MD-PhD Guillaume Cartron
email: cartron@chu-montpellier.fr

MD, PhD Emmanuel Bachy

MD Hervé Tilly

MD Nicolas Daguindau

MD Gian-Matteo Pica

MD Fontanet Bijou

MD Christiane Mounier

Aline Clavert

Laurent Gandhi

Borhane Damaj

Slama

MD, PhD Damaj

MD Borhane Slama

MD Olivier Casasnovas

MD, PhD Roch Houot

MD Krimo Bouabdallah

MD, PhD David Sibon

MD Olivier Fitoussi

MD Nadine Morineau

MD, PhD Charles Herbaux

MD Thomas Gastinne

MD Luc-Matthieu Fornecker

MD, PhD Corinne Haioun

MD Vincent Launay

MD Carla Araujo

MD Omar Benbrahim

MD Laurence Sanhes

MD Remy Gressin

MD Hugo Gonzalez

MD, PhD Franck Morschhauser

PhD David Ternant

MD, PhD Luc Xerri

PhD Karin Tarte

MD Delphine Pranger

Randomized Phase III Trial Evaluating Subcutaneous Rituximab for the First-Line Treatment of Low-Tumor Burden Follicular Lymphoma: Results of a LYSA Study

come

INTRODUCTION

Asymptomatic patients with low-tumor burden follicular lymphoma (FL) represent 20 to 30% of patients with FL at diagnosis. For those patients, the "watch and wait" (W&W) strategy is usually considered as the standard of care 1 . This is justified by a proportion of 19% of patients who did not require any treatment initiation at 10 years 2 and by side effects induced by chemotherapy, the only option available at the time of these reports 2,3 . However, fear of the patient about cancer, patient requests, and difficulty organizing W&W, make this option difficult. In this context, rituximab demonstrated an acceptable toxicity profile and could overcome anxiety associated with W&W 4,5 without increasing the risk of histologic transformation 6 . Thus, National lymphoCare Study 7 showed rituximab used in daily practice for those patients. Indeed four-weekly rituximab induction 4 showed a significant prolonged progression-free survival (PFS) and time to next treatment (TTNT) compared to W&W. The addition of rituximab maintenance for 2 years increased significantly PFS and TTNT compared to rituximab induction 8 but increased the cost of treatment compared to rituximab re-treatment strategy and led to more treatment discontinuations 5 . Although the benefit of a rituximab induction was significant, these results question the use of prolonged rituximab maintenance.

RESORT study points out that 7 years after treatment initiation, 83% of patients were free of cytotoxic treatment 9 with prolonged maintenance. Similarly, 64.1% and 49.4% of patients receiving rituximab induction with or without prolonged maintenance, respectively, were free of new treatment at 10 years in the UK trial 8 . In the meantime, SAKK group demonstrated that a short maintenance with four rituximab infusions every Accepted manuscript -6 -two months following rituximab induction [START_REF] Martinelli | Long-Term Follow-Up of Patients With Follicular Lymphoma Receiving Single-Agent Rituximab at Two Different Schedules in Trial SAKK 35/98[END_REF][START_REF] Moccia | Prolonged rituximab maintenance in follicular lymphoma patients: long-term results of the SAKK 35/03 randomized trial[END_REF] could also be an approach to maintain response to rituximab.

Rituximab is now available either as a biosimilar, with an intravenous (iv.) route of administration, or by sub-cutaneous (sc.) route. The sc. rituximab formulation showed an improvement in the patient's experience, a higher rituximab exposure, and optimization of the medical resources compared to iv. route [START_REF] Salar | Comparison of Subcutaneous Versus Intravenous Administration of Rituximab As Maintenance Treatment for Follicular Lymphoma: Results From a Two-Stage, Phase IB Study[END_REF][START_REF] Rummel | Preference for subcutaneous or intravenous administration of rituximab among patients with untreated CD20+ diffuse large B-cell lymphoma or follicular lymphoma: results from a prospective, randomized, open-label, crossover study (PrefMab)[END_REF] . For all these reasons, the LYSA group designed a phase 3 randomized trial to investigate the use of short rituximab maintenance using sc. rituximab in patients with asymptomatic FL.

PATIENTS AND METHODS

Patients

Patients had to fulfill all the following criteria: histologically confirmed FL CD20 + grade 1, 2, and 3a and bone marrow biopsy (BMB) within 4 months before signing informed consent, no prior therapy, age > 18 years, Ann Arbor stage II-IV, ECOG performance status 0 to 2, measurable disease (at least one single node or tumor lesion > 1.5 cm) and low-tumor burden by the Groupe D'Etude des Lymphomes Folliculaires (GELF) criteria 3 including lactate dehydrogenase and β2-microglobulin <ULN.

The protocol was approved by an independent ethics committee and the Agence Nationale de Sécurité du Médicament et des Produits de Santé; the study was done according to the Declaration of Helsinki, Good Clinical Practices, and applicable regulatory requirements. All patients gave written informed consent before participating. The study was registered with ClinicalTrials.gov number NCT02303119 and completed on June 29th, 2021.

Study Design and Procedures

Diagnostic biopsies were centrally reviewed (LX) to confirm the diagnosis in accordance with WHO guidelines. Patients were randomly assigned (1:1 ratio) to receive the control arm: rituximab 375 mg/m 2 at Day-1 (D1), D8, D15, D22 by iv. or the experimental arm: rituximab: 375 mg/m 2 at D1 by iv. route and 1400 mg total dose by sc. route at D8, D15, and D22, followed by maintenance at months-3 (M3), M5, M7, and M9.

Randomization was stratified according to Follicular Lymphoma International Prognostic Index (FLIPI) score (< 2 vs ≥ 2). Baseline imaging included whole body CTscans and positron emission tomography-computed tomography (PET-CT).

Safety data were collected for up to 30 days after the last infusion (D52 in the control arm, M10 in the experimental arm). Adverse events (AEs) were defined and graded according to the NCI-CTCAE 4.03. Tumor responses were assessed at M3 and M12 by CT-scan and at M12 by PET-CT. To confirm a complete response (CR), patients with positive BMB at screening were required to have BMB within 28 days of first achieving CR. CT-scan was then performed every 6 months for 2 years and every year for 3 years.

Clinical Endpoints

The primary endpoint was the PFS (i.e, from the date of inclusion to the date of first documented disease progression, relapse, or death). Secondary endpoints included response rates at M3 and M12 according to Cheson [START_REF] Cheson | Report of an international workshop to standardize response criteria for non-Hodgkin's lymphomas: NCI-sponsored international working group[END_REF] and Lugano [START_REF] Cheson | Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification[END_REF] , TTNT (i.e from the date of inclusion to the initiation date of the first documented new lymphoma treatment), and overall survival (OS, i.e from the date of inclusion to the date of death).

