Dr Michèle Salmain
email: michele.salmain@sorbonne-universite.fr

Dr Nathalie Fischer-Durand

Prof. Dr Bogna Rudolf

Bioorthogonal conjugation of transition organometallic complexes to peptides and proteins: Strategies and applications

Keywords: Click chemistry, peptide nucleic acid, cycloaddition, ferrocene, manganese

The advent of bioorthogonal chemistry has revolutionized the common practices in protein bioconjugation and contributed to a large extent to the development of chemical biology, a discipline aimed at studying biological / biochemical processes / events in their natural setting (living cells, whole organisms) using dedicated chemical tools. This minireview intends to provide an up-to-date overview on the various bioorthogonal strategies implemented for the conjugation of transition organometallic entities to peptides, peptide nucleic acids and proteins with a focus on targeted applications, i.e. fluorescence-or radio-labeling for imaging, controlled delivery of therapeutic agents and bioanalysis.

Introduction

Within the last two decades or so, protein bioconjugation methods have undergone a dramatic evolution as the concept of bioorthogonal ligation was introduced. [1] Until then, protein bioconjugation had been mostly limited to the modification of amine and thiol nucleophilic functions of lysine and cysteine residues with electrophiles so that they had to be performed on pure protein samples. Moreover, reactions involving lysines are by essence not regioselective owing to the high number of these residues in most proteins giving rise to a complex mixture of bioconjugates. In contrast, bioorthogonal ligation methods allow reactions to take place with high chemoselectivity in complex biological settings, including living cells and higher organisms. [2] To be recognized as bioorthogonal, a chemical transformation must fulfill several criteria. Reagents must tolerate the aqueous environment and nucleophiles abundantly present in cells. They should be kinetically, thermodynamically and metabolically stable and naturally non toxic to living systems. Moreover, when dealing with biomolecule modification in biological settings such as cells, the issue of reaction rate becomes pivotal since species to be conjugated are usually present in low amount. [3] Consequently, the kinetics of the bioorthogonal reaction should be adjusted to reduce the concentration of the reaction partner to the minimum while product formation occurs in a reasonable timescale. [4] Applications of bioorthogonal chemistry in chemical biology are growing steadily. [5] The most popular one is certainly the (metabolic) labeling of biopolymers with luminescent probes for tracking purposes. [6] Bioorthogonal reactions (especially CuAAC, 1 see below) have also proven invaluable for enzyme activity profiling, [7] drug targets identification [8] and other biomedical applications.

On the other hand, synthetic transition organometallic complexes have distinct and sometimes unique properties whose input in life sciences has been recognized from the 1980s specially for the development of new (radio)pharmaceuticals for imaging and therapy as well as optical and electrochemical markers. [START_REF] Jaouen | Bioorganometallics. Biomolecules, Labeling, Medicine[END_REF] Table 1 gathers the range of bioorthogonal reactions that have been used for the bioconjugation of transition organometallic complexes to date. Except for CuAAC and Sonogashira cross-coupling that require metal catalysis to take place, the other ligation methods occur spontaneously and at variable reaction rates. This minireview is intended to give a comprehensive overview of the works reported so far on the bioorthogonal ligation of transition organometallic entities to peptides, peptide-like polymers, proteins and occasionally to an oligonucleotide. Let us note however that those involving proteins are still rather scarce. For reasons of space, articles dealing with coordination / inorganic complexes were intentionally omitted. General methods for labeling of peptides and proteins with luminescent rhenium(I) and iridium(III) complexes have been reviewed recently by Lo and coworkers [START_REF] Yip | [END_REF] and Connell and Donnelly [11] . Radio-labeling of biopolymers by click chemistry has also been reviewed. [12] Synthetic methods to prepare organometallic peptide bioconjugates and their application as antibacterial agents have been comprehensively reviewed in 2016 and 2017, respectively. [13] All the other bioconjugation methods involving native protein functional groups are also intentionally omitted. Such an information may be found to the most recent review on artificial metalloenzymes. [14] 1 Abbreviations : ADIBO, azadibenzocyclooctyne; aTf, apo-transferrin; BBS, bombesin; BCN, bicyclononyne; bpea, bis(pyrazolyl)ethylamine; BPS, bathophenanthroline disulfonic acid; BSA, bovine serum albumin; cMBP, c-Met binding peptide; CORM, carbon monoxide releasing molecule; CMIA, carbonyl metalloimmunoassay; CuAAC, copper-catalysed azide-alkyne cycloaddition; DBCO, dibenzocyclooctyne; DIPEA, diisopropylethylamine; dpa, dipicolylamine; EDC, ethyl diisopropyl carbodiimide; Fc, ferrocenyl; Fp, ( -cyclopentadienyl) iron dicarbonyl; eGFP, enhanced green fluorescence protein; GRPR, gastrin-releasing peptide receptor; HSA, human serum albumin; HTf, holotransferrin; iEDDA, inverse electron-demand Diels-Alder; IgG, immunoglobulin G; Mb, myoglobin; MDM2, mouse double minute 2; MSH, melanocyte stimulating hormone; NHS, N-hydroxysuccinimide; NLS, nuclear localization signal; PNA, peptide nucleic acid; PLIM, photoluminescence lifetime imaging microscopy; ppy, 2-phenylpyridine; pqe, 2-phenylquinoline; ROS, reactive oxygen species; SPAAC, strained-promoted azide-alkyne cycloaddition; SPANC, strained-promoted alkyne-nitrone cycloaddition; SPECT, single photon emission computed tomography; SPPS, solid-phase peptide synthesis; Tat, transactivator of transcription; TBAF, tetrabutylammonium fluoride; TBTA, tris(benzyltriazolylmethyl)amine; TGF, transforming growth factor; THPTA, tris(hydroxypropyltriazolylmethyl)amine; TMS, trimethylsilyl; tpm, tris(pyrazolyl)methane.

1,3-dipolar cycloadditions

Copper-catalysed azide -alkyne cycloadditions (CuAAC)

The 1,3-dipolar [3+2] cycloaddition between azides and terminal alkynes (AAC) also known as the "click reaction" (Table 1, entries 1 and 2) is one of the most powerful ligation methods discovered to date, owing to the small size of the two partner functions involved in the reaction, their relative inertness and their absence in biological molecules and media. Although this reaction has been introduced in the early 60s by Huisgen, [15] the real breakthrough in chemical biology was provided independently by Sharpless and Meldal's groups in 2002, [16] when they both found that Cu(I) was an outstanding catalyst of this reaction. Not only reaction rates are tremendously accelerated but the reaction becomes regioselective as only the 1,4-substituted 1,2,3triazole isomer is obtained. Moreover, the compatibility of copper-catalyzed azidealkyne cycloaddition (CuAAC) with other functional groups qualifies it as a truly bioorthogonal reaction that is now extensively exploited in various fields including peptide / protein conjugation. [17] 2.1.1. Chelate then click strategy Several transition organometallic complexes carrying an azido or a terminal alkynyl substituent (Figure 1) have been synthesized and conjugated to biopolymers carrying the partner handle by CuAAC. Not surprisingly ferrocene was the first one to be conjugated this way to the biologically active peptide[Leu 5 ]-enkephalin, [18] a neuropeptide that binds to opioid receptors and involved in analgesia as well as stress processes. [19] This pentapeptide was prepared by solid-phase peptide synthesis (SPPS) and 4-pentynoic acid was coupled to the -amino group at the N-terminus of the peptide sequence. After cleavage from the solid support, ferrocenylazide 1 was successfully clicked to the functionalized peptide under classical conditions (CuSO4 + ascorbate in t BuOH / H2O 1:1). Alternatively, CuAAC was also achieved with the peptide still on the solid phase in the presence of CuI and excess DIPEA in DMF.

Following this initial report, other teams became interested in coupling transition organometallic moieties to peptides via CuAAC for various purposes. In 2009, Schatzschneider and co-workers designed a photoCORM peptide conjugate for selective delivery of CO to cancer cells. [20] The acronym CORM was initially coined by Motterlini and co-workers in their pioneering work, [21] and refers to transition metal carbonyl complexes that are able to release carbon monoxide, spontaneously or under specific stimulation, [22] for biomedical applications. [23] To this aim, the -amino group at the Nterminus of Thr-Phe-Ser-Asp-Leu, a peptide sequence representative of the transactivation domain of the tumor suppressor protein p53 within the regulatory protein MDM2, was acylated with azidoacetic acid. After cleavage / deprotection, the Mn(CO)3 complex of tris(pyrazolyl)methane (tpm) ligand 2 was clicked to the functionalized peptide under typical Sharpless conditions to afford the modified peptide in good yield. Upon UV irradiation, 1.7 equivalents of CO were released per conjugate. In the same vein, the same team reported the conjugation of the bis(pyrazolyl)imine Mn(CO)3 complex 3 to a pentapeptide representative of TGF-ß, a cytokine involved in cell proliferation, differentiation, motility, adhesion and apoptosis. [24] Slow decomposition of the conjugated peptide was observed probably due to hydrolysis of the imine bond within the tripodal ligand.

Azido methyl ruthenocene 4 was also reported as CuAAC orthogonal partner for the labeling of [Leu 5 ]-enkephalin, either at the N-terminus modified by 4-pentynoic acid or at the side chain of the non natural aminoacid propargylglycine. [25] Figure 1. Transition organometallic complexes designed for CuAAC Rhenium and technetium tricarbonyl complexes of tridentate dipicolylamine (dpa) ligands were conjugated to a peptide analogue of the -melanocyte stimulating hormone (-MSH) by CuAAC for selective imaging of melanoma cells. [26] In the first step, an azido group was appended to the peptide by S-alkylation of the non essential cysteine residue with 2-bromo-N-(3-azidopropyl)-acetamide. In a second step, click reaction with the Re and 99m Tc complexes 5a, 5b, 6a, 6b yielded the expected peptide conjugates in very good yield. High cellular uptake of the 99m Tc conjugate including the carboxylatesubstituted dpa ligand was found in melanoma cells. Coincubation with excess unlabeled peptide significantly reduced cell uptake of peptide conjugates, indicating that it was mediated by the membrane receptor MC1R. Biodistribution studies in vivo showed moderate accumulation of the radiotracer derived from the hydrophilic complex 6b in melanoma xenografts but failed to decrease the hepatobiliary retention.

