Fabien Vidal

Paul Guerby

Cynthia Simon

Florence Lesourd

Géraldine Cartron

Jean Parinaud

Yann Tanguy

Le Gac

Ninon Dupuis

Vidal Fabien

Guerby Paul

Simon Cynthia

Lesourd Florence

Cartron Géraldine

Parinaud Jean

Tanguy Le Gac Yann

Dupuis Ninon

Spontaneous pregnancy rate following surgery for deep infiltrating endometriosis in infertile women

Keywords:

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

Introduction

Deep infiltrating endometriosis (DIE) is a sub-entity of endometriosis traditionally defined as a depth of tissue infiltration > 5mm [START_REF] Koninckx | Deep endometriosis: a consequence of infiltration or retraction or possibly adenomyosis externa?[END_REF]. However its current definition as a fibrous/muscular infiltration of organs and anatomical structure containing endometrial tissue below the peritoneum regardless of depth of infiltration is more consistent with clinical practice and imaging and histological findings. DIE may affect 20% of women with endometriosis and is a leading cause of pain and subfertility and is associated with altered quality of life [START_REF] Fauconnier | Epidemiology and diagnosis strategy: CNGOF-HAS Endometriosis Guidelines[END_REF].

Surgery is a cornerstone in DIE treatment, particularly among women wishing to conceive in whom hormonal therapy must be avoid. The aim of surgery is the complete removal of DIE lesions. Indeed, complete macroscopic resection is associated with better outcomes in subsequent fertility and pain relief compared to incomplete procedures [START_REF] Collinet | Management of endometriosis: CNGOF/HAS clinical practice guidelines -Short version[END_REF]. Focusing on fertility, several studies have reported high rates of spontaneous conception following surgery [START_REF] Cohen | Fertility before and after surgery for deep infiltrating endometriosis with and without bowel involvement: a literature review[END_REF][START_REF] Iversen | Does surgery for deep infiltrating bowel endometriosis improve fertility? A systematic review[END_REF][START_REF] Roman | High postoperative fertility rate following surgical management of colorectal endometriosis[END_REF]. On the other hand, complete removal may require more complex procedures that trigger potentially severe postoperative complications [START_REF] Bourdel | Long-term evaluation of painful symptoms and fertility after surgery for large rectovaginal endometriosis nodule: a retrospective study[END_REF][START_REF] Donnez | Complications, pregnancy and recurrence in a prospective series of 500 patients operated on by the shaving technique for deep rectovaginal endometriotic nodules[END_REF]. Hence, DIE surgery has to be performed in referral centers providing a multidisciplinary approach and trained surgeons [START_REF] Working Group Of Esge | Recommendations for the surgical treatment of endometriosis. Part 2: deep endometriosis[END_REF].

In contrast, data addressing the learning curve of laparoscopic DIE conservative surgery are sparse. In their retrospective study of 60 first cases, Carmona et al have observed a significant reduction in operative time, blood loss, rates of incomplete removals and recurrence with increasing surgeon's experience [START_REF] Carmona | Does the learning curve of conservative laparoscopic surgery in women with rectovaginal endometriosis impair the recurrence rate?[END_REF]. These data support the existence of a learning curve. Moreover, postoperative spontaneous pregnancy rate (SPR) may also be a good indicator of surgeons' skills, especially in patients presenting with endometriosis-associated infertility. However, to our knowledge, no study has considered the learning curve from this point of view.

The aim of the present study was thus to investigate the impact of the learning curve of DIE conservative surgery on the SPR in infertile women.

Patients and methods

Study design

From January 2015 to December 2018, the first 50 consecutive infertile patients referred to a single surgeon (FV) for DIE conservative surgery were included in this retrospective study. All procedures were performed in a single tertiary referral center for endometriosis (Academic Hospital, Toulouse, France). Inclusion criteria comprised:

-Age ranging from 18 to 42 years infertility of at least 12 months sperm features compatible with spontaneous fertility suspected DIE on clinical examination and preoperative pelvic MRI, confirmed at the time of surgery -FV as the leading surgeon.

The sample size of the population was based on previous reports on the learning curve for complex laparoscopic procedures [START_REF] Carmona | Does the learning curve of conservative laparoscopic surgery in women with rectovaginal endometriosis impair the recurrence rate?[END_REF][START_REF] Akladios | Laparoscopic sacrocolpopexy for female genital organ prolapse: establishment of a learning curve[END_REF][START_REF] Vignali | Surgical treatment of deep endometriosis and risk of recurrence[END_REF]. Hence the study population was stratified as follows:

early group included the first 25 cases; -late group included the 25 subsequent cases.

According to French law on ethics, all patients received information regarding the potential use of their medical data for clinical research purpose, and all of them agreed to participate to the study. The University Hospital of Toulouse signed a commitment of compliance to the reference methodology MR-004 of the French National Commission for Informatics and Liberties (CNIL). After evaluation, the present study was approved by the ethics committee of the University Hospital of Toulouse which confirmed that ethic requirements were fully respected. It was thus referenced in the register of retrospective studies (registration number: RnIPH 2020-26) and covered by the MR-004 (CNIL number: 2206723 v 0).

Objectives of the study

Our primary objective was to evaluate the impact of the learning curve on postoperative SPR. SPR was defined as a clinical pregnancy, according to the International Glossary on Infertility [START_REF] Zegers-Hochschild | The International Glossary on Infertility and Fertility Care[END_REF], occurring spontaneously in the postoperative period.

Our secondary objectives investigated the impact of the learning curve on the following items:

live birth rate (LBR) after spontaneous conception, as defined by the World Health Organization overall PR, compiling both spontaneous and assisted reproductive technology (ART) clinical pregnancies and overall LBR postoperative complication rate according to Clavien-Dindo classification [START_REF] Dindo | Classification of surgical complications: a new proposal with evaluation in a cohort of 6336 patients and results of a survey[END_REF] clinical recurrence rate. Clinical recurrence was defined by both recurred symptoms and recurred lesions on MRI.