Pre-planned Exploratory Endpoints

FcγRIIIA-158VF polymorphism has been described to influence response to rituximab [START_REF] Cartron | Therapeutic activity of humanized anti-CD20 monoclonal antibody and polymorphism in IgG Fc receptor FcγRIIIa gene[END_REF] and was determined as previously described [START_REF] Dall'ozzo | Rapid single-step FCGR3A genotyping based on SYBR Green I fluorescence in real-time multiplex allele-specific PCR[END_REF] . Rituximab serum concentrations were evaluated before rituximab (H0) and 2 hours after the end of rituximab infusion (H2) at D1, D8, D15, D22, at M3 (H0) for all patients and at M5, M7, M9 (H0) in the experimental arm. Concentrations were measured using a validated enzyme-linked immunosorbent assay [START_REF] Blasco | Evaluation of a peptide ELISA for the detection of rituximab in serum[END_REF] and were available for 113 patients (control arm: 51, experimental arm: 62). Pharmacokinetics (PK) was assessed using a twocompartment population PK model, with time-varying clearance, and SC absorption described as a first-order rate constant as reported [START_REF] Gibiansky | Population pharmacokinetic and exposure-response analyses of intravenous and subcutaneous rituximab in patients with chronic lymphocytic leukemia[END_REF] (see Supplemental Methods).

Exposure was assessed by computing the area under the concentration-time curve (AUC) using the PK model from the beginning of treatment to M3 (AUC0-M3).

Statistical analysis

Sample size determination was based on PFS, the primary efficacy endpoint. To provide 90% power to detect a Hazard Ratio (HR) of 0.52, corresponding to an increase of the median PFS for the experimental versus control arm [START_REF] Colombat | Ritux-imab induction immunotherapy for first-line low-tumor-burden follicular lymphoma: Survival analyses with 7-year followup[END_REF] with two-sided alpha (type I error) of 0.05, a total of 102 events from both arms was required implying 202 patients to be randomized (101 patients in each arm). The analysis was in intent to treat and included all patients randomized regardless of the study drug being received or not. Patients were analyzed based on the assigned treatment group at the time of randomization. Response rates were reported as percentages of patients, with 95% CIs. Time-to-event data were presented as Kaplan-Meier plots of time to the first event and as summary tables for fixed time points. Logistic regression models were used to estimate the odd ratios (with 95% CIs) of prognostic factors on response rates (post-hoc analyses), and Cox proportional-hazards regression models were used to estimate hazard ratios and 95% CIs on time-to-event data. Two different approaches, X-Tile and ROC analysis were used to define the optimal cutoff with a minimal p-value of AUC for survival prediction [START_REF] Camp | X-tile: a new bio-informatics tool for biomarker assessment and outcome-based cut-point optimization[END_REF] . AUC0-M3 as time-dependent variable was analyzed with a landmark method with time starting at M3 in both univariable and multivariable analysis (post-hoc analyses). Analyses were done with SAS software (version 9.3), and X-Tile (version 3.6.1).

RESULTS

Patient Characteristics

Between February 2015 and June 2018, 202 patients with asymptomatic FL were enrolled and randomly assigned to the experimental (n=100) or control arm (n=102).

Patient characteristics are summarized in Table 1. Tissue was submitted for central review in 193 patients (96%) and not available for review for 9 (4%). Review confirmed FL in 182 patients (90.1%), 158 being FL grade 1, 2 (78.2%), 24 grade 3A (11.9%).

There was a numerically higher number of women in the control arm (P=0.09).

According to FLIPI score, 79 (39%), 81 (40%) and 42 (21%) had low-(LR), intermediate-(IR) and high-risk (HR) FLIPI score, respectively. One patient had HR, and 121 (60%) and 79 (39%) of patients had IR and LR FLIPI-2 score, respectively.

The median rituximab AUC0-M3 was statistically higher in the experimental arm: 8648 mg/Lxd (5212-21381) compared to the control arm, 6124 mg/Lxd (3237-10324, P<0.001).

Primary Endpoint

Accepted manuscript -10 -A total of 18 patients (9%) discontinued the treatment, 11 patients in the experimental arm, and 7 patients in the control arm (Figure 1). Only four patients discontinued rituximab maintenance. With a median follow-up of 50.2 months (95%IC:48.3-54.5), the primary endpoint of the study was met (Figure 2A.): 4-year PFS of 58.1% (95%CI:47.5-67.4) and 41.2% (95%CI:30.6-51.6) in experimental and control arms, respectively (HR:0.585;0.393-0.871), P=0.008). Univariable analysis demonstrated that the experimental arm, female gender, FLIPI-IR/LR, FLIPI-2-LR, and high AUC0-M3 were associated with prolonged PFS (Table 2.). While stratified on the treatment arm, a significant difference was observed for PFS between patients with low (≤6750 mg/Lxd) and (high >6750 mg/Lxd) AUC0-M3 (HR:0.458; 95%CI:0.261-0.802, P=0.005).

PFS curves stratified on the treatment arm are provided in Appendix Figure 1. In multivariable analysis, AUC0-M3 was the only parameter significantly associated with PFS; a cut-off of 6750 mg/Lxd allowed to separate two groups of patients having a significant different 4-year PFS of 23.7% (95%IC:8.1-43.8) for those having an AUC0-M3≤6750 mg/Lxd compared to 60.9% (95%IC:47.3-72.1) for those with an AUC0-M3>6750 mg/Lxd (P=0.001, Figure 3A). Of note, 45/62 (72%) and 19/51 (37%) patients had AUC0-M3>6750 mg/Lxd in experimental and control arms, respectively.

Secondary Endpoints

Toxicities

Before M3, 14 patients in each arm experienced AEs. Seven in each arm had at least one AE ≥ grade 3, for a total of 15 events. AEs ≥ grade 3 observed in more than one patient were lymphopenia (3 patients in each arm) and an injection site reaction (3 patients in the experimental arm). Eight patients experienced serious AE: injection site reaction (2 patients in experimental arm, one in control arm), ulcer (n=2), arrhythmia (n=1), skin cancer (n=1), cystitis (n=1). From M3, 17 patients in the experimental arm experienced at least one AE. Five had a total of 5 AE ≥ grade 3: benign neoplasm, thyroid cancer, lymphopenia, myocardial ischemia, and hepatitis. Six patients had serious AE: benign neoplasm, skin cancer, thyroid cancer, migraine, peripheral neuropathy, and myocardial ischemia.

Response to rituximab

According to Cheson criteria [START_REF] Cheson | Report of an international workshop to standardize response criteria for non-Hodgkin's lymphomas: NCI-sponsored international working group[END_REF] According to Lugano criteria including both PET-CT and BMB [START_REF] Cheson | Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification[END_REF] , ORR at M12 were 73.0% (95%CI:63.2-81.4) in experimental arm and 52.0% (95% CI: 41.8-62.0) in control arm (Figure 4.) (P=0.002). CR rates were 59.0% (95%CI:48.7-68.7) in experimental arm and 36.3% (95%CI:27.0-46.4) in control arm (P=0.001). Univariable analysis demonstrated an association between CR and the experimental arm, FLIPI-2 LR, and AUC0-M3>7508 mg/Lxd (Table 2.). Multivariable analysis showed that FLIPI-2 IR was associated with a lower probability of CR (OR: 0.325, 95%CI:0.140-0.752, P=0.008) whereas a high AUC0-M3 was significantly associated with a higher CR rate (OR:7.449, 95%CI:1.446-38.368, P=0.016).

