Keywords: Chromosome number, Crepis aurea subsp. aurea, C. aurea subsp. glabrescens, C. aurea var. bosniaca, karyomorphology, polyploidy

Chromosome numbers and karyotypes were studied in eight populations of Crepis aurea from Alps, Dinaric Alps and Apennines. The populations from Alps and Apennines exhibit diploid chromosome number (2n = 10) while the populations from Central Dinaric Alps and one population from Julian Alps were tetraploid (2n = 4x = 20). For this reason, a detailed comparative analysis of the two cytotypes was undertaken. The hypothesis of auto-polyploidy seems to be the most plausible one. Additionally, it was interesting to deal with the taxonomic status of Crepis aurea var. bosniaca growing in Central Dinaric Alps and whose populations are tetraploid.

Introduction

Crepis aurea (L.) Cass. belongs to the Asteraceae family (sub-family Cichorioideae Chevall., 1828;tribe Cichoriae Lam. & DC., 1806;sub-tribe Crepidinae Cass., 1827). This is a perennial hemicryptophyte growing in grass and on rocky slopes of the subalpine and alpine regions of South European mountains (from 1000 to 2900 m). This species has often changed its taxonomic status, which explains the existence of many synonyms: Leontodon aureus L., 1759; Hieracium aureum (L.) Scop., 1772; Apargia aurea (L.) F.W.Schmidt, 1795; Calliopea aurea (L.) D.Don, 1829; Geracium aureum (L.) Rchb., 1831; Crepis kitaibelii Froel., 1838; Aracium aureum (L.) D.Dietr., 1847; Brachyderea aurea (L.) Sch.Bip., 1866; Hieracioides aureum (L.) Kuntze, 1891. Currently this species comprises three accepted subspecies: Crepis aurea (L.) Cass. subsp. aurea, mainly located in the Alps, Crepis aurea subsp. glabrescens (Caruel) Arcang. located in Apennines, Apuan Alps and mountains of Southwest Balkans, and Crepis aurea subsp. olympica (K. Koch) Lamond which is limited to Turkey.

Of the eight populations studied, four had the diploid (2n = 10) and four the tetraploid (2n = 4x = 20) chromosome numbers. This led us to make a comparative karyological study of two ploidy levels and to try to understand the origin of polyploidy within Crepis aurea species. Two of these seven populations (one diploid -Col de Galibier and one tetraploid -Mt. Jahorina) are used for karyomorphological analyses. In addition, given that Bosnian populations are all tetraploid, the question arises regarding the real taxonomic status of Crepis aurea var. bosniaca described by [START_REF] Maly | Nove biljke iz Bosne I Hercegovine. -Glas[END_REF]. The material from the Col de Galibier population was used for the fine analysis of the diploid karyotype and construction of a karyogram and idiogram which presents the mean value of the five metaphases belonging to the different individuals (Figs 1, 1a & 1b). Chromosome types were determined according to the usual recommendation and nomenclature of Levan & al. (1964).

Karyotype was composed of two metacentric pairs (pairs 4 and 5), one submetacentric (pair 2) and one satellite subtelocentric pair (pair 3). The karyotype formula was as follows: 2n = 4m + 2sm + 2sm-st + 2st-SAT = 10 chromosomes (Table 1).

Several chromosome counts of 2n = 10 were previously reported for this taxon [START_REF] Siljak-Yakovlev | IOPB chromosome number reports LXXIII[END_REF], 1982;Lippert & Heubl 1988;[START_REF] Gemeinholzer | New chromosome counts for some Lactuceae (Compositae). -Compositae Newslett[END_REF] The chromosomal number of 2n = 10 already reported [START_REF] Chichiricc | Numeri cromosomici per la flora italiana: 652-661[END_REF](Chichiricc & al. , 1981;;Siljak-Yakovlev 1985) has been confirmed again in this work for the population from Apennins. 2b,3 & 4). The tetraploid cytotypes was detected in four populations, three from Bosnia (Central Dinaric Alps) and one from Slovenia (Julian Alps). All these populations grow on limestone while the diploid cytotype was found mainly on granitic substratum. This chromosome number and the new ploidy level were reported for the first time by Siljak-Yakovlev (1982, 1985).

Crepis aurea var. bosniaca

BH: Central

For karyological analyses of Crepis aurea var. bosniaca material from population of Mt. Jahorina (Central Dinaric Alps) was used.

Karyotype of this tetraploid cytotypes is composed of four pairs of metacentric chromosomes (pairs 7, 8, 9 and 10), three pairs submetacentrics (pair 2, 3 and 4), and three pairs subtelocentric (pair 1, 5 and 6) from which two bearing the satellites (Figs 2,2a,2b; Table 1). The chromosomal formula was as follows: 2n = 4x = 20 = 8m + 6sm + 6st (4 with satellites).

Comparative analysis of diploid C. aurea subsp aurea and tetraploid C. aurea var. bosniaca suggests an autopolyploid origin of this last taxon. In fact, var. bosniaca shows a marked clustering of chromosomes by four. Only the first two pairs are of different types which can be the consequence of chromosomal restructuring during diploidization of tetraploid cytotype. Evidence of strong diploidization in var. bosniaca is also expressed by the formation, in the great majority, of the bivalents during the meiosis. Only a few rare tetravalents can be observed in diakinesis (Figs 3 and 4,arrows).

According to all these results it would be legitimate to consider that var. bosniaca merits the rank of a new subspecies within Crepis aurea and that it occupies a part of the area of distribution (mountains of Southwest Balkans) that was previously assigned to C. aurea subsp glabrescens.

1994.

