Dr Nhat Tam Vo

Dr Yasmina Mekmouche

Dr Thierry Tron

Prof Régis F Guillot

Frédéric Banse

Zakaria Halime

Marie Sircoglou

Dr Winfried Leibl
email: winfried.leibl@cea.fr

Ally Aukauloo
email: ally.aukauloo@u-psud.fr

Dedicated To

Shunichi Fukuzumi

Dr Z Banse

Dr M Halime

Prof A Sircoglou

Prof A Aukauloo

Reversible Electron Relay to Exclude Sacrificial Electron Donor in Photocatalytic Oxygen Atom Transfer Reaction with O 2 in Water

Keywords: oxygen atom transfer, photocatalysis, timeresolved spectroscopy, iron complexes, electron relay

Using light energy and O2 for the direct chemical oxidation of organic substrates is a major challenge in the development of clean and sustainable processes. A stubborn limitation in this strategy resides in the use of sacrificial electron donors to activate O2 through a reductive quenching process of the photosensitizer thereby generating undesirable side products. We found that a reversible electron acceptor, methyl-viologen, can act as electron shuttle to oxidatively quench the photosensitizer, [Ru(bpy)3] 2+ , generating the highly oxidized chromophore and the powerful reductant methyl-viologen radical MV + . MV + can then reduce an iron(III) catalyst to the iron(II) form and concomitantly O2 to O2 -in an aqueous medium to generate an active iron(III)-(hydro)peroxo species. The oxidized photosensitizer is reset to its ground state by oxidizing an alkene substrate to an alkenyl radical cation. Closing the loop, the reaction of the iron reactive intermediate with the substrate or its radical cation leads to the formation of two oxygenated compounds, the diol and the aldehyde following two different pathways. Our report provides a new paradigm to perform photocatalytic oxidation of organic substrates with solely light as energy input and O2 as oxygen atom source.

Dioxygen is ultimately the only true green oxidant. [1,2] Expelled from photosynthesis [3] it constitutes a crucial molecular brick for the energy supply chain in biology. It also serves as the main supplier of O-atoms in the biosyntheses of essential organic molecules. [4,5] Although the thermodynamics behind these chemical reactions are favorable, kinetic limitations come from the fundamental paramagnetic state of O2. This limitation can be lifted off when O2 is partnered with paramagnetic species or excited triplet states that can undergo single electron transfer reactions. [6][7][8][9] Chemists have taken inspiration from biology to develop metal complexes that can bind and activate dioxygen in presence of co-reductants. [10][11][12][13] Photoactivating O2 at a metal complex through light-induced electron transfer is an even more desirable target. [14][15][16] However, this quest is dramatically challenging and has lagged behind the great boom we have witnessed during the last decade in the field photocatalysis. In fact O2 is considered as an external deleterious impurity in the vast majority of the reported photo-chemical transformations. [17] This classical approach also suffers from the necessity of sacrificial electron donors (SED) to activate O2 for oxygen atom transfer (OAT) reactions thereby limiting the preparative scope. [18,19] Nocera and coworkers have developed face to face bis-iron(III)--oxo porphyrin where they have shown that upon visible light irradiation dioxygen acts both as the final oxidant and the oxygen atom donor in the oxidation of alkenes albeit in benzene. [20] While, Fukuzumi and coll. took profit of the high energy long-lived charge separated state of 9-mesityl-10methylacridinium ion to generate O2 -and an alkenyl radical cation that couple to give an unstable dioxetane derivative that cleaves into ketones as only products. [21,22] Henceforth, much effort is still needed in the quest towards using light and O2 without sacrificial electron donor to manage and enlarge the reactivity of reduced oxygen species under mild conditions. In this study we interrogate a counter intuitive approach for the light-driven reductive activation of O2 by using a reversible electron acceptor to preclude the use of sacrificial electron donor. We found that the introduction of methylviologen dication (MV 2+ ) in a mixture of the [Ru(bpy)3] 2+ , abbreviated as ([Ru II ]), photosensitizer and a semi-hemic iron(III) catalyst allows aerobic oxidation of alkene substrate in aqueous medium. We show that the oxidative quenching of the photosensitizer generates the highly oxidized chromophore and the powerful reductant methyl-viologen radical MV + that can then concomitantly reduce the iron(III) complex to the iron(II) form and O2 to O2 -. Further reaction between the iron(II) complex and O2 -generates an active iron(III)-peroxo species. [10,23,24] The oxidized photosensitizer is reset to its ground state by oxidizing an alkene substrate to an alkenyl radical cation. Closing the loop, the reaction of the active iron complex and the organic radical or the alkene lead to the formation of two oxygenated compounds, the aldehyde and the diol respectively. Isotopic labelling experiments support that O2 is at the origin of the inserted oxygen atoms. For this study, we prepared an iron complex with the DPPy (DipyrrinDiPyridine) ligand we previously designed in our lab (Fig. 1 left). [25] Metalation of the DPPy ligand with Fe(OTf)2 led to the formation of the iron(II) precursor complex that upon exposure to air yielded the {[(DPPy)(EtOH)Fe III ]2O}(OTf)2, a -oxo iron(III) dimer shorthanded as I(OTf)2 (see SI). The underlying reactivity is reminiscent of that of the corresponding iron(II) porphyrin (Por) derivatives where O2 binding and subsequent O-O bond cleavage leads to the highly oxidized iron(IV)-oxo species that ultimately reacts with the starting iron(II) complex to generate the [(Por)Fe III ]2O derivative. [26] An ORTEP view of I is given in Figure 1. The coordination sphere of each iron(III) ion is described by the four nitrogen atoms of the DPPy ligand in a meridional plane and oxygen atoms from the bridging oxo and one ethanol molecule in apical positions. Two triflate counter anions assure electroneutrality. Given the hemiporphyrinic nature of the DPPy ligand, we observed two Fe-N bond lengths (av. 2.05 Å) within the same range as those for a typical iron(III) porphyrin and two longer Fe-N bonds (av. 2.21 Å) with the pyridine groups (see Table SI1 & SI2 for all the metric parameters). Upon continuous illumination using white light (LED lamp equipped with a Wratten 2E filter,  > 415nm) and under an aerobic atmosphere no oxidation product was detected. In a subsequent experiment, MV 2+ was added to the previous mixture followed by irradiation in air. Remarkably, in presence of MV 2+ , two oxygenated products were detected, the diol and the benzaldehyde derivatives (Table SI3, Fig. SI5), with an overall TON of ca. 80 (Scheme 1). This value falls roughly within the range observed for highly oxidized iron species generated upon reaction of iron complex models with O2 in presence of electron and proton donors. [27,13,28] Isotopic labelling experiments using 18 O2 were carried out to determine the origin of the oxygen atom(s) inserted in the products. The HPLC-HRMS analysis of the corresponding photocatalytic experiments indeed confirmed that the oxygen atoms stem from 18 O2 (Fig. SI13). Such an intriguing scenario, where the only presence of a reversible electron acceptor ousts the SED for the reductive activation of O2, provided us with a strong incentive to delineate the photocatalytic reaction scheme. A series of control experiments combined with the detection of relevant intermediate species by Laser Flash Photolysis allowed us to propose a plausible photocatalytic mechanism for the oxygenation reaction. In a first blank experiment, we excluded both the -oxo Fe III dimer (I) and the MV 2+ (see Table SI3, Fig. SI5). No traces of oxygenated products were detected under such experimental conditions, allowing us to expedite the singlet O2 pathway that could interfere in the oxidation of the organic substrate. Of note, this experimental configuration also sets aside any organic radical formation that could trigger autooxidation reaction with O2. [START_REF] Pryor | Organic Free Radicals[END_REF] Furthermore, no photodegradation of the photosensitizer was observed under our irradiation conditions (Fig. SI3) ruling out the participation of chemically altered intermediate such as [Ru(bpy)2(H2O)2] 2+ as potent photooxidation catalyst. [30] In a subsequent experiment, where a mixture of [Ru II ], S and O2 was irradiated in presence of MV 2+ , only trace amounts of oxidized substrate were detected, bringing unambiguous support that the presence of the iron complex is essential for the observed photocatalytic reaction. The photoexcitation with a laser pulse at 460 nm of an aqueous mixture of [Ru II ] and MV 2+ in presence and absence of O2 resulted in both cases in the formation of MV + detected by its characteristic absorption maximum around 605 nm, and [Ru III ] probed by the bleaching of the MLCT band at 450 nm (Fig. SI7). However, the faster decay of the MV + radical compared to the [Ru III ] species in the presence of O2, clearly supports a rapid electron transfer from MV + to O2 (Fig. SI8). [31,32] Back electron transfer to [Ru III ] occurs in a second order reaction regenerating the [Ru II ] state quantitatively with similar kinetics as back electron transfer from MV + in the absence of O2. Interestingly, in a deaerated solution and in presence of the olefin, we found that the recovery of the [Ru II ] is faster than the lifetime of MV + (Fig. 2 & Fig. SI9). This observation can be assigned to the oxidation of the alkene by [Ru III ] through an intermolecular electron transfer process to form an alkenyl radical cation (step 4). [33] The chemical oxidation of the alkene by [Ru III ] complex was performed and confirmed by the EPR detection of an organic radical (Fig. SI6) which brings further support for this reaction pathway. The trace amount of oxidized substrate (<1% of aldehyde) observed under these conditions i.e. in the absence of I may thus originate from a minor side reaction of the singly oxidized olefin derivative with O2. [34] In Scheme 2, we recapitulate the photophysical events in the absence of complex I. In this experimental set, the lack of the iron complex leads to the rapid annihilation of the charge separation state by recombination of the superoxide radical with the oxidized photosensitizer ([Ru III ]), step 7 or the oxidized olefin.