Survival and Outcome at First Relapse

Accepted manuscript

-12 -4-year OS was not different according to treatment arm: 95.0% (95%CI:88.5-97.9) for control arm, 96.7% (95%CI: 89.9-98.9) for experimental arm (Figure 2B). The lymphoma was the cause of death in only one patient. TTNT and time to next chemotherapy treatment (TTNCT) did not differ (Figure 2C, 2D) with 4-year TTNCT of 71.4% (95%CI:60.7-79.8) in the experimental arm and 60.8 % (95%CI:49.6-70.3) in the control arm (P=0.13). In univariable analysis, female gender, experimental arm, FLIPI-2 LR, and high AUC0-M3 were associated with longer TTNT (Table 2.). While stratified on the treatment arm, a significant difference was observed for TTNT between patients with low (≤6200 mg/Lxd) and (high >6200 mg/Lxd) AUC0-M3 (HR:0.458; 95%CI:0.242-0.865, P=0.014). TTNT curves stratified on the treatment arm are provides in Appendix Figure 1. FLIPI-2 LR (HR 1.944; CI95%:1.027-3.681, P=0.041) and high AUC0-M3 (HR:0.332; 95%CI:0.182-0.608, P=0.003) were associated with prolonged TTNT in multivariable analysis (Table 2., Figure 3B). Ninety-seven patients experienced progression (experimental arm:42, control arm: 55) and 53 patients (experimental arm: 22, control arm: 31) started treatment at first progression: immunochemotherapy (n=40), immunotherapy (n=6), radiation-therapy (n=8) or surgery (n=1). There was no significant difference in 18 months-PFS-2 (i.e progression after a second line treatment): 66.7% (95%IC:47.6-80.2) and 75% (95%IC:60.1-85.1) for patients included in experimental and control arms, respectively.

Post-hoc Analysis

Because AUC0-M3 was associated with PFS, TTNT, and CR at M12, we analyzed how patient' characteristics could influence AUC0-M3. Female gender was associated with a significantly higher median of AUC0-M3: 7658.3 mg/Lxd (3526-21381) in women versus 7332.2 mg/Lxd (3237-14884) in men (P=0.048, Figure 3C). This was observed significantly in both arms (Figure 3D). Patients with a sum of the product of the greatest diameters of 6 largest nodes (SPD) lower than the median at baseline had also a higher median AUC0-M3, but this association was observed only in the control arm (P=0.042). AUC0-M3 was not different according to age, FCGR3A polymorphism, FLIPI, FLIPI-2, and Ann Arbor stage.

CR at M12 (Lugano criteria) and female gender were both associated with a prolonged PFS and TTNT in multivariable analysis: 3-year PFS was 75.7% (95%CI:64.9-83.6) when CR was obtained compared to 35% (95%CI:23.3-46.9) when no CR was reached at M12 (HR:0.285; 95%CI: 0.175-0.465, P<0.001, Figure 5A); 3-year TTNT were 86.8% (95%CI:77.1-92.5) when CR was reached compared to 33.6% (95%CI:23.8-43.7) when no CR was obtained (HR:0.114; 95%CI:0.061-0.211, P<0.001, Figure 5B).

DISCUSSION

For patients with asymptomatic FL, the question remaining unanswered is whether an optimal rituximab maintenance modality can delay chemotherapy initiation without safety concerns and increasing resources use. Our results show that sc. rituximab used for induction and short maintenance increased CR and PFS compared to conventional iv induction. However, the rituximab exposure observed within the first three months was independently associated with response, PFS and TTNT suggesting that a short rituximab maintenance has a little impact on outcome.

We demonstrated that sc. rituximab as induction and maintenance increased significantly PFS compared to rituximab induction with a 4-year PFS of 58.1% and 41.2% in experimental and control arms, respectively. The PFS observed in the control arm appears lower than that observed in the UK trial 4 with a 4-year PFS around 55% with similar iv. induction. This could be related to differences in inclusion criteria, and more follow-up CT-scan in our trial whereas patient characteristics seem similar. The magnitude of the difference in PFS between the two arms in our trial seems like that observed in a similar trial using prolonged maintenance 4 .

The lack of effect on OS is mainly explained by the indolent course of FL, highlighted in our study with only one lymphoma-related death. We could not, therefore, confirm the influence of the progression of disease within 2 years (POD24) on OS [START_REF] Casulo | Validation of POD24 as a robust early clinical end point of poor survival in FL from 5225 patients on 13 clinical trials[END_REF] . TTNT is an important goal for such patients and the lack of TTNT improvement is disappointing even if a tendency was observed with TTNCT. This was also found in initial analysis of the UK trial 4 but its recent update 8 , with a longer follow-up, has shown a significant advantage of prolonged maintenance over no maintenance. Progression is the usual endpoint in FL and was chosen as the primary endpoint to calculate the number of patients to be included. Thus, our study might not be powered to demonstrate a difference in TTNT that would have to require consensus on second-line treatment initiation criteria to avoid potential bias for analysis. Similar treatment initiation rates, delay to treatment initiation, and PFS-2 suggest that the policy of re-treatment at progression was probably not different according to the treatment arm. The post-hoc analysis demonstrated that CR at M12 was associated with a longer PFS and TTNT; 86.8% of patients in CR being free of treatment 4 years after treatment initiation. CR at the end of treatment could be an interesting endpoint for physicians and patients to offer individualized follow-up.

The experimental arm is associated with a significant different rituximab exposure during the first three months as demonstrated by higher median AUC0-M3 in experimental arm. Higher AUC0-M3 was, independently of the treatment arm, associated with higher PFS, TTNT, and CR rate at M12, and seems therefore an Accepted manuscript -15 -important driver of rituximab efficacy in asymptomatic FL. We have no demonstration that sc. route could improve exposure by itself. The cumulative theoretical doses of rituximab for induction were lower in iv. arm (1500 mg/m 2 ) than in sc. arm (375 mg/m 2 + 4200 mg) explain probably the difference of the AUCM0-M3 observed according to the arm of treatment. Thus, CR, TTNT, and PFS were related to rituximab exposure during rituximab induction, the best exposure being obtained more frequently in experimental arm using higher doses of rituximab. The female gender and low SPD were associated with higher AUC0-M3, this association was found in both arms with gender and only in the control arm for SPD. The influence of tumor volume on rituximab PK has been demonstrated in a murine model [START_REF] Daydé | Tumor burden influences exposure and response to rituximab: pharmacokinetic-pharmacodynamic modeling using a syngeneic bioluminescent murine model expressing human CD20[END_REF] , diffuse large B-cell lymphoma (DLBCL) [START_REF] Tout | Rituximab exposure is influenced by baseline metabolic tumor volume and predicts outcome of DLBCL patients: a Lymphoma Study Association report[END_REF] and FL [START_REF] Ternant | Nonlinear pharmacokinetics of rituximab in non-Hodgkin lymphomas: A pilot study[END_REF] .