  Crepis aurea (L.) Cass. subsp. aurea -2n = 10 (Figs 1a & 1b). Fr: French Alps: Aussois, near to the village, alt. 1450 m, Sept 1980, leg. S. Siljak-Yakovlev, s.n. -Col de Galibier, alt. 2200 m, Sept 1980, leg. S. Siljak-Yakovlev, s.n. -Col de Balme, alt. 2190 m, Aug 1981, leg. D. Cartier & S. Blaise, s.n.

Figs

  Figs 1-4: 1, Mitotic metaphase chromosome plate of diploid, 2n = 10, Crepis aurea subsp. aurea from French Alps (Galibier), corresponding karyogram (1a) and ideogram (1b); 2, Metaphase chromosome plate of tetraploid, 2n = 4x = 20, C. aurea var. bosniaca from Central Dinaric Alps (Mt. Jahorina), corresponding karyogram (2a) and idiogram (2b); 3 and 4, Meiotic chromosome plates of tetraploid C. aurea var. bosniaca in diakinesis stage. -The rare tetravalents are indicated by arrows.

Table 1 .

 1 ;[START_REF] Lippert | Chromosomenzahlen von Pflanzen aus Bayern und anderen Gebieten[END_REF][START_REF] Enke | Shrinking genomes? Evidence from genome size variation in Crepis (Compositae)[END_REF]. Numerical data of chromosome set for diploid Crepis aurea s. s.

	Flora Mediterranea 30 -2020

It: Apennins: Peisey Nancroix, alt. 1700 m, 1983, material from Botanical garden, s.n.

  Dinaric Alps of Bosnia: Mt. Jahorina, alt. 1600 m, Aug 1979, leg. S. Siljak-Yakovlev, s.n. -Central Dinaric Alps of Bosnia: Mt. Treskavica, alt. 1600 m, Aug 1979, leg. S. Siljak-Yakovlev, s.n. -Central Dinaric Alps of Bosnia: Mt. Vlasic, alt. 1500 m, Aug 1979, leg. S. Siljak-Yakovlev, s.n. Slo: Julian Alps: Mangart, alt. 2100 m, Aug 1981, leg. T. Wraber, s.n.

Table 2. Numerical data of chromosome set for tetraploid Crepis aurea var. bosniaca.


Amélia Messara

Armen Panossian

Dr Koichi Mikami

Gilles Hanquet
email: ghanquet@unistra.fr

Frederic Leroux
email: frederic.leroux@unistra.fr

Frédéric R Leroux

Dr ] A A Messara

Dr G Panossian

Dr F R Hanquet

Leroux

Direct Deprotonative Functionalization of α,α-Difluoromethyl Ketones using a Catalytic Organosuperbase

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Fluorinated molecules often lead to unique bioactivities compared to their non-fluorinated analogs. [1] Currently, 53% of agrochemicals [2] and 18% of pharmaceuticals [START_REF] Inoue | [END_REF] entering the global market contain at least one fluorine atom. Among fluorine synthons, the difluoromethylene group is an attractive structural motif [START_REF] Saphier | properties and synthesis of CF2-contaning products[END_REF] and presents a great importance in medicinal chemistry thanks to its bioisosteric relationship with the carbonyl motif and the oxygen atom. [1c] In particular, a,a-difluoromethyl ketones and a,a-difluoro-b-hydroxy ketones are versatile building-blocks allowing access to various difluoromethylene compounds. [5] Furthermore, bioactive molecules containing the difluoroketone unit have proved to be efficient inhibitors of many enzymes such as the HIV protease or the GABAB receptor due to their ability to form stable hydrates, hemiacetals or acetals. [5b], [6] The generation of difluoroenolate is a method of choice to construct difluoroketone substructures. [7] Several strategies have already been developed for the preparation of a,a-difluoro-b-hydroxy ketones involving diverse precursors leading to the enolate (Scheme 1). [START_REF] Liao | For selected examples of Mukaiyama aldol reactions see: a)[END_REF][9][START_REF] Zhang | For selected examples of aldol reactions promoted by trifluoroacetate release see: a)[END_REF][START_REF] Decostanzi | For selected examples of aldol reactions by a Brook rearrangement see[END_REF][12][13][14][START_REF] Tarui | For selected examples of decarboxylative aldol reactions see: a)[END_REF] Many of these routes involve Mukaiyama aldol reactions via synthesis of the difluoroenol silyl ether [START_REF] Liao | For selected examples of Mukaiyama aldol reactions see: a)[END_REF] or Reformatsky-type reactions. [9] However, these approaches suffer drawbacks like the poor stability of the silyl enol ether or the use of stoichiometric amounts of organometallic reagents. Other strategies allowing for milder conditions have been described. such as the trifluoroacetate release to generate the difluoroenolate from a stable precursor developed by Colby et al. [10c] However, this method requires the pre-functionalization of the substrate. A Brook rearrangement/fluoride elimination process was also disclosed by Leclerc et al. [11a] but this strategy is limited by the difficult access to the acyl silanes. More significantly, none of these methods report the direct deprotonation of a,a-difluoromethyl ketones presumably because of the poor stability of the generated carbanion leading to the corresponding fluorocarbene due to electronic repulsion. In this context, our group focused on the deprotonation of difluoromethyl scaffolds [16] and we already reported the deprotonation of difluoromethyl sulfoxides to access a,a-difluorob-hydroxy sulfoxides using the Schwesinger superbase (P4-tBu).