Scheme 2: Predominating photophyscial events: steps 1, 2 and 7 in the text, and minor event step 4 upon irradiation of a mixture of the photosensitizer / methylviologen / substrate / O2.

We then assessed the role of complex I. In a first control experiment where we omitted MV 2+ but introduced complex I, no oxidized substrate was detected. This result indicates that no charge shift process is undergoing from the excited state of the photosensitizer to complex I in agreement with the absence of quenching of the emission life time of *[Ru II ] upon addition of I (Fig. SI10). Furthermore, the absence of any oxidized products corroborates the lack of photocatalytic activity of the {[(DPPy)Fe III )2O} 2+ compound (I) in aqueous medium. [35] We then interrogated the role of I in presence of MV 2+ . Under an inert atmosphere, the oxidative quenching of the photosensitizer and the formation of MV + again prevailed. However, a rapid fading of the absorption features of the MV + radical is observed that matched with the formation of the reduced (DPPy)Fe II , detected by two absorption bands in the visible region at around 550 and 590 nm (Fig. 3) while the feeble broad bleaching band around 650 nm detected at 1 ms can be attributed to the disappearance of the Fe(III) complex I. The recovery of [Ru II ] is quite slow under these conditions and can reasonably be attributed to recombination with Fe(II) (compare blue and red traces in Fig. 3, bottom) to form Fe(III) (black trace). In presence of O2, the electronic absorption signature of the (DPPy)Fe II can still be detected (Fig. SI12) albeit with lower intensity than in the absence of O2. The lower yield in presence of O2 is compatible with the competitive reduction of I vs. O2 by MV + to generate the (DPPy)Fe II and O2 - species respectively with a branching ratio determined essentially by the relative concentrations of I and O2. Scheme 3 illustrates the different events occurring after excitation of the photosensitizer leading to the formation of the two main oxidized products i.e., the diol and benzaldehyde. Importantly, our global photocatalytic cycle is in sharp contrast with the classical photoactivation scheme, inasmuch as there is no intervention of a SED. Traditionally, the function of the SED serves to aliment the photocatalytic process with electrons for the activation of O2. [36] As depicted in Scheme 2, the first photoinduced sequence relies on the oxidative quenching of the photosensitizer to form the highly oxidizing [Ru III ] and the powerful reductant MV + (step 1). Laser Flash Photolysis experiments supported by the redox properties of each partner (E°(MV 2+ / MV + ) = -0.69 V; [37] E°(O2/O2 -) = -0.40 V vs. SCE; [38] E°(Fe III Fe III /Fe III Fe II ) = 0.23 V and E°(Fe III Fe II /Fe II Fe II ) = -0.09 V (Fig. SI14)) ascertain that the MV + radical can reduce both the iron(III) complex and O2 (steps 2 and 2' in Scheme 3). The resulting iron(II) complex and O2 -species ultimately combine to form an iron(III)-peroxo type intermediate (step 3). Note that at pH 4, the superoxide radical anion is most likely to be protonated to produce a hydroperoxyl radical (pKa (  OOH/ O2 -) = 4.7) [38,39] that reacts with Fe(II) to produce Fe(III)-OOH. [40] All attempts to trap the iron(III)-(hydro)peroxo intermediate in aqueous medium from the reaction of a chemically prepared (DPPy)Fe II and superoxide anion were unfruitful. However, such intermediates have been caught with other iron complexes, spectroscopically characterized and their reactivity modes were demonstrated in organic medium. [41,42] Turning our attention to the oxidant issued from the first photophysical event; the [Ru III ] species can oxidize the alkene to form an alkenyl radical cation thereby recycling the photosensitizer to its resting state (step 4). The formed organic radical species leads to one of the two main photoproducts that we evidenced, namely the benzaldehyde sulfonate. As already elucidated from previous studies, this product can derive from the formation of an unstable dioxetane species where O-O and C-C bonds cleavage delivers the benzaldehyde derivative. The direct reaction of the superoxide radical anion with the singly oxidized alkenyl radical cation to form the dioxetane intermediate can be ruled out under our experimental conditions. Indeed, as already mentioned, the blank experiment where a mixture of [Ru II ], [MV 2+ ], S and O2 was irradiated only lead to a minute amount of oxidized photoproduct. Henceforth, we can arguably propose that the formation of the dioxetane results from the reaction of the alkenyl radical cation, formed by the electron transfer from the alkene to the oxidized [Ru III ] (step 4), with the Fe III -peroxo intermediate (step 5). The other characterized photoproduct was the diol derivative (step 6). Its formation emanates from the Fe III ( 2 -OOH) species which, in turn, can evolve via heterolytic O-O cleavage to form an Fe V (O)(OH). [43][44][45] This intermediate can concertedly fix two oxygen atoms to the alkene to yield the cis-diol product. 18 O isotopic labelling experiments were undertaken to interrogate the origin and the pattern of the inserted oxygen atoms. When the photocatalytic run was realized in presence of a mixture of 18 O2 and 16 O2, the cis-diol with two inserted 18 O atoms was detected in the HRMS together with the 18 O 16 O and 16 O 16 O labelled diol products. This experimental finding clearly supports that O2 is the actual source of oxygen atoms. The presence of mixed oxygen-labelled diol derivative can be rationalized through dynamic water exchange between an iron-bound hydroxo ligand and bulk water. [46][47][48] Alternatively the formation of the diol may come from the ring opening of an epoxide formed from the high valent Fe-oxo intermediate. When the photocatalytic run was realized at pH 6, only the epoxide and the aldehyde were revealed (Table SI3, Fig. SI5). This subtle reactivity control brings further confirmation that the oxygen atom transfer reactions are guided through activated forms of O2 at the metal center. These mechanistic aspects have been developed in literature and are recalled in the SI (Scheme. SI1). Further control experiment where complex I was substituted by an iron(III) salt (FeCl3) revealed only a trace of aldehyde exempting the reactivity through a radical process (Fig. SI5).

