Gaelle Fiard
email: g.fiard@ucl.ac.uk

Joseph M Norris

An Truong

Nguyen

Vasilis Stavrinides

Jonathan Olivier

Mark Emberton

Caroline M Moore

What to expect from a non-suspicious prostate MRI? A review

Keywords:

Contexte : La réalisation d'une IRM multiparamétrique (IRMmp) est désormais recommandée avant la réalisation de biopsies prostatiques. En revanche, la conduite à tenir en présence d'une IRMmp non-suspecte (Score Likert ou PIRADS 1-2) est toujours débattue.

Objectifs : Faire une synthèse de la littérature récente pour répondre à trois questions. 1) Faut-il réaliser des biopsies systématisées en présence d'une IRMmp non suspecte ? 2) Quels facteurs prédictifs permettent de définir les patients candidats à une biopsie systématisée ?

3) Le manque de visibilité de certains cancers peut-elle être expliquée et quelles en sont les conséquences cliniques ? Sources : Une revue narrative de la littérature a été réalisée à partir des bases de données Medline utilisant deux recherches avec les termes "MRI" AND "prostate cancer" AND ("diagnosis" OR "biopsy") AND ("non-suspicious" OR "negative" OR "invisible") ; "prostate cancer MRI visible". Les références des articles sélectionnés ont été analysées à la recherche d'articles supplémentaires.

Sélection des études

: Les études publiées dans les 5 dernières années en anglais ont été analysées et retenues si les données disponibles permettaient de répondre à l'une des 3 questions posées. Résultats : Considérant les cancers de grade ISUP ³ 2 cliniquement significatifs, la valeur prédictive négative (VPN) de l'IRMmp était comprise entre 76% et 99%, dépendante de la prévalence du cancer et du type de test de référence utilisé. La VPN était plus élevée chez les patients aux antécédents de biopsie négative (88-96%), et plus faible chez les patients en surveillance active (85-90%). La densité de PSA (PSAd) avec un seuil de PSAd<0.15ng/ml/ml était le facteur prédictif le plus étudié et le plus pertinent associé à l'IRMmp pour éliminer un cancer significatif. Enfin, les tumeurs non visibles à l'IRMmp présentaient des différences au niveau histopathologique et génétique, conférant un intérêt clinique à la visibilité IRM. Limites du travail : La plupart des données proviennent de centres experts et les résultats peuvent ne pas être reproductibles en dehors. Conclusion : L'IRMmp fait preuve de performances diagnostiques élevées pour éliminer un cancer cliniquement significatif. La densité de PSA peut être utilisée pour sélectionner patients devant avoir une biopsie. Une meilleure connaissance des mécanismes à l'origine de la visibilité du cancer devrait aider le développement de nomogrammes et biomarqueurs plus précis.

factors that can help decide which patient should have a biopsy? 3) Can the low visibility of some cancers be explained and what are the implications? Sources: A narrative review was performed in Medline databases using two searches with the terms "MRI" AND "prostate cancer" AND ("diagnosis" OR "biopsy") AND ("non-suspicious" OR "negative" OR "invisible"); "prostate cancer MRI visible". References of the selected articles were screened for additional articles.

Study selection: Studies published in the last 5 years in English language were assessed for eligibility and selected if data was available to answer one of the three study questions.

Results: Considering clinically significant cancer as ISUP grade ³ 2, the negative predictive value (NPV) of mpMRI in various settings and populations ranges from 76% to 99%, depending on cancer prevalence and the type of confirmatory reference test used. NPV is higher among patients with prior negative biopsy (88-96%), and lower for active surveillance patients (85-90%). The PSA density (PSAd) with a threshold of PSAd<0.15ng/ml/ml was the most studied and relevant predictive factor used in combination with mpMRI to rule out clinically significant cancer. Finally, mpMRI-invisible tumours appear to differ from a histopathological and genetic point of view, conferring clinical advantage to invisibility.

Limitations: Most published data come from expert centres and results may not be reproducible in all settings.

Conclusion: mpMRI has high diagnostic accuracy and in cases of negative mpMRI, PSA density can be used to determine which patient should have a biopsy. Growing knowledge of the mechanisms and genetics underlying MRI visibility will help develop more accurate risk calculators and biomarkers.

Introduction

Prostate cancer diagnosis has considerably evolved in the past decade thanks to the progress of multiparametric magnetic resonance imaging (mpMRI) and the development of MRI-targeted prostate biopsies. In the presence of level 1 evidence, there is now consensus toward using mpMRI before the initial or repeat biopsy [START_REF] Kasivisvanathan | MRI-Targeted or Standard Biopsy for Prostate-Cancer Diagnosis[END_REF].

However, there is still disagreement on the attitude toward non-suspicious mpMRI (PI-RADS or Likert score 1-2). Therefore, systematic biopsies are still often used, driving a potential for overdetection of insignificant cancers [START_REF] Kasivisvanathan | MRI-Targeted or Standard Biopsy for Prostate-Cancer Diagnosis[END_REF]. Some centres have already chosen to biopsy only in case of mpMRI-visible lesion, but this attitude is not supported by all recommendations [START_REF] Rozet | French ccAFU guidelines -Update 2018-2020: Prostate cancer[END_REF].

A systematic review and meta-analysis from the European Association of Urology Prostate Cancer Guidelines Panel including studies published between 2005 and 2015 estimated a combined negative predictive value between 67% and 88%, depending on the overall prostate cancer prevalence [START_REF] Moldovan | What Is the Negative Predictive Value of Multiparametric Magnetic Resonance Imaging in Excluding Prostate Cancer at Biopsy? A Systematic Review and Meta-analysis from the European Association of Urology Prostate Cancer Guidelines Panel[END_REF]. A very recent review considering various definitions of non-suspicious mpMRI and clinically significant cancer provided an estimated NPV of 90.8% of a PIRADS/Likert 1-2 MRI for ISUP grade ³ 2 disease in biopsy-naïve patients [START_REF] Sathianathen | Negative Predictive Value of Multiparametric Magnetic Resonance Imaging in the Detection of Clinically Significant Prostate Cancer in the Prostate Imaging Reporting and Data System Era: A Systematic Review and Meta-analysis[END_REF].

Materials and methods

Search strategy

We conducted a narrative review of the literature based on a non-structured search strategy in Medline databases, going back to 2015. The initial search terms were ("Magnetic Resonance Imaging" OR "MRI") AND "prostate cancer" AND ("diagnosis" OR "biopsy") AND ("non-suspicious" OR "negative" OR "invisible"). For the section on mpMRI invisible cancer, a second search including the terms "prostate cancer MRI visible" was performed. All English titles and abstracts were reviewed and included if providing sufficient available data to answer the study questions. References of the selected articles were screened for additional articles.

Definition of clinically significant cancer

Unless stated otherwise, clinically significant cancer was defined as ISUP ≥ 2.

Results

Should we continue to offer biopsy to patients with a non-suspicious mpMRI?

To answer to this question, we will look at the negative predictive value of mpMRI, taking into account that it will vary depending on the population considered (biopsy-naïve versus previous negative biopsy, prostate cancer prevalence), the definition of clinically significant cancer used, and the type of confirmatory exam (density of biopsy sampling) performed.

Transperineal template biopsy as reference test: NPV 76-92%

Transperineal biopsy has been used as a confirmatory reference test to evaluate the performance of mpMRI to diagnose clinically significant prostate cancer. Details are provided in Table 1.

Biopsy-naïve patients

Two prospective multicentre studies provide us with a high level of evidence in this population. In the PROMIS study, 576 biopsy-naïve patients had a systematic pre-biopsy mpMRI. Multiparametric MRI findings were compared to a 5-millimetre transperineal template biopsy mapping (reference test), and a 12-core transrectal systematic biopsy. Using such an extensive and thorough confirmatory measure, the negative predictive value of a nonsuspicious mpMRI (Likert 1-2; n=158) was 76% (95% CI: 69-82) to rule out any cancer with ISUP grade ³ 2 [START_REF] Ahmed | Diagnostic accuracy of multi-parametric MRI and TRUS biopsy in prostate cancer (PROMIS): a paired validating confirmatory study[END_REF]. Reassuringly, a recent post-hoc analysis of the PROMIS data showed that cancers overlooked by MRI were of lower grade and volume [START_REF] Norris | Which prostate cancers are overlooked by mpMRI? An analysis from PROMIS[END_REF].

Hansen and colleagues recruited 807 consecutive biopsy-naïve patients in a multicentre prospective outcome study. Among them, 236 had no suspicious lesion on multiparametric mpMRI. Comparison with systematic sampling according to the Ginsburg protocol (median: 22 cores) demonstrated an NPV of 80% for mpMRI [START_REF] Hansen | Multicentre evaluation of magnetic resonance imaging supported transperineal prostate biopsy in biopsy-naïve men with suspicion of prostate cancer[END_REF].

Another retrospective study, looking at 288 patients, including 131 with nonsuspicious mpMRIs biopsied by a transperineal approach, reported an NPV of 84%, where clinically significant cancer included any grade with a maximum cancer core length of > 4 mm.

These results have to be interpreted in light of a lower number of cores taken (14 cores) [START_REF] Washino | Combination of prostate imaging reporting and data system (PI-RADS) score and prostate-specific antigen (PSA) density predicts biopsy outcome in prostate biopsy naïve patients[END_REF].

Similarly, the NPV of 85% demonstrated by Otti and colleagues accounts for the fact that transperineal biopsies (10 cores) were taken to sample anterior regions only, otherwise, transrectal sextant biopsies were performed [START_REF] Otti | The diagnostic accuracy of multiparametric magnetic resonance imaging before biopsy in the detection of prostate cancer[END_REF].

Thompson and colleagues included 364 patients in a prospective cohort study including 79 men with a non-suspicious mpMRI, demonstrating an NPV of 92% for ISUP grade ³ 2 disease with transperineal template mapping (median 30 cores) as reference test. Of note, double reporting of all mpMRIs was done by two expert radiologists (> 1000 prostate mpMRIs each) [START_REF] Thompson | The Diagnostic Performance of Multiparametric Magnetic Resonance Imaging to Detect Significant Prostate Cancer[END_REF].

Biopsy-naïve men and those who have had a previous negative TRUS biopsy

Distler and colleagues retrospectively analysed the performance of mpMRI in a mixed population (42% previous negative biopsy) using transperineal template biopsy mapping with a median of 27 cores as reference test. Based on the analysis of 1040 patients including 344 with non-suspicious mpMRIs (PIRADS 1-2), the NPV was 79% [START_REF] Distler | The Value of PSA Density in Combination with PI-RADSTM for the Accuracy of Prostate Cancer Prediction[END_REF].