Patients' management

Preoperative workup systematically comprised:

for women: full hormone measurement (AMH, FSH, LH, estradiol), high quality transvaginal ultrasound and pelvic MRI; additional transrectal ultrasound was performed when rectal or sigmoid involvement was suspected on MRI in order to determine the depth of infiltration and to accurately define modalities of subsequent surgical management (conservative or radical); -for men: sperm examination.

Treatment strategy was validated in multidisciplinary meetings prior surgery in all cases.

All procedures were performed under general anesthesia. Antimicrobial prophylaxis was administered in all cases (intravenous infusion of Cefazolin 2g). Ureteric catheters were inserted cystoscopically in case of bladder infiltration or ureteral involvement. All procedures were conducted through laparoscopic route using a 10mm infra-umbilical port and 3 additional 5mm ports (1 in the supra pubic midline, 1 in each lower quadrant). Following steps were performed during the surgeries:

evaluation of tubal patency; -adnexal adhesiolysis;

conventional ovarian cystectomy when applicable; -identification of both ureters after opening of the peritoneum until their penetration in the cardinal ligaments;

opening of pararectal spaces; -identification of splanchnic nerves in case of parametrial extension;

excision of all endometriotic lesions, either superficial or deeply infiltrating;

disease stage according to ASRM classification.

The management of bowel infiltration was planned according to the preoperative workup. Superficial lesions (infiltration limited to the serosa or the muscularis layer) were treated with conservative resection (shaving). Infiltration of the submucosa were managed with either conservative (deep shaving) or radical (segmental resection) surgery, depending on lesion size and location. Mucosa infiltration systematically led to segmental resection.

Bladder infiltration was managed by partial cystectomy. In such cases, bladder catheterization was maintained postoperatively for 7 days.

Statistical analysis

All data were collected retrospectively. They were anonymized and de identified prior analysis. Statistical analyses were performed using SPSS ® software (IBM, USA). For quantitative variables, we performed average comparison (Student's t-test) or rank tests (Mann-Whitney) according to the normality of the variable. We used the Chisquare test for the comparison of qualitative variables. Kaplan-Meier curves were built to estimate the probability of spontaneous pregnancy according to postoperative time and subgroup assignation. A logistic regression model was performed to identify prognostic factors of postoperative spontaneous pregnancy. A p-value <0.05 was considered significant.

Results

Demographics

Except for age, which was significantly higher in the late subpopulation there was no significant difference between the 2 groups for demographic parameters (Table 1).

Moreover, the 2 sub-populations displayed no significant difference regarding endometriosis features (Table 2). Most patients (78%) presented with ASRM stages III and IV. Surgical parameters and outcomes (Table 3) All procedures were performed through laparoscopic route and none required conversion to laparotomy. The blood loss significantly decreased with surgeon experience (67ml versus 110 in the early group, p=0.04). The other surgical parameters did not significantly differ between the 2 groups. Mean EFI score was similar between groups as well. Severe postoperative morbidity (Clavien Dindo > 3) was relatively low, accounting for 4 patients (8%), and was not impacted by surgeon's learning curve. Two patients suffered from postoperative hemoperitoneum at postoperative day 1 which systematically required reoperation through laparoscopic route. None of them had required additional blood transfusion. They both belonged to the early group. One patient presented with vaginal scar dehiscence that was managed by simple sutures through vaginal route (early group).

One patient had a renal colic at postoperative day 2 due to ureter external compression that was managed with ipsilateral ureteric stenting (late group). The clinical recurrence rate was 10%, with a mean follow up of 34.1 months, and did not differ between groups (16% in the early group versus 4% in the late group, p=0.16).

As expected, follow up duration was higher in the early group (44.7 months versus 23.4 in the late group, respectively; p<10 -5 ).

Fertility outcomes (Table 4)

In the whole study population, SPR and overall PR were 48% and 72%, respectively.

Spontaneous and overall LBR were 42% and 57%. Subgroup analysis did not show any difference in spontaneous PR: 40% in the early group versus 56% in the late group (p=0.25). Similarly, spontaneous LBR was similar in both subgroups (40% versus 44%, p=0.77). Time to spontaneous pregnancy did not differ either (Figure 1).

In contrast, overall LBR was significantly higher in early patients (76% versus 48% in late group, respectively; p=0.008). Noteworthy, early patients were more likely to benefit from ART (60% versus 28% in the late group, p=0.02).

Logistic regression analysis revealed that the learning curve did not impact the spontaneous PR (Table 5). In contrast, ASRM stage, EFI score, and body mass index appeared as significant prognostic factors.

Discussion

The results of our study show that surgical resection of deep infiltrating endometriosis (DIE) in infertile women is associated with high spontaneous pregnancy rate (SPR) and that the surgeon's experience does not significantly impact postoperative fertility outcomes. To our knowledge, we provide the first study that specifically addresses the influence of surgical training on the likelihood of subsequent spontaneous pregnancy in the setting of DIE and infertility.

