PhD Alexis Broisat
email: alexis.broisat@inserm.fr

PhD Jakub Toczek

PhD Laurent Dumas

MSc Mitra Ahmadi

PhD Sandrine Bacot

PhD; Pascale Perret

PhD Lotfi Slimani

Gilles Barone-Rochette

Audrey Soubies

Nick Devoogdt

PhD Gilles Barone- Rochette

; Audrey Soubies

PhD Tony Lahoutte

PhD; Daniel Fagret

PhD; Laurent M Riou

PhD Catherine Ghezzi

99mTc-cAbVCAM1-5 Imaging Is a Sensitive and Reproducible Tool for the Detection of Inflamed Atherosclerotic Lesions in Mice

Keywords: 99m Tc-cAbVCAM1-5, Atherosclerosis, VCAM-1, Molecular Imaging

Introduction.

Atherosclerosis constitutes a worldwide health challenge [START_REF] Sanz | The year in atherothrombosis[END_REF]. Despite major advances in imaging technologies [START_REF] Libby | The vascular biology of atherosclerosis and imaging targets[END_REF], a major need for imaging probes targeting vulnerable plaques (VP) still exists. Such a tool could be used for diagnosis and prognosis as well as for the monitoring of treatment efficacy [START_REF] Berman | Emerging anti-inflammatory drugs for atherosclerosis[END_REF]. A major criterion for the identification of VP is inflammation [START_REF] Fuster | Atherothrombosis and high-risk plaque: part I: evolving concepts[END_REF]. Vascular cell adhesion molecule 1 (VCAM-1) plays a major role in the infiltration of inflammatory cells into atherosclerotic lesions [START_REF] O"brien | Neovascular expression of Eselectin, intercellular adhesion molecule-1, and vascular cell adhesion molecule-1 in human atherosclerosis and their relation to intimal leukocyte content[END_REF]. Indeed, in human atherosclerotic lesions, VCAM1 expression was observed at the level of the luminal endothelium as well as on neovessels, macrophages and activated smooth muscle cells of advanced lesions [START_REF] O"brien | Neovascular expression of Eselectin, intercellular adhesion molecule-1, and vascular cell adhesion molecule-1 in human atherosclerosis and their relation to intimal leukocyte content[END_REF][START_REF] O"brien | Vascular cell adhesion molecule-1 is expressed in human coronary atherosclerotic plaques. Implications for the mode of progression of advanced coronary atherosclerosis[END_REF][START_REF] Davies | The expression of the adhesion molecules ICAM-1, VCAM-1, PECAM, and E-selectin in human atherosclerosis[END_REF]. Therefore, the assessment of VCAM-1 expression levels in atherosclerotic plaques could potentially be highly relevant in order to identify prone-torupture lesions [START_REF] Naghavi | From vulnerable plaque to vulnerable patient: a call for new definitions and risk assessment strategies: Part II[END_REF]. Due to the small size and location of VP, imaging agents with optimal characteristics are required. Single domain antibody (sdAb)-derived radiotracers, that have originally been developed in the field of oncology [START_REF] Xavier | Synthesis, preclinical validation, dosimetry, and toxicity of 68Ga-NOTA-anti-HER2 Nanobodies for iPET imaging of HER2 receptor expression in cancer[END_REF], have recently been proposed by our group as a new class of imaging agents with optimal characteristics for cardiovascular imaging [START_REF] Broisat | Nanobodies targeting mouse/human VCAM1 for the nuclear imaging of atherosclerotic lesions[END_REF]and the radiolabelled anti-VCAM-1 camel antibody fragment 99m Tc-cAbVCAM1-5 compound was selected among 10 VCAM-1-specific sdAbas the most potent candidate.

Accordingly, aortic plaques were successfully visualized non-invasively by single photon emission computed tomography (SPECT) in an Apolipoprotein E (ApoE) deficient mouse model of atherosclerosis, with binding specificity being further demonstrated by in vivo competition experiments. Importantly, the production and selection processes of VCAM-1 sdAbwere specifically designed to produce cross-reactive,murine & human binders. The nanomolar affinity of 99m Tc-cAbVCAM1-5 for both human and murine VCAM-1 therefore makes the tracerpotentially suitable for clinical translation [START_REF] Broisat | Nanobodies targeting mouse/human VCAM1 for the nuclear imaging of atherosclerotic lesions[END_REF].

The main objective of the present study was to investigate the sensitivity of 99m Tc-cAbVCAM1-5 for the imaging of VCAM-1 expression in murine atherosclerotic lesions. Indeed, high sensitivity is a key requirement for VP imaging as well as for the preclinical assessment of the efficacy of novel anti-atherogenic therapies. In accordance with the major role of inflammatory processes in the development of VP, the anti-inflammatory effect of new therapeutic agents targeting at the lipid profile such as cholesteriylesterasetransfert protein inhibitors is currently being investigated [START_REF] Barter | Cholesteryl ester transfer protein inhibition as a strategy to reduce cardiovascular risk[END_REF]. In addition, therapeutic interventions aimed at directly targeting the inflammatory process are also under evaluation(3) using drugs such as methotrexate, canakinumab or losmapimod [START_REF] Elkhawad | Effects of p38 mitogen-activated protein kinase inhibition on vascular and systemic inflammation in patients with atherosclerosis[END_REF][START_REF] Everett | Rationale and design of the Cardiovascular Inflammation Reduction Trial: a test of the inflammatory hypothesis of atherothrombosis[END_REF][START_REF] Ridker | Interleukin-1β inhibition and the prevention of recurrent cardiovascular events: rationale and design of the Canakinumab Antiinflammatory Thrombosis Outcomes Study (CANTOS)[END_REF]. A specific and sensitive imaging agent targeting at the inflammatory process occurring in atherosclerotic lesions would therefore be of great relevance for the evaluation of novel anti-atherogenic agents.

Statins are well established and widely used therapeutics in clinical practice, and atorvastatin has previously been employed for the evaluation of new imaging agents in mouse models of atherosclerosis [START_REF] Bot | Atorvastatin inhibits plaque development and adventitial neovascularization in ApoE deficient mice independent of plasma cholesterol levels[END_REF][START_REF] Khanicheh | Noninvasive ultrasound molecular imaging of the effect of statins on endothelial inflammatory phenotype in early atherosclerosis[END_REF][START_REF] Nahrendorf | Noninvasive vascular cell adhesion molecule-1 imaging identifies inflammatory activation of cells in atherosclerosis[END_REF].In the present preclinical study, atorvastatin was used in order to evaluate the potential of 99m Tc-cAbVCAM1-5for the monitoring of treatment efficacy in ApoE deficient mice.

Methods

Animal model

All experimental procedures werein accordance with institutional guidelines and approved by the Animal Care & Use committee (ComEth) of the University ofGrenoble.

Twelve [START_REF] Elkhawad | Effects of p38 mitogen-activated protein kinase inhibition on vascular and systemic inflammation in patients with atherosclerosis[END_REF] 40-wks old female ApoE-deficient mice (Charles River) fed a western type diet were used for the ex vivo comparison between 99m Tc-cAbVCAM1-5 uptake in atherosclerotic lesions and VCAM-1 expression.

Eighteen female ApoE-deficient mice were used for the non invasive evaluation of a reference therapy.At the age of 15 weeks, mice were either fed a western diet (control group, n=9) or a western diet supplemented with a reference therapy (0.01% atorvastatin) (treated group, n=9). In these two groups, average food consumption and animal weight were assessed weekly and blood sampling was performed before and 10 weeks following the onset of western diet for total cholesterol determination (BioMerieux). The effect of the statin therapy on 99m Tc-cAbVCAM1-5 uptake in atherosclerotic lesions was evaluated in vivo using longitudinal SPECT/CT imaging on 25 and 35 weeks-old mice, and ex vivo by gamma well counting (GWC) and autoradiography.

Radiolabeling.

cAbVCAM1-5 labeling with 99m Tc was performed as previously described [START_REF] Broisat | Nanobodies targeting mouse/human VCAM1 for the nuclear imaging of atherosclerotic lesions[END_REF]. Briefly, [ 99m Tc(H 2 0) 3 (CO) 3 ] + ( 99m Tc-tricarbonyl) was synthesized by adding 1 mL of 99m TcO 4 -solution to an Isolink kit (PSI). The vial was incubated at 100°C for 20 min and neutralized with HCl.

Then, 0.5mL of 99m Tc-tricarbonyl was added to 50 µg of cAbVCAM1-5 and 50 μl of 50mM carbonate buffer pH 8.0, and this mixture was incubated for 90 min at 50°C. The 99m Tc-cAbVCAM1-5 solution was further gelfiltrated on Sephadex G25 (NAP-5; GE Healthcare) and filtered (0.22 µm Millex, Millipore). Radiochemical purity, determined by RP-HPLC, was >95% up to 6h following radiolabelling.