Selected examples of previous aldol-type reactions in the literature

+ R 1 OTMS R 1 O R 3 OH F F R 2 R 3 O F F Lewis Acid + R 1 CF 2 Br O R 1 O R 2 OH F F R 2 H O Metal + R 1 O R 1 O R 2 OH F F R 2 H O Base CF 3 F F HO OH + R 1 TMS O R 1 O R 2 OH F F R 2 H O Mukaiyama-
[ 16c-d] This base was already demonstrated by Shibata and Mikami [17] to stabilize "naked" a-fluorinated carbanions by the counterion P4-tBu/H + with increased reactivity towards electrophiles. Its catalytic use has been highlighted by both Mikami's [17d] and Shibata 's [17b] groups when employing silylated additives such as 1-trimethylsilylpropyne (TMSP) or tris(trimethylsilyl)amine, respectively. These additives could act as a relay base or regenerate the P4-tBu base. [17b, 18] Herein, inspired by this new "superbase organocatalyst system", we desired to develop the unprecedented deprotonative functionalization of a,a-difluoromethyl ketones using substoichiometric amounts of the P4-tBu base in the presence of aldehydes as first electrophiles to access highly valuable difluoromethylene compounds.

Results and Discussion

Firstly, a,a-difluoromethyl ketones 3a-c, [19] 3e [20] , 3i-j [19] , 3k, [21] 3l [22] and 3m [23] were prepared following reported procedures in the literature (see Supporting Information for details). To synthesize unknown a,a-difluoromethyl ketones 3d-h, we designed a new strategy relying on cheap aldehydes as starting materials (Scheme 2). A Reformatsky-type reaction was performed to afford the corresponding hydroxy esters 1 that were further oxidized with DMP. The last step involved a Krapcho dealkoxycarbonylation to obtain the desired ketone 3. This threestep methodology is efficient, practical and only implies the use of non-expensive reagents (see Supporting Information for more details).

Scheme 2. Synthesis of aryl a,a-difluoromethyl ketones (see Supporting Information for more details).

Then we started to investigate the aldol reaction using mesityl ketone 3g and p-anisaldehyde (Table 1). These compounds are substrates of choice since the corresponding signals in NMR facilitate the reaction monitoring. Furthermore, since the mesityl ketone 3g is not volatile unlike many difluoromethyl ketones, its use is more convenient. Inspired by Mikami's [17d] and Shibata's [17b] reports and after a slight optimization, our best conditions were defined as follows: 1.0 equivalents of a,a-difluoromethyl ketone, 1.2 equivalents of aldehyde, 1.5 equivalents of TMSP, 10 mol% of P4-tBu in THF (C = 0.66M) at 25 °C for 24 h under argon atmosphere. Delightfully, under these conditions and after desilylation with TBAF, the targeted product 4l was obtained in a high isolated yield of 93% (Entry 1). By employing tris(trimethylsilyl)amine (N(TMS)3), a similar yield of 90% was achieved (Entry 2). A control experiment showed that no reaction occurs in the absence of the P4-tBu base (Entry 3). Another additional experiment was conducted without TMSP leading to a significantly lower yield of 43 % (Entry 4). The use of another base such as KHMDS did not lead to an effective transformation with only 32% yield (Entry 5). In this case, the K + counterion is presumably more coordinating thus making the formed anion less reactive, whereas P4-tBu/H + allows the formation of a "naked" carbanion with increased nucleophilicity. [16] In addition, unmasking the alkyne by fluoride-promoted desilylation with CsF or AgF was ineffective (Entry 6 and 7). Finally, DMF was used as an alternative solvent, since it is known to stabilize fluorinated carbanions by forming hemiaminolate species [24] but the yield drastically decreased to 59% (Entry 8).

Table 1. Optimized conditions and deviation effect. [a] Entry Deviation from standard conditions Yield (%) [b] 1 Next, with the optimal conditions in hand, we decided to investigate the scope and limitations of this organocalytic aldol reaction using various difluoromethyl ketones with benzaldehyde as the electrophile (Scheme 3). When employing difluoroaceto-phenone 3a, the desired compound 4a was observed in 45% 19 F NMR yield along with the by-product 5 coming from the selfcondensation of 3a. In addition, we never managed to obtain compound 4a as a pure sample due to degradation during purification as also described by Leclerc et al. for the same product. [11a] In order to avoid the formation of the by-product, a methoxy group was introduced in the para position leading to aldol 4b in 39% yield. On the contrary, with a a-CF3 substituent, the desired product 4c was not obtained and only the selfcondensation adduct was identified. The use of ortho di-substituted ketones with methoxy or chloro moieties led to similar yields of 68% and 72% (4e-f), respectively. As well, we performed the reaction with mesityl and pentamethyl difluoromethyl ketones to access the aldols 4g-h in high yields. The structure of derivative 4g was confirmed by X-ray crystallography. [25] Furthermore, heteroaryl ketones were employed such as thiophene or indole derivatives without any success as only traces of the desired aldols were observed. Finally, the reaction was carried out with aliphatic ketones. When adamantyl ketone was reacted under the optimized conditions, product 4k was only obtained in yield along with two side products 6 and 7 coming from the addition of the alkynide to the ketone and aldehyde starting materials (see mechanism below). By switching the silane source to N(TMS)3 to overcome the generation of 6 and 7, an excellent yield of 91% was obtained, probably due to the lower nucleophilicity of the silane employed. Then, by conducting the reaction with an enolizable ketone such as a cyclohexyl derivative, only traces of the aldol 4l were detected and the substrate was fully recovered.