In 2014, Gasser and co-workers reported the labeling of the lipopeptide myr-Lys-Tat with the luminescent rhenium tricarbonyl complex 7. [27] Tat peptide is part of the transactivator of transcription of HIV-1 and was the first cell penetrating peptide to be identified. [28] -Azidolysine was inserted within the lipopeptide sequence in between the myristyl chain and the Tat peptide sequence by SPPS. The click reaction took place under the conditions reported by Fokin (CuSO4 + ascorbate + TBTA). Fluorescence microscopy of HeLa incubated with the conjugate showed higher cellular uptake compared to the rhenium complex alone.

The iClick reaction was used once for conjugation of gold(I) complexes to a biologically active peptide. [29] In short, iClick is the version of azido-alkyne cycloaddition for which the azide and / or the alkyne is coordinated to a transition metal. [30] Interestingly, no catalyst is required for the cycloaddition to take place since the azide / alkyne is sufficiently activated through its metal coordination. In the work by Metzler-Nolte and co-workers, the mitochondria-targeting sequence L-4-I-Phe-D-Arg-Phe-Lys was synthesized by SPPS. With the peptide still on the solid support, a terminal alkyne moiety was introduced by Sonogashira reaction with ethynyl-TMS followed by deprotection with TBAF. Cycloaddition with the Au(I)(phosphine) azido complexes 8 proceeded in DMF in the absence of copper catalyst (Scheme 1) to afford, after cleavage / deprotection, gold-peptide conjugates where gold is coordinated to the formed 1,2,3triazole ligand via a gold-carbon bond. [31] The cytotoxic activity of the gold-peptide conjugates on the breast cancer cell line MCF-7 was found to be lower than that the Au(I) precursors, most likely because of poor cellular uptake. Nevertheless, one of the gold-peptide conjugates was shown to induce overproduction of ROS, decrease of the mitochondrial membrane potential and eventually trigger apoptosis.

Scheme 1. Labeling of a peptide by iClick

Few examples of CuAAC between a transition organometallic complex and a protein have been reported to date. Two of them aimed at incorporating a metal carbonyl entity into a protein to take advantage of its strongly absorbing properties in the mid-IR spectral range owing to the presence of the CO ligands giving rise to bands in the 1800-2150 cm -1 region. In the first example, the cyrhetrenyl complex 9 carrying a terminal alkyne group was site-selectively conjugated to the C-terminal domain of the ribosomal protein L9 (CTL-9) including an azidohomoalanine residue at position 109. [32] Quantitative incorporation of the metal carbonyl entity was reached and had no effect on the protein structure. Furthermore, the presence of the rigid triazole linker prevented any non specific interaction with the protein surface. In the second example, we successfully labeled a model protein, namely bovine serum albumin (BSA), with cyclopentadienyl iron dicarbonyl (Fp) entities using a two-step process. [33] Azido groups were first introduced on BSA by diazo transfer reaction with imidazole-1-sulfonyl azide with the amino groups carried by the lysine residues (scheme 2). [34] Scheme 2. Azidination of BSA The second step consisted in CuAAC with the Fp derivative 10 in the presence of CuSO4, ascorbate and BPS. In average, 8 Fp entities were found to be incorporated into BSA as assayed by IR spectroscopy. In a similar fashion, the luminogenic, cyclometalated iridium(III) complex carrying an azide handle 11 was conjugated to alkyne-tagged HSA in the presence of CuSO4, ascorbate and THPTA. [35] The photoluminescent cyclometalated iridium(III) complex carrying a terminal alkyne group 12 was very elegantly used to image protein synthesis within living HeLa cells by photoluminescence lifetime imaging microscopy (PLIM). In brief, HeLa cells were metabolically labeled with azidohomoalanine and further treated with complex 12 in the presence of Cu2O nanoparticles as catalyst. Labeling of newly synthesized proteins by 12 was monitored in real time in living cells in a wash-free fashion thanks to the large difference of luminescence lifetime between the unreacted azido complex and the resulting triazole that allowed perfect discrimination between both forms of complex. [36] CuAAC has also been employed for the ligation of transition organometallic entities to peptide nucleic acids (PNA). PNA are synthetic surrogates of nucleic acids (DNA and RNA) where the sugar-phosphodiester backbone is replaced by a pseudopeptidic backbone of repeating N-(2-aminoethyl)glycine units. [37] Compared to their natural counterparts, PNA display higher affinity for the complementary DNA / PNA sequence, better mismatch sensitivity and are insensitive to nuclease / protease degradation. [38] PNA are typically synthesized by SPPS using Fmoc-protected monomers. [39] Metzler-Nolte and co-workers introduced several routes to "click" an organometallic entity to PNA. The first pathway made use of the alkyne-containing PNA monomer 13 (figure 2), which was conveniently inserted either at the C-terminus, the N-terminus or in the middle of the PNA sequence during SPPS. Conjugation of ferrocenylazide 1 was then achieved on the solid phase as described above. [40] The stability of the duplexes formed by hybridization between Fc-labeled PNA and complementary DNA sequence was found to depend on the position of ferrocenyl entity in the PNA sequence. While insertion at the C-or N-terminus of the sequence did

N N S O N 3 O N 3 N 3 N 3 N 3 N 3 N 3
not affect the melting temperature of the hybrids, positioning in the middle of the sequence markedly destabilized the duplexes. [41] In the same vein, the PNA monomer 13 was inserted into a 22mer PNA at the N-terminus and the luminescent, azide-containing bis(quinoline)Re(CO)3 complex 14 was clicked to the PNA on the solid phase. Upon excitation at 347 nm, the PNA-Re(CO)3 -DNA duplex showed emission features similar to the starting rhenium complex. The labeled PNA oligomer was successfully transfected by electroporation in HeLa cells as shown by fluorescence microscopy. Furthermore, a PNA-Re(CO)3 conjugate targeting eGFP behave as an antisense agent since it significantly decreased its expression in genetically modified HeLa cells.

The second pathway consisted in coupling a terminal alkyne or an azide by acylation of the -amino group at the N-terminus of the PNA sequence followed by CuAAC with the organometallic complex carrying the partner function. For example, coupling of propynoic acid or azidoacetic acid followed by CuAAC with each of the four ferrocenyl derivatives 1, 15, 16 and 17 with PNA still on the solid support afforded the expected PNA conjugates for 1, 15 and 16 after deprotection/cleavage. [42] Mass analysis of the click product of 16 revealed that the ferrocenyl entity was missing, presumably because it did not sustain the harsh conditions required for cleavage and deprotection. This pitfall was easily remedied by carrying out CuAAC after cleavage. The four PNA-Fc conjugates displayed distinct redox profiles with E1/2 ranging from 256 to 536 mV vs. Ag/AgCl in MOPS buffer pH 7.4 making them potential electrochemical probes for DNA analysis.

Ethynylferrocene 15 was also reported to react by CuAAC with an azido-proline residue carried by a macrocyclic peptide to yield the corresponding ferrocenyl triazole that showed activity as an inhibitor of HIV-1 cell infection by suppressing gp120 receptor binding. [43] 2.1.2. Click-then-chelate strategy An alternative pathway is to conjugate a chelating ligand (Figure 3) to the peptide by CuAAC then perform the metalation reaction at the last step. This synthetic strategy is particularly well suited to prepare radiotracers for SPECT owing to the short half lives of gamma-emitting radioelements (6 h for 99m Tc). For instance, the azide-bearing dpa derivative 18 was clicked to a PNA oligomer carrying a terminal alkyne group at the N-terminus. [44] After cleavage from the solid support, metalation with 99m Tc was performed via the precursor species [ 99m Tc(CO)3(OH2)3] + using the IsoLink® kit "Carbonyl labeling Agent". Very high radiolabeling yield was obtained. Biodistribution studies in normal rats showed accumulation of the conjugate in the kidneys.

Alternatively the alkyne-bearing dpa ligands 19 and 20 were clicked under standard Sharpless conditions to the -MSH derived peptide previously used in the chelate then click approach (see above). [26] After purification of the conjugated peptides, metalation with [Re(CO)3(OH2)3](TfO) yielded species with the right molecular mass but different retention times. This was rationalized by the persistence of coordinated copper ion in the peptide conjugates after CuAAC that hindered proper coordination of rhenium to the dpa tripodal ligand. The tridentate macrocyclic ligand 21 was clicked to a cyclic pentapeptide comprising the RGD sequence and propargylglycine. Metalation with [Re(CO)3(OH2)3](Br) yielded the expected peptide conjugate as shown by HR-MS analysis. [45] The click-then-chelate approach is also well suited when the organometallic entity does not withstand the conditions used in SPPS. An O,O-chelating hydroxypyrone entity carrying an azido group 22 was coupled to [Leu 5 ]-enkephalin carrying an terminal alkyne at its N-terminus. [46] After deprotection / cleavage, metalation with [Ru(pcym)Cl2]2 yielded a Ru-peptide conjugate whose structure was confirmed by top-down mass spectrometry. The Ru-enkephalin conjugate displayed significant cytotoxic activity in vitro on the human ovarian carcinoma cell line CH1 but no activity on colon and nonsmall lung cancer cells.

Click-to-chelate strategy

The click-to-chelate strategy differs from the two former approaches in that the generated 1,2,3-triazole linker becomes involved in metal coordination as a N-donor within a tridentate ligand system. Consequently, CuAAC and metalation can be achieved simultaneously. [47] Scheme 3. Click-to-chelate approaches for the complexation of the [M(CO)3] + core (M = Re, 99m Tc)

This ingenious concept was introduced by Mindt and Schibli in 2006 for the radiolabeling of an analogue of the biologically active peptide bombesin (BBS) with the -emitting radioisotope 99m Tc. [48] BBS shows high affinity for the G-protein coupled gastrin-releasing peptide receptor (GRPR) which is overexpressed in a large number of tumors. Initially, two strategies were set up whether the azide or the alkyne partner is appended to the peptide at the -amino group at the N-terminus of the peptide sequence. Click reaction with propargyl glycine or azidoalanine affords N,N,O tripodal ligands, called "regular click ligand" or "inverse click ligand", respectively providing a coordination site for [M(CO)3] + (M = Re, 99m Tc) (scheme 3). It appeared that the "inverse click ligand" approach gave rise to lower metalation yields. Moreover, the radio-labeled peptide conjugates appeared to be unstable. In contrast, nearly quantitative metalation was achieved with the "regular click ligand" approach. Radiolabeled peptides were rapidly internalized in prostate cancer cells. Biodistribution studies in mice bearing tumor xenografts, showed that the glycated radiolabeled peptide was rapidly taken up in the colon and the pancreas in addition to the tumor and that accumulation was blocked by co-injection of unlabeled BBS. The same pathway was employed to radiolabel the peptide Lys-Cys-Cys-Tyr-Ser-Leu targeting the type 1 receptor tyrosine kinase ErbB-2 which is overexpressed in a significant proportion of breast cancers. [49] Alternatively, the "regular click ligand" was introduced within peptide sequences by reaction of propargylglycine from the -amino group of a lysine residue previously modified with azidoacetic acid. In this way, 99m Tc-labeled conjugates derived from the peptides BBS and cMBP were prepared and shown to retain very good affinity for their respective membrane receptors GRPR and c-Met.

