Jetty Jean-Marie Galano

Jetty Chung-Yung Lee

Cécile Gladine

Blandine Comte

Jean-Yves Le Guennec

Camille Oger

Thierry Durand

Cecile Gladine

Non-enzymatic cyclic oxygenated metabolites of adrenic, docosahexaenoic, eicosapentaenoic and α-linolenic acids; bioactivities and potential use as biomarkers

Keywords:

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Free radicals are implicated in a wide variety of human diseases [START_REF]Free Radicals in Biology and Medicine[END_REF] and the consequences are the oxidation of biomolecules, including DNA, proteins and lipids. Among lipids, polyunsaturated fatty acids (PUFAs) have reactive skipped dienes, or methylated interrupted double bonds, that can participate to form acyclic, and subsequently, stable cyclic oxygenated metabolites [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF]. Since the discovery of F 2 -isoprostanes (F 2 -IsoPs) by [START_REF] Morrow | A series of prostaglandin F2-like compounds are produced in vivo in humans by a noncyclooxygenase, free radical-catalyzed mechanism[END_REF] derived from arachidonic acid (ARA, 20:4 n-6) peroxidation in vivo [START_REF] Morrow | A series of prostaglandin F2-like compounds are produced in vivo in humans by a noncyclooxygenase, free radical-catalyzed mechanism[END_REF], an important field of research has been developed. Nowadays, elevation of F 2 -IsoP levels in biological fluids (e.g. plasma and urines) is recognized as the reference biomarker for lipid peroxidation and oxidative stress [START_REF] Kadiiska | Biomarkers of oxidative stress study II: are oxidation products of lipids, proteins, and DNA markers of CCl4 poisoning? Free Radic[END_REF]. Because of the high reactivity and short life span of free radicals, oxidative stress is evaluated by the measurement of damaged biological products, which can be considered as biomarkers of lipid peroxidation. Beyond their capacity of oxidative stress evaluation, isoprostanes also demonstrate to be biologically active [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF][START_REF] Milne | Isoprostane generation and function[END_REF][START_REF] Galano | Isoprostanes and neuroprostanes: total synthesis, biological activity and biomarkers of oxidative stress in humans[END_REF]. Docosahexaenoic (DHA, 22:6 n-3) and eicosapentaenoic (EPA, 20:5 n-3) acids, the main n-3 PUFAs, form neuroprostanes (NeuroPs) [START_REF] Nourooz-Zadeh | F4-isoprostanes: a novel class of prostanoids formed during peroxidation of docosahexaenoic acid (DHA)[END_REF][START_REF] Roberts | Formation of isoprostane-like compounds (neuroprostanes) in vivo from docosahexaenoic acid[END_REF] and EPA-derived isoprostanes [START_REF] Nourooz-Zadeh | Evidence for the formation of F3isoprostanes during peroxidation of eicosapentaenoic acid[END_REF], respectively, under free radical reactions. Also, the n-6 PUFA adrenic acid (AdA, 22:4) located in brain white matter and other tissues, such as the adrenal gland and kidney, is the precursor of dihomo-isoprostanes (dihomo-IsoPs) [START_REF] Vanrollins | F2-dihomo-isoprostanes arise from free radical attack on adrenic acid[END_REF]. Finally α-linolenic acid (ALA, 18:3 n-3) from plants may be converted into phytoprostanes (PhytoPs) [START_REF] Parchmann | Evidence for the formation of dinor isoprostanes E1 from alpha-linolenic acid in plants[END_REF].

This review will focus on the isoprostanes, neuroprostanes, dihomoisoprostanes and phytoprostanes generated from ALA, AdA, EPA and DHA with regard to (i) the synthesis of these new cyclic oxygenated metabolites of PUFA, (ii) the use of such lipid metabolites as biomarkers of oxidative stress in humans, and (iii) data relative to their biological activities in vitro and in vivo.

Biosynthesis of cyclic oxygenated metabolites of PUFA

In 1990, Roberts, Morrow and co-workers discovered novel prostaglandin (PG)-like isomers, which are named isoprostanes. In contrast to PG produced by cyclooxygenases, the mechanism of formation proceeds via a non-enzymatic free radical peroxidation of ARA esterified in phospholipids and not from free ARA [START_REF] Morrow | A series of prostaglandin F2-like compounds are produced in vivo in humans by a noncyclooxygenase, free radical-catalyzed mechanism[END_REF]. The main structural characteristics compared to PGs are the cis-relationship of the side chains, the large number of potential isomers and the generation of racemic metabolites [START_REF] Porter | Peroxy radical cyclization as a model for prostaglandin biosynthesis[END_REF][START_REF] Pryor | Suggested mechanism for the production of malonaldehyde during the autoxidation of polyunsaturated fatty acids. Nonenzymic production of prostaglandin endoperoxides during autoxidation[END_REF]. Once formed, the isoprostanes can then be released by phospholipases in the circulating fluids [START_REF] Stafforini | Release of free F2-isoprostanes from esterified phospholipids is catalyzed by intracellular and plasma platelet-activating factor acetylhydrolases[END_REF] (Scheme 1). Later, it was uncovered that PUFAs such as ALA, EPA, AdA and DHA having at least two-skipped diene units, i.e. three consecutive methylene interrupted units, can form isoprostane-like structures [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF] (Scheme 2). In plants, ALA can generate PhytoPs [START_REF] Parchmann | Evidence for the formation of dinor isoprostanes E1 from alpha-linolenic acid in plants[END_REF] which were originally named dinor-IsoPs. DHA and EPA, the main n-3 PUFAs found in humans, release NeuroPs [START_REF] Nourooz-Zadeh | F4-isoprostanes: a novel class of prostanoids formed during peroxidation of docosahexaenoic acid (DHA)[END_REF][START_REF] Roberts | Formation of isoprostane-like compounds (neuroprostanes) in vivo from docosahexaenoic acid[END_REF] and isoprostanes respectively, when subjected to free radical reactions [START_REF] Nourooz-Zadeh | Evidence for the formation of F3isoprostanes during peroxidation of eicosapentaenoic acid[END_REF]. Another important n-6 PUFA, AdA, highly present in brain white matter, is known to generate dihomo-IsoPs [START_REF] Vanrollins | F2-dihomo-isoprostanes arise from free radical attack on adrenic acid[END_REF].

Similar to the biosynthesis of PGs, the intermediate G-IsoPs can lead to numerous types of IsoPs. Besides the F-type, E-, D-, A-, B-, and L-types (see ref. [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF]) of IsoPs, PhytoPs and NeuroPs are also formed in vivo depending on the surrounding conditions of the membrane phospholipids (Scheme 3) [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF].

In 2002, a completely novel structure of compounds was uncovered that follows the same free radical cascade pathway of IsoPs. The addition of molecular oxygen after initial cyclization leads to the generation of isofurans (IsoFs) from ARA [START_REF] Fessel | Discovery of lipid peroxidation products formed in vivo with a substituted tetrahydrofuran ring (isofurans) that are favored by increased oxygen tension[END_REF]. It was shown that IsoF levels augment in elevated oxygen conditions (above 21%) while not so for IsoPs. Similar mechanisms are proposed to access such biosynthesis [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF], including neurofurans (Scheme 4) [START_REF] Arneson | Measurement of products of docosahexaenoic acid peroxidation, neuroprostanes, and neurofurans[END_REF][START_REF] Song | Neurofurans, novel indices of oxidant stress derived from docosahexaenoic acid[END_REF] (NeuroFs) and dihomo-Isofurans [START_REF] De La Torre | Synthesis, discovery, and quantitation of dihomo-isofurans: biomarkers for in vivo adrenic acid peroxidation[END_REF] (dihomo-IsoFs) from DHA and AdA respectively.

Chemical synthesis of cyclic oxygenated metabolites

The total synthesis of cyclic oxygenated metabolites is of greatest importance for the general understanding of their in vivo formation and biological functions, but also to explore their potential diagnostic applications. Different strategies to produce PhytoPs, IsoPs, dihomo-IsoPs and NeuroPs have been reported in the literature by organic chemists around the world (see few reviews [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF][START_REF] Durand | Total syntheses of iso-, neuro-and phytoprostanes: new insight in lipid chemistry[END_REF][START_REF] Jahn | Recent approaches to the total synthesis of phytoprostanes, isoprostanes and neuroprostanes as important products of lipid oxidative stress and biomarkers of disease[END_REF]). All these strategies developed so far confirmed the biological importance of IsoPs, NeuroPs, and recently PhytoPs, and potential applications as biomarkers of oxidative stress in vivo. Lately, the successful synthesis of dihomoisofuran compounds did uncover their potential as novel oxidative stress biomarkers [START_REF] De La Torre | Synthesis, discovery, and quantitation of dihomo-isofurans: biomarkers for in vivo adrenic acid peroxidation[END_REF].