An ynone was also used but without success since a complete degradation of the latter was observed. In summary, the substituents linked to the aryl difluoromethyl ketone have a significant role since the reaction is more efficient with electron-rich and ortho-substituted aryl ketones. On the one hand, the introduction of electron-donating substituents allows to limit/avoid the formation of the self-condensation side product by decreasing the electrophilicity of the ketone. On the other hand, regarding ortho-substituted substrates, the bulky aromatic ring is twisted out of conjugation, thus protecting the carbonyl from this dimerization. Concerning aliphatic ketones, only the nonenolizable derivatives seem to be tolerated, probably due to a deprotonation competition on both sides of the carbonyl function. [9c] To follow our investigations, we then evaluated the impact of the starting aldehyde on the course of the reaction. Interestingly, difluoroacetophenone 3a and para-trifluoromethyl benzaldehyde afforded the corresponding aldol 4n in 70% yield. As anticipated, the use of a more electron-poor electrophile instead of benzaldehyde prevents the dimerization of the ketone. Then, diverse aldehydes were reacted with the mesityl ketone 3g. Aryl aldehydes bearing electron-donating or electron-withdrawing groups at the para position of the phenyl ring gave the targeted products 4o-t in good yields (68-88%). Ortho-and metasubstituted benzaldehydes also gave excellent results with yields up to 85% (4u-v). Pleasingly, heteroaryl aldehydes such as furan, pyridine or indole derivatives provided products 4w-z in satisfying yields (67-87%). The reaction was also performed with cinnamaldehyde leading to the 1,2-addition product 4aa in 71% F NMR yield. The use of alkyl aldehydes (enolizable or not) allowed the access to the desired compounds 4ab, 4ac, 4ad in moderate to good yields ranging from 50 to 81%. We also demonstrated the feasibility of this aldol reaction on a gram scale (1 gram of 3d gave 71% of 4d and 1 gram of 3g gave 90% of 4g). Afterwards, we developed the diastereoselective version of this aldol reaction using enantiopure and/or diastereopure aldehydes. Gratifyingly, with 2-(benzyloxy)propionaldehyde displaying central chirality, a good d.r. (70:30) was achieved and the major diastereoisomer 4ae was isolated in 30% yield. Unfortunately, this diastereoisomer was obtained as a racemic mixture probably due to a racemization of the parent aldehyde during the reaction (with reprotonation by the aldehyde or the difluoroketone). Conversely, a related aldehyde with two contiguous stereocenters involved in an acetonide moiety led to 4af in 83% yield, 93:7 d.r. and >99% e.e. We then employed an atropisomeric (hetero)biaryl described by Wencel-Delord and Ackermann, [26] and the targeted product 4ag was obtained in a high yield with 85: 15 d.r. and 97.5% e.e. The atropisomeric biaryl reported by Shi et al. [27] gave the corresponding aldols 4ah-ah' in a low d.r. of 55:45. However, the diasteroisomers were separated by column chromatography and obtained with 99% e.e. Based on previous reports by Mikami [17d] and Shibata, [17b] a plausible mechanism can be proposed for this aldol-type reaction (Scheme 4). According to our observations, the mechanism would imply two pathways. The path one would firstly involve the deprotonation of the difluoromethyl ketone 3 by the P4-tBu base and condensation on the aldehyde to form the ion pair A. The generated alkoxide should activate the trimethylsilyl group on the alkyne to access the desired compound C. At this time, the formed alkynide B would act as a base to deprotonate another equivalent of the ketone. The generated carbanion could then react with the aldehyde forming again the ion pair A, leading to the targeted product C after reaction with TMSP. Prior to desilylation, the silyl ether C was observed by analysis of the crude mixture, thus supporting our mechanistic hypothesis. As the reaction can still proceed without the silane, although a significantly lower yield was obtained (i.e. 43% vs 93% with TMSP), a complementary mechanism was considered. This second pathway relies on the deprotonation of the ketone 3 by the alkoxide formed leading directly to the aldol 4. However, in the presence of TMSP, the generation of volatile propyne seems to be a putative driving force in this aldol process. Notably in both pathways and as described by Mikami [17d] and Shibata, [17b] the counterion P4-tBu/H + is supposed to play an important role in this mechanism. The latter might indeed form a stabilized ion pair with the alkoxide and by its non-coordinating character, enhance the nucleophilicity of the anion. In addition, following our hypothesis and in accordance with the literature, the P4-tBu base should not be regenerated during the reaction given its high basicity (pKa = 42.6 in MeCN). [28] To shed light on the mechanism, we monitored the aldol reaction by 31 P NMR for several hours (see Supporting Information for more details) and only the protonated base was detected, thus supporting our assumption.

Finally, to exploit the synthetic potential of our a,a-difluoro-bhydroxy ketones, we carried out several transformations (Scheme 5). First, a diastereoselective reduction using DIBAL allowed us to form the anti-diol 8d in a quantitative yield. Then, in the presence of magnesium and trimethylsilyl chloride, the amonofluorinated ketone 9d was isolated in 70% 19 F NMR yield with a satisfying Z/E ratio of 92:8. Unfortunately, no pure sample was obtained due to degradation during purification by flash chromatography on silica gel. Next, to convert the aryl moiety introduced by the difluoroketone into a more transformable group, a Baeyer-Villiger oxidation provided the corresponding b-hydroxy ester 10d in an unoptimized 59% yield. This product was then converted into amide 11d and carboxylic acid 12d with excellent yields.

Scheme 5. Follow-up chemistry.

