 2011, all women who underwent mammography with subsequent percutaneous biopsy in our center were consecutively included (n = 202). We excluded patients with only craniocaudal breast tomosynthesis (n = 14), patients lost to follow-up (n = 7), patients with breast implants (n = 9) and patients lost to our picture archiving and communication system (PACS) (n = 17).

The final cohort consisted in 155 women (mean age, 51.3 years, range: 24-92 years).

Seventy-one patients (45.8%) were menopausal and 84 (54.1%) were non menopausal in.

Familial history of breast cancer was found in 36.1% (56/155) and a personal history of breast cancer in 9% (14/155). Indications for mammography were screening (n = 118), 6 months' follow up of BI-RADS 3 lesion (n = 2), systematic follow-up after breast cancer (n = 13) and clinical abnormality (n = 21) including palpable lump (n = 19), nipple discharge (n = 1) and nipple retraction (n = 1).

Acquisition

Mammography was performed on a digital breast mammography system (Selenia Dimensions 3D System, Hologic (Bedford, Massachussetts, USA) ). All women underwent digital mammography in two views (craniocaudal [CC] and mediolateral [MLO]) of both breasts, systematically followed by bilateral tomosynthesis in one view (MLO). The acquisition protocol was set to 11 projection images over a 15° arc from -7.5° to +7.5° on a breast compressed in exactly the same MLO position as the mammographic acquisition. The image receptor was a 70-micron pixel pitch selenium direct-capture detector. Four radiologists (two seniors: R1 and R2; two juniors: R3 and R4), with respectively 30 years, 10 years, 3 years and 1 year of experience in breast imaging, independently reviewed exams in 2 steps. The readers were blinded to the pathological results but were not blinded to clinical examination or to prior mammography when available as routine practice.

In a first step, readers only analyzed mammographic acquisition including oblique and craniocaudal views: breast density was subjectively assessed from a global evaluation of parenchymal density and was categorized as per the American College of Radiology's BI-RADS lexicon for breast density descriptors, from fatty replaced (grade A), to extremely dense (grade D). The most suspicious mammographic abnormality was characterized as mass, asymmetric density, cluster of microcalcifications and architectural distortion. Lesion size was recorded using the two mammographic views. Finally, readers classified the abnormality according to BI-RADS classification (BI-RADS MAMMO ) in seven steps increasing with the probability of malignancy, according to the American College of Radiologists: 1 = BI-RADS 1 (negative), 2 = BI-RADS 2 (benign finding), 3 = BI-RADS 3 (probably benign finding), 4 =BI-RADS 4A (low suspicious abnormality), 5 = BI-RADS 4B (medium suspicious abnormality), 6 = BI-RADS 4C (highly suspicious abnormality) and 7 = BI-RADS 5 (highly suggestive of malignancy). Only the most suspicious finding was considered per patient.

In a second step, immediately after the first step, readers analyzed breast tomosynthesis.

The abnormality was characterized as mass, asymmetric density, cluster of microcalcifications and architectural distortion. Lesion size was recorded using breast tomosynthesis acquisition on the slice judged as the best for the measurement by each reader.

Finally, readers included tomosynthesis information to obtain a new BI-RADS classification, named "BI-RADS MAMMO+TOMO ".

A c c e p t e d M a n u s c r i p t 9 At the end of the procedure, the side and the location of the abnormality subsequently biopsied were given to each reader. If the lesion described did not correspond to the location of the biopsy, the score of the lesion was re rated as BI-RADS 1 and the lesion was considered as missed either by mammography alone or by both mammography and tomosynthesis.

Reference standard

Histopathological findings included 90 benign lesions, 4 high-risk lesions and 61 malignant tumors (Table 1). The diagnoses were established by surgical pathology (n = 74), or percutaneous biopsy followed by a 1-year negative follow-up (n = 81). All malignant tumors and high-risk lesions were confirmed by surgical excision. Among patients with benign lesions, 9 underwent surgery (8 radial scar and one papilloma).

Statistical analysis

Descriptive analysis was performed using a nonparametric Mann-Whitney test for continuous variables and Fisher's exact test for categorical or nominal variables.

Confidence level ratings of the images were also used to calculate the sensitivity, A receiver operating characteristic (ROC) curve analysis was performed to compare the results of readings of mammography and of tomosynthesis for each reader in adjunct with mammography (www.medcalc.be). Overall ROC curves (BIRADS scores) averaged over four readers for mammography and tomosynthesis in adjunct with mammography were also compared using Metz-ROC software (http://metz-roc.uchicago.edu/). A P value of less than 0.05 was considered to indicate a statistically significant difference. Statistical analyses were performed using MedCalc software (www.medcalc.be, Belgium).

A c c e p t e d M a n u s c r i p t 11

Results

Descriptive results

Breast density was rated by the four readers as A from 5/155 to 9/155 (3.2% to 5.8%), as B from 42/155 to 45 /155 (27% to 29%), as C from 74/155 to 84/155 (47.7% to 54.1%) and D from 21/155 to 30/155 (13.5% to 19.3%) of the population studied. Whatever the reader considered, breast density was rated C or D in more than 50% of the patients studied.