Cyclic oxygenated metabolites as biomarkers of lipid peroxidation

Eicosapentaenoic and docosahexaenoic acids

Among the identified n-3 fatty acids, EPA and DHA are the most notable ones for (patho)physiological functions. They are present in all human tissues at different levels, and DHA is foremost concentrated in the retina and brain. The structural occurrence of multiple double bonds allows the generation of oxygenated metabolites in the presence of free radicals. Oxidation of EPA can generate 6 series of F 3 -IsoPs, of which 96 racemic derivatives can be potentially measured in vivo (see above Scheme 1 for details) [START_REF] Nourooz-Zadeh | Evidence for the formation of F3isoprostanes during peroxidation of eicosapentaenoic acid[END_REF]. From DHA, a total of 128 theoretical compounds can be formed at basal oxygen level in vivo and these are categorized into 8 regioisomer series (4, 7, 10, 11, 13, 14, 17 or 20) of NeuroPs, in which levels of 4-and 20-series are eminently high in vivo compared to the 6 other series [START_REF] Roberts | Formation of isoprostane-like compounds (neuroprostanes) in vivo from docosahexaenoic acid[END_REF][START_REF] Yin | Regiochemistry of neuroprostanes generated from the peroxidation of docosahexaenoic acid in vitro and in vivo[END_REF]. The ratio between the type of oxygenated metabolites generated can also differ according to oxygen concentration, i.e. under hyperoxia NeuroFs are predominant over NeuroPs simply because of the differences in biosynthesis pathways (see above). At this stage, a total of 516 compounds of two families, each comprising 8 regioisomers, can be present in vivo [START_REF] Song | Neurofurans, novel indices of oxidant stress derived from docosahexaenoic acid[END_REF].

DHA is the main n-3 PUFA in vivo and is highly concentrated in the brain. It exists in the fetus through the maternal diet whereas it almost exclusively comes from food in humans. It is amenable to explore the role of NeuroPs and NeuroFs in the brain, however they were recently found to have multiple roles in other parts of the body, including the heart. Nevertheless, there is a smaller number of reports on NeuroPs and NeuroFs compared to IsoPs. To date, there is only a small number of synthetic standards that can be used for either gas chromatographymass spectrometry (GC-NICI-MS or GC-NICI-MS/MS) or liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS) (Table 1) [START_REF] Vigor | Non-Enzymatic Lipid Oxidation Products in Biological System: Assessment of the Metabolites from Polyunsaturated Fatty Acids[END_REF].

F 3 -Isoprostanes as oxidative stress biomarkers

The level of F 3 -isoprostanes (F 3 -IsoPs) is a reliable index of specific lipid peroxidation of EPA and could be considered for an evaluation of oxidative stress in biological systems. In comparison to other biomarkers, they are chemically stable but there is still a lack of knowledge to appreciate them as such. Only recently that biological roles of F 3 -IsoPs started to be investigated. In humans, stimulation of inflammation by injection of bacterial lipopolysaccharide (LPS) to healthy volunteers augmented urinary F 3 -IsoPs within 4-6 h and an intravenous injection to mice showed no effect on systemic arterial pressure [START_REF] Song | Novel eicosapentaenoic acid-derived F3-isoprostanes as biomarkers of lipid peroxidation[END_REF]. In dietary study, supplementation of fish oil to mice increased urinary F 3 -IsoPs [START_REF] Song | Novel eicosapentaenoic acid-derived F3-isoprostanes as biomarkers of lipid peroxidation[END_REF] and in LDLR -/-mice, it was found that western diet supplemented with EPA and/or DHA to reduce non-alcoholic steato-hepatitis (NASH) also increased urinary F 3 -IsoPs as compared to controls [START_REF] Depner | Docosahexaenoic acid attenuates hepatic inflammation, oxidative stress, and fibrosis without decreasing hepatosteatosis in a Ldlr-/-mouse model of western diet-induced nonalcoholic steatohepatitis[END_REF]. Other investigations showed the acute exposure of fish to hydrogen peroxide increased F 3 -IsoPs in muscles when compared to controls [START_REF] Chung | Profiling of oxidized lipid products of marine fish under acute oxidative stress[END_REF]. F 3 -IsoPs were also assessed in invertebrates such as Caenorhabditis elegans in different environments, i.e. oxidative and aging conditions. In the report, whole organism including mitochondria and peroxisomes were measured, and F 3 -IsoPs were shown to be elevated in conditions with mutated mitochondrial electron transport proteins, and in aged nematodes compared to young ones [START_REF] Labuschagne | Quantification of in vivo oxidative damage in Caenorhabditis elegans during aging by endogenous F3-isoprostane measurement[END_REF]. At cellular level, F 3 -IsoPs were also measured in Jurkat cells to evaluate the physical effect of microbubbles during sonoporation, and it was shown to be elevated when compared to non-treated cells [START_REF] Leung | Microbubble-mediated sonoporation amplified lipid peroxidation of Jurkat cells[END_REF].

Neuroprostanes and neurofurans as oxidative stress biomarkers

The measurement of F 4 -NeuroPs was initially performed in animals, such as normal rat and newborn pig brains, and the level was considerably higher in the cortex of the newborn pig brain [START_REF] Roberts | Formation of isoprostane-like compounds (neuroprostanes) in vivo from docosahexaenoic acid[END_REF]. Thereafter, F 4 -NeuroPs were identified, in particular occipital and temporal lobes of brain tissues of Alzheimer's disease (AD) patients [START_REF] Nourooz-Zadeh | F4-isoprostanes as specific marker of docosahexaenoic acid peroxidation in Alzheimer's disease[END_REF], and also in cerebrospinal fluid (CSF) of aneurismal subarachnoid hemorrhage patients. It was found to be nearly two-fold and ten-fold higher, respectively, compared to controls [START_REF] Roberts | Formation of isoprostane-like compounds (neuroprostanes) in vivo from docosahexaenoic acid[END_REF][START_REF] Hsieh | Correlation of F4-neuroprostanes levels in cerebrospinal fluid with outcome of aneurysmal subarachnoid hemorrhage in humans[END_REF]. These findings opened a new area of research in neurodegenerative diseases as the involvement of reactive oxygen species (ROS) and oxidative stress is highly hypothesized in their developments. Thereafter, most of the observational studies (Table 1) focused on brain tissues of patients of periventricular white matter injury, mild cognitive impairment and in late stage of AD, transgenic mice, and in rare disease models such as Smith-Lemli-Opitz syndrome [START_REF] Song | Neurofurans, novel indices of oxidant stress derived from docosahexaenoic acid[END_REF][START_REF] Reich | Brain regional quantification of F-ring and D-/E-ring isoprostanes and neuroprostanes in Alzheimer's disease[END_REF][START_REF] Back | Selective vulnerability of preterm white matter to oxidative damage defined by F2-isoprostanes[END_REF][START_REF] Montine | F2-isoprostanes in Alzheimer and other neurodegenerative diseases[END_REF][START_REF] Korade | Lipid biomarkers of oxidative stress in a genetic mouse model of Smith-Lemli-Opitz syndrome[END_REF]. It was recently reported that, in Mecp2 mutant mouse models of Rett syndrome (RTT), the brain concentration of F 4 -NeuroPs is elevated in symptomatic and pre-symptomatic phases, in which the latter can lead to the onset of overt behavioral abnormalities. Moreover, Mecp2-null animals had inversed relationships between F 4 -NeuroPs levels and brain weight and body weights [START_REF] De Felice | Oxidative brain damage in Mecp2-mutant murine models of Rett syndrome[END_REF]. RTT is a known neurodevelopment disorder by loss of function due to mutation in the gene encoding the methyl-CpG binding protein 2 (MECP2), and considered as a genetic model of infantile autism in female.

In a recent study, two specific regioisomers of F 4 -NeuroPs, 4(RS)-4-F 4t -NeuroP and 10-F 4t -NeuroP, were quantified in brain prefrontal and medial prefrontal cortex of preterm pigs and it was found that 4(RS)-4-F 4t -NeuroP was predominant, indicating that not all types of NeuroPs may be actively released under oxidative stress conditions. Not many data (Table 1) are yet available on NeuroFs. A quantitative method was recently developed [START_REF] Arneson | Measurement of products of docosahexaenoic acid peroxidation, neuroprostanes, and neurofurans[END_REF], and NeuroFs were measured in the brain cortex and cerebellum of AD transgenic mice and reported to be predominant in the cortex [START_REF] Song | Neurofurans, novel indices of oxidant stress derived from docosahexaenoic acid[END_REF]. An increase in oxygen tension to N 21% in newborn pigs has been shown to substantially increase levels of NeuroFs in the brain prefrontal cortex [START_REF] Solberg | Resuscitation with supplementary oxygen induces oxidative injury in the cerebral cortex[END_REF].

Evaluation in brain tissues in humans and rodents revealed F 4 -NeuroPs to be a valuable biomarker of neuronal disorders. Similar findings were found in plasma of Parkinson's disease patients. Seet et al. [START_REF] Seet | Oxidative damage in Parkinson disease: measurement using accurate biomarkers[END_REF] have shown that F 4 -NeuroP plasma levels of Parkinson's disease patients were elevated when compared to controls and were independent of the severity of the disease. In addition, plasma of adolescent RTT patients had increased levels of free F 4 -NeuroPs in comparison with healthy controls, and the levels correlated with the severity of the illness [START_REF] Signorini | F4-neuroprostanes mediate neurological severity in Rett syndrome[END_REF]. Aside from neurodegenerative diseases, onset of ischemic-stroke also showed to be associated with augmented plasma concentrations of free and esterified F 4 -NeuroPs, and the levels remained high after the onset, especially for the free form [START_REF] Seet | Oxidative damage in ischemic stroke revealed using multiple biomarkers[END_REF]. Levels of F 4 -NeuroPs were also investigated in cigarette smokers who had augmented plasma concentrations in comparison to controls. The concentration was further elevated in the smokers immediately after cigarette smoking session [START_REF] Seet | Biomarkers of oxidative damage in cigarette smokers: which biomarkers might reflect acute versus chronic oxidative stress? Free Radic[END_REF]. Furthermore, plasma of maternal and cord blood of pre-eclampsia women had higher F 4 -NeuroPs levels compared to normal pregnant women [START_REF] Barden | Is there a role for isofurans and neuroprostanes in pre-eclampsia and normal pregnancy?[END_REF]. Nevertheless, not all observational studies showed elevated in vivo F 4 -NeuroPs levels; it was suppressed in plasma of patients with influenza A, and remained lower than in controls at 3 months post-infection [START_REF] Ng | Does influenza A infection increase oxidative damage?[END_REF]. In cells, the effect of sonoporation in Jurkat cells showed no difference in F 4 -NeuroPs concentrations when compared to non-treated cells [START_REF] Leung | Microbubble-mediated sonoporation amplified lipid peroxidation of Jurkat cells[END_REF].