While underlying mechanisms are still not fully understood [START_REF] Tanbo | Endometriosis-associated infertility: aspects of pathophysiological mechanisms and treatment options[END_REF], endometriosis is undoubtedly associated with impaired fertility [START_REF] Eijkemans | Pregnancy chances on an IVF/ICSI waiting list: a national prospective cohort study[END_REF]. As regards DIE, spontaneous PR without disease removal is low, ranging from to 8.7% to 13% [START_REF] Barri | Endometriosisassociated infertility: surgery and IVF, a comprehensive therapeutic approach[END_REF][START_REF] Bianchi | Extensive excision of deep infiltrative endometriosis before in vitro fertilization significantly improves pregnancy rates[END_REF][START_REF] Vercellini | Reproductive performance in infertile women with rectovaginal endometriosis: is surgery worthwhile?[END_REF]. Hence recent French guidelines have advocated for active management in women suffering from DIE and seeking pregnancy [START_REF] Mathieu D'argent | Deeply infiltrating endometriosis and infertility: CNGOF-HAS Endometriosis Guidelines[END_REF]. Indeed, in a retrospective study including 505 patients with rectovaginal endometriosis, spontaneous PR was significantly lower in patients managed expectantly compared to those who had undergone surgical removal of the lesions (17.3% versus 35.7%, p<0.001) [START_REF] Roberti Maggiore | Spontaneous fertility after expectant or surgical management of rectovaginal endometriosis in women with or without ovarian endometrioma: a retrospective analysis[END_REF]. Consistently, numerous studies have reported favorable fertility outcomes following DIE surgery (4, 8), including bowel endometriosis [START_REF] Iversen | Does surgery for deep infiltrating bowel endometriosis improve fertility? A systematic review[END_REF][START_REF] Bourdel | Long-term evaluation of painful symptoms and fertility after surgery for large rectovaginal endometriosis nodule: a retrospective study[END_REF]. However, most of them reported outcome in both infertile patients and women with a desire for pregnancy, whereas the impact of surgery might not be similar in those 2 different subgroups [START_REF] Roman | High postoperative fertility rate following surgical management of colorectal endometriosis[END_REF][START_REF] Hudelist | Pain and fertility outcomes of nerve-sparing, full-thickness disk or segmental bowel resection for deep infiltrating endometriosis-A prospective cohort study[END_REF]. Furthermore, several trials have described the overall PR rather than the spontaneous PR alone.

When focusing on recent data addressing postoperative spontaneous conception in infertile patients, PR ranged from 38 to 42.6% [START_REF] Roman | High postoperative fertility rate following surgical management of colorectal endometriosis[END_REF][START_REF] Hudelist | Pain and fertility outcomes of nerve-sparing, full-thickness disk or segmental bowel resection for deep infiltrating endometriosis-A prospective cohort study[END_REF][START_REF] Centini | Impact of Laparoscopic Surgical Management of Deep Endometriosis on Pregnancy Rate[END_REF]. In the subgroup of infertile women with colorectal DIE, a review by Darai et al reported a spontaneous PR of 31.4% [START_REF] Darai | Colorectal endometriosis and fertility[END_REF]. Our results are in line with such findings, with spontaneous PR and LBR of 48% and 42% during a follow up period of 34.1 months. However, despite the use of rigorous inclusion criteria particularly regarding infertility definition, our fertility outcome may have been overestimated for the following reasons:

the causality between DIE and patients' infertility might be overrated in our population. Indeed, 56% of patients suffered from dyspareunia which necessarily exposes to reduced exposure to pregnancy through avoidance of sexual intercourses. Hence it is unclear whether all patients presented with a "true infertility", defined as failure to get pregnant despite adequate exposure to conception.

-In our department, infertile patients with DIE and normal sperm features do not systematically undergo surgery. Thus, some of them are managed with upfront assisted reproductive technology (ART). Our local policy regarding management of DIE associated-infertility involves several parameters, including woman's age and medical history, ovarian reserve, associated pain and impaired quality of life, foreseeable extent of surgery and preference for patient. A benefit/risk ratio is defined for each patient, which might expose to a potential risk of selection bias towards preferential recruitment of patients with a better prognosis regarding spontaneous conception.

In the setting of infertility and DIE, it is of tremendous importance to accurately predict the probability of postoperative pregnancy, especially among women whose quality of life is not harshly impaired by endometriosis. When sperm features are compatible with natural conception, EFI displays the major advantage over ASRM classification to compile pre and per operative parameters associated with postoperative spontaneous fertility. Since its first description [START_REF] Adamson | Endometriosis fertility index: the new, validated endometriosis staging system[END_REF], its reliability in the prediction of postoperative non ART pregnancy have been confirmed by several trials and meta-analyses [START_REF] Tomassetti | Reproducibility of the Endometriosis Fertility Index: a prospective inter-/intra-rater agreement study[END_REF][START_REF] Vesali | Endometriosis Fertility Index for predicting non-assisted reproductive technology pregnancy after endometriosis surgery: a systematic review and metaanalysis[END_REF]. Recent French guidelines have thus recommended its systematic use following endometriosis surgery to accurately define subsequent fertility management (Grade C) [START_REF] Boujenah | First line management without IVF of infertility related to endometriosis: Result of medical therapy? Results of ovarian superovulation? Results of intrauterine insemination? CNGOF-HAS Endometriosis Guidelines[END_REF]. As expected, EFI was a significant prognostic factor of spontaneous PR in our study population. Other factors included ASRM stage and body mass index. In contrast, it is noteworthy that the surgical learning curve did not impact the likelihood of spontaneous conception. DIE surgery is commonly considered as a challenging situation for several reasons:

the aim of the procedure is full disease resection whilst preserving fertility (3); -DIE often distort anatomy through its invasiveness of surrounding organs; complete lesions removal thus requires appropriate surgical skills including a perfect knowledge of anatomical structures and landmarks; -complete resection may expose patients to potentially severe complications, particularly when bowel or parametrium resections are required [START_REF] Bourdel | Long-term evaluation of painful symptoms and fertility after surgery for large rectovaginal endometriosis nodule: a retrospective study[END_REF]; -severe postoperative complications may reduce the likelihood of subsequent spontaneous fertility (29); -although endometriosis is a benignant condition, recurrence rate is high, even when complete resection is obtained.