Repeat biopsy (including prior positive biopsies)

In a population with a high prevalence of prostate cancer, Simmons and colleagues reported an NPV of 91.4% of a non-suspicious mpMRI in ruling out clinically significant disease (ISUP grade ³ 2) using transperineal template biopsy mapping as a reference test (median 49 cores) in the PICTURE trial [START_REF] Simmons | The PICTURE study: diagnostic accuracy of multiparametric MRI in men requiring a repeat prostate biopsy[END_REF].

Transrectal systematic biopsy as reference test: NPV 82-99%

Looking at studies using a less extensive reference test numbers logically provides higher NPVs as non-visible cancer is less likely to be found where the sampling density is lower.

Detailed results are presented in Table 2 (biopsy-naïve and prior negative biopsy) and Table 3 (prior positive biopsy).

Biopsy-naïve patients

In the French MRI-FIRST trial, 45 of the 275 men enrolled had no suspicious lesion on mpMRI (PIRADSv2 or Likert 1-2) and transrectal systematic biopsy led to the diagnosis of clinically significant prostate cancer (ISUP grade ³ 2) in 5 (11%) [START_REF] Rouvière | Use of prostate systematic and targeted biopsy on the basis of multiparametric MRI in biopsy-naive patients (MRI-FIRST): a prospective, multicentre, paired diagnostic study[END_REF]. Among the 643 patients recruited in the 4M study, 309 received systematic biopsies (12 cores) following a non-suspicious mpMRI. The NPV of mpMRI, taking into account one significant cancer diagnosed at 1-year follow-up, was 96% [START_REF] Van Der Leest | Head-to-head Comparison of Transrectal Ultrasound-guided Prostate Biopsy Versus Multiparametric Prostate Resonance Imaging with Subsequent Magnetic Resonance-guided Biopsy in Biopsy-naïve Men with Elevated Prostate-specific Antigen: A Large Prospective Multicenter Clinical Study[END_REF].

In another recent cohort of 833 biopsy-naïve men undergoing upfront mpMRI, systematic sampling was performed for 140 patients with a Likert 1-2 score using a transrectal (12 cores -65%) or transperineal (24 cores -35%) approach. The NPV of a non-suspicious mpMRI was 92.8%. Of note, 344 patients with a non-suspicious mpMRI did not undergo biopsy [START_REF] Barrett | Three-year experience of a dedicated prostate mpMRI pre-biopsy programme and effect on timed cancer diagnostic pathways[END_REF]. Very similar results were obtained by Falagario and colleagues based on a retrospective cohort of 266 men among whom 117 had non-suspicious mpMRIs (PIRADS 1-2).

A clinically significant cancer was detected in 9 patients (NPV 92%) [START_REF] Falagario | Avoiding Unnecessary Magnetic Resonance Imaging (MRI) and Biopsies: Negative and Positive Predictive Value of MRI According to Prostate-specific Antigen Density, 4Kscore and Risk Calculators[END_REF]. Similarly, an NPV of 92% was calculated by Zhang and colleagues looking at 273 non-suspicious mpMRIs in patients undergoing 24-core systematic biopsy [START_REF] Zhang | How to make clinical decisions to avoid unnecessary prostate screening in biopsy-naïve men with PI-RADs v2 score ≤ 3?[END_REF].

Prior negative biopsy

Higher NPVs are achieved in this category of patients, presumably because they are at lower risk of prostate cancer, especially in the most recent studies where patients likely had an MRI before their initial biopsy.

Boesen and colleagues focused their retrospective analysis on the 3-year follow-up of 194 patients with a history of negative biopsy. Patients were included if the mpMRI performed at the beginning of the study was non-suspicious. In this population (prior negative biopsy + non-suspicious mpMRI), the NPV was 95% [START_REF] Boesen | Clinical Outcome Following Low Suspicion Multiparametric Prostate Magnetic Resonance Imaging or Benign Magnetic Resonance Imaging Guided Biopsy to Detect Prostate Cancer[END_REF]. Kotb and colleagues in another study including 81 non-suspicious mpMRIs found an NPV of 87.6% calculated [START_REF] Kotb | The role of mpMRI and PSA density in patients with an initial negative prostatic biopsy[END_REF].

Lo and colleagues retrospectively reviewed the mpMRIs of 138 patients including 73 that were non-suspicious. Even with long-term follow-up (median 6.7 years), the NPV remained at 96% [START_REF] Lo | Negative Predictive Value of Prostate Multiparametric Magnetic Resonance Imaging among Men with Negative Prostate Biopsy and Elevated Prostate Specific Antigen: A Clinical Outcome Retrospective Cohort Study[END_REF]. Subgroups of patients with previous history of negative biopsy in studies reporting the results of mixed populations showed respective NPVs of 83.3%, 92%, 97%, 100% and 100% [START_REF] Regis | The role of negative magnetic resonance imaging: can we safely avoid biopsy in P.I.-R.A.D.S. 2 as in P.I.-R.A.D.S. 1?[END_REF][START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF][START_REF] Wang | Determination of the Role of Negative Magnetic Resonance Imaging of the Prostate in Clinical Practice: Is Biopsy Still Necessary?[END_REF][START_REF] An | Ruling out clinically significant prostate cancer with negative multi-parametric MRI[END_REF][START_REF] Lu | Negative Multiparametric Magnetic Resonance Imaging of the Prostate Predicts Absence of Clinically Significant Prostate Cancer on 12-Core Template Prostate Biopsy[END_REF].

Mixed populations

The results of studies including biopsy-naïve, prior negative biopsy and prior positive biopsy/active surveillance patients are difficult to interpret. Nonetheless, these studies provide us with pooled NPVs reflecting daily practice. Of note, all data shown here are retrospective.

Two recent retrospective studies including 222 and 391 cancer-naïve patients with non-suspicious mpMRIs reported NPVs of 96% and 89.8%, respectively [START_REF] Regis | The role of negative magnetic resonance imaging: can we safely avoid biopsy in P.I.-R.A.D.S. 2 as in P.I.-R.A.D.S. 1?[END_REF][START_REF] Visschere | What kind of prostate cancers do we miss on multiparametric magnetic resonance imaging?[END_REF] . Interestingly, in the second study by De Visschere and colleagues, only 47% of mpMRIs were still classified as non-suspicious in retrospect, in light of clinical data revealing a diagnosis of prostate cancer at 2-year follow-up in 124/391 (32%) patients [START_REF] Visschere | What kind of prostate cancers do we miss on multiparametric magnetic resonance imaging?[END_REF]. With 4-year follow-up, Panebianco and colleagues from a large series comprising 1255 non-suspicious MRIs provided an NPV of 96% among patients with a previous history of prostate biopsy and 91% in biopsy-naïve patients [START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF].

Adding patients with prior positive biopsy, the retrospective evaluation of a mixed cohort including 27/135 patients with prior positive biopsy performed by Oishi and colleagues provided an NPV of 82% [START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF]. Wang and colleagues similarly assessed a mixed cohort of 464 patients including 84 negative mpMRIs whose NPV was 87% [START_REF] Wang | Determination of the Role of Negative Magnetic Resonance Imaging of the Prostate in Clinical Practice: Is Biopsy Still Necessary?[END_REF].

Conversely, three retrospective studies reported NPVs ranging from 96.5% to 99% [START_REF] An | Ruling out clinically significant prostate cancer with negative multi-parametric MRI[END_REF][START_REF] Lu | Negative Multiparametric Magnetic Resonance Imaging of the Prostate Predicts Absence of Clinically Significant Prostate Cancer on 12-Core Template Prostate Biopsy[END_REF][START_REF] Rozas G De | Impact of PI-RADS v2 on indication of prostate biopsy[END_REF]. However, although all three studies included a significant number of men with non-suspicious mpMRIs (114, 100 and 201, respectively), the NPVs described were likely driven by the majority of patients with previous negative biopsies and the very low rate of significant cancers diagnosed among them.

Active surveillance

In patients on active surveillance for ISUP 1 prostate cancer, the NPV of mpMRI to rule out clinically significant prostate cancer is lower, presumably because this is a population with a higher prevalence of prostate cancer.

The ASIST trial randomised patients between confirmatory biopsy versus mpMRI plus confirmatory biopsy. Among the 137 men in the mpMRI arm, 45 had a non-suspicious mpMRI and the NPV was 85% [START_REF] Klotz | Active Surveillance Magnetic Resonance Imaging Study (ASIST): Results of a Randomized Multicenter Prospective Trial[END_REF]. The same estimate was obtained by Chesnut and colleagues in a retrospective evaluation including 207 men with a 3-year follow-up. Multiparametric MRI at 3 years was non-suspicious in 72 men, and a clinically significant cancer was detected in 11 (15%) [START_REF] Chesnut | Role of Changes in Magnetic Resonance Imaging or Clinical Stage in Evaluation of Disease Progression for Men with Prostate Cancer on Active Surveillance[END_REF].

In a recent retrospective study including 111 patients on active surveillance, 48 had a non-suspicious mpMRI and a significant cancer was detected by systematic transrectal biopsy in 5 (10%) [START_REF] Osses | Prostate cancer upgrading with serial prostate MRI scans and repeat biopsy in men on active surveillance: are confirmatory biopsies still necessary?[END_REF].

What predictive factors can we use to help decide which patients with a non-suspicious mpMRI should have a biopsy?

Patients with non-suspicious mpMRIs may avoid prostate biopsy, but 5-20% of clinically significant prostate cancer may be missed [START_REF] Kasivisvanathan | MRI-Targeted or Standard Biopsy for Prostate-Cancer Diagnosis[END_REF][START_REF] Ahmed | Diagnostic accuracy of multi-parametric MRI and TRUS biopsy in prostate cancer (PROMIS): a paired validating confirmatory study[END_REF]. The NPV of a non-suspicious mpMRI is dependent on the prevalence of the disease, therefore the performance of MRI can be deceiving in a very high-risk population and risk-stratification appears critical before omitting biopsy [START_REF] Moldovan | What Is the Negative Predictive Value of Multiparametric Magnetic Resonance Imaging in Excluding Prostate Cancer at Biopsy? A Systematic Review and Meta-analysis from the European Association of Urology Prostate Cancer Guidelines Panel[END_REF]. The prevalence of significant cancer will vary by patient group (biopsy naïve> active surveillance or previous negative biopsy), but also will vary within the health care context eg. whether PSA testing is commonly done at a population level or not.

The NPV will also vary with the threshold set for clinical significance, with a higher NPV as the threshold is raised. Some groups use ISUP grade alone to set a significance threshold, whilst others will also incorporate a proxy for tumour volume, such as maximum cancer core length.