Neuroprostanes and neurofurans as biomarkers in metabolic studies

Intervention studies on NeuroPs were mainly conducted on analyses of their effects on specific areas of rodent brain and rare diseases (Table 2). Studies were highly focused on the effect of antiinflammatory and antioxidant agents in brain upon injury by chemical adulteration, and viral or bacterial infections. Both types of agents showed to be effective in reducing F 4 -NeuroPs levels after injury, in particular in the cerebrum [START_REF] Montine | Peripheral F2-isoprostanes and F4-neuroprostanes are not increased in Alzheimer's disease[END_REF][START_REF] Milatovic | Pharmacologic suppression of neuronal oxidative damage and dendritic degeneration following direct activation of glial innate immunity in mouse cerebrum[END_REF][START_REF] Milatovic | Suppression of murine cerebral F2-isoprostanes and F4-neuroprostanes from excitotoxicity and innate immune response in vivo by αor γ-tocopherol[END_REF][START_REF] Zaja-Milatovic | Pharmacologic suppression of oxidative damage and dendritic degeneration following kainic acid-induced excitotoxicity in mouse cerebrum[END_REF]. Levels of F 4 -NeuroPs in ischemicinduced rodent brain (cerebral cortex, hippocampus, gray matter) were also determined after α-lipoic acid treatment but no significant effect was found [START_REF] Quinn | Chronic dietary α-lipoic acid reduces deficits in hippocampal memory of aged Tg2576 mice[END_REF]. However, treatment with melatonin after brain ischemic injury reduced concentrations of F 4 -NeuroPs in both sides of prefrontal cortex, and particularly NeuroFs in the right side [START_REF] Balduini | The use of melatonin in hypoxic-ischemic brain damage: an experimental study[END_REF]. Likewise, tamoxifen also lowered F 4 -NeuroPs in brain striatum and cortex of ischemic-induced rodent brain [START_REF] Zhang | Neuroprotection by tamoxifen in focal cerebral ischemia is not mediated by an agonist action at estrogen receptors but is associated with antioxidant activity[END_REF]. Supplementation of Ataxiatelangiectasia -/ -mice with salen-manganese (catalytic scavenger of hydrogen peroxide and cytoprotective agent) was able to reduce both levels of F 4 -NeuroPs and NeuroFs in the forebrain and cerebellum, with a stronger effect on NeuroFs. Ataxia-telangiectasia also known as Louis-Bar Syndrome, is a recessive disease that can lead to cerebellar degeneration and genomic instability as well as suppression of immune functions [START_REF] Browne | Treatment with a catalytic antioxidant corrects the neurobehavioral defect in ataxia-telangiectasia mice, Free Radic[END_REF]. Such findings are important in alleviating oxidative stress role in neurological diseases related to brain prefrontal cortex, as it has been associated with bipolar disorders and schizophrenia, and to cognitive dysfunction [START_REF] Euston | The role of medial prefrontal cortex in memory and decision making[END_REF][START_REF] Andreazza | Specific subcellular changes in oxidative stress in prefrontal cortex from patients with bipolar disorder[END_REF].

In the transgenic mice model of AD (Tg 2576), the injection of carbon tetrachloride (CCl 4 ), a strong inducer of lipid peroxidation, raised levels of F 4 -NeuroPs and NeuroFs in the liver with a peak at 1 h and 2.5 h [START_REF] Song | Neurofurans, novel indices of oxidant stress derived from docosahexaenoic acid[END_REF]. This is comparable to data reported by Morrow et al. [START_REF] Morrow | Formation of novel non-cyclooxygenase-derived prostanoids (F2-isoprostanes) in carbon tetrachloride hepatotoxicity. An animal model of lipid peroxidation[END_REF] on F 2 -IsoPs, showing a raise in liver, 2 h after an oral administration of CCl 4 . Regardless of the type of rodent used in the model, it appears that the generation of F 4 -NeuroPs and NeuroFs is rapid, like for F 2 -IsoPs. Gladine et al. showed that liver samples of LDLR -/-mice supplemented with different doses of DHA had increased F 4 -NeuroP levels in a dose-dependent manner. The increase correlated with reduced plaque formation and atherosclerotic lesions, strongly suggesting that F 4 -NeuroPs might play an active role in atherosclerosis prevention [START_REF] Gladine | Lipid profiling following intake of the omega 3 fatty acid DHA identifies the peroxidized metabolites f4-neuroprostanes as the best predictors of atherosclerosis prevention[END_REF].

Aside from the brain and liver, F 4 -NeuroPs levels were measured in plasma of type 2 diabetic patients, before and after zinc supplementation and no significant change was observed [START_REF] Mori | Effect of eicosapentaenoic acid and docosahexaenoic acid on oxidative stress and inflammatory markers in treated-hypertensive type 2 diabetic subjects, Free Radic[END_REF]. The effect of hydrogen peroxide on these compounds was recently evaluated in marine fish, showing a rate of increase in F 4 -NeuroPs levels faster in males than in females [START_REF] Chung | Profiling of oxidized lipid products of marine fish under acute oxidative stress[END_REF].

Adrenic acid

AdA is the third most important PUFA in the brain, after DHA and ARA, and particularly in the myelin lipids. It is also abundant in the adrenal gland and kidney. AdA is not found in everyday diet but is formed from ARA by chain elongation. Similar to ARA, AdA is metabolized by COX into dihomo-PGs derivatives [START_REF] Tobias | The biosynthesis of 1a,1b-dihomo-PGE2 and 1a,1b-dihomo-PGF2α from 7,10,13,16-docosatetraenoic acid by an acetonepentane powder of sheep vesicular gland microsomes[END_REF][START_REF] Sprecher | Dihomo-prostaglandins and -thromboxane. A prostaglandin family from adrenic acid that may be preferentially synthesized in the kidney[END_REF][START_REF] Campbell | Synthesis of dihomoprostaglandins from adrenic acid (7,10,13,16-docosatetraenoic acid) by human endothelial cells[END_REF]. The non-enzymatic peroxidation of AdA leads to the release of dihomo-IsoP derivatives and was first reported by VanRollins et al. in 2008 [START_REF] Vanrollins | F2-dihomo-isoprostanes arise from free radical attack on adrenic acid[END_REF]. The F 2 -dihomo-IsoPs are present as 4 regio-isomers (7, 10, 14 or 17) in which 7-and 17-series are the most present in vivo. Recently, dihomo-IsoFs which can add up to 256 metabolites were discovered and quantified in pig brain samples [START_REF] De La Torre | Synthesis, discovery and quantitation of dihomo-isofurans: novel biomarkers of in vivo adrenic acid peroxidation[END_REF].

F 2 -dihomo-IsoPs and F 2 -dihomo-IsoFs as oxidative stress biomarkers

In 2008, the discovery of F 2 -dihomo-IsoPs showed in particular that the formation of F 2 -dihomo-IsoPs and F 4 -NeuroPs was of phospholipid origin and time-dependent (gray matter, white matter and myelin) [START_REF] Vanrollins | F2-dihomo-isoprostanes arise from free radical attack on adrenic acid[END_REF]. The ratio of AdA/DHA in the different samples was consistent with F 2 -dihomo-IsoPs to NeuroPs at homeostatic conditions, but after in vitro oxidation, the myelin lipids of the white matter consistently showed highest increases compared to the gray matter (154% vs 50% at 24 h). Furthermore, in urine of adult volunteers, F 2 -dihomo-IsoPs were not detected, whereas in brain tissues of Alzheimer's disease patients' frontal lobe white matter, a 2-fold higher level compared to healthy volunteers was reported.

In 2014, a novel isofuran derivative of AdA, termed dihomo-IsoF was synthesized; the compound 17(RS)-SC-Δ 15 -11-dihomo-IsoF [START_REF] De La Torre | Synthesis, discovery and quantitation of dihomo-isofurans: novel biomarkers of in vivo adrenic acid peroxidation[END_REF]; represents one of the 8 series of dihomo-IsoF (each series with its 32 potential isomers). Quantitation in brain of preterm pigs showed that, out of the isofuran derivatives of ARA, DHA and AdA, dihomo-IsoF was the highest and had level comparable to 4-F 4t -NeuroPs which can potentially be valuable for assessing neuronal disorders. Knowing that AdA level was more than 10 times lower than DHA, and that both PUFAs mainly represent gray and white matter, respectively, This suggests that both dihomo-IsoFs and 4-F 4t -NeuroPs should be used as complementary biomarkers when evaluating neuronal damage and disease.

F 2 -dihomo-IsoPs were also measured in RTT patients and found to be an early disease biomarker. It was shown that these metabolites were two-orders of magnitude elevated in plasma of first stage RTT patients compared to controls [START_REF] De Felice | F2-dihomo-isoprostanes as potential early biomarkers of lipid oxidative damage in Rett syndrome[END_REF]. These data indicate for the first time, that quantification of F 2 -dihomo-IsoPs in plasma can represent an early biomarker of the disease. Further research on RTT showed that 6 months of n-3 fish oil supplementation can dramatically reduce the clinical severity of the disease together with a significant decrease in all the examined oxidative stress biomarkers and mainly of F 2 -dihomo-IsoPs (by 82%) [START_REF] De Felice | Partial rescue of Rett syndrome by ω-3 polyunsaturated fatty acids (PUFAs) oil[END_REF].