Our results suggest that in asymptomatic FL, the higher exposure obtained more frequently in experimental arm reduced the influence of tumor volume on rituximab efficacy. Female gender has been associated with more favorable rituximab PK in patients with a DLBCL. This was observed especially in elderly women where a slower rituximab clearance led to a longer exposure and better clinical outcome [START_REF] Muller | The role of sex and weight on rituximab clearance and serum elimination half-life in elderly patients with DLBCL[END_REF][START_REF] Pfreundschuh | Suboptimal dosing of rituximab in male and female patients with DLBCL[END_REF] but had never been described in FL. The sc. route using higher dose of rituximab seems the best option to obtain optimal rituximab exposure whatever the gender and SPD.

Rituximab induces deep and prolonged B-cell depletion that can hamper immune response to SARS-CoV2 [START_REF] Thakkar | Patterns of seroconversion for SARS-CoV-2 IgG in patients with malignant disease and association with anticancer therapy[END_REF] , increase the risk of severe COVID-19 [START_REF] Passamonti | Clinical characteristics and risk factors associated with COVID-19 severity in patients with haematological malignancies in Italy: a retrospective, multicentre, cohort study[END_REF] and prevent immunization [START_REF] Herishanu | Efficacy of the BNT162b2 mRNA COVID-19 vaccine in patients with chronic lymphocytic leukemia[END_REF] . We do not report COVID-19 infection in our cohort of patients, the last patient being randomized more than 18 months before the SARS-CoV2 wave. The rituximab option must be accompanied by clear and fair information on the potential advantages and risks associated. If the patient agrees, the physician must first ensure that his/her patient is vaccinated and will have access if necessary to antibodies and/or antivirals that reduce significantly COVID-19-related complications [START_REF] El Chaer | How I treat and prevent COVID-19 in patients with hematologic malignancies and recipients of cellular therapies[END_REF] .

Our study has however several limitations. First, we did not observe a significant impact of maintenance on TTNT, probably because our study was not powered to demonstrate a difference in TTNT. Second, the influence of AUC0-M3 on CR at M12, PFS, and TTNT observed independently to treatment strongly suggest that rituximab maintenance is not useful if an appropriate dosing of rituximab is use as induction.

However only a randomized study using similar sc. rituximab induction followed by maintenance or not could definitively conclude on that point. Third, the increased exposure observed in the experimental arm is probably more related to the dosage allowed by sc. route than by the route itself and we can hypothesize that similar results could be obtained with appropriate dosage using iv. route.

Low-tumor burden FL is an indolent clinical situation where the physician must preserve the patient quality of life, and delay chemotherapy use without exposing the patient to significant side effects. Our study clearly demonstrates that rituximab exposure during the first 3 months is an independent parameter influencing response and survival outcomes. In this regard, sc. rituximab used as induction allow to improve rituximab exposure and can be considered by physicians and patients as an optimal option for low-tumor burden FL.

Table 1. Patient Characteristics

Accepted manuscript

-22 -

Table 2. Prognostic Factors Analysis

Supplemental methods

Pharmacokinetic data analysis was made using compartmental models and nonlinear mixed-effects modeling (population approach) using Monolix Suite 2020 (Lixoft®, Antony, France). The final model was used to compute values of area under the concentration curve (AUC) for each patient.

Structural model

Our model was based on a two-compartment model with first-order absorption, distribution, and elimination rates. As in previous studies, the effect of antigen mass on rituximab pharmacokinetics [1, 2] was implemented as a time-varying clearance component as in previous studies [3-5], which led to a better description of concentration-time data than target-mediated drug disposition (TMDD) model with irreversible binding approximation. [6-9] The model was implemented as follows:

𝑑𝑑𝑑𝑑 𝐶𝐶 𝑑𝑑𝑑𝑑 = 𝐼𝐼𝐼𝐼(𝑑𝑑) - 𝑑𝑑𝐶𝐶 0 + 𝑑𝑑𝐶𝐶 1 . 𝑒𝑒𝑒𝑒𝑒𝑒(-𝑘𝑘 𝑑𝑑𝑑𝑑𝑑𝑑 . 𝑑𝑑) 𝑉𝑉 1 . 𝑑𝑑 𝐶𝐶 - 𝑄𝑄 𝑉𝑉 1 . 𝑑𝑑 𝐶𝐶 + 𝑄𝑄 𝑉𝑉 2 . 𝑑𝑑 𝑃𝑃 𝑑𝑑𝑑𝑑 𝑃𝑃 𝑑𝑑𝑑𝑑 = 𝑄𝑄 𝑉𝑉 1 . 𝑑𝑑 𝐶𝐶 - 𝑄𝑄 𝑉𝑉 2 . 𝑑𝑑 𝑃𝑃
Where CC and CP are rituximab concentrations in central and peripheral compartments, respectively, In(t) is rituximab input function, V1 andV2 are central and peripheral volumes of distribution, respectively, CL0 and Q are target-free systemic and intercompartment clearances, respectively, CL1 is time-varying component of systemic clearance and kdes is first-order decline of CL1. In addition, since rituximab was administered either by IV or subcutaneous (SC) route, SC bioavailability was estimated. Rituximab absorption kinetics following SC injection was described using a first-order absorption rate constant (ka) as for most of SC monoclonal antibodies. [1] Statistical models Interindividual model. Pharmacokinetic parameters were assumed to follow a lognormal law, interindividual model was therefore exponential i.e. θi = θTV . exp(ηi), where θi is the estimated individual parameter, θTV is the typical value of the parameter and ηi is the random effect for the i th patient. Values of ηi were assumed to be normally distributed with mean 0 and variance ω 2 . The parameter F was assumed to follow a probit low since varies strictly between 0 and 1. Interindividual variances that could not be estimated properly were fixed to 0. In the present study, interindividual variances of V1, CL0, CL1, V2 and F. Interindividual variances of ka, kdes and Q were not estimable and were therefore fixed to 0.

Residual model. Additive, proportional and mixed additive-proportional models were tested.

The final statistical model was therefore:

𝐹𝐹 = 0.

Figure 1 Figure 2 .

 12 Figure 1. CONSORT Diagram

Figure 3 .

 3 Figure 3. Landmark Survival by Rituximab AUC0-M3 and Factors Affecting AUC0-

Figure 4 .