Using mammography alone, an abnormality was detected in 118/155 (76.1%), 121/155 (78%), 81/155 (52.2%) and 71/155 (45.8%) women, for readers 1, 2, 3 and 4, respectively. These lesions were characterized as an asymmetric density (nR 1 =12, nR 2 =14, nR 3 =3, nR 3 =8), as a mass (nR 1 =33, nR 2 =31, nR 3 =25, nR 4 =30), as a distortion (nR 1 =38, nR 2 =42, nR 3 =17, nR 4 =18) or as a cluster of microcalcifications (nR 1 =35, nR 2 =34, nR 3 =36, nR 4 =35) (figure 1).

When tomosynthesis was added, an abnormality was detected in 124/155 (80%), 130/155 (83.8%), 106/155 (68.3%) and 99/155 (63.8%) for readers 1, 2, 3 and 4, respectively. Thus, mammography classified as negative (BIRADS 1 or 2) was reclassified as positive (BIRADS 3, 4, 5) in 6/37 (16.2%) including 5 distortions and one mass, 9/34 including 8 distortions and one mass (26.4%), 27/74 including 22 distortions, 4 masses, and one cluster of microcalcifications (36.4%) and 28/64 including 23 distortions and 5 masses (43.7%), for readers 1, 2, 3 and 4, respectively (figure 2 and3).

Comparative performance of mammography and the combination of mammography and tomosynthesis according to reader experience

Interobserver agreement

A c c e p t e d M a n u s c r i p t 12 Using mammography alone, there were an almost perfect agreement for lesion characterization between the two junior readers (R3 and R4) and between the two senior readers (R1 and R2) but there was a poor agreement between junior and senior readers.

When breast tomosynthesis was added, these differences disappeared, with an almost perfect agreement whatever the combination performed (between junior readers, between senior readers or between senior and junior readers) (Kappa values from 0.731 to 0.880) (Table 2).

ROC analysis

Calculated by averaging the curves from the 4 readers, the mean area under the ROC for BIRADS MAMMO+TOMO (Az=0,809) was higher than that calculated for BIRADS MAMMO (Az=0,685) (p<0,01).

The area under the ROC (Az) BIRADS MAMMO+TOMO was 0.792, 0.819, 0.806, and 0.822 for readers 1, 2, 3, and 4, respectively. Az BIRADS MAMMO was 0.741, 0.711, 0.651, and 0.665 for readers 1, 2, 3, and 4, respectively. There was a significant difference between BIRADS MAMMO and BIRADS MAMMO+TOMO for all readers but the most experienced one, for whom there was only a tendency for BIRADS MAMMO + TOMO to be superior to BIRADS MAMMO (Table 3). (Figure 4)

Comparison of the accuracy of mammography with and without tomosynthesis (Table 4) Whatever the experience of the reader considered, the addition of breast tomosynthesis improved the sensitivity and negative predictive value of mammography read alone.

The accuracy of the tomosynthesis in adjunct with mammography was higher than that of mammography alone for reader 2 (P = 0.02) and reader 3 (P = 0.03). For reader 4, the accuracy of the combination of mammography and tomosynthesis was higher than that of A c c e p t e d M a n u s c r i p t 13 mammography alone only in the malignant lesion subgroup (P < 0.0001) due to the high rate of false positives for this junior reader (12/94). For reader 1, no difference was found between mammography alone and mammography with tomosynthesis. The addition of tomosynthesis increased correctly the diagnostic confidence (i.e. the level of confidence increased in truepositive cases and decreased in true-negative cases) in 3.87% (6/155), 7% (11/155), 10.4% (13/155) and 3.87% (6/155) cases for readers 1, 2,3 and 4, respectively (Table 5).

The proportion of cancers undiagnosed by mammography alone that were well diagnosed by the addition of breast tomosynthesis was 6.5% (4/61), 13.1% (8/61), 27.8% (17/61) and 26.2% (16/61) for readers 1, 2, 3 and 4, respectively. These lesions corresponded to architectural distortion in 100% (4/4), 100% (8/8), 88% (15/17) and 75% (12/16) of cases for readers 1, 2, 3 and 4, respectively. All these lesions were invasive cancers whatever the reader considered and were invasive lobular carcinoma in 3/4 (75%), 4/8 (50%), 4/17 (23.5%) and 4/16 (25%) of cases for readers 1, 2, 3 and 4, respectively.

The proportion of false-positive cases that were induced by the addition of breast tomosynthesis to mammography was 2/94 (2.1%), 2/94 (2.1%), 9/94 (9.5%) and 12/94 (12.7%) for readers 1, 2, 3 and 4, respectively.

A c c e p t e d M a n u s c r i p t Discussion

Our study demonstrates that adding one-view digital breast tomosynthesis to mammography improved diagnostic performance and reproducibility, with a decrease of between 6.5% and 26.2% in the proportion of cancers that remained undiagnosed. There was a significant difference between BIRADS MAMMO and BIRADS MAMMO+TOMO for all readers but the most experienced one, for whom there was only a tendency for BIRADS MAMMO + TOMO to be superior to BIRADS MAMMO .