α-Linolenic acid

ALA is an essential fatty acid and precursor in humans of the n-3 PUFAs such as EPA and DHA. It is found in algae and higher plants, and can be highly enriched in certain oils such as linseed oil (up to 65% total fatty acid (FA). Despite being an essential FA, it is a minor component of animal tissues and mainly used for energy, elongation and desaturation to a more complex PUFA, and oxygenated by lipoxygenases. ALA can be oxidized non-enzymatically to produce oxygenated cyclic compounds known as phytoprostanes (PhytoPs). They were first described in 1998 by Mueller and Parchmann in plants [START_REF] Parchmann | Evidence for the formation of dinor isoprostanes E1 from alpha-linolenic acid in plants[END_REF]. Only two series can be found, the 9th and 16th series, and so far the families found in plants are the F-, D-, E-, A, deoxy-J, B-and L-PhytoPs [START_REF] Imbusch | Analysis of oxidative stress and wound-inducible dinor isoprostanes F1 (phytoprostanes F1) in plants[END_REF][START_REF] Imbusch | Formation of isoprostane F(2)-like compounds (phytoprostanes F(1)) from alpha-linolenic acid in plants, Free Radic[END_REF][START_REF] Thoma | Cyclopentenone isoprostanes induced by reactive oxygen species trigger defense gene activation and phytoalexin accumulation in plants[END_REF][START_REF] Loeffler | B1-phytoprostanes trigger plant defense and detoxification responses[END_REF]. PhytoPs are known to be biomarkers of oxidative stress in plants and biologically active but their impact in humans is still unknown. The only study of PhytoPs in human was conducted by Barden et al. [START_REF] Barden | Flaxseed oil supplementation increases plasma F1-phytoprostanes in healthy men[END_REF] who found that supplementation of flaxseed oil (62% of ALA, 5.4 g/d) increased plasma levels of F 1 -PhytoPs as well as plasma ALA, but to a rather low extent. It is clear that PhytoPs remain to date under-investigated, as a potential biomarker of oxidative stress and it may be limited to plants and vegetable oils.

Bioactive lipids and potential signaling molecules

The biological activities of non-enzymatic-derived cyclic oxygenated metabolites are well recognized but the focus has been mainly on IsoPs (from ARA) [START_REF] Roberts | Isoprostanes[END_REF]. Of the F 2 -IsoPs, 15-F 2t -IsoP is the most studied where it is able to induce vasoconstriction and platelet activation. In addition, F 2 -IsoPs induces inflammation by expression of adhesion molecules (e.g. ICAM-1) leading to enhanced adhesion of monocytes, mitogenesis of smooth muscle cells and proliferation of fibroblasts. Collectively, they are all related to the pathogenesis of atherosclerosis and associated with cardiovascular diseases (see [START_REF] Jahn | Beyond prostaglandinschemistry and biology of cyclic oxygenated metabolites formed by free-radical pathways from polyunsaturated fatty acids[END_REF] for details regarding the mechanisms of action).

In contrast, the biological activities of n-3 derived IsoPs and NeuroP remain largely unexplored probably because of the difficulties linked to their chemical synthesis and their analysis in vivo. However, several lines of evidence in the literature showed that some peroxidized metabolites of n-3 PUFAs are bioactive molecules and substantially beneficial. The group of Sethi et al. was the first to demonstrate that peroxidation of EPA and DHA contributes to anti-inflammatory activities [START_REF] Sethi | Inhibition of phagocyte-endothelium interactions by oxidized fatty acids: a natural anti-inflammatory mechanism?[END_REF]. The authors showed that ex vivo oxidation of EPA and DHA (obtained with CuSO 4 and ascorbic acid) reduced the adhesion of U937 monocytes to endothelial cells and decreased the expression of adhesion molecules whereas EPA and DHA had no effect. The nature of peroxidized metabolites from EPA and DHA was not identified at this time but the authors demonstrated that the peroxidation of EPA and DHA was a mandatory prerequisite to make them bioactive on endothelial cells. The reduction of adhesion molecules expression was later linked to the inhibition of NFκB binding activity and associated with PPARγ dependent mechanism [START_REF] Sethi | Oxidized omega-3 fatty acids in fish oil inhibit leukocyte-endothelial interactions through activation of PPARα[END_REF]. Another study from the same group showed that endothelial cells exposed to oxidized EPA reduced the production of inflammatory cytokines (IL-8, MCP-1) [START_REF] Mishra | Oxidized omega-3 fatty acids inhibit NF-κB activation via a PPARα-dependent pathway[END_REF].

The bioactivity of oxidized EPA and DHA was also investigated in hepatocytes and found to be associated with ApoB100 degradation [START_REF] Pan | Lipid peroxidation and oxidant stress regulate hepatic apolipoprotein B degradation and VLDL production[END_REF] and iNOS expression [START_REF] Araki | Peroxidation of n-3 polyunsaturated fatty acids inhibits the induction of iNOS gene expression in proinflammatory cytokine-stimulated hepatocytes[END_REF]. Moreover, the impact of EPA and DHA on the ionic potential of cardiac function is well-defined [START_REF] Leaf | Prevention of sudden cardiac death by n -3 polyunsaturated fatty acids[END_REF] and it has been shown that this effect, at least in rat cardiac ventricular myocytes, is due to peroxidation of DHA [START_REF] Judé | Peroxidation of docosahexaenoic acid is responsible for its effects on ITO and ISS in rat ventricular myocytes[END_REF]. In support, one of the oxidized DHA product, 4(RS)-4-F 4t -NeuroP has been recently elucidated to have cardiac anti-arrhythmic properties and potentially be a therapeutic agent [START_REF] Le Guennec | Methods and pharmaceutical composition for the treatment and prevention of cardiac arrhythmias[END_REF].

Morrow and coworkers, pioneers in the in vivo identification of IsoPs and NeuroPs, were the first to speculate that EPA and DHA-related isoprostanes could be bioactive molecules involved in atherosclerosis prevention [START_REF] Saraswathi | Fish oil increases cholesterol storage in white adipose tissue with concomitant decreases in inflammation, hepatic steatosis, and atherosclerosis in mice[END_REF]. This hypothesis was more thoroughly investigated using an integrated approach associating a dose-response intervention study with DHA in LDLR -/-mice, targeted lipidomic analysis, and unbiased statistical analysis including correlation analyses, hierarchical cluster and projection to latent structure discriminate analysis [START_REF] Gladine | Lipid profiling following intake of the omega 3 fatty acid DHA identifies the peroxidized metabolites f4-neuroprostanes as the best predictors of atherosclerosis prevention[END_REF]. The main finding of this study was the identification of F 4 -NeuroPs that negatively correlated with plaque size and the best predictive variable of atherosclerosis prevention. Altogether, the results reinforced the hypothesis that F 4 -NeuroPs could contribute to the anti-atherogenic effects of DHA. In parallel, several in vitro experiments showed that EPA and DHA-related isoprostanes (namely 15-A 3t -IsoP, J 3 -IsoP, A 4 /J 4 -NeuroP and 4-F 4t -NeuroP) possessed potent anti-inflammatory properties linked notably to the inhibition of the NFκB and/or Nrf-2 pathways [START_REF] Gao | Novel n-3 fatty acid oxidation products activate Nrf2 by destabilizing the association between Keap1 and Cullin3[END_REF][START_REF] Musiek | Cyclopentenone isoprostanes inhibit the inflammatory response in macrophages[END_REF][START_REF] Brooks | The fatty acid oxidation product 15-A3t-Isoprostane is a potent inhibitor of NFκB transcription and macrophage transformation[END_REF][START_REF] Majkova | Omega-3 fatty acid oxidation products prevent vascular endothelial cell activation by coplanar polychlorinated biphenyls[END_REF]. However, contrasting outcome was found in supplementation of RTT patients with n-3 PUFA from fish oil in which plasma free F 4 -NeuroPs concentrations were lower when compared to controls. Also, the level of free F 4 -NeuroPs released was inversely associated with cardiac left ventricular systolic function in the RTT patients after fish oil supplementation [START_REF] Signorini | F4-neuroprostanes mediate neurological severity in Rett syndrome[END_REF][START_REF] De Felice | Partial rescue of Rett syndrome by ω-3 polyunsaturated fatty acids (PUFAs) oil[END_REF][START_REF] Maffei | Effects of omega-3 PUFAs supplementation on myocardial function and oxidative stress markers in typical Rett syndrome[END_REF].