99m Tc-cAbVCAM1-5 uptake versus VCAM-1 expression. 99m Tc-cAbVCAM1-5 uptake in atherosclerotic lesions and VCAM-1 expression level were determined using autoradiographicimagingand immunohistochemistry , respectively (n=12). Three (3) hours following intraveinousinjection of 37±3MBq (mean±SD), mice were euthanized using CO 2 .

The aortic arch was cleaned in 10% formalin (Sigma) under a binocular (Discovery V8, Zeiss), embedded in optimal cutting temperature (OCT) medium and frozen in -40°Cisopentane. Serial 20μm or 8μm-thick adjacent slices were obtained for Autoradiography and immunohistochemistry, respectively (HM 505E, Microm).For the purpose of this study, longitudinal orientation was preferred for it allowed simultaneous examination of several lesions, located in the ascending aorta, small curvature of the aortic arch, innominate, left common carotid and left subclavian arteries, and descending aorta.

Autoradiography

Autoradiographieswere acquiredusing overnight exposure with a phosphor-Imager (BAS-5000, Fujifilm). All slices were then stained using standard hematoxylin-eosinsafrantrichrome staining (HES), digitalized, andHES and autoradiographicimages were coregistered using GIMP2 and ImageJsoftwares. Regions of interest (ROIs) were drawn on atherosclerotic lesions based on HES staining. Internal references with known amounts of radioactivity were used to express tracer activity as percent injected dose per gram (%ID/g)following background and decay correction.

Immunohistochemistry

VCAM-1 immunostaining(sc-1504, santa-Cruz) was performedas previously described( 10)onslices adjacent to those used for autoradiography / HES. VCAM-1 expression level in atherosclerotic lesions (n=94) was ranked as low, moderate or strong by a trained observer blinded to the autoradiographicimages. This analysis was reproduced 2 months later by the same observer in order to assess the reproducibility of themethodology.

Non invasive evaluation of a reference therapy.

SPECT/CT imaging

SPECT/CT acquisitions were performed two hours following an intravenous injection of 55±5 MBq(mean±SD) of 99m Tc-cAbVCAM1-5.The mice were anesthetized using isoflurane 1.5% in a 1:1 mixture of room air and oxygen, and then placed in a temperature-controlled bed for SPECT/CT acquisitions focused on the thoracic region (nanoSPECT, Bioscan). First, the helicoidal SPECT acquisition was performed with 4 heads equipped with multi-pinholes collimators (9 x 1.4 mm diameter pinhole per head) using 24 projections and 45 min of acquisition. Then, a fast, 1.5min-long CT acquisition was performed immediately following retro-orbital injection of 150µl of a vascular contrast agent (Hexabrix), using the following acquisition parameters: 65kvp, 180 projections and 500ms per projection. Contrast-CT and SPECT acquisitions were reconstructed fused and quantified using dedicated software (InVivoScope).

SPECT/CT quantification

Contrast-CT based SPECT quantification was performed blinded to the SPECT images.

Briefly, 4 Volumes of Interest (VOIs) of 2.2mm 3 each were drawn at the level of the aortic sinus and ascending aorta based on contrast-CT images. 99m Tc-cAbVCAM1-5 activity was expressed as apercent injected dose per cube centimeter (%ID/cm 3 ) and uptake in atherosclerotic lesions was defined as the maximumvalue fromquantification of 4 VOIs.

Moreover, in order to assess the inter and intra-observer variability, 35 weeks SPECT images were further quantified by 3 additional independent experimenters, and this quantification was reproduced 2 weeks later by one of the experimenters.

Ex vivo quantification

Following SPECT/CT imaging, anesthetized mice were euthanized using CO 2 and ascending aortas including the aortic sinus were carefully harvested along with major organs. Tissue samples were weighed and their activity was determined by GWC (Wizard 2 , Perkin). The results were corrected for background and decay and expressed as a percent of injected dose per gram of tissue (%ID/g). Adjacent transversal 40-and 10μm-thick cryosections were obtained at the level of the aortic sinus for autoradiographicimaging and immunostaining, respectively, and autoradiography quantification was performed following HES staining as described above. ROIs were also used to determine lesion area in mm 2 . 99m Tc-cAbVCAM1-5 uptake was expressed as a %ID per gram of lesion ("concentration") based on internal references.Alternatively, lesion volumein the analyzed slice was determined as the product between its surface and the slice thickness (40µm), and 99m Tc-cAbVCAM1-5 uptake was then expressed as a %ID present in the analyzed slice ("total uptake").

Statistical analysis.

All results are presented as mean±s.e.m. F-test was employed for variances comparisons.

Student t, Mann &Witney U, Pearson,intraclass coefficient (ICC) and Kappa tests were employed forpaired/unpaired datasets with equal variances, unpaired datasets with unequal variances,correlation analysis,and inter/intra experimenters variability, respectively.

Differences were considered significant for P<0.05.

Results

99m Tc-cAbVCAM1-5 uptake versus VCAM-1 expression.

Heterogeneous VCAM-1 expression levels were observed following immunostainingof longitudinal slices from the aortic arch of Apo-deficient mice (figure 1A&C). VCAM-1 was expressed by endothelial as well as intra-plaque cells. Intra-observer ranking of VCAM-1 expression level was found to be reproducible (kappa=0.70). Robust 99m Tc-cAbVCAM1-5 uptake was observed following autoradiographicimaging of VCAM-1 positive lesions (figure 1B&D). Autoradiographyquantification confirmed the relationship between 99m Tc-cAbVCAM1-5 uptake and the level of VCAM-1 expression (figure 1E). Indeed, a graded tracer uptakeof 1.4 ± 0.2, 2.5 ± 0.2 and 3. 2 ± 0.3 %ID/g was observed in low, moderate and strong VCAM-1 expressing lesions, respectively (P<0.001 between low and moderate or strong, and P = 0.029 between moderate and high).

Non invasive evaluation of a reference therapy

Lesion extension.

The results are presented in Table 1 and Figure 1. Similar cholesterol levels were observed between treated and control animals prior to switching from chow to western dietcontaining (treated) or not (control) atorvastatin (20.3±2.2 vs 18.8±2.2 mmol/L, P = NS). Average atorvastatin intake was 12.9±0.2 mg/kg/day/animal and resulted in a significant 29.1%

decrease in total cholesterol level in the atorvastatin-treated group in comparison with the control group (60.7±6.6 vs 85.5±8.1 mmol/L; P = 0.034). Lesion extension in the aortic sinus was significantly reduced by 39.9% in the treated group in comparison to that of the control group (0.70 ± 0.07 vs 1.07 ± 0.11 mm 2 , P = 0.011) (Table 1 and suppl. fig. 1). Finally, modest variations in VCAM-1 expression in the aortic sinus were observed between control and treated animals following immunohistochemistry(suppl. fig. 1).

In vivo SPECT/CT imaging.

99m Tc-cAbVCAM1-5 allowed the non-invasive monitoring of atorvastatin effect on atherosclerosis. Indeed, 99m Tc-cAbVCAM1-5 uptake in aortic lesions was readily visible on SPECT images (figure 2) and the trend towards a reduction of 99m Tc-cAbVCAM1-5 uptake that was observed in 25 weeks-old atorvastatin-treated mice (0.83 ± 0.09 %ID/cm 3 vs 0.97 ± 0.06 %ID/cm 3 in control group, P=NS) reached statistical significance at 35 weeks (0.87 ± 0.06 %ID/cm 3 vs 1.11 ± 0.09 %ID/cm 3 in control group, P = 0.035). Contrast-CT acquisitions allowed the accurate delineation of the ascending aorta in all animals, and contrast-CT based SPECT quantification was reproducible, with inter-and intra-experimenter ICC of 0.97 and 0.90, respectively (Figure 3).

Ex vivo gamma-well counting.

99m Tc-cAbVCAM1-5 biodistribution is presented in Table 2. 99m Tc-cAbVCAM1-5 uptake in atorvastatin-treated animals was significantly decreased by 24.1 % in the ascending aorta of atorvastatin-treated animals (0.9 ± 0.1 vs 1.2 ± 0.1 %ID/g, P = 0.015). The tracer was mainly eliminated through the kidneys (138.7 ± 8.6 %ID/g) with minimal uptake in all other investigated tissues (< 2 %ID/g) with the exception of lymphoid organs. Indeed, tracer uptake in the spleen, thymus, bone marrow and lymph node was of 8.8 ± 0.7; 2.1 ± 0.2; 4.0 ± 0.4 and 2.8 ± 0.3 %ID/g, respectively.

Exvivo autoradiography.

