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Mme NOEL DE JAEGHER Sophie (fin 31/08/2021) Médecine générale Je remercie tout d'abord le service de médecine nucléaire qui m'a aider dans ce projet et particulièrement le Pr Nicolas Aide qui m'en a proposer l'idée et qui a toujours été disponible ainsi que le Dr Charline Lasnon et le Dr Catherine Nganoa qui y ont participer.

Merci également à ce service de m'avoir accueilli pendant 6 mois, bien qu'il ne s'agisse pas de ma spécialité, j'ai trouvé cela très formateur et très complémentaire dans mon parcours.

Merci au Pr Damaj d'avoir bien voulu faire partie de cette étude et de mon jury de thèse, pour apporter un regard clinique à tout cela.

Merci à mes co-internes avec qui j'ai passé ces 5 années, qui finalement sont passer tellement vite.

Merci à ma famille qui m'a supportée durant toutes ces années, notamment à mes parents qui me soutiennent dans mes études depuis le début, et qui je l'espère sont fières de me voir arriver au bout.

Merci, tout particulièrement, à ma femme Pauline, avec moi depuis la P1, de Paris à Caen, qui m'a soutenu toutes ces années, qui m'a servi de public pour ma présentation et surtout qui a fait les petits fours ;)

Pour finir merci à mes filles Jade et Iris qui me donnent maintenant d'autres objectifs dans la vie.

Abréviations

Préambule

Dans la pratique quotidienne nous avons constaté, au cours de leurs suivi par Tomographie par émission de positons (TEP), que certains patients atteints de lymphome B diffus à grandes cellules, présentaient une hyperfixation splénique avec une inversion du rapport hépato/splénique, non présent sur les TEP initiales. Ces constations avaient également déjà été remarquées dans d'autres études et dans d'autres pathologies sur la rate et sur l'os notamment. Nous nous sommes alors intéressés aux facteurs supposés altérer la biodistribution du FDG chez les patients cancéreux recevant une chimiothérapie. Parmi ces facteurs il y a les facteurs stimulant la formation de colonies de granulocytes (G-CSF), qui sont utilisés pour réduire l'incidence de la neutropénie en stimulant l'hématopoïèse. Cette hématopoïèse a lieu essentiellement dans la moelle osseuse mais certaines études évoquent également la présence d'une hématopoïèse résiduelle dans la rate.

La proportion de patients atteints de lymphome de Hodgkin et de lymphome non hodgkinien recevant du G-CSF est élevée, car les schémas de chimiothérapie utilisés tendent à induire une leucopénie. Plusieurs médicaments sont disponibles (pegfilgrastim, filgrastim et lénograstim), nécessitant en moyenne 1 à 5 injections sous-cutanées quotidiennes, commençant 2 jours après la fin de la chimiothérapie. Les directives 2014 de l'EANM pour l'imagerie des tumeurs par la TEP et les recommandations de l'ASCO pour l'imagerie TEP dans les lymphomes recommandent un intervalle de temps de 10 jours entre la chimiothérapie et l'imagerie TEP. Par conséquent, il est de pratique courante de programmer un PET intermédiaire (i-PET) et en fin de traitement (EoT-PET) pas trop près de la dernière injection de G-CSF. Cela n'est toutefois pas toujours réalisable en pratique quotidienne parce qu'un traitement de chimiothérapie peut être différé pour diverses raisons, notamment une récupération insuffisante de la numération sanguine. Par conséquent, certains patients peuvent réaliser une imagerie peu de temps après leur dernière chimiothérapie et les dernières injections de G-CSF, entraînant une augmentation de l'absorption de la moelle osseuse et de la rate. Il en résulte une inversion du rapport foie / rate qui pourrait altérer l'évaluation post-traitement à l'aide du score de Deauville (DS). La séquestration de traceurs dans la moelle osseuse, appelée « sink effect » (ou vol métabolique), affecte également la biodistribution du FDG et potentiellement le DS. Il a été signalé que ce phénomène réduisait la disponibilité du traceur dans les tissus sains chez les patients atteints de tumeurs neuroendocrines volumineuses. Dans le cas des patients atteints de lymphome, cela pourrait affecter l'absorption hépatique et/ou l'absorption tumorale résiduelle.

Les objectifs de la présente étude, qui portait sur une population homogène de patients atteints de lymphome B diffus à grandes cellules et soumis à une analyse intermédiaire après immunochimiothérapie, consistaient : premièrement à effectuer une analyse complète du délai entre la dernière injection de G-CSF et la TEP sur la biodistribution du FDG, en mettant l'accent sur l'absorption du foie, de la rate et de la moelle osseuse; deuxièmement examiner si une inversion du rapport foie / rate affecte le score de Deauville.

Background

Amongst the factors thought to alter the FDG biodistribution in cancer patients receiving chemotherapy are granulocytes colony stimulating factors (G-CSF), which are used to reduce the incidence of neutropenia [START_REF] Lieschke | Granulocyte colony-stimulating factor and granulocytemacrophage colony-stimulating factor (1)[END_REF][START_REF] Lieschke | Granulocyte colony-stimulating factor and granulocytemacrophage colony-stimulating factor (2)[END_REF]. The use of G-CSF close to the FDG PET examination affects the FDG biodistribution, by significantly increasing the FDG uptake in bone marrow and in the spleen [START_REF] Jacene | Effects of pegfilgrastim on normal biodistribution of 18F-FDG: preclinical and clinical studies[END_REF][START_REF] Sugawara | Splenic fluorodeoxyglucose uptake increased by granulocyte colony-stimulating factor therapy: PET imaging results[END_REF]. The proportion of Hodgkin lymphoma and non-Hodgkin lymphoma patients receiving G-CSF is high, as the chemotherapy regimens used tend to induce leucopenia. Several drugs are available (Pegfilgrastim, Filgrastim and Lenograstim), requiring 1 to 5 daily subcutaneous injections on average, starting 2 days after the end of chemotherapy.

G-CSFs act on the monocyte-macrophage hematopoietic cell lineage to stimulate progenitor proliferation, differentiation, and functional activation of the mature hematopoietic cells. Due to their renal clearance, Filgrastim and Lenograstim are short-acting G-CSF and require daily injections. Pegfilgrastim has the same mechanism of action as filgrastim, but is pegylated and therefore has a reduced renal clearance, compared with that of filgrastim, prolonging the serum half-life of the drug in vivo and requiring a single injection.