Data addressing the impact of the surgeon's learning curve on surgical outcomes are scarce. Carmona et al have observed a significant relationship between surgeon's experience and surgical completeness and, consistently, recurrence rate [START_REF] Carmona | Does the learning curve of conservative laparoscopic surgery in women with rectovaginal endometriosis impair the recurrence rate?[END_REF]. They have also reported a decrease in operating time and in blood loss along the learning curve. In our study, the surgeon's experience only impacted blood loss. The current widespread use of laparoscopic route for surgical management of DIE may explain the lack of significant difference regarding other parameters. Indeed, our study surgeon has participated to many laparoscopic procedures (for endometriosis and other indications) during his residency and fellowship, which has probably favored the acquisition of specific gesture and surgical steps. Therefore, our data suggest that a young surgeon with appropriate curriculum and multidisciplinary environment may manage DIE patients without hindering subsequent fertility nor further disease evolution.

Our study does suffer from limitations. First, its retrospective design reluctantly exposes to missing data. Then, patients' allocation to study arm was not randomized since it was based on the date of surgery. Nevertheless, study groups were comparable regarding baseline demographics, disease extent and type of surgical procedures performed. Additionally, a single practitioner performed all surgeries in a single tertiary facility, and all procedures, during the defined learning curve, were included. We thus believe that the data depicted here are reproducible.

In conclusion, surgical management of DIE is a challenging situation that should be discussed in multidisciplinary meetings, especially in women seeking pregnancy or with a desire for fertility preservation. Such patients should thus be systematically referred to dedicated facilities. Surgery triggers favorable fertility outcomes, with a high rate of spontaneous pregnancies, regardless of the leading surgeon's experience. Indeed, we do believe that the surgeon's curriculum is probably more important than the crude number of past procedures she/he has actually performed.

Tables

Table 1 .

 1 Comparative demographics according to study groups

				Early Group	Late Group	p-value
				N=25	N=25
	Age, mean (years)		31.7 ± 3.9	34.0 ± 3.5	0.04
	BMI, mean (kg/m 2 )		24.0 ± 4.3	22.6 ± 3.5	0.2
	Parity, median		0 (0-1)	0 (0-2)	0.14
	Nulliparous			24 (96%)	21 (84%)	0.16
	Infertility duration (months)	26.7 ± 24.2	19.4 ± 18.5	0.19
	History of ART				0.7
	No			22 (88%)	20 (80%)
	Yes			5 (12%)	20 (20%)
	Baseline	AMH,	mean	3 ± 2.8	3.2 ± 3.5	0.77
	(ng/ml)
	Pelvic pain
	Dysmenorrhea		22 (88%)	21 (84%)	1
	Dyspareunia		13 (52%)	15 (60%)	0.57
	Non cyclic pelvic pain	10 (40%)	17 (68%)	0.05
	Pain on defecation		11 (44%)	9 (36%)	0.56
	Urinary symptoms		3 (12%)	5 (20%)	0.7
	BMI = body mass index; ART = assisted reproductive technology; AMH = anti-
	mullerian hormone

Table 2 .

 2 Endometriosis features according to study groups 400

					Early Group	Late Group	p-value
					N=25	N=25
		Endometriotic cyst		0.76
		Absence			16 (64%)	15 (60%)
		Unilateral			5 (20%)	4 (16%)
		Bilateral			4 (16%)	6 (24%)
		Greater	diameter	of
		endometriotic cyst, mean (mm)	40 ± 2	39 ± 1.8	0.92
		DIE lesions location
		Uterosacral ligaments		18 (72%)	20 (80%)	0.51
		Torus			13 (52%)	15 (60%)	0.57
		Rectovaginal space		9 (36%)	7 (28%)	0.54
		Parametrium		2 (8%)	4 (16%)	0.4
		Bladder			2 (8%)	1 (4%)	0.51
		ASRM score, mean		38 ± 26.7	38 ± 22.5	0.97
		ASRM classification		0.85
		Stage I			0	0
		Stage II			6 (24%)	5 (20%)
		Stage III			8 (32%)	7 (28%)
		Stage IV			11 (44%)	13 (52%)
	401	mm = millimeter; DIE = deep infiltrating endometriosis; ASRM = American Society of
	402	Reproductive Medicine

Table 4 .

 4 Postoperative fertility outcomes

		Early Group	Late Group	p-value
		N=25	N=25
	Spontaneous pregnancy rate	40%	56%	0.26
	Overall pregnancy rate	80%	64%	0.21
	Live birth rate after spontaneous
	pregnancy	40%	44%	0.77
	Overall live birth rate	76%	48%	0.008
	Patients managed with IVF/ICSI	15	7	0.02
	Time to spontaneous pregnancy	9.8 ± 7.2	7 ± 4.6	0.29
	(months)
	IVF = in vitro fertilization; ICSI = intracytoplasmic sperm injection

Table 5 .

 5 Prognostic factors of postoperative spontaneous pregnancy after logistic Time to spontaneous pregnancy according to study groups (Kaplan-Meier curves)

	regression analysis
		B	SE	Wald	df	OR (CI 95%)	p-value
	Learning curve	0.335	0.717	0.57	1	1.4 (0.34-5.7)	0.45
	Blood loss	-0.02	0.006	1.67	1	0.99 (0.98-1.01) 0.2
	Procedure duration -0.01	0.005	2.61	1	0.99 (0.98-1)	0.11
	BMI	-0.23	0.12	5.7	1	0.79 (0.64-0.98) 0.02
	EFI score	0.6	0.23	8.43	1	1.82 (1.16-2.87)	0.004
	ASRM stage	1.21	0.47	8.31	1	3.35 (1.34-8.35) 0.004
	BMI = body mass index; EFI = Endometriosis Fertility Index; ASRM = American
	Society of Reproductive Medicine

spontaneous pregnancy.