The study we present here provides a new paradigm to perform photoinduced oxygen atom transfer reactions with solely light and O2 in aqueous solution, without the "evil necessity" of a sacrificial electron donor. An introspection of the photocatalytic cycle points to the crucial role of the reversible charge carrier to produce O2 -and reduce an iron(III) complex to form the activated Fe III -(hydro)peroxo as the archetypal OAT reactive species. Meanwhile, the oxidized photosensitizer is reset to its resting state through oxidation of the olefin substrate to produce an alkenyl radical cation. The latter and the olefin can react with the active catalytic species to form oxygenated products. The quantum yield for formation of the oxidized products is estimated to about 2.5% (see SI). Work is now in progress to interrogate the limiting steps in the light-induced electron transfer processes.

Entry for the Table of Contents

COMMUNICATION

We found that the use of a reversible electron acceptor (methylviologen) ousts the "evil necessity" of sacrificial electron donors (SED) in the photoactivation of O2. It intervenes as an electron carrier from the excited photosensitizer to reduce both O2 and an iron(III) catalyst to form a reactive Fe III -peroxo species for oxygen atom transfer reactions. Oxidation of an organic substrate closes the photocatalytic cycle.

Figure 1 :

 1 Figure 1: Molecular drawing of DPPyH proligand and ORTEP view of the X-ray crystallographic structure of {[(DPPy)(EtOH)Fe III ]2O} 2+ (I). The hydrogen atoms have been omitted for clarity. I(OTf)2 was engaged in a B&R buffer (pH 4) aqueous mixture with the [Ru II ] photosensitizer and an excess of a water-soluble alkene, sodium styrene-4-sulfonate (hereby shorthanded as S).Upon continuous illumination using white light (LED lamp equipped with a Wratten 2E filter,  > 415nm) and under an aerobic atmosphere no oxidation product was detected. In a subsequent experiment, MV 2+ was added to the previous mixture followed by irradiation in air. Remarkably, in presence of MV 2+ , two oxygenated products were detected, the diol and the benzaldehyde derivatives (TableSI3, Fig.SI5), with an overall TON of ca. 80 (Scheme 1).

Scheme 1 :

 1 Scheme 1: Photocatalytic oxygen atom transfer reaction of styrene sulfonate with O2 in absence of sacrificial electron donor.

Figure 2 :

 2 Figure 2: Time resolved absorption changes of a B&R (pH 4) buffer solution of [Ru(bpy)3]Cl2 (30 µM) and MV 2+ (4 mM) in presence of sodium 4styrenesulfonate (100 mM) at 605 nm (green) and 450 nm (blue) under argon; at 605 nm (black) and 450 nm (red) in aerobic conditions.

Figure 3 :

 3 Figure 3: Top: Transient absorption spectra from an Ar-saturated B&R buffer solution of [Ru(bpy)3] 2+ (30 µM), MV 2+ (4 mM) and I (30 µM) at the indicated delay times after excitation and (inset) UV-visible spectrum of (DPPy)Fe II in water under argon. Bottom: Time resolved absorption changes at 390 nm (green), 450 nm (red), 605 nm (blue) and 630 nm (black) corresponding to the contribution of MV + , [Ru II ], both MV + and Fe(II) complex, mainly Fe(III)

Scheme 3 :

 3 Scheme 3: Proposed mechanism of the photocatalytic oxidation of sodium styrene-4-sulfonate by the photosensitizer / iron catalyst / methylviologen mixture to form the diol and aldehyde products.

  Thierry Tron, b Régis Guillot, a Frédéric Banse, a Zakaria Halime, a Marie Sircoglou, a Winfried Leibl, *c and Ally Aukauloo *a,c Page No. -Page No.Reversible Electron Relay to Exclude Sacrificial Electron Donor in Photocatalytic Oxygen Atom Transfer Reaction with O2 in Water

Acknowledgements

This work was supported by the ANR Multiplet (ANR-15-CE07-0021-01), LABEX CHARMMMAT (ANR-11-LABX-0039), and the French Infrastructure for integrated Structural Biology (FRISBI) ANR-10-INSB-05-01.


Clément Beitone
email: clement.beitone@univ-grenoble-alpes.fr

Gaëlle Fiard
email: gfiard@chu-grenoble.fr

Jocelyne Troccaz
email: jocelyne.troccaz@univ-grenoble-alpes.fr

Towards real-time free-hand biopsy navigation

Towards real-time free-hand biopsy navigation

accuracy and time performances. These modifications and their in-depth evaluation on real clinical cases and comparison to this previous work are described. We performed static and dynamic evaluations along biopsy trajectories on a very large amount of data acquired under uncontrolled routine conditions. The computed transforms are compared to a ground truth obtained either from corresponding manually detected fiducials or from an already evaluated registration method.

Results: All results show that the current method outperforms its previous version, both in terms of accuracy (the average error reported here is 12 to 17% smaller depending on the experiment) and processing time (from 20 to 60 times faster compared to the previous implementation). The dynamic registration experiment demonstrates that the method can be successfully used for continuous tracking of the biopsy location w.r.t the prostate at a rate that varies between 5 and 15 Hz. Conclusions: This work shows that on the fly 2D/3DUS registration can be performed very efficiently on biopsy trajectories. This allows us to plan further improvements in prostate navigation and a clinical transfer.

I. INTRODUCTION

Prostate cancer is the second most common cancer in men and the fourth most common cancer overall according to the World Research Cancer Fund (WRCF). Prostate screening tests may include a Prostate Specific Antigen test (PSA) or a Digital Rectal Examination test (DRE), but to determine whether or not prostate cancer is present, biopsy series must be performed. If some samples are positive, they will also be used as raw material to determine the cancer grade (through the Gleason score [START_REF] Hurst | Selenium and prostate cancer: Systematic review and meta-analysis[END_REF]) and to make decisions about the more appropriate treatment.

As a result, performing transrectal ultrasound (TRUS) biopsy of the prostate is an essential proficiency for urologists. The procedure itself (see Figure IV) is a complex task that requires extensive anatomical and technical knowledge and good hand-eye coordination. In many countries, medical authorities currently recommend the biopsy of twelve regions uniformly distributed over the prostate, along with some specific targeted locations if additional MRI exams have revealed suspicious regions.

With current 2D live ultrasound imaging equipment, the false negative rate for this procedure could reach thirty percent [START_REF] Silva | Quantification of prostate deformation due to needle insertion during TRUS-guided biopsy: Comparison of hand-held and mechanically stabilized systems[END_REF]. This is a consequence of the poor visibility of cancerous tissues in TRUS images and the limited anatomical context available in the 2D TRUS plane. This results in a very limited knowledge about the actual position of biopsy cores. Over the years, significant efforts have been made to lower this rate through the accurate localization of biopsy.

Accuracy requirements may be related to the notion "clinically significant tumour": 0.5cc is a consensus value accepted by the urology community [START_REF] Cornud | TRUS-MRI image registration: A paradigm shift in the diagnosis of significant prostate cancer[END_REF]. This corresponds approximately to a sphere having a radius of 5mm.