The optimal approach to identify patients with non-suspicious mpMRI but a higher risk of significant prostate cancer is not yet well established. In an editorial on PRECISION, Nzenza and colleagues proposed that in case of non-suspicious mpMRI, "systematic biopsy still has a role in patients with red flags based on factors such as family history, PSA density, PSA velocity, BRCA mutation, and abnormal digital rectal exam" [START_REF] Nzenza | PRECISION delivers on the PROMIS of mpMRI in early detection[END_REF]. Combining mpMRI score with additional predictive factors may increase the negative predictive value (NPV) of mpMRI and reduce the number of prostate biopsies for men whose risk of significant cancer is low, as well as detecting cancers in men with equivocal or non-suspicious MRIs. Few studies reported predictive factors of clinically significant cancer in patients with non-suspicious mpMRIs.

Clinical factors and PSA density

Factors like family history, abnormal digital rectal exam or ethnicity have been studied and failed to prove significant predictive factor of clinically significant cancer in non-suspicious mpMRI populations [START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF][START_REF] An | Ruling out clinically significant prostate cancer with negative multi-parametric MRI[END_REF][START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF][START_REF] Numao | Usefulness of prebiopsy multiparametric magnetic resonance imaging and clinical variables to reduce initial prostate biopsy in men with suspected clinically localized prostate cancer[END_REF]. Studies looking at age, PSA and prostate volume showed conflicting results [START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF][START_REF] Wang | Determination of the Role of Negative Magnetic Resonance Imaging of the Prostate in Clinical Practice: Is Biopsy Still Necessary?[END_REF][START_REF] An | Ruling out clinically significant prostate cancer with negative multi-parametric MRI[END_REF][START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF][START_REF] Numao | Usefulness of prebiopsy multiparametric magnetic resonance imaging and clinical variables to reduce initial prostate biopsy in men with suspected clinically localized prostate cancer[END_REF]. It is acknowledged that the prostate changes with age.

Young men often have 'bright young prostates' which can harbour low volume ISUP 2 disease, which is less readily seen than in older men with greater differentiation between the transition and peripheral zones. Age, total PSA and prostate volume alone were found to be significant predictive factor of clinically significant prostate cancer in only one study [START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF], 2 studies [START_REF] Wang | Determination of the Role of Negative Magnetic Resonance Imaging of the Prostate in Clinical Practice: Is Biopsy Still Necessary?[END_REF][START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF] and 2 studies [START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF][START_REF] Numao | Usefulness of prebiopsy multiparametric magnetic resonance imaging and clinical variables to reduce initial prostate biopsy in men with suspected clinically localized prostate cancer[END_REF] respectively. Previous negative biopsy status was reported as a significant predictive factor of clinically significant cancer in 2 studies [START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF][START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF]. Oishi and colleagues reported an OR = 5.2(1.6-16.5), p = 0.005 when no previous negative biopsy has been done [START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF].

Conversely, PSA density (PSAd) <0.15ng/ml/ml was found to be a significant predictive factor in 8 studies [START_REF] Hansen | Multicentre evaluation of magnetic resonance imaging supported transperineal prostate biopsy in biopsy-naïve men with suspicion of prostate cancer[END_REF][START_REF] Washino | Combination of prostate imaging reporting and data system (PI-RADS) score and prostate-specific antigen (PSA) density predicts biopsy outcome in prostate biopsy naïve patients[END_REF][START_REF] Otti | The diagnostic accuracy of multiparametric magnetic resonance imaging before biopsy in the detection of prostate cancer[END_REF][START_REF] Distler | The Value of PSA Density in Combination with PI-RADSTM for the Accuracy of Prostate Cancer Prediction[END_REF][START_REF] Kotb | The role of mpMRI and PSA density in patients with an initial negative prostatic biopsy[END_REF][START_REF] Oishi | Which Patients with Negative Magnetic Resonance Imaging Can Safely Avoid Biopsy for Prostate Cancer?[END_REF][START_REF] Hansen | Multicentre evaluation of targeted and systematic biopsies using magnetic resonance and ultrasound image-fusion guided transperineal prostate biopsy in patients with a previous negative biopsy[END_REF][START_REF] Bryant | Comparison of Prostate Biopsy with or without Prebiopsy Multiparametric Magnetic Resonance Imaging for Prostate Cancer Detection: An Observational Cohort Study[END_REF]. The NPV of the combination of mpMRI and PSAd <0.15ng/ml/ml ranged from 84% to 100% in these studies. Panebianco and colleagues found that PSAd >0.15ng/ml/ml had a hazard ratio >7 for the diagnosis of clinically significant disease in patients with a non-suspicious mpMRI [START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF].

A recent meta-analysis by Pagniez and colleagues showed that PSAd was the most studied and relevant predictive factor of clinically significant cancer. Indeed, when associated with a PSAd <0.15ng/ml/ml, the NPV of mpMRI in cancer-naïve, biopsy-naïve and previous negative biopsy groups increased from 83.7%, 82.7%, 88.2% to 90.4%, 88.7% and 94.1%, respectively [START_REF] Pagniez | Predictive Factors of Missed Clinically Significant Prostate Cancers in Men with Negative MRI: A Systematic Review and Meta-Analysis[END_REF].

Biomarkers and risk calculators

Biomarkers such as PCA3, PHI, 4K score or risk calculators have been studied as potential prognostic factors. Perlis and colleagues presented results based on 128 nonsuspicious mpMRIs. No patient with a non-suspicious mpMRI and a normal PCA3 score had significant cancer on biopsy (NPV=100% (p <0.0001)) [START_REF] Perlis | Defining a Cohort that May Not Require Repeat Prostate Biopsy Based on PCA3 Score and Magnetic Resonance Imaging: The Dual Negative Effect[END_REF]. Gnanapragasam and colleagues reported the results of a PHI test combined with a non-suspicious mpMRI in 94 patients. In patients with a PHI score ≥35, the NPV for significant disease was 97% (84-100%) whereas the NPV of mpMRI alone was 75.5% [START_REF] Gnanapragasam | The Prostate Health Index adds predictive value to multi-parametric MRI in detecting significant prostate cancers in a repeat biopsy population[END_REF]. Falagario and colleagues presented results of the 4K score combined with non-suspicious mpMRI in 117 patients. NPV was 96.9% and 97.1% for patients with low or intermediate 4Kscore risk [START_REF] Falagario | Avoiding Unnecessary Magnetic Resonance Imaging (MRI) and Biopsies: Negative and Positive Predictive Value of MRI According to Prostate-specific Antigen Density, 4Kscore and Risk Calculators[END_REF]. These biomarkers seem interesting when combined with mpMRI to increase the NPV, but further validation studies are needed before they can be established in clinical practice.

Risk calculators also appear of interest to determine the individual risk of each patient. On multivariate analysis, the Prostate Cancer Prevention Trial Risk Calculator (PCPT-RC) was a significant predictive factor of clinically significant cancer in the study conducted by Wang and colleagues (OR 1.01, p <0.01) [START_REF] Wang | Determination of the Role of Negative Magnetic Resonance Imaging of the Prostate in Clinical Practice: Is Biopsy Still Necessary?[END_REF]. A new tool from the European Randomized Study of Screening for Prostate Cancer risk calculator (ERSPC-RC) comprising mpMRI results has been published recently and may help selecting patients for biopsy. Falagario and colleagues presented the results of ERSPC-RC in 117 patients. Negative predictive value was 98.7% for ERSPC-RC <2% [START_REF] Falagario | Avoiding Unnecessary Magnetic Resonance Imaging (MRI) and Biopsies: Negative and Positive Predictive Value of MRI According to Prostate-specific Antigen Density, 4Kscore and Risk Calculators[END_REF].

How does mpMRI-invisible prostate cancer differ from mpMRI-visible cancer (and is this clinically useful)?

Perhaps the most intriguing question about prostate cancer undetected by mpMRI is -how does this differ from disease that we detect? Early evidence suggests that mpMRI-invisible cancer differs from its visible counterpart in almost every way, from the molecularlevel through to the population-level. Furthermore, these differences may account for the mechanisms that underpin mpMRI-visibility and potentially the clinical utility afforded by mpMRI-invisibility.

Firstly, and reassuringly, tumour visibility on mpMRI is positively associated with cancer grade, volume and stage. In other words, the larger and more aggressive the cancer, the greater the probability of detection [START_REF] Ahmed | Diagnostic accuracy of multi-parametric MRI and TRUS biopsy in prostate cancer (PROMIS): a paired validating confirmatory study[END_REF][START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF][START_REF] Miyai | Histological differences in cancer cells, stroma, and luminal spaces strongly correlate with in vivo MRIdetectability of prostate cancer[END_REF][START_REF] Borren | Accurate prostate tumour detection with multiparametric magnetic resonance imaging: dependence on histological properties[END_REF][START_REF] Houlahan | Molecular Hallmarks of Multiparametric Magnetic Resonance Imaging Visibility in Prostate Cancer[END_REF]. This characteristic of prostate mpMRI is fundamental and is likely the reason for incorporation of mpMRI into national guidelines [START_REF] Rozet | French ccAFU guidelines -Update 2018-2020: Prostate cancer[END_REF].

In a post hoc analysis of PROMIS, mpMRI-invisible cancers had significantly lower overall and maximum Gleason scores (p = 0.0007 and p < 0.0001, respectively) and shorter maximum cancer core lengths (median difference: 3mm [5 vs. 8], p < 0.0001; 95% CI 1-3) compared to mpMRI-visible cancers [START_REF] Norris | Which prostate cancers are overlooked by mpMRI? An analysis from PROMIS[END_REF]. Indeed, this makes radiobiological sense; smaller tumours are likely to fall below the threshold of spatial resolution of mpMRI (and therefore, will be invisible) and lower grade peripheral zone tumours are likely to have sparse tissue density (and therefore, less restricted diffusion on mpMRI).

Secondly, there are additional histopathological features (beyond tumour grade and size) that account for mpMRI conspicuity [START_REF] Norris | Prostate cancer visibility on multiparametric magnetic resonance imaging: high Gleason grade and increased tumour volume are not the only important histopathological features[END_REF]. Miyai and colleagues recently compared mpMRI-visible and mpMRI-invisible tumours on whole-mount radical prostatectomy; they found that visible tumours had higher architectural density with increased proportions of cancer cells (60.9% vs. 42.7%, p < 0.0001), decreased stromal proportions (33.8% vs. 45.1%, p = 0.00089) and decreased luminal proportions (5.2% vs. 12.2%, p < 0.0001) [START_REF] Miyai | Histological differences in cancer cells, stroma, and luminal spaces strongly correlate with in vivo MRIdetectability of prostate cancer[END_REF]. These results confirm previous findings demonstrating that restricted diffusion was more strongly linked to the distribution of epithelial, luminal and stromal components than to glandular differentiation [START_REF] Chatterjee | Changes in Epithelium, Stroma, and Lumen Space Correlate More Strongly with Gleason Pattern and Are Stronger Predictors of Prostate ADC Changes than Cellularity Metrics[END_REF][START_REF] Kwak | Prostate Cancer: A Correlative Study of Multiparametric MR Imaging and Digital Histopathology[END_REF]. Again, association of increased tissue density and tumour visibility has biological plausibility -diffusion of water on mpMRI would be further restricted in tissue with higher density, thus increasing tumor conspicuity on diffusion. In a similar study, Borren and colleagues found that mpMRI-visible tumours had higher cellular and microvessel density compared to mpMRI-invisible tumours (cell density: 3560 cells/mm2 vs. 2910 cells/mm2; microvessel density: 115 vessels/mm2 vs. 90 vessels/mm2) [START_REF] Borren | Accurate prostate tumour detection with multiparametric magnetic resonance imaging: dependence on histological properties[END_REF]. In this case, tumour visibility is explained by higher microvessel density, which would generate higher dynamic contrast enhanced signal through higher tissue concentrations of gadolinium within microvessels.