The first pilot studies on breast tomosynthesis showed that this technique allows a better image quality than digital mammography [START_REF] Good | Digital breast tomosynthesis: a pilot observer study[END_REF], with the potential to decrease the recall rate when used adjunctively with digital mammography by improving specificity [START_REF] Poplack | Digital breast tomosynthesis: initial experience in 98 women with abnormal digital screening mammography[END_REF]. In fact, Gur et al. demonstrated that the added value of breast tomosynthesis was only found when it was added to the reading of 2D mammography (P > 0.0001), while no significant difference was found between breast tomosynthesis alone and 2D mammography [START_REF] Gur | Digital breast tomosynthesis: observer performance study[END_REF]. However, most of the subsequent papers published between 2008 and 2011 compared breast tomosynthesis alone to mammography alone and showed that tomosynthesis alone did not outperform digital mammography, especially using a one-view tomosynthesis acquisition [START_REF] Teertstra | Breast tomosynthesis in clinical practice: initial results[END_REF][START_REF] Gennaro | Digital breast tomosynthesis versus digital mammography: a clinical performance study[END_REF][START_REF] Wallis | Two-view and single-view tomosynthesis versus full-field digital mammography: high-resolution X-ray imaging observer study[END_REF]. One possible explanation is that mammography is slightly more sensitive than breast tomosynthesis to detect calcification [START_REF] Spangler | Detection and classification of calcifications on digital breast tomosynthesis and 2D digital mammography: a comparison[END_REF], while tomosynthesis seems to improve visualization of masses and architectural distortions. [START_REF] Rafferty | Digital mammography: novel applications[END_REF]. Thus, our study was based on the hypothesis that mammography and breast tomosynthesis complement each other and that their combined use might reduce the error rate for false negatives compared to mammography alone, in line with more recently published findings [START_REF] Rafferty | Assessing radiologist performance using combined digital mammography and breast tomosynthesis compared with digital mammography alone: results of a multicenter, multireader trial[END_REF][START_REF] Zuley | Digital breast tomosynthesis versus supplemental diagnostic mammographic views for evaluation of noncalcified breast lesions[END_REF]. Our results confirm that a combined interpretation of mammography and tomosynthesis improve diagnostic accuracy, as previously demonstrated [START_REF] Gur | Digital breast tomosynthesis: observer performance study[END_REF][START_REF] Michell | A comparison of the accuracy of film-screen mammography, full-field digital mammography, and digital breast tomosynthesis[END_REF]. In the for combined reading, compared to a sensitivity of 88% and a specificity of 60% for mammography alone) [START_REF] Gur | Digital breast tomosynthesis: observer performance study[END_REF]. In comparison with the results of Gur et al., our mammographic and combined mammographic and tomosynthesis sensitivities were relatively low because we considered our BIRADS-3 findings as negative as Rafferty et al., who obtained comparable values [START_REF] Rafferty | Assessing radiologist performance using combined digital mammography and breast tomosynthesis compared with digital mammography alone: results of a multicenter, multireader trial[END_REF].

In contrast to the study by Rafferty et al., our work details the specific added value for each reader and reveals that it mainly depends on reader experience. In fact, using ROC curve analysis, we found a significant difference between BIRADS MAMMO and BIRADS MAMMO+TOMO for three readers, in line with previous reports [START_REF] Rafferty | Assessing radiologist performance using combined digital mammography and breast tomosynthesis compared with digital mammography alone: results of a multicenter, multireader trial[END_REF][START_REF] Michell | A comparison of the accuracy of film-screen mammography, full-field digital mammography, and digital breast tomosynthesis[END_REF], but for the most experienced reader there only a tendency for superiority of BIRADS MAMMO + TOMO in comparison with BIRADS MAMMO . Reader experience is an important parameter to consider when evaluating the accuracy of the added value of tomosynthesis. Our study emphasizes that the added value of breast tomosynthesis when combined with mammography depends on reader experience. This is in line with Wallis et al., who found that two-view tomosynthesis outperformed 2D mammography, but only for readers with the least experience [START_REF] Wallis | Two-view and single-view tomosynthesis versus full-field digital mammography: high-resolution X-ray imaging observer study[END_REF]. Their study differs from ours in that it compared two-view and single-view tomosynthesis alone with digital mammography alone. Moreover, our study demonstrates that tomosynthesis improves reproducibility of the reading, especially between junior and senior readers, and that tomosynthesis makes mammographic interpretation easier for juniors and homogenizes diagnostic performance, with a lower impact of experience on diagnostic accuracy.

Our study confirms that adding tomosynthesis to mammography improves the cancer detection rate, as previously demonstrated in an unblinded study by Anderson et al. [START_REF] Andersson | Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings[END_REF] and, more recently, in a large population-based screening program [START_REF] Skaane | Comparison of Digital Mammography Alone and Digital Mammography Plus Tomosynthesis in a Population-based Screening Program[END_REF][START_REF] Ciatto | Integration of 3D digital mammography with tomosynthesis for population breast-cancer screening (STORM): a prospective comparison study[END_REF]. In our study, the A c c e p t e d M a n u s c r i p t 16 addition of tomosynthesis decreased the proportion of cancers that remained undiagnosed by between 6.5% and 26.2%. Moreover, our study confirms that the tomosynthesis enables the detection of more invasive cancer (12): In our experience, all cancers detected by tomosynthesis when combined with mammography were invasive cancers. Our data demonstrate that the assessment was accurate, even in a population where more than 50% of the patients were considered, whatever the reader, to have dense breast. This probably explains why our increasing detection rate was lower than that recently reported by Skanne et al. (27% increase) [START_REF] Skaane | Comparison of Digital Mammography Alone and Digital Mammography Plus Tomosynthesis in a Population-based Screening Program[END_REF]. Moreover, our inclusion criteria introduced a selection bias with an incompletely blinded reading. However, this potential bias did not appear to have an impact on false-positive rates, which remained lower, whatever the level of reader experience, than the 15% decrease reported by Per Skanne [START_REF] Skaane | Comparison of Digital Mammography Alone and Digital Mammography Plus Tomosynthesis in a Population-based Screening Program[END_REF].