As a first attempt for computer-assisted prostate biopsy, some authors proposed to follow the probe during the examination using an external measurement device. We will refer to these approaches as sensor-driven. Various types of devices have been used, from external tracking (optical / magnetic [START_REF] Xu | Real-time MRI-TRUS fusion for guidance of targeted prostate biopsies[END_REF]) to inertial units or robotized arms [START_REF] Bax | Mechanically assisted 3D ultrasound guided prostate biopsy system[END_REF] attached to the probe. These approaches generally use a 3D MR reference image acquired during the preoperative stage. This 3D image is rigidly registered to a 3D TRUS image acquired at the start of the intraoperative phase. This first 3D / 3D registration serves as a reference and is continuously updated by "adding" the probe movement during the examination estimated using the tracking device. If these solutions can be performed at a high frequency, none of them takes into account the fact that the prostate can roll over or become deformed due to contact with the head of the probe during the procedure. Some authors [START_REF] Karnik | Assessment of image registration accuracy in three-dimensional transrectal ultrasound guided prostate biopsy[END_REF] report large errors even in the initial MR/TRUS registration phase: up to 10mm. Due to prostate drifts during the operation, these errors will increase and obviously lead to biopsies far from the targets. Finally, most of these methods do not use an appropriate TRUS 3D probe but reconstruct 3D volumes from 2D images using the information given by the tracking device. This reconstruction process is not free from the introduction of prostate movements and deformations resulting from the movement of the probe itself.

To cope with these motions and deformations, techniques based on image fusion have given promising results. We refer to them as organ-driven approaches. One of the first attempts was proposed by Baumann et al. [START_REF] Baumann | Prostate biopsy tracking with deformation estimation[END_REF]. In this work a first stage consists in the elastic registration of preoperative MR images with 3D TRUS images acquired at the start of the intraoperative phase. Unlike the previously introduced methods, this initial MR/TRUS registration is updated using another registration performed during the procedure. It relates the initial 3D TRUS volume to 3D TRUS volumes acquired all along the procedure. This allows to update the target positions based on the real live observed anatomy. For example, in the Urostation (a commercial platform from Koelis SAS), 3D TRUS images are acquired before each biopsy and are registered rigidly or elastically on this first 3D TRUS image. This allows to provide very accurate maps of targeted locations in a reference volume (MRI and TRUS).

However, even with this approach, the physician has no information other than their mental representation between two 3D acquisitions, while they are navigating with the flow of 2D TRUS images. To guide them towards the biopsy locations as efficiently and accurately as possible, an important issue is to link the 2D TRUS flow to the initial 3D image. Refreshing the target position information from 10 to 15 times per second is most likely sufficient to guide the clinician. Some authors have proposed methods for registering the 2D TRUS images to a 3D TRUS reference image. For instance, De Silva et al. [START_REF] Silva | 2D-3D rigid registration to compensate for prostate motion during 3D TRUS-guided biopsy[END_REF] use normalized cross-correlation as an objective similarity function to rigidly register 2D images onto the 3D reference. A passive arm holding the US probe allows to initialize the unknown transform before registration. The functional is optimized with the Powell Brent method in order to speed up the computation time by avoiding the computation of derivatives. But even with an optimized version of this method and the delegation of parallelized computation to a GPU [START_REF] Gillies | Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy[END_REF], they had to sub-sample the input images by a factor of 4 to reach the real-time constraint, i.e. 10-15 Hz. However, to perform a GPU calculation, the ultrasound platform must be equipped with a specific board which is a strong constraint on current existing hardware. Moreover, this approach also requires a passive arm holding the probe. This potentially makes US probe motion less natural.

To alleviate these constraints, our team [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] has proposed a different organ-based approach to achieve real-time registration on a standard CPU without the need for a passive arm. This method can be seen as a variant of the iterative closest point method (ICP). An hybrid metrics combines image similarity and geometric proximity of detected features. It is used to match points that are finally registered by means of a rigid transform. This first version was tested on a clinical database of more than 100 3D US volumes from 20 patients.

Based on this first evaluation which was already very promising and to which we will compare, further work was necessary to increase accuracy (i.e. decrease average error and variability) while decreasing computation time. We also wanted to evaluate the method on a much larger clinical dataset. In this paper, we present the modifications and optimizations we made to the method and the evaluations we performed on a large dataset composed of more than 900 biopsy volumes from real clinical data. Moreover, our previous work was limited to static 2D/3D registrations. Additional experiments have been conducted to test the ability to track the prostate all along the procedure by testing high frequency 2D/3D registrations along probe trajectories. These dynamic experiments are also reported.

II. MATERIALS AND METHODS

A. Proposed approach

The inputs of the algorithm are a 3D TRUS reference image and a 2D TRUS image. Let us underline that a single 3D US probe allows both acquisition modes. The first 3D reference is acquired just before starting the biopsy series. During the procedure, a new 3D reference is acquired just before the needle insertion for each tissue sampling. The 2D image comes from the US flow acquired when navigating the US probe from one biopsy site to the next. Matching the 2D image on the fly to the latest 3D reference volume will provide information suitable for guiding the physician towards the next biopsy site. Figure 2 illustrates the integration of our method in a routine clinical process, where continuous 2D/3D registrations would be performed between two biopsies. The following sections provide information about the different steps of the registration method. We invite the interested reader to refer to [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] where different solutions and their parametrizations have been studied and are presented in full details.

Multi-resolution approach

In order to improve the seminal work proposed by Selmi [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF], we have introduced a multi-resolution approach to the orignal workflow. Multi-resolution approaches are used to obtain more precise and accurate results with a generally better computation time. Regarding registration, this results in finding more distant solutions since a larger search radius can be used at the coarser levels (see section II A 3). In other words, it allows the method to perform a more efficient and extensive search within the solution spaces which size increases with the level. The computational efficiency is also improved as many iterations (inexpensive in computing time) are performed at coarser levels to align the set of points globally and fewer iterations (more expensive in computing time) are needed at finer levels to refine this alignment.

Our algorithm repeats the steps described in the sections II A 2, II A 3 and II A 4 at each resolution level and uses the result (the rigid transformation) of one level as input for the next one. As rather classically done, for a trade-off between efficacy and accuracy, we used a three-level pyramid of images with a halving shrinking factor at every level. The process performed for each 2D live image is summarized by the flowchart of figure 3.

Features detection & Description

As it has been shown by Gillies et al. [START_REF] Gillies | Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy[END_REF], performing 2D/3D registration based on image similarity analysis requires offloading calculations to a GPU unit. To achieve real-time registration on a standard CPU, it is necessary to shift toward a less greedy registration technique. This is why we decided to use, instead of the full voxel matrix, a sparser representation of image: features points. They correspond to specific locations inside the images which are selected by a feature detector chosen to be reliable and coherent inside a stream of successive images. In our implementation, we use the well-known Harris detector [START_REF] Harris | A combined corner and edge detector[END_REF]. This simple but robust detector works on both 2D and 3D images. This ability ensures the consistency of the detected points for the next steps of our algorithm. This detector use a gradient-based strategy to detect robust features named "corners".

A descriptor is attached to each of these corners. It contains the coordinates of the corner expressed in the ultrasound probe coordinate frame -we call it feature point. The descriptor also includes grey level information about the point and its neighborhood Ω (the average intensity and a local histogram of the region aound the corner). Based on the results of previous experiments [START_REF] Selmi | 3D-2D ultrasound feature-based registration for navigated prostate biopsy: A feasibility study[END_REF], this neighborhood is a 5x5 pixels or 5x5x5 voxels region whatever the resolution level where it is computed.