Interestingly, there are two (potentially aggressive) prostate cancer sub-types that have reduced detection on mpMRI, namely ductal and cribriform [START_REF] Schieda | Prostatic ductal adenocarcinoma: an aggressive tumour variant unrecognized on T2 weighted magnetic resonance imaging (MRI)[END_REF][START_REF] Truong | A Comprehensive Analysis of Cribriform Morphology on Magnetic Resonance Imaging/Ultrasound Fusion Biopsy Correlated with Radical Prostatectomy Specimens[END_REF]. However, this claim is contested; Tonttila and colleagues recently examined a cohort of men undergoing radical prostatectomy and found that preoperative mpMRI identified 90.5% (86/95) of tumours containing any cribriform or ductal pattern (95% CI 82.5-95.6), and so clearly this area warrants future research [START_REF] Tonttila | Multiparametric MRI prior to radical prostatectomy identifies intraductal and cribriform growth patterns in prostate cancer[END_REF].

Thirdly, there has been significant recent interest in uncovering the genetics that underpin different mpMRI phenotypes [START_REF] Norris | Genetic correlates of prostate cancer visibility (and invisibility) on multiparametric magnetic resonance imaging: it's time to take stock[END_REF]. Purysko and colleagues correlated the Decipher Genomic Classifier with mpMRI appearances for men undergoing radical prostatectomy and found significantly higher Decipher scores in mpMRI-visible tumours (mean difference 0.22, 95% CI 0.13-0.32; p < 0.001). This suggests enrichment of high-risk cancer genes (for early metastasis) in mpMRI-visible disease; however, the authors, crucially, did not control for tumour grade and size [START_REF] Purysko | Correlation between MRI phenotypes and a genomic classifier of prostate cancer: preliminary findings[END_REF]. In contrast, Houlahan and colleagues specified inclusion of only 'clinically significant cancer' (in their case, above Gleason grade 3+4 and 1.5 cm diameter) and through genomic and transcriptomic profiling showed again, that even in a matched cohort comparison, mpMRI-visible tumours were enriched with aggressive molecular and microenvironmental features, which they described as "nimbosus" (gathering of stormy clouds, Latin) [START_REF] Houlahan | Molecular Hallmarks of Multiparametric Magnetic Resonance Imaging Visibility in Prostate Cancer[END_REF][START_REF] Chua | A Prostate Cancer "Nimbosus": Genomic Instability and SChLAP1 Dysregulation Underpin Aggression of Intraductal and Cribriform Subpathologies[END_REF]. However, not all of the extant genomic evidence has confirmed lack of aggressive molecular features in invisible disease. For example, Parry and colleagues compared mpMRI-visible and mpMRI-invisible tumours (obtained at radical prostatectomy) using low-pass whole genome sequencing, methylation arrays and RNAseq. Somewhat concerningly, they found that three of six cores obtained from mpMRI-invisible tumours harboured genetic alterations observed in metastatic castration-resistant prostate cancer, however, this finding was heavily limited by the associated biases of radical prostatectomy and their small sample size (n = 6) [START_REF] Parry | Genomic Evaluation of Multiparametric Magnetic Resonance Imaging-visible and -nonvisible Lesions in Clinically Localised Prostate Cancer[END_REF].

Lastly, and possibly most importantly, tumour visibility (and invisibility) on mpMRI appears to confer clinical utility. PROMIS demonstrated this, in that the most significant cancers (i.e. aggressive disease, that we wish to detect and treat) were visible, and the least significant cancers (i.e. indolent disease, that we do not wish to detect and treat) were invisible [START_REF] Ahmed | Diagnostic accuracy of multi-parametric MRI and TRUS biopsy in prostate cancer (PROMIS): a paired validating confirmatory study[END_REF][START_REF] Norris | Which prostate cancers are overlooked by mpMRI? An analysis from PROMIS[END_REF]. This was then validated in the randomised PRECISION trial, in which men who were assigned to the mpMRI-directed arm had favourable diagnostic pathological outcomes [START_REF] Kasivisvanathan | MRI-Targeted or Standard Biopsy for Prostate-Cancer Diagnosis[END_REF]. In a longitudinal trial, Panebianco and colleagues grouped men with baseline negative mpMRI according to their biopsy status; firstly, biopsy-naïve men, and secondly, men with prior negative biopsy. They showed that 95% of biopsy-naïve men, and 96% of men with previous negative biopsy, remained free of clinically significant prostate cancer after four years of follow-up; showing the important utility held by negative mpMRI [START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF] . Finally, it is worth noting that we may soon be in a position in which our threshold for 'significant cancer' (liable to cause cancer-specific death) actually aligns with mpMRI visibility phenotypes. In a large cohort study of MRI-based active surveillance, Stavrinides and colleagues showed that the outcomes of non-visible Gleason grade 2 (3+4) cancers were similar to Gleason grade 1 (3+3) lesions, whilst visible Gleason 3 + 4 cancers were more likely to progress. [START_REF] Stavrinides | Five-year Outcomes of Magnetic Resonance Imaging-based Active Surveillance for Prostate Cancer: A Large Cohort Study[END_REF].

In the 29-year follow-up of the SPCG-4 trial, Bill-Axelson and colleagues found that in men treated with radical prostatectomy, Gleason score 3 + 4 disease was not associated with prostate-cancer-related death; however, they found that Gleason score 4 + 3 disease (or worse) was in fact associated with a prostate-cancer-related death (adjusted relative risk 5.73; 95% CI 1.59-20.67). This potentially suggests a new threshold for clinically significant disease, which remarkably aligns with conspicuity of prostate cancer on mpMRI, given that in PROMIS, no men with overall Gleason score 4+3 had mpMRI-invisible disease [START_REF] Bill-Axelson | Radical Prostatectomy or Watchful Waiting in Prostate Cancer -29-Year Follow-up[END_REF]. Therefore, peripheral evidence suggests that there is utility in invisibility, however, this does need further validation with bespoke MRI-correlated longitudinal studies.

Discussion

Upfront mpMRI has been included in clinical practice by many institutions, often in anticipation with the latest guidelines, and is now supported by the results of high-quality international studies.

The negative predictive value of non-suspicious mpMRI has proven to be excellent (90-95% in biopsy-naïve patients), and it is fascinating to see the initial results obtained by small retrospective studies confirmed in large, multicentre cohorts and randomised control trials [START_REF] Van Der Leest | Head-to-head Comparison of Transrectal Ultrasound-guided Prostate Biopsy Versus Multiparametric Prostate Resonance Imaging with Subsequent Magnetic Resonance-guided Biopsy in Biopsy-naïve Men with Elevated Prostate-specific Antigen: A Large Prospective Multicenter Clinical Study[END_REF][START_REF] Panebianco | Negative Multiparametric Magnetic Resonance Imaging for Prostate Cancer: What's Next?[END_REF][START_REF] Ahdoot | MRI-Targeted, Systematic, and Combined Biopsy for Prostate Cancer Diagnosis[END_REF]. Those who still doubt the ability of MRI to rule out clinically significant prostate cancer and put a higher confidence in systematic transrectal biopsy must remember that this biopsy scheme has been proven inferior to MRI in a randomised clinical trial [START_REF] Kasivisvanathan | MRI-Targeted or Standard Biopsy for Prostate-Cancer Diagnosis[END_REF]. However, as often in clinical practice, uncertainty remains, and the answer to the question -should we biopsy in the presence of a non-suspicious mpMRI?-depends on how well we are dealing with this uncertainty. And how confident we are in explaining this uncertainty to our patients and not turn it into anxiety.

We are in an opening era of personalised medicine, and the field of prostate cancer diagnosis makes no exception. No test is perfect, particularly when applied in very "extreme" conditions, i.e. in populations with a very high prevalence of the disease considered. The accuracy of MRI is such that many clinical factors, biomarkers and risk calculators have failed to demonstrate a significant added value, especially when assessed in a population with a low prostate cancer prevalence. The PSA density with a threshold at PSAd<0.15ng/ml/ml was able to increase the performances of mpMRI in biopsy-naïve patients and patients with previous negative prostate biopsies. Known biomarkers (PCA3, PHI, 4Kscore) and risk calculators (PCPT-RC, ERSPC-RC) still have to be validated prospectively in multicentric larger cohorts before considering their inclusion in clinical practice. New blood or urine biomarkers are crucially needed to better define each patient's individualised risk and document the decision to avoid -or proceed with-biopsy. When deciding to proceed with biopsy, in these patients deemed at higher risk of prostate cancer despite a non-suspicious mpMRI, an adjustment of the biopsy strategy should be considered. Indeed, this review also outlines the superior diagnostic yield of a transperineal mapping biopsy approach compared to systematic transrectal biopsy, suggesting that it may be useful in these patients to increase sampling density.

The progress made in understanding the biology and genetics behind mpMRI visibility is still in its early phase, and future data obtained from MRI-correlated longitudinal studies will prove critical in determining the potential impact of this knowledge and translating the findings into clinical practice.

There are limitations of our review. The majority of included studies were conducted after mpMRI was already introduced in daily practice with many men already avoiding biopsy.

It is therefore very likely that all retrospective studies reporting results of biopsies performed in patients with non-suspicious mpMRIs suffer of a degree of selection bias as these patients had already been judged at higher risk to warrant biopsy rather than surveillance. Furthermore, evidence cited here has frequently been produced by highly-trained, expert centres, which potentially limits generalisability to smaller centres. However, we believe that every centre can become expert with a strong collaboration between urologists, radiologists, pathologists, and the possibility for those who report mpMRIs to obtain feedback and discuss cases with those who do the biopsies.