Mindt and co-workers introduced an alternative click-to-chelate approach where the tripodal chelating ligand includes two 1,2,3-triazoles and a primary amine (scheme 4). [50] The bis-alkyne, diprotected aminoacid 23 was appended at the N-terminal position of a modified BBS fragment by SPPS. CuAAC with azidoacetic acid afforded the bis-1,2,3-triazole motif which was subsequently used to chelate Tc(CO)3 to form a SPECT radiotracer targeting cells overexpressing GRPR. Biodistribution studies on PC-3 xenografts in mice showed high specific uptake in GRPR-positive pancreas, colon and tumor with renal excretion.

Scheme 4. Bis(triazole) ligand for the click-to-chelate approach Although the organometallic entities conjugated via CuAAC to peptides / proteins sustained the reactional conditions required for the cycloaddition to take place, specially the presence of the Cu(I) catalyst, it may not be the case for other more sensitive organometallic complexes.

Strained-promoted azide-alkyne cycloadditions (SPAAC)

The requirement of cytotoxic copper catalyst limits the usage of CuAAC in biological contexts. One way to overcome this problem is to use strain-promoted azide-alkyne cycloaddition (SPAAC), developed by Bertozzi and co-workers (Table 1, entry 3). [51] SPAAC reactions rely on strained cyclooctyne derivatives that show a remarkably decreased activation energy in contrast to terminal alkynes, allowing [3+2] 1,3-dipolar cycloadditions with azides to take place at a reasonable rate in the absence of metal catalyst. Amongst the various bioorthogonal reactions, the SPAAC reaction is extensively used to study the dynamics of biological processes in vitro and in vivo. [52] Over the time an increasing number of reports has appeared in the literature on the bioconjugation of modified peptides and proteins with partner azide or cyclooctyne derivatives. However only few of them actually deal with organometallic transition metal complexes with azide or cyclooctyne-containing ligands. The number of applications of such metal complexes in biological studies is even more limited.

Lo and co-workers have reported highly emissive biscyclometalated iridium(III) [53] 24 and tricarbonyl rhenium(I) [54] 25 complexes functionalized with dibenzocyclooctyne (DBCO) unit as azide-reactive bioorthogonal handle. Reaction of the synthesized probes with BSA, HSA and apotransferrin (aTf) previously treated with azidoacetic acid, EDC and NHS was examined, and it was found that all the resulting bioconjugates inherited their emission properties from the conjugated organometallic entities (Figure 4). [53,54] Furthermore imaging of CHO cells metabolically labeled with N-azidoacetyl sialic acid and further treated with the Ir complex 24 or the Re complex 25 showed that fluorescence was mainly located in the cells plasmatic membrane. As part of a study on artificial photosynthesis system, azide-functionalized Rh-based electron mediator 26 (Figure 5) was conjugated to formate dehydrogenase via SPAAC reaction. A double SPAAC reaction was performed with the homobifunctional crosslinker DBCO-PEG4-DBCO between 26 and formate dehydrogenase carrying a pazidophenylalanine residue at a permissive site. The obtained conjugate retained the ability to regenerate NADH either chemically in the presence of formate or photocatalytically in the presence of the photosensitizer eosin Y and a sacrificial electron donor. [55] Figure 5. Azide-functionalised Rh-based electron mediator.

Application of SPAAC to the radiolabeling of HSA by the chelate-then-click approach was reported by Lee, Im and co-workers (Scheme 5). [56] In the first step, azide-functionalized 2,2′-dipicolylamine 27 was allowed to react with [ 99m Tc(CO)3(H2O)3] + to afford the [(dpa)Tc(CO)3] + complex, followed by SPAAC reaction with azadibenzocyclooctynefunctionalized HSA (ADIBO-HSA). Click conjugation efficiency was between 76 and 99% depending on the number of ADIBO moieties attached to HSA. The obtained conjugate 99m Tc-dpa-HSA showed significantly enhanced blood pool uptake compared to 99m Tc-HSA. The high stability of 99m Tc-dpa-HSA in vivo makes it a good candidate as potential blood pool imaging agent. [56] Scheme 5. Complexation of azide-functionalized 2,2′-dipicolylamine ligand by [ 99m Tc(CO)3] + (chelate-then-click labeling strategy by SPAAC).

Recently we have reported the synthesis of the Fp complex carrying an ADIBO handle 28 (Scheme 6). [33] Its reactivity was examined towards BSA and PAMAM dendrimer both carrying azide groups. Covalent coupling of 28 to azido modified macromolecules was assessed by IR spectroscopy. Although the SPAAC reaction works well, the metallocarbonyl motif was found to be unstable in the presence of the strained alkyne. [33] This finding exemplifies that the SPAAC strategy may not be compatible with all the organometallic entities, most likely owing to the intrinsic reactivity of strained alkynes towards nucleophiles. [57] Scheme 6. Synthesis of Fp complex carrying a cyclooctyne handle.

1,3-dipolar cycloadditions between alkynes and sydnone or nitrone

Lo and co-workers described a series of luminescent transition metal complexes containing different bioorthogonal reactive groups able to target labeled biomolecules for imaging and therapeutic applications. [START_REF] Yip | [END_REF] Among them, they investigated sydnone and nitrone moieties, to serve as both emission quenchers and dipole partners in metalfree cycloadditions with strained alkynes appended to proteins. Sydnones have recently been investigated as new cycloaddition partners of terminal or strained alkynes yielding substituted pyrazoles, after elimination of CO2 by retro Diels-Alder reaction, [58] while nitrones were only described in strain-promoted alkyne-nitrone cycloaddition (SPANC) reactions, affording isoxazoline derivatives (Table 1, entries 4 and 5). [59] Lo and co-workers took advantage of emission quenching effects of sydnone and nitrone motifs for the design of new cyclometalated iridium (III) complexes with phosphorogenic properties to probe 1,3-cycloaddition reactions with strained alkyne derivatives. [60,61] As expected, appended sydnone or nitrone units induced a decrease of emission intensity compared to sydnone-free or nitrone-free complexes depending on the substituents on the (N^C -) ligand. Cycloaddition reactions of sydnone and nitrone complexes 29 and 30 were first validated with the model strained alkyne (1R,8S,9S)bicyclo[6.1.0]non-4-yn-9-yl)methanol (BCN-OH). Upon conversion to pyrazole or isoxazoline, complexes recovered their luminescent properties, with higher emission enhancements observed with nitrone complexes (I/I0= 60.5 for 30b compared to 7.9 for 29b, and 135.0 for 30c compared to 2.5 for 29c). These complexes were then reacted with model BCN-modified proteins (bovine serum albumin (BSA), human serum albumin (HSA) and holo-transferrin (HTf)) in order to explore their bioorthogonal labeling abilities and photophysical properties (Scheme 7). Again, luminescent properties were turned-on when reacted with BCN-modified proteins, while emission intensities remained low when incubated with unmodified protein, showing the orthogonality of the dipole partners. Again more pronounced enhancement effects were observed with nitrone than sydnone complexes (I/I0= 292.8 for 30b compared to 24.9 29b, and 618.0 for 30c compared to 5.2 for 29c, with BCN-BSA). Furthermore, emission enhancements are higher with BCN-modified proteins than with BCN-OH, which is attributed to increased hydrophobicity and rigidity brought by the protein in the proximal environment of cyclometalated iridium (III) polypyridine complexes, [61][62][63] and this behavior is an additional asset when developing bioorthogonal imaging agents.

Scheme 7. Structures of phosphorogenic sydnone-based and nitrone-based cyclometalated iridium(III) polypyridine complexes and strained-promoted sydnone/nitrone-alkyne cycloaddition reactions with proteins (BSA, HSA, HTf) modified with orthogonal BCN handle to afford luminescent conjugates for imaging applications. [60,61]

Photoclick 1,3-dipolar cycloaddition

Gasser and co-workers tried a metal-free 1,3-dipolar cycloaddition between a nitrile imine generated by mild photoactivation of a tetrazole, and an alkene (scheme 8), [64] coined photoclick, to append two organometallic probes, namely IR-active cymantrene and redox-active ferrocene to molecules with biological activities, to extend their properties. [65] Scheme 8. Principle of photoclick 1,3-dipolar cycloaddition.

They investigated the labelling of a tetrapeptide derivative known as nuclear localization signal (NLS), able to target cell nucleus [66] and a PNA sequence, described as antisense agent inhibiting hepatitis B virus reverse transcription. [67] They introduced the tetrazole moiety into the peptide or the PNA sequence by SPPS using acid 31 to yield orthogonal partners NLS-tetrazole and PNA-tetrazole (figure 6). [65] These compounds were then reacted with maleimide-modified cymantrene 32 and/or ferrocene 33 upon 302 nm light irradiation at room temperature. It appeared that cymantrene was not the optimal organometallic candidate since the main product of the photoclick cycloaddition with NLS-tetrazole was the byproduct 34 arising from hydrolysis of the cycloadduct and concomitant decomposition of Mn(CO)3 moiety, known to be unstable upon light irradiation. With ferrocene derivative, expected NLS-pyrazoline-ferrocene conjugate 35 was obtained in 20 % yield after optimization, while the photoclick performed with PNA-tetrazole afforded a mixture of four compounds including the expected photoclick product 36 in 6.5 % yield, the doubly Fc labeled product 37 resulting from photoclick and Michael addition of the cysteine onto the maleimide double bond in 8% yield, the mono hydrolysed product 38 in 14 % yield, and the unlabeled hydrolysed product 39 as the main compound (30 % yield). The yield of the photoclick compound 36 was not greater than 10% after optimization. Eventually, this photoclick reaction seems unsuitable for the labelling of organometallic moieties, whatever their light sensitivity. Structures of isolated compounds after their reaction with NLStetrazole and/or PNA-tetrazole. Adapted from ref. [65] . Copyright 2016 with permission from The Royal Society of Chemistry.