The biological activities of PhytoPs have been mainly demonstrated in plants. They can trigger the first adaptive responses to oxidative stress by inducing notably the expression of genes involved in detoxification and secondary metabolism [START_REF] Mueller | Archetype signals in plants: the phytoprostanes[END_REF][START_REF] Durand | Isoprostanes and phytoprostanes: bioactive lipids[END_REF]. It is evidently shown in humans, where consumption of plant food sources rich in ALA or inhalation of pollen had relatively noticeable levels of PhytoP in vivo [START_REF] Karg | Biologically active oxidized lipids (phytoprostanes) in the plant diet and parenteral lipid nutrition[END_REF][START_REF] Traidl-Hoffmann | Pollen-associated phytoprostanes inhibit dendritic cell interleukin-12 production and augment T helper type 2 cell polarization[END_REF]. However, reports on bioactivity of PhytoPs in the mammalian systems are scarce and to date, findings mainly rely on in vitro experiments, despite their occurrence has been demonstrated in vivo in humans [START_REF] Barden | The effects of oxidation products of arachidonic acid and n3 fatty acids on vascular and platelet function[END_REF]. Nevertheless, different types of PhytoPs (mainly the cyclopentenone ring structure, A-, deoxy-J-, and their precursors E-and D-expect the B-type structures) have been shown to exert potent inflammatory regulation properties illustrated by the inhibition of nitric oxide production by LPS-stimulated mice macrophages (RAW 264.7) via NFkB inhibition [START_REF] Karg | Biologically active oxidized lipids (phytoprostanes) in the plant diet and parenteral lipid nutrition[END_REF], and by the decreased dendritic cell IL-12 production and stimulation of TH2 polarization of naïve T cells [START_REF] Gilles | Pollen-derived E1-phytoprostanes signal via PPAR-γ and NF-κBdependent mechanisms[END_REF]. Another study showed putative anti-aggregation properties of ent-16-F 1 -PhytoP [START_REF] Barden | Flaxseed oil supplementation increases plasma F1-phytoprostanes in healthy men[END_REF]. Recently, Minghetti et al. investigated the neuroprotective effects of B 1 -PhytoPs, by protecting undifferentiated neuronal cells (SH-SY5Y cells) against oxidative stress induced by hydrogen peroxide, and promoting myelination [START_REF] Minghetti | Nonenzymatic oxygenated metabolites of α-linolenic acid B1-and L1-phytoprostanes protect immature neurons from oxidant injury and promote differentiation of oligodendrocyte progenitors through PPAR-γ activation[END_REF].

Conclusions

In this review, we have discussed findings showing that nonenzymatically-derived cyclic oxygenated metabolites of n-3 and n-6 PUFA, i.e. isoprostanes, neuroprostanes, dihomo-isoprostanes and phytoprostanes can be useful oxidative stress biomarkers, especially in neuronal disorders and diseases, but can also exhibit bioactivities contributing to signaling and regulatory events in vivo. There is scope to explore how the relative prevalence of these oxygenated cyclic products of PUFA can elucidate the beneficial or detrimental effects of their precursor fatty acids in different (patho)physiological conditions.

Table 1

 1 Summary of observational studies reporting levels of neuroprostanes and neurofurans.

	Model of study	Sample	Metabolites measured Method of	Reference
				measurement
	Human
	Smokers and age-matched controls; Ischemic-stroke patients	Plasma	F 4 -NeuroPs	GC-NICI-MS	[38,39]
	and age-matched controls
	Pre-eclampsia patients and normal pregnant women	Plasma of maternal and umbilical cord blood	F 4 -NeuroPs	GC-NICI-MS	[40]
	High cardiovascular risk subjects	Plasma	F 4 -NeuroPs	GC-NICI-MS	Seet et al.
					(2013)
	Adolescent Rett Syndrome patients and age-and	Plasma	F 4 -NeuroPs	GC-NICI-MS/MS [37]
	gender-matched healthy controls
	Influenza A patients and age-matched controls	Plasma	F 4 -NeuroPs	GC-NICI-MS	[41]
	PD patients and age-matched healthy controls	Plasma	F 4 -NeuroPs	GC-NICI-MS	[36]
	Healthy subjects	Urine	7-F 4c -NeuroP	GC-NICI-MS	[88]
				LC-MS/MS
	Non-aSAH control patients and aSAH patients	CSF	F 4 -NeuroPs	GC-NICI-MS	[29]
	Patients with severe aSAH and TBI, and age-and	CSF	4(RS)-F 4t -NeuroP	GC-NICI-MS	[89]
	gender-matched healthy controls
	Normal and patients with aSAH	CSF	F 4 -NeuroPs	GC-NICI-MS	[90]
	AD and healthy controls	Brain: Occipital, temporal and parietal lobes	F 4 -NeuroPs	GC-NICI-MS	[28]
	AD patients and age-and gender-matched healthy controls	Post-mortem brain samples: superior and middle	Total (D 2 /E 2 -IsoPs +	GC-NICI-MS	[30]
		temporal gyri, hippocampus, inferior parietal	D 4 /E 4 -NPs)
		lobule and cerebellar cortex	F 4 -NeuroPs
	Early PWMI and age-matched controls	Post-mortem brain samples	F 4 -NeuroPs	GC-NICI-MS	[31]
	Healthy control, MCI, and late AD patients	Post-mortem brain samples of: frontal and occipital	F 4 -NeuroPs	GC-NICI-MS	[91]
		lobes, inferior parietal lobule, and hippocampus
	Animals
	AD and age-matched control; rats; newborn pigs	CSF, whole rat brain, brain cortex of newborn pig	F 4 -NeuroPs	GC-NICI-MS	[8]
	Fischer 344 rats	Young and old brains	F 4 -NeuroPs	GC-NICI-MS	Youssef et al.
					(2003)
	Tg 2576 mice: Transgenic mice model of AD	Brain cortex	F 4 -NeuroPs	GC-NICI-MS	[17]
			NeuroFs	LC-MS/MS
	Newborn pigs	Brain prefrontal cortex	F 4 -NeuroPs	GC-NICI-MS	[35]
			NeuroFs
	Dhcr7-KO Mice Dhcr7-KO (Dhcr7 tm1Gst/J ): genetic mouse model	Brain and liver	F 4 -NeuroPs	GC-NICI-MS	[33]
	of Smith-Lemli-Opitz syndrome
	Preterm pigs	Brain prefrontal and medial prefrontal cortex	F 4 -NeuroPs	LC-MS/MS	[18]
			NeuroFs
	Mecp2 mutant mouse models of Rett Syndrome including	Plasma and brain	F 4 -NeuroPs	GC-NICI-MS/MS [34]
	Mecp2-null (pre-symptomatic, symptomatic, and rescued)
	and Mecp2-308 mutated (pre-symptomatic and symptomatic)
	mice and wild type littermates

NeuroPs: neuroprostanes; NeuroP: neuroprostane; NeuroFs: neurofurans; GC-NICI-MS: gas chromatography-mass spectrometry, negative chemical ionization; LC-MS/MS: liquid chromatography tandem mass spectrometry; CSF: cerebrospinal fluid; AD: Alzheimer's disease; PWMI: periventricular white matter injury; MCI: mild cognitive impairment; PD: Parkinson's disease; aSAH: aneurysmal subarachnoid hemorrhage; TBI: traumatic brain injury.

Table 2

 2 Summary of metabolic studies reporting levels of neuroprostanes and neurofurans.

	Model of study and type of samples	Treatment	Metabolite measured Outcome of the study	Reference
	Human
	Type 2 diabetic patients and age matched controls: plasma Zinc supplementation	F 4 -NeuroPs	Supplementation did not change free or total (free + esterified) F 4 -NeuroPs levels. [92]
	Adolescent Rett Syndrome patients: plasma	ω-3 PUFA (fish oil)	F 4 -NeuroPs	Supplementation of ω-3 PUFA for 6 and 12 months decreased free F 4 -NeuroPs.	[37]
	Young children of Rett Syndrome patients: plasma	ω-3 PUFA (fish oil)	F 4 -NeuroPs	Supplementation of ω-3 PUFA for 6 months decreased free F 4 -NeuroPs	[60]
	Adolescent Rett Syndrome patients: plasma	ω-3 PUFA (fish oil)	F 4 -NeuroPs	Supplementation of ω-3 PUFA for 6 and 12 months	[80]
				decreased free F 4 -NeuroPs and was inversely
				correlated to left ventricular systolic velocity of blood flow.
	Rat
	Sprague-Dawley: cerebrum, plasma and urine	Subcutaneous injection of KA	F 4 -NeuroPs	Only, cerebrum F 4 -NeuroPs elevated 2 h post KA treatment.	[42]
				Plasma and urine were not affected by KA.
	Sprague-Dawley: brain	Ethanol withdrawal	F 4 -NeuroPs	F 4 -NeuroPs were elevated in the cerebral cortex and brainstems of rats	[93]
				with ethanol withdraw versus control.
	Sprague-Dawley: brain	Carbonfuran with/without memantine HCl and	F 4 -NeuroPs	Carbonfuran increased F 4 -NeuroPs alone and then inhibited by	[94]
		atropine sulfate		memantine HCl and atropine sulfate compared to non-treated rat.
	Ischemia-induced Sprague-Dawley: brain ipsilateral	Treatment with or without tamoxifen	F 4 -NeuroPs	Tamoxifen reduced ipsilateral cortex, contralateral striatum, striatum and	[48]
	striatum, ipsilateral cortex, contralateral striatum,			contralateral cortex F 4 -NeuroPs compared to non-treated rats.
	and contralateral cortex
	Wistar: brain	Manganese chloride	F 4 -NeuroPs	F 4 -NeuroPs levels of rats treated manganese chloride increased	[95]
				compared to control group.
	Hypoxia-ischemia induced Sprague-Dawley:	Melatonin	F 4 -NeuroPs	F [47]
	brain, prefrontal cortex		NeuroFs
	Mice
	C57BL/6: cerebrum	Pre-treated with indomethacin and ibuprofen for	F 4 -NeuroPs	F 4 -NeuroPs elevated after KA and LPS exposure, the latter had higher increase.	[42]
		2 weeks and then ICV injection with KA or LPS		Treatment of indomethacin or iburopfen reduced F 4 -NeuroPs.
	C57BL/6: cerebrum	1. ICV LPS with or without N-tert-butyl-α-	F 4 -NeuroPs	1. F 4 -NeuroPs elevated after LPS exposure and then inhibited by	[43-45]
		phenylnitrone and NSAIDs		N-tert-butyl-α-phenylnitrone and NSAIDs.
		2. ICV LPS with or without α-tocopherol		2. Elevated F 4 -NeuroPs by LPS reduced by α-tocopherol or γ-tocopherol.
		or γ-tocopherol		Kainic acid increased F 4 -NeuroPs and was reduced by
		3. ICV kainic acid with or without α-tocopherol,		α-tocopherol, N-tert-butyl-a-phenylnitrone, or ibuprofen.
		N-tert-butyl-a-phenylnitrone, or ibuprofen
	ATM -/-and ATM +/+: forebrain and cerebellum	Supplementation of EUK-189 is a low-molecular	F 4 -NeuroPs	Both F 4 -NeuroPs and NeuroFs decreased after supplementation	[49]
		weight salen-manganese for 84 days.	NeuroFs	compared to placebo but was statistically significant for NeuroFs only.
	BALB/c: brain	Intracerebral inoculation of either herpes simplex	F 4 -NeuroPs	F 4 -NeuroPs elevated after acute herpes simplex virus type 1 infection.	[96]
		virus type 1 or normal saline into the left
		cerebral hemisphere
	TTg2576: left forebrain cerebral cortex, hippocampus,	α-Lipoic acid supplementation.	F 4 -NeuroPs	No effect of α-Lipoic acid on F 4 -NeuroPs levels compared to non-treated mice.	[46]
	and deep gray matter
	C57B6J: brain cortex and cerebellum	Induced vitamin E deficiency	F 4 -NeuroPs	Lower α-tocopherol levels were associated with lower F 4 -NeuroPs.	[97]
	L-gulono-γ-lactone oxidase (C57BL/6J): brain, medial	Low and high dose of ascorbic acid supplementation F 4 -NeuroPs	Low L-gulono-γ-lactone oxidase mice with low ascorbic acid	[98]
	cortex and cerebellum			showed elevated F 4 -NeuroPs in cerebellum compared to high
				L-gulono-γ-lactone oxidase mice with high ascorbic acid and wild type.
	APPS we /PSEN1ΔE9 bigenic: cortical tissues	Low vitamins C and E, and high vitamins C and E	F 4 -NeuroPs	Treatment of low vitamins C and E but not high vitamins C and	[99]
		supplementation		E reduced F 4 -NeuroPs compared to control.
	Tg 2576, transgenic mice model of AD: liver samples	Carbon tetrachloride	F 4 -NeuroPs	Carbon tetrachloride injection increased F 4 -NeuroPs after 1 h	[17]
			NeuroFs	and after 2.5 h for NeuroFs compared to controls.
	Atherosclerosis (LDLR -/-): liver samples	DHA	F 4 -NeuroPs	Supplementation of DHA increased F 4 -NeuroPs in dose-dependent	[53]
				manner. This increase had inverse relationship with risk of atherosclerosis.
	Fish
	Marine (medaka): body muscle	Hydrogen peroxide	F 4 -NeuroPs	F 4 -NeuroPs elevated after 2 h and 6 h exposure in male and female	[25]
				medaka respectively.