Matching

The next step consists in matching the sets F 2D and F 3D of feature points respectively describing the 2D and 3D images. A first transformation is necessary to map the set of feature points describing the current 2D image into the 3D reference space as illustrated in Figure 4. This initial transformation would be given either by the result of the 2D/3D registration of the previous 2D image to the 3D current reference or by the last 3D/3D registration when navigation to the next biospy site starts. Let us remind that a single probe enables both 2D and 3D acquisitions: without probe motion, the 3D volume is acquired by rotating the 2D sensor from its resting position (most often the volume is symmetric with respect to this resting position its median slice corresponds to the 2D live image position). Calibration information allows representing 2D and 3D acquired information in a single reference frame. Therefore, having registered a volume to the reference (panorama), the median slice of this volume can be easilly mapped to the panorama. This gives a good prior for next live image.

Pairing combines feature similarity and geometric consistency. Each 2D feature f 2D ∈ F 2D has to be paired to a 3D feature f 3D ∈ F 3D located in its neighborhood. Let us remind that, during registration, the method has to iteratively determine the neighbourhood of feature points as ICP iteratively computes closest points. To do this efficiently, a KD-Tree is precomputed from the set of 3D features once for all 2D/3D registrations during navigation to the next biopsy site. This first selection based on geometric distance allows to work only on a subset of potential but realistic 3D matches for each 2D feature.

Then, the previously selected pairs, based on geometric distance, are matched using image intensity information. For each pair we compute a distance d:

d(f 2D , f 3D ) = α 1 d 1 + α 2 d 2 + α 3 d 3 , (1)
where

3 i=1 α i = 1
, d 1 compares the mean intensity in the neighborhood Ω of the features, d 2 uses the Bhattacharyya distance which quantifies the similarity of two normalized histograms, d 3 is the sum of squared differences computed in Ω. Finally, for each point of the 2D set, only the best 3D match is kept.

In order to improve the registration quality, one solution is to keep among all 2D/3D pairs resulting from the previous stages, only those with the highest similarity values. This selection is based on a fixed rejection rate of the worst pairs and requires implementing an efficient sorting method with respect to the similarity values. Conversely to [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] where this rejection rate was not used because of its computational cost, the current implementation makes efficient use of a sorted multi-set container of C++. Such special container can support multiple elements with the same similarity value while maintaining an insertion rate with a logarithmic complexity. The position of the previously inserted element and the comparison to this element is used to estimate the location of the new element. In this special case the computational complexity can even be constant amortized.

Finding the transform

When the feature points are paired, the algorithm proposed by Arun [START_REF] Arun | Least-Squares Fitting of Two 3-D Point Sets[END_REF] for non iterative least square minimization allows to compute the rigid transform that best matches the pairs. This algorithm aims to minimize the geometric distance between the given pairs. The computed transformation is given in the form of an Euclidean transform T with 6 degrees of freedom. To give more importance to information inside the prostate, we use a variant that allows the assignment of weights. T is computed to minimize

n i=1 w i × d(a i , T (b i )) 2 (2)
where w i is the weight given to one of the n pairs of matched features (a i , b i ) ∈ F 3D × F 2D . Pairs that have a 3D point inside the pre-segmented prostate are considered more meaningful and are therefore weighted with a higher coefficient than points in the rest of the image. Favouring information inside the prostate combined with the high frequency registration partially overcome the lack of elastic registration.

Optimization -Stopping Criterion

Subsections II A 3 and II A 4 are repeated until a stable transformation is found. The algorithm stops when the Euclidean distance between the 2D points registered between two successive iterations is lower than a given threshold or after reaching a maximum number of iterations given as input.

B. Evaluation on reference [10] dataset

To assess the presented method, we firstly used the same protocol and database than what was used to evaluate the method proposed by Selmi [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF]. This protocol focuses on the evaluation of the method under controlled conditions using data from clinical examinations. Here, the objective is to explore in a systematic way the limits of the presented approach on static 2D/3D registrations. This first evaluation is intended to show, in a direct way, the effect of the additions we made to [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF]. The following section presents the details of this benchmark. We are also taking advantage of this first evaluation to carry out a study of the sensitivity of the method to the main parameters (search radius and rejection rate).

Patient data set

In this experiment, the database is composed of 160 TRUS volumes for a total of 20 patients. These volumes were acquired during routine clinical biopsy series using two different commercial ultrasound systems (Urostation and Trinity from Koelis SAS). The clinical procedures were performed by six different operators from two different hospitals (Grenoble University Hospital and Paris La Pitié University Hospital). Acquired data include for each patient an initial 3D image, named reference or panorama volume (T RU S pano ) and a set of 3D images (T RU S biopsy ) acquired all along the biopsy protocol. To simulate 2D images, the median slice of each T RU S biopsy volume is extracted for 2D/3D registration to T RU S pano . As mentioned in section II A 3, this median slice corresponds to the live image that would be produced using the 2D mode instead of the 3D one having ths US probe in the same position.

Ground truth

For all the patients, we used fiducials (visible micro-calcifications) in order to compute the ground truth: the 6D transform that maps the 2D image to the 3D reference. Four to six anatomical landmarks within the prostate (visible both in T RU S biopsy and in T RU S pano ) were required to create fiducial pairs. Volumes that did not contain enough visible micro-calcifications were discarded from the validation database (and are not included in the 160 mentioned above). These fiducial pairs allow to compute the ground truth T GT (cf. figure 5) using paired-point matching. The fiducial localization error was evaluated to 0.38 mm and the fiducial registration error FRE after pair-point matching was 0.74 mm (±0.34) (cf. reference [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] for more details).

Simulated transforms

To simulate the movements of the TRUS probe or prostate, artificial rotations and translations were generated from the initial T GT to produce T Initial from which 3D/2D registration will be executed. For each volume in the biopsy sequence and each simulated perturbation, T Initial is applied to the biopsy volume (see Figure 6) before extracting the median slice to be registered to the reference volume.

Similarly to [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF], two different experiments were conducted. In the first one, rigid transforms are generated by modifying one of the six degrees of freedom at a time. The range of allowed perturbations is systematically explored: rotations (resp. translations) range from -15 • to 15 • (resp. -15; mm to 15 mm). The step is 1 • (resp. 1 mm) for rotations (resp. translations). In the second experiment, random rigid transforms are produced by changing the 6 position and orientation parameters at the same time. The explored ranges of perturbations were [-5 • , 5 • ] and [-7.5 mm, 7.5 mm]. These ranges are chosen deliberately larger than the values encountered during examinations (as if the method operated in real time on the 2D image stream) in order to show its limits. The obtained transform is noted T Reg .

To evaluate the registration method described in section II A, two TRE values between the reference volume fiducials and the matched biopsy volume fiducials are obtained. The first TRE value is computed before the registration process when T Initial has been applied to the biopsy volume fiducials. The second TRE value is determined after registration when T Reg has been applied to the biopsy volume fiducials. The TRE formula is written has:

T RE(mm) = N f i=1 f i ref -T (f i biopsy ) 2 N f ( 3
)
where T stands for the homogeneous transform matrix T Initial or T Reg and f i ref , f i biopsy corresponds to the N f pairs of fiducials manually selected in the reference and biopsy volumes. The Figure 6 shows the different transforms involved in the computation of the TRE.