The 2014 EANM guidelines for PET tumour imaging [START_REF] Boellaard | FDG PET/CT: EANM procedure guidelines for tumour imaging: version 2.0[END_REF][START_REF] Boellaard | FDG PET and PET/CT: EANM procedure guidelines for tumour PET imaging: version 1.0[END_REF] and the ASCO recommendations for PET imaging in lymphoma [START_REF] Juweid | Use of positron emission tomography for response assessment of lymphoma: consensus of the Imaging Subcommittee of International Harmonization Project in Lymphoma[END_REF] recommend a time-lapse of 10 days between chemotherapy and PET imaging. It is therefore common practice to schedule interim PET (i-PET) and end-of-treatment PET (EoT-PET) not too close to the last G-CSF injection. This is however not always feasible in busy PET centres and also because a chemotherapy regimen may be postponed for various reasons including insufficient blood count recovery. Consequently, some patients may be imaged shortly after their last chemotherapy and G-CSF injections, harbouring an increased bone marrow and spleen uptake. This results in an inversion of the liver to spleen ratio that could alter the posttreatment evaluation using the Deauville score (DS) [START_REF] Barrington | FDG PET for therapy monitoring in Hodgkin and non-Hodgkin lymphomas[END_REF]. Also affecting FDG biodistribution and potentially the DS is tracer sequestration in bone marrow, known as the sink effect. This phenomenon has been reported to reduce tracer availability in healthy tissues in patients with bulky neuroendocrine tumours [START_REF] Beauregard | The tumour sink effect on the biodistribution of 68Ga-DOTA-octreotate: implications for peptide receptor radionuclide therapy[END_REF]. In the case of lymphoma patients, this could affect the liver uptake and/or the residual tumour uptake.

The aims of the present study that focused on a homogeneous population of diffuse large B cell lymphoma patients scanned for interim evaluation after immune-chemotherapy were (1) to perform a comprehensive analysis of the time elapsed between the last G-CSF injection and the PET examination on the biodistribution of FDG, with emphasis on liver, spleen and bone marrow uptake; (2) to investigate whether an inversion of the liver to spleen ratio affects Deauville Scoring.

Materials and methods

Patients' recruitment

This study retrospectively included consecutive patients referred to our PET unit for baseline and interim examinations (after 4 cycles of chemotherapy), diagnosed with DLBCL between December 2014 and December 2017. EoT-PET were not included, as these scans are usually performed several weeks after completion of treatment, when effects of G-CSF tend to be negligible. All selected patients had received (R)-CHOP (Rituximab, cyclophosphamide, doxorubicin, vincristine, prednisone) or (R)-ACVBP (Rituximab, doxorubicin, cyclophosphamide, vindesine, bleomycin, prednisone) and G-CSF. For each patient, age, gender, Ann Arbor staging, baseline bone, spleen or liver involvement, Deauville scoring at interim PET, the number of injections of G-CSF and date of the last one, the type of G-CSF, and the date of the last injection of chemotherapy were recorded from the patients' medical files. Criteria of exclusion were chemotherapy other than R-CHOP or R-ACVBP, history of splenectomy, interim examinations not performed after 4 cycles and no use of G-CSF.

Approval to collect data for our study was validated by the national committee for data privacy, the National Commission on Information technology and Liberty (CNIL), with registration n° 2204611 v 0 and patients' consent to use anonymised data for research purposes was sought on an opt-out basis.

PET-CT acquisition and reconstruction parameters

PET examinations were performed as per the EANM guidelines for PET tumour imaging [START_REF] Boellaard | FDG PET/CT: EANM procedure guidelines for tumour imaging: version 2.0[END_REF][START_REF] Boellaard | FDG PET and PET/CT: EANM procedure guidelines for tumour PET imaging: version 1.0[END_REF].

Quantitative data presented in this study are EARL-compliant. Patients fasted at least 6 hours before intravenous injection of 18F-FDG and were scanned on a Biograph TrueV system (Siemens Heathineers) from the skull base to the mid-thighs. A free-breathing CT acquisition (60 mAs, 130 kVp, pitch 1, and 6 × 2 mm collimation) was followed by a PET acquisition with time per bed position of 160 and 220 s for normal weight (BMI ≤ 25 kg/m²) and overweight patients (BMI > 25 kg/m²), respectively.

PET studies were planned to be performed 60 ± 5 min post injection. Extraction of data from the PET DICOM headers showed the following information: mean injected dose ± SD was 4 ± 0.1MBq/Kg. Mean delay between injection and acquisition ± SD was 59.

PET-CT analysis

All PET-CT examinations were reviewed on Syngo.via Software (Siemens Medical Solution). A 6,3 mm Gaussian filter, determined as per the EARL accreditation program, was applied using the EQ.PET software [START_REF] Aide | EANM/EARL harmonization strategies in PET quantification: from daily practice to multicentre oncological studies[END_REF][START_REF] Lasnon | Generating harmonized SUV within the EANM EARL accreditation program: software approach versus EARLcompliant reconstruction[END_REF]. For each PET-CT examination, maximum standardized uptake values (SUVmax) were measured as follows:

-For liver and spleen, an automatic 3cm diameter volume of interest (VOI) was placed in the right liver lobe, avoiding liver or spleen lesions in the case of tumour involvement. A manually-set VOI fitting the size of the spleen was used in cases where spleen was smaller than the 3 cm VOI.

-For bone marrow assessment, a VOI of 2 cm was placed on the sacral promontory, avoiding sacral foramens.

Liver mean Hounsfield units (HU) were measured to seek hepatic steatosis [START_REF] Salomon | Assessment of alteration in liver (18)F-FDG uptake due to steatosis in lymphoma patients and its impact on the Deauville score[END_REF]. Baseline metabolic active tumour volume (MATV) was measured for each patient using a 41% isocontour method as per the EANM guidelines. In the case of multiple lesions MATV of all lesions were summed.

Statistical analysis

Quantitative data are presented as mean ± standard deviation (SD). Baseline and interim PET technical PET characteristics (injected dose, glycaemia, delay), as well as patient's BMI and liver densities were compared using the non-parametric Wilcoxon test for paired samples. To seek a difference between %Variation_BONE, %Variation_LIVER or %Variation_SPLEEN among the three types of G-CSF, Kruskal-Wallis test was used. Spearman correlations were performed to seek a link between %Variation_BONE, %Variation_LIVER or %Variation_SPLEEN and BMI percentage variation (%Variation_BMI), glycaemia percentage variation (%Variation_Glycaemia), baseline MATV as well as the time elapsed between the end of chemotherapy or the last G-CSF injection and interim PET acquisition. Spearman correlation was also used to search for a correlation linking the timelapse between chemotherapy or G-CSF last injection and interim PET. To seek a difference between SUVmaxEARL among different groups of patients, non-parametric Mann-Whitney or Kruskal-Wallis tests were used as appropriate. When needed, complementary multivariate analysis was performed using ANCOVA. With regards to the inversion of the liver to spleen ratio, differences in the time-lapse between the end of chemotherapy or the last G-CSF injection and interim PET in patients with this pattern versus those without were tested using Mann-Whitney test. Moreover, difference in the repartition of G-CSF type used between these 2 groups of patients was tested using Fischer's exact test.

