Elodie Chartron
email: elodie.chartron@icm.unicancer.fr

Nelly Firmin
email: nelly.firmin@icm.unicancer.fr

Célia Touraine
email: celia.touraine@icm.unicancer.fr

Angélique Chapelle
email: a.chapelle@oncogard.com

Eric Legouffe

Lobna Rifai
email: lobna.rifai@icm.unicancer.fr

Stéphane Pouderoux
email: stephane.pouderoux@icm.unicancer.fr

Lise Roca
email: lise.roca@icm.unicancer.fr

William Véronique D'hondt
email: veronique.dhondt@icm.unicancer.fr

Jacot

Eric Legouf

Véronique D'hondt

William Jacot
email: william.jacot@icm.unicancer.fr

A Phase II Multicenter Trial on High-Dose Vitamin D Supplementation for the Correction of Vitamin D Insufficiency in Patients with Breast Cancer Receiving Adjuvant Chemotherapy

Keywords: vitamin D insufficiency, breast cancer, adjuvant chemotherapy, hypercalciuria

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

Introduction

Therapies for early-stage and locally advanced breast cancer (BC) may induce bone loss [START_REF] Pfeilschifter | Osteoporosis Due to Cancer Treatment: Pathogenesis and Management[END_REF]. Indeed, chemotherapy is often associated with premature ovarian failure and direct cytotoxic bone effects, resulting in bone mineral density reduction that increases the skeletal morbidity risk compared with women without BC history [START_REF] Pfeilschifter | Osteoporosis Due to Cancer Treatment: Pathogenesis and Management[END_REF][START_REF] Chen | Fracture Risk Among Breast Cancer Survivors: Results from the Women's Health Initiative Observational Study[END_REF][START_REF] Mincey | Osteoporosis in women with breast cancer[END_REF][START_REF] Saarto | Chemical castration induced by adjuvant cyclophosphamide, methotrexate, and fluorouracil chemotherapy causes rapid bone loss that is reduced by clodronate: A randomized study in premenopausal breast cancer patients[END_REF]. Moreover, adjuvant aromatase inhibitors, used in postmenopausal patients with BC, are associated with higher loss of bone mineral density and osteoporosis risk [START_REF] Heeke | Bone-Modifying Agents in Early-Stage and Advanced Breast Cancer[END_REF].

Vitamin D (VD) insufficiency is extremely frequent in the general population (around 50%) [START_REF] Tangpricha | Vitamin D insufficiency among free-living healthy young adults[END_REF] and even more in patients with cancer. For example, 70-90% of women with early BC present VD insufficiency [START_REF] Goodwin | Prognostic Effects of 25-Hydroxyvitamin D Levels in Early Breast Cancer[END_REF][START_REF] Neuhouser | Vitamin D insufficiency in a multiethnic cohort of breast cancer survivors[END_REF][START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF]. In BC, VD insufficiency is associated with adverse prognosis [START_REF] Freedman | Prospective Study of Serum Vitamin D and Cancer Mortality in the United States[END_REF], higher histological grade [START_REF] Goodwin | Prognostic Effects of 25-Hydroxyvitamin D Levels in Early Breast Cancer[END_REF], and higher BC stage [START_REF] Palmieri | Serum 25-hydroxyvitamin D levels in early and advanced breast cancer[END_REF]. In early BC (EBC), low 25-hydroxy VD (25-OH VD) serum concentration is associated with increased risk of distant recurrence and death [START_REF] Goodwin | Prognostic Effects of 25-Hydroxyvitamin D Levels in Early Breast Cancer[END_REF]. In women with EBC receiving neoadjuvant chemotherapy, 25-OH VD level is inversely correlated with the percentage of pathological complete response, a strong prognostic factor, especially in HER2-positive (HER2 + ) and triple-negative BC [START_REF] Viala | Impact of vitamin D on pathological complete response and survival following neoadjuvant chemotherapy for breast cancer: A retrospective study[END_REF]. This negative correlation could be partly explained by the potential anticancer effect of VD. Normal and tumor breast tissues express 1-alpha hydroxylase [START_REF] Segersten | 25-Hydroxyvitamin D31α-hydroxylase expression in breast cancer and use of non-1α-hydroxylated vitamin D analogue[END_REF]. This enzyme hydroxylates 25-OH VD, the major circulating VD metabolite, into its biologically active form (1,25-OH VD) that interacts with the nuclear VD receptor to modulate the expression of more than 200 genes involved in various aspects of tumorigenesis. Indeed, it has been reported that VD has antiproliferative and antiangiogenetic effects, and it induces breast cancer cell differentiation and apoptosis [START_REF] Carlberg | Current Understanding of the Function of the Nuclear Vitamin D Receptor in Response to Its Natural and Synthetic Ligands[END_REF][START_REF] Pendás-Franco | Vitamin D regulates the phenotype of human breast cancer cells[END_REF]. Furthermore, VD can influence the response to chemotherapeutic agents. In vitro results showed that VD potentiates the antitumor activities of anthracyclines and taxanes, two cytotoxic compounds widely used in EBC adjuvant and neoadjuvant chemotherapies [START_REF] Chaudhry | The vitamin D3 analog, ILX-23-7553, enhances the response to adriamycin and irradiation in MCF-7 breast tumor cells[END_REF][START_REF] Hershberger | Calcitriol (1,25-dihydroxycholecalciferol) enhances paclitaxel antitumor activity in vitro and in vivo and accelerates paclitaxel-induced apoptosis[END_REF].

Current guidelines recommend VD daily supplementation varying from 400 to 800 IU [START_REF] Dhesy-Thind | Use of Adjuvant Bisphosphonates and Other Bone-Modifying Agents in Breast Cancer: A Cancer Care Ontario and American Society of Clinical Oncology Clinical Practice Guideline[END_REF] to 2000 IU [START_REF] Holick | Evaluation, Treatment, and Prevention of Vitamin D Deficiency: An Endocrine Society Clinical Practice Guideline[END_REF] of VD in order to achieve a 25-OH VD serum target concentration higher than 30 ng/mL (75 nmol/L) for patients with EBC. However, clinical trials that investigated VD supplementation and cancer risk and prognosis yielded inconsistent results. VD supplementation at the recommended doses (400 IU/day) failed to reduce BC risk in the Women's Health Initiative support study [START_REF] Chlebowski | Calcium Plus Vitamin D Supplementation and the Risk of Breast Cancer[END_REF]. Conversely, in another randomized trial in which higher VD doses (1100 IU/day) were used, the overall cancer risk was reduced [START_REF] Lappe | Vitamin D and calcium supplementation reduces cancer risk: Results of a randomized trial[END_REF]. The low-dose supplementation in the first study might not have corrected VD insufficiency, and this could explain the contrasting results. Indeed, other studies showed that, in most cases, low doses of VD (<1000 IU/day) do not correct 25-OH VD concentration in patients with BC and VD insufficiency [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF][START_REF] Crew | High Prevalence of Vitamin D Deficiency Despite Supplementation in Premenopausal Women with Breast Cancer Undergoing Adjuvant Chemotherapy[END_REF][START_REF] Peppone | The effect of various vitamin D supplementation regimens in breast cancer patients[END_REF]. On the other hand, recent trials confirmed the safety of VD supplementation with doses > 5000 IU/day [START_REF] Diamond | Effect of oral cholecalciferol 2,000 versus 5,000 IU on serum vitamin D, PTH, bone and muscle strength in patients with vitamin D deficiency[END_REF][START_REF] Khan | Effect of vitamin D supplementation on serum 25-hydroxy vitamin D levels, joint pain, and fatigue in women starting adjuvant letrozole treatment for breast cancer[END_REF]. We previously demonstrated in a dedicated phase 3 study that, in patients with EBC and VD insufficiency receiving adjuvant chemotherapy, high-dose VD supplementation doubled the percentage of women who achieved 25-OH VD concentration normalization compared with the supplementation at the recommended dose (30% versus 12.6%) [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF]. However, 70% of patients in the highdose VD arm still presented VD insufficiency at the intervention end. These findings indicate that, to increase VD normalization rate, higher doses and optimal observance are required. Therefore, we designed a phase II trial to assess whether high-dose VD oral supplementation can correct VD insufficiency in patients with EBC treated with adjuvant chemotherapy. We report here the results of the safety and efficacy analyses.

Materials and Methods

Eligibility Criteria

Women, older than 18 years of age, with histologically confirmed EBC, indication for adjuvant sequential chemotherapy (six cycles of sequential anthracycline and taxanes), Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, and confirmed VD insufficiency (defined as a serum concentration <30 ng/mL or 75 nmol/mL) were eligible for enrollment in this study. All patients provided their written informed consent before inclusion. Trastuzumab was given concurrently with taxanes, for a total duration of 1 year, in patients with HER2 + EBC. HER2 + tumors were defined as 3+ positive by immunohistochemistry (IHC) or with HER2 gene amplification by in situ hybridization for ambiguous (2+) tumors by IHC. Tumors were defined as triple-negative when the expression of estrogen receptor and progesterone receptor was lower than 10% by IHC and HER2 was not amplified or 0/1+ or 2+ by IHC.

Patients were excluded in case of abnormal hematologic, hepatic, or renal function, metastatic disease, personal history of another cancer treated in the previous 5 years, or contraindication to calcium or VD (hypersensitivity to VD or calcium compounds, diseases inducing hypercalcemia or hypercalciuria, calcium nephrolithiasis or tissue calcifications, and hypervitaminosis D (>75 ng/mL or 187.5 nmol/mL)). Patients with significant comorbidities (e.g., uncontrolled endocrine disease, pre-existing calcium and VD balance disorders in the last 3 years, osteopenia or osteoporosis requiring VD supplementation ≥ 1000 IU/day, and medical or psychological conditions not allowing to give informed consent), patients receiving another experimental treatment, and pregnant or nursing women were not eligible. The protocol was approved by the local Ethics Committee (Comité de Protection des Personnes Sud Méditerrannée III, reference 2013.03.06 bis, 27 May 2013) and was registered at ClinicalTrials.gov (Identifier: NCT04091178).