In both groups, robust 99m Tc-cAbVCAM1-5 uptake in atherosclerotic lesions was readily observable at the level of the aortic sinus (suppl. fig. 1 A-D). A strong and statistically significant 41.5% decrease in 99m Tc-cAbVCAM1 total uptake was observed in the atorvastatin-treated group in comparison to that of the control group (table 3). Indeed 99m Tc-cAbVCAM1 uptake represented 8.9x10 -5 ± 1.1x10 -5 %ID/slice in the control group and 5.2 10 -5 ± 0.9 10 -5 %ID/slice in the treated group. Interestingly,autoradiography quantification indicated a trend toward a 15.2% decrease of 99m Tc-cAbVCAM1-5 concentration in atherosclerotic lesions from atorvastatin-treated animalswhen tracer uptake was corrected for plaque area (1.8 ± 0.2 %ID/g vs 2.1 ± 0.2 %ID/g in control group, P=NS),

Comparison between SPECT/CT, autoradiography, and gamma-well counting data

Further data analysis indicated that SPECT/CT quantification was strongly correlated to ex vivo gamma-well counting biodistribution (r = 0.83; P<0.0001) (figure 4A). Moreover, the results from SPECT/CT image quantification were significantly correlated to 99m Tc-cAbVCAM1 total uptake in aortic sinus lesions as determined by autoradiography (r = 0.51; P = 0.04), rather than to 99m Tc-cAbVCAM1 concentration or to lesion area (P=NS for both)

(figure 4 B-D).

Discussion

Atorvastatin significantly reduced lesion extension in the aortic sinus of ApoE-deficient mice, and this effect was successfully monitored non-invasively using 99m Tc-cAbVCAM1-5 molecular imaging with high reproducibility. 99m Tc-cAbVCAM1-5 is therefore a specific, sensitive and reproducible tool for the imaging of VCAM-1 expression in murine atherosclerotic lesions.

Effect of statin therapy.The anti-atherosclerotic effects of statins are mainly mediated by their cholesterol-lowering properties leading to reduced plaque volume [START_REF] Brautbar | Pharmacological strategies for lowering LDL cholesterol: statins and beyond[END_REF]. In addition, statins also exert pleiotropic effects which go beyond the drop in plasma cholesterol and which mainly result in an inhibition of inflammatory processes responsible for vulnerable plaque development [START_REF] Rasmussen | Diverse effects of inhibition of 3-hydroxy-3-methylglutaryl-CoA reductase on the expression of VCAM-1 and E-selectin in endothelial cells[END_REF][START_REF] Ridker | Rosuvastatin to prevent vascular events in men and women with elevated C-reactive protein[END_REF]. However, depending on the dose &duration of the treatment and on study design, the reduction in plasma cholesterol, plaque volume and inflammatory markers are not always consistently or concomitantly observed in experimental studies.

Indeed, in an ApoE-deficient mouse model of carotid artery lesions induced by perivascular collar placement, Bot and coll. observed that a low dose of atorvastatin (0.003%w/w) significantly reduced lesion size by 40% despite no reduction in total plasma cholesterol or macrophage positive areas [START_REF] Bot | Atorvastatin inhibits plaque development and adventitial neovascularization in ApoE deficient mice independent of plasma cholesterol levels[END_REF]. Conversely, a twelve week atorvastatin treatment (1 mg/kg/day) resulted in a significant reduction in the circulating inflammatory markers Interleukin-6 and Monocyte Chemoattractant Protein-1 as well as macrophage infiltration in aortic lesions of apoE-deficientmice despite no significant change in plasma cholesterol and plaque area [START_REF] Grothusen | Combined effects of HMG-CoA-reductase inhibition and renin-angiotensin system blockade on experimental atherosclerosis[END_REF].

The western-type diet-fed apoE-deficient mice that were used in the present study had a mean total blood cholesterol level of 85.5±8.1 mmol/L, in good accordance with the 28-114 mmol/L range reported on a similar model by Nakashima and coll [START_REF] Nakashima | ApoE-deficient mice develop lesions of all phases of atherosclerosis throughout the arterial tree[END_REF]. Supplementation of the western-type diet with 0.01% w/w atorvastatin resulted in an expected administered dose of 10mg/kg/day [START_REF] Khanicheh | Noninvasive ultrasound molecular imaging of the effect of statins on endothelial inflammatory phenotype in early atherosclerosis[END_REF]. Atorvastatin significantly decreased total cholesterol by 29% and lesion size by 40%. These results are in accordance with the range of atorvastatin-induced modifications reported by other groups [START_REF] Khanicheh | Noninvasive ultrasound molecular imaging of the effect of statins on endothelial inflammatory phenotype in early atherosclerosis[END_REF][START_REF] Nahrendorf | Noninvasive vascular cell adhesion molecule-1 imaging identifies inflammatory activation of cells in atherosclerosis[END_REF]. Modest changes in the lesional expression of VCAM-1 were observed in atorvastatin-treated animals, in contrast with other studies showing a significant 30-80% reduction in VCAM-1 expression [START_REF] Khanicheh | Noninvasive ultrasound molecular imaging of the effect of statins on endothelial inflammatory phenotype in early atherosclerosis[END_REF][START_REF] Nahrendorf | Noninvasive vascular cell adhesion molecule-1 imaging identifies inflammatory activation of cells in atherosclerosis[END_REF][START_REF] Nahrendorf | 18F-4V for PET-CT imaging of VCAM-1 expression in atherosclerosis[END_REF]. However, Nachtigal and coll found no significant change in VCAM-1 lesion expression in double knockout, LDLR -/-ApoE -/-mice in the presence of atorvastatin at a similar dose to that used in the present study [START_REF] Nachtigal | Atorvastatin has hypolipidemic and antiinflammatory effects in apoE/LDL receptor-double-knockout mice[END_REF].

Overall, atorvastatin administered at a dose of 0.01% w/w for 20 weeks to ApoE-deficient mice fed a western-type diet therefore had significant anti-atherogenic effects that allowed the evaluation of the potential of 99m Tc-cAbVCAM1-5 for treatment effect monitoring.

Sensitivity of 99m Tc-cAbVCAM1-5 imaging.

99m Tc-cAbVCAM1-5 uptake occurred in atherosclerotic lesions as well as in lymphoid organs constitutively expressing VCAM-1 following tracer injection to ApoE-deficient mice fed a western type diet, in accordance with previously published results [START_REF] Broisat | Nanobodies targeting mouse/human VCAM1 for the nuclear imaging of atherosclerotic lesions[END_REF]. Autoradiography and immunohistochemistryindicatedthat 99m Tc-cAbVCAM1-5 uptake in atherosclerotic lesion significantly increased together with the level of VCAM-1 expression. Importantly, 99m Tc-cAbVCAM1-5lesion uptake was significantly reduced in 35 weeks-old atorvastatin-treated mice as indicated by ex vivo GWC and autoradiography as well as in vivonon invasiveSPECT/CT molecular imaging. In vivo image quantification was reproducible and yielded results that were highly correlated withtracer biodistributionas determined ex vivo.

More precisely, VOIsfrom in vivo images were reproducibly drawn at the level of the aortic sinus based on contrast-CT images. In the hypothesis that the VOI exclusively contained atherosclerotic lesional tissues and according to the fact that 99m Tc-cAbVCAM1-5 uptake in murine atherosclerotic lesion significantly increased together with the level of VCAM-1 expression, SPECT quantification would then have directly reflected the levelof VCAM-1 expression in atherosclerotic lesions. However, due to the relatively small size of atherosclerotic lesions, and despite the use of a state-of-the-art, sub-millimetric resolution system, partial volume effect necessarily occurred while performing SPECT imaging of murine aortic plaques. Therefore, the VOI used for the assessment of tracer uptake in atherosclerotic lesions contained a mixture of the various tissues composing the aortic sinus i.e. atherosclerotic lesions, normal vessel wall and bloodrather than the atherosclerotic lesion only. Consequently, the total activity in a VOI, and therefore the result of in vivo quantification, depended not only upon the level of VCAM-1expression in the lesions but also upon the amount of lesions included in the VOI, and therefore lesion extension. This was demonstrated in the present study by the fact that the results from SPECT/CT image quantification were significantly correlated to 99m Tc-cAbVCAM1 total uptake in aortic sinus lesions as defined by the product of 99m Tc-cAbVCAM1 concentration in lesion by lesion volumerather than with any one of these two parameters considered separately.In conclusion, 99m Tc-cAbVCAM1-5 SPECT/CT imaging allowed the sensitive and reproducible non-invasive quantification of the net effect of a reference statin therapy on lesion size and inflammation in the apoE-deficient mouse model of atherosclerosis.

Comparison with other radiotracers and molecular targets.