Conclusion

Non-suspicious mpMRI has a high negative predictive value in ruling out significant cancer, especially in patients with previous negative biopsies. Recent studies support that mpMRIinvisible tumours differ from a histopathological and genetic point of view and we are getting closer to understanding the mechanisms of mpMRI visibility. Biopsy-naïve men with increased PSA density over 0.15 should be offered biopsy as they are at higher risk of harbouring mpMRIinvisible lesions. Further work is needed to validate the best sampling approach and strategy in this situation. Table 3. Negative predictive value of mpMRI based on studies using transrectal biopsy as reference test for patients with prior positive biopsy. ( * including followup; a when several definitions are used in the study, we present here the results for ISUP ≥ 2; TRUS = transrectal ultrasound-guided; NA = not available).

  Should we offer biopsy to patients with a non-suspicious mpMRI? What additional factors might help in deciding which patients should still have a biopsy? Can the non-visibility of the cancer be explained and what are the implications? We conducted a review of the most recent literature to help provide answers to these questions.

Table 1 .

 1 Negative predictive value of mpMRI based on studies using transperineal biopsy as reference test ( a when several definitions are used in the study, we present here the results for ISUP ≥ 2; b ISUP ≥ 2+ means a broader definition is used. TP = transperineal).

	Reference	Inclusion period	Design	Entry criteria	MRI type	Definition non-suspicious MRI	Main biopsy type (N cores)	Patients having mpMRI (N)	Non-suspicious mpMRI and biopsy (N)	Clinically significant cancers N(%)	Definition clinically-significant cancer a,b	NPV (%)
	Biopsy-naïve patients
	Ahmed 2017 (PROMIS) [5]	2012-2015	Prospective	Raised PSA, abnormal DRE or family history	1.5T	Likert 1-2	TP (50)	576	158	38 (24%)	ISUP ≥ 2	76
	Hansen 2018 [7]	2012-2016	Prospective	Raised PSA, abnormal DRE or family history	1.5 or 3T	PIRADS 1-2	TP (22)	807	236	48 (20%)	ISUP ≥ 2	80
	Washino 2017 [8]	2010-2014	Retrospective	mpMRI + biopsy	1.5 or 3T	PIRADS 1-2	TP (14)	288	131	21 (16%)	ISUP ≥ 2 +	84
	Otti 2019 [9]	2013-2016	Retrospective	mpMRI + biopsy	1.5T	PIRADS 1-2	TP (10)	1023	348	52 (15%)	ISUP ≥ 2	85.1
	Thompson 2016 [10]	2012-2014	Prospective	Age>40, abnormal PSA or DRE	1.5 or 3T	PIRADS 1-2	TP (30)	364	79	6 (8%)	ISUP ≥ 2	92
	Biopsy-naïve + prior negative biopsy
	Distler 2017 [11]	2012-2015	Retrospective	PSA>4ng/ml or abnormal DRE	3T	PIRADS 1-2	TP (27)	1040	344	71 (20.6%)	ISUP ≥ 2	79.4
	Repeat biopsy (including prior positive biopsy)
	Simmons 2017 (PICTURE) [12]	2012-2014	Prospective	Indication for repeat biopsy	3T	Likert 1-2	TP (49)	249	35	3 (8.6%)	ISUP ≥ 2	91.4

Table 2 .

 2 Negative predictive value of mpMRI based on studies using transrectal biopsy as reference test for biopsy-naïve patients and patients with prior negative biopsy. ( * including follow-up; a when several definitions are used in the study, we present here the results for ISUP ≥ 2; b ISUP ≥ 2+ means a broader definition is used; TRUS = transrectal ultrasound-guided; NA = not available).

	Reference	Inclusion period	Design	Entry criteria	Follow-up	MRI type	Definition non-suspicious MRI	Main biopsy type (N cores)	Patients having mpMRI (N)	Non-suspicious mpMRI and biopsy (N)	Clinically significant cancers N(%)	Definition clinically-significant cancer a	NPV (%)
	Mixed including prior positive biopsy
	Oishi 2019 [22]	2011-2017	Retrospective	Non-suspicious mpMRI		3T	PIRADS 1-2	TRUS (12)	395	135	24 (18%)	ISUP ≥ 2	82
	Wang 2016 [23]	2012-2015	Retrospective	Non-suspicious mpMRI		3T	PIRADS 1-2	TRUS (12)	464	84	11 (13%)	ISUP ≥ 2	87
									Biopsy-naïve	39	4 (10%)		90
									Prior negative biopsy	30	5 (16%)		83.3
									Prior positive biopsy	15	2 (13%)		86.7
	An 2018 [24]	2013-2017	Retrospective	Non-suspicious mpMRI		3T	PIRADS 1	TRUS (12)	NA	114	4 (3.5%)	ISUP ≥ 2	96.5
									Biopsy-naïve	20	0		100
									Prior negative biopsy	53	0		100
									Prior positive biopsy	41	4 (9.8%)		90
	Lu 2017 [25]	2012-2016	Retrospective	Non-suspicious mpMRI		3T	Low suspicion on PIRADS 1-2 3-point Likert scale	TRUS (12)	670	100	3 (3%)	ISUP ≥ 2	97
									Biopsy-naïve	38	1 (2.6%)		97.4
									Prior negative biopsy	33	0		100
									Prior positive biopsy	29	2 (6.9%)		93.1
	Rozas 2019 [28]	2015-2016	Retrospective	mpMRI		3T	PIRADS 1-2	TRUS (18)	342	201	2 (1%)	ISUP ≥ 2	99
									Prior negative biopsy	182	NA		NA
									Prior positive biopsy	19	NA		NA
	Active surveillance
	Klotz 2019 (ASIST) [29]	2011-2015	Prospective	ISUP 1 prostate for repeat biopsy cancer + indication		3T	Likert 1-2	TRUS (12)	137	45	5 (11%)	ISUP ≥ 2	85
	Chesnut 2020 [30]	2013-2016	Retrospective	ISUP 1 prostate cancer + 2 mpMRIs	3 years	3T	PIRADS 1-2	TRUS (14)	207	72	11 (15%)*	ISUP ≥ 2	85
	Osses 2020 [31]	2013-2019	Retrospective	ISUP 1 prostate cancer + mpMRI		3T	PIRADS 1-2	TRUS (8-12)	111	48	5 (10%)	ISUP ≥ 2	90

Acknowledgments

Gaelle Fiard receives funding from the Fondation de France and the European Urology Scholarship Program. Joseph Norris is funded by the Medical Research Council (MRC) (Grant Reference: MR/S00680X/1). Vasilis Stavrinides is funded by the Medical Research Council (MRC) (Grant Reference: MR/S005897/1). Mark Emberton receives research support from the United Kingdom's National Institute of Health Research (NIHR) UCLH / UCL Biomedical Research Centre. He was appointed to an NIHR Senior Investigator position in 2013. Caroline M. Moore is supported by the UK NIHR, Movember, PCUK, and the EAU Research Foundation.

Conflict of interest None


M Taupin

G Knebel

T D Matsuda

G Lapertot

Y Machida

K Izawa

J.-P Brison

J Flouquet

Thermal conductivity through the quantum critical point in YbRh 2 Si 2 at very low temperature

Keywords: numbers: 71.27.+a, 72.15.Eb, 74.40.Kb, 75.50.Ee

The thermal conductivity of YbRh 2 Si 2 has been measured down to very low temperatures under field in the basal plane. An additional channel for heat transport appears below 30 mK, both in the antiferromagnetic and paramagnetic states, respectively below and above the critical field suppressing the magnetic order. This excludes antiferromagnetic magnons as the origin of this additional contribution to thermal conductivity. Moreover, this low temperature contribution prevails a definite conclusion on the validity or violation of the Wiedemann-Franz law at the field-induced quantum critical point. At high temperature in the paramagnetic state, the thermal conductivity is sensitive to ferromagnetic fluctuations, previously observed by NMR or neutron scattering and required for the occurrence of the sharp electronic spin resonance fracture.

Traditionally, heavy fermion intermetallics are viewed as systems lying close to the instability to an ordered magnetic state. The instability is driven by the competition between Kondo screening of the local moments, and long range order of these moments, induced by RKKY interactions. Along the past decades, experimental and theoretical studies have endeavored to unveil the evolution of heavy fermions through the instability, focusing on the role of quantum fluctuations around the quantum critical point (QCP) [1]. Presently, the most prominent scenarios involve instabilities approaching the critical point from the paramagnetic (PM) side, either on some "hot spots", which is the so-called "spin density wave" scenario, or extended over the whole surface, for the "local quantum critical scenario". In the last case, the Kondo screening mechanism would breakdown near the quantum critical point, leading to a change from a large Fermi surface (including the local moments) in the paramagnetic state, to a "small Fermi surface" when Kondo coupling disappears [2]. As a consequence, it is also believed that in this last scenario, which involves a collapse of the mechanism driving the heavy quasi-particles formation, when approaching the well-defined QCP, the low energy excitations would not be described by quasiparticles anymore. So experiments probing this local quantum critical scenario, are mainly trying to reveal a change of Fermi surface (FS) volume across the QCP or a clear violation of predictions based on the notion of quasiparticles.

The antiferromagnetic (AF) heavy fermion YbRh 2 Si 2 , has been a main playground for both experimental approaches, and strongly pushed forward as an archetype of heavy fermion driven by the local quantum criticality scenario [3,4]. The proximity of YbRh 2 Si 2 to AF quantum criticality is attested by the low value of its Néel temperature T N ∼ 70 mK, far smaller than its Kondo temperature T K ∼ 25 K [5]. Experimentally, a major appeal of this system is that fine field tuning of the AF-PM border can be used to monitor the proximity to the QCP [3,5]. Due to the large anisotropy of the magnetic properties, the critical field H c driving the AF-PM instability is also anisotropic, respectively 0.066 T and 0.6 T in the easy magnetization plane (a,b), and along the c axis of the body centered tetragonal crystal.

Evidence of FS reconstruction at H c are mainly based on Hall effect measurements [6,7].

However, heavy fermions are multiband systems, so that the interpretation of the Hall effect is not straightforward. Other concomitant proof of the FS reconstruction in YbRh 2 Si 2 must be found. No convincing changes of the FS at H c appear on the thermoelectric power [8,9].

Recently, the debate has been focused on the detection of a breakdown of the Fermi-liquid regime at H c , using thermal transport at low temperature as a probe: A violation of the Wiedemann-Franz law (WFL) would point out a deep change of the electronic excitations responsible for charge and heat transport [5,11,12]. In metallic systems, at T → 0 K, when quasiparticle scattering is dominated by elastic mechanisms, all reported cases but one satisfy the WFL, stating that L → L 0 in the low temperature limit, where L = κρ/T is the Lorenz ratio and L 0 = L(T → 0) is the Lorenz number (L 0 = (π 2 /3)(k B /e) 2 ). The only case reported so far that would not satisfy the WFL in this limit is CeCoIn 5 , for the heat current along the c-axis [13], which has been put forward as a demonstration of breakdown of the quasiparticle picture in a "hot spot" QCP scenario. But even in this last case, one cannot exclude that measurements below 30 mK (the lowest temperature reached in [13]) would invalidate the violation of the WFL.