[START_REF] Kadiiska | Biomarkers of oxidative stress study II: are oxidation products of lipids, proteins, and DNA markers of CCl4 poisoning? Free Radic[END_REF]

-NeuroPs decreased on both side of prefrontal cortex and NeuroFs decreased on right side of prefrontal cortex in rats treated with melatonin after 24 h from the hypoxia-ischemia injury.

NeuroPs: neuroprostanes; NeuroFs: neurosfurans; LPS: lipopolysaccharide; KA: Kainic acid; ICV: Intracerebroventricular; AD: Alzheimer's disease; NSAID: non-steroidal anti-inflammatory drug; DHA: docosahexaenoic acid; PUFA: polyunsaturated fatty acid; ATM: ataxia-telangiectasia mice.

Scheme 2. Summary of the biosynthesis of F 1 -PhytoPs, F 3 -IsoPs, F 2 -Dihomo-IsoPs, and F 4 -NeuroPs from their respective PUFA precursors. Scheme 3. Generation of substituted isoprostanes through stabilization of G 2 -IsoPs. Scheme 4. Summary biosynthetic pathway of neurofuran DHA.


Michael Baudoin
email: michael.baudoin@univ-lille1.fr

Jean-Claude Gerbedoen

Olivier Bou Matar

Nikolay Smagin

Antoine Riaud

Jean-Louis Thomas

Folding a focalized acoustical vortex on a flat holographic transducer: miniaturized selective acoustical tweezers

Acoustical tweezers based on focalized acoustical vortices hold the promise of precise contactless 3D manipulation of millimeter down to sub-micrometer particles, microorganisms and cells with unprecedented combined selectivity and trapping force. Yet, the widespread dissemination of this technology has been hindered by severe limitations of current systems in terms of performance and/or miniaturization and integrability. In this paper, we unleash the potential of focalized acoustical vortices by developing the first flat, compact, single-electrodes focalized acoustical tweezers. These tweezers rely on holographic Archimedes-Fermat spiraling transducers obtained by folding a spherical acoustical vortex on a flat piezoelectric substrate. We demonstrate the ability of these tweezers to grab and displace micrometric objects in a standard microfluidic environment with unique selectivity. The simplicity of this system and its scalability to higher frequencies opens tremendous perspectives in microbiology, microrobotics and microscopy.