 4 Figure 4. Response at M12 According to Lugano ClassificationResponses assessed at M12 according to Lugano Classification[START_REF] Rummel | Preference for subcutaneous or intravenous administration of rituximab among patients with untreated CD20+ diffuse large B-cell lymphoma or follicular lymphoma: results from a prospective, randomized, open-label, crossover study (PrefMab)[END_REF] . CR: complete

Figure 5 .

 5 Figure 5. Landmark Survival by Response Status at M12

Figure 1

 1 Figure 1. CONSORT Diagram

Figure 2 .Figure 3 .

 23 Figure 2. Kaplan Meier Curves of Survival

Figure 4 .

 4 Figure 4. Response at M12 According to Lugano Classification

Figure 5 .

 5 Figure 5. Landmark Survival by Response Status at M12

Table 1 .

 1 76. 𝑒𝑒 η 𝐹𝐹,𝑖𝑖 𝑒𝑒 0.027.𝑁𝑁𝑁𝑁𝑁𝑁 . 𝑒𝑒 η 𝐶𝐶𝐶𝐶0,𝑖𝑖 𝑑𝑑𝐶𝐶 1 = 𝑒𝑒 0.090.𝑁𝑁𝑁𝑁𝑁𝑁 . 𝑒𝑒 η 𝐶𝐶𝐶𝐶1,𝑖𝑖 Pharmacokinetic parameter estimates for base and final models. Legends. RSE: relative standard error, ka: first-order absorption rate constant, F: bioavailability, V1 andV2: central and peripheral volumes of distribution, respectively, CL0 and Q: target-free systemic and intercompartment clearances, respectively, CL1: time-varying component of systemic clearance, kdes is first-order decline of CL1, ω: interindividual standard deviation, σ: residual standard deviation.

	𝑉𝑉 1 = 3.5. � 1.87 𝐵𝐵𝐵𝐵𝐵𝐵 � 0.74	. � 169 𝐻𝐻𝐻𝐻	1.4 �	. 𝑒𝑒 η 𝑉𝑉1,𝑖𝑖
	𝑑𝑑𝐶𝐶 0 = 0.21. � 1.87 𝐵𝐵𝐵𝐵𝐵𝐵 � 2.0 . 𝑉𝑉 2 = 3.5. � . � -0.27 𝑑𝑑𝐶𝐶𝐶𝐶𝐵𝐵𝐻𝐻 70 � 1.6 𝐵𝐵𝐵𝐵𝐵𝐵 1.87 � . 𝑒𝑒 η 𝑉𝑉0,𝑖𝑖

Acknowledgments

The authors would like to thank patients, families, caregivers, and investigators who participated in the FLIRT clinical study, the Lymphoma Academic Research Organisation (LYSARC). GC thanks Dr. P. Solal-Céligny, particularly for the passionate discussions on the care of patients with FL, for his review and advices in writing this manuscript.

. Roche provided rituximab (MabThera  ) but had no role in study design, or data collection, analysis, or interpretation. Roche provided a courtesy review, with comments, of the Article before submission, with the authors having final decisions for content reporting in the Article. LYSARC, GC, and DP had access to the raw data. Proposals should be submitted to the study PI and Coordinating Investigator, Guillaume Cartron. If he agrees with the collaboration/ sharing, the project should be presented to LYSA Scientific Committee. If the project is validated by LYSA Scientific Committee, a Data Transfer Agreement compliant with GDPR and French Data Protection laws should be signed. DTA includes

data protection rules and responsibilities of each party, data security, and storing information. For more information, please visit https://experts-recherche-lymphome.org/lysarc/or contact contact@lysarc.org.

CONCLUSION. Sc. rituximab improves PFS for patients with low-tumor burden FL when used in induction followed by short maintenance. High rituximab exposure during the first 3 months after treatment initiation is however the only parameter influencing patient outcome.

Supplemental Figure. Landmark Survival by treatment arm according to AUC0-M3.

Model comparison and selection

Several structural models were tested, one-compartment and two compartment models with first-order distribution and elimination rate constants, then irreversible binding target-mediated elimination as in our previous works [6-9] and time-varying clearance as in previous other works. [3-5] Structural models were compared using Akaike's information criterion (AIC), defined as AIC = OFV + 2.p, where OFV is the value of the objective function and p is the number of model parameters to estimate. Interindividual and residual models were chosen by comparing nested models on the basis of the OFV tested using a likelihood ratio test (LRT). The two-compartment model with time-varying clearance led to a better description of concentration-time data (AIC=10504.28) compared to irreversible binding target-mediated elimination (AIC=10556.00), two-compartment model with first-order elimination rate (AIC=10572.70) or one-compartment model with first-order elimination rate (AIC=11519.22).

Model goodness of fit and evaluation

The goodness-of-fit was assessed for each model by plotting population-predicted (PRED) and individually predicted (IPRED) concentrations versus observed concentrations (DV) and IPRED and DV versus time. Population predictions were obtained using typical parameters, which include explained variability (i.e. population estimates and covariates), whereas individually predicted concentrations were obtained using individual parameters, which include both explained and unexplained (i.e. the random effects ηi for each PK parameter). In addition, the goodness-of-fit was evaluated by the distribution of residuals evaluated by graphical inspection of population (PWRES) and individual (IWRES) weighted residual distributions, visual predictive checks (VPC), and normalized prediction distribution errors (NPDE). These residuals should follow a standard normal distribution (i) to confirm a satisfactory description of the data using the model and (ii) to allow LRT tests (figure 1.)

Covariate analysis

Continuous covariates that were tested were baseline levels of alanine (ALAT) and asparagine (ASAT) aminotransferases, bilirubin (BILI), creatinine (CREAT), gammaglutamyl trasferase (GGT), immunoglobulins (IGG), lactate deshydrogenase (LDH), white blood cell (WBC) and lymphocyte (LYM) counts, number of nodal sites, (NNS), number of nodal areas (NNA), median of maximal standardized uptake value obtained by PET-CT (SUV), body weight (BW), body surface area (BSA) and height (HT). All of these covariates, except for NNS and NNA were coded as a power function and centered to their median. Categorical covariate was sex, with females taken as a reference. The influence of each covariate on statistical models was based on the During univariable step, the association of each covariate was tested. Each covariate showing a significant influence (α < 0.1) was kept for multivariable step. During the multivariable step, a forward and backward stepwise selection process was performed, where covariates were added and then removed during forward and backward steps, respectively. Covariates which inclusion (α<0.05) in forward or which exclusion (α<0.01) during backward steps were retained in the final model.