The sensitivity of 99m Tc-cAbVCAM1-5 imaging favorably compared with previously evaluated radiotracers. In a rabbit model of atherosclerosis,Haider and coll. observed a decrease in the uptake of two SPECT agents directed against matrix metalloproteinases(MPI) and apoptosis (AA5)followingtreatment with fluvastatin [START_REF] Haider | Dual molecular imaging for targeting metalloproteinase activity and apoptosis in atherosclerosis: molecular imaging facilitates understanding of pathogenesis[END_REF].Although SPECT image quantification was not performed,thesequalitative visual observations were further confirmed by quantitative ex vivo analysis. Similarly, a significant 30% reduction in 18 F-4V was found by in vivo positron emission tomography(PET)image quantification in a similar model to that employed in the present study [START_REF] Nahrendorf | 18F-4V for PET-CT imaging of VCAM-1 expression in atherosclerosis[END_REF]. A number of studies have investigated the potential of 18 F-FDG for the non-invasive assessment of treatment efficacy. Such potentialhas been validated in rabbits using the anti-oxydantprobucol [START_REF] Ogawa | Application of 18F-FDG PET for monitoring the therapeutic effect of antiinflammatory drugs on stabilization of vulnerable atherosclerotic plaques[END_REF], thereby allowing the use of 18 F-FDGfor the evaluation of novel therapeutics in preclinical [START_REF] Vucic | Pioglitazone modulates vascular inflammation in atherosclerotic rabbits noninvasive assessment with FDG-PET-CT and dynamic contrast-enhanced MR imaging[END_REF][START_REF] Vucic | Regression of inflammation in atherosclerosis by the LXR agonist R211945: a noninvasive assessment and comparison with atorvastatin[END_REF] and clinical studies [START_REF] Elkhawad | Effects of p38 mitogen-activated protein kinase inhibition on vascular and systemic inflammation in patients with atherosclerosis[END_REF][START_REF] Tawakol | Intensification of statin therapy results in a rapid reduction in atherosclerotic inflammation: results of a multicenter fluorodeoxyglucosepositron emission tomography/computed tomography feasibility study[END_REF]. However, high myocardial uptake remains a potential limitation for the imaging of coronary lesions with 18 F-FDGdespite the use of imaging protocols aimed at reducing myocardial tracer uptake [START_REF] Harisankar | Utility of high fat and low carbohydrate diet in suppressing myocardial FDG uptake[END_REF].

VCAM-1 protein is strongly and specifically expressed during the inflammatory process, and therefore constitutes a highly relevant target for VP imaging, similarly to other inflammatory markers such as macrophages. Other biological processes related to plaque rupture such as apoptosis, matrix degradation or neoangiogenesis [START_REF] Sadeghi | Imaging atherosclerosis and vulnerable plaque[END_REF] have been proposed as potential targets. These processes occur at different times and intraplaque locations over the course of plaque development. Ultimately, prospective clinical trials will be needed in order to select the most appropriate target and corresponding imaging agent.

Conclusions

SdAbsderived radiotracers have been initially developed in the field of oncology, and a first phase I clinical trial is currently been performed with an anti-human epidermal growth factor receptor 2radiotacer for PET imaging of breast cancer patients. Thereafter, anti-VCAM-1 sdAb extended the field of sdAb imaging to cardiovascular applications. As demonstrated in the present study, 99m Tc-cAbVCAM1-5 is a sensitive tool for the non-invasive imaging of atherosclerosis. Indeed, 99m Tc-cAbVCAM1-5 uptake in mouse atherosclerotic lesions was correlated to the level of VCAM-1 expression, and the effect of a reference therapy was successfully and reproducibly monitored non-invasively by SPECT/CT imaging quantification.

99m Tc-cAbVCAM1-5 therefore exhibits suitable characteristics for evaluation of novel antiatherogenic agents.

Disclosures: none

Acknowledgments:

Antony Coradin, Pierre-Francois Meyer and AudreyGenoud, students of Grenoble University, were involved in data collection and analysis during their training course in RadiopharmaceutiquesBiocliniques Laboratory. This work was partly funded by the French program "Investissementd"Avenir" run by the "AgenceNationale pour la Recherche" ; grant 'Infrastructure d"avenirenBiologie Santé -ANR-11-INBS-0006" as well as by the ANR-09-TECS-017-01 "PLAQUIMAG" grant.

FIGURE 1 .

 1 FIGURE 1. 99m Tc-cAbVCAM1-5 uptake and VCAM-1 expression. A and C: Representative

TABLE 1 .

 1 Effect of treatment on lesions extension.Atorvastatin 0.01% significantly decreased total plasma cholesterol as well as lesion extension at the level of the aortic sinus.

		Control	Treated
	As. Aorta	1.2±0.1	0.9±0.1*
	Blood	0.6±0.1	0.5±0.0
	Heart	0.3±0.0	0.3±0.0
	Lung	1.7±0.1	1.8±0.1
	Liver	1.5±0.1	1.4±0.1
	SM	0.1±0.0	0.3±0.1
	SG	0.7±0.2	0.7±0.1
	Thyroid	1.2±0.2	0.9±0.2
	Stomach	0.7±0.1	0.7±0.1
	Bile	0.4±0.0	0.5±0.1
	Kidney	138.7±8.6	165.0±6.8
	Spleen	8.8±0.7	7.9±0.5
	Thymus	2.1±0.2	1.8±0.2
	BM	4.0±0.4	4.1±0.7
	LN	2.8±0.3	2.7±0.2

TABLE 2 .Ex vivo biodistribution of 99m Tc-cAbVCAM1-5 3h post-injection in ApoE- deficient mice.

 2 Results are expressed as %ID/g (mean ± s.e.m.). * P =0.015 vs control group. SM, skeletal muscle; SG, salivary glands; BM, bone marrow; LN, lymph node.

This work was partly funded by the French program "Investissementd"Avenir" run by the "AgenceNationale pour la Recherche" ; grant 'Infrastructure d"avenirenBiologie Santé -ANR-11-INBS-0006" as well as by the ANR-09-TECS-017-01 "PLAQUIMAG" grant.

Parameter

Unit Control Treated % change

Total uptake %ID/slice (.10 -6 ) 8.9 ± 1.2 5.2 ± 0.9 -41.5 (P=0.024)

Concentration %ID/g 2.1 ± 0.2 1.8 ± 0.2 NS TABLE 3.Ex vivo autoradiography quantification on the aortic sinus lesions.Atorvastatin therapy resulted in a statistically significant decrease in 99m Tc-cAbVCAM1 total uptake in atherosclerotic lesions. Furthermore, there was also a trend toward a 15.2% decrease of 99m Tc-cAbVCAM1-5 concentration in atorvastatin-treated group when tracer uptake was corrected for plaque area (P = NS)


L Chôné

P Beyer

Y Sarazin

G Fuhr

C Bourdelle

S Benkadda

L-H transition dynamics in fluid turbulence simulations with neoclassical force balance

Spontaneous transport barrier generation at the edge of a magnetically confined plasma is reproduced in fluxdriven three-dimensional fluid simulations of electrostatic turbulence. Here, the role on the radial electric field of collisional friction between trapped and passing particles is shown to be the key ingredient. Especially, accounting for the self-consistent and precise dependence of the friction term on the actual plasma temperature allows for the triggering of a transport barrier, provided the input power exceeds some threshold. In addition, the barrier is found to experience quasi-periodic relaxation events, reminiscent of Edge Localised Modes. These results put forward a possible key player, namely neoclassical physics via radial force balance, for the Low-to High-confinement regime transition observed in most of controlled fusion devices.

Regions of reduced energy and particle diffusion are observed in magnetic fusion devices such as tokamaks and stellarators 1,2 . These regions are named transport barriers and are equivalent to those observed in atmospheric and oceanic turbulent flows 3 . The high confinement mode or H-mode barrier, which forms at the edge of magnetic fusion devices was the earliest observed and the most studied 4 . Since then many theoretical models have been devoted to the study of this very promising confinement mode 2 . These theories share in common the fact that the potential structure that is observed in the H-mode regime, and which gives rise to a strong negative radial electric field, is indeed responsible for the turbulence suppression by shear effects in the E × B velocity at which fluctuations are convected 5 . On another hand, theory shows that the plasma gradients in the H-mode barrier are limited by pressure driven ballooning modes leading to relaxation oscillations of the barrier, known as Edge-Localized Modes (ELMs) 6 . These violent relaxation events bear similarities with solar flares 7 . The transition from a regime of low confinement to one of high confinement at the edge, or L-H transition occurs when externally injecting power into the plasma and is generally followed by quasi-periodic relaxations of the barrier, which is a characteristic of the ELMs. The importance of achieving high confinement makes H-mode one of the ITER baseline scenarios, however it could be seriously hindered by the harmful nature of ELMs to the wall components. Because of this, the understanding of the creation, control and removal of external transport barriers is of crucial importance to the success of magnetic fusion. Although the L-H transition has been widely observed and the conditions for triggering H-mode have been extensively studied experimentally, theoretical understanding of the underlying physical mechanisms remains unresolved 2,[8][9][10][11][12][13][14][15][16][17] . In particular, although the self-generation of sheared flows and subsequent turbulence reduction is observed in the few flux-driven three-dimensional (3D) plasma edge turbulence simulations addressing this issue, no clear transition is reported [14][15][16][17] . When reported, such a transition is neither well characterised nor prop-erly understood 18 .