We also recorded for every fiducial f i and every transform T j , the residual error on the transformed fiducial

Df (mm) = f i ref -T j (f i biopsy ) (4)
As explained previously, T GT is computed using a direct least square minimization of the distance between corresponding fiducials from two different volumes. T GT can be interpreted as the best transform that can be computed from the handled experimental data and the residual error can be seen as the lowest bound of registration accuracy achievable for such an experiment. Therefore, a useful information for the evaluation of T Reg is to compare it to T GT . This can be done by measuring the distance between the fiducials of the biopsy image transformed by T GT and by T Reg :

δ reg (mm) = N f i=1 T GT (f i biopsy ) -T Reg (f i biopsy ) 2 N f ( 5
)
Thanks to our 3D data, the evaluation is not restrained to bi-dimensional fiducials as it is often the case for evaluation of 2D/3D registration (cf. reference [START_REF] Silva | 2D-3D rigid registration to compensate for prostate motion during 3D TRUS-guided biopsy[END_REF]). This might have led to an under estimation of the out-of-plane motion. In this paper, the evaluation is based on true 3D point pairs from two 3D volumes and results give a more accurate view of the performance of the method. Let us remind that the 2D/3D registration result is to be applied to the whole reference volume for navigation purpose towards a target which is most often not included in the 2D image plane; this is why such a 3D evaluation is more adequate.

Parameter settings

Except for the search radius and rejection rate for which the settings have been studied specifically (see section III A 1), the other parameters were set according to results of [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF]. The maximum number of 2D and 3D feature points is 900 and 40,000 respectively. The size of the neighborhoods is 5x5 pixels in 2D and 5x5x5 voxels in 3D. The weight assigned to feature points is 4 when they are located inside the prostate and 1 otherwise. Regarding the stopping criteria, the convergence threshold is set to 1e-3mm and the maximum number of iterations is 50.

C. Evaluation on a larger dataset

Patient data set

In this experiment, again focused on static 2D/3D registration, a larger database was used; it was composed of 900 additional TRUS volumes for a total of 80 additional patients. These volumes were acquired during routine biopsy series with two different commercial US-based guidance systems (Urostation and Trinity from Koelis SAS), by urologists from the Grenoble University Hospital. No constraints or special protocols were imposed on physicians to perform these procedures. These data have been declared to the CNIL (French data protection authority) under the reference MR3711140520.

Ground truth

Because of the large dataset, it was not feasible to define fiducials on each volume in order to get the ground truth value of the searched transform as previously. Therefore, we have evaluated the registration quality differently. When using the cited guidance systems, in order to map MRI targets to the US data, urologists have first to segment the prostate on the first acquired US volume (named panorama or reference volume). Moreover, during the intraoperative phase, the guidance software provided by the platform, also estimates the 3D/3D rigid transform between the reference volume and volumes acquired whole along the biopsy procedure using a widely evaluated image-based registration [START_REF] Baumann | Prostate biopsy tracking with deformation estimation[END_REF][START_REF] Oderda | Accuracy of elastic fusion biopsy in daily practice: Results of a multicenter study of 2115 patients[END_REF]. This transform will be considered as the ground truth T GT for this evaluation. In a way rather similar to what was described in section II B 2, the accuracy of the registration method is measured by computing the point-topoint distance between the mesh of the reference volume transformed by T GT and the mesh transformed by another transform: T Initial (before registration) or T Reg (after registation). It is defined as:

T RE(mm) = N i=1 mesh i ref -T T -1 GT mesh i ref 2 N (6)
where T stands for T Initial and T Reg , mesh i ref is the i t h vertex of the reference mesh, N is the number of vertices of this mesh. We also applied this mesh-based evaluation to a subset of 100 volumes taken in the dataset of the fiducial-based evaluation (cf II B 1). This enabled the comparison between the fiducial-based evaluation and the mesh-based evaluation.

Simulated transforms

To simulate only realistic transformations we used the same protocol that has been used for the second experiment of the previous section (see II B 3 and see Figure 5). The random rigid transforms composed to T GT include variations of the 6 position and orientation parameters at the same time to produce T Initial . The range used to simulate rotations was [-5 • , 5 • ] and was [-7.5 mm, 7.5 mm] for the translations.

D. Evaluation on trajectory

Data generation & Ground truth

As introduced in section I, all previous evaluations concerned 2D/3D static registration. Because the intended use of the method is for navigational assistance during biopsy, additional evaluation along biopsy trajectories of the TRUS probe was mandatory. Capturing live 2D images along real trajectories during clinical procedures and being able to compute a ground truth raises both technical difficulties including the need for probe tracking, clinical additional burden and regulatory issues. This is why we designed a different approach based on a biopsy simulator developed by our team [START_REF] Selmi | A virtual reality simulator combining a learning environment and clinical case database for image-guided prostate biopsy[END_REF] and thoroughly evaluated ( [START_REF] Fiard | Initial validation of a virtual-reality learning environment for prostate biopsies: Realism matters![END_REF][START_REF] Fiard | Validating the Transfer of Skills Acquired on a Prostate Biopsy Simulator: A Prospective, Randomized, Controlled Study[END_REF]). This simulator provides a virtual environment for educational and research purposes. It includes patient data collected from real biopsy series when using the Urostation or Trinity guidance system (Koelis, France). Again, preoperative MRI scans, intraoperative 3D TRUS volumes and meshes are associated with each recorded patient among other information. Using a mock-up of the US probe attached to a haptic device (Phantom Omni, Sensable Devices Inc.), the trainee can train and execute virtual biopsy series. Thanks to the haptic device, the position and orientation of the probe is known and a 2D live US image can be generated from the recorded TRUS volume and displayed to to him/her in real-time.

Using the simulator, real biopsy trajectories can be executed and the associated 2D on-the-fly images can be generated from the T RU S pano volume acquired at the beginning of the examination. Thus, the ground truth T GT is easily known by tracking the probe mock-up.

Simulated trajectories

For the purposes of this experiment, we executed two types of stereotyped trajectories. The first one is a classical exploration of the anatomical environment with combined rotations of the probe. This type of trajectory is generally encountered during exams when the urologist moves the probe to find the target area. The second is a pure rotation of the probe. This movement is usually performed when the urologist wants to align the needle to a localized target position, without losing the line of sight he/she has on it [START_REF] Gillies | Ring navigation: an ultrasound-guided technique using realtime motion compensation for prostate biopsies[END_REF].

For each trajectory, we tested two different registration strategies. One (noted sequential) consists in using the result of the previous 2D/3D registration as input for the current one. In this case, two image processing frequencies are used: 1 out of 2 and 1 out of 5 images. This corresponds approximately to physical acquisition frequencies ranging from 5 to 15 Hz. The other strategy (noted non-sequential) is to register all the images independently. In this case, for each new image, the initial transformation is the same as the one that was used for the first image in the sequence.

The method used to evaluate the registration quality is mesh-based as presented in section II C (cf. equation 6).

III. RESULTS

A. Evaluation on reference [10] dataset

The results obtained for the comparative experiments aiming at evaluating our additions to [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] are synthesized in Table I. TRE is given before and after registration for the two methods. For complete comparison to [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF], this table also provides the percentage of registrations which resulting TRE is lower than 5 mm.

The results show that we have improved the performance of the method in terms of accuracy (average value and standard deviation) compared to reference [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF]. Indeed for the first experiment, Table I shows that the average error is 12% smaller while the standard deviation is divided by 3. Regarding the clinical threshold, more than 80% of the results were already lower than 5 mm. It is now 11% better. Decreasing the variance is also crucial because it shows the repeatability of the method. The results of the second experiment follow the same trend in a more realistic evaluation, since the movement of the hand is never done on a single degree of freedom. Whilst starting farer ("TRE before" is larger), our method results in an improvement of performances : 17% less for the average error, the standard deviation is divided by 1.6 and 11% more registrations result in TRE values below the clinical threshold.