Study Design and Treatment

In this phase II, open-label, nonrandomized multicenter study, patients received one dose of 100,000 IU 25-OH VD per os every 3 weeks, for outpatient clinic chemotherapy, from day 1 of cycle 1 (D1C1) to day 1 of cycle 5 (D1C5), with a daily supplementation of 1000 mg of calcium. VD administration was stopped in case of VD serum reaching the upper normal value and clinical or biological adverse event(s) related to VD or calcium metabolism (hypercalcemia > 2.65 mmol/L; hypercalciuria above the upper limit of the norm), leading to early discontinuation of the patient's participation. At the end of the adjuvant chemotherapy cycles, VD (100,000 IU VD quarterly) and calcium (1000 mg/day) supplementation could be continued at the investigator's discretion.

Endpoints and Safety Analysis

The primary endpoint was the percentage of patients with serum VD concentration normalization on day 1 of cycle 6 (D1C6). Secondary endpoints were VD normalization rate 6, 12, 18, and 24 months after VD supplementation initiation, safety, and calcium parameters (blood calcium, phosphorus, parathyroid hormone levels, urinary calcium excretion, serum VD level), as well as creatinine and uremia at baseline and their changes during adjuvant chemotherapy, and the identification of baseline clinical factors and biomarkers that could predict VD normalization on D1C6. All patients who received at least one dose of VD were included in the safety analysis.

Assessments

Baseline assessments included medical history, physical examination, performance status (ECOG scale), VD and calcium supplementation in the last year, complete blood count and metabolic profile including electrolytes, hepatic and renal function, and VD and calcium parameters (corrected blood calcium, phosphorus, albumin, parathormone levels, and urinary calcium excretion). All biological samples were analyzed centrally. VD levels were measured using the DiaSorin 25-HydroxyvitaminD-125 RIA kit (DiaSorin France).

The same clinical and laboratory assessments were repeated on day 1 of each 21 day chemotherapy cycle, as well as the evaluation of VD-related side-effects and compliance. After chemotherapy completion, patients were followed (clinical and laboratory analyses) every 6 months for 2 years. Adverse events were graded according to the National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE), version 4.0.

Statistical Analysis

Analyses were done on the evaluable population, defined as the eligible treated patients that completed the six chemotherapy cycles.

The primary endpoint was the percentage of serum VD level normalization on D1C6. Based on a Fleming single-stage design with p 0 (largest response probability) = 30%, p 1 (smallest response probability) = 55%, α = 5%, and β = 5%, 40 patients needed to be evaluated on D1C6. The normalization goal was considered as achieved if the number of successes was at least 17. Considering a 10% rate of non-evaluable patients, it was planned to include 44 patients. As the VD insufficiency prevalence in the population with EBC was evaluated to reach 70%, 63 patients needed to be included to evaluate 40 patients with VD insufficiency on D1C6.

Baseline characteristics were described by medians and range (quantitative variables) and number of observations and percentages (qualitative variables). The number of miss-ing values was reported, and the percentages were calculated without missing values. The primary endpoint was reported with the 95% confidence interval (CI) calculated using a logit transform. Laboratory parameter changes at each chemotherapy cycle were analyzed using linear mixed models assuming linear (or piecewise linear, if more appropriate) trajectories of the laboratory parameters for each group, defined by the VD normalization status on D1C6 (yes or no). They included fixed effects (intercept, group effect, time effect (slope), and group-by-time interaction effect) and random intercept and slope effects. The final models included only the significant effects at the 5% level. Logistic regressions were used to determine what baseline laboratory parameters and clinical factors were associated with VD concentration normalization on D1C6. A p-value <0.05 was considered for statistical significance. All analyses were performed using the Stata software (version 13.0).

Results

Patient Characteristics

Among the 57 patients selected at the two centers, 45 patients were finally included from June 2013 to June 2014. Twelve patients were excluded because of nonconfirmed VD insufficiency (n = 5), baseline hypercalciuria (n = 5), synchronous metastases (n = 1), and withdrawal of consent (n = 1). The primary endpoint could be evaluated in 44 patients (Figure 1).

successes was at least 17. Considering a 10% rate of non-evaluable patients, it was planned to include 44 patients. As the VD insufficiency prevalence in the population with EBC was evaluated to reach 70%, 63 patients needed to be included to evaluate 40 patients with VD insufficiency on D1C6.

Baseline characteristics were described by medians and range (quantitative variables) and number of observations and percentages (qualitative variables). The number of missing values was reported, and the percentages were calculated without missing values. The primary endpoint was reported with the 95% confidence interval (CI) calculated using a logit transform. Laboratory parameter changes at each chemotherapy cycle were analyzed using linear mixed models assuming linear (or piecewise linear, if more appropriate) trajectories of the laboratory parameters for each group, defined by the VD normalization status on D1C6 (yes or no). They included fixed effects (intercept, group effect, time effect (slope), and group-by-time interaction effect) and random intercept and slope effects. The final models included only the significant effects at the 5% level. Logistic regressions were used to determine what baseline laboratory parameters and clinical factors were associated with VD concentration normalization on D1C6. A p-value < 0.05 was considered for statistical significance. All analyses were performed using the Stata software (version 13.0).

Results

Patient Characteristics

Among the 57 patients selected at the two centers, 45 patients were finally included from June 2013 to June 2014. Twelve patients were excluded because of nonconfirmed VD insufficiency (n = 5), baseline hypercalciuria (n = 5), synchronous metastases (n = 1), and withdrawal of consent (n = 1). The primary endpoint could be evaluated in 42 patients (Figure 1). The baseline patient characteristics are summarized in Table 1. The median age was 47.5 years, and 65.9% of patients were premenopausal. Moreover, 93% (n = 41) of patients had stage I or II BC, and 6.8% (n = 3) had stage III BC. Six tumors (13.6%) were HER2 + , six (13.6%) were triple-negative, and 79% were hormone receptor-positive and HER2-negative. At inclusion, the median VD serum concentration was 19.15 ng/mL (range: 6.4-29.5). Baseline calcium parameters (blood calcium, phosphorus, parathyroid hormone, and albumin levels) were normal except in five patients with low urinary calcium excretion, and two and seven patients with abnormal parathyroid hormone and phosphorus concentration, respectively (Table 2). Baseline urea and creatinine levels were in the normal range for all the included patients.

Treatment Compliance and Vitamin D Normalization

All patients completed the adjuvant chemotherapy treatment (D1C6) at the date of data analysis (22 February 2018), with a median follow-up of 106 weeks (30-116 weeks).

All patients took the planned VD supplementation because it was delivered at the time of outpatient chemotherapy (Supplementary Table S1). During the follow-up, the percentage of patients taking VD supplementation decreased to 65.9%, 50%, and 31.8% at months 6, 12, and 18, respectively (supplementation continued at the investigator's discretion, Supplementary Table S2). During the chemotherapy cycles, VD intake was prematurely stopped in 10 patients due to asymptomatic hypercalciuria (safety section), while the other 34 patients (77.3%) took the VD supplementation up to D1C5. Concerning calcium supplementation, 73.8% of patients took at least 80% of the oral daily calcium supplementation on D1C1, but this percentage decreased to 59.3% on D1C6 (Supplementary Table S3).

The percentage of patients with serum 25-OH VD concentration normalization on D1C6 (primary endpoint of the study) was 47.7% (95% CI: 33.0-62.8), with a median D1C6 VD serum concentration of 29.25 ng/mL (range: 19.3-61.4). Among the first 40 evaluable patients, 18 patients (45.0%; 95% CI: 29.9-61.1) showed 25-OH VD concentration normalization on D1C6. VD normalization rates at 6, 12, 18, and 24 months were 50%, 28.9%, 80%, and 60.9%, respectively.

No baseline clinical or biological marker significantly predicted 25-OH VD concentration normalization on D1C6.

Toxicity

VD and calcium supplementation were well tolerated. No clinical toxicity event linked to the VD treatment was reported. However, 13 patients (29.5%) presented asymptomatic grade 1 hypercalciuria, without kidney function changes or clinical symptoms, but leading to VD supplementation interruption in 10/13 patients during adjuvant chemotherapy (D1C1 to D1C5). This interruption was rapidly followed by a reduction in VD level. The median serum VD concentration in these 13 patients was 23.1 ng/mL (range: 9.2-42.7) at hypercalciuria occurrence and 25.5 ng/mL (range: 20.1-34.6) on D1C6, and VD normalization was achieved only by three patients (23%).

Laboratory Parameter Changes during Adjuvant Chemotherapy

VD serum concentration significantly increased during chemotherapy. The mean increase was +3.73 ng/mL/cycle in patients with VD normalization on D1C6 and +1.78 ng/mL/cycle in patients without VD normalization.

Calcium parameter levels (corrected blood calcium, phosphorus, parathyroid hormone levels, and urinary calcium) significantly increased during adjuvant chemotherapy, while albumin levels significantly decreased. No correlation between VD serum concentration normalization status and calcium parameter changes was found.

The predicted trajectories of the calcium parameters (corrected blood calcium, phosphorus, parathormone levels, and urinary calcium) and albumin during adjuvant chemotherapy were not different in patients with and without VD concentration normalization on D1C6 (Figure 2). Overall, the models predicted a significant increase in the calcium parameter levels and a significant decrease in the albumin levels during chemotherapy compared with baseline. Specifically, the models estimated a mean increase by cycle of 0.013 mmol/L for corrected calcium, of 0.040 mmol/L for phosphorus, of 2.35 ng/mL for parathyroid hormone, and of 0.25 mmol/L for urinary calcium during chemotherapy. On the other hand, uremia changes were different between patients with and without VD normalization on D1C6. Specifically, urea levels increased in patients without VD normalization on D1C6 (estimated mean increase of 0.144 mmol/L/chemotherapy cycle), while they remained stable in women with VD normalization on D1C6. Creatinine levels remained stable in patients without VD normalization on D1C6. Conversely, in patients with VD normalization, they increased up to D1C3 and then progressively decreased.

Discussion

VD insufficiency is very frequent in patients with EBC and influences prognosis. We performed a prospective phase II, open-label, nonrandomized, multicenter trial in which 44 patients with EBC received high-dose VD supplementation during adjuvant chemotherapy to increase the VD normalization rate.

The daily recommended dose of VD (400 to 800 IU of VD with 1200 mg of calcium per day) is insufficient to normalize the 25-OH VD level in most patients undergoing adjuvant chemotherapy. For instance, in a previous study, we found that serum VD concen-

Discussion

VD insufficiency is very frequent in patients with EBC and influences prognosis. We performed a prospective phase II, open-label, nonrandomized, multicenter trial in which 44 patients with EBC received high-dose VD supplementation during adjuvant chemotherapy to increase the VD normalization rate.