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.


Farid Bakir

Jianfei Song

Smaine Kouidri
email: smaine.kouidri@limsi.fr

Numerical study on flow topology and hemodynamics in tortuous coronary artery with symmetrical and asymmetrical stenosis

Keywords: Tortuous coronary artery, Wall shear stress, Hemodynamics, Flow topology, Computational Fluid Dynamics

Introduction:

Atherosclerosis as a chronic disease has been found to be responsible for 1/3 deaths in developed and developing countries [START_REF] Gupta | Clinical profile of patients with coronary tortuosity and its relation with coronary artery disease[END_REF][START_REF] Van Dalen | Left ventricular twist and untwist in aortic stenosis[END_REF]. Narrowed artery will be observed due to the stenosis formation when disease happens. Numerous studies have been published to elucidate the hemodynamic variations due to disturbed flow in stenotic artery [START_REF] Razavi | Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models[END_REF][START_REF] Long | Numerical investigation of physiologically realistic pulsatile flow through arterial stenosis[END_REF][START_REF] Foong | Numerical study for blood rheology inside an artery: The effects of stenosis and radius on the flow behavior[END_REF][START_REF] Yan | Numerical investigation of non-Newtonian blood flow within an artery with cone shape of stenosis in various stenosis angle[END_REF][START_REF] Akbar | Non-Newtonian model study for blood flow through a tapered artery with a stenosis[END_REF]. In 2018, T. Sood et al. [START_REF] Sood | Effect of pulse rate variation on blood flow through axisymmetric and asymmetric stenotic artery models[END_REF] demonstrated that varied pulse rates of blood flow greatly affect vortices formation downstream the stenosis. Increased pulse rate brings more disturbed flow downstream especially for asymmetric stenosis.

Arterial tortuosity is commonly found in human body especially in the left anterior descending coronary artery [START_REF] Khosravani-Rudpishi | The significant coronary tortuosity and atherosclerotic coronary artery disease; What is the relation?[END_REF]. In the recent years the relationship between artery tortuosity and stenosis occurrence has caused great interest among researchers. Many studies have been carried out focusing on the curved artery [START_REF] Zhang | Flow patterns and wall shear stress distribution in human internal carotid arteries: the geometric effect on the risk for stenoses[END_REF][START_REF] Qiao | Numerical study of nonlinear pulsatile flow in S-shaped curved arteries[END_REF][START_REF] Xie | Computation of hemodynamics in tortuous left coronary artery: a morphological parametric study[END_REF]. M. Jarrahi et al. [START_REF] Jarrahi | Laminar sinusoidal and pulsatile flows in a curved pipe[END_REF], M.R. Najjari et al. [START_REF] Najjari | Evolution of vortical structures in a curved artery model with non-Newtonian blood-analog fluid under pulsatile inflow conditions[END_REF] and J.H. Siggers et al. [START_REF] Siggers | Steady flows in pipes with finite curvature[END_REF] have experimentally studied the flow pattern in curved pipe to better understand the development of vortices structure through curvature. Recently numerical simulation as a research tool has been employed widely to investigate the physics of blood flow in the tortuous vessel [START_REF] Shahcheraghi | Unsteady and three-dimensional simulation of blood flow in the human aortic arch[END_REF]. The effects of morphological parameters of curvature on flow pattern and hemodynamics have been commonly discussed among the existing literature [START_REF] Dash | Flow in a catheterized curved artery with stenosis[END_REF][START_REF] Wang | Pressure drop in tortuosity/kinking of the internal carotid artery: simulation and clinical investigation[END_REF][START_REF] Santamarina | Computational analysis of flow in a curved tube model of the coronary arteries: effects of time-varying curvature[END_REF]. Wall shear stress (WSS) as a key hemodynamic indicator to potential atherosclerosis sites has been found to be strongly affected by tortuosity. X. Xie et al. [START_REF] Xie | Impact of coronary tortuosity on the coronary blood flow: a 3D computational study[END_REF] have shown that the increased curvature angle larger than 120 o contributes to a lower WSS zone. Through works in 2019 by A. Buradi et al. [START_REF] Buradi | Impact of coronary tortuosity on the artery hemodynamics[END_REF], it is found severe coronary tortuosity with small curvature radius, small distance between two curvatures and high angle of curvature will contribute to low WSS zones at inner wall downstream of tortuosity section. Among these existing investigations up to now, many of them either mainly focus on the effect of vessel tortuosity or mainly focus on the effect of stenosis. The studies considering both stenosis and tortuosity are really limited. G.Y. Liu et al. [START_REF] Liu | Numerical simulation of flow in curved coronary arteries with progressive amounts of stenosis using fluid-structure interaction modelling[END_REF], B.Y. Liu [START_REF] Liu | The influences of stenosis on the downstream flow pattern in curved arteries[END_REF] and M. Biglarian et al. [START_REF] Biglarian | Computational investigation of stenosis in curvature of coronary artery within both dynamic and static models[END_REF] have considered the stenosis located at curvature site and studied the flow topology and WSS distribution at inner wall and outer wall.

However, it should be noticed that through clinical investigations in 2018 [START_REF] Li | Coronary tortuosity is negatively correlated with coronary atherosclerosis[END_REF], the stenosis located at the non-tortuous segment before the tortuosities has been confirmed and the hemodynamic variations affected by the interactions between stenosis and tortuosity still remain interesting in this case.

Therefore, in view of the literature, the present study aims to investigate the flow topology and hemodynamics through 3D tortuous artery model with symmetrical and asymmetrical stenosis located before the tortuous segment. As the previous studies focused mainly on the curved artery, in this study both curved and spiral tortuosity have been considered based on the clinical review by H.C. Han [START_REF] Han | Twisted blood vessels: symptoms, etiology and biomechanical mechanisms[END_REF]. Different stenosis severities of 20%, 35%, and 50%, different pulse rates of 75 bpm, 100 bpm and 120 bpm, and different distances of 0 mm, 3 mm and 6 mm between stenosis and tortuosity as controlling parameters have been investigated using commercial CFD tool of Comsol in version 5.1.