N N N N R 1 R 2 N R 1 N R 2 + - 302 nm N N R 1 R 2 1,3-cycloaddition R 4 R 3 R 5 R 6 R 3 R 5 R 4 R 6

Inverse electron-demand Diels-Alder (iEDDA) cycloaddition

One of the most promising bioorthogonal conjugation methods is the inverse electrondemand Diels-Alder (iEDDA) reaction between 1,2,4,5-tetrazines and alkenes or alkynes (Table 1, entry 6). The "tetrazine ligation" attracted much attention because of fast reaction kinetics, high selectivity and high compatibility with water. [68] Mechanistically, the iEDDA reaction proceeds via [4+2] cycloaddition between electron-rich or strained alkenes and tetrazines, followed by a retro-Diels-Alder reaction to release N2 and prototropic rearrangement to afford 1,4-dihydropyridazines as a mixture of isomers (Scheme 9). Alternatively, iEDDA reactions between tetrazines and strained alkynes afford pyridazine products (Scheme 9). Besides this, tetrazine derivatives exhibit emission quenching properties due to Föster resonance energy transfer (FRET) mechanism that no longer occurs after formation of non-quenching dihydropyridazines. [69] All these features make iEDDA useful for biological labeling and imaging of live cells. [70] Although there are many studies on iEDDA reaction, those dealing with transition metal complexes remain limited. Lo and co-workers reported that a series of mononuclear and dinuclear rhenium(I) tricarbonyl complexes incorporating a tetrazine moiety formed a new class of phosphorogenic probes reacting with dienophile-labeled biomolecules. [71] The complexes were firstly tested in reaction with model alkene and alkyne derivatives to give the expected dihydropyridazine and pyridazine products with enhanced phosphorescence emission. BCN-modified proteins were also successfully labeled with the binuclear rhenium complex 40 (Figure 7) and the resulting conjugates displayed strong phosphorescence upon excitation. In another study, BCN-modified BSA was bioorthogonally labeled with phosphorogenic tetrazine labels derived from cyclometalated iridium(III) complexes 41. [62] The emission of these complexes was efficiently quenched by FRET and /or PET process and turned on while the reaction of BCN-BSA occurred with extremely large emission enhancement factors. Complex 41 was applied to image azide-modified N-glycans in live cells.

Labeling was achieved by a two-step procedure: a bis-BCN homobifunctional cross linker was reacted with azido-modified N-glycans, followed by reaction with complex 41. [62] An even smarter example reported by the same group concerns the labeling of biomolecules by iridium(III) pyridyl-tetrazine complexes 42. In this study, the tetrazine unit serves as the chemical reporter group which easily reacts with alkene or alkyne but also as the luminophore because of the strong emission upon the iEDDA reaction. Lo and coworkers designed three complexes 42e-g with luminogenic bioorthogonal labeling properties where the pyridyl-tetrazine unit is coordinated to the metal center (Figure 7). The incorporation of the electron-deficient tetrazine ligand to the iridium complex provides very weakly emissive compounds. The bioorthogonal reaction of these compounds with cyclooctyne derivatives caused very strong emission as a result of the conversion of coordinated tetrazine unit into a pyridazine derivative. Reaction with BSA carrying BCN entities gave rise to even stronger emission than observed for the reaction with BCN-OH itself. The depicted strategy was further applied to label a GST-HaloTag fusion protein alone and expressed in HeLa cells (Scheme 10). [63] Scheme 10. Bioorthogonal reaction of BCN modified GST-HaloTag with pyridyl-tetrazine iridium complex 42g.

All the examples reported so far involved complexes carrying the tetrazine handle while the protein carried the strained alkyne partner. The challenge is now to develop reverse reactions.

Polar reactions

Sonogashira cross-coupling

Palladium-mediated Sonogashira cross-coupling [72] between terminal alkyne and aromatic halide (Table 1, entry 7) was reported to install organometallic moieties onto biologically relevant peptides, either by incorporating the unnatural amino acid 4-iodophenylalanine in place of phenylalanine, or 4-iodobenzoic acid at the N-terminus. These modified peptide sequences were obtained by SPPS followed by cleavage from the solid support before performing the Sonogashira cross-coupling.

After their pioneering work demonstrating the Pd-catalyzed coupling of C-terminus alkynyl amino acids and a tripeptide with ferrocenyl iodoarene [73] or, conversely, alkynyl ferrocene derivative and iodobenzene amino acids, [74] Metzler-Nolte and coworkers described the conjugation of the alkynyl ferrocene derivative 16 to p-iodophenylalanine [Leu 5 ]-enkephalin and p-iodobenzoyl N-terminated [Leu 5 ]enkephalin (scheme 11). [75] Pd-catalyzed coupling proceeded in DMF/ NEt3 (1:1) due to solubility problems and organometallic peptides 43 and 44 were obtained in 47.6 and 22.5 % yield respectively, after purification by preparative HPLC. The electroactive properties of the ferrocene label, evaluated by cyclic voltammetry and square wave voltammetry, can serve to detect such biomolecules using techniques such as HPLC with electrochemical detection (HPLC-ECD). [75,76] Scheme 11. Synthesis of ferrocene-[Leu 5 ]-enkephalin conjugates via Sonogashira crosscoupling. Adapted from ref. [75] . Copyright 2006 with permission from American Chemical Society. [75] Another example of Sonogashira cross-coupling was reported in the field of CORMs. Schatzschneider and co-workers reported the synthesis of conjugates of Thr-Phe-Ser-Asp bearing a photoactivatable CORM based on tricarbonyl manganese(I) complex coordinated to the tpm ligand. [20] The modified peptide sequences were obtained by SPPS by incorporating the same iodoarene derivatives (4-iodo-phenylalanine within the peptide sequence or 4-iodobenzoic acid at the N-terminus), again in DMF/ NEt3 (1:1). After cleavage from the solid support, these peptides were orthogonally conjugated to the propargyl ether of the tpm-manganese tricarbonyl moiety 2 via Sonogashira crosscoupling (scheme 12). Peptide with N-terminal iodoarene gave conjugate 45 in moderate yield (48%) but in high purity (98%), whereas peptide with 4-iodophenylalanine side chain led to conjugate 46 in better yield (62%) but slightly lower purity (91%).

H N R 1 O N H O H N O N H O H N O CO 2 H OH R 2 R 1 = CH 3 , R 2 = I R 1 = p-I-C 6 H 4 CO, R 2 = H Fe O HN H N H 3 C O N H O H N O N H O H N O CO 2 H OH H N O N H O H N O N H O H N O CO 2 H OH N H O Fe N H O Fe 44
Scheme 12. Synthesis of [Mn(CO)3(tpm)] + -peptide conjugates via Sonogashira crosscoupling. Adapted from ref. [20] . Copyright 2009 with permission from The Royal Society of Chemistry.

Conversely to the previous examples when the Sonogashira coupling reaction was performed after cleavage from the solid support, the next one exploited the reaction onsupport in the field of oligodeoxynucleotides (ODNs) labeling. Grinstaff and co-workers described the first on-column site-selective derivatization of halo-substituted nucleobases with alkyne-terminated ferrocene derivative (ferrocenoyl propargylamide 47) in combination with standard automated DNA synthesis. [77,78] Ferrocene was chosen for its redox and spectroscopic properties that could be used to develop DNA diagnostic technologies and to study DNA-mediated charge transfer. Halonucleoside phosphoramidite precursors, 2'-deoxy-5-iodouridine or 2'-deoxy-8-bromoadenosine, were incorporated at the desired position on the ODN through standard automated DNA synthesis. The procedure implies to remove the column from the synthesizer and to dry by flushing with argon or nitrogen before filling with DMF/ NEt3 (9:1) to perform the Sonogashira cross-coupling in sealed column for 6 h. The column was then rinsed with DMF-NEt3 and CH3CN, dried and replaced on the synthesizer to continue the oligonucleotide synthesis (Scheme 13). This method afforded labelled ODNs with up to 50 % yield after HPLC purification. [77] Ferrocene-uridine phosphoramidite 48 was also prepared off-column and incorporated in oligodeoxynucleotides by standard automated DNA synthesis to compare the two methods. The on-column procedure was found to be more suitable for the synthesis of ferrocene-labeled ODNs which were obtained with higher yields. [78] In term of stability of labeled duplexes, thermal denaturation experiments showed that modification of uridine with ferrocene has little influence on the duplex stability contrary to the modification of adenosine that induces disruption of duplex structure to some extent.

R 1 N H H N N H H N N H CO 2 H O O O O OH R 2 CO 2 H OH N H H N N H H N N H CO 2 H O O O O OH CO 2 H OH H 2 N H N N H H N N H CO 2 H O O O O OH
R 1 = p-I-C 6 H 4 CO, R 2 = H or R 1 = H, R 2 = I
Scheme 13. On-column Sonogashira cross-coupling for the labelling of ODNs with ferrocenoyl propargylamide 47 in combination with standard automated ODN synthesis. Insert: ferrocene-uridine phosphoramidite 48 used for standard ODN synthesis to compare the procedures. [77,78] Although these three examples exploit reactive functions that are not naturally occurring in biological molecules, they all perform in DMF/NEt3 for solubility reasons, conditions that are not exactly bioorthogonal since they do not operate in physiological media. Truly bioorthogonal Sonogashira cross-coupling reactions were reported in 2007 in the field of protein labeling in aqueous medium with copper salt and additives, but in low yield, [79] and improved yields were later reported with the development of new water-soluble palladium complexes allowing copper-free carbon-carbon bond formation inside bacterial cells. [80] But none of these examples involve the conjugation of organometallic complexes.