In our study, subgroup analysis demonstrates that breast tomosynthesis is mainly useful for helping radiologists to detect architectural distortion (depending on reader experience, 75% to 100% of all cancers missed by mammography were well-diagnosed by breast tomosynthesis), as suggested by Skaane et al. [START_REF] Skaane | Comparison of Digital Mammography Alone and Digital Mammography Plus Tomosynthesis in a Population-based Screening Program[END_REF]. Regarding the type of cancer detected, breast tomosynthesis led to improved detection of invasive lobular cancer compared to mammography, mainly for experienced readers (75% and 50% of missed cancers) but not for less experienced readers (23.5% and 25% of missed cancers) as described by Teertstra et al. [START_REF] Teertstra | Breast tomosynthesis in clinical practice: initial results[END_REF].

Our study has several limitations. First, as suggested by Rafferty et al., we performed breast tomosynthesis in a single view to limit the added radiation dose [START_REF] Rafferty | Digital mammography: novel applications[END_REF]. However, some authors have suggested the superiority of both MLO and CC projections for breast tomosynthesis [START_REF] Teertstra | Breast tomosynthesis in clinical practice: initial results[END_REF]. In addition, MLO acquisition was chosen, which could be more frequently responsible for inadequate visualization due to more frequent patient motion. Moreover, Andersson et al. reported that cancers were more obvious in the CC view in the A c c e p t e d M a n u s c r i p t majority of cases because of a smaller overlap of fibroglandular tissue than in MLO views [START_REF] Andersson | Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings[END_REF].

As these authors emphasize, the problem of obscuring tissue is related to the morphology of the lesion and mainly affects the detection of round masses [START_REF] Andersson | Breast tomosynthesis and digital mammography: a comparison of breast cancer visibility and BIRADS classification in a population of cancers with subtle mammographic findings[END_REF]. This is probably why, in our study, all of the cancers missed by mammography were detected using tomosynthesis by an architectural distortion. Thus, our study likely underestimates the added value of tomosynthesis for round masses. Second, due to our inclusion criteria (all women who underwent mammography with subsequent percutaneous biopsy), the interpretation of mammography and breast tomosynthesis could have produced 'distorted' ROC results, because readers would have forced a sort of "lesion searching" process. However, this bias is equivalent for both procedures.

Conclusion

In conclusion, adding breast tomosynthesis to mammography improves reproducibility and diagnostic performance especially for radiologists with lower experience in mammography. However, for the overall readers, our study demonstrated a substantial decrease of between 6.5% and 26.2% in the proportion of cancers that remained undiagnosed, especially by improving the detection of architectural distortion.

4 Conclusion:

 4 Adding breast tomosynthesis to mammography improved sensitivity and negative predictive value for all readers except for the most experienced one, in whom only a tendency for improvement was noted. Keywords: Breast tomosynthesis • Mammography • cancer • diagnosis A c c e p t e d M a n u s c r i p t Introduction Mammography is the first-line technique for diagnostic imaging of breast pathology.

  specificity and accuracy for each image data set in the diagnosis of malignancy. Ratings of BI-RADS 1, 2 or 3 indicated a reading of a benign lesion. Ratings of 4 and 5 indicated a reading of a malignant lesion. The accuracy of mammography and of mammography and tomosynthesis combined was compared using McNemar's two-tailed test. The following hypotheses were tested: (a) same number of lesions correctly classified by both image data sets; (b) different number of lesions correctly classified by both image data sets. Quadratic κ coefficients were calculated to assess interobserver agreement between the two junior and two experienced breast imaging radiologists for lesion characterization, using A c c e p t e d M a n u s c r i p t 10 the following scale: 0.00-0.20 indicating slight agreement; 0.21-0.40, fair agreement; 0.41-0.60, moderate agreement; 0.61-0.80, substantial agreement; and 0.81-1.00, almost perfect agreement).

  Gur et al. on 125 patients, the authors found that tomosynthesis improved both sensitivity and specificity (with a sensitivity of 93% and a specificity of 72%

A c c e p t e d M a n u s c r i p t FIGURESFig. 1

 t1 FIGURES

Fig. 2

 2 Fig. 2 Invasive ductal carcinoma in a 52-year-old menopausal woman without any personal or familial history of breast cancer and referred for screening. All readers considered breasts as dense rated type 3. a Digital mammogram suggests the presence of an asymmetric density in the left breast which is considered as a subtle image on oblique view (a and b) and as invisible on craniocaudal view (c and d) e Breast tomosynthesis clearly demonstrates an architectural distortion associated with a mass (arrow).