Modelling establishment and methodology

Geometrical model and computational mesh distribution

Since the present study focuses on the blood flow in tortuous artery with stenosis, 3D geometrical models of coronary artery have been established both for curved and spiral tortuosity as shown in Fig. 1-(a) and (b). In order to ensure the geometrical independence, the artery lengths before and after tortuosity are 40mm and 50mm separately. The stenosis is located upstream the tortuosity with stenosis length of 6 mm.

The horizontal length of one single curvature is 20 mm. The heights of curved and spiral tortuosity are 8 mm and 6 mm separately. The distance between stenosis and curvature as controlling parameter is named L taking the following values: 0mm, 3mm and 6mm. Comparison will be made between symmetrical and asymmetrical stenosis as shown in Fig. 1-(c). Stenosis severity as another controlling parameter is defined as (Dd)/D*100. D is the artery diameter of 3 mm. d is the artery diameter at the narrawed site with stenosis shown in Fig. 1-(c). Different stenosis severities of 20%, 35% and 50% are studied.

[Fig. 1 near here]

In order to check the mesh independence, four mesh sizes of 210078, 570010, 1524838 and 2352717 have been studied. The WSS is investigated at these four different mesh sizes. After the third mesh size, WSS accuracy can be achieved around 2%. Taking the same way, the final determined mesh distributions can be obtained both for curved and spiral artery as shown in Fig. 2. The multigrilles method is used to generate the unstructured tetrahedral mesh elements and the average size of mesh element is 6.5e-13 m 3 .

[Fig. 2 near here]

Mathematical model and boundary conditions

The blood flow is considered as incompressible and Newtonian fluid along with density of 1060 kg/m 3 and dynamic viscosity of 0.0035 Pa•s respectively [START_REF] Gundelwein | Personalized stent design for congenital heart defects using pulsatile blood flow simulations[END_REF]. Navier-stokes equations including mass conservation equation (Eq. 1) and momentum conservation equation (Eq. 2) are adopted in unsteady case. For boundary conditions, the vessel wall is considered as rigid since the diseased coronary vessels experience peak circumferential strain below 5% which makes the assumption reasonable around the plaque location [START_REF] Chabi | Critical evaluation of three hemodynamic models for the numerical simulation of intra-stent flows[END_REF][START_REF] Kelle | Coronary artery distensibility assessed by 3.0 Tesla coronary magnetic resonance imaging in subjects with and without coronary artery disease[END_REF]. At the inlet, the pulsed flow at different pulse rates (bpm: beat per minute) will be imposed as shown in Fig. 3 which are reconstructed through an eight-coefficient Fourier equation (Eq. 3) and a good fitting has been achieved with the velocity profile of blood at 75 bpm [START_REF] Chabi | Critical evaluation of three hemodynamic models for the numerical simulation of intra-stent flows[END_REF]. According to the literature [START_REF] Heusch | Heart rate in the pathophysiology of coronary blood flow and myocardial ischaemia: benefit from selective bradycardic agents[END_REF][START_REF] Kim | Developing computational methods for three-dimensional finite element simulations of coronary blood flow[END_REF], the velocity profile in one cycle can be confirmed as well with pulse rate of 100 bpm and 120 bpm. At the outlet, a constant pressure of 13330 Pa is imposed [START_REF] Gudiño | 3D mathematical model for blood flow and non-Fickian mass transport by a coronary drug-eluting stent[END_REF]. The laminar blood flow is considered to be fully developed with parabolic velocity profile as Reynolds number is in the range of 90~570. The iterative methods have chosen GMRES with the maximum iteration number of 500. The time step of 0.001 s has been adopted meeting the requirement of CFL<1. The residual criteria for momentum and continuity equations is set as 10 -5 . To make sure the periodic stability and accuracy of the results, four pulsatile cycles have been carried out. The works concerning the modelling, meshing and computing all have been done with Comsol 5.1.

0 = ⋅ ∇ V (1) V p V V t V 2 ∇ + -∇ = ∇ ⋅ + ∂ ∂ µ ρ ρ (2)
Where V is the flow velocity, p is the pressure, ρ is the flow density and µ is the viscosity.

∑ = + + = 8 1 0 ) sin( ) cos( ) ( n n n t n W t n V V t V ω ω (3) Where ∫ = T dt t V T V 0 0 ) ( 1 for , 0 = n ∫ = T n dt t n t V T V 0 ) cos( ) ( 2 ω for 1 ≥ n , ∫ = T n dt t n t V T W 0 ) sin( ) ( 2 ω for 1 ≥ n
. ω is the angular velocity.

[Fig. 3 near here]

• WSS: w r r r u WSS = ∂ ∂ = µ (4)
• TAWSS:

∫ = T dt WSS T TAWSS 0 1 ( 5
)
Where T is the total time of one cycle for blood flow. TAWSS represents the shear load over time the arterial wall is subjected to and the threshold value is 0.4 Pa [START_REF] Malek | Hemodynamic shear stress and its role in atherosclerosis[END_REF].

• Artery surface of TAWSS below 0.4 Pa ( TA S ):

∫ < = T S TA ds TAWSS if S ) 0 , 1 , 4 . 0 ( (6)
Where T S is the total surface of artery wall. The "if" function has been used in order to integrate the surface where TAWSS<0.4 Pa (=1 if so, =0 if not). Thus TA

S

represents the surface area of potential disease sites.