Carbonyl ligation techniques

Older ligation techniques exploiting the orthogonal carbonyl group as chemical reporter are still widely used to react with functional groups that are not naturally occurring in biomolecules such as oxyamines and hydrazides to form oximes and hydrazones respectively (Table 1, entries 8 and 9). [START_REF] Hermanson | Bioconjugate Techniques[END_REF] Carbonyl reporter groups can be appended to biomolecules by different techniques, such as mild oxidation of glycoproteins, Nterminal serine or threonine, site specific incorporation of unnatural amino acids by the biosynthetic pathway [START_REF] Zhang | [END_REF] or genetic encoding of specific nucleotides sequence expressing formylglycine-containing proteins, [83] to name a few.

Hydrazone ligation

We are involved in the site-specific labeling of antibodies (immunoglobulins G or IgG) with multiple copies of transition metal carbonyl complexes for use as new universal detection reagents in a modified solid-phase format of the carbonyl metallo immunoassay (CMIA) we introduced in the early 1990s. [START_REF] Salmain | Bioorganometallics, biomolecules[END_REF] CMIA takes advantage of the specific and intense vibration bands owing to CO ligands (CO) in the mid-infrared (IR) spectral range allowing their quantification by measuring the height of the CO bands. As the height is proportional to the quantity of metal carbonyl complex (IR probe), the more metal carbonyl moieties are attached to the antibody, the higher the resulting IR signal is. Consequently, tiny quantities of antibody could be detected if labeled with numerous copies of IR probes. In this objective, (polyamido)amine (PAMAM) dendrimers [85] seemed ideal carriers to covalently couple multiple IR probes to antibodies. [86] Indeed these synthetic biopolymers are available in a variety of sizes (termed generations) and terminal reactive groups (amines, alcohols, carboxylic acids) for further chemical modifications and are soluble in aqueous medium. These features have made them popular for biomedical applications. [87] We worked with generation 4 (G4), which has 64 theoretical amine end groups. PAMAM-G4 was functionalized with 22 to 29 Fp units and 4 to 5 hydrazide groups by reaction of complex 49 and heterobifunctional linker carrying an nitroaniline NMR probe 50, respectively (Scheme 14). [88] IgGs are glycoproteins with carbohydrate moieties located in the Fc region, far from the antigen binding sites. Consequently these carbohydrates are ideal targets for site-selective and orthogonal conjugation to hydrazide-functionalized compounds after mild oxidation to generate carbonyl reactive groups. Using this strategy, we were able to orthogonally conjugate 1.0 to 1.5 dendrimer carrying Fp units per antibody, depending on the dendrimer sample (Scheme 15), corresponding to the loading of 30 Fp probes on average per antibody. Hydrazone linkages were stabilized by reduction with NaBH3CN before further evaluation as detection reagent in solid-phase CMIA. As a proof of concept, Fp-labeled goat anti-rabbit IgG antibody was evaluated to quantify known quantities of rabbit IgG spotted onto nitrocellulose membranes in the range 1.3-266.7 pmol by IR spectroscopy (Figure 8). Scheme 14. Synthetic route to hydrazide-based metal carbonyl PAMAM-G4 dendrimers. Adapted from ref. [88] . Copyright 2010 with permission from Elsevier.

Scheme 15. Synthetic route to IgG-dendrimer conjugate by orthogonal ligation. Adapted from ref. [88] . Copyright 2010 with permission from Elsevier.

Figure 8. Schematic antigen-antibody interaction between rabbit IgG (antigen) and goat anti-rabbit IgG carrying IR probes (antibody) at the membrane surface and quantification of rabbit IgG spotted onto nitrocellulose membranes (in the range 1.3-266.7 pmol) incubated with an excess of Fp-labeled goat anti-rabbit IgG (0.3 nmol per assay). IR measurements were done in the transmission mode on dried membranes. Reproduced from ref. [88] . Copyright 2010 with permission from Elsevier.

Oxime ligation

Schatzschneider and co-workers described the synthesis of a peptide-photoCORM conjugate by oxime ligation. [89] The TGF- peptide sequence was used as the carrier part of the conjugate to deliver photoactivated carbon monoxide from the photoCORM tricarbonylmanganese(I) complex coordinated to the 2,2-bis(pyrazolyl)ethylamine (bpea) ligand. Here, the aldehyde group was appended to the complex by reductive amination between 4-(diethoxymethyl)benzaldehyde and bpea by followed by hydrolysis of the acetal protective group, and reaction with Mn(CO)5Br to afford the aldehyde-functionalized photoCORM 51. The peptide sequence was obtained by SPPS, then N-terminal functionalization to attach the orthogonal aminoxy handle was carried out with (aminoxy)acetic acid. After cleavage from the solid support, the aminoxypeptide 52 was conjugated to the aldehyde-functionalized photoCORM 51 under mild and catalyst-free conditions to afford peptide-photoCORM conjugate 53 (Scheme 16) in moderate yield (58%) but in high purity (98%). This conjugate proved to be stable in pure water for 4 days in the dark. The myoglobin assay indicated that ca. 2 equiv. of CO were released per conjugate 53 upon irradiation at 365 nm.

Scheme 16. Synthesis of [Mn(CO)3(bpea)] + -peptide conjugate 53 via oxime ligation. Adapted from ref. [89] . Copyright 2014 with permission from Wiley-VCH.

The selectivity of the carbonyl ligation reactions is controlled by the pH of the reaction medium which should be slightly acidic to prevent side reactions with the amines of proteins. Consequently, this requirement precludes to apply these bioconjugation reactions inside cells. [57]

Conclusions and perspectives

To summarize, a large variety of bioorthogonal ligation methods has now been implemented to introduce transition organometallic complexes onto biologically active peptides, proteins, and peptide-like oligomers, taking benefit from the high chemoselectivity of this family of chemical reactions. Let us note however that most of the examples reported in the literature so far have been dealing with reactions in organic solvents on pure molecules and that bioorthogonal reactions involving organometallic complexes in biological settings are still rare. Moreover, bioconjugation of organometallic complexes has essentially been done to take advantage of their optical, electrochemical or radio-emitting properties, much less often for their therapeutic properties and never for their catalytic properties. Consequently, this still provides numerous opportunities for bioorganometallics to take a larger space in the ever growing area of chemical biology.

Supporting information: sequences of peptides used in bioorthogonal ligations with organometallic complexes; structures of ligands for CuAAC

Acknowledgement

The work was financially supported by Sorbonne Université and CNRS, France and the University of Lodz, Faculty of Chemistry, Poland.

Figure 2 .

 2 Figure 2. PNA monomer 13 for labeling by CuAAC

Figure 3 .

 3 Figure 3. Clickable chelating ligands for the click-then-chelate strategy

Figure 4 .

 4 Figure 4. Biscyclometallated iridium(III) and tricarbonyl rhenium(I) complexes carrying a dibenzocyclooctyne (DBCO) handle.

Figure 6 .

 6 Figure 6. Structure of tetrazole derivative 31 used to prepare NLS-tetrazole and PNAtetrazole. Structures of maleimide-modified cymantrene 32 and ferrocene 33 as orthogonal partners. Structures of isolated compounds after their reaction with NLStetrazole and/or PNA-tetrazole. Adapted from ref.[65] . Copyright 2016 with permission from The Royal Society of Chemistry.

Scheme 9 .

 9 Scheme 9. iEDDA reaction between tetrazine and alkene or alkyne

Figure 7 .

 7 Figure 7. Structure of transition organometallic complexes for iEDDA.

16 PdCl 2 (

 162 PPh 3 ) 2 , CuI, DMF, Et 3 N 43

2 PdCl 2 (

 22 PPh 3 ) 2 , CuI, DMF, Et 3 N 45 46

Table 1 .

 1 Bioorthogonal reactions used to conjugate transition organometallic complexes

	entry 1,3-dipolar cycloadditions
	1	OM	, Cu(I)
		CuAAC
	2
			, Cu(I)
		CuAAC
	3
		OM
		SPAAC
	4
		SPANC
	5
	Diels-Alder reactions
	6
		iEDDA
	Polar reactions
	7
		OM
			, Pd(II), Cu(I)
		Sonogashira cross-
		coupling
	8
	9

Graphical Abstract

The recent developments in bioorthogonal ligations of transition organometallic complexes to peptides and proteins and their application in fluorescence or radioisotopic imaging and targeted delivery of pharmaceutical agents are reviewed


Éloïse Grossiord

Nicolas Passat

Hugues Talbot

Benoît Naegel

Salim Kanoun

Ilan Tal

Pierre Tervé

Soléakhéna Ken

Olivier Casasnovas

Michel Meignan

Laurent Najman

Shaping for PET image analysis

Component-trees constitute an efficient data structure for hierarchical image modeling. In particular they are relevant for processing and analyzing images where the structures of interest correspond either to local maxima or local minima of intensity. This is indeed the case of functional data in medical imaging. This motivates the use of component-treebased approaches for analyzing Positron Emission Tomography (PET) images in the context of oncology. In this article, we present a simple, yet efficient, methodological framework for PET image analysis based on componenttrees. More precisely, we show that the second-order paradigm of shaping, that broadly consists of computing the component-tree of a component-tree, provides a relevant way of generalizing the threshold-based strategies classically used by medical practitioners for handling PET images. In addition, it also allows to embed relevant priors regarding the sought cancer lesions.

Introduction

The component-tree, introduced by [START_REF] Salembier | Anti-extensive connected operators for image and sequence processing[END_REF] twenty years ago, constitutes one of the most popular hierarchical data structures for image modeling, processing and analysis. Defined and developed in the context of connected operators [START_REF] Salembier | Connected operators. A review of region-based morphological image processing techniques[END_REF]) -a subdomain of mathematical morphology-the component-tree allows one to model, in a lossless way, any grey-level image, based on the representation of the inclusion hierarchy of connected components obtained at the successive level sets of the image.

Its successful involvement in various application fields mainly relies on its computational efficiency. Indeed, on the one hand, the component-tree can be constructed in (quasi-)linear time. Various sequential and distributed algorithms were developed for that purpose; a recent survey was proposed by [START_REF] Carlinet | A comparative review of component tree computation algorithms[END_REF]. On the other hand, the component-tree can be processed efficiently either by local attribute-based strategies (i.e. node selection, democratized by [START_REF] Jones | Connected filtering and segmentation using component trees[END_REF]) or by global optimization strategies (i.e. tree-cut computation, formalized by [START_REF] Guigues | Scale-sets image analysis[END_REF]), leading once again to linear time costs.