To go one step further, we envisioned to extend our method to other electrophilic partners (Scheme 6). Pleasingly, diverse electrophiles were well tolerated. The use of imines led to the formation of compounds 13a and 13b in high yields. By employing an a,b-unsaturated ketone, only the 1,4-addition compound 13c was obtained in 60% yield contrary to the use of acrolein that only afforded the 1,2-addition product 4aa. Next, diketone 13d was obtained in 30% yield in the presence of benzoic anhydride. We also studied the reaction with chalcogen derivatives such as diphenyl disulfide or diphenyl diselenide giving the corresponding products 13e-f with yields around 60%. Finally, using an alkynyl bromide, we managed to form a-bromo-a,a-difluoromethyl ketone 13g in 62% of NMR yield. Unfortunately, the compound could not be properly isolated since degradation always occurred during purification. To gain insight on this process using other electrophiles, control experiments were carried out in the absence of TMSP notably in the case of alkynyl bromide and dichalcogenides. As well as for the aldol reaction, a decrease in yield and conversion was noticed (see Supporting Information for more details). These results are consistent with the previous hypothesis that propyne generation is the driving force of the reaction. Scheme 6. Deprotonation of a,a-difluoromethyl ketones in the presence of other electrophiles.

Furthermore, in view of our previous work on a,a-difluoromethyl sulfoxides, [16a,c-d] we desired to assess them in our deprotonative functionalization strategy as an interesting electron-poor CHF2containing alternative to difluoromethyl ketones (Scheme 7). Thus, by submitting racemic sulfoxide 14 in the presence of benzaldehyde to the above-mentioned conditions, the corresponding b-hydroxysulfoxide 15 was isolated in 62% yield and 54:46 d.r. Noteworthily, this selectivity has to be compared to the similar one obtained with stoichiometric potassium tertbutoxide as the base (ca. 60:40) whereas stoichiometric amounts of P4-tBu led to 99:1 d.r. under kinetic resolution by degradation of one diastereomer. [16c-d] Scheme 7. Deprotonative functionalization of an a,a-difluoromethyl sulfoxide.

Conclusion

In conclusion, we have developed the first direct aldol reaction of a,a-difluoromethyl ketones via their deprotonation using a catalytic organosuperbase. This condensation proved to be highly efficient and led to a wide range of a,a-difluoro-b-hydroxy ketones in the presence of aryl, heteroaryl as well as alkyl aldehydes with yields up to 95%. We also managed to perform the diastereoselective version of the latter reaction using enantiopure aldehydes displaying central or axial chirality with diastereoisomeric ratios up to 93:7. Furthermore, we demonstrated the synthetic potential of the obtained a,a-difluorob-hydroxy ketones by submitting them to different transformations. Finally, this deprotonative functionalization strategy was applied to various other electrophiles such as imines or chalcogen derivatives giving access to highly valuable difluoromethylene compounds. The use of another CHF2-containing substrate, namely an a,a-difluoromethyl sulfoxide, was also well tolerated in this deprotonation process.

Experimental Section

The data that support the findings of this study are available in the Supporting Information of this article.

Entry for the Table of Contents

The deprotonation of a,a-difluoromethyl ketones is underinvestigated due to the instability of the generated carbanion that can evolve into a fluorocarbene. A method for the deprotonative functionalization of these compounds is described herein under an organocatalytic system using various electrophiles, and is also applied to a related a,a-difluoromethyl sulfoxide. This strategy gives access to highly valuable difluoromethylene scaffolds.

Institute and/or researcher Twitter usernames: @Leroux_group, @LIMA_UMR7042, @AmeliaMessara

Scheme 1 .

 1 Scheme 1. Selected examples to access a,a-difluoro-b-hydroxy ketones and our strategy.

  aldol reaction by Zhou et al. Brook rearrangement/fluoride elimination by Leclerc et al.

  See the Supporting Information for more details.[b] Isolated yield.

Scheme 4 .

 4 Scheme 4. Proposed mechanism to access a,a-difluoro-b-hydroxy ketones.

• Poor stability of silyl enol ether • Stoichiometric metal use • Pre-functionalization of the substrate • Indirect method • Difficult access to acyl silanes

		42 examples
		42-98%
		16 examples
		40-86%
		16 examples
		64-95%
		18 examples
		38-70%
	• Direct deprotonative functionalization	36 examples
	• No pre-functionalization	30-95%
	• Metal-free
	• Various electrophiles

Scheme 3. Scope of the deprotonative functionalization of a,a-difluoromethyl ketones in the presence of aldehydes to access a,a-difluoro-b-hydroxy ketones.

Acknowledgements

The authors are very grateful to the French Ministry of Higher Education, Research and Innovation and the University of Strasbourg (PhD grant for A. Messara) and the CNRS for support. We thank the USIAS (Université de Strasbourg Institut d'Études Avancées) for a short visit grant to Dr. Mikami. The authors thank the FRC (Foundation for Frontier Research in Chemistry, Université de Strasbourg) for granting the DiFluChir project. The GIS CNRS Réseau Français du Fluor is also kindly acknowledged. We are much grateful to Dr. J. Wencel-Delord, Pr. Dr. L. Ackermann and Dr. N. Jacob for providing the heterobiaryl aldehyde. We also thank L. Karmazin and C. Bailly from the Service de Radiocristallographie de la Fédération de Chimie Le Bel FR 2010 for SCXRD analyses. Keywords: Aldol reaction • Deprotonation • Difluoromethyl • Difluoromethylene • Fluorine


João Victor Galvão Da Mata

Henry Krumb

Utkarsh Mishra

Anirban Mukhopadhyay

Caroline Essert
email: essert@unistra.fr.