Results

Population and PET characteristics:

Population characteristics can be seen in Table 1 and PET characteristics in Table 2. On paired comparison, the injected doses for baseline and interim PETs were not significantly different; neither was the time-lapse between injection and acquisition and liver densities. Mean BMI and glycaemia were significantly different between baseline and interim PET acquisition (Table 2, p<0.0001 and p=0.044, respectively). The mean bone uptake %variation between baseline and interim PETs (%Variation_BONE) was equal to 32.0 ± 46.9 % (n=57), the mean liver uptake %variation (%Variation_LIVER) was equal to 16.1 ± 42.8 % (n=73) and the spleen uptake %variation (%Variation_SPLEEN) was equal to 10.6 ± 51.1 % (n=66). None of them were influenced by the %variation_BMI: ρ=0.210 (p=0.117) for %Variation_BONE, ρ=-0.071 (p=0.548) for %Variation_LIVER and ρ=0.151 (p=0.227) for %Variation_SPLEEN. None of them were influenced by the %variation_Glycaemia: ρ=-0.039 (p=0.772) for %Variation_BONE, ρ=0.138 (p=0.244) for %Variation_LIVER and ρ=0.012 (p=0.921) for %Variation_SPLEEN. The mean time-lapse between the end of chemotherapy and i-PET for the whole series of patients (n=74) was equal to 16 ± 5 days (median=17 days) and the mean time-lapse between G-CSF injection and i-PET was equal to 8 ± 5 days (median=8 days). There was a significant correlation between these two variables (ρ=0.629, p<0.0001).

Characteristics

Bone %variations between baseline and interim PETs:

This analysis was performed on the 57 patients with no bone involvement at baseline and interim PET examinations.

%Variation_BONE between baseline and interim was not correlated to the baseline MATV (p=0.199, Fig. 1a). Moreover, there was no statistically significant difference in bone %variations between progressive disease patients (n=5) and non-progressive patients: 45.2 ± 74.8 % versus 30.8 ± 44.3 %, p=0.924. %Variation_BONE was not significantly different depending on which type of G-CSF was used (p=0.512, Fig. 1b). %Variation_BONE was negatively correlated to the time elapsed between the end of chemotherapy and i-PET acquisition but not correlated to the mean delay between G-CSF injection and interim PET acquisition: ρ=-0.342 (p=0.010) and ρ=-0.208 (p=0.12) (Fig. 1c). At interim PET, patients with a time-lapse between the end of chemotherapy and i-PET acquisition < 17days (representing the median value of the data) displayed higher bone SUVmaxEARL than the other patients (p<0.0001). Of note, there were no significant differences in bone SUVmaxEARL at baseline between these two groups of patients (p=0.087).

Representative images of patients with a short (< 17 days) or long time-lapse (≥ 17 days) between the end of chemotherapy and i-PET acquisition scan be seen on Fig. 2 and3, respectively.

Liver %variations between baseline and interim PETs:

This analysis was performed on the 73 patients with no liver involvement at baseline and interim PET examinations.

%Variation_LIVER between baseline and interim was positively correlated to the baseline MATV (ρ=0.243, p=0.039, Fig. 4a). Moreover, %Variation_LIVER was lower in progressive disease patients (n=5): -8.7 ± 11.1% versus 17.9 ± 43.7 %, p=0.013. Patients displaying a high baseline MATV ≥ 177cc (representing the median of the data) had significantly lower liver SUVmaxEARL at baseline (p=0.0002). This difference was no longer observed at interim PET (p=0.305). %Variation_LIVER was significantly different depending on which type of G-CSF was used (p=0.026).

%Variation_LIVER was higher when using Lenograstim as compared to Filgrastim or Pegfilgrastim, with a mean %variation of 42.6 ± 62.0 %, 14.6 ± 41.4 % and 0.2 ± 10.8 %, respectively. Baseline liver SUVmaxEARL were significantly lower for patients who received Lenograstim, whereas there was no significant difference at interim PET (Fig. 4b) %Variation_LIVER was not correlated to the time elapsed between the end of chemotherapy and i-PET acquisition (p=0.946, Fig. 4c) nor to the mean delay between G-CSF injection and interim PET acquisition (p=0.870).

On multivariate analysis accounting for baseline MATV and the type of GCSF used, baseline MATV was the only independent explanatory variable for %Variation_LIVER (p<0.0001, Fig. 2).

Spleen %variations between baseline and interim PETs:

This analysis was performed on the 66 patients with no spleen involvement at baseline at baseline and interim PET examinations. %Variation_SPLEEN between baseline and interim was not correlated to the baseline MATV (ρ=0.085, p=0.497, Fig. 5a). There was no statistically significant difference in %Variation_SPLEEN between progressive disease patients (n=5) and non-progressive patients: -5.6 ± 17.6 % versus 11.9 ± 52.8 %, p=0.45. %Variation_SPLEEN was significantly different depending on which type of G-CSF was used (p=0.034). %Variation_SPLEEN was higher when using Lenograstim as compared to Filgrastim or Pegfilgrastim, with a mean %variation of 58.9 ± 110.3 %, 1.0 ± 24.1 % and 10.3 ± 44.8 %, respectively (Fig. 5b). Baseline spleen SUVmaxEARL were significantly lower for patients who received Lenograstim, whereas there was no significant difference at interim PET. %Variation_SPLEEN was negatively correlated to the time elapsed between the end of chemotherapy and i-PET acquisition (ρ=-0.529, p<0.0001, Fig. 5c) as well as to the mean time-lapse between G-CSF injection and interim PET acquisition (ρ=-0.343, p=0.005). At interim PET, patients with a time-lapse between the end of chemotherapy and i-PET acquisition < 17days

(representing the median value of the data) displayed higher spleen SUVmaxEARL than the other patients (p=0.0002). Of note, there were no significant differences in spleen SUVmaxEARL at baseline between these two groups of patients (p = 0.199). Representative images of patients with a short (< 17 days) or long time-lapse (≥ 17 days) between the end of chemotherapy and i-PET acquisition scan be seen on Fig. 2 and3, respectively.

On multivariate analysis accounting the type of GCSF used, the time elapsed between the end of chemotherapy and i-PET acquisition and the mean time-lapse between G-CSF injection and interim PET acquisition, the use of Lenograstim and the time-lapse between the end of chemotherapy and i-PET acquisition were independent explanatory variables for %Variation_SPLEEN with p value 0.007 and 0.033, respectively.

Occurrence of inversion of the hepatosplenic ratio:

This analysis was performed on the 65 patients with no spleen or liver involvement at baseline and interim PET examinations.

Inversion of the hepatosplenic ratio occurred in 17 patients (26.1%). Patients with an inversion of the liver-to-spleen ratio had lower time-lapse between the end of chemotherapy and i-PET acquisition as compared to others: 11 ± 5 days versus 18 ± 4 days, respectively (p<0.0001). There was no significant difference in type of G-CSF used between patients displaying an inversion of the liver-to-spleen ratio and those who did not (p=0.218).