The final covariate model presented (table 1) increased V1 with BSA (p=4. 19.10 -6 ) and HT (p=0.00041), increased or decreased CL1 with BSA (p<10 -16 ), and NNA (p=0.0027), or CREAT (p=0.01), respectively, increased CL1 with NNA (p=0.0055) and increased V2 with BSA (p=7.2.10 -7 ).


domain: phys spi

text:
Mohamed Sahraoui
email: mohamed.sahraoui@univ-msila.dztaleb@uphf.fr

Abd Elmalik Taleb-Ahmed

A Firey Algorithm for Energy Ecient Clustering in Wireless Sensor Networks

Keywords: WSN, Firey, Clustering, Optimization, Coverage, Load balancing

The fundamental metric token by clustering algorithms in Wireless Sensor Networks (WSN) is energy enhancement to maximize network lifetime. One of the crucial issues is network coverage in order to use all of the network's resources, which increases the lifetime of the network. Moreover, load balancing techniques play an essential role in improving network lifetime due to their ecient way of distributing the load between nodes. The goal of this work is to assemble these two approaches in clustered WSN in order to improve resources utilization and increase network lifetime. Thus, we present a new clustering algorithm named Firey optimization based Adaptive Clustering for Energy Eciency (FACEE) which uses a novel clustering based rey optimization algorithm for coverage improvement and load balancing. The simulation results indicate that our proposed algorithm can signicantly improve the network lifetime as well as the delivery rate.

Introduction

In order to sense and monitor certain events in the environment, such as temperature, sound, and pressure, numerous sensors are placed across the concerned area to form a wireless sensor network (WSN). Then, the gathered information is transmitted via the network to the sink node which is typically more potent than the other nodes. To this end, The BS allows for the analysis and transmission of information via the internet [START_REF] Karaki | Routing techniques in WSN: A survey[END_REF]. Every sensor node is a low-power, single-antenna device with a half-duplex radio that should operate for a very long time as much as possible. In the absence of an energy-ecient method, a node's battery would quickly run out. Furthermore, the energy consumed in communication is more signicant than the energy consumed in computations [START_REF] Ridha | Multichannel assignment protocols in wireless sensor networks: A comprehensive survey[END_REF].

Over the last decade, extensive research has been done on clustering, one of the most eective power-saving techniques. The use of clustering allows for energy-ecient communication between sensor nodes, which are organized into various clusters. The node in charge of each cluster is called the Cluster Head (CH). The goal of clustering is to reduce the number of nodes or CHs that may communicate with other clusters and shorten the distance that data must travel.

Additionally, clustering stops redundant information from being transmitted utilizing data aggregation [START_REF] Zhang | Optimization and Application of Clustering Algorithm in Community Discovery[END_REF]. Although clustering is energy ecient, it is dicult to exploit routing information to achieve clustering process with proper load balancing. As a result, the issue becomes NP-hard, and is made considerably more dicult in wide WSNs because the weight of overhead has to be shared by all the nodes. Hence, an appropriate clustering strategy has become to be crucial for extending the WSN's lifetime.

Consequently, many optimization algorithms have been used to propose different clustering solutions such as in [916]. The use of Firey optimization Algorithms (FAs) can be either independently such as in [1416] or hybridized with another optimization algorithm such as in [START_REF] Maheshwari | Energy ecient cluster based routing protocol for WSN using buttery optimization algorithm and ant colony optimization[END_REF][START_REF] Shahbaz | Multipath routing through the rey algorithm and fuzzy logic in wireless sensor networks[END_REF].

However, the absence of a good clustering strategy that focuses on optimal coverage and load balance aspects between the nodes can lead to the disjointing of a certain number of nodes and overloading of some clusters compared to the others. Thus, the network lifetime can be decreased by the loss of the disjointing nodes and the fast death of the overloaded cluster members which can occur due to the increased level of both collisions and communication overhead. To overcome this limitation, we have proposed the Firey optimization based Adaptive Clustering for Energy Eciency (FACEE) Algorithm to improve coverage and balance the load between the cluster heads in the network. The purpose is to improve the network lifetime and the delivery rate which ultimately makes the entire network reliable and live more time.

The remainder of this paper is structured as follows: In Section 2, a summary of related work is provided. In Section 3, we present our algorithm FACEE. In Section 4, the simulation experiment ndings and discussions of those results are provided. In section 5, we conclude this work with further extension proposals.

Related works

Clustering methods have been widely used in wireless sensor networks to provide ecient routing algorithms. Some of them don't take into account the load balance aspect. The most popular algorithms for WSNs is the Low Energy Adaptive Clustering Hierarchy (LEACH) protocol introduced by the authors of [START_REF] Heinzelman | Energy ecient communication protocol for wireless sensor networks[END_REF].

According to LEACH, an ideal number of cluster heads is estimated to be 5% of the total nodes. Also, the CH list change randomly from a round to another in order to balance the energy consumption of nodes. The node makes this determination by selecting at random a value between 0 and 1. If the number is below a predetermined threshold, the node n becomes a CH for the current round. This protocol has seen several enhancement giving rise to new versions of hierarchical routing protocols.The literature contains numerous proposals for improved versions of LEACH, such as the LEACH-C presented in [START_REF] Heinzelman | An application-specic protocol architecture for wireless micro sensor networks[END_REF] by the same authors of LEACH. Hence, the energy level is included in the cluster selection process in LEACH-C made by the BS, which leads to an improvement in the network lifetime. In [START_REF] Khiati | Bod-leach: broadcasting over duty-cycled radio using leach clustering for delay/power ecient dissimulation in wireless sensor networks[END_REF], an other improved version of LEACH is suggested to guarantee scalability and speed up broadcasting by adding static and dynamic periods utilized for broadcast messages, however the nding results reveal increased energy usage.

Some other works have focused on load balancing issue such as the loadbalanced clustering protocol for WSNs (LBCP) proposed in [START_REF] Souissi | Optimal load balanced clustering in homogeneous wireless sensor networks[END_REF].It is a compromise between three models: an energy-aware cluster head selection model (EACH) for optimal cluster head selection, which performs clustering based on distances and residual energy, giving clusters the ability to choose their CHs with the least amount of intra-cluster distance, and a delay and energy-aware routing model (DEAR) for optimal inter-cluster communication, which is used to provide the best routes to the BS and calculates the amount of energy used. Furthermore, In order to perform load-balanced clustering according to the amount of energy consumed by given CH nodes, which can be reduced by supporting fewer cluster members, equal trac for energy-ecient clustering (EQTEEC) is applied. Based on routing overhead, EQTEEC is performed to redistribute cluster members among CHs. Even though this protocol resolves the load balance problem, it suers from the huge communication overhead needed to route the necessary information to the sink in order to execute the three models. In [START_REF] Shashikumar | Cluster based on Load Balancing for Environmental Monitoring in Wireless Sensor Network[END_REF], the authors have proposed a hybrid unequal clustering algorithm for load balancing which focuses on partitioning the network into number of layers and cluster of various groups. The number of neighboring nodes, energy available, available data in the node and the distance to the sink are parameters considered to select the nodes as CHs. Clustering is formed with unequal number of nodes with an equal load to balance the data in the network in such a way that the nodes which are present within a threshold distance will become a part of cluster.