MANGO: Low-Cost Open Source Needle Guidance

Keywords: Low-cost navigation systems, Optical tracking, Needle guidance

Validating experiments in intra-operative planning for percutaneous interventions requires to localize the needle with a tracking system. As commercial optical trackers are expensive, we present MANGO, a low-cost OpenSource solution for needle tracking. We first present the design of our system, which localizes colored orbs using a stereo-camera setup. Based on this setup, we investigate the static and dynamic error of the system, and experiment with signal filtering to improve tracking performance. With the MANGO, we are able to meet the positional accuracy margin of 5 mm usually required in percutaneous interventions. Orientational accuracy, measured by needle tip localization accuracy as a proxy measure, exceeds this margin. We plan to investigate this further in future research. Releasing our code, data and 3D models, we aim to provide a low-cost and reproducible platform for needle tracking and validation of intra-operative planning in research environments.

Introduction

Needle tracking is an essential tool to experimentally evaluate intra-operative planning methods for percutaneous interventions, such as biopsies in the abdomen, in laboratory settings. Thanks to its precision, optical tracking is a suitable technology for needle tracking in such phantom studies. However, although commercial solutions for optical needle tracking exist, those are often prohibitively expensive for small research labs. Further, commercial optical tracking systems require pre-calibrated infrared markers which are delicate in the handling and are relatively expensive themselves. While aiming at minimizing that cost, our goal is to create a tracking system suitable for needle biopsy which meets the accuracy requirements of such procedures. For instance, the accuracy margin of tumor ablation in liver is deemed to lie between 5 mm and 10 mm [START_REF] Goldberg | Image-guided tumor ablation: Standardization of terminology and reporting criteria[END_REF].

The high prices of commercial tracking systems motivated several works aiming at developing low cost tracking systems. For instance, Asselin et al. [START_REF] Asselin | A training tool for ultrasoundguided central line insertion with webcam-based position tracking[END_REF] used the information of a single webcam and a depth sensor to track markers attached to medical tools. However, their approach does not meet the required accuracy margin of 10 mm. Wang et al. [START_REF] Wang | The Kinect as an interventional tracking system[END_REF] proposed to use the Microsoft Kinect to track needle-shaped objects.

Although this low-cost approach met the required accuracy margin, the source code for needle tracking is not publicly available, which impedes reproducibility.

In this work, we introduce MANGO, a low-cost open source two-camera system targeted at researchers and engineers working in the field of computer assisted surgery. The system itself is comprised of two low-cost USB webcams that are rigidly aligned inside a 3D printed enclosure. With this setup, it is possible to track colored orbs that can be attached to surgical instruments and needles.

First, we outline the design of our system, as well as the software we used to track the colored markers. We then explore the limitations of our custom system and investigate filtering techniques and spatial constraints to improve the tracking accuracy. Using a commercial tracking system for the purpose of validation, we finally verify that our system meets the required accuracy margin.

Methods

The MANGO system is composed of a specific system made of two webcams in a 3D printed case and some colored orbs attached to the needle, as well as a software pipeline to calibrate the cameras, track the 3D markers, and estimate the pose of the needle and the position of its tip. The design of the system and the pipeline are described below.

System Design

The hardware setup of the MANGO system consists of two webcams and a 3D printed case which protects the two cameras and constrains them not to move in relation to each other, as can be seen in Fig. 1 left. Several camera models were tested. In the most advanced models, which are often the most expensive, the autofocus results in a variable camera matrix, that makes it inappropriate for this project where a fixed matrix is required to avoid recalibration. On the other hand, the simplest (and cheapest) cameras usually have a lot of radial distortion resulting in large errors. The Logitech C270 HD camera was chosen because it combines low cost (under 30 USD/EUR per camera at the time of this experiment) with low levels of radial distortion and no autofocus feature. Finally, the system is completed by four plastic orbs of different colors fixed on a holder attached to the needle, as illustrated on Fig. 1 right. For the experiment, the MANGO orbs were placed on one side of the holder, while NDI Polaris infrared reflective orbs were placed symmetrically on the reverse side of the holder.

Calibration

The two cameras are calibrated using a Direct Linear Transformation (DLT)-like method as proposed by Zhang [START_REF] Zhang | A flexible new technique for camera calibration[END_REF]. This method uses several images of a planar object (in this work a chessboard pattern is used, as seen in Fig. 2) and returns the camera matrix with the intrinsic parameters and the transformation between the camera frame and the object frame for each picture. The average reprojection error found for all the points was 0.01533 pixels for the right camera and 0.01461 pixels for the left camera.

For each pair of images, the transformation between the two camera frames is com- puted from the transformations between each camera frame and the chessboard frame.

Then the final transformation is given by the average translation vector and the rotation matrix generated by the average Euler angles for all the transformations for each pair of images.

Orb Tracking

A color-based tracking strategy is used to localize the colored orbs, compute the position and orientation of the needle and its tip. For each image, the first step is to convert the color space from the traditional RGB to the HSV color space, where it is easier to segment colors just defining a hue range, and then refining the segmentation using the saturation and value. With that segmentation, a mask is created and used as basis for a contour detection algorithm [START_REF] Suzuki | Topological structural analysis of digitized binary images by border following[END_REF]. The center of mass of this contour is then recovered as an estimate for the orb center. This process is illustrated in Fig. 3.

In order to estimate the 3D pose of the needle, at least three non-aligned orbs need to be detected successfully. A fourth orb is attached to the marker as a backup in case another orb is not visible, e.g. due to reflections or occlusion. Each orb has its own color, which allows their individual tracking independently, as shown in Fig. 4.

The 3D position of each orb can be then deduced from their center position on the image of both cameras, the transformations between the cameras, and the camera matrices, using triangulation.

Estimation of the Coordinate Frame and Needle Tip Tracking

The shape of the multi-orb marker was chosen to allow recovery of all six degrees of freedom of the instrument and provide some redundancy.