The daily recommended dose of VD (400 to 800 IU of VD with 1200 mg of calcium per day) is insufficient to normalize the 25-OH VD level in most patients undergoing adjuvant chemotherapy. For instance, in a previous study, we found that serum VD concentration was normalized at adjuvant chemotherapy end in only 12% of patients when using the recommended doses of calcium and VD [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF]. As VD levels have been associated with EBC prognosis in patients receiving adjuvant or neoadjuvant chemotherapy [START_REF] Goodwin | Prognostic Effects of 25-Hydroxyvitamin D Levels in Early Breast Cancer[END_REF][START_REF] Viala | Impact of vitamin D on pathological complete response and survival following neoadjuvant chemotherapy for breast cancer: A retrospective study[END_REF][START_REF] Chiba | Serum Vitamin D Levels Affect Pathologic Complete Response in Patients Undergoing Neoadjuvant Systemic Therapy for Operable Breast Cancer[END_REF], VD insufficiency correction is an important issue. In the present trial, we demonstrated that high-dose VD supplementation increased the serum 25-OH VD level normalization rate on D1C6 to 47% in patients with EBC. This is better than the 30% value at 6 months we reported in a previous study in which patients with BC received a tailored high-dose VD supplementation [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF]. This effect does not seem to be transient because, at month 24 of follow-up, serum 25-OH VD levels were still below the recommended levels in only 39.1% of patients with baseline VD deficiency. This value is even lower than the percentage of patients with VD insufficiency on D1C6, although only 36% of patients were still taking VD supplementation at month 24 of follow-up. This could be partly explained by previous studies showing a decrease in 25-OH VD concentration during chemotherapy and a recovery after treatment end [START_REF] Kim | Changes in serum hydroxyvitamin D levels of breast cancer patients during tamoxifen treatment or chemotherapy in premenopausal breast cancer patients[END_REF][START_REF] Kim | Association between Changes in Serum 25-Hydroxyvitamin D Levels and Survival in Patients with Breast Cancer Receiving Neoadjuvant Chemotherapy[END_REF][START_REF] Kok | Changes in Circulating Levels of 25-hydroxyvitamin D3 in Breast Cancer Patients Receiving Chemotherapy[END_REF]. It has been suggested that taxanes, corticosteroids, behavioral changes (such as sunlight exposure, dietary intake), and gastrointestinal side-effects play a role in this initial decrease in 25-OH VD levels [START_REF] Kim | Changes in serum hydroxyvitamin D levels of breast cancer patients during tamoxifen treatment or chemotherapy in premenopausal breast cancer patients[END_REF][START_REF] Kim | Association between Changes in Serum 25-Hydroxyvitamin D Levels and Survival in Patients with Breast Cancer Receiving Neoadjuvant Chemotherapy[END_REF][START_REF] Kok | Changes in Circulating Levels of 25-hydroxyvitamin D3 in Breast Cancer Patients Receiving Chemotherapy[END_REF][START_REF] Miyoshi | Prediction of response to docetaxel by CYP3A4 mRNA expression in breast cancer tissues[END_REF]. This could explain the important 25-OH VD concentration decrease at month 12 of follow-up (only 28.9% of patients with normalized 25-OH VD level). However, this observation must be interpreted with caution due to the small size of the study population and the fact that it was not a primary outcome of this study.

The high-dose VD supplementation regimen used in our study appears safe in the context of adjuvant chemotherapy. VD levels higher than the upper normal value were not observed in any patient, and clinical adverse effects that could be associated with VD supplementation (i.e., hypercalcemia and kidney stones) were not reported, in agreement with previous studies [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF][START_REF] Khan | Effect of vitamin D supplementation on serum 25-hydroxy vitamin D levels, joint pain, and fatigue in women starting adjuvant letrozole treatment for breast cancer[END_REF]. For instance, Khan et al. did not detect any clinical adverse effect in women with BC taking even higher VD doses (50,000 IU/week for 12 weeks) [START_REF] Khan | Effect of vitamin D supplementation on serum 25-hydroxy vitamin D levels, joint pain, and fatigue in women starting adjuvant letrozole treatment for breast cancer[END_REF]. However, in our study, 29.5% of patients presented an asymptomatic increase in urinary calcium excretion that exceeded the upper normal value. The occurrence of asymptomatic hypercalciuria could not be predicted by the baseline calcium metabolism parameters and was not associated with hypercalcemia or hypervitaminosis D when detected (the highest 25-OH VD value at hypercalciuria onset was 47.2 ng/mL). We observed a similar hypercalciuria rate (35.4%) in a previous trial [START_REF] Viala | Changes in vitamin D and calcium metabolism markers in patients undergoing adjuvant chemotherapy for breast cancer[END_REF], in which 82 patients with EBC received adjuvant chemotherapy and VD supplementation at the investigator's discretion (recommended dose) between D1C1 and D1C6. In this previous study, hypercalciuria rates were comparable in patients with/without baseline VD insufficiency and with/without VD supplementation. In the present trial, asymptomatic hypercalciuria led to VD treatment interruption and was associated with VD insufficiency persistency in 10/13 patients at the primary objective time (D1C6), thus increasing the number of patients in which serum VD concentration was not corrected by the supplementation at the primary endpoint.

Hypercalciuria is considered a sensitive indicator of VD supplementation effect [START_REF] Vieth | Efficacy and safety of vitamin D3 intake exceeding the lowest observed adverse effect level[END_REF]. However, in our previous study, hypercalciuria rate was high, without any significant difference between patients with/without VD supplementation, and VD levels were far below the upper value at hypercalciuria detection [START_REF] Viala | Changes in vitamin D and calcium metabolism markers in patients undergoing adjuvant chemotherapy for breast cancer[END_REF]. Therefore, this high hypercalciuria incidence could be linked to a direct effect of chemotherapy, concomitant corticosteroid medications, changes in nutritional habits, or early ovarian failure [START_REF] Crew | High Prevalence of Vitamin D Deficiency Despite Supplementation in Premenopausal Women with Breast Cancer Undergoing Adjuvant Chemotherapy[END_REF][START_REF] Suzuki | Importance of increased urinary calcium excretion in the development of secondary hyperparathyroidism of patients under glucocorticoid therapy[END_REF][START_REF] Duzen | The Course of Hypercalciuria and Related Markers of Bone Metabolism Parameters Associated with Corticosteroid Treatment[END_REF][START_REF] Atkinson | Mineral homeostasis and bone mass in children treated for acute lymphoblastic leukemia[END_REF][START_REF] Damasio | The role of salt abuse on risk for hypercalciuria[END_REF][START_REF] Garg | Effects of Dietary Carbohydrates on Metabolism of Calcium and Other Minerals in Normal Subjects and Patients with Noninsulin-Dependent Diabetes Mellitus[END_REF]. Hypercal-cemia or hypercalciuria directly induced by hypervitaminosis D is caused by increased intestinal calcium absorption and bone reabsorption [START_REF] Pak | Gastrointestinal Calcium Absorption in Nephrolithiasis[END_REF]. However, this is a rare event, generally associated with extended daily VD intake higher than 10,000 IU and 25-OH VD serum concentrations >150 ng/mL [START_REF] Vieth | Efficacy and safety of vitamin D3 intake exceeding the lowest observed adverse effect level[END_REF]. In our trial, the highest 25-OH VD serum concentration was 61.4 ng/mL on D1C6, below the upper normal value. Unfortunately, Khan et al. did not quantify urinary calcium excretion during treatment [START_REF] Khan | Effect of vitamin D supplementation on serum 25-hydroxy vitamin D levels, joint pain, and fatigue in women starting adjuvant letrozole treatment for breast cancer[END_REF].

Hypercalciuria is associated with urinary lithiasis that was not observed in our sample. This could be explained by the limited number of patients who developed hypercalciuria (n = 13). However, we did not record any case of urolithiasis in our previous studies (total = 277 patients) [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF][START_REF] Viala | Changes in vitamin D and calcium metabolism markers in patients undergoing adjuvant chemotherapy for breast cancer[END_REF]. The association of urolithiasis and VD supplementation remains debated. A systemic review of observational studies (total = 23,228 patients) showed that 1,25-OH VD blood concentration was higher in patients with than without kidney stones [START_REF] Hu | Association between Circulating Vitamin D Level and Urolithiasis: A Systematic Review and Meta-Analysis[END_REF]. This review also found that 25-OH VD concentration was higher in patients with hypercalciuria-related urolithiasis than in controls and in patients with urolithiasis and normocalciuria. Recently, a meta-analysis on 32 studies that included patients taking daily VD doses ≥2800 IU for at least 1 year did not find any increased risk of clinical adverse effects, kidney stones, hypercalcemia, or hypercalciuria [START_REF] Malihi | Adverse events from large dose vitamin D supplementation taken for one year or longer[END_REF]. Thus, the etiology of hypercalciuria and its possible complications remains to be defined. However, the causality with VD supplementation and the risk of clinically significant side-effects appears extremely low. On the other hand, VD discontinuation was often associated with VD insufficiency persistence. Thus, considering the clinical-pathological consequences of VD insufficiency, continuation of VD supplementation appears reasonable in patients with asymptomatic increase of urinary calcium clearance.

Compliance remains a critical point in oral drug efficacy, especially in conditions associated with emesis, such as chemotherapy. In our trial, only 59.3% of patients presented a satisfactory compliance, defined as a dose intensity >80% for oral daily calcium supplementation. This low rate, similar to that of our previous randomized study [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF], could be linked to the tedious nature of daily intake in the context of an emetic condition. Compliance optimization appears mandatory to reach VD correction. A discontinuous regimen, associated with a medical consultation (e.g., the visit for outpatient chemotherapy), could allow increasing the compliance rate. Indeed, in our study, the VD supplementation compliance rate was 77.3% on D1C6, and the only patients who did not take VD were the 10 patients who stopped the supplementation due to asymptomatic hypercalciuria.