Discussion

G-CSF are recommended after the two main chemotherapy regimens used to treat DLBCL, namely R-CHOP and R-ACVB, and have been reported to induce increased uptake in the spleen and in the bone marrow [START_REF] Jacene | Effects of pegfilgrastim on normal biodistribution of 18F-FDG: preclinical and clinical studies[END_REF], the latter also being affected by normal regeneration following chemotherapy.

Previous studies reported effects of G-CSF on the biodistribution of FDG at a time when only one type of G-CSF was available (Pegfilgrastim [START_REF] Jacene | Effects of pegfilgrastim on normal biodistribution of 18F-FDG: preclinical and clinical studies[END_REF]), and did not account for the time elapsed between both the chemotherapy and the last injection of G-CSF and that PET scan. Indeed, while the physiopathological basis of G-CSF makes obvious the link between this treatment and the observed increased uptake in the spleen [START_REF] Tsoi | Splenic hematopoiesis after granulocyte-colony stimulating factor therapy in a lupus patient[END_REF], increased bone marrow uptake could be due to either G-CSF and/or bone marrow regeneration. Sequestration of FDG within the skeleton could alter residual tumour uptake and therefore Deauville scoring. Given the observed variability in the type and duration of G-CSF treatment, a better knowledge of the phenomenon responsible for an altered bone marrow and spleen biodistribution and the duration of these patterns would be useful for a better scheduling of patients' scans in the busy PET unit. It would also help in deciding whether a PET scan has to be postponed when a patient shows up early after the last injection of G-CSF.

In our study, Lenograstim was associated with a higher percentage of variation in liver and spleen between baseline and interim PET. However, the variation in the liver and spleen was linked to a lower uptake in the two organs at baseline, likely due to tumour sequestration in bulky tumour masses, and was therefore not due to the G-CSF itself. This hypothesis is supported by the fact that we found that %Variation_LIVER was lower in progressing patients compared to the non-progressing patients.

The time elapsed between the last injection of G-CSF and the interim PET examination appeared less decisive than the time-lapse between the end of chemotherapy and the i-PET examination, even if a strong correlation was observed. Indeed, no association between the variation in bone marrow, liver and spleen and the time-lapse between the last injection of G-CSF and the interim PET examination was found on multivariate analysis. On the other hand, a delay inferior to 17 days between the end of chemotherapy and the i-PET examination led to increased bone and spleen uptakes on interim PET images. These findings have practical consequences when planning PET examinations: as an a priori knowledge of the type and dose of G-CSF, as well as patients' compliance to injections is difficult to apprehend, scheduling PET scans at least 15 days after the last injection of chemotherapy may be recommended. Of note, guidelines for PET imaging in lymphoma patients recommend a 10 days delay after chemotherapy [START_REF] Juweid | Use of positron emission tomography for response assessment of lymphoma: consensus of the Imaging Subcommittee of International Harmonization Project in Lymphoma[END_REF], which appears insufficient based on our data. Indeed, our results show that a time-lapse of 15 days could allow to eliminate the majority (9/12, 75%, Fig 2c and3c) of patients displaying a percentage of variation in the bone uptake greater than 50%, while taking the 10-day time-lapse would identify only a few of these patients (3/12, 25%, Fig 2c and3C).

Of note, despite its longer half-life compared to Filgrastim and Lenograstim due to its PEGylated nature, we did not observe larger variations in bone marrow and spleen uptake in the group of patients having received Pegfilgrastim. In the study from Jacene et al [START_REF] Jacene | Effects of pegfilgrastim on normal biodistribution of 18F-FDG: preclinical and clinical studies[END_REF] involving breast cancer patients receiving Docetaxel plus Pegfilgrastim, the time-lapse between the last injection of chemotherapy and PET scan was 7 ± 0.7 days, and the time-lapse between the last injection of GCSF and PET scan was 6 ± 0.7 days, compared to 16 ± 5 and 8 ± 5 days in our study, respectively.

We feel likely that the greater increase in bone marrow and spleen they observed compared to our data {% variation-BONE and %variation-SPLEEN equal to 244.6 ± 127.3 % and 171.3 ± 60.6 % versus 32.0 ± 46.9 % and 10.6 ± 51.1, respectively}, is related to a shorter time-lapse post chemotherapy.

On multivariable analysis percentage variation in the liver was only influenced by the baseline MATV via the well-known sink effect that led to low liver uptake at baseline, this phenomenon being reversible after chemotherapy, when bulky tumour masses had shrunk, as shown in Figure 4.

Interestingly, hepato-splenic ratio inversion, which is only associated with a shorter time-lapse between the end of chemotherapy and the i-PET acquisition, is therefore only due to an increase in spleen uptake. Lower FDG hepatic uptake in lymphoma patients due to a tumour sink effect has already been suspected by Wu et al [START_REF] Wu | The Association Between Liver and Tumor [18F]FDG Uptake in Patients with Diffuse Large B Cell Lymphoma During Chemotherapy[END_REF]. Another confounding factor potentially decreasing liver metabolism is liver steatosis [START_REF] Salomon | Assessment of alteration in liver (18)F-FDG uptake due to steatosis in lymphoma patients and its impact on the Deauville score[END_REF].However, in the present series, steatotic liver was only observed in 14 patients (18.9%) and liver densities were not different between baseline and interim PET examinations, meaning that %Variation_LIVER is certainly not biased by steatosis. Therefore, overall, inversion of the hepato-splenic ratio is unlikely to have any influence on Deauville score determination. However, Deauville scoring could still be influenced by a sink effect [START_REF] Beauregard | The tumour sink effect on the biodistribution of 68Ga-DOTA-octreotate: implications for peptide receptor radionuclide therapy[END_REF] due to tracer sequestration in the bone marrow: Teoh et al predicted the tumour uptake to be reduced by a maximum of 11.5 % in the case of G-CSF-induced hypermetabolism in the bone marrow [START_REF] Teo | Correcting tumour SUV for enhanced bone marrow uptake: retrospective 18F-FDG PET/CT studies[END_REF].

Based on all these findings together, maintaining the time-lapse between the chemotherapy and the PET examination greater than 15 days appears to be a simple way of avoiding disturbance in FDG biodistribution and detrimental effect on Deauville scoring in interim PET.

Conclusion

Neither the type of G-CSF used nor the time elapsed between its last injection and interim PET examination independently influences bone, hepatic or splenic uptakes. The liver uptake is not influenced by any of these factors and therefore the occurrence of a hepato-splenic ratio inversion is only due to spleen hypermetabolism, making unlikely an impact on Deauville scoring. The major determinant for the occurrence of a bone or spleen hypermetabolism on interim PET is the timelapse between the chemotherapy and the PET examination, which should be maintained greater than 15 days.