Using a single orb, only the three positional coordinates of the orb can be recovered. With two orbs, a direction vector can also be found. With three or more orbs the entire six Degrees of Freedom (DOF) of the instrument can be detected, i.e. both the three coordinates and the orientation of the needle can be tracked, so that the position of the tip can be found.

A coordinate frame for the marker is defined as shown in Fig. 5. Knowing the position of the center of each orb in this coordinate frame and the coordinate frame of the camera, the transformation between both frames can be found. Then as the needle tip position is known in relation to the marker frame, it can be described in the camera coordinate frame.

Validation Protocol

We assessed the tracking accuracy of the MANGO system by comparing the tracking results with an NDI Polaris Vicra system. The Polaris Vicra has a stated accuracy of 0.5 mm (CI-95), and thus serves as a proper reference standard we can use for our experiments. The needle and attached marker set was partly inserted and fixed into a rigid foam structure to reduce oscillations due to movements, as shown in Fig. 6 (right). This setup was manually moved so that the needle tip sequentially covered a grid of points evenly spaced by 2 cm×2 cm. The positions of the orbs were measured with both MANGO and Polaris systems simultaneously and continuously recorded. At each point of the grid, we let the needle and markers stabilize for 20 s. The recorded data points were first aligned to a common coordinate frame by using Horn's method [START_REF] Horn | Closed-form solution of absolute orientation using orthonormal matrices[END_REF] under the use of eight extra calibration points that were collected with a similar protocol.

The time vector for both system was collect using the UNIX timestamp. As the MANGO sample rate is 30 Frames per Second (FPS) and the Polaris NDI sample rate is 50 FPS, the reference time vector used was that of MANGO. For each data point of the MANGO the comparison was done with the closest corresponding timestamp of the NDI Polaris.

In a second step, we estimated the series of positions of the needle tip for both tracking devices to properly compare the systems in six DOF. A sequence of stabilized positions was computed for the marker and the needle tip by clustering the time series of positions. DBSCAN was used for this clustering [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF] (ϵ = 1.5 mm, 200 samples), as it is well-established and separates noisy samples outside the cluster centers (we used these outliers to calculate the dynamic error in Sec. 4.3). Unlike traditional k-means, DBSCAN does not require the number of cluster centers to be known beforehand. Rather, DBSCAN separates data points based on the cluster density, such that the distribution of cluster points would not need to be spherical. The density parameter ϵ was gauged between twice the stated accuracy of the Polaris (1 mm) and half the distance between measuring points (10 mm), to allow for slight deviations of measurements from the stated tracking accuracy still being considered static measurements when analyzing static vs. dynamic accuracy.

All experimental code was written in Python with the use of OpenCV framework [START_REF] Bradski | The OpenCV Library[END_REF].

Experimental Results

In this section, we present the experimental results we obtained by following the measurement protocol described in Sec. 3. Fig. 7 shows the comparison between the positions in x, y, and z obtained with the Polaris system and the MANGO system without any filtering strategy applied.

Filtering Strategies

Variations in the amount of light in the room, movements in the background, and the cameras' auto-exposure feature affected the color tracking strategy and caused oscillations in detecting the center of each orb in the images as can be seen in Fig. 7, especially in z direction. A Gaussian filter was applied with a window size of 15 samples (0.5 seconds). This size was chosen to attenuate the oscillations due the color without attenuating the natural oscillations of the needle. The new results after the filtering can be seen in Fig. 8. The first two rows of Tab. respectively. The filtering slightly improved the error in the y and z directions.

Optimal Tracking Volume

Looking at Fig. 8, it can be noted that the error increased when the needle approached the sides or the front of the working space. This effect is probably due to the radial distortion of the lens. Using a color scale, Fig. 9 shows the the error for each measured position in the x-z plane, as well as the optimal area where the smallest errors can be found (represented as a red trapezoid).

As can be seen in Tab. 1 (rows 3 and 4) errors inside the optimal volume were half of the error in the overall area in the x and z directions, and around two thirds in the y direction. MANGO 9. Left: Positional error of the MANGO in its X -Z plane, the red trapezoid highlights the optimal tracking volume. Right: Illustration of possible and optimal tracking space.

Static vs. Dynamic Error

To assess the dynamic and static error of the MANGO, we separated the stabilized points obtained with the DBSCAN clustering from the outliers, the latter corresponding to the needle movements in between the points. For each corresponding timestamp of the two datasets (Polaris and MANGO), we compared the corresponding points for (a) static inliers and (b) dynamic outliers to calculate an error estimate. The static and dynamic errors are reported in Tab. 2 for both the full and the optimal tracking volumes.

We can see that the MANGO also meets the accuracy requirements if the needle is in motion, as the dynamic tracking error is only slightly higher but still below the 5 mm margin. The dynamic accuracy is sufficient in the full tracking volume, but is significantly better when confined to the optimal tracking space.

Needle Tip Tracking Error

Until now we only evaluated the tracking of three DOF of the marker, i.e. the tracking of the orb at the origin of the marker coordinate frame (or the translation vector between the marker frame and the camera frame). In this section we evaluate the tracking of the needle tip, which requires all six DOF, and allows to indirectly assess the measured orientation of our marker.

Fig. 10 shows the comparison between the tracking of the needle tip with MANGO and with the Polaris System inside the optimal volume. Tab. 3 shows the errors for the three coordinates. The Polaris system itself provides measurement data for all six degrees of freedom out-of-the-box. While the error is below the accuracy margin of 5mm [START_REF] Goldberg | Image-guided tumor ablation: Standardization of terminology and reporting criteria[END_REF] requested for our intended use case in the x and y directions, it can be observed that the error in the z coordinate is around ten millimeters, which exceeds the margin. As the main cause of this error, we identified the oscillations in the color tracking of each orb due to slight variations of light, that remained too high even with the Gaussian filter. Indeed, due to the length of the needle, a slight inaccuracy in the tracking of the marker set has a high influence on the accuracy of the tracking of the needle tip, specially in the depth direction.