Since the clustering process with adequate load balancing is an NP-hard problem, many optimization algorithms have been used to propose dierent clustering solutions such as Ant-Colony Optimization (ACO) in [START_REF] Ghosh | On-demand fuzzy clustering and ant-colony optimisation based mobile data collection in wireless sensor network[END_REF], Particle Swarm Optimization (PSO) in [START_REF] Sahoo | GAPSO-H: A hybrid approach towards optimizing the cluster based routing in wireless sensor network[END_REF][START_REF] Song | Hybrid PSO and Evolutionary Game Theory Protocol for Clustering and Routing in Wireless Sensor Network[END_REF] and Firey optimization Algorithms (FAs) which are detailed in this section due to their relevance to our proposed algorithm.

Hence, FA based algorithms can be categorized into two types: independent FAs and FAs hybrid with an other optimization algorithm such as the hybridization with the ACO algorithm in [START_REF] Maheshwari | Energy ecient cluster based routing protocol for WSN using buttery optimization algorithm and ant colony optimization[END_REF], where the authors developed the Buttery Optimization Algorithm (BOA) and ACO based energy ecient cluster based routing scheme for WSNs. Using the BOA, a number of factors are taken into account for choosing optimal CH, including node degree and centrality, distance to the sink node, distance to neighbors, and node residual energy. The ACO is used to determine the best route between the CH and the sink node while taking into account a number of factors, including distance, residual energy and node degree. An other hybridization between FA and fuzzy logic approach is made in [START_REF] Shahbaz | Multipath routing through the rey algorithm and fuzzy logic in wireless sensor networks[END_REF], where the authors suggested a three-phase multi-phase routing system, consisting of clustering the network nodes, guring out the paths between CHs and maintaining the paths. The nodes are clustered using the rey technique, then the proper primary path and backup path using fuzzy logic is determined.

Hence, CHs use backup paths in the event that the primary paths fail while still transmitting data packets to the sink node.

Although the hybridization of the FA can achieve good results in terms of latency and delivery rate, it requires more data control exchanges resulting in more collisions and overhead communication costs.

As mentioned before, some other works are based on the independent FAs. In [START_REF] Hossein | Cluster-based routing scheme for wireless sensor network using PSO and Fire[END_REF], routing using rey algorithm in wireless sensor networks is used. To convey aggregated data, a spanning tree is used in the routing process. Thus, each node in the network reports its energy consumption, and based on various including throughput, packet lost rate, distance between nodes and residual energy, each node compares the obtained values to nd the best attracted rout. The network lifetime has been increased in [START_REF] Manshahia | A rey based energy ecient routing in wireless sensor networks[END_REF] by using an enhanced rey algorithm. The clusters are formed with based on the rey algorithm, which is also utilized to choose the cluster head. Two critical aspects in the CH selection are token in the proposed function: rst is the energy dissipation of the communication between cluster members and the CH, and second, the energy required for data aggregation and transmission to the sink. Furthermore, the technique includes a step that substitutes a pseudo-random solution produced inside the search space for the worst solution from the population. In [START_REF] Miodrag | Wireless Sensor Networks Life Time Optimization Based on the Improved Firey Algorithm[END_REF], an approach called EM-FIREFLY is proposed in order to increase the power of WSN by gathering common data based on ecient clustering. In this method, the network is divided into hexagon which is divided into equal zones. For each zone a xed sink is assigned to rely data to the BS. Thus, the rey algorithm replaces the light intensity with the remaining energy of the node, making attraction inversely proportional to distance and directly correlated with energy. Using the four criteria of residual energy, noise rate, number of hops, and distance, the most optimal node is selected as a CH based on the tness function to transfers the data packets of its cluster to the dependent sink.

It is observed that the main focus of all the previous works is the energy balancing issue with giving less consideration to the coverage aspect even though it plays an important role in reliability guarantees as it increases the use of the network resources, and thus improves the network lifetime and delivery rate. Consequently, our proposed FA takes into account the coverage aspect in addition of the energy balancing one.

Firey optimization based Adaptive Clustering for

Energy Eciency (FACEE)

Network model

We dene a WSN as a set G of N nodes. We denote the i th sensor by n i and the corresponding sensor node set SN= n1, n2 , nN. The network's nodes are dispersed across a square region, with M denoting the length of each side.

We suppose that:

Every node also knows the BS coordinate value in addition to its own. BS is situated in a predetermined location, either within or outside the sensor eld.

Nodes in the network are pseudo-static. The energy of the BS is unlimited. Battery power restrictions apply to all sensor nodes. They have a limited communication range too.

Firey Optimization Alghorithm

Firey algorithm (FA) was introduced in 2008 which is inspired by the behavior and ashing patterns of reies in nature [START_REF] Tilahun | Continuous versions of rey algorithm: A review[END_REF]. FA belongs to swarm-based metaheuristics and replicates the way that reies communicate by ashing their lights. Since all reies are assumed to be unisex, any rey can be attracted to any other rey, and a rey's attractiveness is directly proportionate to its brightness, which depends on the objective function. Hence, a rey will be drawn to a rey that is more visible and the brightness diminishes with distance according to the inverse square law as in 1.

I ≺ 1 r 2 (1)
The light intensity with a light absorption coecient λ at a distance of r from the source can be described as in 2.

I = I 0 exp -γr 2 (2)
where I 0 represents the source's light intensity. The brightness can also be expressed as in 3.

β(r) = β 0 exp -γr 2 (3)
The algorithm assigns a light intensity to reies, which are randomly produced feasible solutions, based on how well they perform in the objective function. The brightness of the rey will be calculated using this intensity. For minimization issues, the solution with the lowest functional value will receive the most light. Each rey will thereafter follow reies that have better light intensity. A rey that shines the brightest will conduct a local search by randomly walking around its neighborhood. However, for two reies i and j, rey i will migrate in the direction of rey j using the updating method in 4, if rey j is brighter than rey i.

X i = X i + β 0 exp -γr(i,j) 2 (X j -X i ) + α(rand -1/2) ( 4
)
Where rand is the random number drawn from either a uniform distribution or a Gaussian distribution, and alpha is the randomization parameter.

The ow diagram of the rey algorithm is shown in Fig 1.

FACEE Proposed Algorithm

FACEE approach utilizes adaptive clustering scheme in such a way that if the number of clusters changes over time and the nodes' membership changes, a clustering system is referred as adaptive. For absorbing data transmission overload in FACEE, nodes with a specic high condition (Ich) can serve as the CH.

All nodes should alternately take turns serving as CH in order to prevent early mortality from high energy consumption. Hence various considerations must be taken into account when choosing a CH candidate. Node-weight, residual energy, node-to-node distance and distance from the BS are taken into account in FACEE. Consequently, we dene the following equations :

IW ij = 1 - W i W j ∀i, j (5)
Where, W i and W j are node-weight of nodes i and j respectively. The nodeweight of node n represents the length of its the cluster members and it dened by 6 as follow:.