On the one hand, the component-tree is designed for handling grey-level images, i.e. images where values are organized with respect to a total ordering. In particular, it is based either on the ≤ or the ≥ order on Z or R, leading to the so-called max-trees or min-trees, that emphasize regions of interest of locally maximal or locally minimal values, respectively.

On the other hand, except for the ≤ or ≥ total ordering and the chosen topological structure of the image support, the component-tree is a parameter-free data structure. This implies that the construction of the componenttree from an image deterministically leads to a unique result. This property, together with the fact that the component-tree is a lossless model (i.e. it allows for reversible, non-altering transformations from image to tree and from tree to image), opened the way to the involvement of component-trees in the design of grey-level image processing and analysis methods and tools, in particular in the context of antiextensive filtering and segmentation [START_REF] Salembier | Anti-extensive connected operators for image and sequence processing[END_REF][START_REF] Jones | Connected filtering and segmentation using component trees[END_REF].

Among many other application areas, the componenttree has been involved in the field of nuclear imaging, and more specifically Positron Emission Tomography (PET). Indeed, based on its specific properties, it constitutes a relevant data structure for modeling and processing functional medical images, where the strength of the signal is correlated to the intensity of the observed physiological phenomenon. In this context, the first domain where component-trees were involved was angiographic imaging, that emphasizes the flowing blood in vascular networks. Various filtering, vessel enhancement and segmentation methods were designed based on component-trees, as proposed e.g. by [START_REF] Wilkinson | Shape preserving filament enhancement filtering[END_REF]; [START_REF] Caldairou | Attributefiltering and knowledge extraction for vessel segmentation[END_REF]; [START_REF] Dufour | Filtering and segmentation of 3D angiographic data: Advances based on mathematical morphology[END_REF].

Relying on the fact that high metabolic activity regions appear as hyperintense areas in PET images, methods were designed to take advantage of the mixed spatialspectral organization of PET information in componenttrees to develop classification strategies [START_REF] Alvarez Padilla | Multicriteria 3D PET image segmentation[END_REF][START_REF] Grossiord | Automated 3D lymphoma lesion segmentation from PET/CT characteristics[END_REF] or filtering / segmentation methods [START_REF] Urien | Brain lesion detection in 3D PET images using max-trees and a new spatial context criterion[END_REF]Alvarez Padilla and et al., 2018a,b). Indeed, PET visualizes metabolic activity characterized by the intensity of an injected radiotracer. It is routinely used in cancer imaging for diagnosis and characterization of malignant tissues, corresponding to hyperfixations of a tracer (expressing e.g. the consumption of glucose by cancerous cells). The idea is then to highlight tumours, i.e. maximal intensities in the PET images.

In this article -which is an extended and improved version of the conference paper by Grossiord and et al. (2015a)-we present a simple, yet efficient, method for carrying out PET image analysis via a component-treebased strategy. The novelty of this approach relies on the use of the concept of shaping, recently introduced by [START_REF] Xu | Connected filtering on tree-based shape-spaces[END_REF]. Broadly speaking, shaping consists of computing two layers of component-trees. A first component-tree aims at modeling the grey-level image, based on intensity information. A second componenttree, built upon the first one, aims at organizing the nodes of the first tree based on second-order information. Carrying out basic operations, e.g. threshold-based tree-cut, in this second tree then allows the user to easily take into account both low-level information on the image signal and higher-level information on the structures of interest. We present this paradigm in the context of PET imaging, with the purpose of proposing a threshold-based methodology for detection of cancer lesions, guided by intensity and compacity priors.

The sequel of this article is organized as follows. In Section 2, we provide a minimal set of basic notions required to make the article self-contained. In Section 3 we recall the concepts of component-tree and shaping, and we emphasize the way of unifying shaping and standard component-tree construction from an image, via the usual graph formalism. In Section 4, we describe the methodological aspects of attribute-based filtering of componenttrees with shaping. In Section 5, we instantiate our framework for tackling the issue of PET image analysis, and more precisely tumoural lesion detection based on intensity and compacity attributes. In Section 6, we describe technical details, including software production and experimental works. Section 7 briefly concludes the article by emphasizing perspective works.

Basic notions

Let Ω be a nonempty finite set. Let be an adjacency (irreflexive, symmetric) relation on Ω. The set (Ω, ) is a (non-directed) graph. Let X ⊆ Ω be a subset of Ω. The reflexive-transitive closure of (the restriction of) on X induces the connectedness relation on X. It is an equivalence relation, and the set of the equivalence classes of X, called connected components, is noted C[X]. In the sequel, we will assume that (Ω, ) is connected, i.e.

C[Ω] = {Ω}.
Let V be a nonempty finite set equipped with a total order relation ≤.

A valuation V (of Ω) is a mapping V : Ω → V. For any x ∈ Ω, V(x) ∈ V is the value of x. The triple G = (Ω, , V) is called a (vertex-)valued graph.
Let X ⊆ Ω and v ∈ V. The thresholding function λ v is defined by

λ v : V Ω → 2 Ω V → {x ∈ Ω | V(x) ≥ v} (1)
In other words, it associates to any valuation V of Ω the subset of the elements of Ω with a value greater than a given threshold parameter v.

The cylinder function C (X,v) is defined by

C (X,v) : Ω → V x → v if x ∈ X ⊥ otherwise (2)
where ⊥ is the minimal value (on V) for the elements of Ω. A valuation V : Ω → V can be decomposed into cylinder functions induced by thresholding operations and, symmetrically, V can be reconstructed by composition of these cylinder functions

V = v∈V X∈C[λ v (V)] C (X,v) ( 3
)
where ∨ is the point-wise supremum on functions of V Ω . In other words, the mapping V is obtained by combining, for each value v of the space V and each connected component X of each binary level-set, the contribution of the cylinder function C (X,v) defined for the connected component X at value v. All these contributions are combined via a supremum paradigm, i.e. by considering the highest values obtained pointwise.

Component-trees and shaping

Component-tree

The component-tree T = (Ψ, ) of a valued graph (Ω, , V) is the Hasse diagram (i.e. the reflexive-transitive reduction) of the partially ordered set (Ψ, ⊆), where Ψ is the set of all the connected components obtained from all the successive level sets of (Ω, , V), namely

Ψ = v∈V C[λ v (V)] (4)
Each connected component / element of Ψ is called a node of the component-tree. The root of the componenttree, namely Ω is the unique connected component of λ ⊥ (V); it is the maximum of (Ψ, ⊆). The leaves of the component-tree are all the nodes which are minimal elements of (Ψ, ⊆).

For two nodes N 1 , N 2 ∈ Ψ, we have N 1 N 2 iff N 1 ⊆ N 2 , and there is no

N 3 ∈ Ψ such that N 1 ⊂ N 3 ⊂ N 2 .
In such case, we say that N 1 is a child node of N 2 and that N 2 is the parent node of N 1 (such parent node is unique, by definition). The root is the only node without parent node. The leaves are the only nodes without children nodes.

Component-tree of a grey-level image

A grey-level image I is composed of a finite set of points, e.g. pixels in 2D, voxels in 3D. We note Γ this set of points.

The points of Γ are generally organized with respect to a neighbourhood relation, for instance the 2n-or (3 n -1)adjacencies classically defined in digital topology. Such relation is indeed an adjacency relation, and is noted Γ . Two points x, y ∈ Γ are neighbours if we have x Γ y.

For each point x ∈ Γ, the image provides a specific grey-level value within a finite set K = [[⊥, ]] with the maximal value for the elements of Γ (without loss of generality, we can assume K ⊂ Z). For each point x ∈ Γ, we note I(x) this value; in other words we have I : Γ → K.

Based on these facts, the image can be modeled as a triple I = (Γ, Γ , I), i.e. as a valued graph (see Section 2). As a consequence, we can relevantly build the component-tree T I of this image.

Basically, building a component-tree, namely either a max-tree or a min-tree, depending on the order ≤ or ≥ chosen on the grey-level values, consists of (1) building the binary connected components of the image and (2) organizing these connected components from the greatest (i.e. the root) to the lowest (i.e. the leaves) according to the standard inclusion relation ⊆. In the case of a max-tree (resp. min-tree), the root corresponds to the (a) whole support Γ, obtained by a thresholding at the lowest (resp. greatest) value, whereas the leaves are antagonistically obtained at the local maxima (resp. local minima) of the image. Building these connected components and ordering them in a hierarchical way can be considered via various paradigms, for instance by flooding or Tarjan union-find. A discussion on such construction is out of the scope of this article, and the reader is refered to [START_REF] Carlinet | A comparative review of component tree computation algorithms[END_REF] for a comprehensive survey.

I A B C D,E K L M N F,G H,I,J O,P (b) T I A (c) λ 0 (I) D H B D (d) λ 1 (I) D I C F E (e) λ 2 (I) J C G K O (f) λ 3 (I) N C L M P (g) λ 4 (I)
An example of component-tree for a grey-level image is given in Figure 1.

Shaping: component-tree of a component-tree

A component-tree T = (Ψ, ) is a data structure where the nodes / connected components of Ψ are hierarchically organized by with respect to the value of their level sets, from the lowest value (at the root of the componenttree) to the highest values (at the leaves of the componenttree). In other words, the component-tree expresses a value space in a spatial fashion.

A usual way to take advantage of a component-tree consists of endowing each node N ∈ Ψ by an attribute A(N), generally defined as a scalar valuation. For instance, a very classical attribute is the size of the nodes, i.e. their number of points A(N) = |N|. Once such attribute, namely a mapping A : Ψ → V (with V being any set isomorphic to a part of Z) has been defined, it is possible to perform node selection, i.e. to carry out filteringbased operations.

Endowing a component-tree T = (Ψ, ) with a valuation A : Ψ → V is equivalent to defining a valued graph T = (Ψ, , A). (In such a case, the non-symmetric relation is considered, without loss of generality, as a symmetric one.) From such valued graph, it is in then possible to build its own component-tree; this constitutes the very paradigm of shaping.