Three different groups have recently published thermal conductivity (κ) experiments coupled with careful resistivity (ρ) experiments in YbRh 2 Si 2 , in order to study the temperature dependence of the Lorenz ratio L(T ) = κρ/T . Contradictory conclusions have been drawn by the three groups. The first one [5] claims that the WFL is violated at H c , as L(T → 0) ∼ 0.90L 0 , while the others concluded conservatively that L(T → 0) at H c is L 0 [11,12]. However, all the experimental data of the three groups are in good agreement:

The main differences lie in the interpretation, and in the lowest temperature reached, i.e. in the extrapolation of the zero temperature values. This last point is a very sensitive issue, as an additional contribution to the electronic thermal conductivity appears at very low temperatures (below 30 mK) in YbRh 2 Si 2 , which is very difficult to separate from the quasiparticles contribution. The measurements we report in the present paper, were realized down to 10 mK, twice lower than in those reported in [5], and with a strong emphasis on the analysis of this extra contribution, notably to detect if anything specific happens at the critical field H c .

The single crystal investigated in the present study was grown out of In flux. It is the same as used in Ref. [14] for the thermoelectric power and magnetoresistance studies. The residual resistivity ratio RRR = ρ(300K)/ρ(0K) of the crystal is 65, the observation of quantum oscillations in the resistivity indicates its high quality. The magnetic field was applied parallel to the current (longitudinal configuration: H//j Q //[1,1,0]), up to 4 T. The zero field measurements have been performed with a zero field cooled magnet. At low field, a calibrated Hall sensor has been used to determine precisely the applied magnetic field. The thermal conductivity was measured using a standard two thermometers-one heater setup, and was checked to be independent of the heat gradient applied, with ∆T /T in the range 0.5-10 %. Calibration of the thermometers was realized in situ, against a CMN paramagnetic salt in zero field for temperatures below 0.1K and down to 7 mK, and against reference thermometers (calibrated with the CMN) placed in the compensated zone of the magnet for field measurements. The electrical resistivity was measured simultaneously, with a conventional lock-in detection at low frequency (around 2 Hz, for minimum quadrature signal), allowing a precise determination of L(T ).

Figure 1 compares the electrical resistivity ρ, and the thermal resistivity w th = L 0 T κ , at low temperature (below 0.15 K), for zero magnetic field (H = 0 T) and very slightly above the critical field H c (H = 70 mT). This is the most important result, but let us first describe the insert which gives a broader view thanks to an extended temperature range (from 7 mK up to 7 K). It displays the Lorenz ratio L(T )/L 0 for both fields, with a logarithmic temperature scale: There is a large temperature range, from 3 K down to 0.02 K, where the normalized ratio L(T )/L 0 is clearly below 1, down to a value L(T )/L 0 ≈ 0.87. This is indicative of dominant inelastic scattering (the so-called "vertical processes"), which affect more strongly thermal than electrical transport. The rather unusual feature is that despite a large residual resistivity (the RRR is "only" 65 for our sample), inelastic scattering has a significant contribution down to such low temperatures. But this is consistent with the marked temperature dependence of the resistivity down to the lowest measured temperatures (8 mK), as can be seen on the main graph. Inversely, the fast increase of the Lorenz ratio above 2 K, overpassing 1 above 3 K, indicates additional contributions to the heat transport (like phonons).

These "bosonic" contributions are expected to vanish rapidly below 1 K, and therefore, the new increase of the Lorenz ratio above 1 below 20 mK is again a very unusual feature, which could not be anticipated from the resistivity behavior. This low-temperature increase of the Lorenz ratio has been already observed below 30 mK by Pfau et al. [5], on a slightly more resistive sample (RRR ≈ 45 instead of 65). But we insist that this is probably the most puzzling feature of thermal transport in YbRh 2 Si 2 : How is it that new bosonic excitations, able to contribute as a new heat channel, appear at such low temperatures? Moreover, contrary to the statement in [5], we observe that this increase is essentially unchanged for a field of 70 mT, suppressing the long range AF order, and the putative magnon (long lived) excitations expected in this ordered phase. Discussion of the origin and field evolution of this contribution is continued later in this paper.

The main plot of Fig. 1 shows the detailed evolution of ρ and w th below 0.15 K, down to 10 mK: In particular, one clearly observes a kink at T N in zero field on the electrical and thermal transport. It is suppressed by an applied field of 70 mT (very close to H c ), which also lowers both resistivities. It demonstrates that the critical fluctuations emerging in the neighborhood of the AF transition contribute to the scattering of the quasiparticles. However, this scattering seems to be rapidly damped below T N , as no change of w th is observed below 50 mK, between zero field and 70 mT. Concerning now the additional low temperature contribution, the strong decrease of w th below 30 mK appears independent of the applied field. It already shows the difficulty to discuss the validity of the WFL: The linear extrapolation of the data of w th between 30 and 50 mK is compatible, within the dispersion of the points, with that of the resistivity at 0 K. The whole question is to control these extrapolations, or to estimate the amplitude and range of the extra contribution responsible for the low temperature drop of w th . But in any case, on the bare data, no drastic change is seen between zero field and H c . Figure 2 compares the relative temperature variation of L(T )/L 0 for fields above H c , up to 4 T (see Supplementary Material A, figure 5 for the data of κ and ρ). It appears that the low temperature increase of the Lorenz ratio is field sensitive above 100 mT, and rapidly suppressed for rather weak fields (above 0.2 T). This supports a magnetic origin for this additional heat channel, which is reasonable as we did not expect a sizable phonon contribution at such low temperatures. In parallel, we do observe that the decrease below one of the Lorenz ratio above 30 mK is also progressively suppressed under field, pointing to a magnetic origin of the low temperature inelastic scattering. However under field, for H > 0.5 T (see also insert up to 4 T), L(T → 0) seems to saturate at 0.97 L 0 . This small deviation from L 0 may be due to experimental precision, or related to the complex multiband structure of the FS. In any case, the fact that this value does not change with fields much larger than H c means that it cannot be seen as a violation of the WFL at the QCP. In the following, particularly to estimate the electronic contribution, the Lorenz number is taken at this value found for T → 0 K: L(0) = 0.97L 0 .

As regards the question of the origin of the additional contribution to thermal transport appearing below 30 mK (hereafter labelled κ add ), all hints point to a magnetic origin: (i) even if it survives the critical field, it is rapidly suppressed by fields of order of 0.5 T; (ii) a new phononic contribution is completely unexpected in this temperature range: It would require a strong lattice instability, which has not been detected so far; (iii) besides the antiferromagnetic long range order at 70 mK, other magnetic transitions have been reported at 12 mK [15] and/or 2 mK [16]. In reference [5], κ add has been attributed to magnons, an assumption supported by comparison to the specific heat (C p ) data: The temperature dependence of C p has a bare T 3 regime below T = 55 mK [3,5], which is attributed to AF magnons. Because it exists even when the long range ordered state is suppressed, we would rather compare κ add in YbRh 2 Si 2 to a similar additional contribution to heat transport observed in the ferromagnet UCoGe, both above and below T Curie , and also in a very low temperature range (for the heat current along the b-axis) [17]. Obviously, "paramagnons" or overdamped spin fluctuations, can also contribute to an additional heat transport channel.

Quantitatively, we will perform a similar analysis as in [17], assuming that we can separate the electronic contribution in a quasiparticle κ qp channel, which should follow (or not!) the WFL, and a "spin-fluctuation" contribution κ add , expected for example to be much less sensitive to the RRR. As for the case of UCoGe, a difficulty for quantitative estimation of κ add is that the quasiparticle contribution is badly known, due to the importance of inelastic scattering even at 30 mK (see the Lorenz ratio in figure 1). So we assume that κ qp can be described by [18]:

κ qp T = L(0) ρ 0 + α(ρ -ρ 0 ) (1)
This expression takes into account the stronger effect of the electronic inelastic scattering on the thermal transport (than on the electrical transport), through the factor α. ρ 0 is the residual resistivity and α = 1 + W vert /W hor , where W vert and W hor are respectively the scattering rates due to vertical (small wave-vector transfer q, inelastic) and horizontal (large q, mostly elastic) processes, assuming that Mathiessen's rule holds. The crude simplification is to take α constant, which can be valid for temperatures much smaller than the typical energy of the fluctuations responsible for the inelastic scattering. This simplification has already been widely used for the heavy fermion systems like UPt 3 [19], CeRhIn 5 [20] and

UCoGe [17]. The figure 3 For point (i), it will be very difficult to reach firmer conclusions, as even lower temperature measurements would face the problem of the dominant additional contributions, and of the difficulty of a robust quantitative analysis, together with the regimes introduced by the additional transitions at 12 and 2 mK [15,16]. For point (ii), this is similar to observations on the thermopower, where the change of regime under field occurs far above H c [8,9], and little is seen when crossing H c .

Moreover, the question of the role of magnetic fluctuations in the heat transport in YbRh 2 Si 2 is not limited to the low temperature regime. Also at high temperatures, above 1K, we can detect a field dependence of w th , which (like for resistivity), points to a contribution of magnetic fluctuations on the scattering mechanisms. In this temperature range, microscopic measurements have revealed a complex situation: NMR experiments [21] have

shown that AF fluctuations with finite wavevectors compete with ferromagnetic (FM) fluctuations; recent investigations by NMR [1] gives the image of interfering Fermi liquid and non Fermi liquid component close to H c . Neutron scattering experiments [2] down to 0.1 K up to 10 T along the c-axis confirm that incommensurate AF correlations become dominant on cooling against the FM correlations, while the magnetic field induces a Zeeman resonant excitation. These FM fluctuations could be an important ingredient to understand the observation of a well defined electron spin resonance in YbRh 2 Si 2 [24,25]. So at least far from

T N or at high magnetic field, FM coupling may be dominant, pointing to the proximity of a FM QCP [26,27]. We do find (see Supplementary material B) that the thermal resistivity above 1K behaves as predicted by Ueda and Moriya [3] when inelastic scattering is controlled by ferromagnetic fluctuations.

To summarize we have investigated in detail the thermal transport of YbRh 2 Si 2 , in the AF phase and in the PM phase, below and above H c , and extended the measurements down to 10 mK. This study clearly shows that an additional magnetic contribution to thermal conductivity appears below 30 mK, with a gradual decrease for fields above the critical field H c . This has been deduced with an electronic quasiparticle contribution, which also has no peculiar singularity at H c , and satisfies the WFL even at H c . To conclude unambiguously, by direct measurements, if the WFL is satisfied or violated, would require measurements down to the mK temperature range, where the additional contribution should eventually disappear. But other recent experiments also challenge the "local QCP scenario", which could have led to the violation of the WFL at the critical field: For example, ARPES measurements [29,30] show that above T N , the 4f-electrons in the paramagnetic phase are clearly itinerant, which leaves open the validity of the image of small and large Fermi surface fluctuations developed in the Kondo breakdown scenario. A new appealing approach is the so-called "strong coupling theory" of heavy-fermion quantum criticality, where large critical spin fluctuations at the AF wave-vector induce fluctuations at small wave-vectors, producing a diverging effective mass over the entire Fermi surface [31]. It would be interesting to see if these fluctuations could be responsible for the detected low temperature contribution, as well as to the large inelastic scattering observed down to very low temperatures ?