Fig. 3 Fig 4 :FigureFigure(s) 4

 344 Fig.[START_REF] Zhou | A computer simulation platform for the optimization of a breast tomosynthesis system[END_REF] Invasive Lobular carcinoma in a 54 year-old menopausal woman with a familial history of breast cancer without any palpable mass addressed for screening. Breasts were considered dense, rated as type 3 by all readers. All readers missed the cancer reading digital mammography (BI-RADS 2) (a, b, c, d) but reclassified as BIRADS 5 breast imaging using breast tomosynthesis (arrow) (e and additional material fileVideo corresponding to figure3e)

21 TABLES Table 1

 TABLES1 Pathological diagnosis

			Population
			(n = 155)
	Establishment of final	Surgical pathology	47.7% (74)
	diagnosis	Percutaneous biopsy + short-term follow-up	52.2% (81)
	Final diagnosis	BENIGN LESIONS	58.1% (90)
		Ductal ectasia	2.6% (4)
		Intramammary lymph node	1.3% (2)
		Fat necrosis	0.6% (1)
		Apocrine metaplasia	4.5% (7)
		Epithelial hyperplasia	5.2% (8)
		Fibrocystic changes	18.7% (29)
		Papilloma	2.6% (4)
		Fibroadenoma	16.8% (26)
		Radial scar	5.8% (9)
		HIGH-RISK LESIONS	2.6% (4)
		Atypical ductal hyperplasia (ADH)	0.6% (1)
		Lobular carcinoma in situ (LCIS)	1.3% (2)
		Atypical lobular hyperplasia (ALH)	0.6% (1)
		MALIGNANT TUMORS	39.3% (61)
		Ductal carcinoma in situ (DCIS)	6.4% (10)
		Invasive ductal carcinoma	27% (42)
		Invasive lobular carcinoma	5.8% (9)

Table 2

 2

	Interobserver agreement
			BIRADS MAMMO	BIRADS MAMMO+TOMO
	Between senior readers	R1-R2	0.814 (+/-0.08)	0.874 (+/-0.08)
	Between junior readers	R3-R4	0.792 (+/-0.08)	0.880 (+/-0.08)
	Between junior and	R2-R3	0.446 (+/-0.07)	0.731 (+/-0.07)
	senior readers	R1-R3	0.482 (+/-0,07)	0.746 (+/-0.08)
		R2-R4	0.527 (+/-0.07)	0.738 (+/-0.08)
		R1-R4	0.528 (+/-0.07)	0.755 (+/-0.08)
	*Numbers are quadratic Kappa values (+/-SD)

Table 3

 3 Comparison of area under the ROC curve (Az), according to reader experience. Az and standard error (SE) are presented as measures of the discrimination between benign or high-risk and malignant lesions P value corresponds to the difference between Az BIRADS MAMMO and Az BIRADS MAMMO+TOMO

	Az	Overall	R1	R2	R3	R4
	BIRADS MAMMO	0,692 (+/-0.02) 0.741 (+/-0.04) 0.711 (+/-0.04) 0.651 (+/-0.04) 0.665 (+/-0.05)
	BIRADS MAMMO+TOMO 0,809 (+/-0.02) 0.792 (+/-0.04) 0.819 (+/-0.03)* 0.806 (+/-0.03) 0.822 (+/-0.03)
	P	<0,01	0.07	0.01	<0.001	<0.001

*

Table 4

 4 Differentiation between benign or high risk and malignant lesions

		Mean		R1	R2		R3		R4
		M	M+T	M	M+T	M	M+T	M	M+T	M	M+
											T
	Sensitivity (%)	72,9	89,3 83.6	86.8	81.9	90.1	59	86.8	67	93.4
	Specificity (%)	50,5	50,7	50	54.2	43.6	54.8	58.5	54.2	50	39.3
	PPV (%)	48,9	53,4	52	55.2	48.5	53.9	48	55.2	46.5	50
	NPV (%)	74,2	88,2 82.4	86.4	78.8	90.4	68.7	70.1	70.1 90.2
	Accuracy (%)	53,9	66,7 63.2	67	58.7	72.2	58.7	67	56.7 60.6
	TP = true positive, TN = true negative, FP = false positive, FN = false negative, PPV =
	positive predictive value, NPV = negative predictive value
	No. = Total number of lesions

Table 5 .

 5 Comparison of tomosynthesis according to reader experience

		Reader 1		Mammo + Tomo
		P = 0.17	No. correct	No. misclassified	Total
	Mammo	No. correct No. misclassified Total	94 (45+49) 10 (6+4) 104 (51+53)	4 (2+2) 47 (41+6) 51 (43+8)	98 (47+51) 57 (47+10) 155 (94+61)
	No. = total number of lesions (benign + malignant)
		Reader 2		Mammo + Tomo
		P = 0.02	No. correct	No. misclassified	Total
	Mammo	No. correct No. misclassified Total	86 (39+47) 16 (8+8) 102 (47+55)	5 (2+3) 48 (45+3) 53 (47+6)	91 (41+50) 64 (53+11) 155 (94+61)
	No. = total number of lesions (benign + malignant)
		Reader 3		Mammo + Tomo
		P = 0.03	No. correct	No. misclassified	Total
	Mammo	No. correct No. misclassified Total	82 (46+36) 22 (5+17) 104 (51+53)	9 (9+0) 42 (34+8) 51 (43+8)	91 (55+36) 64 (39+25) 155 (94+61)
	No. = total number of lesions (benign + malignant)
		Reader 4		Mammo + Tomo
		P = 0.36	No. correct	No. misclassified	Total
	Mammo	No. correct No. misclassified Total	76 (35+41) 18 (2+16) 94 (37+57)	12 (12+0) 49 (45+4) 61 (57+4)	88 (47+41) 67 (47+20) 155 (94+61)