Regarding the current method described in this paper, we performed a statistical analysis of performances. Figure 7 illustrates the distribution of errors (TRE and Df) obtained for the experiments 1 and 2 on the dataset. Table II gives the percentage of errors below the clinical threshold for the conducted experiments. The Shapiro-Wilk test allowed to verify that the Df and TRE distributions were not normal. Therefore, we performed a Wilcoxon statistical test between pre and post registration Df and TRE values. This test shows a very significant difference between the TRE values before and after registration. For experiment 1, conducted on 29,760 samples, the p-value is 2.34e -18 . For experiment 2, on 4,000 samples, the p-value is 3.62e -17 . Regarding Df, Wilcoxon returns a zero value, highlighting a very significant difference between before and after registration error distributions (on respectively 127,000 and 17,000 samples).

For the experiments 1 and 2 the δ reg distance is respectively equal to 3.09 mm (±0.82) and 2.59 mm (±0.46). Since the typical voxel size of an ultrasound image is about 0.33 mm on each dimension after reconstruction, this corresponds to a relatively small error (less than 8 voxels). For comparison, let us remind that the FRE corresponding to T GT is 0.74 mm (±0.34).

Finally, in terms of computing time, the proposed algorithm is able to perform 2D/3D registrations at a frequency that varies between 5 and 15 Hz on a standard CPU (Intel Xeon W2145 with 8 cores @3.74 Ghz). These performances vary according to the value of the parameters and these variations are mostly correlated to the size of the chosen search radii. Indeed, with larger search radii, more points are considered potential matches and need to be evaluated.

The effect of parameter settings on the performances are discussed in the next section.

Sensitivity to parameter changes

a. Search radius Table III shows the analysis of the registration accuracy when varying the search radius parameter within the KD tree tested by running experiment 2. The impact of this parameter on the method is clearly visible: the larger the radius, the more it will be possible to find a large perturbation. However, this will have a slightly negative impact on the accuracy of the method in case of small perturbations. The underlying reason is that this search introduces more false positives at the beginning of the optimization as more points can be falsely coupled. IV shows the impact of the rejection rate (RR) tested by running experiment 2. One can see that this parameter allows to obtain more precise results. Indeed, the results with a non-zero RR are better than zero RR where all the pairs are kept. This is a direct consequence of eliminating the worst pairs that can be considered false positives. Nevertheless, increasing the RR improves the quality of the registration to a certain extent. Beyond this threshold, too many pairs are removed and the optimization fails to find a precise transformation, especially for larger perturbation. This setting also has a positive impact on computation time because fewer pairs are used in the registration process.

b. Rejection rate Table

From these two sensitivity analyses, we decided to use two different parameter configurations depending on the computing time requirements. The first one was used for the static registration experiments (sections III A and III B): the search radii was (5, 3, 2) mm and the rejection rate was 10%. The second one used for prostate tracking experiments on trajectories (section III C) was chosen to be faster: the search radius was [START_REF] Cornud | TRUS-MRI image registration: A paradigm shift in the diagnosis of significant prostate cancer[END_REF][START_REF] Cornud | TRUS-MRI image registration: A paradigm shift in the diagnosis of significant prostate cancer[END_REF][START_REF] Cornud | TRUS-MRI image registration: A paradigm shift in the diagnosis of significant prostate cancer[END_REF] mm and the rejection rate was 10%.

B. Evaluation on a larger dataset

For each of the 900 volumes, 10 perturbations were randomly generated and used 3D/2D registration was performed for these 1000 cases. The corresponding results are summarized in Table V. This experiment demonstrates that scaling up is consistent with the results of the section III A. The average accuracy is almost similar to what was obtained in section III A (3.80mm now versus 3.60) as well as the percentage of registrations below the clinical threshold (86% versus 87). It can also be seen that the standard deviation is lower than in the previous experiment (0.48 versus 1.59). This can be explained by the better quality of the input images which were acquired with a more recent ultrasound platform which has a better image quality.

As for the smaller dataset, we performed a stastical analysis of performances. Figure 8 plots the distribution of TRE errors obtained for this experiment. Again, the Shapiro-Wilk showed that the TRE distributions were not normal and the Wilcoxon statistical test between pre and post registration TRE values gave a very significant difference (p-value = 0) between before and after registration error distributions.

Finally, regarding the comparison of mesh-based and fiducial-based evaluation on the subset of a 100 volumes from the data-set of the fiducial-based evaluation, the average post-registration TRE found was 3.43 mm (±0.51) when using fiducials and 3.88 mm (±0.53) when using the meshes.

As our mesh based TRE calculation is based on a single mesh for both images, the meaning of this mesh-based TRE value is rather similar to the distance (δ reg ) obtained with the fiducials in the section III A. Indeed, the mesh is transformed with the help of the ground truth transformation, to bring it from the panorama to the biopsy image.

The residual error computed on the biopsy fiducials was equal to 2.98 mm (±0.89) while the mesh evaluation gives 3.88mm. Considering that the vertices of the meshes are much more numerous than fiducials and distributed in a larger volume, these results look consistent.

Therefore, all these results prove that the mesh-based evaluation is consistent to the fiducial-based evaluation and that the results obtained for the 900 volumes can be trusted.

C. Evaluation on trajectory

Although, we tested more trajectories, we selected only one trajectory of each type to illustrate this experiment. All conducted experiments worked very similarly to these two.

The results for the exploration trajectory are given in Figure 9. They demonstrate the advantage of using the sequential approach over the non-sequential approach. Indeed, even if the non-sequential approach is able to register the images (the TRE is always better after registration than before), the efficiency of the approach is limited and shows more limitations when the initial position is far from the solution. The sequential approach is more efficient as the previous registration result is used to initialize the current registration. This figure also shows that in the case of fast motions in different directions, corresponding to the peaks of the TRE before registration, the ability to perform registrations at a higher frame rate makes the method more robust. This is shown by the two peaks on the orange curve that are not present on the green curve.

Regarding pure rotation trajectories, the results are presented in Figure 10. This experiment shows very clearly the advantages of the sequential registration. When the method is applied in a non-sequential way, it is unable to find a solution when the TRE increases very strongly (values higher than 10 mm). In the case of this stereotyped trajectory, the frequency at which the registration is performed is less crucial because the movement is relatively smooth during the trajectory. We can nevertheless notice that the light bump at the beginning of the movement is better smoothed in the case where one image out of two is processed (green curve).

By observing the results from these two scenarii, it seems that the TRE in the sequential approach is even smaller that what was described in the previous sections. However, let us underline that no deformation exists between the 3D volume and the 2D image due to the use of the simulator. Getting the real TRE value will require extensive clinical experiments. This is a further step.

IV. DISCUSSION AND CONCLUSION

In this paper, we have described a method for efficiently registering a live stream of TRUS 2D images to a TRUS 3D reference image. The ultimate objective is to improve the quality and reliability of the prostate biopsy procedure. Our method is based exclusively on the live 2D stream and a 3D image acquired at the beginning of the procedure; no external sensors or robotic arms are required. In addition, our method can operate in near real time on a conventional ultrasound platform and does not require a dedicated GPU unit. These performances are reached because we use feature points, a subset of key landmarks that are automatically detected on the images, instead of processing all the pixels of these images in a conventional image-to-image registration framework.

Although previous work regarding 3D/3D registration proved that the prostate moves and is deformed during the biopsy process, our guess was that these movements and deformations would keep small between two successive 2D US live images processed at a high rate. This is why we implemented a rigid registration method. This allows to keep computational cost compatible with navigation requirements (around 10 to 15 Hz). To make registration more accurate, we also gave more importance to information inside the prostate. Results demonstrate that these choices provide a good trade-off between accuracy and processing time requirements.