Less formally, carrying out shaping consists of building the component-tree of a component-tree. In general, the first component-tree is built from a grey-level image (i.e. with a spectral valuation) whereas the second is built by considering an attribute on the nodes of the first (i.e. with a semantic valuation). The second component-tree then gathers, in a same data-structure, various kind of spatial (nodes), spectral (first valuation) and semantic (second valuation) information.

In particular, it is then possible to develop filtering procedures on such component-trees.

Attribute-based filtering with shaping -Methodology

4.1. The antiextensive filtering scheme Let I = (Γ, Γ , I) be a grey-level image. As evoked in Section 2, this image I can be expressed as the supremum of the nodes of its associated component-tree T I . More precisely, Equation (3) can be rewritten as

I = K∈Ψ C (K,v K ) ( 5
)
where )]} is the maximal value that defines K as a connected component of the corresponding level set of the image. In particular, Equation ( 5) can be seen as a simplified version of Equation (3), where only the connected components K which are sufficiently large and with a sufficiently high value for contributing to the definition of the image I are considered (the other ones are indeed "hidden" below these large / intense components, and then useless for defining the image). Equation ( 5) leads to a well-defined image from Ψ, but also from any subset of Ψ nodes. For image processing purposes, it is possible to filter the image I by discarding some of the nodes, and then reconstructing a resulting image from the subset of preserved nodes. Each point x ∈ Γ in the filtered image then presents a value that is lower or equal to the initial image; the induced operators are antiextensive.

v K = max{v ∈ V | K ∈ C[λ(I
This antiextensive filtering paradigm was formalized by [START_REF] Salembier | Anti-extensive connected operators for image and sequence processing[END_REF]; [START_REF] Jones | Connected filtering and segmentation using component trees[END_REF]. It is basically composed of three successive steps, also illustrated in Diagram ( 6) :

(i) construction of the component-tree T associated to I; (ii) reduction of Ψ, leading to a reduced component-tree T ; and (iii) reconstruction of a filtered image I induced by T .

I (i) ------→ T           (ii) I ≤ I (iii) ← ------T (6)

Attribute-based node selection

By assuming that each node N ∈ Ψ is equipped with a relevant attribute value A(N) ∈ K, the choice to preserve or discard N depends on a Boolean predicate ρ : K → {true, false} acting on the attribute values.

When these attribute values are monotonic along the tree (i.e., ρ(N) is true for a given node N implies the same for all the nodes between N and the root), they can be handled similarly to the grey-level of the nodes, in the sense where the node selection proceeds as a simple thresholding.

However, most attributes are not monotonic, in general. For instance, this is the case for shape attributes such as elongation or compacity, or for texture descriptors. This means that the decision for a given node does not imply its validity for the remainder of the branch. This is not an issue in the context of automated processing, where the tree is fully scanned, and ad hoc pruning policies can be applied a posteriori to homogeneize the results of the different branches of the tree; see [START_REF] Salembier | Anti-extensive connected operators for image and sequence processing[END_REF]; [START_REF] Jones | Connected filtering and segmentation using component trees[END_REF]) for a discussion on this topic.

However, our purpose is to carry out threshold-based interactive segmentation from non-monotonic attributes.

To tackle this issue, we can then take advantage of the shaping paradigm.

Indeed, let us suppose that we build a second component-tree T = (Ψ , ) from the first component-tree T = (Ψ, ), i.e. from the valued graph T = (Ψ, , A). By construction, in this new tree, each node N ∈ Ψ corresponds to a set of T nodes (connected with respect to ). In addition, for any two nodes N 1 , N 2 such that N 1 N 2 , we have the following properties

N ∈ N 1 ⇒ N ∈ N 2 (7) and min{A(N) | N ∈ N 1 } ≥ min{A(N) | N ∈ N 2 } (8)
In other words, the attribute A is monotonic within T , even if it is not within T .

The shaping antiextensive filtering scheme

It is then possible to process any grey-level image in the framework initially proposed by [START_REF] Salembier | Anti-extensive connected operators for image and sequence processing[END_REF]; [START_REF] Jones | Connected filtering and segmentation using component trees[END_REF], simply by performing node selection in the second component-tree T , built from the first one T . In particular, since the attribute computed from the nodes of T is now monotonic in T , we can operate thresholding / pruning approaches. The overall procedure, illustrated on Diagram (9), is quasi-linear in time and space, since we only duplicate the standard componenttree anti-extensive filtering process (Diagram ( 6)) to nonmonotonic attributes. More precisely, the cost of the construction of a component-tree is quasi-linear in time, S log S κ.S , where S is the size of the physical support of the image and κ a quasi-constant value. Then, the cost of (i) is approximately |Γ| whereas the cost of ( i trees. Overall, the whole computational cost is dominated by the size |Γ| of the support of the image, due to the first and last steps of the process, leading to a quasi-linear cost with respect to the size of the image. In particular, this allows us to perform real-time threshold-based node selection.

I (i) ------→ T (i ) ------→ T           (ii) I ≤ I (iii ) ← ------T (iii) ← ------T (9)

Attribute-based filtering with shaping -Application to PET image analysis

We now instantiate a PET image lesion detection framework based on the above-described methodology.

Adequacy of component-trees for PET image thresholding

As an extrema-oriented data structure, the componenttree is well adapted for emphasizing oncological lesions that correspond to maximal intensity values. In particular, the best-adapted component-tree is the max-tree, organized from the lowest to the highest values. More precisely, for a given PET image, the root of its componenttree T is the node Γ (i.e. the whole image support) obtained from the lowest level set, at value ⊥ = 0. Conversely, the leaves of T (i.e. the nodes that are minimal elements for the inclusion relation ⊆) are the flat zones of the image of (locally) maximal values; they correspond to tumoural (lesions) and physiological (organs) high metabolic activity areas.

Another strength of the component-tree is that it intrinsically models the space of all the potential thresholding operations that can be carried out on a grey-level image. This allows for the generalized processing of all the regions of the PET image at once within the same structure. The choice of a solution within this data-structure can be performed by scanning the (decreasing) grey-level values along the branches of the tree, from its leaves to its root. In particular, this process is compliant with the major thresholding strategies:

• fixed thresholding (i.e., horizontal cut in the tree);

• adaptive thresholding (i.e., branch-specific cut in the tree);

• bounding-box thresholding (i.e., explicit choice of leaves of branches to cut in the tree).

These different strategies are illustrated in Figure 2. Therefore, the component-tree satisfies mandatory properties for developing interactive segmentation processes in PET, in real-time thanks to its low space and time cost properties.

Shaping analysis of the component-tree based on compacity attribute

Let I be a PET image, and let us assume that we have computed its component-tree -more precisely, its maxtree-T (step (i) in Diagram (9). In this tree T , the nodes The second tree T is the min-tree of T , based on the attribute level-sets. Each node of T is then valued with respect to the difference between the attribute value of the leaf and that of the node (in red). The node selection is based here on a threshold of 0.1 in T with respect to this relative attribute (discarded nodes are dashed). The remaining nodes are then propagated back from the second tree to the image support, via the first tree.

that are close to the leaves correspond to the areas of highest intensity; they can be either lesions or hyper-fixating organs.

Our purpose is to develop an interactive attribute-based procedure for identifying automatically active tumours in I. A segmentation strategy based only on PET value thresholding may over-segment the high intensity areas, including true positives but also many false positives. As a consequence, it is indeed required to choose and compute a relevant attribute in order to discriminate the nodes of interest within T .

Our working hypothesis, that is in particular valid in the case of lymphoma -where the number of lesions is high and their shape is compact (similar to a sphere), compared to physiological uptakes (e.g., heart, kidneys, etc.)-is that a compacity criterion, in addition to the intensity criterion, could allow us to better discriminate the active lesions, especially in the thorax.

Consequently, we define an attribute A : 2 Γ → [0, 1] that associates to any connected subset of Γ, a numerical value describing how the corresponding shape is compact. This attribute is computed from the eigenvalues λ 1 ≥ λ 2 ≥ λ 3 associated to the eigenvectors of the 3 × 3 matrix of inertia of the (binary) shapes N ⊆ Γ. In particular, we define A(N) = λ 3 /λ 1 (10) namely, the ratio between the lowest and highest eigenvalues, lying in [0, 1]. If A(N) is close to 1, then λ 3 and λ 1 (and thus λ 2 ) present similar values, and N then has a compact shape. When A(N) decreases toward 0, N becomes more elongated. This attribute A is indeed non-monotonic. In particular, it is impossible to interactively process T in a threshold-based fashion, based on the information carried by A. In order to tackle this issue, we rely on the shaping paradigm.

A second component-tree T is then built from the tree T = (Ψ, ), i.e. from the valued graph T = (Ψ, , A) (step (i ) in Diagram ( 9)).

Contrary to T , that was a max-tree based on ≤, this second tree T is a min-tree, based on ≥. Indeed, the root is the node of greatest value for A (i.e. with the highest compacity), whereas the leaves are those of locally lowest values (i.e. with the lowest compacity). The nodes that are close to the leaves then correspond to the sets of connected components of Γ that are of least relevance, and should then be removed preferentially.

In order to segment the active lesions versus the hyperfixating organs (step (ii) in Diagram ( 9)), two distinct strategies can be considered:

• the first is an absolute thresholding along the branches of T , thus pruning the distal parts of the tree, composed of the nodes that have a compacity value A lower than a chosen threshold value t ∈ [0, 1]. This strategy enables to filter out nodes that are the least likely to be part of the expected shape, by assuming that their attribute values are in a common interval. However, it can be difficult to achieve an optimal result with a unique threshold;

• the second is a relative thresholding that considers the "gap" between the compacity value A(N) of a node N and the value A(L) of the leaf of its branch. This gap A(N) -A(L) still varies monotonically within [0, 1] along the branches, with 0 values at the leaves. This strategy consists of comparing each node with its neighbourhood in terms of shape, by taking the leaf nodes as references, namely the nodes that are the least likely to correspond to the criterion. Nodes with a shape similar to the leaf (i.e. elongated structure in this case) in each branch are associated with low difference values, and can be eliminated in that way. On the contrary, nodes corresponding to the expected shape (i.e. compact shape) are kept thanks to larger gaps in attribute values. This strategy is more flexible, since it does not require to find the optimal compacity threshold, and relies on local information. However, it can be associated with a larger variability in attribute values of preserved/eliminated nodes within the different branches, and therefore a possibly higher shape variability, compared to the absolute strategy. For instance, there is a risk of eliminating compact nodes, corresponding to branch leaves or near leaves, if there is no more elongated nodes in the branch.