Xavier Devroey

Gilles Perrouin

Maxime Cordy

Mike Papadakis
email: mike.papadakis@uni.lu

Axel Legay
email: axel.legay@inria.fr

Pierre-Yves Schobbens

A Variability Perspective of Mutation Analysis Technical Report

Keywords: D.2.4 [Software Engineering]: Software/Program Verification-Validation Mutation Testing, Featured Transition Systems 1. BEHAVIOURAL MUTATION TESTING Traditionally, research on mutation analysis

Mutation testing is an effective technique for either improving or generating fault-finding test suites. It creates defective or incorrect program artifacts of the program under test and evaluates the ability of test suites to reveal them. Despite being effective, mutation is costly since it requires assessing the test cases with a large number of defective artifacts. Even worse, some of these artifacts are behaviourally "equivalent" to the original one and hence, they unnecessarily increase the testing effort. We adopt a variability perspective on mutation analysis. We model a defective artifact as a transition system with a specific feature selected and consider it as a member of a mutant family. The mutant family is encoded as a Featured Transition System, a compact formalism initially dedicated to model-checking of software product lines. We show how to evaluate a test suite against the set of all candidate defects by using mutant families. We can evaluate all the considered defects at the same time and isolate some equivalent mutants. We can also assist the test generation process and efficiently consider higher-order mutants.

However, the recent years this situation has changed [START_REF] Offutt | A mutation carol: Past, present and future[END_REF] and mutation has also been applied for testing various design models. This situation is reported in the recent survey of Jia and Harman [START_REF] Jia | An analysis and survey of the development of mutation testing[END_REF] motivating the need for additional research on applying mutation testing on program artifacts other than code. Among the several works mentioned in the mutation testing survey [START_REF] Jia | An analysis and survey of the development of mutation testing[END_REF], Fabbri et al. [START_REF] Fabbri | Proteum/fsm: A tool to support finite state machine validation based on mutation testing[END_REF] proposed 9 mutation operators injecting faults in states, events and outputs of Finite State Machines (FSMs). Other formalisms were targeted such as EFSMs [START_REF] Bombieri | A mutation model for the SystemC TLM 2.0 communication interfaces[END_REF], statecharts [START_REF] Fabbri | Mutation testing applied to validate specifications based on Statecharts[END_REF] or UML state machines [START_REF] Aichernig | Killing strategies for model-based mutation testing[END_REF].

The formal nature of these specification languages was exploited to enable the use of verification tools in the context of mutation testing. For example, Amman et al. demonstrated the use of the model-checker SMV by mutating specifications and using counterexamples (violation of a temporal logic property) as test cases [START_REF] Ammann | Using model checking to generate tests from specifications[END_REF]. In addition, simulation techniques exists to detect and remove equivalent mutants. Aichernig et al. improved such simulation techniques using the ioco conformance relation [START_REF] Aichernig | Improving fault-based conformance testing[END_REF].

FEATURED TRANSITION SYSTEMS

Software Product Line (SPL) engineering is a sub-discipline of software engineering based on the idea that products of the same family can be built by systematically reusing assets, some of them being common to all members whereas others are only shared by a subset of the family. Such variability is commonly captured by the notion of feature. Individual features can be specified using languages such as UML, while their inter-relationships are organized in a Feature Diagram (FD) [START_REF] Kang | Feature-Oriented domain analysis (FODA) feasibility study[END_REF].

The main challenge in SPL engineering is to deal with the combinatorial explosion induced by the number of possible products (2 N for N features in worst case). To face this problem, Classen et al. introduced Featured Transition Systems (FTSs) [START_REF] Classen | Featured transition systems: Foundations for verifying variability-intensive systems and their application to ltl model checking[END_REF] in order to perform efficient behavioural model checking for SPLs. FTSs are Transition Systems (TSs) where each transition is labelled with a feature expression specifying which products of the SPL may fire the transition. A FTS is thus a compact representation of the behaviour of a whole product line. Formally, an FTS is a tuple (S, Act, trans, i, d, γ), where S is a set of states; Act a set of actions; trans ⊆ S × Act × S is the transition relation (with (s1, α, s2) ∈ trans sometimes noted s1 α -→ s2); d is a FD; and γ : trans → [[d]] → {⊤, ⊥} is a total function labelling each transition with a boolean expression over the features, which specifies the products that can execute the transition ([[d]] corresponds to the semantics of the FD d, i.e., all the different products that may be derived from d). Regarding the initial state, we define a total function init : S → ([[d]] → ⊤, ⊥) that indicates if a state i ∈ S is an initial state for a product p ∈ [[d]]. This function allows to model mutants that change the initial state of the system. A model checker for FTSs has been implemented in ProVeLines [START_REF] Cordy | Provelines: A product-line of verifiers for software product lines[END_REF], a product line of model checkers for the verification of SPLs' behavioural models.

APPROACH

The key aspect of our vision is to consider mutants as member of a family rather than perceived and analysed in isolation. Thus, we envision to exploit and adapt variability-management and analysis techniques to perform better and faster mutation testing , be it for single systems or highly-configurable systems such as software product lines.