INTRODUCTION

The precise contactless manipulation of physical and biological objects at micrometric down to nanometric scales promises tremendous development in fields as diverse as microrobotics, tissue engineering or micro/nanomedicine. In this regard, acoustical tweezers is a prominent technology since it is non-invasive, biocompatible [START_REF] Hultström | Proliferation and viability of adherent cells manipulated by standing-wave ultrasound in a microfluidic chip[END_REF][START_REF] Wiklund | Acoustofluidics 12: Biocompatibility and cell viability in microfluidic acoustic resonators[END_REF][START_REF] Burguillos | Microchannel acoustophoresis does not impact survival or function of microglia, leukocytes or tumor cells[END_REF], label-free and enables trapping forces several orders of magnitudes larger than their optical counterparts at same actuation power [START_REF] Baresch | Threedimensional acoustic radiation force on an arbitrarily located elastic sphere[END_REF][START_REF] Baresch | Observation of a single-beam gradient force acoustical trap for elastic particles: acoustical tweezers[END_REF]. First reported observations of particles levitation in acoustic wavefields date back to the work of Boyle and Lehmann [START_REF] Boyle | A new photographic method to demonstrate the interference of longitundinal wave trains. the velocity of high frequency sound in a liquid[END_REF]. Nevertheless, only recent simultaneous developments of advanced wave synthesis systems, microfluidic setups and theory of acoustic radiation pressure enabled to harness the potential of acoustophoresis [START_REF] Baresch | Observation of a single-beam gradient force acoustical trap for elastic particles: acoustical tweezers[END_REF][START_REF] Shi | Acoustic tweezers: patterning cells and microparticles using standing surface acoustic waves (ssaw)[END_REF][START_REF] Tran | Fast acoustic tweezers for the two-dimensional manipulation of individual particles in microfluidic channels[END_REF][START_REF] Ding | On-chip ma-nipulation of single microparticles, cells, and organisms using surface acoustic waves[END_REF][START_REF] Barnkob | Acoustic radiation-and streaming-induced microparticle velocities determined by microparticle image velocimetry in an ultrasound symmetry plane[END_REF][START_REF] Foresti | Acoustophoretic contactless transport and handling of matter in air[END_REF][START_REF] Peng | Cell separation using tilted-angle standing surface acoustic waves[END_REF][START_REF] Courtney | Independent trapping and manipulation of microparticles using dexterous acoustic tweezers[END_REF][START_REF] Ochiai | Three-dimensional mid-air acoustic manipulation by ultrasonic phased arrays[END_REF][START_REF] Marzo | Holographic acoustic elements for manipulation of levitated objects[END_REF][START_REF] Collins | Two-dimensional single-cell patterning with one cell per well driven by surface acoustic waves[END_REF][START_REF] Augustsson | Vlodman, Iso-acoustic focusing of cells for size-sensitive acousto-mechanical phenotyping[END_REF][START_REF] Ng | Acoustic tweezing of particles using decaying opposing travelling surface acoustic waves (dotsaw)[END_REF][START_REF] Riaud | Selective manipulation of microscopic particles with precursos swirling rayleigh waves[END_REF]. Until recently, the vast majority of acoustical tweezers relied on a single or a set of orthogonal standing waves that create a network of nodes and antinodes where particles are trapped [7-12, 14, 16-18]. These systems are highly efficient for the collective manipulation of particles and cells but the multiplicity of traps and the agglomeration of several particle at the same node or antinode preclude any selectivity. While limited localization of the acoustic energy can be achieved by the original sub-time-of-flight technics [START_REF] Collins | Acoustic tweezers via sub-time-of-flight regime surface acoustic waves[END_REF], only strong focalization of wavefields enables selectively at the single particle level. Focalized acoustic waves are natural candidates to achieve this localization [START_REF] Lee | Single beam acoustic trapping[END_REF][START_REF] Li | A simple method for evaluating the trapping performance of acoustic tweezers[END_REF][START_REF] Hwang | Cell deformation by single-beam acoustic trapping: A promising tool for measurements of cell mechanics[END_REF], but many particles of practical interest migrate to the nodes of standing wavefields like rigid particles and cells [START_REF] Gor | On the forces acting on a small particle in an acoustical field in an ideal fluid[END_REF][START_REF] Settnes | Forces acting on a small particle in an acoustical field in a viscous fluid[END_REF] and are thus expelled from the wave focus. This radial expelling and the condition to get a restoring axial force are the main difficulties that thwarted research on selective acoustical tweezers. The combination of strong localization and the existence of a minimum of the pressure wavefield at the focus point surrounded by a bright ring is fulfilled by so-called cylindrical or spherical acoustical vortices, some helical waves spinning around a phase singularity [START_REF] Nye | Dislocations in wave trains[END_REF][START_REF] Hefner | An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems[END_REF][START_REF] Thomas | Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices[END_REF][START_REF] Baresch | Spherical vortex beams of high radial degree for enhanced single-beam tweezers[END_REF]. These waves are the separate variable solutions of Helmholtz equation in cylindrical and spherical coordinates respectively. The former are invariant in the z-direction and thus enable only 2D particle trapping, while focalized spherical vortices enable 3D particle trapping with a single beam, as first demonstrated theoretically by Baresch et al. [4,[START_REF] Baresch | Spherical vortex beams of high radial degree for enhanced single-beam tweezers[END_REF], following recent developments in the theory of acoustic radiation force [START_REF] Marston | Axial radiation force of a bessel beam on a sphere and direction reversal of the force[END_REF][START_REF] Marston | Radiation force of a helicoidal bessel beam on a sphere[END_REF]. A wealth of systems [START_REF] Baresch | Observation of a single-beam gradient force acoustical trap for elastic particles: acoustical tweezers[END_REF][START_REF] Courtney | Independent trapping and manipulation of microparticles using dexterous acoustic tweezers[END_REF][START_REF] Marzo | Holographic acoustic elements for manipulation of levitated objects[END_REF][START_REF] Riaud | Selective manipulation of microscopic particles with precursos swirling rayleigh waves[END_REF][START_REF] Thomas | Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices[END_REF][START_REF] Riaud | Taming the degeneration of bessel beams at an anisotropic-isotropic interface: Toward threedimensional control of confined vortical waves[END_REF][START_REF] Riaud | Anisotropic swirling surface acoustic waves from inverse filtering for on-chip generation of acoustic vortices[END_REF][START_REF] Riaud | Saw synthesis with idts array and the inverse filter: toward a versatile saw toolbox for microfluidic and biological applications[END_REF][START_REF] Jiang | Convert acoustic resonances to orbital angular momentum[END_REF][START_REF] Jimenez | Formation of high order acoustic bessel beams by spiral diffraction gratings[END_REF][START_REF] Terzi | Generation of a vortex ultrasonic beam with a phase plate with an angular dependence of the thickness[END_REF] have been proposed since the seminal work by Marston [START_REF] Hefner | An acoustical helicoidal wave transducer with applications for the alignment of ultrasonic and underwater systems[END_REF] for the synthesis of acoustical vortices. Nevertheless the ability to obtain a 3D trap and to pick up one particle independently of its neighbors was only demonstrated recently by Baresch et al [START_REF] Baresch | Observation of a single-beam gradient force acoustical trap for elastic particles: acoustical tweezers[END_REF] .This operation requires a strong focalization of the acoustical vortex [START_REF] Baresch | Spherical vortex beams of high radial degree for enhanced single-beam tweezers[END_REF]. In addition, all acoustical vortices synthesis systems developed up to date rely on either arrays of transducers [START_REF] Baresch | Observation of a single-beam gradient force acoustical trap for elastic particles: acoustical tweezers[END_REF][START_REF] Courtney | Independent trapping and manipulation of microparticles using dexterous acoustic tweezers[END_REF][START_REF] Marzo | Holographic acoustic elements for manipulation of levitated objects[END_REF][START_REF] Thomas | Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices[END_REF][START_REF] Riaud | Taming the degeneration of bessel beams at an anisotropic-isotropic interface: Toward threedimensional control of confined vortical waves[END_REF][START_REF] Riaud | Anisotropic swirling surface acoustic waves from inverse filtering for on-chip generation of acoustic vortices[END_REF] or passive systems [START_REF] Jiang | Convert acoustic resonances to orbital angular momentum[END_REF][START_REF] Jimenez | Formation of high order acoustic bessel beams by spiral diffraction gratings[END_REF][START_REF] Terzi | Generation of a vortex ultrasonic beam with a phase plate with an angular dependence of the thickness[END_REF] that are cumbersome, hardly miniaturizable and not compatible with microscopes or microfluidics chips. Recently, Riaud et al. [START_REF] Riaud | Selective manipulation of microscopic particles with precursos swirling rayleigh waves[END_REF] showed that it is possible to generate cylin-drical acoustical vortices with swirling surface acoustic waves synthesized with spiraling InterDigitated Transducers (IDTs) printed at the surface of a piezoelectric substrate. This system is flat, transparent, compatible with disposable substrates and its fabrication with standard lithography is straightforward to miniaturize and cheap as proved by its widespread use in modern electronic devices [START_REF] Emanetoglu | Epitaxial zno piezoelectric thin films for saw filters[END_REF]. This wave synthesis system nevertheless suffers from major limitations: (i) lateral focalization of cylindrical acoustical vortices is weaker than 3D focalization of their spherical counterparts and leads to the existence of spurious secondary rings of weaker amplitude (see Fig. 2.e) that can also trap particles, hence severely limiting the tweezers selectivity, (ii) the anisotropy of piezoelectric substrates leads to an anisotropy of surface waves and hence of the trapping force, (iii) 3D trapping is not possible with cylindrical acoustical vortices. In summary, the swirling SAW technology has come with its own set of challenges and limitations, and a paradigm shift is needed to reach true selectivity without compromising on miniaturization.

In this paper, we harness the potential of selective acoustical tweezers by folding an isotropic focalized acoustical vortex on a flat surface and synthesize it with single spiraling interdigitated electrodes reminiscent of a Archimedes-Fermat spiral. The radial contraction of the spiral enables wave focusing without the requirement of a curved transducer or a lens, a major advantage compared to existing systems. In addition the limitations of the cylindrical vortex based tweezers are overcome. We demonstrate the high selectivity of this tweezer (i) by measuring the acoustic field with a laser interferometer and quantifying the fast radial decrease of secondary rings and (ii) by selectively trapping and moving one particle independently of its neighbors in a standard microfluidic environment.

MATERIALS AND METHODS

Theory: Folding a spherical acoustical vortex on a flat surface.

Spherical acoustical Bessel beams (spherical vortices) constitute excellent candidates to create localized acoustic trap. Indeed, these acoustic fields both focalize the acoustic energy in 3D and create a shadow zone at the center of the vortex surrounded by a bright shell, wherein particles can be trapped [START_REF] Baresch | Spherical vortex beams of high radial degree for enhanced single-beam tweezers[END_REF]. In the same way that a plane standing wave can be seen as the combination of two counter-propagating traveling waves, a spherical Bessel beam results from the interference between a converging and a diverging spherical Hankel beam (of the first and second kind respectively). Hence a Bessel beam can be produced by a single Hankel converging beam, which will interfere with its diverging counterpart generated at the focus, i.e. at the vortex central singularity. In this paper, we demonstrate that converging Hankel beams can be synthesized by materializing the intersections between some isophases surfaces and a plane, with metallic electrodes sputtered at the surface of a piezoelectric substrate (see Fig. 1 a.). Indeed, the electric excitation of these electrodes provokes localized vibrations of the piezoelectric substrate, which in turn produce a bulk acoustic vortex inside a glass slide. This original holographic method combines the underlying physical principles of Fresnel lenses in optics (wherein an isophase is folded on a flat surface), the specificity of Bessel beams topology and the principles of wave synthesis with IDTs in the field of microelectronics.

The general expression of a Hankel spherical vortex in the complex plane is given by Ψ * (r, θ, ϕ) = Ah l P m l (cos(θ))e i(-mϕ+ωt) , with r, θ, ϕ the spherical coordinates, k = ω/c a the wave number, c a the sound speed, A > 0 the wave amplitude, P m l the Legendre polynomial of order (l, m), ω the frequency, t the time and h l the spherical Hankel function of the first kind. To compute the intersection of the Hankel beam with a plane, we introduce the cylindrical coordinates ρ, ϕ, z, with: r = ρ 2 + z 2 and z the axis normal to the plane (see Fig. 1.c). For the sake of simplicity we also introduce the dimensionless parameters r = kr, ρ = kρ, z = kz. In the far field (z 1 and thus r 1), Hankel functions of the first kind can be approximated by h l (r) = (-i) l+1 e ir /r and thus isophases of Ψ * are simply given by the equation:

φ = arg(Ψ * ) = arg(h l (r)) + arg(e i(-mϕ+ωt) ) (1) ≈ r -(l + 1) π 2 -mϕ + ωt = C 1
with C 1 a constant. Since t and the constant (left hand side) are arbitrary chosen, this equation reduces to the simple expression: φ = rmϕ = C 2 , with r = ρ2 + z2 and C 2 a constant. Because of the piezoelectric effect, the mechanical vibrations of the bulk acoustic waves are coupled to the electrical potential. Following the principle of wave synthesis with IDTs, we model the electrodes as perfect wires (isopotential lines). If we consider two spirals in opposition of phase (∆φ = π), we obtain the following polar equations of the metallic tracks:

ρ = (mϕ + C 2 ) 2 -z2 and ρ = (mϕ + C 2 + π) 2 -z2
(2) These simple equations correspond to spirals, as represented on Fig. 1.b (with z = 55.4, m = 1). It is an intermediate situation between the Fermat spiral (ρ ∝ ϕ 2 ) and the Archimedes spiral (ρ ∝ ϕ). The radial distance between consecutive elecrodes decreases progressively (as shown by the second derivative of these equations) and the spirals converge asymptotically toward Archimedes arithmetic spirals of equation ρ = mϕ + K (with K = 0 or π). This geometric regression of the radial distance between consecutive tracks ensures the beam focusing. A pure Archimedes spiral would generate a cylindrical vortex invariant in the z direction, while a pure Fermat spiral would require an infinitely thick substrate. We can note that equation ( 2) is only a far-field approximation of the exact solution of the problem. The exact shape of the spirals can be obtained by solving directly the nonlinear equation [START_REF] Hultström | Proliferation and viability of adherent cells manipulated by standing-wave ultrasound in a microfluidic chip[END_REF]. We solved numerically this equation with an interior-point method and observed that the approximate and exact spirals only differ in the vicinity of the spiral center (see Image I1 in SM). Since the center of the spiral is not materialized in the present tweezers (to leave space for visualization), this difference does not affect the synthesized wavefield.