In this letter we present non-linear results of fluxdriven resistive ballooning simulations of the plasma edge, taking into account the effect of neoclassical friction on the E × B flow. Such an effect has recently been explored in the frame of a 1D predator-prey model 19 . Here it is found by means of 3D simulations that competition between the neoclassical friction and zonal-flows (ZFs) allows for the existence of two distinct regimes depending on the imposed heat flux. These regimes correspond to a low-confinement state dominated by turbulence, and above a certain input power, a state of improved confinement with the onset of a transport barrier. In contrast to previous investigations, radial and temporal variations of the friction coefficients are retained. This feature is found to have a strong impact on the dynamics of the system, so that taking it into account is necessary to obtain generation of this transport barrier. A reduced 1D model which reproduces qualitatively the 3D result is derived, and 1D simulations show intermittent bursts of turbulent flux corresponding to relaxations of the established barrier.

In the following simulations, the non-linear evolution of electrostatic resistive ballooning turbulence is studied with the EMEDGE3D code 20 in toroidal geometry with circular, non-diverted poloidal cross-section. The dimensionless coordinates (x, y, z) of the 3D toroidal geometry refer to the minor radius, and the poloidal and toroidal angles, respectively. The code solves standard reduced MHD (RMHD) equations [20][21][22][23] , in the limit of large aspect ratios and with the slab approximation:

∂ t ∇ 2 ⊥ φ + φ, ∇ 2 ⊥ φ = -∇ 2 φ -Gp + ∂ x F neo + ν ⊥ ∇ 4 ⊥ φ , (1)
∂ t p + {φ, p} = δ c Gφ + χ ∇ 2 p + χ ⊥ ∇ 2 ⊥ p + S . (2)
Equations (1,2) correspond respectively to the charge and energy balance, the two fields φ and p being the electric potential and the total pressure. Poisson brackets {φ, •} = ∂ x φ∂ y • -∂ y φ∂ x • account for the advection by the electric drift velocity. ∇ and∇ ⊥ are respectively the parallel and perpendicular gradients with respect to the magnetic field lines and G is a toroidal curvature operator. ν ⊥ is the classical viscosity, while χ and χ ⊥ account for parallel and perpendicular collisional heat diffusivities. S (x) is a heat source term (all numerical results presented here are from flux-driven simulations). Here, the novel term in Eq. ( 1) is ∂ x F neo φ, p , where φ = φ -φ and p = p -p indicate flux-surface averaged quantities, with φ and p the associated perturbations. It ensures that the poloidal flow relaxes towards its expected neoclassical value on collisional time, as a result of the friction between trapped and passing particles. The key steps for the derivation of F neo are outlined in the following (for the full derivation, see 24 ).

The system (1,2) is dimensionless: time is normalised to the interchange time,

τ int = √ R0Lp √ 2c S0
, with c S0 = p 0 /n 0 m i the typical acoustic speed and L p the typical pressure gradient length. The perpendicular length scale is the resistive ballooning length, ξ bal = ρη τint Ls B0 , with the magnetic shear length L s being the parallel length scale. The fields φ and p are normalised respectively to Lp . Because the MHD model does not separate density and temperature, an assumption is made that the former is constant n = n 0 , therefore p s = n 0 T s . Furthermore, the ratio between ion and electron temperatures is kept constant

T i = T T e .
The starting point of this reasoning is the radial force balance equation which, if we consider toroidal rotation to be negligible (generally true in the absence of torque injection), can be written thus:

∂ x φ + T T + 1 τ int p 0 ξ bal L p en 0 B 0 ∂ x p = ūy . (3)
In the fluid model, the poloidal velocity is not normally constrained, however an expression emerges from the neoclassical theory: ūneo

y = T T +1 τintp0 ξ bal Lpen0B0 K (ν i, * ) ∂ x p25,26 .
The collisionality is expressed as a function of p (since ν i, * ∝ nT -2 i ∝ p-2 , at constant density), and a heuristic closure 24 allows for this constraint to be taken into account in the fluid model through a friction term which enforces relaxation towards this equilibrium:

F neo = -µ neo (p) ∂ x φ -K neo (p) ∂ x p , (4)
where

K neo = T T +1 τintp0 ξ bal Lpen0B0 [K (ν i, * ) -1], and µ neo = α neo µ i q(x) ε(x)

2

, with q (x) the safety factor and ε (x) the inverse aspect ratio. The Hinton and Hazeltine formula is used to determine K (ν i, * ) for all neoclassical regimes 25 , and an approximate fit for µ i is found in 24 . One can see in Eq.4 that alleviating the assumption of constant density would actually reinforce the coupling near the edge where n is small. For instance, under the assumption that n ∝ T , the friction term in Eq.4 would have a similar structure with ∂ x p replaced by ∂ x p/ √ p. As a consequence, the neoclassical drive would be even stronger at the plasma edge. Under the assumptions of the electrostatic RMHD model, ZF amplitude is likely overestimated. Indeed, the competition between Reynolds and Maxwell stresses is unaccounted for, and so is the saturation by collisional friction on the ZF (both effects are discussed in 28 ). A factor α neo > 1 is therefore introduced to recover the competition between zonal and neoclassical flows expected during the L-H transition (here α neo = 6 is sufficient to achieve this). Note that the value of α neo affects the magnitude of the transition threshold, but not the qualitative behaviour of the system. Importantly, two mechanisms can lead to sheared radial electric field here: on the one hand, pressure gradient and radial electric field get coupled, allowing for a possible positive feedback loop, and strong radial variations of K neo will result in a sheared neoclassical flow on the other hand.

The simulations are carried out in the range of minor radius between 0.85 < r/a < 1. This main simulation domain is bounded by buffer zones where the turbulence is artificially stabilised by large χ ⊥ and ν ⊥ coefficients. The precise value of χ ⊥ in the buffer zones is chosen so as to maintain a gradient of order unity (in the buffers,

Q 0 = Q coll = -χ ⊥ ∂ x p).
All simulations are flux-driven with a volume source S (x) located in the x < x in buffer zone, imposing the heat flux Q 0 = S (x) dx. Here x denotes the normalised minor radius (to ξ bal ), x in and x out are the positions of the main simulation domain's boundaries, with x out corresponding to r = a. The safety factor is hyperbolic, between q (x in ) = 2.5 and q (x out ) = 3.5 . The set of parameters used here is representative of medium to large present tokamaks. In particular, collisionality is in the range 10 -1 < ν i, * < 10 2 (near banana to collisional regime), which is in agreement with what is observed in L-mode at the edge [START_REF] Bourdelle | [END_REF] , and happens to be where K (ν i, * ) varies the most rapidly. This is with the exception of ν ⊥ and χ ⊥ , chosen large enough to ensure damping at sub-Larmor scales. Here we take χ ⊥ = ν ⊥ = 0.93 and χ = 2 (these values are normalised to ξ 2 bal /τ int in the perpendicular direction and L 2 s /τ int in the parallel direction). Several simulations are done in the range of 5 ≤ Q 0 ≤ 30 to study the impact of this friction on confinement.

The results on figure 1 show the confinement deterioration expected in L-mode with increasing heat flux for Q 0 < 14, followed by a sharp increase and again a deterioration if the source is increased further. This corresponds to strong changes in the profiles of the flux-surface averaged pressure and poloidal component of the drift velocity ūEy = ∂ x φ. Indeed, when the heat flux is below Q 0 = 14, the pressure profile is roughly a straight line and the poloidal velocity is low with minor radial corrugations. Above the threshold, the poloidal velocity profile is strongly modified. In the main part of the simulation domain it stays at low amplitude and changes sign, but between 0.95 < r/a < 1 it peaks strongly, generating a localised sheared flow. Note that throughout the domain below the threshold and outside the barrier above, the turbulent flux is one order of magnitude larger than the collisional flux. The stabilising effect of sheared flows on turbulence, which is a well documented result from reduced models to gyrokinetic simulations 12,14,[29][30][31] , allows for steeper pressure gradients to be reached, giving a pedestal-like pressure profile. In the higher range of heat flux, the poloidal velocity tends towards the forcebalance value, ūEy = K neo ∂ x p , while it departs from it for the lower sources. Furthermore, the shape of the velocity profile shows good qualitative agreement with measurements of the radial electric field in H-mode [START_REF] Sauter | Rathgeber and the ASDEX Upgrade Team[END_REF][START_REF] Wolfrum | Viezzer and the ASDEX Upgrade Team[END_REF][START_REF] Viezzer | Wolfrum and the ASDEX Upgrade Team[END_REF] , even though the radial electric field at the last closed field-surface (LCFS) is not constrained by scrape-off layer physics in the model (i.e. E r is allowed to vary freely inside the buffer zones. Notice however that E r becomes positive in the outer buffer region, as expected in the SOL). We also show that the mean value of the poloidal velocity at the peak, and consequently the associated shear, is significantly increased (here about 3 times larger) when K neo and its radial variations are taken into account (see Fig. 2). Correspondingly, the friction coefficients, as calculated from the equilibrium pressure in the code, show large changes before and after the transition. In particular, as shown on Fig. 3 (left panel) the maximum value of K goes from -1 for Q 0 < 14 (transition from collisional to plateau neoclassical regime) to 0 (plateau regime) after the transition. Moreover, after the transition the profile of K is ranging from -2.1 to 0 with a strong gradient at the position of the barrier. Correspondingly, the value of µ neo doubles at the position of the barrier after the transition (as illustrated in Fig. 3, right panel), and shows a very sharp gradient outward from this position. This supports the fact that the radial and temporal variations of both coefficients should be taken into account, K in order to allow for strong enough shear flows, and µ neo in order to allow for competition between neoclassical friction and ZF. Smooth approach of the threshold has shown dithering of the poloidal velocity, reminiscent of the I-phase in slow L-H transitions [35][36][37][START_REF] Cheng | the HL-2A Team[END_REF][39][40] . This is clearly seen when looking at the time evolution of the poloidal velocity and the associated shearing rate, as shown on Fig. 4. Before the formation of the transport barrier the normalised velocity shear fluctuates in between 1 and 2 . An increase to twice this value is then observed shortly after 1 ms, soon followed by a sharp fall back to its original level. This is repeated twice, each time towards higher velocities, before a new state is reached at t > 2 ms and a barrier is established. As can be seen on the lower panel of Fig. 4, the radial maximum of the velocity corresponds to the peak observed in Fig. 1d in the case of a steady barrier.