Lastly, one important question remains regarding the prognostic impact of VD levels in EBC patients, as studies have linked VD levels to various carcinogenetic events in breast cancer (for a review, see [START_REF] Welsh | Vitamin D and breast cancer: Past and present[END_REF]), albeit with conflicting results in the clinical setting [START_REF] Markowska | Role of vitamin D3 in selected malignant neoplasms[END_REF]. While the number of patients included in this trial remains too low to allow an accurate evaluation of this correlation, a survival analysis including all the patients from our three VD trials in adjuvant BC ( [START_REF] Jacot | Impact of a tailored oral vitamin D supplementation regimen on serum 25-hydroxyvitamin D levels in early breast cancer patients: A randomized phase III study[END_REF][START_REF] Viala | Changes in vitamin D and calcium metabolism markers in patients undergoing adjuvant chemotherapy for breast cancer[END_REF] and the current work) is planned in order to evaluate this association.

Conclusions

High-dose VD regimen increased the percentage of serum 25-OH VD concentration normalization in patients with EBC undergoing adjuvant chemotherapy. Asymptomatic hypercalciuria was frequent, but without clinical consequences. VD interruption, due to asymptomatic hypercalciuria, was associated with a rapid decrease in VD serum concentration. This indicates that it is important to better understand the causes of hypercalciuria and to determine whether and when VD supplementation can be safely continued.

Supplementary Materials:

The following are available online at https://www.mdpi.com/article/10.3 390/nu13124429/s1: Table S1. Compliance with VD supplementation during adjuvant chemotherapy; Table S2. Compliance with VD supplementation during follow-up; Table S3. Compliance (at least 80% of the target dose) with calcium supplementation during adjuvant chemotherapy.

Figure 1 .

 1 Figure 1. Study flowchart (VD: vitamin D).Figure 1. Study flowchart (VD: vitamin D).

Figure 1 .

 1 Figure 1. Study flowchart (VD: vitamin D).Figure 1. Study flowchart (VD: vitamin D).

12 Figure 2 .

 122 Figure 2. Predicted mean trajectories (solid lines) from the linear mixed models in patients with and without VD concentration normalization on D1C6 or in the whole population if the trajectories were or were not significantly different between groups, respectively. Dashed lines, observed median values in patients with (blue) and without VD concentration normalization (red). Abbreviations: PTH: parathormone, VD: vitamin D.

Figure 2 .

 2 Figure 2. Predicted mean trajectories (solid lines) from the linear mixed models in patients with and without VD concentration normalization on D1C6 or in the whole population if the trajectories were or were not significantly different between groups, respectively. Observed median values (dashed lines) in patients with (blue) and without (red) VD concentration normalization. Abbreviations: PTH: parathormone, VD: vitamin D.

Table 1 .

 1 Baseline patients' characteristics.

	N	%

Table 2 .

 2 Baseline VD and calcium parameters.

		N	%	Median	Range
	Parathyroid hormone (ng/mL)
	Normal Abnormal	36 2	94.7 5.3	40.5	16-89
	Missing	6
	Corrected calcium * (mmol/L)
	Normal Abnormal	43 0	100	2.225	2.1-2.395
	Missing	1
	Urine calcium (mmol/L)
	Normal Abnormal	35 5	87.5	3.14	0.93-6.7
	Missing	4	12.5
	Phosphorus (mmol/L)
	Normal Abnormal	35 7	83.3 16.7	0.995	0.73-1.4
	Missing	2
	25-OH VD (ng/mL)
	Normal Abnormal	0 44	0 100	19.15	6.4-29.5
	Missing	0

* Corrected calcium: calcium serum concentration corrected to the albumin level with the following formula: total calcium -(albumin level (g/L) -40)/40).

Data Availability Statement:

The data presented in this study are available on request from the corresponding author.

Informed Consent Statement: Written informed consent was obtained from all subjects involved in the study.

Conflicts of Interest:

The authors declare no conflict of interest.


Hamid Ahaggach
email: hamid.ahaggach@u-bourgogne.fr

Lylia Abrouk
email: lylia.abrouk@u-bourgogne.fr

Sebti Foufou
email: sfoufou@u-bourgogne.fr

Eric Lebon
email: elebon@syartec.com

Predicting car sale time with data analytics and machine learning

Keywords: Product Lifecycle Management, data analysis, machine learning

There is no doubt that marketing is an important step in Product Lifecycle Management (PLM) and obviously decreasing timeto-market is crucial to reduce storage costs and increase profit. This paper aims to improve marketing strategies in the automotive field for car dealers and car selling supply chain. Due to the cost of new cars and the high risk of car value depreciation it becomes necessary for car dealers to know which type of cars can be sold faster than others, this will allow dealers to adapt their marketing strategies and satisfy the need of their customers. We propose to use data analysis (DA) and machine learning (ML) to address this problem and create models to help these companies in their decision-making processes. In our experiments, we used sale data from two big dealers of multi-maker cars. The dataset contains the sale history of around 73200 cars over a period of 8 years. We compared the different machine-learning algorithms and got promising results classifying cars into different predicted sale time ranges.

Introduction

PLM is an important strategy that helps companies in the representation, storage, and processing of product information throughout its lifecycle phases [START_REF]What is PLM[END_REF]. At every stage of the lifecycle, PLM solutions ensure integrated processing of all relevant information. Although the term PLM is much more used in the manufacturing sector than any other sector, PLM is expanding to cover more and broader applications such as software industry and marketing strategies.

PLM organizes and integrates data to provide a detailed view of each product manufactured and how it is received in the marketplace, maximizing efficiency in the following areas [START_REF] Plm | [END_REF]:

-Design and manufacturing integration : A company's production process can use a range of software applications for design and manufacturing. With PLM, the entire production process can be optimized in real time. Without PLM, valuable data may not be shared across all these systems and people. -Virtual environments that support global operations : PLM provides a central repository for product data management (PDM) that integrates the entire global process from concept to customer.

-Accessible data : PLM makes all product information available to each department, improving production efficiency and allowing for a closed-loop for all teams involved. -Product commercialization : PLM assures products are ready for global rollout, with effective, reliable data, document management and process governance. Unified data and collaborative workflows across the organization keep things running smoothly and allow teams to respond quickly when challenges arise.

In this paper, we consider the car commercialization aspect of PLM to help solving the inventory problems of car dealers. Indeed, car dealerships buy cars from the manufacturers and sell them to their customers to make profit. Dealers cannot just send the unsold cars back to the manufacturer. Keeping unsold cars in the parking lots for more than six months is extremely costly and may even threaten the financial prosperity of these companies. Therefore, they will have to find a way to get rid of these cars and get prepared to receive newer models, but this cannot be done without losing a lot of money. This paper proposes to use DA and ML to predict the time required to sell car models. Car properties and sales history are taken into consideration to compute ML models capable of making the correct prediction in most of the cases. The contributions of this paper can be summarized as follows: (i) using DA to find car properties with the highest influence on car sales, (ii) build several ML algorithms to predict car selling time, (iii) conduct experiments to test these algorithms, compare and discuss their results.

The rest of the paper is organized as follows. Section 2 presents the state of the art of using Machine-learning in PLM. Section 3 describes our method to improve marketing strategies in the automotive field for car dealers. Section 4 presents and discusses the experimental results obtained with the proposed ML based algorithms. Section 5 concludes the paper and gives few perspectives to extend and improve this work.

PLM and Machine Learning

As Big Data becomes more prevalent, ML is opening up new opportunities for data processing to support decision making in all areas of manufacturing, from customer engagement to design and supply chain to PLM. The combination of Big Data and advanced, low-cost computing systems has made ML viable in many real world work applications, e.g. cultural heritage [START_REF] Belhi | Leveraging known data for missing label prediction in cultural heritage context[END_REF], leading to positive changes in the product development lifecycle [START_REF] Meet | [END_REF]. Today, companies are entering a new era of digital transformation in PLM where ML is one of the enablers of forth Industrial Revolution (usually called Industry 4.0 ), which is almost twice as likely to be used as any other tool [START_REF] Meet | [END_REF]. Currently, ML models used to enhance the PLM power in offering additional insights into the product lifecycle [START_REF] Meet | [END_REF].

Machine Learning in Product Design

ML algorithms are used to support product design at least in two major aspects: analyze market trends and assist designers to achieve a fast and personalized design processes. The conceptual design stage is increasingly seen as an essential step in product development and customization. Effective conceptual design is inseparable from proper market investigation, as it has a critical impact on market prospects, customer acceptance and product lifecycle, among the works realized in this context we mention [START_REF] Hu | Constrained functional knowledge modelling and clustering to support conceptual design[END_REF][START_REF] Liu | Particle swarm optimization based on dynamic niche technology with applications to conceptual design[END_REF]. Market analysis aims to identify target customers, recognize their requirements, and translate these requirements into product features. Compared to manual market analysis, market research based on data mining can discover the implicit associations of market data by integrating ML and analytic algorithms such as Support vector machine [START_REF] Pal | Business health characterization: A hybrid regression and support vector machine analysis[END_REF], Apriori [START_REF] Kumar | Consumer buying pattern analysis using apriori association rule[END_REF], ARIMA [START_REF] Gurnani | Forecasting of sales by using fusion of machine learning techniques[END_REF].

Machine Learning in Product Manufacturing

ML improves the product manufacturing framework, including material procurement, resource configuration, production scheduling, machining, assembly, quality control, warehousing, logistics, etc. ML contributes to improving the manufacturing phase of products in two ways: optimizing the information flow within the manufacturing processes, and monitoring smart devices to execute repetitive tasks. In addition, the integration of ML and production systems enables significant advances in human-machine collaboration, defect prediction, intelligent decision-making, and other aspects, Among the works realized in this context we mention intelligent supplier selection decision [START_REF] Keskin | The Fuzzy ART algorithm: A categorization method for supplier evaluation and selection[END_REF][START_REF] Parkouhi | A resilience approach for supplier selection: Using Fuzzy Analytic Network Process and grey VIKOR techniques[END_REF], Human-robot collaborative manufacturing control [START_REF] Neto | Gesture-based humanrobot interaction for human assistance in manufacturing[END_REF][START_REF] Cwikla | The expert system supporting design of the manufacturing information acquisition system (MIAS) for production management[END_REF].