Our vision can be seen as a generalisation at the model level of mutant schemata proposed by Untch et al [START_REF] Untch | Mutation analysis using mutant schemata[END_REF], but with additional benefits such as programming language independence, higher-order mutation, weak mutation automated test-case generation and equivalent mutants analysis. We will see these assets in the next section, while we focus here on modelling mutants families.

Let us consider a simple drink vending machine, whose behaviour is represented by the original transition system on left of Figure 1. We consider the application of three transition systems mutation operators [START_REF] Fabbri | Proteum/fsm: A tool to support finite state machine validation based on mutation testing[END_REF], removing a state, (see a) StateMissing), changing an event by another one (see b) EventExchanged) and changing the initial state of the system (see c) WrongStartState). These three mutants together with the original transition system can be compactly modelled using the FTS formalism presented in the previous section as depicted on the right of Figure 1. Our mutant family is therefore composed of a feature model and its accompanying FTS. As opposed to "usual" product lines, features do not map to a particular option or functionality to be be offered by the system but rather a mutation that can be applied to it.

We organize our feature hierarchy in two (the "root" layer, compulsory, is not really significant) layers: the "mutation operator" level where we define mutation operators available for the mutation family (features: sm, eex, wass) and the "mutation instance" where each leaf feature (e.g. sm_4) represents a specific mutation to be applied to the model (e.g. sm_4 stands for state 4 is missing). It is of course possible to use more sophisticated variability management constructs to exclude/require mutants or force the selection of only one mutant instance (using group cardinalities) for each mutation operator.

Once mutations are described in terms of a feature diagram, we can model the impact of mutations on the behaviour of the systems, by building a mutation FTS. The first step is to "lift" our original transition system into an equivalent FTS. To do so, we tag all transitions with the root feature whose only value is true since it is mandatory. Then for each mutation concerned we either tag the concerned transitions with mutations instances features or their negation (this how we mapped the missing state 4 corresponding to mutant a))

or add a new transition (exx_t_o) to describe an alternative behaviour when this mutant is applied. 1 This modelling proposal allows to finely configure the desired mutants by activating or deactivating features in the feature model. Exploiting our research on configurators' generation [START_REF] Boucher | Deriving configuration interfaces from feature models: A vision paper[END_REF], we can derive tailored mutants configurators. These configurators would allow testers to tune mutant generation exactly the same way they would configure their future car, while avoiding configurations forbidden by the feature model. Our approach can be used to describe first-order mutants (only one feature is selected at a time) or higherorder mutants (several features can be selected). Several mutations can also be modelled on the same element (e.g. changing both the destination and the event of a transition), by detailing feature expressions on transitions.

APPLICATIONS & CHALLENGES

Scalable Mutation Analysis

Variability-aware Mutation Analysis. The computational cost of executing a large number of mutants has been recognised as an obstacle to the practical application of mutation testing. Handling a large number of products is also challenging for SPL testing and was the raison d'être of FTS. Evaluating all products at the same time allowed significant gains (from 2 to 1000 times faster) for model-checking purposes [START_REF] Classen | Featured transition systems: Foundations for verifying variability-intensive systems and their application to ltl model checking[END_REF]. Recent work in SPL testing [START_REF] Kästner | Toward variability-aware testing[END_REF][START_REF] Kim | Shared execution for efficiently testing product lines[END_REF][START_REF] Nguyen | Exploring variability-aware execution for testing plugin-based web applications[END_REF] confirms the potential of this research direction. While there are similarities with Mutant Schemata [START_REF] Untch | Mutation analysis using mutant schemata[END_REF] at the program level, runtime execution differs. Indeed, in mutant schemata's approach mutants are independently run against each test case while as we traverse FTS transitions feature expressions indicate which mutants are being killed and which ones are surviving. Thus, we do not only compactly represent all the mutants as for metaprograms but also save time during execution by exploiting commonalities between mutants' behaviour. Jia and Harman claim that bottlenecks moved from compilation time to runtime [START_REF] Jia | MILU: A Customizable, Runtime-Optimized Higher-Order Mutation Testing Tool for the Full C Language[END_REF]. Our vision clearly adheres to this claim.

Selective Mutation. As surveyed by Jia and Harman [START_REF] Jia | An analysis and survey of the development of mutation testing[END_REF], selective mutation approaches are popular amongst cost reduction techniques. Selective mutation aims at reducing the number of mutants to consider using various criteria (e.g. random sampling, clustering or limiting the number of applicable mutation operators). Such selections can be easily modelled and verified (thanks to their translation in constraint solvers' inputs) using feature diagrams. For example, it can be interesting to assess criteria commonly applied to feature models such as t-wise coverage [START_REF] Perrouin | Pairwise testing for software product lines: comparison of two approaches[END_REF][START_REF] Cohen | Interaction testing of highly-configurable systems in the presence of constraints[END_REF] derived from combinatorial interaction testing. T-wise coverage select configurations so that all t-combinations of features are present, observing that most bugs are due to (undesired) feature interactions.