Conclusion finale

RESUME DE LA THESE EN ANGLAIS :

Aims:(1) To perform a comprehensive analysis of the time elapsed between the last G-CSF injection and the PET examination on the biodistribution of FDG, with emphasis on liver, spleen and bone marrow uptake; (2) To investigate whether an inversion of the liver to spleen ratio affects Deauville Scoring. Materials and methods: Retrospectively included were 74 consecutive diffuse large-B-cell lymphoma (DLBCL) patients referred for baseline and interim examinations and receiving immunochemotherapy with various G-CSF regimens. A comprehensive evaluation considering baseline MATV, factors affecting liver uptake, the type of G-CSF and the time elapsed between chemotherapy/G-CSF and interim PETs was performed.

Results: Mean (±SD) percentage variation between baseline and interim pets (i-PET) for bone marrow (%Variation_BONE), liver (%Variation_LIVER) and spleen (%Variation_SPLEEN) were equal to 32.0(±46.9) %, 16.1(±42.8) % and 10.6(±51.1) %, respectively. %Variation_LIVER and %Variation_SPLEEN were higher in patients using lenograstim but this was linked to lower uptakes at baseline and was therefore likely not due to G-CSF itself. The mean delay between G-CSF injection and i-PET acquisition was not an independent explanatory variable for %Variation_BONE, %Variation_LIVER and %Variation_SPLEEN. On the contrary, %Variation_BONE and %Variation_SPLEEN were negatively correlated to the time-lapse between the end of chemotherapy and i-PET: ρ=-0.342 (p=0.010) and ρ=-0.529 (p<0.0001), respectively. Patients with a time-lapse since the last injection of chemotherapy < 17days displayed higher bone and spleen SUVmaxEARL. %Variation_LIVER was positively correlated to baseline MATV: ρ=0.243 (p=0.039). Patients displaying a high baseline MATV≥177cc had significantly lower liver SUVmaxEARL at baseline. This difference was no longer observed at i-PET, after tumours had shrunk. Conclusions: Neither the type of G-CSF used nor the time elapsed between its last injection and i-PET examination independently influences bone, hepatic or splenic uptakes at i-PET. The major determinant for the occurrence of a bone or spleen hypermetabolism on i-PET is the time elapsed between the chemotherapy and the examination, which should be maintained above 15 days. Inversion of the liver to spleen ratio appeared to be due to increased spleen hypermetabolism on i-PET, making unlikely an impact on Deauville scoring.

KEY WORDS : Lymphoma; PET; FDG; G-CSF; Lenograstim; Filgrastim; Pegfilgrastim; sink effect; Deauville score

  PET/CT: Positron emission tomography / computed tomography FDG: 18F-Fluorodeoxyglucose DLBCL: Diffuse large-B-cell lymphoma G-CSF: Granulocytes colony stimulating factors DS: Deauville Scoring MATV: Metabolic active tumour volume i-PET: Interim PET Eot-PET: End-of-treatment PET VOI: Volume of interest HU: Hounsfield unit BMI: Body Mass Index %Variation_BONE : percentage variation between baseline and interim PETs for bone marrow %Variation_LIVER: : percentage variation between baseline and interim PETs for liver %Variation_SPLEEN: : percentage variation between baseline and interim PETs for spleen %Variation_BMI: percentage variation between baseline and interim PETs for BMI %Variation_Glycaemia: percentage variation between baseline and interim PETs for glycaemia Sommaire Remerciements Abréviations Sommaire Préambule .…….…………………..……………………….……………………. 1 Article ...…………………………..……………………..………………………. 3 Background ..………………………..……………………..……………… Materials and methods .………………..………..………………………… Results .…………………………..……………………..…………………. Discussion ..……………….…………..……………………..……………. Conclusion ……..…………..………..……………………..……………... Conclusion finale ..…………..……………………………..……………………. Bibliographie ..………………..……..……………………..……………………. Annexes ..…..……………..………………..…………………………………….

  Les G-CSF agissent sur la lignée cellulaire hématopoïétique monocyte -macrophage pour stimuler la prolifération des progéniteurs, la différenciation et l'activation fonctionnelle des cellules hématopoïétiques matures. En raison de leur clairance rénale, le Filgrastim et le Lénogastrim sont des G-CSF à courte durée d'action qui nécessitent des injections quotidiennes. Le pegfilgrastim a le même mécanisme d'action que le filgrastim, mais il est pégylé et présente donc une clairance rénale réduite par rapport à celle du filgrastim, prolongeant la demi-vie sérique du médicament in vivo et nécessitant une seule injection.

  3 ± 5.2 min on baseline and 4 ± 0.2MBq/Kg and 60.3 ± 5.0 min on interim TEP, respectively. Raw data were reconstructed with point spread function (PSF) modeling (HD; TrueX, Siemens Heathineers), with 3 iterations and 21 subsets and no filtering. Matrix size was 168 × 168 resulting in voxels of 4.07 × 4.07 × 4 mm.

Figure 1 :

 1 Figure 1: Percentage variation (right panels) or absolute value (left panels) for bone marrow uptake

Figure 2 :

 2 Figure 2: 52-year-old male patients imaged at baseline (a and b) and after 4 cycles of R-ACVBP (c and d).Interim PET was performed 7 days and 6 days following the last injection of chemotherapy and G-CSF, respectively. The injected G-CSF was Lenograstim, at a dosage of 34MUI daily for a 4-day period. In this case, low hepatic FDG uptake can be observed at baseline because of a tracer sequestration in the bulky mass. This pattern resolves after the tumour at shrunk on interim PET but because of a short time-lapse between the last chemotherapy injection and interim PET, an increased bone marrow and splenic uptakes are observed.

Figure 3 :

 3 Figure 3: A 47-year-old female patient imaged at baseline (a, b) and after 4 cycles of R-ACVP (c, d). Interim PET/CT was performed 17 days and 12 days following the last injection of chemotherapy and G-CSF, respectively. The injected G-CSF was lenograstim, at a dosage of 34MUI daily for a 5-day period. Thanks to a time-lapse between the last chemotherapy injection and interim PET/CT, no significant increased bone marrow or splenic uptake are observed.

Figure 4 :

 4 Figure 4: Percentage variation (right panels) or absolute value (left panels) for liver uptake between

Figure 5 :

 5 Figure 5: Percentage variation (right panels) or absolute value (left panels) for spleen uptake

Table 1 : Patients' characteristics (n=74).