Machine Learning in Product Services

The combined application of Deep Learning and recommendation algorithms (e.g., Deep Neural Networks (DNN) and collaborative filtering) can improve the personalized decision level of recommendations by analyzing user and product group information associated with demand [START_REF] Lecouteux | Distant speech recognition in a smart home: Comparison of several multisource ASRs in realistic conditions[END_REF]. Moreover, the time series network can extract preference features based on the user's historical purchase behavior and make recommendations by modeling the content of the product sale network and user profile [START_REF] Kulkarni | BANK CHAT BOT an intelligent assistant system using NLP and machine learning[END_REF]. Moreover, product services need technical guidance for product maintenance according to consumer requirements. Traditionally, it is difficult for customers to perceive gradual changes in the condition, quality, and performance of products. Therefore, unnoticed product deterioration affects the user experience and reduces the quality of customer service. That is why product status monitoring is an important part of product lifecycle information processing as it is used to evaluate equipment performance and prevent product failures [START_REF] Shen | Random-forest-based failure prediction for hard disk drives[END_REF][START_REF] Kalsoom | A dimensionality reduction-based efficient software fault prediction using Fisher linear discriminant analysis (FLDA)[END_REF].

Methodology

This section presents the proposed solution to help car dealers in their effort to car inventory problems. As stated in the introduction section dealerships cannot afford keeping unsold cars in their parking lots for an extended period, so effective solutions must be offered to find out which cars could be sold within a short period of time, and which cars could require longer sale time. This classification will allow dealerships to put better marketing strategies for example reducing the number of car models that are not easy to sell. Time series could be used as a tool to predict which cars will be sold in the next months, but this method is not practical in our case because the sales information, in the datasets we are using, do not follow a precise pattern. For example, if we take car C that was sold once since the company was established, where {c 1 , c 2 , . . . , c t } are the monthly sale values, then most of the values are equal to zero. Given the sale values {c s , . . . , c e } over a period [s, e], where c s and c e are respectively the sale value of the start and the end of the period, if we train a network based on sequential models like (LSTM, RNN ...), or based on a statistical analysis model like ARIMA to predict Y (t + 1) = F (c s , . . . , c e ), the sale value for the next period t + 1, then we will get wrong results. Therefore, we propose to use car characteristics to predict selling time. So we have dataset of pairs D = {(x 1 , y 1 ), . . . , (x n , y n )} where X = {x 1 , x 2 , . . . , x n } contains the characteristics of cars such as the color, the price, the power of the engine. . . and Y = {y 1 , y 2 , . . . , y n } is the time taken to sell the vehicles (see Table1). We need to find function f (x i ) = y i that will be able to predict the time needed to sell a car, this function can be any machine-learning algorithm. As shown in Figure 1 the proposed system operates in three steps: (i) data processing, (ii) dimensionality reduction, and (iii) model training. In the next sections, we will describe the dataset, the ML models and highlight their similarities and their differences.

Dataset

The dataset used in this work was provided by two major multi-brand car dealerships in the European Union. The dataset covers the dealerships activities for a period of 8 years from Oct. 2013 to Nov. 2021. It contains more than 73200 data samples and 33 attributes for each data sample. A brief description of these attributes is given in Table 1.

Data Processing

This step is very important and sensitive because it directly affects the results of the model; in our case, we noticed missing data for several attributes. For example attributes such as Couleur Vehic and Cons Exurb are lucking about 5000 data, but luckily the missing data is not so important for all the attributes, e.g. There are less than 10 missing data for attributes Tp Boite Vit, Energie and Code Moteur. Depending on the influence of different attributes on car sales and the amount of missing data, we treat the problem in different ways, for attributes with a high number of missing data and little impact on car sales, for example, Color Vehic, we first group the data by Label, then fill each group's attribute by the mode value. For attributes with some missing data but having a significant impact on car sales, we design an accurate filling method. For anomalous data and missing data that cannot be filled, we opt for zero filling to minimize their impact on prediction accuracy. In addition, some data elements are anomalous due to possible recording errors and must be filtered out. We also noticed the presence of data of the same type but written in different formats for example Sale date and Entry date written respectively in YYYY-MM-DD and MM/DD/YY formats. A data integration step is therefore required to address these kinds of discrepancies and bring attributes of the same type into a unique format. In addition, non-numerical data cannot be used directly for prediction as the same information is rarely expressed in a unique e.g. passenger front door, passenger side door, front right door, right front door are all used to refer to the same information, therefore, it is essential to transform the non-numeric data into numeric data in a way that best preserves the information and facilitates feature extraction.

Dimensionality Reduction

With such a large amount of data, the variety of attributes and their formats, we must carefully select the intrinsic features to achieve a high prediction accuracy while reducing computation costs. We also need to apply a dimensionality reduction method to allow visualizing the data in a reduced space. We distinguish two classes of dimensionality reduction methods: 2, we display the data of new vehicles of the first company in 2D space with PCA.

Machine Learning Algorithms

To predict whether a car would, or would not, be sold in a predetermined period of time we use classification algorithms. To this end, the different classes of cars are identified, and a label is assigned to each car in the dataset to mark to which class it belongs. This type of learning is named "supervised" because we give our algorithm the data with their labels to learn, then predict the label of a car never seen before. Among ML algorithms we used. Support Vector Machines (SVM) is the best-known form of kernel methods inspired by Vladimir Vapnik's statistical theory of learning. SVM is a method of classification by supervised learning introduced by Vapnik in 1995 [START_REF] Cortes | Support vector machine[END_REF]. This method searches for the hyperplane that separates the positive data samples from the negative ones, ensuring that the margin between the closest positive and negative is maximal. This ensures a generalization of the principle because new examples may not be too similar to those used to find the hyperplane but may be located on one side or the other of the border. The interest in this method is the selection of support vectors, which represent the discriminant vectors by which the hyperplane is determined. The examples used during the search for the hyperplane are then no longer useful and only these support vectors are used to classify a new data sample, which can be considered as an advantage for this method. Decision trees (DT) can be used for classification and regression problems, it is called a decision tree because, similar to a tree, it starts with the root node, which grows on other branches and builds a tree structure. In a decision tree, there are two type of nodes, which are the decision nodes and the leaf nodes. The decision nodes are used to make any decision and have several branches, while the leaf nodes are the output of these decisions and do not contain other branches. To build a tree and find out the attribute that should be selected for its initialization one can use the CART algorithm [START_REF] Breiman | Cart. Classification and Regression Trees[END_REF], which is based on the Gini index, or the ID3 or C4.5 algorithms, which are both based on the notion of entropy [START_REF] Quinlan | Induction of decision trees[END_REF][START_REF] Salzberg | C4. 5: Programs for machine learning by j. ross quinlan[END_REF]. Random forests (RF) are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest [START_REF] Breiman | Random forests[END_REF]. The generalization error for forests converges to a limit as the number of trees in the forest becomes large. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation between them. K-Nearest Neighbors (KNN) is one of the simplest supervised ML algorithms. KNN stores all available data and classifies new data based on similarity to its neighbors.

Experimental Results

To test the above algorithms and compare their prediction results, we use the dataset provided by two car dealership companies. The dataset of the first company contains 40700 among these cars there are 18800 new cars and 21900 used cars, and for the second company there are in total 32500 cars among which there are 18700 new cars and 14000 used cars. Our goal is to predict the time margin that a car will stay in stock before being sold, we will build two models for each company, one model for used cars and the other for new cars. The dataset is randomly split into two parts: training set (80% of the dataset), is used to train and test set (20% of the dataset) to evaluate our model, during the train we validate our training process using 10-Folds cross-validation. The accuracy and training-time are considered as a comparison criterion between algorithms on the test set. The accuracy in our case is defined as follows:

Accuracy = The number of well-classified cars/The total number of cars (1)

The results of our experiments are reported in Table 2. To train our models we used a Dell OptiPlex-7070 computer with Intel(R) Core(TM) i7-9700 @ 3.00GHz 8-Core CPU and 16GB DDR4 RAM on Windows 10 Pro 64-bit. Table 2 shows that the random forest gives much better results in comparison with other models, and this is because RF is composed of several decision trees that collaborate with each other. In the case of the first company, both the DT and RF give the same accuracy score on a new vehicle because the data in this case are easy to be discriminated by the decision tree. We also note that KNN generally gives good results because it is based on data. SVM takes a lot of time to learn in comparison with other models because SVM tries to find a hyperplane that separates the margin between the nearest samples of each class, generally maximization problems take more time and depend on the performances of the machine used to train the model. In figure 3, the confusion matrix for each type of cars for the two companies with the model that we found the best score. One can see that the models are able to classify the cars in the correct category. There is a little confusion between class 0 and 1. That is because we can find two cars of the same type, one sold in three months and the other in three months and a day, for the model, they are two cars of two different classes. This kind of confusion are solvable with regression models: instead of predicting the sales time intervals we will predict the exact number of days to sell a car, but generally companies are not interested in predicting the exact day but the time interval of sales.

Conclusion and Perspectives

In this paper, we proposed to implement SVM, DT, KNN, and RF to predict the time required for dealers to sell cars. A large-scale car sales dataset provided by two multi-maker dealership companies has been pre-processed to complete missing data and identify the car characteristics that have the greatest impact on car sales. This sale time prediction gives companies better ideas about the commercialization of vehicles and hence help them putting the right marketing strategy to avoid buying cars that are not easy to sell. In future work, we intend to extend this work towards customer behavior analyses to build a recommendation system based on association rules, to target customers who can buy specific cars based on the profile of former customers.

Fig. 1 .

 1 Fig. 1. The system architecture of the proposed solution

Fig. 2 .

 2 Fig. 2. Scatter Plot of data of the new vehicles for the first company in 2D with PCA.

Fig. 3 .

 3 Fig. 3. Confusion matrix of the prediction on the two datasets

Table 1 .

 1 Attributes of car sales dataset.

	Attributes	Description	Example
		Label of vehicle:
		0: if selling the vehicle takes less than 3 months.
	Label	1: if selling the vehicle takes between 3-6 months. 2: if selling the vehicle takes between 6-8 months.	0
		3: if selling the vehicle takes between 8-12 months.
		4: if selling the vehicle takes more than 12 months.
	Entry date	The vehicle entry date	2013-10-10
	company name Name of company	Com1
	Sale date	The vehicle sale date	2013-12-02
	Carrosserie	Vehicle bodywork	COUPE
	C02	C02 emissions in g per km	185
	Couleur Vehic Color of vehicle	GRIS F
	Cylindree	The volume of gas that can be burned in the cylinders	1995
	Date 1ere Cir Date of 1st entry into service	20040629
	Depollution	Depollution device	OUI
	Empat	Wheelbase of vehicle	273
	Energie	Fuel type of vehicle	GAZOLE
	Genre V	Type of vehicle	VP
	Immat	Registration of vehicle	BX368SQ
	Marque	Marker of vehicle	BMW
	Modele	Model of vehicle	SERIE 3
	Nb Cylind	Number of cylinder	4
	Nb Pl Ass	Number of seats or payload	5
	Nb Portes	Number of doors	2
	Nb Soupapes Number of valves	4
	Nb Vitesses	Number of speeds for manual gearboxes	5
	Propulsion	Propulsion	ARRIERE
	Puis Ch	Real power in steam horsepower	150
	Puis Fisc	Fiscal power in fiscal horsepower	9
	Tp Boite Vit Gearbox type	B.V.A.
	Turbo Compr Presence of turbo	TURBO
	Version	Version of vehicle	320 CD
	Code Moteur Motor code	204D4/M47TUD20
	Cons Urb	Urban consumption	9,7
	Cons Exurb	Extra-urban consumption	5,4
	Cons Mixte	Mixed consumption	6,9
	Prix Vehic	The selling price of the vehicle	28 800 €
	C code	If the vehicle is used or new	NV

Table 2 .