W n = |CL n | (6)
Where CL n represents the cluster headed by the node n which includes the node n to initialize the length of the CL n list by 1. Note that each node have two lists:

cluster list (CL) for the cluster members and parent list (PR) for the temporary elected CHs.

ID ij = 1 - D Bs,i D Bs,j if i ̸ = j 1 - D Bs,i D M ax otherwise (7)
The Cartesian distances between the node i and the sink (s) and the node neighbor j and the sink are denoted as D Bs,i and D Bs,j respectively. D M ax is the maximum distance between all the nodes and the BS, and it is equal to M that represents the length of the side. The equation 8 calculates the Cartesian distance between nodes (i and j).

D i,j = (x i -x j ) 2 + (y i -y j ) 2 (8)
Where, (x i ,y i ) and (x j ,y j ) are the coordinate values of the node i and j respectively.

IE ij = Eri Erj if i ̸ = j Er i otherwise (9)
Where Er i and Er j are the residual energy of the nodes i and j respectively. According to 10, the residual energy of the node n Er n is determined as follows:

Er n = E Rm (n) E Init (n) (10)
E Rm (n) and E Init (n) are the remaining and initial energies of the node n.

Finally, the dierent node compete to be a Ch by the maximization of the sum of the equations 7, 5 and 9 according to the equation 11.

Ich i = M ax Wi j=1 λ1IE i,j + λ2ID i,j + λ3IW i,j (11)
Where λ1, λ2 and λ3 are parameters that control the importance of the metrics in such a way that λ1 + λ2 + λ3 = 1.

In order to get a suitable cluster distribution (unresolved problem with several protocols), FACEE algorithm uses threshold distance for each rey in such a way that the nodes belonging to this distance compete to select the best CH, however the other nodes (far from this distance) have an other choice to select an other CH. By this way, our proposed method can ensure the coverage and thus the reliability of all the network.

Algorithm

The application and adaptation of the FACEE algorithm to address coverage and load balancing in clustered WSN are described in this section. FACEE algorithm is presented in Algorithm1.

In fact, there are 4 phases involved in running the FACEE algorithm:

Step 1: in rst step, all the nodes are taken as population with initialization of the dierent parameters (line1 to 4). Algorithm 1: FACEE 1. Generate initial population of solutions ni, (i = 1, 2, 3, . . . , N); 2. Light intensity Ii is dened by Ichi 3. Dene Threshold(∆), λ1, λ2 and λ3 4. Dene number of iterations Nit 5. while t < Nit do 6. for i = 1 to N do 7.

for j = 1 to N do 8.

if (Ichj < Ichi) and (Di,j< Threshold(∆)) then 9.

Move solution j towards solution i (Add j to CLi) 10.

Update parent list of the node i (P Ri(j)) 11.

Update parent list of the node j (P Rj(i, P chi))

22.end while

Step 2: In the second stage, The equation 11 is used to determine the attractiveness of each articial rey i in comparison to another rey j. Hence the equation 3 is dened by 12 as follows:

β i = P ch i (12)
In our work, we took into account the idea that a rey's attraction is solely dependent on the amount of light it emits through its objective function.

Therefore, the distance between the reies does not have the only eect on how attractive they are.

Step 3: The algorithm explores the search space in this step to produce new solutions. Therefore, Adding the moved reies to the destination rey's cluster list and updating the parent lists of both the moved and the destination reies in such a way that the moved rey updates the parent only if it has the largest β i , but the destination rey deletes the moved one from its parent list if it exists, are how new solutions are generated by moving reies that are at a certain threshold distance away from better solutions (from 8 to 12).

Step 4: Any meta-heuristic's eectiveness is achieved by fusing the exploration and exploitation behaviors that are used to nd the optimal solution.

According to our method, the exploitation is carried out by using a local search around the best solution (solution with the highest light intensity).

The local search consists on selecting other CH at a time. This process is repeated until the number of iterations is reached, then optimal CHs will be selected (from 17 to 21).

Simulation and Results

The simulation results of our algorithm FACEE in comparison to the protocols LEACH-C and EM-FIREFLY [START_REF] Miodrag | Wireless Sensor Networks Life Time Optimization Based on the Improved Firey Algorithm[END_REF] are presented in this section. In addition to our FACEE algorithm, we have implemented EM-FIREFLY due to the lack of its source code. The simulation is performed in MATLAB and the collection of outputs after specic number of rounds considered by 1000. The same simulation parameters are used for the dierent protocols. These simulation parameters are shown in Table1. In order to give priority to the energy parameter in our protocol FACEE, we have xed the parameters that control the importance of the metrics presented by λ1, λ2 and λ3 by 0.5, 0.3 and 0.2 respectively. Also the threshold(∆) is xed by 20m (the same as radio range).

The execution of the dierent protocols is presented in Figures 2(a

Conclusion

In this paper, we propose a novel scheme for coverage improvement with energy balancing in clustered wireless sensor networks based Firey optimization algorithm. The main challenge of such work is the improvement of the network lifetime. For this reason, a special consideration is given to the coverage process that is less considered in the previous works. In addition, a load balance mechanism is added in order to achieve the maximum of the network lifetime improvement. Through simulations and experiments, we demonstrate that our protocol FACEE signicantly reduces the energy consumption and improves the network lifetime with good amounts of packet delivery. As a future work, it seems more suitable to design a decentralized version of our technique and compared it with the present work.

Fig. 1 :

 1 Fig. 1: The rey algorithm's owchart.

Fig. 2 :

 2 Fig. 2: (a) LEACH-C Coverage, (b) EM-FIREFLY Coverage and (c) FACEE Coverage

Fig. 3 :Fig. 4 :

 34 Fig. 3: (a)(a)Network lifetime for the three protocols: LEACH-C, EM-FIREFLY, FACEE, (b) Delivery packets in LEAH-C, (c) Delivery packets in EM-FIREFLY and (d) Delivery packets in FACEE.

Figures 4 (

 4 Figures 4(a) and 4(b) show the average of CHs load through the execution in dierent rounds by the two protocols EM-FIREFLY and FACEE. It must be noted that our protocol succeeds more than the protocol EM-FIREFLY in load balance between CHs. This is proved by the fact of exploiting more number of CHs then EM-FIREFLY in addition of the butter dividing of nodes between CHs more than EM-FIREFLY.

  12.

		end if
	13.	end for
	14.	end for
	15. end wile
	16. for j = 1 to SN do
	17.	if P Rj ̸ = ∅ then
	18.	Select the best i as CH
	19.	else
	20.	Select j as CH
	21.	end if

Table 1 :

 1 Simulation parameters.

	Parameters	Values
	Number of nodes	100
	Area	150m*150m
	Radio range	20m
	Initial energy	0.5j
	Sink location	In the middle
	Data packet size	4000bit
	Control packet size	500bit