In our context, this corresponds to mutant interactions: 1-wise selection would ensure that every mutation is covered at least once, that is assessing a test suite against all first-order mutants, the classical "pairwise" (2-wise) would ensure that all possible combination of 2 nd -order mutants are covered. Usual t-wise approaches would not prevent higher-order (t=3,4,...) mutants from being generated. The main advantage of such techniques is that they drastically 1 See https://staff.info.unamur.be/xde/fts-testing/ mutation.html for more information. reduce the number of mutants to consider (few hundred even for feature models allowing billions of possibilities). It is also possible to mix criteria for a more fine grained selection and to prioritize mutants selection of interest, by assigning weights [START_REF] Johansen | Generating better partial covering arrays by modeling weights on sub-product lines[END_REF] on mutation operators/instances in the FM and/or considering multi-objective selection [START_REF] Henard | Multi-objective test generation for software product lines[END_REF][START_REF] Jia | An analysis and survey of the development of mutation testing[END_REF]. Mutant selection is enacted in the FTS using the projection operator [START_REF] Classen | Featured transition systems: Foundations for verifying variability-intensive systems and their application to ltl model checking[END_REF] that prunes unselected transitions and related states.

Coverage criteria can also be specified on the mutant family model ensuring that some states/transitions/actions are covered. Only these will be analysed for mutation (weak mutation). This can be done either by adapting transition systems' coverage criteria [START_REF] Devroey | Coverage Criteria for Behavioural Testing of Software Product Lines[END_REF] or formalising this search as a temporal logic formula to be checked by, e.g. our ProVeLines family of model-checkers [START_REF] Cordy | Provelines: A product-line of verifiers for software product lines[END_REF].

Test Case Generation

Thanks to the formal foundations of FTSs, various test and verification techniques can be invented or re-adapted to derive efficient mutant killing test suites. In our framework, a test case is simply a trace allowed by the FTS, that is a succession of actions in which the conjunction of feature expressions accumulated over the associated transitions is satisfiable w.r.t the FD [START_REF] Devroey | Coverage Criteria for Behavioural Testing of Software Product Lines[END_REF]. The necessity constraint [START_REF] Demillo | Constraint-based automatic test data generation[END_REF], expressing difference in behaviours between the original and mutated programs, can be easily translated as an LTL formula expressing a certain condition that is satisfied on the original system (all paths in which all transitions are only labelled by m). Thus, all counter-examples produced by ProV-eLines are behaviours killing mutants and for each behaviour, the feature expression indicating the combination of mutants covered is also provided. For weak mutation, we can negate a formula involving the particular state or action this mutant affects: counter-examples will necessarily reach the targeted mutant. This offers a complementary set of techniques to coverage and constraint-based generation [START_REF] Demillo | Constraint-based automatic test data generation[END_REF].

Equivalent Mutants Detection

Madeyski et al. recently surveyed the Equivalent Mutant Problem (EMP) [START_REF] Madeyski | Overcoming the equivalent mutant problem: A systematic literature review and a comparative experiment of second order mutation[END_REF] and categorized existing techniques falling in three categories: detection, suggestion and avoidance. In our context, EMP is: are there products of the FD whose associated behaviour are identical? Simulation [START_REF] Cordy | Simulation-based abstractions for software product-line model checking[END_REF] and language equivalence relations may be part of the solution. Such relations can be used to detect equivalent mutants and to remove them when incrementally building the FTS as explained in Section 3. Yet, computing these relations is expensive (EXPTIME for simulations). An alternative strategy is the selection of higher-order mutants as proposed in the survey [START_REF] Madeyski | Overcoming the equivalent mutant problem: A systematic literature review and a comparative experiment of second order mutation[END_REF] and discussed above.

Challenges

Model v.s. code-based. Our vision deliberately resides at the model level as opposed to code-based mutation analysis. This allows to reason on test suites qualities early in the process and to produce platform-independent test cases. As for any model-based approach, the availability of an accurate model is crucial. We rely on model inference techniques such as n-grams derived from logs [START_REF] Devroey | Towards statistical prioritization for software product lines testing[END_REF], automata learning approaches [START_REF] Lorenzoli | Automatic generation of software behavioral models[END_REF] and feature modelling reverse-engineering [START_REF] Acher | On extracting feature models from product descriptions[END_REF]. Since these methods are not exact, the toughest challenge is to characterize and reduce the impact of extraction issues in the testing process [START_REF] Henard | Towards automated testing and fixing of re-engineered feature models[END_REF].

Mutation Analysis. While our variability-based approach can exploit all innovations in VIS selection of configurations and behaviours, the theoretical underpinnings and practical relevance of (higher-order) mutants interaction need to be researched [START_REF] Ammann | Establishing theoretical minimal sets of mutants[END_REF]: What are their subsuming [START_REF] Jia | An analysis and survey of the development of mutation testing[END_REF] abilities? Are they harder to kill than HOMs constructed with another techniques?

CONCLUSION

In this paper, we presented our vision for improving modelbased behavioural mutation testing by considering mutants as part of a family rather than individually. This approach can speed up mutation analysis by running test cases against all mutants at the same time, rather than independently, thus efficiently addressing "explosion" of the number of mutants. The proposed approach also provides additional benefits, such as the precise modelling of mutants dependencies and easy mutant selection. Thanks to the formal nature of FTS and dedicated model-checking facilities, we target an universal framework where several new and existing mutant analysis techniques can be formalized and implemented.

Figure 1 :

 1 Figure 1: Approach Overview