 2 Results of the prediction on the datasets of the two companies.

						Models
	Company Vehicle type	Metrics	KN N	SV M	DT	RF
			Accuracy	0.971	0.951	0.990	0.990
	1	VN	Accuracy Training time 0.096 secs 8.431 secs 0.996 secs 0.140 secs 0.849 0.854 0.814 0.863
		VO	Training time 0.058 secs 13.52 secs 0.057 secs 0.647 secs
			Accuracy	0.967	0.944	0.987389	0.994
	2	VN	Accuracy Training time 0.079 secs 20.76 secs 0.140 secs 1.145 secs 0.845 0.862 0.802 0.870
		VO	Training time 0.066 secs 47.15 secs 0.187 secs 1.484 secs


domain: sde chim

text:
Clément Chatre

Eric Ehret

Thierry Ondarçuhu

Philippe Steyer

Karine Masenelli-Varlot

Francisco José Cadete

Santos Aires

Barbara Nozière

Influence of Surface-Active Substances and Substrates on the Wettability of Individual Aerosol Particles during Condensation by Environmental Scanning Electron Microscopy

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Water uptake on atmospheric aerosols is a key phenomenon in the climate radiative budget as it controls liquid cloud formation and properties (droplet size, concentrations, precipitation…). The activation of aerosol particles into cloud droplets in the atmosphere is described by Köhler theory, that takes into account the competition between evaporation (Kelvin effect) and condensation. [START_REF] Köhler | The nucleus in and the growth of hygroscopic droplets[END_REF] The latter is either favored by the initial particle size or, for particles smaller than 1 µm, by Raoult's law and surface tension effects depending on the particle chemical composition. A major challenge in this field of study is, however, that most experimental approaches monitoring the water uptake on aerosol populations are not able to capture directly the key input parameters for Kohler equation. These approaches are especially insensitive to surface effects, leading most models to assume the surface tension of pure water for growing droplets [START_REF] Krieger | Exploring the complexity of aerosol particle properties and processes using single particle techniques[END_REF][START_REF] Prisle | Surfactant effects in global simulations of cloud droplet activation[END_REF] although a growing number of studies has evidenced the presence of surface-active compounds in atmospheric aerosols, able to reduce the surface tension of the droplets and favor their growth. [START_REF] Gérard | Anionic, cationic, and nonionic surfactants in atmospheric aerosols from the baltic coast at Askö, Sweden: implications for cloud droplet activation[END_REF] To overcome these limits, single-particle approaches have been developed recently, which have the advantage of capturing the details necessary to better understand the role of surface-active compounds in soluble materials. [START_REF] Krieger | Exploring the complexity of aerosol particle properties and processes using single particle techniques[END_REF] The individual particle analysis approach can be performed by numerous techniques including electrodynamic balance, [START_REF] Davis | A History of Single Aerosol Particle Levitation[END_REF] acoustic trap, [START_REF] Duranty | Acoustic levitation and infrared thermography: a sound approach to studying droplet evaporation[END_REF] optical tweezers [START_REF] Bzdek | contactless measurements of the surface tension of picolitre aerosol droplets[END_REF] and microscopies (such as atomic force microscopy, environmental scanning electron microscopy (ESEM), transmission electron microscopy (TEM), and scanning transmission X-ray microscopy). [START_REF] Morris | Humidity-dependent surface tension measurements of individual inorganic and organic submicrometre liquid particles[END_REF][START_REF] Ebert | Environmental scanning electron microscopy as a new technique to determine the hygroscopic behaviour of individual aerosol particles[END_REF][START_REF] Posfai | Nature and Climate Effects of Individual Tropospheric Aerosol Particles[END_REF] For instance, ESEM equipped with an energy dispersive Xray (EDX) analysis can provide detailed information on hygroscopic behavior, mixing composition and morphological changes of individual aerosol particles. Pioneering researches have studied the hygroscopic behavior of atmospheric aerosols and different laboratorygenerated salt particles up to 100% RH. [START_REF] Ebert | Environmental scanning electron microscopy as a new technique to determine the hygroscopic behaviour of individual aerosol particles[END_REF] Deliquescence and efflorescence relative humidity values (hereafter, DRH and ERH, respectively) of pure salt particles and binary mixed salt particles have been determined by ESEM. [START_REF] Hoffman | Sodium nitrate particles: physical and chemical properties during hydration and dehydration, and implications for aged sea salt aerosols[END_REF][START_REF] Matsumura | Hygroscopic Growth of an (NH4)2SO4 Aqueous Solution Droplet Measured Using an Environmental Scanning Electron Microscope (ESEM)[END_REF] However, the high energy electrons used to probe the particles require specific operating conditions for observations. ESEM also requires particle deposition on a solid substrate. The nature of these substrates could affect water condensation on individual particles. [START_REF] Eom | Influence of Collecting Substrates on the Characterization of Hygroscopic Properties of Inorganic Aerosol Particles[END_REF][START_REF] Laskina | Substrate-Deposited Sea Spray Aerosol Particles: Influence of Analytical Method, Substrate, and Storage Conditions on Particle Size, Phase, and Morphology[END_REF] In addition, particles with different morphologies and shapes induced by the generation process on these substrates could control the ability of water uptake and surface wetting. [START_REF] Wang | Hygroscopic properties of NaCl nanoparticles on the surface: a scanning force microscopy study[END_REF] In this work, we take advantage of the in-situ and near-real time observations of the ESEM to explore the potential effect of the presence of a surfactant (SDS) in laboratorygenerated inorganic particles ((NH4)2SO4) upon the water uptake. Specifically, the wetting dynamics of condensing droplets on hydrophilic and hydrophobic substrates with pure (NH4)2SO4 or mixed SDS/(NH4)2SO4 particles is investigated. In addition, the hygroscopic properties (deliquescence relative humidity (DRH) and hygroscopic growth factor (GF)) of pure (NH4)2SO4 and mixed SDS/(NH4)2SO4 particles on hydrophobic substrates are determined under influence of relative humidity and discussed in detail.

METHODS AND MATERIALS

Materials

Sodium dodecyl sulfate (SDS) and ammonium sulfate ((NH4)2SO4) with a purity of ≥ 99% were purchased from Sigma-Aldrich and used without further purification. Water from a Milli-Q system (resistivity = 18.2 MΩ.cm) was used for solution preparation. All solutions were prepared in glass containers that were cleaned first with acetone and then with ethanol and finally rinsed with Milli-Q water. The solutions were used within 24 h from their preparation.

Substrate preparation

In this study, all substrates, both hydrophilic and hydrophobic, were produced from modified silicon surfaces. Single-side polished Si(100) wafers (Sil'tronix) were first cut in 5 × 5 mm 2 surfaces and cleaned in an ultrasonic bath. All these surfaces were then cleaned in acetone, methanol and subsequently in isopropanol (IPA) for 15 min to remove organic contaminants. Hydrophilic functional groups were added onto the Si surface by using the RCA cleaning method. The substrates were boiled at 80 °C for about 15 min in a mixed solution of ammonium hydroxide (NH4OH, Sigma-Aldrich, 30 %) and hydrogen peroxide (H2O2, Sigma-Aldrich, 33 %) and Milli-Q water (NH4OH : H2O2: H2O = 1: 1: 3, by volume). The wafers were then rinsed thoroughly with Milli-Q water and subsequently placed in a boiling piranha solution during 1h at 100°C (H2SO4:H2O2 = 3:1 by volume). In this process, a fresh oxide layer, which is terminated with a hydrophilic OH group, was grown on the Si surface after removing the native oxide layer.

The hydrophobic silicon surface was obtained by functionalization of the surface with 1octadecene. 20 mL of the 1-octadecene was placed in a small round bottom flask and deoxygenated with dry nitrogen for at least 45 min, the bottom flask was placed in an oil bath at 180°C. The silicon wafer was etched for 2 min in 1 % hydrofluoric acid, blown dry with nitrogen, and immediately placed in the deoxygenated alkene for at least 1h. Subsequently, the silicon piece was removed from the solution, sonicated for 5 min in ethanol (96 %), sonicated for 5 min in dichloromethane, sonicated another time in ethanol, and dried in a stream of nitrogen. This preparation resulted in the formation of highly stable dense alkyl monolayers on the hydrogen-terminated silicon (100) surface. [START_REF] Sieval | Highly Stable Si-C Linked Functionalized Monolayers on the Silicon (100) Surface[END_REF] Surface modification was confirmed by contact angle analysis with an OCA 15EC (dataphysics instruments), using a computer controlled contact angle calculation program, available from the manufacturer. The analysis showed that macroscopic water droplets form a contact angle of less than 30 ° on hydrophilic silicon and larger than 110 ° on hydrophobic silicon.

Laboratory generation of soluble particles

Spray-coating was found to produce strongly non-homogeneous mixtures, especially in the presence of SDS as indicated in Figure S1 of the Supporting Information (S.I.).

To overcome this problem, the salt and mixed particles were deposited onto the Si surface, using a micropipette with micron scale aperture connected to a injector (Narishige IM300, Japan) controlled by a X, Y, Z motorized micromanipulator (Scientifica, PatchStar, UK). This resulted in a network of liquid droplets of spherical shape and controlled size (Figure 1). These droplets maintained their geometry during evaporation which led to solid homogeneous and micrometersized particles. In all the mixed particles thus produced the concentration of SDS was larger than the critical micellar concentration (8 mM for SDS) regardless of the water uptake. Two particle sizes with diameter distributions centered on 4 µm and 30 µm were prepared by changing the injected volume.