 1

	Age (yr), mean ± SD [min-max]	60 ± 14 [21;80]
	Sex n (%)
	Female		35 (47.3) %
	Male		39 (52.7) %
	Age-adjusted IPI, n (%)
	0		8 (10.8) %
	1		28 (37.8) %
	2		24 (32.4) %
	3		14 (19.0) %
	Deauville score at i-PET, n (%)
	1		23 (31.1) %
	2		13 (17.6) %
	3		11 (14.9) %
	4		13 (17.6) %
	5		14 (18.9) %
	Growth factor type (G-CSF), n (%)
	Filgrastim		52 (70.3) %
	Lenograstim		10 (13.5) %
	Pegfilgrastim		12 (16.2) %
	First line of chemotherapy, n (%)
	(R)CHOP		68 (91.9) %
	(R)ACVBP		6 (8.1) %
	Bone involvement*, n (%)		17 (23.0) %
	Spleen involvement*, n (%)		8 (10.8) %
	Liver involvement*, n (%)		1 (1.3) %
	Baseline MATV (cc), mean ± SD	449.4 (732.0) %
	Characteristics (mean ± SD)	Baseline PET	Interim PET	P value
	Injected dose (MBq/Kg)	4.0 ± 0.2	3.9 ± 0.4	0.132
	Post-injection time (min)	59.2 ± 5.1	59.7 ± 4.9	0.602
	BMI (Kg/m²)	26.6 ± 5.6	25.7 ± 5.5	<0.0001
	Glycaemia (g/L)	1.00 ± 0.15	1.05 ± 0.19	0.044
	Liver density (HU)	49.4 ± 10.1	48.8 ± 12.5	0.721

IPI: International Prognostic Index, i-PET: interim PET, MATV: metabolic active tumor volume, * based on PET analysis

Table 2 : PET characteristics.

 2

  Ni le type de G-CSF utilisé ni le temps écoulé entre sa dernière injection et l'examen TEP intermédiaire n'influencent de manière indépendante l'absorption osseuse, hépatique ou splénique. L'absorption par le foie n'est influencée par aucun de ces facteurs et, par conséquent, la survenue d'une inversion du rapport hépato / splénique n'est due qu'à un hypermétabolisme de la rate, ce qui rend peu probable l'impact sur le score de Deauville. Le principal déterminant de la survenue d'un hypermétabolisme osseux ou splénique sur une TEP intermédiaire est l'intervalle de temps entre la chimiothérapie et l'examen TEP, qui devrait être supérieur à 15 jours. Analyse de l'influence des facteurs de croissance granulocytaires sur la biodistribution du FDG chez les patients atteints de lymphome RESUME DE LA THESE EN FRANÇAIS : Effectuer une analyse complète du délai entre la dernière injection de G-CSF et l'examen PET sur la biodistribution du FDG, en mettant l'accent sur l'absorption du foie, de la rate et de la moelle osseuse; (2) Déterminer si une inversion du rapport foie / rate affecte le score de Deauville. Matériels et méthodes: 74 patients consécutifs atteints de lymphome B diffus à grandes cellules (DLBCL) adressés pour des examens initiaux et intermédiaires, ainsi qu'une immunochimiothérapie sous divers schémas de G-CSF ont été inclus rétrospectivement. Une évaluation complète prenant en compte le MATV de base, les facteurs affectant l'absorption hépatique, le type de G-CSF et le temps écoulé entre la chimiothérapie / G-CSF et les PET intermédiaires a été réalisée. Résultats: Le pourcentage de variation moyen (± DS) entre les TEP initiales et intermédiaires (i-TEP) pour la moelle osseuse (% Variation_OS), le foie (% Variation_FOIE) et la rate (% Variation_RATE) était égale à 32.0 (± 46,9)%, 16.1 ( ± 42.8)% et 10.6 (± 51.1)%, respectivement. Le % Variation_FOIE et le % Variation_RATE étaient plus élevés chez les patients traités par le lénograstim, mais ceci était lié à des absorptions plus faibles au départ et n'était donc probablement pas dû au G-CSF lui-même. Le délai moyen entre l'injection de G-CSF et l'acquisition d'i-PET n'était pas une variable explicative indépendante pour le % Variation_OS,% Variation_FOIE et le % Variation_RATE. Au contraire, le % Variation_OS et le % Variation_RATE étaient corrélés négativement au laps de temps entre la fin de la chimiothérapie et l'i-PET: ρ = -0,342 (p = 0,010) et ρ = -0,529 (p <0,0001), respectivement. Les patients présentant un délai depuis la dernière injection de chimiothérapie < 17 jours présentaient un SUVmaxEARL plus élevé au niveau des os et de la rate. Le % Variation_FOIE était positivement corrélé au MATV de base: ρ = 0,243 (p = 0,039). Les patients présentant un MATV≥177cc au début du traitement avaient un taux de SUVmaxEARL au foie significativement plus bas au départ. Cette différence n'a plus été observée au i-PET après la réduction des tumeurs. Conclusions: Ni le type de G-CSF utilisé, ni le temps écoulé entre sa dernière injection et l'examen i-PET n'influencent de manière indépendante l'absorption osseuse, hépatique ou splénique sur le i-PET. Le principal déterminant de la survenue d'un hypermétabolisme osseux ou splénique sur un i-PET est le temps écoulé entre la chimiothérapie et l'examen, qui doit être maintenu au-dessus de 15 jours. L'inversion du rapport foie / rate semble être due à une augmentation de l'hypermétabolisme de la rate sur i-PET, rendant peu probable un impact sur le score de Deauville.

	ANNEE DE SOUTENANCE : 2019
	NOM ET PRENOM DE L'AUTEUR : PEREIRE DE OLIVEIRA Magno
	TITRE DE LA THESE : Objectifs: (1)
	VU, le Doyen de la Faculté
	VU et permis d'imprimer
	en référence à la délibération
	du Conseil d'Université
	en date du 14 Décembre 1973
	Pour le Président
	de l'Université de CAEN et P.O
	Le Doyen

MOTS CLES : Lymphome ; TEP ; FDG ; G-CSF ; Lenograstim; Filgrastim; Pegfilgrastim; vol métabolique ; Score de Deauville TITRE DE LA THESE EN ANGLAIS : Comprehensive analysis of the influence of G-CSF on the biodistribution of FDG in lymphoma patients: insights for PET scheduling.

Remerciements

Annexes

Article publié dans l'European Journal of Nuclear Medicine and Molecular Imaging Research (EJNMMI Research) le 20 Août 2019. https://ejnmmires.springeropen.com/ https://ejnmmires.springeropen.com/articles/10.1186/s13550-019-0546-1 « Par délibération de son Conseil en date du 10 Novembre 1972, l'Université n'entend donner aucune approbation ni improbation aux opinions émises dans les thèses ou mémoires. Ces opinions doivent être considérées comme propres à leurs auteurs ».


Eric Benoit
email: eric.benoit@univ-savoie.fr

Stephane Perrin

Didier Coquin

Body posture measurement in a context of example-based teaching

This paper presents a measurement process of body postures operated in a context of humanoid robot learning. The basic measured quantities are the angle joints of a human skeleton and the angle joints of a humanoid robot. Due to the differences between the two mechanical structures, the measurement results are expressed into a common representation space by the way of fuzzy scales. This paper shows how the common representation space can be defined, and presents a method to match weakly defined postures with uncertain measurements of a human posture.

Introduction

The era of humanoid robots now enters into a new step with the introduction of products for nonprofessional users. The set of applications of such robots is quickly growing and the conventional systems for the configuration and the robot programming stay dedicated to specific users. A solution to extend the set of potential robot programmers is to map education techniques on the context of robots. In particular, we suppose that it is possible to teach postures and gestures to a humanoid robot with a sample-based teaching method. The chosen process to perform such method is given:

• a human called teacher performs a posture, • this posture is measured then interpreted, • following the interpretation, the robot tries to perform the same posture.