RM SE

X RM SE Y RM SE Z M AE X M AE Y M AE Z 2.
Three main solutions can be investigated in a future study in order to reduce the error in the tracking of the needle tip, such as considering tracking approaches that would not rely on color or less sensitive to light variations, working in a controlled environment without light variations, using orbs with a different material or trying active markers such as LEDs, improving the filtering, or trying different marker geometries.

Conclusion

In this paper, we have presented MANGO, a low-cost open source optical tracking system for needle navigation intended to be used in lab studies for needle tracking in percutaneous intervention guidance. Based on a stereo-camera system and colored orbs, markers attached to a biopsy needle are tracked in six DOF thanks to a colorbased approach. Using a commercial tracker as a reference system, we observed that MANGO met the positional accuracy requirements in terms of 3D position of the marker set. Using the estimation of the needle tip position as a proxy for orientation, we found that the detection of the orientation in the plan perpendicular to the cameras (x and y directions) also met the expected accuracy. However, one current limitation of our system is that tracking the orientation in the z direction (depth of the needle tip) was negatively affected by slight variations of light that caused oscillations in the individual orb detection. In the future, we plan to address this issue by investigating alternative tracking techniques, environments, or markers. We further aim to explore the potential of cascading multiple MANGOs to increase the tracking volume and accuracy, as illustrated in Fig. 11. With a total price of only 60 USD/EUR, our proposed system is by far cheaper than commercial systems, which may cost up to several thousands of USD/EUR. By making all our code, 3D models and experimental data public1 under a free license, we aim to facilitate the reproduction of the system in other research labs to accelerate research in the field of pre-operative planning and needle guidance for percutaneous interventions.

Figure 1 .

 1 Figure 1. Left: The MANGO stereo-camera tracking system mounted on an adjustable arm. Right: Needle and 3D printed holder with infrared-reflective (Polaris) and colored (MANGO) orbs.

Figure 2 .

 2 Figure 2. One of the chessboard patterns used in the calibration.

Figure 3 .

 3 Figure 3. (Left) Double-sided marker as seen by the stereo camera system. (Center) Mask of the green orb which is used for tracking (Right). The Polaris system in the background is used for validation.

Figure 4 .

 4 Figure 4. (Left) 4 orbs. (Right) Tracking result.

Figure 5 .

 5 Figure 5. Marker geometry and coordinate frame.

Figure 6 .

 6 Figure 6. Left: Comparing the MANGO to the NDI Polaris with a two-faced marker fixture. Right: The needle is positioned precisely with the styrofoam fixture.

Figure 7 .

 7 Figure 7. Comparison between the raw data of MANGO (blue) and the data collected with the Polaris System (orange).The three figures correspond respectively to the x, y and z coordinates measured by both systems.

Figure 8 .

 8 Figure 8. Comparison between the filtered data of MANGO and the data collected with the Polaris System.

Figure 10 .

 10 Figure 10. Comparison between the tracking of the needle tip with MANGO and with the Polaris System inside the optimal volume.

Figure 11 .

 11 Figure11. Cascading multiple MANGO systems potentially increases the maximum optimal tracking volume (red). Positioning two MANGOs side-by-side, the two cameras C 2 and C 3 with intersecting fields-of-view can be leveraged to generate a continuous optimal volume in the shape of a wide trapezoid.

Table 1 .

 1 1 show the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) of the x, y and z coordinates for filtered and unfiltered data RMSE X RMSE Y RMSE Z MAE X MAE Y MAE Z Comparison of the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) of the x, y and z coordinates for filtered and unfiltered data, optimal tracking volume (with filter applied). All values are denoted in mm. RMSE X RMSE Y RMSE Z MAE X MAE Y MAE Z

		[mm]	[mm]	[mm]	[mm]	[mm]	[mm]
	Full volume, no filter	2.75	0.68	4.49	2.27	0.55	3.62
	Full volume, Gaussian filter	2.75	0.64	4.39	2.27	0.52	3.53
	Optimal volume, G. filter	1.29	0.43	1.89	0.99	0.37	1.60
	Decrease of error	53.1%	32.8%	56.4%	56.4%	28.8%	54.7%
		[mm]	[mm]	[mm]	[mm]	[mm]	[mm]
	Static, full volume	2.72	0.68	4.47	2.25	0.55	3.60
	Static, optimal volume	1.14	0.49	2.06	0.87	0.41	1.72
	Dynamic, full volume	3.29	0.81	4.84	2.62	0.63	3.98
	Dynamic, optimal volume	2.38	0.66	2.91	1.94	0.55	2.51

Table 2 .

 2 Comparison of the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) of the x, y and z coordinates static vs. dynamic error (with filter) in both full and optimal volume. All values are denoted in mm.

Table 3 .

 3 Comparison of the Root Mean Squared Error and Mean Absolute Error of the x, y and z coordinates for the needle tip inside the optimal volume. All values are denoted in mm.

	62	0.58	11.48	2.38	0.45	9.29

Code, data and models: https://github.com/Jvictormata/mango

Acknowledgements

This work of the Interdisciplinary Thematic Institute HealthTech, as part of the ITI 2021-2028 program of the University of Strasbourg, CNRS and Inserm, was supported by IdEx Unistra (ANR-10-IDEX-0002) and SFRI (STRAT'US project, ANR-20-SFRI-0012) under the framework of the French Investments for the Future Program.