Environmental Scanning Electron Microscopy (ESEM)

The growth of the laboratory generated particles upon application of various RH was studied in the chamber of an environmental scanning electron microscope (ESEM, Quattro, ThermoFisher Scientific, USA). The water pressure in the ESEM chamber was regulated by a computer controlled valve and could be varied in steps of 5 Pa in the range of 0-2000 Pa. A Peltier cooling stage inside the ESEM chamber allowed the control of the sample temperature. A resistive temperature sensor allowed temperature measurements with an accuracy of ± 0.1 °C. Pressure and surface temperature allowed the control of thr RH in the chamber, defined by 𝑅𝑅𝑅𝑅 = 𝑃𝑃 𝑤𝑤 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 × 100 where Pw is the water vapor pressure inside the chamber and Psat is the saturation water vapor pressure at temperature T. The value of Psat can be calculated using Tetens formula, an approximation of the Clausius-Clapeyron relation [START_REF] Buck | New equations for computing vapor pressure and enhancement factor[END_REF] :

𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃(𝑘𝑘𝑃𝑃𝑃𝑃) = 0.611 × 𝑒𝑒 � 17.5×𝑇𝑇 241+𝑇𝑇 � (1)
Thus, by maintaining the sample at 2°C, water vapor pressure of 0-705 Pa corresponded to a relative humidity (RH) range of 0-100 %. The ± 0.1 °C of accuracy on the temperature corresponded to a relative uncertainty of around 0.8 % for RH.

In the experiments, water condensation/evaporation was controlled by fixing the temperature of the sample surface at 2°C and varying the water vapor pressure by small pressure increments.

A picture of the droplets was taken at each pressure step, thus recording their growth. The time resolution of such analysis was limited by the acquisition time between two micrographs.

The choice of observational conditions was based on the determination of the best contrast for visualization, while minimizing the effect of electron beam. Great care was taken to limit the beam effects on the samples, while simultaneously taking the pictures. The observational conditions were optimized so that well-focused pictures were obtained while maintaining the sample in good condition. These optimal conditions were an accelerating voltage of 10 keV, a mid-range scanning speed (line time = 1 µs) and a maximum magnification of 10000. With these parameters, the images of water dropplets were found to be similar to what occurred on nonirradiated regions of the sample. All ESEM images were analyzed with the ImageJ software (ImageJ V.1.52q, Wayne Rasband, Maryland, USA).

ESEM measurements of contact angle and droplet volume

The volume of the droplets sitting on the substrates in the experiments were determined by assuming a spherical cap shape. In that case, the droplet volume can be expressed by simple geometrical considerations from the droplet height H and contact angle θ.

To determine the droplet contact angle, the observations were performed with a tilt angle of 80° using a pre-tilted sample holder.

To determine the real contact angle θ from a sample tilted at an angle α, a mathematical model [START_REF] Brugnara | Contact Angle Analysis on Polymethylmethacrylate and Commercial Wax by Using an Environmental Scanning Electron Microscope[END_REF] assuming a spherical cap geometry was used, in which θ is calculated from the tilt angle α and the projected contact angle β:

𝜃𝜃 = 2 tan -1 � �tan 𝛽𝛽 2 � 2 +(cos(90°-𝛼𝛼)) 2 -1+tan 𝛽𝛽 2 cos(90°-𝛼𝛼)+1 (2)
The equation cannot be used if the tilting angle α ≤ 90°-θ and if α ≤ θ -90° (for θ ≥ 90°).

An example given in Figure 2 shows the main geometrical elements to determine the real contact angle θ of a spherical cap-shaped droplet at a tilt angle.

RESULTS AND DISCUSSION

In this work, droplet growth on pure (NH4)2SO4 and mixed SDS/(NH4)2SO4 particles were compared on hydrophilic and hydrophobic substrates.

Hydrophilic substrates

For pure (NH4)2SO4 particles on the hydrophilic substrate, the experiments showed that water condensed and first formed a spherical cap enveloping the particle. Then, the droplet continued growing by moving down and spreading outside on the substrate along the tilt direction of the ESEM (Figure 3). The image indicates partially dissolved core particles adjacent to the liquid droplet spreading on the hydrophilic substrate. Once the hydrophilic substrate is locally wet, the excessive interfacial energy which keeps the liquid droplet on the edge of the particle is released allowing a fast droplet spreading. When the ESEM stage is tilted, the in-plane gravitational force component is an additional driving force acting on the droplet spreading. Similar phenomena have been observed for the wetting of droplets on strip-patterned heterogeneous surfaces. [START_REF] Dai | Hydrophilic directional slippery rough surfaces for water harvesting[END_REF][START_REF] Wang | Anisotropic Wetting of Droplets on Stripe-Patterned Chemically Heterogeneous Surfaces: Effect of Length Ratio and Deposition Position[END_REF] For mixed SDS/(NH4)2SO4 particles, the wetting process was found to be more isotropic, possibly because the droplet was less sensitive to the edge irregularities of the particle. Here, due to the presence of SDS, the surface tension of the droplet decreases drastically which leads to a much lower pinning force on the particle. 21

Hydrophobic substrates

With hydrophobic substrates, the dry particles of pure (NH4)2SO4 were egg-shaped and had a large contact angles (Figure 4), while the mixed SDS/(NH4)2SO4 particles were round-shaped and had a smaller contact angles. These observations provide a clear evidence of the role of surfactants in the mixed SDS/(NH4)2SO4 particles. In order to be able to compare their growth in the experiments, a hydratation/dehydratation pretreatment was tested on the pure (NH4)2SO4

particles. These particles were hydrated above the DRH, then dried under N2, which gave them shapes that were closer to those of the mixed particles (Figure 4c). This is due to the fact that during drying the contact line remains pinned at its maximum diameter and does not retract. In the water condensation experiments, no appreciable change in morphology was observed when RH increased from 0 to 81.7 %. As shown in Figure 5, at 81.7 % RH, the particles began to adsorb water onto the edges of (NH4)2SO4 surface grains. Between RH = 81.7 and 84.7 %, the surface grains continued to dissolve from the edges, accentuating the roughness effect of the particle. Finally, with a slight increase of pressure of 5 Pa, reaching RH = 84.7 %, a fully aqueous droplet was formed. At 84.7 % RH, the water droplet had enveloped the partially dissolved particle and had a near spherical cap shape droplets owing to surface energy minimization. The early stages of condensation were not modified by the addition of SDS in the particle (Figure S3 in S.I.). In addition, the contact angle of the water droplet with the hydrophobic surface seemed to be independent of the presence of SDS in the particles but is strongly dependent of the initial shape of the dry particles. Unlike the hydrophilic surfaces where anisotropy in the spreading occured, the hydrophobic surfaces showed isotropic spreading behavior. Here, the contact line resembles a circle. The edge of the spreading droplet wrapped the edge of the particle (Figure 5 at 84.7 % RH). At this stage, in presence or absence of SDS, the droplet contact line is pinned to the substrate-particle interface and both the contact angle and the droplet height increase as condensation progresses. When the volume of a droplet is increased, the contact angle reaches a maximum value, which is referred to as an advancing contact angle θedge. Moreover, the droplet is not allowed to move to its equilibrium shape, the stress on the edge increases as the condensation continues. In others words, the energy barrier formed by the particle edges cannot be overcome and the excessive interfacial free energy of the droplet cannot yet be released by wetting the surface. When the droplet reaches its maximum contact angle (θedge), the droplet line depins suddenly, its base diameter starts to increase leading to a decrease of the contact angle and the water droplet spreading on the hydrophobic surface.

Such process is shown in Figure 6 in the case of pure (NH4)2SO4 particles. From this point, clear differences emerge between pure (NH4)2SO4 and mixed SDS/(NH4)2SO4. For pure (NH4)2SO4, once depinned at the particle edge, further condensation results in an inflation of the droplet on the hydrophobic substrate. A continuous increase of the contact angle is observed up to a new advancing contact angle θmax while the droplet base diameter remains constant until a sharp depinning takes places as shown in Figure 6. of the growth factor defined as the ratio of the particle apparent volume V at a certain RH by the initial dry particle apparent volume V0, as a function of RH. Here, the pretreated pure (NH4)2SO4 particles with hydrated/dehydrated pretreatment, like those shown in Figure 4c were used to minimize the particle shape effects.

The wetting of the hydrophobic surface follows a step-by step mechanism that can be attributed to successive pinning-depinning phenomena at the triple phase line frontier. Unlike the pure (NH4)2SO4 solution, the mixed solution does not provide such strong energy barriers during the condensation phase on the hydrophobic substrate as shown in Figure 7. We observe a weak contact angle deviation and a continuous increase of the droplet diameter in contact with the hydrophobic surface. Through the contact line dynamics, the wetting process is schematically depicted in Figure 8 for pure (NH4)2SO4 and mixed SDS/(NH4)2SO4 particles on the hydrophobic substrate. In the past, both Marangoni force (i.e. induced by surface-tension gradient) and capillarity force (i.e. due to the unbalanced tensions in the three-phase contact region) have been proposed as driving forces that promote the droplet spreading on the hydrophobic substrate owing to the presence of surfactants. [START_REF] Nikolov | Superspreading driven by Marangoni flow[END_REF] In this study, these driving forces could be behind this phenomenon. However, many additional factors complicating our result interpretation have to be taken into account such as the surfactant solubility in the aqueous medium, the adsorption at interfaces, the droplet shape and the interaction with the inorganic ((NH4)2SO4) phase. on the edge of the particle with an apparent advancing angle θedge, (iii) wetting of the droplet onto the hydrophobic substrate with a contact angle θ, (iv) the droplet is pinned on the surface with an apparent advancing angle θmax, (v), (vi) and (vii) the droplet is depinned and spreads onto the surface with low variation of the contact angle. The partial dissolution of the particle is not represented in these images.

These results show that the hydrophobic-hydrophilic character of the substrate play an important role in the stability and dynamics of liquid droplets nucleation by water vapor condensation. In particular, hydrophilic substrates seem not to be suited for the investigation of water vapor condensation and cloud droplet formation because of the anisotropic growth observed with pure salt particles, making it difficult to compare with that of mixed particles. In addition, the anisotropy make the determination of the droplet geometry (contact angle, volume, and base contour shape) more difficult.