• the robot posture is measured and compared to the teacher posture.

In order to be compared, the postures of the teacher and of the robot need to be expressed in a common space. Unfortunately, the numerical space in which the angles of the human joints are expressed cannot be the same than the numerical space used to represent the angles of the robots joints. This difference mainly comes from the distribution of the DOF (degrees of freedom) that differs between the teacher and the robot.

The solution we propose is to perform measurements with fuzzy scales [1][2]. This allows to represent a measurement indication as a fuzzy lexical set with dimension 6, each dimension leading to a part of the body : legs, torso, arms and head. For each dimension, i.e. for each body part, the posture of this part is represented with a usual Lexical Fuzzy Subset (LFS). A LFS is then a fuzzy subset of lexical terms, each lexical term being associated to a characteristic posture of this body part. The indication given by the measurement of the full body is then defined as a 6 components vector of LFSs.

The main advantage of this approach is that the same set of lexical terms can be used to characterise a part-posture of the teacher or the equivalent part-posture of the robot. This means that the measurements of full body postures of the teacher and of the robot are expressed into the same representation space and can be compared. It has been shown before that fuzzy scales are metrical scales and restrict the set of relations between measurement results to the comparisons of distances. But these relations are enough to perform the comparisons we need and to manage the measurement uncertainty.

Numerical measurements

The body posture measurements of the teacher and of the robot are performed with 2 different systems. The body of the teacher is acquired with an image depth sensor (a Azuz Xtion pro in our case) [START_REF] Yang | Automatic measurement of scanned human body in fixed posture Computer-Aided Industrial Design Conceptual Design[END_REF]. A middle-ware extracts the body shape and computes the 3D coordinates of the joints to give a skeleton approximation as for [START_REF] Handrich | A robust method for human pose estimation based on geodesic distance features Systems, Man, and Cybernetics[END_REF] [START_REF] Xie | Image Processing[END_REF]. Each joint is either a 1DOF joint or a 3DOF joint. Each 1DOF joint is characterized by a single angle. Each 3DOF joint is characterized by a normal rotation axe and an angle. The robot used for this study is a Nao robot from Aldebaran Robotics. It holds 13 joints with a total of 25DOF. Each rotation axe has a proprioceptive sensor that is used for the measurement of the body posture.

The teacher body and the robot body are decomposed into 6 parts that are the left and right arms, the left and right legs, the torso, the head. For each part, the information entities used to express indications and measurement results are vectors of numerical data.

Thanks to the proprioceptive sensors, the measurement uncertainty is negligible for the robot posture, but needs to be managed for the teacher posture. Actually the measurement process with an image depth sensor induces two kind of uncertainties. The first uncertainty is an ontic uncertainty [START_REF] Dubois | Ontic vs. epistemic fuzzy sets in modeling and data processing tasks[END_REF] and comes from the common statistical dispersion of the 3D coordinates of joints and can be estimated with a type A evaluation [7] [8]. The second uncertainty comes from the fact that a joint can be hidden by another part of the body or can simply be confused with another object (see figure 1). A third source of uncertainty named epistemic uncertainty [START_REF] Dubois | Ontic vs. epistemic fuzzy sets in modeling and data processing tasks[END_REF] is not directly linked to the measurement but depends on the definition of postures that can be imprecise. In this case a posture is no more defined with a value (actually a vector), but with a set of values. Such set doesn't define a probability distribution but a possibility distribution. As the simultaneous management of the measurement uncertainty and the epistemic uncertainty is not simply performed within a pure probabilistic approach, we use the Dempster-Shafer evidence theory that allows to handle in the same approach probabilities and possibilities [START_REF] Smets | Data fusion in the transferable belief model Proc. of the 3rd conf. on Information Fusion[END_REF].

The transferable belief model

The Dempster-Shafer evidence theory, also named the transferable belief model (TBM) is a general approach for uncertainty management based on the assignment of belief to sets. In this section, we present a short introduction to this theory.

The main element of the TBM is the frame of discernment denoted Ω and presented as a set of elementary events, or as a discourse set for the expression of the belief in a piece of evidence. The belief in a piece of evidence E is then expressed with a mapping m[E] (or simply m) called belief function, or basic belief assignment (BBA). This mapping is defined from the set of subsets of Ω, denoted 2 Ω , to the set [0, 1]. It represents the distribution of a weight of belief over the event sets. A non null amount of belief assigned to an event set means that the occurrence of the given events are compatible with the piece of evidence.

Any belief function verifies:

A∈2 Ω m(A) = 1 (1)
The set {A | m(A) > 0} is called the set of focal elements of m, and the couple ({A | m(A) > 0}, m) is called a body of evidence of a variable with values on Ω. The link with the probability theory is performed with the body of evidences of the form (A ∈ Ω, m). In this case the focal sets are singletons and the BBA m, qualified as a Bayesian BBA, is a probability distribution over Ω. The other categories of BBA used in our studies are the consonant BBAs which focal sets are nested sets. These last BBAs lead to possibility distributions. The belief in two pieces of evidence E 1 and E 2 issued from 2 independent sources can be computed with a conjunctive combination operator:

m[E 1 ∩ E 2 ](A) = B∩C=A m[E 1 ](B)m[E 2 ](C), ∀A ⊆ Ω (2)
This operator can be used if both sources are reliable. In this case, it concentrates the amount of belief on events that are compatible with both pieces of evidence. This operator has the property to assign some belief on the empty set. The value m[E 1 ∩ E 2 ](∅) is actually representative of the degree of conflict between sources. In order to moderate the degree of conflict it is possible to weaken the confidence into a source with a transfer of belief to the set Ω.

The fuzzy linguistic representation of the measured values

The method used to build a linguistic representation of measured postures is similar to the method previously used for hand posture measurement in [10]. In the initial study, only measurement indications were considered as measurement results. If we apply this approach to our case, each posture indication is represented by a LFS (Lexical Fuzzy Subset) defined on the cross product Ω of 6 lexical sets, each one corresponding to a body part. Within the scope of evidence theory used in this paper, Ω is interpreted as the exhaustive set of mutually exclusive representations of a posture.

L Body = {vertical, bent, lef t, right} (3)
L Head = {f ront, lef t, right, up, down, lef tbent, rightbent}

L RightLeg = L Lef tLeg = {down, up, behind, outside}.{open, square, closed}

L RightArm = L Lef tArm = {down, up, behind, outside, bodyside}.{open, square, closed}

Building the epistemic knowledge

The first step before any measurement is to define the universe of discourse on which any measurement is expressed. In our approach, the universe of discourse is made of labels that identify postures. So each posture is identified by a unique label but a label fits with a set of postures. For example, the label chekingHand identifies several postures with several left arm locations.