We performed three different evaluations on a very large amount of data acquired under uncontrolled routine conditions (more than a hundred patients and more than a thousand volumes in total). We also used two different methodologies to assess our results. They both rely on 3D transformations estimated from 3D data from manual and automatic methods for more reliability. To our knowledge, no other approach in this field has used such a large amount of data from real clinical patients to validate their algorithm. From a technical point of view, most of the other methods proposed in the literature like [START_REF] Silva | 2D-3D rigid registration to compensate for prostate motion during 3D TRUS-guided biopsy[END_REF][START_REF] Gillies | Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy[END_REF][START_REF] Gillies | Ring navigation: an ultrasound-guided technique using realtime motion compensation for prostate biopsies[END_REF] do not use motorized 3D probes but reconstruct these volumes by combining the data from a localization device and the captured stream of 2D images. This acquisition protocol does not allow them to estimate their ground truth from real 3D data, which in our opinion may introduce an underestimation of out-of-plane displacements.

Compared to our previous work [START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF], we have introduced several changes such as the multi-resolution approach, a rejection ratio of matched feature pairs and a more robust stopping criterion computed using displacement error. Combined with optimizations in the choice of data structures and in the implementation, these improvements have allowed us to achieve better performance both in terms of computation time (initially 0.25 Hz now 5-15Hz) and accuracy (15 % on average with a standard deviation divided by 1.5). In all conducted experiments, TRE after registration is lower than before registration. The difference has been statistically tested when possible (i.e. for fiducial-based evaluation) and is very significant. Coming back to the clinical requirements, let us remind that 5mm is considered as the minimum radius of clinically significant tumors. Therefore, ideally, all biopsy targets should be located with a maximum error of 5 mm. Observing directly the error on fiducials (Df) on a large sample of registration experiments and on many data coming from routine acquisitions allows to be optimistic about the clinical applicability of the method: for experiment 1 (resp. 2), Df after registration is in average equal to 3.23 mm (resp. 3.41 mm) and is below 5mm for 89% (resp. 87%) of the cases. To avoid any mislocation of prostate cores, a final check of the current position with respect to the target can be performed using 3D/3D registration before tissue sampling.

The complementary experiments we have conducted allow us to show that registrations can be carried out even more efficiently on trajectories using a sequential approach. Similar trends were found in [START_REF] Silva | 2D-3D rigid registration to compensate for prostate motion during 3D TRUS-guided biopsy[END_REF], on phantom data and on a small number of clinical images (16 registrations in total): they report an improvement of the registration accuracy (from 1.63 to 1.81 mm in average). Nevertheless, their method require the use of an arm to initialize the registration algorithm for each acquisition. As a final remark, let us stress the fact that our algorithm, when used in a tracking context (which is our final goal), is not very sensitive to variations in the input parameters. The good performances of our approach relies more on its ability to work at high frequencies as illustrated by our experience with trajectories.

Our next objective will be to integrate this approach on an ultrasonic platform in order to achieve real-time 2D/3D registrations on trajectories performed in clinical routine by an urologist.

Captions 1 . 6 . 7 .

 167 TRUS-guided biopsy procedure 2. Workflow of the biopsy procedure 3. Main steps of a 2D/3D registration of the live 2D image to the 3D reference image. 3D features are extracted once before series of 2D/3D registrations 4. Features iterative matching. In blue (resp. orange: the 3D (resp. 2D) feature points set from the reference US volume (resp. 2D on-the-fly US image) for a given stage of the iterative registration 5. Computing the ground truth: T GT is computed from visible fiducials in two US volumes and allows to evaluate the accuracy of registering the median slice extracted in one volume to the other volume. Transformations used by the method. T GT is the ground truth transformation from the biopsy volume and the panorama, T Initial is the initial transformation applied on the biopsy volume and T Reg is the output of the registration algorithm. Distribution of Df (top) and TRE (bottom) errors for experiments 1 (left) and 2 (right).

8 .

 8 Distribution of TRE errors for the experiments on the large dataset. 9. Results of the registration for the trajectory simulating an exploration around a given position. 10. Results of the registration for the trajectory simulating a pure rotation around the probe axis.

Figure 1 .

 1 Figure 1. TRUS-guided biopsy procedure

Figure 4 .Figure 5 .

 45 Figure 4. Features iterative matching. In blue (resp. orange: the 3D (resp. 2D) feature points set from the reference US volume (resp. 2D on-the-fly US image) for a given stage of the iterative registration

Figure 6 .

 6 Figure 6. Transformations used by the method. TGT is the ground truth transformation from the biopsy volume and the panorama, T Initial is the initial transformation applied on the biopsy volume and TReg is the output of the registration algorithm.

Figure 7 .

 7 Figure 7. Distribution of Df (top) and TRE (bottom) errors for experiments 1 (left) and 2 (right).

Figure 8 .

 8 Figure 8. Distribution of TRE errors for the experiments on the large dataset.

Figure 9 .

 9 Figure 9. Results of the registration for the trajectory simulating an exploration around a given position.

Figure 10 .

 10 Figure 10. Results of the registration for the trajectory simulating a pure rotation around the probe axis.

Table I .

 I Summary of the results obtained for the two experiments (section II B) with registration initializations and datasets similar to[START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] -reminder of[START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] performances. Df was not computed in[START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF] and is replaced by *

	Experiment 1	TRE before	TRE after	TRE after < 5 mm	Df before	Df after	Df after < 5 mm
	Reference [10] 8.06 mm (±4.83) 3.91 mm (±3.22)	81%		*	*	*
	Proposed	8.06 mm (±4.83) 3.44 mm (±1.11)	92%	7.98 mm (±5.12) 3.23 mm (±1.88)	89%
	Experiment 2
	Reference [10] 7.48 mm (±2.25) 4.37 mm (±2.62)	76%		*	*	*
	Proposed	8.02 mm (±1.95) 3.60 mm (±1.59)	87%	7.94 mm (±3.21) 3.41 mm (±1.91)	87%
			Experiment 1 Before After
			Df		44% 89%
			TRE	40% 92%
			Experiment 2
			Df		19% 87%
			TRE	20% 87%

Table II .

 II Percentage of errors below the clinical threshold (5mm) before and after registration. Extract the 2D features Initialize T (last 3D/3D or previous 2D/3D) Apply T to the 2D features Select all the 3D features in the search radius of each 2D features For each 2D features having possible matches, choose the 3D features maximizing d (eq. 1) Reject worst pairs based on d Weight remaining pairs (prostate / non-prostate) Figure 3. Main steps of a 2D/3D registration of the live 2D image to the 3D reference image. 3D features are extracted once before series of 2D/3D registrations

	Search radii per level		TRE (std)
	(4., 2., 1.)	4.17 mm (±1.97)
	(3., 3., 3.)	3.54 mm (±1.32)
	(5., 3., 2.)	3.48 mm (±1.04)
	Find best transform T (eq. 2)
	End?		no
	yes
	Rejection rate per level	TRE (std)
	(0.3, 0.3, 0.3)		3.70 mm (±1.36)
	(0.3, 0.2, 0.1)		3.60 mm (±1.30)
	(0., 0., 0.)		3.48 mm (±1.04)
	(0.1, 0.1, 0.1)		3.44 mm (±1.11)

Table

III

. Impact of the search radius in mm (rejection rate: 0., maximum iteration number: 50) Figure

2

. Workflow of the biopsy procedure

Table IV .

 IV Impact of the rejection rate (maximum iteration number: 50, search radii in mm: (5., 3., 2.))

	Experiment TRE before (mm) TRE after (mm) TRE after < 5 mm
	Proposed	8.56 (±4.83)	3.80 (±0.48)	89%

Table V .

 V TRE errors for experiments on the large dataset.

ACKNOWLEDGMENTS

This work was partly supported by the Investissements d'Avenir programme (Labex CAMI) under reference ANR-11-LABX-0004

The authors have no conflicts to disclose.