This work has been supported by the French ANR grant SINUS and the ERC grant "NewHeavyFermion".

Supplementary Materials

SUPPLEMENTARY MATERIAL A: DETAILS ON THE TRANSPORT MEASURE-

MENTS

As a complement to figure 1 of the main paper, displaying the thermal and electrical resistivities below 0.15 K, figure 4 presents ρ and w th at 0 T up to 7 K: This shows the strong temperature dependence of ρ in the whole temperature range, as well as the saturation of w th above 3 K, due to the growing contribution of bosonic excitations to heat transport. If several (parallel) channels contribute to the thermal transport, it is better to discuss the thermal conductivity rather than w th . It is displayed on figure 5, at low temperature and up to 0.1 T, and the corresponding electrical resistivity is shown in the inset. The smooth variation of the thermal conductivity through H c is confirmed by the temperature dependence of κ/T below 100 mK on each side of H c for different magnetic fields.

As explained in the main paper, we could analyze the quasiparticle contribution, taking into account the peculiar effects of inelastic scattering on heat transport, and with no

w th = ρ + BT (2)
So, even if the electrical resistivity has no real simple temperature dependence (see figures 3-4 of reference [3], the additional thermal resistance for weak ferromagnets above T Curie or near ferromagnets at high enough temperatures is roughly linear in temperature (with our definition of w th ): See figure 5 of [3]. Naturally, in this temperature range, we also expect a phononic contribution, limited by electron-phonon scattering, which should follow a quadratic temperature dependence: κ ph = P T 2 , with P temperature and field independent.

We obtain thus for the thermal conductivity at high temperature:

κ = κ qp + κ ph (3) = L 0 T ρ + BT + P T 2 (4)
Once the phonons are subtracted, the thermal resistance w th ≡ w qp = L 0 T κqp represents the electronic heat channel with the scattering of quasiparticles by FM fluctuations. We call the additional linear term in the thermal resistivity w qp-f luc = BT . Contrary to the low temperature situation, the magnetic fluctuations above 1 K do not contribute with their own channel to heat transport: They only have the "usual" contribution to the inelastic scattering of the quasiparticles. The expression 4 is very simple, as ρ is determined experimentally and the parameter P is field independent. Only the parameter B can vary with the field. Such a decomposition of the thermal conductivity has already been successfully used for the weak ferromagnet ZrZn 2 [4]. Surprisingly, after removal of the phonon and resistivity contribution, we do find that w qp-f luc is linear above 1 K, for fields up to 4 T, as shown in figure 7, for a field independent parameter P = 0.022 W.K -3 .m -1 , close to 0.017 W.K -3 .m -1 used by Pfau et al. [5]. At lower temperatures, a deviation of w qp-f luc from linearity appears, which may be due to the growing importance of AF fluctuations.

The evolution of the B coefficient is shown in figure 8: It increases linearly with the magnetic field, as if the applied field and the warming reinforce the ferromagnetic fluctuations. This behaviour is quite singular and may be related to the intermediate valent character of YbRh 2 Si 2 . In Ce compounds, like in the CeRu 2 Si 2 family, ferromagnetic fluctuations are just enhanced at the metamagnetic field where simultaneously the AF interactions drops [6].

FIG. 2 .

 2 FIG. 2. (color online)Ratio L(T )/L 0 at low temperatures below 1 T. The dashed lines are the extrapolation to L(0) = 0.97L 0 when T > 30 mK. In inset, L(T )/L 0 at higher fields, which extrapolates also to 0.97 at low temperature.

2 FIG. 3 .

 23 FIG. 3. (color online)Comparison of the electronic thermal conductivity using the expression 1 with α = 1 and α = 2.2. The latter value was chosen to optimize the low temperature contribution of κ qp .

2 (

 2 compares the bare data with different estimates of κ qp for α = 1 i.e L(T ) = L(0) and α = 2.2, at 0 T (in the AF state), 70 mT (close to H c ) and 0.27 T (in the PM state). Clearly, α = 1 overestimates the quasiparticle contribution, whereas α = 2.the best value we found) gives an estimate of κ qp compatible with the data for the three fields. It even gives a fair account of the data between 30 mK and 100 mK at 0.27 T. The extracted extra contribution is shown in the Supplementary Material A, figure6.The most important information from the analysis shown on figure3is that little change is observed between zero field and H c , apart from the suppression of the anomaly at T N .Otherwise, (i) it is possible to analyze the data of thermal transport in YbRh 2 Si 2 , assuming that the quasiparticle contribution follows the WFL even at H c , and with the same coefficient α = 2.2 describing the effect of inelastic scattering; (ii) κ add is little influenced by the suppression of the Néel temperature at H c , and really starts to decrease only above this field (see also figure6of the Supplementary Material A), pointing to a contribution of driven (robust) short range correlations.

FIG. 4 .

 4 FIG. 4. (color online) Electrical and thermal resistivities at 0 T in the whole temperature range from 10 mK up to 7 K.

FIG. 5 .FIG. 6 .

 56 FIG. 5. (color online) Thermal conductivity of YbRh 2 Si 2 at low temperature below 0.1 T. In inset, the corresponding electrical resistivity. The dash line shows the Néel temperature at zero field.

FIG. 7 .FIG. 8 .

 78 FIG. 7. (color online) Electronic thermal resistivity w qp-f luc up to 5 K after subtraction of the electrical resistivity. For clarity, an offset has been added to each curve (+0.2 µΩ.cm at each field step). Dashed lines are guides to the eyes.

2.8 2.4 2.0 1.6 w th , ρ (µΩ.cm) 0.15 0.10 0.05 0.00 T (K)

	1.4
	1.0 L _ L 0	0T 70mT L/L 0	YbRh 2 Si 2 j // [110] H // [110]
	0.01	0.1	T (K)	1
					0T 70mT
					w th ρ
	FIG. 1. (color online) Electrical resistivity (full squares) and thermal resistivity (open circles) of
	YbRh 2 Si 2 at 0 T (in black) and at 70 mT, close to H c (in red) at low temperature. Clear anomalies
	are observed in zero field at T N , and a new channel for heat transport appears below 30 mK (see
	text). Inset: Normalized ratio L(T )/L 0 in the whole temperature range at 0 T and 70 mT.


V Brien

S Kenzari

P Weisbecker

S Weber

F Machizaud

J.-M Dubois

.Synthesis, characterization and optical behaviour of vapour grown nano-crystalline Al-Cr-Fe-Mo thin films

Keywords: A. thin films, B. vapour deposition, C. Scanning and transmission electron microscopy, C. X-ray diffraction

Thermal evaporation process was employed in production of thin films of an Al-Cr-Fe-Mo alloy. Microstructural and chemical features were respectively evaluated by grazing X-ray diffraction, transmission electron microscopy and sputtered neutral mass spectroscopy.

Solidification structures reveal a homogeneous nanosized (2 -70 nm) granular morphology.

Experimental synthesis parameters leading to films purely made of the known O 1 approximant phase have been defined. The other films were made of two phase particles, ie.

O 1 grains mixed with pure cubic aluminium grains. Optical reflectance of the O 1 film over the infra-red and visible wavelength domains is presented.

Introduction

Glass industries are highly interested in modifying surface and optical properties of their glass in order to produce new products for new markets. Such added value can be performed depositing a coating of a well-chosen material. Many studies on quasicrystals and, more and more commonly, their approximant phases show their growing importance in the coating technology owing to their appropriate properties [1][2][3][4][5][6][START_REF] Bergman | Proceedings of the fifth International Conference on Quasicrystals[END_REF][8][START_REF] Janot | Matières à Paradoxes[END_REF][START_REF] Brien | [END_REF][11]. For instance, their low adhesion, high hardness, excellent corrosion resistance and reduced optical conductivity at low frequencies make them very attractive for forming films on substrates [12][13][14][15][16]. Indeed, optical properties of quasicrystalline matter, and approximant phases compared to the one of the metallic constituents, exhibit an important absorption (40 % in infra-red domain) [14,[START_REF] Eisenhammer | Proceedings of the fifth International Conference on Quasicrystals[END_REF][START_REF] Eisenhammer | [END_REF][19][20]. This ability could be exploited for making infra-red absorbers. Such an advantage combined with good corrosion behaviour thanks to particular chemical species is attractive. Previous work has already been performed on Al-Cr-Fe films showing it was possible to get as-deposited Al-Cr-Fe approximant thin films grown from the vapour phase on glass substrates [15,16]. The obtained films were made of a mixture of approximant phases and were shown to exhibit the optical properties of approximant phases over the visible domain.

They could however not be tested in the infra-red domain as they were not thick enough implying so an alteration of the optical measurements due to the glass substrate. The Al-Cr-Fe, like the Al-Cr-Fe-Cu system is rich in approximant phases of the decagonal phase [15,[START_REF] Eisenhammer | [END_REF]21]. The idea here is to be able to get a thick enough film made of a single phase, either approximant or quasicrystalline (decagonal, icosahedral). The challenge is also to explore the possibility to extend the corrosion resistance of this approximant hoping a substitution of Cr by the iso-electronic atom Mo in order to investigate modifications (and improvement) in terms of physical and chemical properties.

(O 1 , O 2 , γ brass…)

Experiment

Techniques of preparation

Thermal evaporation was performed in an Edwards AUTO 306 vacuum coater using tungsten filaments. The evaporation set-up allows the heating of the substrate thanks to Joule effect up to 320°C. Heating is produced by a resistance located just behind the holders. The temperature of the substrate T s was controlled by the means of a thermocouple located behind and in contact with the substrate holders. The set-up also allows the control of the distance d between the source and the substrate. Vacuum condition before deposition was 10 -7 mbar. The films were deposited on glass substrates. They were produced from small pieces of matter (50 mg) placed on tungsten basket. These pieces were cut out of an ingot obtained by radio-frequency melting, by mixing high purity elements (99.999 % for Al, 99.99% for Cr and Fe and 99.95% for Mo) under helium atmosphere in an induction copper furnace cooled by interior water circulation. Different nominal compositions were tried aiming at a composition near the known one of the Al-Cr-Fe/O 1 -phase: Al 82.8 Cr 13.9 Fe 3.2 [15,16] analyses show that the ingot is made of two main phases (cf. Figure 1). One of them is an orthorhombic approximant of the decagonal phase. Such a checking lead us to show that sufficient homogenization of the ingots could be achieved by performing three melts. Each melt was followed by a cooling down in the induction furnace (see § 3.1).