Results analysis

Blood flow in curved artery with symmetrical and asymmetrical stenosis

Table 1 displays the TAWSS distribution for curved artery at different stenosis severities of 0%, 20%, 35% and 50% under symmetrical and asymmetrical cases at 75 bpm. In order to better understand the results analysis, some locations used in the analysis have been displayed in [Table 1 near here]

[Fig. 4 near hear]

[Fig. 5 near hear] Physical activities of patients are closely related to the hemodynamic variation through changed flow pattern [START_REF] Khosravani-Rudpishi | The significant coronary tortuosity and atherosclerotic coronary artery disease; What is the relation?[END_REF]. Thus, the TAWSS distribution is also studied at different pulse rates of 75 bpm, 100 bpm and 120 bpm with symmetrical and asymmetrical stenosis of 35% as shown in Table 2. Even though the changed pulse rate will bring hemodynamic variation overall the artery, in order to be consistent to the analysis above we still mainly focus on the stenosis part and the near part of tortuosity. As can be seen that larger pulse rate greatly increases the TAWSS value and low TAWSS regions located right downstream the stenosis and at the outer wall of tortuosity are both decreased because of the more sharply varied velocity pattern. The quantified comparisons between symmetrical and asymmetrical stenosis regarding arterial surface area of TAWSS below 0.4 Pa affected by different pulse rates are shown in Fig. 6 which has well confirmed the observations in Table 2. The obviously negative relationship between TA S and pulse rate has been proved and a larger value of TA S at asymmetrical case can be always observed.

[Table 2 near here]

[Fig. 6 near hear]

Following the effect of stenosis severities and pulse rates on hemodynamic variation, the influence of distance between stenosis and tortuosity is discussed as well. Similarly, Table 3 shows the TAWSS distribution at different distances of 0 mm, 3 mm and 6 mm between stenosis and tortuosity with symmetrical and asymmetrical stenosis of 35% at 75 bpm. As can be seen, the increased distance between stenosis and tortuosity contributes to lower value of TAWSS especially when we focus on the inner wall of tortuosity and the reduction of TAWSS is more obvious for symmetrical case. The increased distance in our case tends to increase the low value regions of TAWSS.

Compared to the symmetrical stenosis, larger value of TAWSS can be got at up wall after asymmetrical stenosis because there is no geometrical change along up wall.

Similarly, the corresponding quantified analysis has been made with Fig. 7 investigating the effects of distances between stenosis and tortuosity on the surface area of TAWSS below 0.4 Pa for symmetrical and asymmetrical cases. It is displayed that the value of TA S is increased in asymmetrical case with the increasing of distance between stenosis and tortuosity. However, for symmetrical case, the value of TA S is decreased with distance increased from 3 mm to 6 mm. The reason is that the flow after stenosis is still not be able to fully developed with effects of the formed recirculation downstream the asymmetrical stenosis and tortuosity. However, for symmetrical stenosis, the flow has been recovered to be fully developed when the distance is 6 mm. The larger value of TA S at symmetrical case has been observed compared to the asymmetrical case with the increased distance of 3 mm and 6 mm which is in contrast to the results with effects of stenosis severity and pulse rate. For the reason, it is because the increased distance between stenosis and tortuosity leads to more low value region for the symmetrical case compared to the asymmetrical case which can balance and even over the effect of stenosis geometrical characteristics.

[Table 3 near here]

[Fig. 7 near hear]

In order to check out the flow variations, two cross sections S1 and S2 are selected as shown in Fig. 8. The streamlines and velocity distribution on these two cross sections are studied at different stenosis severities as shown in Table 4. When focusing on S1 in [Fig. 8 near here]

[Table 4 near here]

Blood flow in spiral artery with symmetrical and asymmetrical stenosis

As spiral tortuosity is one of the existing arterial morphological states found in human body, it is necessary to study how the hemodynamics are affected by spiral non-planar structure of artery instead of curved planar structure. Similarly, some location definitions used in analysis have been shown in Fig. 9. Table 5 shows the TAWSS distribution with symmetrical and asymmetrical stenosis of 0%, 20%, 35% and 50% at 75 bpm for the spiral artery. The results are displayed from front and back views. When focusing on the case of 0%, it is found that low value of TAWSS is mainly located at entry and exit parts of the tortuosity. Along the tortuous segment, larger value of TAWSS is always found at outer wall compared to the inner wall. Since the effect of stenosis is limited to the near region, in the following analysis the region in black square is mainly focused. With the increasing of stenosis severity, the high value region of TAWSS is greatly increased. The low value region of TAWSS is found to be mainly located downstream the stenosis both in front view and back view. Quantified analysis has been followed with Fig. 10 which evaluates the surface area of TAWSS below 0.4

Pa under different stenosis severities for symmetrical and asymmetrical cases. Larger value of TA S can be found mainly in the symmetrical case compared to the asymmetrical case. The positive relationship between TA S and stenosis severity found in curved artery has been disturbed with increased stenosis severity of 50% in spiral artery.

[Fig. 9 near here]

[Table 5 near here]

[Fig. 10 near hear] Table 6 shows TAWSS distribution at different pulse rates for symmetrical and asymmetrical stenosis of 35% for spiral artery. Larger pulse rate leads to overall increased TAWSS because of the increased velocity variation near wall. The low value region downstream the stenosis is decreased at both front and back views with increased pulse rate. The corresponding quantified analysis has been made in Fig. 11 where the surface area of TAWSS below 0.4 Pa at different pulse rates has been plotted for the cases of symmetrical and asymmetrical stenosis. The negative relationship between TA S and pulse rate can be observed and the larger value of TA S is obtained with symmetrical stenosis compared to the asymmetrical stenosis.