It is instructive to realise that similar characteris- tics can be obtained with a reduced 1D model, provided neoclassical friction is properly accounted for. This model derives from Eqs. 1-2, when only retaining resonant modes, characterised by k = 0, and one single poloidal mode of wave vector k. Then, p and φ can be decomposed into their equilibrium and fluctuating parts: f = f + f e ıky + c.c., with f = (p, φ). The following four-fields 1D system is obtained 41 :

∂ t p = -ık∂ x p φ * -p * φ + χ ⊥ ∂ 2 x p + S (x) , (5)
∂ t ūEy = ık∂ x φ∂ x φ * -φ * ∂ x φ -µ neo (ū Ey -K neo ∂ x p) + ν ⊥ ∂ 2 x ūEy , (6)
∂ t p = ık φ (∂ x p -κ) -ūEy p -α p |p| 2 p + χ ⊥ ∂ 2 x p, (7)
∂ t φ = ı g k p p -kū Ey φ -α φ | φ| 2 φ + ν ⊥ ∂ 2 x φ, (8)
The α f | f | 2 f terms account for saturation via mode coupling. Here t is normalised to

1 ω S = mi eB0 , x to ρ S = √ mik B Te eB0
. In this case, partial stabilisation of the turbulence is achieved above a certain threshold of the injected power, as illustrated on Fig. 5, showing that this reduced model still contains the minimal elements to reproduce this behaviour. In the parameter range considered so far, it turns out that for low fluxes, the collisional and turbulent fluxes are of the same order of magnitude (Fig. 5, right panel). This 1D model offers the advantage of allowing for long simulation runs, on several energy confinement times. Especially, when the input power exceeds the L-H transition threshold, a complex dynamics emerges: here turbulence is not steadily suppressed but shows instead quasi-periodic bursts. Interestingly the pseudo-period increases with the injected power (see Fig. 6). This behaviour bears similarities with type-III ELMs, which were already suggested to be governed by the resistive ballooning instability 16,20,30,42,43 . In conclusion, 3D nonlinear simulations of flux-driven edge turbulence are performed in a fluid model including neoclassical friction via a heuristic closure. They have shown the existence of two distinct regimes of confinement depending on the imposed heat flux. The transition scenario from one regime to another is the following: increasing the input power leads to more violent avalanches, triggering strong stabilising ZF. The resulting steepening of the pressure gradient further generates a sheared mean flow via the neoclassical friction. If the shear becomes strong enough to prevent a new burst, the barrier locks on because of this positive feedback loop between pressure gradient and poloidal flow, mediated by neoclassical terms. If not, it collapses in a strong transport event, starting another similar cycle. This can be repeated before the transition, resembling limit cycle oscillations observed in L-I-H transition experiments [35][36][37][START_REF] Cheng | the HL-2A Team[END_REF][39][40] . The stability of this barrier over long periods has been explored by means of a reduced 1D model, which reproduces the general behaviour of the 3D model, and revealed the existence of relaxations reminiscent of type-III ELMs.

The authors thank X. Garbet, Y. Camenen and D. F. Escande for fruitful discussions and insightful ad-vices. This work is supported by the French National Research Agency, project ANR-2010-BLAN-940-01. Computations have been performed at the Mésocentre d'Aix-Marseille Université. This work, supported by the European Communities under the contract of Association between Euratom and CEA, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

B0ξ 2 bal

 2 τint and ξ bal p0

30 FIG. 1 .

 301 FIG. 1. (Color online). Evolution of the mean energy confinement time (a), defined as τE = 1/Q0 x out x in p dx, and the volume-averaged mean pressure gradient (b) as functions of the heat source amplitude in the 3D case. Error bars on (a) and (b) show the standard deviation in time. (c) and (d) show mean profiles of the pressure and the E × B velocity. The vertical dashed lines on (c) and (d) mark the LCFS. All time-averaged quantities are taken over a statistically stationary period of the order of 1000 τint.

FIG. 2 . 20 FIG. 3 .

 2203 FIG. 2. (Color online).Comparison of the friction-imposed drift velocity ūEy = Kneo∂x p with K (νi, * ) = 0 and K (νi, * ) = K (p), in the lower and higher range of heat flux.This illustrates that the barrier could not form or maintain itself if the radial and temporal variations of K where not taken into account.

FIG. 4 .

 4 FIG. 4. (Color online). Time evolution of the poloidal velocity when crossing slowly the threshold. Upper panel shows evolution of the average shearing rate in the range 0.95 ≤ r/a ≤ 1, with black wedges pointing at the repeated drops during the transition. Lower panel time evolution of the poloidal velocity radial profile, with the white dashed line highlighting the position r/a = 0.95. Here the statistically stationary phase is not shown.

FIG. 5 . 3 FIG. 6 .

 536 FIG. 5. (Color online). Evolution of the confinement efficiency as a function of the heat source amplitude in the 1D case.


Donatello Conte

Guillaume Damiand

Remove noise in video with 3D topological maps ⋆

Keywords: Video denoising, 3D Topological Maps, Betti numbers

In this paper we present a new method for foreground masks denoising in videos. Our main idea is to consider videos as 3D images and to deal with regions in these images. Denoising is thus simply achieved by merging foreground regions corresponding to noise with background regions. In this framework, the main question is the definition of a criterion allowing to decide if a region corresponds to noise or not. Thanks to our complete cellular description of 3D images, we can propose an advanced criterion based on Betti numbers, a topological invariant. Our results show the interest of our approach which gives better results than previous methods.

Introduction

Several video analysis applications, like video surveillance or traffic monitoring, require as a preliminary sub-task the identification within the scene of the moving objects (foreground) as opposed to the static parts of the scene (background).

Many algorithms have been proposed in the literature most based on the background subtraction technique [START_REF] Stauffer | Learning patterns of activity using real-time tracking[END_REF][START_REF] Barnich | Vibe: A universal background subtraction algorithm for video sequences[END_REF][START_REF] Haque | Perception-inspired background subtraction[END_REF]. These algorithms are quite efficient but no one is the best for all situations (see [START_REF] Conte | An experimental evaluation of foreground detection algorithms in real scenes[END_REF] for a comparison of the most widely used background subtraction algorithms). Some authors give up looking for an algorithm that directly provides the ideal foreground mask, and apply, instead, some post-processing in order to reduce or eliminate noise pixels, that is pixels erroneously detected as foreground. For example in [START_REF] Prati | Detecting moving shadows: algorithms and evaluation[END_REF] the authors show a method to remove shadows, or in [START_REF] Conte | Evaluation and improvements of a real-time background subtraction method[END_REF] the authors propose some heuristics for removing some errors in the foreground mask. Even if these approaches are efficient, they are based on some assumptions that are not always true, being too dependent from the specific video characteristics. Our paper fall in the last category: we propose an approach to reduce noise on foreground masks. But we present a general method that can be used on any video, in contrast to the more video-dependent approaches in the literature.

The basic idea of the method is that noise cannot be detected and removed analyzing a single frame of the video (as the other approaches do), but noise is easier to detect if more successive frames are examined: in fact real objects present, over the sequence, a regularity that noise seems not to have. Therefore the approach is based on a 3D structural representation of the foreground for a certain number of frames, and noise removal is done through structural operations on that data structure.

The remainder of the paper is organized as follows: in Sect. 2 the 3D structural representation of the scene is presented and explained, then in Sect. 3 the noise removal algorithm is given; the validation of the method, together with a comparison with other approaches, is made by a robust quantitative experimentation in Sect. 4; finally conclusions and perspectives are drawn in Sect. 5.