Techniques of characterization

Chemical depth profiles of the films were obtained by Sputtered Neutral Mass Spectroscopy (SNMS). All the chemical compositions are given within an experimental error of 5 at. %. The thickness of the films was estimated by performing profilometry on the SNMS craters and was found to be in the 50-200 nm range. Grazing incidence X-Ray Diffraction (GXRD) using the CoK α1 radiation and a curved detector (INEL CPS120) was performed at 0.5° incidence for the identification of the phases. Carbon coated copper electron microscopy grids were systematically placed just next to the film on the substrate holder to perform transmission electron diffraction and imaging. Transmission Electron Microscopy (TEM) observations were carried out on a PHILIPS CM200 microscope. An accelerating voltage of 200 kV was used. EDS spectra recorded in the analyzed zones do not exhibit a copper signal, which proves that no copper diffusion in the film from the grid occurred. In order to get a complementary overview of films, they were all systematically analysed by these four techniques (cf. Table 1). The reflectance spectra were measured at room temperature using a Perkin-Elmer spectrometer on the 200 -2600 nm range at nearly normal incidence.

Results and discussion

Control of the chemistry and homogeneity of the source matter

The chemical dispersion studied by EPMA shows that an ingot prepared by radiofrequency melting in the used copper furnace exhibits chemical gradients from the core towards the external part. These gradients follow a radial symmetry lead by the geometry of the cooling device. Fig. 1a shows the transverse shape of such an ingot. It appears three consecutive meltings are necessary to reach a sufficient chemical homogenization. EPMA results of analysis performed along the lines 1, 2 and 3, which have been drawn in fig. 1.a, can be seen in Fig. 1(b). 50 mg of matter approximately correspond to a volume like a piece whose diameter would be around 3 mm. EPMA analysis was performed every tenth of a mm. Consequently, graphs are presented so that each point is the average composition of the 10 closest points. One can notice the central part located at the crossing of the lines 1 and 3 is the most chemically homogeneized zone. The corresponding microstructure is an intermediate microstructure between the one of zone B and the one of zone C (cf. Fig. 1.a and c) and is fine enough. The composition in this zone can be calculated from the EPMA results and is around Al 73.2 Cr 10 Fe 5.3 Mo 11.6 . Matter to evaporate was then taken from this zone which is schematized in Fig. 1.a (grey central part).

Chemical and structural analysis of the films

A serie of films was prepared setting the distance d and substrate temperature T s at different values: d = 6, 9 and 13 cm, T s = 285 and 325 °C (Table 1 compiles all the experiments).

All films are nano-crystallized as the TEM dark field micrograph taken from the film prepared at T s = 325 and d = 9 cm stands for (Fig. 2). Size of crystallites ranges from 2 to 70 nm. Average size of particles inside films increase with increasing T s and d.

Two types of TEM diffraction patterns were obtained: one type (type I) exhibits rings that could be identified as the one of the O 1 phase as Fig. 3(a) shows. The O 1 phase is an orthorhombic phase, of Bmm2 space group. It was first discovered in the Al-Cr-Cu-Fe diagram by Dong and Dubois [22] and identified as an approximant of a Al-Cr-Cu-Fe quasicrystalline decagonal phase [22,23]. The O 1 phase was also noticed in the Al-Cr-Fe diagram [15,21] diffraction. This means that the TEM diffraction analysis has missed the Al grains because of their dispersion, and that at high substrate temperatures, big distances between the source and the substrate lead to films whose homogeneity is apparently of poorer quality than for the other conditions.

One concludes that all the films are made of mixed phases (type II) cubic aluminium and O 1 approximant, except one film which is pure and made of the O 1 phase only (type I).

The O 1 pure film can be obtained by setting a small distance between the source and the substrate and by setting the substrate temperature at 285 °C.

The influence of d and T s can then be synthesized: the smallest d is, the most homogeneous are the films. This can be linked to the angular dispersion of matter from the source during the evaporation. High substrate temperatures lead to films composed of approximant phase mixed with metallic f.c.c. aluminium. Above all, the way to get a pure approximant film is to take a small distance and a small temperature.

The chemical composition and in-depth chemical profiles were checked by SNMS analyses. All the profiles (either type I or II) look alike as the SNMS profile of the type I film (d = 6cm, Ts = 285 °C) stands for (Fig. 5). Transverse compositions of elements are not constant all along the depth. Net and progressive increase (respectively decrease) of Al (Cr, Fe and Mo) with increasing depth can be observed. All the films also exhibit a superficial zone of about 5 to 10 nm in thickness where oxidation and species diffusion seem to have occurred. Composition of the films was then calculated on the whole thickness without taking in account the superficial layer affected with oxidation and diffusion, giving average values. The type I film (pure O 1 ) is of Al 79 Cr 12 Fe 7 Mo 3 composition. Compositions of the mixed films which do not correspond to any single phase, have then not been worked out.

Taking the limits among the data presented in Fig. 5, one may conclude that the solid solution O 1 presents an existence domain ranging at least from 65 to 87% for Al, 9 to 14 % for Cr, 4 to 12 % for Fe and 0 to 8 % for Mo. Experimental error on composition analysis being 5%, one concludes that the solubility of Mo in the O 1 phase is at least of about few atomic %.

Optical reflectance

The optical reflectivity curves of the as-deposited pure O 1 film and the one of the polished Al 74 Cr 10 Fe 6 Mo 10 ingot, used for making the films, are presented in figure 6. As expected of approximant materials [11,[14][15], one can see the obtained approximant film and the ingot effectively reflect around 60% of light over the infra-red domain. This result is similar to the one recorded on massive Al-Cr-Fe approximant samples made of a mixture of approximant phases by Demange et al. [14] and informs that the insertion of Mo inside the O 1 phase does not alter its optical behaviour.

The work should have to be completed by a study on the influence of the Mo on the corrosion resistance. Indeed, Al-Cr-Fe samples have been proved to behave excellently [15,16] and Mo influence in these specific films was not yet characterized.

Conclusion

The following important issues were pointed out in our study: -It also allowed us to determine the average lattice parameters of the O 1 -Al-Cr-Fe-Mo phase.

-Optical properties are conserved over the infra-red domain by the insertion of Mo in the Al-Cr-Fe system. Identification of the phases present inside all the films prepared for this study according to the two diffraction techniques: grazing X-ray and electron diffraction. Type I = O 1 phase, type II = face centred cubic aluminium + O 1 phase, T s : temperature of the substrate, d:

distance between the source and the substrate.

  . The second type of TEM diffraction patterns (type II) exhibits fcc-Al dotted rings with traces of O 1 -ring like pattern of Fig. 3(b) shows it. Table 1 gives the type of pattern we have obtained versus the two process parameters d and T s . The Al rings of the type II film prepared at d = 9 cm and T s = 325 °C are less continuous than the other ones and are punctuated by spots. This is the result of the bigger size of the Al crystallites when d increases. Basically, according to TEM diffraction, all films are of type II except two films: the one prepared at low d (6 cm), low T s (285 °C), and the one prepared at high d (13 cm), high T s (325 °C). GXRD results also show the patterns are of two types. First type of pattern exhibits only the peaks of the O 1 structure (type I, fig.4.a) and happens only when d = 6 cm and T = 285°C. The parameters found here for the O 1 structure are a = 2.46 ± 0.04 nm, b = 1.28 ± 0.04 nm and c = 3.37 ± 0.04 nm, to be compared with a = 3.25 nm, b = 1.25 nm and c = 2.36 nm for O 1 -Al-Cr-Cu-Fe [22, 23] and with a = 2.37 nm, b = 1.23 nm and c = 3.25 nm for the O 1 -Al-Cr-Fe [15, 21]. Second type of pattern informs that the films prepared in the other conditions and even the one prepared at d = 13 cm, T s = 325 °C, contain two phases: the O 1 phase and the face centred cubic Al phase (Fig.4.b) For clear understanding of the GXRD patterns: signal produced by the glass substrate itself before any deposition has been recorded and can be seen on Fig. 4(c). Analysed volume by GXRD is bigger than by TEM

-

  Al-Cr-Fe-Mo films have been prepared and systematically analyzed. They are all continuous and small-grained (nanometer size). Films are generally homogeneous except at high d, high T s . -Most films are made of O 1 -phase and fcc-Al phase (approximant previously existing in Al-Cr-Fe and Al-Cr-Cu-Fe systems), one is purely composed of the O 1 -phase. -Decorrelated and crossed influence of the temperature of the substrate and the distance between the source and the substrate have been worked out. Conditions of preparation for a film purely made of the O 1 -phase correspond to the smallest temperature and to the smallest distance tested.-This work shows the O 1 -phase has an existence domain in the Al-Cr-Fe-Mo system.

Figures captionsFigure 1 :

 1 Figures captionsFigure1: Characterization of the ingot containing the source matter to be evaporated. a/

Figure 2 :Figure 3 :

 23 Figure 2: TEM Dark field image showing the nanosized granular morphology of a film

Figure 4 :

 4 Figure 4: 0.5° incidence GXRD patterns, a/ film deposited at d = 6 cm, T s = 285 °C, b/ film

Figure 5 :

 5 Figure 5: SNMS graph showing the composition of the pure approximant O 1 film across its

Figure 6 :

 6 Figure 6: Room temperature reflectance curves over the visible and infra-red domain of the

  Figure 2

Figure 6 21

 6 Figure 6

Al 66 Cr 22 Fe 7 Mo 5 and Al 74 Cr 10 Fe 6 Mo 10 . Due to the observed relative abilities of elements to condense on substrates (after chemical SNMS expertise -cf. section 2.2-performed on films) the ingot of nominal composition Al 74 Cr 10 Fe 6 Mo 10 was chosen for the preparation of the

  to prepare the films: Al 72.5 Cr 20 Fe 6 Mo 1.5 , Al 70 Cr 18 Fe 7 Mo 5 , Al 68 Cr 20 Fe 7 Mo 5 ,

	evaporated films. Its chemical composition and distribution of the elements were checked by
	Electron Probe Microanalysis (EPMA) (precision on chemical composition is 1 at.%). X-ray
	diffraction (θ -2θ) and Field Emission Gun Scanning Electron Microscopy (FEG-SEM)

Table captions Table 1

 captions1

Acknowledgements

The authors would like to thank V. Demange for fruitful discussions, and J.-P. Houin for his excellent technical contribution on the temperature substrate device. The financial support offered by Ministère de la Recherche et des Nouvelles Technologies under contract ERT Quasicristaux Industriels is gratefully acknowledged.