Study of droplet growth -DRH determination for (NH4)2SO4 particles

The first step in validating the use of ESEM to study the growth of water droplets is to ensure that RH is properly controlled in the instrument. To achieve this, the droplet growth on (NH4)2SO4 particles is studied and their deliquescence points determined. As described in the previous section, for (NH4)2SO4 particles, an aqueous droplet is formed on the particle surface at 84.7 % RH and results in partially dissolved particles, i.e. a solution coating surrounding a salt core, as also observed elsewhere. [START_REF] Ma | Subsecond measurement on deliquescence kinetics of aerosol particles: Observation of partial dissolution and calculation of dissolution rates[END_REF] Therefore, the measurement of their deliquescence point is very close to 84.7 % RH at 2°C ( i.e. 83 % RH at 25°C) in this study. This value of DRH is larger than the DRH value usually evaluated around of 81 ± 1 % (at 25°C) in the literature for (NH4)2SO4 particules. [START_REF] Ebert | Environmental scanning electron microscopy as a new technique to determine the hygroscopic behaviour of individual aerosol particles[END_REF][START_REF] Mikhailov | Amorphous and crystalline aerosol particles interacting with water vapor: conceptual framework and experimental evidence for restructuring, phase transitions and kinetic limitations[END_REF][START_REF] Lei | Hygroscopicity of organic compounds from biomass burning and their influence on the water uptake of mixed organic ammonium sulfate aerosols[END_REF][START_REF] Wu | Aerosol Hygroscopicity on A Single Particle Level Using Microscopic and Spectroscopic Techniques: A Review[END_REF] Possible reasons include systematic errors in temperature measurement and ESEM beam effects.

We have examined the influence of the beam radiation on the DRH point estimation of particles especially at higher ESEM magnification as the beam effects are positively correlated to the magnification (and thus electron dose rate). In particular, we have observed that heating effects during ESEM direct imaging of particles under water pressure at higher magnification cause fast evaporation rate and induce an erroneous estimation of DRH point. However, with our operating conditions (i.e. magnification < 10000), the thermal effect has a negligible impact on the RH determination.

It should be emphasized here that indirect effects of electron beam other than thermal effect can affect the DRH point estimation. Figure S4 (in S.I.) shows the impact of a pre-exposure to the beam at higher magnification on the water uptake of (NH4)2SO4 particles. The pre-exposure is done on a "dry" particle at low RH (far below the the DRH point), then the magnification is decreased to a value where the heating effects are negligible and the hygroscopic growth of (NH4)2SO4 particles is imaged by increasing the RH. In figure S4, only the particle viewed near the center of the image has been subjected to the pre-exposure. Unlike the two other particles of the image, this particle shows a distinct hygroscopic behavior with a shift of the estimated DRH point to lower RH. This effect contrasts with the electron beam heating effects occurring during ESEM direct imaging of particles under water pressure at high magnification, which overestimates the DRH point. This indirect effect is probably induced by radiation damage involving electrostatic interactions between water vapor and surface. [START_REF] Esmaily | On the capability of in-situ exposure in an environmental scanning electron microscope for investigating the atmospheric corrosion of magnesium[END_REF][START_REF] Yoshimoto | In situ observation of dewetting-induced deformation of vertically aligned single-walled carbon nanotubes[END_REF][START_REF] Rykaczewski | Electron beam heating effects during environmental scanning electron microscopy imaging of water condensation on superhydrophobic surfaces[END_REF] In this work, we have tested and etablished the magnification limit below which the beam effects are negligible on the DRH point estimation. We conclude that in our operating conditions, the beam effects cannot not explain the DRH values obtained for the (NH4)2SO4 particles.

Moreover, the control of the temperature inside the ESEM chamber with a thermocouple (type K thermocouple) shows a difference of 0. -Real-time droplet growth monitoring

The particle water uptake behavior can be described by plotting the growth factor GF = V/V0, defined as the ratio of the particle apparent volume V at a certain RH by the initial dry particle apparent volume V0, as a function of RH. The GFs as a function of the RH were measured by ESEM for a sample of about 20 particles containing pure (NH4)2SO4. This sample can be divided into two distinct particle size populations centered around 4 µm and 30 µm in diameter.

The figure 9a displays the averaged hygroscopic growth curves above the DRH for both particle size populations. Significant differences in GF between the two particle size populations were observed with higher GF values for the larger particle size population. This result contrasts with previous work where no particle size effect on GF was observed for > 100 nm dry diameter aerosols of identical chemical composition in agreement with the predictions based on the Köhler equation. [START_REF] Park | A study on effects of size and structure on hygroscopicity of nanoparticles using a tandem differential mobility analyzer and TEM[END_REF] A potential explanation for the discrepancy in the GF measurements is that smaller particles could exhibit slower hygroscopic growth than larger ones and did not have In addition, the hygroscopic growth rate is strongly affected by the heat transfer and fluid flow both inside and outside the droplet, which are influenced by the interface expansion during growth on the substrate and by the dry particle sizes. [START_REF] Xu | Multiscale Dynamic Growth and Energy Transport of Droplets during Condensation[END_REF] The growth factor (GF) values at different induced by the surfactant on the hygroscopic growth can be neglected when the particle size is above 200 nm. [START_REF] Zhang | Surfactant effect on the hygroscopicity of aerosol particles at relative humidity[END_REF] On the other hand, it has been established that the presence of surfactants on the surface of sub-or micrometer-sized particles can strongly inhibit condensational growth by reducing mass transfer between atmospheric droplets and their surroundings. 35,36 It can be noted that, in our investigations, the time interval between an increment in RH was the same for all the particles analyzed. Therefore, it can be suggested that our hygroscopic growth curves seem to indicate that the presence of surfactants have no impact on the water growth rate.

CONCLUSION

ESEM was used in this work to capture the growth of water droplet on individual particles and to determine their morphology and wettability by contact angle measurement. In this approach, the nature of the substrate was found to have strong effects on the droplet growth. On hydrophilic substrates, the growth on pure (NH4)2SO4 particles was much more anisotropic than on mixed SDS/(NH4)2SO4 particles, suggesting that such substrates are not suited to droplet growth studies.

On hydrophobic substrates, the growth of both types of particles was more comparable, and the presence of SDS mostly impacted the wetting behavior of the liquid droplet. Thus, with all types of substrates, the presence of SDS affected the contact line dynamic behavior of the water droplet during condensation. These results show that there is no clear relationship between the liquidvapor interfacial tension and the contact angle values. Monitoring the growth of water droplets on individual particles deposited on hydrophobic substrates, allowed the determination of the DRH for (NH4)2SO4 particles and the study of the influence of particle size and composition. Our data suggest that the presence of SDS does not seem to modify the DRH and the GF of (NH4)2SO4

particles. Particle size dependent effect on the GFis also observed in the micrometer range. Further study is needed to examine the role of substrate on this dependance.

ASSOCIATED CONTENT

Supporting Information

The following files are available free of charge.

Figure 1 .

 1 Figure 1. Schematic representation of the sample preparation: (a) freshly cleaned Si surface with

Figure 2 .

 2 Figure 2. (a) An ESEM image of a typical spherical cap-shaped droplet at a tilt angle of 80°. The

Figure 3 .

 3 Figure 3. Hygroscopic growth of pure (NH4)2SO4 particles on hydrophilic surface. The dotted

Figure 4 .

 4 Figure 4. SEM images of dry particles deposited on hydrophobic substrate: (a) pure (NH4)2SO4

Figure 5 .

 5 Figure 5. ESEM images of a pure (NH4)2SO4 printed particles on hydrophobic substrate obtained

Figure 6 .

 6 Figure 6. Growth of droplets on pure (NH4)2SO4 particles deposited on hydrophobic substrate:

Figure 7 .

 7 Figure 7. Growth of mixed SDS/(NH4)2SO4 particles on hydrophobic substrate: (a) Sequence of

Figure 8 .

 8 Figure 8. Schematic illustration of the droplet evolution on the hydrophobic substrate from a pure

33 Figure 9 .

 339 Figure 9. Averaged GF curves above the DRH (a) for both pure (NH4)2SO4 particle size

  RH were also measured by ESEM on (NH4)2SO4 particles containing varying amounts of SDS to study the surfactant influence on the hygroscopicity of micrometer sized particles on hydrophobic substrates. The figure 9b displays the hygroscopic growth curves above the DRH for mixed SDS/(NH4)2SO4 particles with relative (NH4)2SO4/SDS mole fractions of 1 and 28 % and pure (NH4)2SO4 particles on hydrophobic substrate. No statistically significant difference was observed in the water uptake on pure (NH4)2SO4 and mixed SDS/(NH4)2SO4 particles regardless of the amount of surfactant. This result agrees with theoretical models based on the Köhler equation, in which the effects of surface tension reduction and bulk-surface partitioning

Figure

  Figure S1 representing a SEM image of inhomogeneous deposition of mixed SDS/(NH4)2SO4

Figure

  Figure S2 representing a top view (0° tilt-view) ESEM images showing the hygroscopic growth

Figure

  Figure S3 representing ESEM images of mixed SDS/(NH4)2SO4 printed particles on hydrophobic

Figure

  Figure S4 representing ESEM images of a printed particles on hydrophilic substrate showing beam

  6 °C between the substrate and the setpoint temperature of the Peltier cooling stage. Such a shift results in RH variation of 3.5 % at 80 % RH. The DRH of NaCl salt was also determined with the same operating conditions of the ESEM. Here too, the value of DRH for NaCl salt is larger than the literature data by approximately 3 % RH (within the standard deviation). The measured, corrected (due to temperature gradient) and literature values of DRH for (NH4)2SO4 and NaCl particles are listed in table S1 in S.I.

Table S1

 S1 reports the DRH values of NaCl, and (NH4)2SO4 determined by ESEM.

ACKNOWLEDGMENT E.E. gratefully acknowledges the Chemistry Institute of Lyon (ICL -Institut de Chimie de Lyon) for providing financial support and the CLYM (Consortium Lyon Saint-Etienne de Microscopie) platform for the access to the ThermoFisher Sientific Quattro S ESEM. The authors thank F. Simonet for her skill assistance in ESEM experiments.

AUTHOR INFORMATION

Corresponding Author *E-mail: eric.ehret@univ-lyon1.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ranging from 80% to 99.5%: Internally mixed adipic acid-ammonium sulfate particles, Atmos.

Environ. 2021, 266, 118725.