Definitions and Representation

We recall here the standard notions around 2D and 3D digital images, before introducing the notions of cellular subdivision and Betti numbers.

Digital 2D and 3D Images and Video

A pixel (resp. voxel ) is an element of the discrete space Z 2 (resp. Z 3 ) denoted by its coordinates (x, y) (resp. (x, y, z)). A 2D (resp. 3D) image is a set of pixels (resp. voxels) and a mapping between these pixels (resp. voxels) and a set of colors or gray levels. Each pixel (resp. voxel) e is associated with its color or gray level c(e). Furthermore, each pixel (resp. voxel) e is associated with a label l(e) from a finite set of labels L. These labels can be obtained from the image by a segmentation algorithm.

In this work, a temporal sequence of 2D images is considered as a 3D image. Each image of the sequence is associated with a time t. Thus each pixel is now considered as a temporal pixel, described by three coordinates (x, y, t), (x, y) being the spatial coordinates and t being the temporal coordinate. Thus, a temporal sequence of 2D images can be seen as a 3D image, where each voxel is in fact a temporal pixel.

We use the classical notion of α-adjacency. Two voxels (x 1 , y 1 , z 1 ) and

(x 2 , y 2 , z 2 ) are 6-adjacent if |x 1 -x 2 | + |y 1 -y 2 | + |z 1 -z 2 | = 1; they are 26- adjacent if max(|x 1 -x 2 |, |y 1 -y 2 |, |z 1 -z 2 |) = 1
and they are 18-adjacent if they are 26-adjacent and if |x 1 -x 2 |+|y 1 -y 2 |+|z 1 -z 2 | = 1 or 2. Adjacency relations are extended to set of voxels: two sets of voxels S 1 and S 2 are α-adjacent if there is v 1 ∈ S 1 and v 2 ∈ S 2 such that v 1 and v 2 are α-adjacent.

Given an α-adjacency, an α-path between two voxels v 1 , v 2 is a sequence of voxels starting from v 1 and finishing from v 2 , such that two voxels of the sequence are α-adjacent. A set of voxels S is α-connected if there is an α-path between any pair of voxels in S having all its elements in S.

A region in 3D is a maximal set of 6-connected voxels having same label. In addition to all the regions present in the labeled image, another region is considered, called R 0 , which contains all the voxels that do not belong to the image. R 0 is the complementary of the image.

Cellular Subdivision of Video

A video seen as a 3D image is thus decomposed in 3D regions which form a partition of the image (i.e. any voxel belongs to exactly one region and the union of all the regions is equal to the entire image). Figure 1 shows an example of the 3D representation of a video. The partition is decomposed in the following cells: 0-cells are vertices, 1-cells are edges, 2-cells are faces and 3-cells are volumes.

Volumes describe the boundaries of 3D regions. Each volume is bounded by a surface, i.e. a set of adjacent faces, each face corresponding to a maximal contact area between two adjacent regions. Faces are bounded by edges, each edge corresponding to a maximal contact between two adjacent faces; and edges are bounded by vertices. Incidence relations are defined between the cells: two cells are incident if they have different dimensions and if one belongs to the boundary of the second one.

This cellular subdivision is a generalization of a region adjacency graph (RAG [START_REF] Rosenfeld | Adjacency in digital pictures[END_REF]) which is a graph having a vertex for each region, and an edge between each pair of adjacent regions. Vertices of the graph correspond to regions, and edges correspond to faces which describe the adjacency relations. This RAG was extended in a multi-graph, called multi-RAG, in order to represent multi-adjacency relations between regions (when two regions are adjacent several times). However our cellular structure is much more rich than RAG and multi-RAG since it describes also the multi-adjacency relations but the relations are ordered (given a region we can iterate through the adjacent regions in an ordered way which is not directly possible with graphs); furthermore in our structure all the cells are represented (RAG instead describes only 3-cells and 2-cells).

The cellular subdivision is represented thanks to 3D topological maps [START_REF] Damiand | Topological model for 3d image representation: Definition and incremental extraction algorithm[END_REF], an efficient 3D model based on combinatorial maps [START_REF] Lienhardt | N-Dimensional generalized combinatorial maps and cellular quasimanifolds[END_REF][START_REF] Damiand | Combinatorial maps. In CGAL User and Reference Manual[END_REF] which represent the subdivisions in cells plus all the incidence and adjacency relations between the cells. In this work, 3D topological maps are used as an external tools and thus we do not go into detailed definitions, see above references for more details.

Having a cellular subdivision makes it possible to use some classical tool of algebraic topology, since our subdivision is an abstract cellular complex [START_REF] Aleksandrov | Elementary concepts of topology[END_REF][START_REF] Kovalevsky | Finite topology as applied to image analysis[END_REF]. In this work we use Betti numbers, a well-known topological invariant [START_REF] Munkres | Elements of Algebraic Topology[END_REF], in order to characterize the topology of regions. These numbers are related to homology groups, but we give here their intuitive presentation. In 3D, there are three non null Betti numbers: b 0 is the number of connected components, b 1 is the number of tunnels and b 2 is the number of voids. For a region R, b 0 (R) = 1 because by definition a region is connected, b 1 (R) is the number of tunnels of R (a tunnel corresponds to a path of voxels in R that cannot be contracted into a point) and b 2 (R) is the number of voids of R (a void is a set of connected voxels that do not belong to R but that are fully surrounded by voxels in R). An incremental method to compute Betti numbers and to update them during region merging is given in [START_REF] Dupas | Region merging with topological control[END_REF].

Our Method

The main principle of our method is detailed in Algo. 1. First a given video of foreground masks is cut in consecutive slices of 2D images. Then each slice is consider as a 3D image (as explained in the previous section) and a 3D topological map is built to describe the corresponding cellular subdivision. This gives a set of regions, each one being labeled 0 or 1 depending if it corresponds to a set of background voxels (0) or of foreground ones (1).

Algorithm 1: Reduce noise on foreground masks

Input: A video of foreground masks V ;

A boolean function criterion(r1, r2). Result: V is modified by merging all the adjacent pairs of regions satisfying criterion.

T ← build the 3D topological map describing V ;

foreach region R1 ∈ T labeled 1, R1 = R0 do foreach region R2 adjacent to R1, R2 = R0 do if criterion(R1, R2) then R ← merge(R1, R2); update region R;
return the partition described by T ;

The 3D topological map corresponding to a given slice is built by using the algorithm given in [START_REF] Damiand | Topological model for 3d image representation: Definition and incremental extraction algorithm[END_REF] (wich is the extension in 3D of similar algorithm in 2D [START_REF] Damiand | Topological model for two-dimensional image representation: Definition and optimal extraction algorithm[END_REF]).

During this construction, a cube is created for each voxel, and 6-adjacent voxels having the same label are merged. Doing the merging during the construction allows to process large video by avoiding to build the full model composed of all the cubes describing all voxels.

Then, each pair of adjacent regions (R 1 , R 2 ) are considered so that R 1 is labeled 1. Indeed in order to reduce the noise, it is enough to merge some white regions with the background, thus there is no need to process black regions. If the pair (R 1 , R 2 ) satisfies a given criterion, the two regions are merged. Merging two regions is done using the algorithm given in [START_REF] Dupas | Region merging with topological control[END_REF] which mainly consists in removing the faces separating the two regions, and possibly updating the edges and the vertices if needed.

Additional information associated with region R (which is the result of the merging of R 1 and R 2 ) must be updated. In this work, each region stores its number of voxels and its label. The number of voxels of R is the sum of the number of voxels of R 1 and the number of voxels of R 2 . The label of R is always fixed to 0. Indeed, R 1 is labeled 1, thus by definition of regions, R 2 is labeled 0 (two adjacent regions can not have the same label). Since our goal is to reduce the noise, region R, considered as noise, and which is the merging of one background region and one foreground region, must stay in the background.

At the end of the algorithm, all the pairs of regions were considered and the new video is returned: this is the partition described by the modified 3D topological map.

The complexity of Algo. 1 is linear in number of adjacencies between regions times the complexity of the criterion. The number of adjacencies between regions is equivalent to the number of edges in the multi-RAG. Indeed thanks to the cellular decomposition we can iterate through all these adjacencies which are explicited by the faces, and the regions around each face are directly retrieved thanks to the incidence relations. Now the main question is the definition of a criterion. Indeed, this is the main tool used during the reduce noise algorithm and only a correct definition will give good results. A first simple criterion, given in Eq. 1, consists in testing if the size of the white region is smaller than a threshold τ given by the user. The idea of this criterion comes from the fact that noise in image produces often small regions comparing to real objects. It is also important to highlight that for real objects there is always an overlapping between their appearances in consecutive frames, even at a low frame rate. Video used in experiments are at 10 fps and the overlapping between masks for real objects is always held.

size(R 1 ) < τ (1)
(R 1 being the region labeled 1)

The main interest of this criterion is to be very simple and computed in constant time since each region stores its size and the sizes are updated incrementally during the region merging. Note that this solution can be implemented using a multi-RAG data-structure instead of 3D topological maps. Indeed additional information described by topological maps are here not used.