In the following, the first strategy was adopted. Once the nodes of T have been selected, the resulting image has to be computed. Each selected node N of T is indeed a connected component of Ψ nodes. In order to re-trieve the subset Ψ ⊆ Ψ of selected nodes within Ψ, from the subset Ψ ⊆ Ψ of selected nodes of T (step (iii) in Diagram ( 9)), we can simply proceed by union, i.e. by setting

Ψ = Ψ = { N ∈ Ψ | ∃ N ∈ Ψ , N ∈ N }.
In other words, a node N is preserved in T if it appears at least once in a preserved node N of Ψ (keeping in mind that such node N generally appears in many nodes N ).

Finally, the last step that consists of embedding the selected nodes N of Ψ back to Γ (step (iii ) in Diagram ( 9)) can be conducted the same way: the subset Γ of detected points of the image I can be defined as

Γ = Ψ = { x ∈ Γ | ∃ N ∈ Ψ, x ∈ N}.
(Note that associated grey-level information can also be retrieved by simply using Equation (5), substituting Ψ to Ψ.)

An application of the proposed framework is exemplified in Figure 3.

Practical aspects

Implementation

Our proposed framework is open-source1 and relies on the LibTIM2 library, developed in C++ under GPL 3.0 License, which allows for the efficient construction, manipulation and processing of morphological hierarchies.

As part of the work on PET lymphoma tumour detection and segmentation, our framework has been also integrated into the Beth Israel Plugin3 for Fiji developped by [START_REF] Kanoun | Beth Israel Plugin for FIJI: Logiciel gratuit et open source pour la recherche scientifique[END_REF], which is a free and open-source software (also under GPL 3.0 License), plugin 4 of ImageJ that is dedicated to PET/CT (X-ray Computed Tomography) image visualization and processing. The purpose of this tool is to provide a collaborative PET/CT platform that is able to integrate research work. This software, developed in Java, is provided as a Fiji / ImageJ plugin. The viewer handles PET and CT visualization and fusion, maximum intensity projection display and a quantification tool, which now integrates the previously described shapings algorithm for detection / segmentation purpose. Our framework is integrated as a module 5 , provided as an executable called by Fiji. It takes the PET exam as an input and provides as output a segmentation mask with labeled lesions.

Proof of concept: experiments on phantom images

To obtain a first validation of our approach, we used the NEMA 2007 IEC image phantom. This phantom contains six spherical areas modeling lesions, with diameters 10, 13, 17, 22, 28 and 37 mm. These spheres were filled with varying 18 F concentrations to three different signalto-background ratios (SBRs), namely 2.59:1, 5.06:1 and 8.40:1. Data were acquired on a Philips GEMINI TF Time-of-Flight PET/CT scanner. The PET images were obtained with the 3D LOR-RAMLA reconstruction and CT-based attenuation correction. They present a spatial resolution of 2.0 mm (Figure 4, first row).

For comparison, all images were registered to the highest contrast image. Reference segmentation was obtained by closest interactive thresholding to the known geometry on this image. The ROC curves of Figure 5 measure the set differences between the reference segmentation and our shaping result. It illustrates the impact of the signal loss on the segmentation results. The obtained results are near perfect for the image with a very high SBR of 8.40:1. In addition, even for more realistic SBRs, including that of value 2.59:1, which is low with respect to real cases, the obtained results remain satisfactory, thus underlining the relevance of the shapings approach.

6.3. Clinical validation -Lymphoma tumour segmentation 6.3.1. Automated lymphoma tumour segmentation framework Finally, we evaluated our method in the context of lymphoma tumours detection on clinical data. The direct usage of the proposed shapings framework on PET lymphoma images, converted into SUV, leads to the automated localization / identification of lesions over the whole-body. More precisely, when lesions are homogeneous, the detected volumes match the entire lesions; however for heterogeneous ones, the most active compact regions within them are detected. Therefore, it is necessary for clinical purpose to combine this detection framework with a segmentation process to retrieve accurate tumour contours and obtain final tumour volumes. A complete procedure combining the shaping detection framework with a standard SUV-based segmentation strategy is available in the Beth Israel Plugin for Fiji software. It works as follows. Considering the detected lesions mask (i.e. the detection framework output), the first step of the segmentation process is to produce automatically a larger region of interest (ROI) encompassing each detected high-intensity region, in order to reproduce the bounding boxes commonly defined manually in local approaches. To do so, we adopt a region-growing based approach using as seeds/markers the compact high-intensity regions automatically identified with the detection procedure. Each new voxel is added to the ROI if its SUV is closer to the seed intensity (i.e. the mean intensity of all the voxels detected and/or iteratively aggregated to the region) compared to the background (i.e. the mean intensity of the voxels that are not included in the mask). To avoid unlimited growing of low contrast uptake and reduce time / memory consumption, we considered intensity values from a modified SUV-based PET image in which SUV intensities below 2.5 are set to 0 (background). At this stage, a manual correction is possible to remove physiological uptakes and / or add missing regions (with low contrast or which do not fulfill the compacity shape criterion). Then any SUV-based segmentation method can be applied in these automatically defined ROIs to produce final tumour contours, such as 41% SUVmax lesion based threshold [START_REF] Meignan | Metabolic tumour volumes measured at staging in lymphoma: methodological evaluation on phantom experiments and patients[END_REF], which is currently integrated in Fiji.

Ongoing clinical evaluation

Introduced as a relevant tumour burden quantification on baseline PET and an additional prognostic factor to predict patient outcome [START_REF] Cheson | Recommendations for initial evaluation, staging, and response assessment of and non-Hodgkin lymphoma: the Lugano classification[END_REF][START_REF] Kanoun | Baseline metabolic tumour volume is an independent prognostic factor in Hodgkin lymphoma[END_REF][START_REF] Cottereau | Prognostic value of baseline metabolic tumor volume in early-stage Hodgkin lymphoma in the standard arm of the H10 trial[END_REF], the total metabolic tumour volume (TMTV) has never reached clinical application due to the lack of a fast and userfriendly automated determination. In this context, our shaping-based software tool could offer a fast, automatic and reproducible setting for tumours and help reduce intra-and inter-user variability for tumour burden assessment. This tool could thus encourage the implementation of TMTV in clinical routine for patients' risk assessment in lymphomas. To this end, a large-scale multi-center clinical study is ongoing, evaluating the variability, accuracy and computation time of TMTV calculation between a standard fully-manual approach and our method.

In particular, in [START_REF] Cottereau | High total metabolic tumor volume at baseline allows to discriminate for survival patients in response after R-CHOP: An ancillary analysis of the REMARC study[END_REF], our method has been used to demonstrate that the TMTV was a strong predictor of the progressions of the disease and deaths in a prospective series of 301 patients with diffuse large B cell lymphomas. In this study the volume has been computed by two independent observers. In a test set of 25 patients, the Lin concordance correlation coefficient was 0.998 (95% CI 0.997-0.999). The inter-observer agreement on the dichotomization of patients in low and high TMTV groups for survival prediction, based on a TMTV cutoff of 200 cm 3 , was excellent with a Cohen's κ = 1.

Conclusion

This article has proposed a methodological scheme for analyzing PET images with the paradigm of shaping, i.e. by computing and processing the component-tree of the component-tree of an image. In this context, we observed that it was possible to embed high-level prior information (here, a compacity attribute; but any other scalar feature may also be considered) whereas preserving the ability to carry out simple, interactive thresholding procedures on the data. In particular, this allows the medical practitioners to effectively act on the method / tool, and easily understand its behaviour.

From a methodological point of view, the perspectives of this work are twofold. First, they can consist of considering no longer one image, but many. Indeed, in the context of nuclear imaging, PET images are generally coupled with X-ray Computed Tomography data. This opens the way to the developement of shaping on hierarchical models designed for multivalued data. In particular, preliminary studies involving component-graphs have been proposed (Grossiord andet al., 2015b, 2019). More generally, many kinds of hierachical models designed to handle multivalued images may also be considered, and involved in shaping approaches. Other perspectives could be to enrich the priors guiding the segmentation. A unique criterion, combining intensity and compacity priors, may not be sufficiently specific and representative for all lymphoma lesions. Therefore, considering machine [START_REF] Grossiord | Automated 3D lymphoma lesion segmentation from PET/CT characteristics[END_REF] or deep learning procedures on morphological hierarchy models could help rely on relevant image descriptors that capture physiological phenomena more comprehensively.

Figure 1 :

 1 Figure 1: (a) A grey-level image I defined on a square subset of Γ ⊂ Z 2 . Each point x ∈ Γ has a value I(x) and is equipped with the standard 4adjacency as neighbourhood relation Γ . The values of the points of the image are within the set K = [[0, 4]] ⊂ Z (from 0 in black; to 4 in white). (c-g) The level sets λ v (I) (in white) for v varying from 0 to 4. (b) The component-tree T associated to I. The letters (A-P) in nodes correspond to the associated connected components (c-g).

Figure 2 :

 2 Figure 2: The component-tree representation is compliant with all major thresholding strategies: fixed threshold (a); adaptive threshold (b); bounding-box threshold (c). Selected subsets of nodes are depicted in red.

Figure 3 :

 3 Figure3: Illustration of the detection framework in PET, based on compacity attribute. The first component-tree T , based on the intensity levelsets, is a max-tree. Each node N of T is then valued with a compacity attribute A(N) (in green). The second tree T is the min-tree of T , based on the attribute level-sets. Each node of T is then valued with respect to the difference between the attribute value of the leaf and that of the node (in red). The node selection is based here on a threshold of 0.1 in T with respect to this relative attribute (discarded nodes are dashed). The remaining nodes are then propagated back from the second tree to the image support, via the first tree.

Figure 4 :

 4 Figure 4: First row: phantom PET images, with three different SBRs. Second row: segmentation results. MIP visualization.

Figure 5 :

 5 Figure5: ROC curves for the relative thresholding based on attributebased approach, for various SBRs (see Figure4).

https://github.com/egrossiord

https://github.com/bnaegel/libtim

https://github.com/ilan/fijiPlugins

http://petctviewer.org

http://petctviewer.org/index.php/feature/ autosegementation