According that, the sets of postures are learned with examples, we propose to model the knowledge on postures with belief functions. Indeed, this knowledge is acquired from various sources and cannot be simply limited to the definition of the labels. It also hold an epistemic uncertainty. The process is the following:

First the meaning of each lexical set L i is defined as a fuzzy partition of the numerical set such that:

• An observation of the posture is performed and gives an indication expressed as a LFS on each lexical set. • An aggregation is performed to compute a LFS on the general lexical set Ω. The membership of the observation to each lexical term is interpreted as a Bayesian basic belief assignment m 1 on Ω 2 . The definition of postures can be interpreted as a classification building problem. The idea is to build a BBA that includes the knowledge related to a posture. We suppose that for a given posture to learn, we have a set of samples given by a teacher and represented by LFSs. One possibility is to consider all samples as independent sources and use the conjunctive combination to build a BBA consistent with all samples. This approach is consistent if the samples are close from each other but cannot be used in our case because a posture is imprecisely defined. In [11] Denoeux proposed to weaken the confidence into samples that are not similar with the previous learned samples. But this option stays unsuitable in our case where two dissimilar samples can be strongly representative of the same posture. Another possibility is to aggregate the Bayesian BBA associated to each sample with a simple mean operator. The resulting Bayesian BBA is then translated into a consonant BBA using the discrete version of the Yamada's algorithm [START_REF] Yamada | Probability-possibility transformation based on evidence theory[END_REF].

Step 1: Let m 1 be the Bayesian basic belief assignment to translate. Let j = 1 be an iterator.

Notice that all focal sets are singletons.

Step 2: Let A = {ω i | m j ({ω i }) = 0} be the set of focal sets of m j that are singleton. Let a be the smallest belief assignment on a singleton in A.

Step 3: Transfer the amount a of belief assignment from each singleton in A to the set A.

∀ω ∈ A, m j+1 (ω) = m j (ω) -a (8)
m j+1 (A) = ω∈A a = a | A | (9)
Step 4: If m j+1 has at least one singleton as focal set, increment the iterator j and go to step 2. At the end of this process, each archetype posture P is weakly defined by a BBA m[P ]. These BBAs are consonant BBAs and are therefore considered as possibility distributions (see figure 3).

Conclusion

As for psycho-physical scales, the scale built for human posture recognition depends on a knowledge on the posture definitions: an epistemic knowledge. Thus, the definitional uncertainty known as the epistemic uncertainty is more related to the consistency of the knowledge than related to statistical events. Such uncertainty is then preferably modeled in the frame of possibility theory that allows to model unknown events. The management of ontic uncertainty issued from measurements is based on statistical approaches and are preferably modelled in the frame of the probability theory that gives a large set of mathematical tools. In this paper ontic and epistemic uncertainties interact at two steps. First when the epistemic knowledge is built with a set a measured samples. Then when a measurement indication is compared with the epistemic knowledge. We see in this paper that the immersion of these two kind of uncertainties into the transferable belief model allows to manage them together.

Figure 1 .

 1 Figure 1. 2D representation of the body perceived by the depth sensor and of the measured joints.

Figure 2 .

 2 Figure 2. Robot used for the study. The joint states are acquired with proprioceptive sensors.

Figure 3 .

 3 Figure 3. Example of a transformation of a Bayesian BBA into a consonant BBA on a frame of discernment Ω made of 5 symbols. The figure gives for each BBA the focal sets and their belief assignment.

Figure 4 .

 4 Figure 4. Conjunctive combination of an indication and a posture definition where the indication globally fits with the posture.

Figure 5 .

 5 Figure 5. Conjunctive combination of an indication and a posture definition where the indication partially fits with the posture. The empty set holds the majority of the belief assignment.


Nicolas Minesi

Sergey Stepanyan

Erwan Pannier

Gabi-Daniel Stancu

Christophe O Laux

Hydro- Dynamic

Hydrodynamic effects induced by nanosecond sparks

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.

Spatial redistribution of energy

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  Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92295 Chatenay-Malabry cedex, France N. Minesi, S. Stepanyan, E. Pannier, G.D. Stancu, С.O. Laux Hydrodynamic effects induced by nanosecond sparks [1] Olsen H. et al, 1952, "Microchronometric Schlieren Study of Gaseous Expansion from an Electric", Spark Journal of Applied Physics 23 1157 [2] Kono M et al, 1989, "Mechanism of flame kernel formation produced by short duration sparks", 22 nd Symp. On Combustion 22 1643-1649 [3] Rusterholtz D et al, 2013, "Ultrafast heating and oxygen dissociation in atmospheric pressure air by nanosecond repetitively pulsed discharges", J. Phys.D: Appl. Phys 46 464010 [4] Castela M et al, 2016, "Direct Numerical Simulations of plasma-assisted ignition in quiescent and turbulent flow conditions", PhD thesis References Conclusions Ns sparks show fast spatial redistribution of the deposited energy (≈5 mm/100 ms in a single pulse) • One of the mechanisms of the spatial energy redistribution is the recirculation of hot gas • Experiments in a pin-to-plane configuration demonstrate the influence of electrode geometry on HD effects • Characteristic size of the active medium is proportional to the number of pulses (energy) in the burst due to synergy between the pulses • Electrode distance is a key factor for tailoring radical species redistribution (rather than total energy or energy density) Hydrodynamic effects induced by ns sparks are monitored by (i) PLIF, (ii) Schlieren and (iii) electrical energy measurement. Asymmetric electrodes OH PLIF in pin-to-plane geometry (P=1 bar, single pulse of 10 ns, U=30 kV) Repetitive nanosecond sparks have numerous applications in combustion : • Ignition/stabilisation of lean/diluted flames • Control of thermo-acoustic instabilities • Reduction of pollutant emission (soot, NO x ) We believe that the hydrodynamic effects induced by ns sparks [1,2] coupled with the production of active species [3] can bring a significant improvement for the applications mentioned above. Effect of gap distance : for fixed energy OH PLIF in pin-to-pin geometry (P=1 bar, single pulse of 10 ns, U=30 kV) Effect of multiple sparks Schlieren (P=1 bar, pulse(s) of 10 ns, U=30 kV) Effect of electrode geometry Schlieren (P=1 bar, single pulse of 10 ns, U=30 kV) Effect of gap distance : for fixed energy density OH PLIF in pin-to-pin geometry (P=1 bar, single pulse of 10 ns, U=30 kV) Mechanism of energy redistribution Simulations from [4] (P=1 bar, single pulse, E=1,8 mJ) ➢ Simulations of [4] predicted toroidal expansion of ns sparks ➢ 6 mm: cylindrical expansion ➢ 2 mm: toroidal expansion due to fresh gas recirculation ➢ Each new pulse is initiated in fresh gas ➢ Synergy promoting expansion ➢ No difference in expansion for symmetric electrodes ➢ A sufficiently thick electrode (plane) blocks the recirculation ➢ Same energy density (1.5 mJ/mm) but a different redistribution of radical species