One problem of this first criterion is that some white regions representing noise can have a size larger than the threshold and thus are not removed. By studying such regions, we have observed that they are often very porous because noise is non regular and noisy adjacent pixels have often different labels. For this reason, these regions have many voids and tunnels contrary to regions describing objects which have generally a small number of voids and tunnels. This observation tends to show that the threshold associated with regions having many voids and tunnels must be increased in order to have an higher chance to be removed. For that, we propose in Eq. 2 a second criterion which mixes the size of the white region and its Betti numbers. This second criterion has two parameters: τ the threshold for the size of small regions, and ϕ, a percentage which is multiplied by the sum of the Betti numbers of R 1 .

size(R 1 ) < τ * (1 + ϕ * (b 1 (R 1 ) + b 2 (R 1 ))) (2)
(R 1 being the region labeled 1)

This second criterion illustrates the interest of having an advanced description of regions (more precise than a RAG) allowing to compute and to mix several characteristics on regions. The complexity of this algorithm is equal to the complexity of the Betti number computation, i.e. linear in number of vertices, edges and faces describing region R 1 . These numbers can be bounded by the number of voxels of R 1 times a constant number (8 for vertices, 12 for edges and 6 for faces).

Experiments

Dataset and Algorithms

We use the PETS 2010 Dataset [START_REF]Pets2001 dataset[END_REF]. This dataset is a standard database widely used for the performance evaluation of tracking and surveillance algorithms.

In order to evaluate the performances of the proposed denoising algorithm, we start from foreground detection masks on PETS video sequences, resulting from the application of a basic background subtraction (BS) algorithm. We expressly used the basic BS algorithm without any improvement and parameter optimization, because we want to show that the proposed algorithm can clean detection masks without any pre-processing prior. This allows to be not dependent on the specific video sequence and it avoids the optimization parameters phase that is tedious and not always possible.

Starting from the same detection masks, we compare our algorithm with:

A1 a denoising algorithm that uses only morphological operations (erosion and dilatation); A2 the algorithm proposed in [START_REF] Conte | Evaluation and improvements of a real-time background subtraction method[END_REF] that adds, to the basic subtraction algorithm, several post-processing improvements;

A3 the algorithm [START_REF] Conte | Evaluation and improvements of a real-time background subtraction method[END_REF] with the addition of the grouping phase proposed by the same authors in [START_REF] Conte | An algorithm for recovering camouflage errors on moving people[END_REF].

As shown in [START_REF] Conte | An algorithm for recovering camouflage errors on moving people[END_REF], these algorithms are effective in reducing noise regardless of the method for foreground detection. Other approaches are not considered because of their high computational complexity. Note that the algorithms A2 and A3 require several parameters to set. A3 also requires a camera calibration phase (for details see [START_REF] Conte | An algorithm for recovering camouflage errors on moving people[END_REF]) for each video (taken with different camera settings). Therefore, in this experimentation we preliminary optimized these parameters, which are therefore specific for each sequence.

Our new method has two parameters: τ the threshold for the size, and nb which is the number of frames grouped in a same 3D slice. The method based on Betti numbers has an additional parameter: ϕ the percentage of Betti numbers added to the size.

Performance Index

We use an evaluation scheme inspired by the method presented in [START_REF] Wolf | Model based text detection in images and videos: a learning approach[END_REF]; it takes into account one-to-one as well as many-to-one and one-to-many matches.

The goal of a detection evaluation scheme, on a frame, is to take a list of ground truth boxes G = G 1 , . . . , G n and a list of detected boxes D = D 1 , . . . , D m and to measure the quality of the match between the two lists. From the two lists D and G two overlap matrices σ and τ are created. The rows i = 1 . . . |G| of the matrices correspond to the ground truth boxes and the columns j = 1 . . . |D| correspond to the detected boxes.

The values are calculated as follows:

σ ij = area(G i ∩ D j ) area(G i ) τ ij = area(G i ∩ D j ) area(D j ) (3)
The matrices can be analyzed for determining the correspondences between the two lists:

One-to-One Matches: G i matches against D j if row i of both matrices contains only one non-zero element at column j and column j of both matrices contains only one non-zero element at row i. The overlap area needs to have a certain size compared to the rectangle in order to be considered successful (σ ij ≥ e 1 and τ ij ≥ e 2 ).

One-to-Many Matches with One Ground Truth Box : G i matches against several detected boxes if row i of the matrices contains several non-zero elements. The additional constraint of j σ ij ≥ e 3 ensures that the single ground truth rectangle is sufficiently detected.

One-to-Many Matches with One Detected Box : D j matches against several ground truth boxes if column j of the matrices contains several non-zero elements. Also here we add the constraint of i τ ij ≥ e 4 .

Parameters e 1 , . . . , e 4 measure how much detected boxes against ground truth have to overlap. For most applications a value of 0.8 (80% of overlapping) is good; therefore we set e 1 = • • • = e 4 = 0.8.

Based on this matching strategy, the recall and precision measures are defined as follows:

recall = i M atch G (G i ) |G| precision = j M atch D (D j ) |D| (4)
where M atch G (G i ) is defined as follows: and M atch D (D j ) accordingly.

M atch G (G i ) =    1 if G i matches
The indexes Recall and Precision for a video sequence are the average values of recall and precision over all the frames of the sequence.

Results

Results of our experiments are given in Table 1 for the precision and recall measures, and in Table 2 for the F-score values (the harmonic mean of precision and recall). In all the arrays, dark grey cells are the best scores for each video, and light grey cells the second best scores. In these experiments, nb is always fix to 15. tXXX is the value obtained by the method with the size criterion with τ = XXX, and tXXX-pYYY is the value obtained by the method with the size and Betti numbers criterion with τ = XXX and ϕ = Y Y Y . 1. The values of the indexes precision and recall for the considered algorithms.

These results show that our new method is competitive comparing with the three previous algorithms. Generally, merging more regions (either by increasing τ or by increasing ϕ) decreases the recall while increases the precision until a certain point. Thus better results are obtained by finding the good thresholds giving the best compromise for precision and recall.

These results show a second important conclusion: the method using Betti numbers can greatly improve the results. This is for example the case for video v7 with τ = 2000, where the precision is improved from 0.23 without Betti to 0.37 with Betti using ϕ = .1.

These results are confirmed by the F-score values given in Table 2 which allow to find the best compromise between precision and recall. For all videos, the best scores are often obtained by the method using Betti numbers with τ = 2000 (best score for 3 videos, and second best score for the 4 other videos). 0.30 0.39 0.46 0.37 0.48 0.32 0.37 t2000-p.05 0.33 0.39 0.45 0.41 0.49 0.41 0.40 t2000-p.1 0.35 0.30 0.34 0.42 0.49 0.41 0.41 t2000-p.15 0.37 0.13 0.14 0.39 0.43 0.37 0.38 t3000-p.05 0.34 0.32 0.44 0.43 0.49 0.41 0.41 t3000-p.1 0.37 0.12 0.13 0.39 0.42 0.36 0.38 t3000-p.15 0.28 0.05 0.05 0.31 0.36 0.30 0.31 t4000-p.05 0.36 0.25 0.30 0.41 0.49 0.41 0.41 t4000-p.1 0.31 0.05 0.05 0.34 0.38 0.31 0.34 t4000-p.15 0.20 0.02 0.01 0.21 0.24 0.25 0.26 Table 2. The values of the F-score for the considered algorithms.

Conclusion

In this paper, we presented a new method of noise reduction on foreground video masks. Thanks to a 3D cellular description of the video, our method is defined in an high abstraction level considering regions and adjacency relations between these regions. This simplifies the denoising algorithm which consists mainly to merge foreground regions with the background. A second main advantage is the possibility of defining high level criteria on the regions. In this paper we use a simple criterion using the size of regions, and a more advanced criterion using Betti numbers (that gives better results). This second criterion can be defined thanks to the full cellular representation, while this is not directly possible using simpler data-structures such as region adjacency graph.

As future work, we first want to work on the automatic computation of the parameters of our method. A second perspective is to define other criteria. Thanks to our representation, many possibilities could be studied mixing geometrical criteria and topological ones. A last perspective is to use similar techniques (considering the 3D cellular description of a video) in other fields of video processing such that objects or activities recognition.

⋆

  Paper published in Proceedings of 18th Joint International Workshops on Statistical Techniques in Pattern Recognition and Structural and Syntactic Pattern Recognition, LNCS 8621, pp. 213-222, August 2014. Thanks to Springer Berlin Heidelberg. The original publication is available at http://dx.doi.org/10.1007/ 978-3-662-44415-3_22

Fig. 1 .

 1 Fig. 1. The 3D representation of a video. (a) The image sequence. (b) The construction of the 3D image. (c) The final representation.

Acknowledgement: This work has been partially supported by the French National Agency (ANR), project Solstice ANR-13-BS02-01.