Experimental design of the tweezer. Experimentally, a system was designed to synthesize focalized vortices of topological order (l, m) = (1, 1) at frequency f = ω/2π = 4.4 MHz. This system relies on spiraling metallic electrodes sputtered at the surface of a 0.5mm thick Y-36 Niobate Lithium (LiNbO3) piezoelectric substrate following a standard lift-off procedure: (i) a negative mask with the electrodes represented on Fig. 1.b is obtained with high resolution printing, (ii) a sacrificial layer (photoresist AZnLOF2020) of thickness 3 µm is deposited on the substrate and patterned using conventional photholithography technique, (iv) a titanium (Ti) layer of 20 nm and a gold (Au) layer of 200 nm are successively sputtered on the LiNbO3 substrate and (v) the sacrificial layer is washed out with N-Methyl-2-pyrrolidone (NMP) based solvent stripper. The vibration of these spiraling electrodes driven by a TEKTRONIX AFG3051C waveform generator and a AR150A250 amplifier instills a converging Hankel beam inside a borofloat glass slide of 6.5 mm thickness glued at the surface of the piezoelectric substrate with EPO-TEK 301-2 (see Fig. 1a). The properties of the glass slide is chosen to match the acoustic properties of a mobile borofloat glass coverslip of 150 µm thickness supporting a PDMS channel of 300 µm depth glued with O 2 plasma. The microfluidic chip (glass coverslip + PDMS chamber) containing the particles is coupled with the glass slide with a drop of oil and moved with a manual precision displacement setup (Fig. 1e.). The electrodes are designed (i) to generate transverse waves of speed c T into the glass slide, (ii) to obtain a focalization at the surface of the coverslip and thus enable optimal wave localization in the microfluidic chamber and (iii) to obtain a transducer aperture of 64 o . Transverse waves in the glass were chosen owing to their lower sound speed (c T = 3280ms -1 ), which ensures better transmission of the acoustic energy from the glass to the liquid. The resulting acoustic field at the surface of the glass coverslip (focal plane, z=0) was measured with a UHF-120 Polytec laser vibrometer Numerical prediction of the resulting acoustic field.

Predictions of the acoustic field expected at the surface of the glass coverslip (in contact with the liquid) were obtained by propagating the vibrations produced by the spiraling transducers in the glass slide and coverslip with an angular spectrum code [START_REF] Booker | The concept of angular spectrum of plane waves, and its relation to that of polar diagram and aperture distribution[END_REF]. This latter method relies on (i) the 2D spatial Fourier transform of a wave field in a source plane (electrode plane), (ii) the propagation of each corresponding plane wave in the Fourier space to a target plane and (iii) the inverse Fourier transform of the

RESULTS

We first compared the field measured experimentally to numerical predictions obtained from angular spectrum (see Fig. 2a-d and movie M1 in SM). Excellent agreement between numerical predictions and experiments is obtained for both the intensity (Fig. 2.a and b) and the phase (Fig. 2.c andd) of the wavefield. In addition, the radial evolution of the rings intensity (in the (x, y) plane) measured experimentally and averaged over all angles ϕ (black continuous line) is compared to (i) the radial evolution of a cylindrical vortex (red dashed line) and (ii) the radial evolution of a spherical vortex (blue dashed-dotted line on Fig. 2e). This figure shows (i) that the radial evolution of the vortex intensity measured experimentally closely follows the one of a spherical vortex and (ii) that the intensity of secondary rings decreases much faster for spherical vortices (∝ 1/r 2 ) than for cylindrical vortices (∝ 1/r). Since radiation pressure is proportional to the intensity of the beam, it means that the selectivity is greatly enhanced by the axial focusing of the beam, compared to cylindrical vortices. Thus 3D focalization of the energy is a major advantage for selective manipulation of particles. The slight differences between the experimentally measured field and the spherical Bessel function can be explained by the fact that we do not literally synthesize a spherical Bessel vortex. Indeed the phase of our signal matches the one of a spherical vortex but not the radial evolution of the amplitude.

To demonstrate the selectivity of this acoustical tweezer, i.e. its ability to pick up one particle and move it independently of its neighbors, we dispersed some monodisperse polystyrene particles of 75 ± 2 µm radius inside a microfluidic chamber of 300 microns height and then picked one particle and moved it around between the other particles. The power of our beam was chosen to produce a sufficient force to move the target particle while keeping the second ring magnitude sufficiently weak not to be able to trap particles. Fig. 3.a and movie M2 in SM clearly show that as long as the distance between the transported particle and the other particles remains larger than the radius of the first ring, only the trapped particles moves. Of course, when the first ring touches a particle located outside it, then the particle is pushed away since the rings are repulsive. It is important to note that, in this video, the center of the vortex is located at the tip of the bottom arrow where the particle is trapped (as demonstrated by the scan of the acoustic field, Movie M3 in SM). We additionally demonstrated the tweezers ability to precisely position a set of 18 polystyrene particles of 75 ± 2 µm radius in a prescribed pattern (MOV: Moving with Vortices), starting from randomly distributed particles (see Fig. 3b-c).

DISCUSSION

Acoustic tweezers have long faced a trade-off between selectivity and miniaturization/integrability. These restrictions have so far prevented the development of many applications in microfluidics and microbiology. In this paper, these limitations are overcome by unifying the physical principles of (i) acoustic trapping with spherical vortices, (ii) holographic wave synthesis with interdigitated transducers and (iii) Fresnel lenses, inside a single compact transparent miniaturized device. With this microsystem, we demonstrate the contactless manipulation of particles in a standard microscopy environment with state of the art selectivity. Owing to the simplicity of the technology and its scalability to higher frequencies, this work paves the way towards individual manipulation and in-situ assembly of physical and biological micro-objects.

FIG. 1

 1 FIG. 1. a. Scheme illustrating the composition of the Archimedes-Fermat acoustical tweezers: A focalized acoustical vortex is synthesized by spiraling metallic electrodes sputtered at the surface of a piezoelectric substrate. The vortex propagates and focalizes inside a glass slide (sealed with the piezoelectric substrate) and a mobile glass coverslip before reaching the liquid contained in a PDMS chamber, wherein the particle is trapped. The mobility of the microfluidic chip (glass coverslip + sealed PDMS chamber) is enabled by a liquid couplant and a manual precision displacement setup represented on Fig.e.. b. Spiraling pattern of the electrodes obtained from approximate equation (2) with z = 55.4 and m = 1. c. Scheme introducing the spherical (r, θ, ϕ) and cylindrical coordinates (ρ, ϕ, z) used for the demonstration of equation (2). d. Comparison of the compactness of the Archimedes-Fermat acoustical tweezers presented in this paper (left) to the transducer array of ref. [5] (right). This figure also shows the transparency of the Archimeded-Fermat acoustical tweezers (particles are trapped on the central axis of the transducer). e. Picture showing the integration of the Archimedes-Fermat acoustical tweezers into a Leica Z16 macroscope. Four tweezers have been patterned on a 3 inch LiNb03 wafer.

2 FIG. 2

 22 FIG. 2. a. Numerical predictions with angular spectrum and b. experimental measurements with a UHF-120 Polytec laser interferometer of the normalized intensity of the vibration at the surface of the glass coverslip (focal plane, (z = 0)). The maximum amplitude measured experimentally (on the first ring) is 10nm. c.Numerical predictions with angular spectrum and d. experimental measurements with the laser interferometer of the phase of the acoustic wave at the surface of the glass coverslip. e. Radial evolution of the normalized intensity of the acoustic wave from the center of the vortex to the side, as a function of the lateral radius r in mm. Black solid line: average over all angles ϕ of the intensity measured experimentally. Red dashed line: evolution expected for a cylindrical vortex (cylindrical Bessel function). Blue dashed-dotted line: evolution expected for a spherical vortex (spherical Bessel). Red dotted line: asymptotic evolution in 1/r. Blue dotted line: asymptotic evolution in 1/r 2 . f. Evolution of the field intensity (up) and phase (down) in the z direction. The direction of the arrow indicates the wave propagation direction. Left to right: distances z = 6, 4, 2, 0 mm respectively (z = 0 corresponds to the focal plane). The upper part of the figure shows the focalization of the acoustic energy and the formation of a localized trap. The lower part shows the transition from a Hankel to a Bessel spherical beam.

FIG. 3

 3 FIG. 3. a. Selective manipulation of a 75 ±2µm radius polystyrene particle with the 4.4 MHz selective acoustical tweezers based on Archimedes-Fermat spirals. This figure shows that only the particle trapped at the center of the vortex (located just above the lowest arrow as shown on movie M3 in SM) is moved while the other particles remain still. The particles at rest have been colored to improve the readability of the figure. See also supplementary movie M2 in SM. b.c. Patterning of 18 polystyrene particles (radius 75 ±2µm) into prescribed position to form the letters MOV (Moving Object with Vortices). b. Initial state: particles randomly dispersed. c. Final states: organized particles.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at ... Image S1: Comparison of the shape of the electrodes obtained by approximated equation ( 2