[Table 6 near here]

[Fig. 11 near hear]

As the stenosis is located at the non-tortuous segment before the spiral tortuosity, the distance between stenosis and spiral tortuosity need to be considered. where the original artery geometry is remained. Fig. 12 shows the surface area of TAWSS below 0.4 Pa at different distances and confirmed the observations from Table 7. The value of TA S is greatly increased with larger distance between stenosis and tortuosity as the flow is not able to be fully developed affected by the spiral tortuosity.

[Table 7 near here] Moreover, with the increasing of stenosis severity, the flow disturbance is more complicated especially at stenosis of 50% and the recirculation downstream stenosis is more clearly observed. Compared to symmetrical case, the formation of recirculation downstream the stenosis in asymmetrical case is more obvious which is affected by the stenosis height. Similarly, the increased pulse rate and distance contribute to more disturbed flow and recirculation formation as well, especially in asymmetrical case which are not shown here.

[Table 8 near here]

Discussion

This present study has provided us an insight for the influences of planar and non-planar arterial tortuosity in the potential risks of plaque generation coupling the existence of stenosis. Besides the qualitative analysis of hemodynamics as commonly conducted in the existing literature [START_REF] Zhang | Flow patterns and wall shear stress distribution in human internal carotid arteries: the geometric effect on the risk for stenoses[END_REF][START_REF] Xie | Computation of hemodynamics in tortuous left coronary artery: a morphological parametric study[END_REF][START_REF] Buradi | Impact of coronary tortuosity on the artery hemodynamics[END_REF], the quantitative analysis of disease onset area is employed strictly following the critical value of evaluation. As described above, both curved and spiral arteries with symmetrical and asymmetrical stenosis have been established in order to investigate the flow disturbance and hemodynamic variations inside separately. As observed through the results, TAWSS distribution tends to be symmetrical through a 2D section in curved artery which is consistent with the works of Liu et al. [START_REF] Liu | Numerical simulation of flow in curved coronary arteries with progressive amounts of stenosis using fluid-structure interaction modelling[END_REF], however, the TAWSS distribution in spiral artery is more complex affected by the non-planar tortuosity structure. The low value region of TAWSS has been focused and pointed out to specify the potential sites of plaque generation. When focusing on the non-tortuous segment, low value region of TAWSS can be always found downstream the stenosis both for curved and spiral artery. Consistently, both invivo and in-vitro works have proved the local platelet aggregation downstream the stenotic site [START_REF] Tricot | Relation between endothelial cell apoptosis and blood flow direction in human atherosclerotic plaques[END_REF][START_REF] Westein | Atherosclerotic geometries exacerbate pathological thrombus formation poststenosis in a von Willebrand factor-dependent manner[END_REF]. Along the curved tortuosity, the low value region of TAWSS has been observed at the outer wall upstream and inner wall downstream for each curvature as shown in Table 1 which is enforced by the direction of centrifugal force. Along spiral tortuous segment, the low value region of TAWSS is prone to be always located at the inner wall as shown in Table 5 which is determined by the more complicated tortuosity structure and the more irregular alterations of centrifugal force direction.

Stenosis located at the non-tortuous segment before the tortuosity is considered following the recent clinical findings [START_REF] Li | Coronary tortuosity is negatively correlated with coronary atherosclerosis[END_REF]. Thus the distance between stenosis and tortuosity as a controlling parameter has been put forward and investigated in our study as well as different pulse rates and stenosis severities. The results revealed that larger risks of atherosclerosis generally go with larger stenosis severity, smaller pulse rate and larger distance between stenosis and tortuosity. However, some exceptions have been observed with the cases of symmetrical stenosis in curved artery with distance of 6 mm and stenosis severity of 50% in spiral artery. This is due to the fully developed blood flow after the stenosis site in the case of symmetrical case in curved artery with increased distance of 6 mm. For spiral artery, when the stenosis severity is increased to 50%, the low value region of TAWSS will be greatly reduced and restricted by the spiral tortuosity structure. Regarding the comparisons between symmetrical and asymmetrical stenosis, it is found that the value of TA S tends to be higher for asymmetrical stenosis compared to symmetrical stenosis for curved artery under the effects of stenosis severity and pulse rate. The reason is that asymmetrical stenosis brings more disturbed flow downstream the stenosis due to the uneven effects on the arterial wall radially compared to the symmetrical stenosis. However, the increased distance between stenosis and tortuosity leads to more low value region of TAWSS especially for the symmetrical case compared to the asymmetrical case which can balance and even over the effect of stenosis geometrical characteristics. The peak inertial force tends to the less narrowed side of vessel wall leading to larger TAWSS at up wall in asymmetrical case instead of comparatively even distribution of smaller TAWSS in symmetrical case. In spiral artery, larger value of TA S can be always found in the case of symmetrical stenosis compared to the asymmetrical stenosis. The effects of asymmetrical stenosis have been totally disturbed and weakened by the spiral tortuosity with more complicated geometrical variations.

Limitations

In the present study, there are some limitations with the established model. The geometrical model of coronary artery is established as a cylinder which is idealized compared to the reality. Thus the patient-specific artery with stenosis and tortuosity need to be further considered into the model closer to the practice. The heart curvature which is much smaller compared to the tortuousity curvature has been neglected.

Referring to the literature [START_REF] Siogkas | Blood flow in arterial segments: rigid vs. deformable walls simulationsn[END_REF], a good agreement on the average WSS has been demonstrated between rigid and deformable vessels. Thus a rigid and no-slip coronary artery wall has been set in this study and the heart movement has been ignored. As several experimental works [START_REF] Haynes | Physical basis of the dependence of blood viscosity on tube radius[END_REF][START_REF] Stadler | Blood viscosity and optimal hematocrit in narrow tubes[END_REF] have confirmed the multicomponent nature of blood, multi-phase approach should be further considered for modeling of blood instead of single phase in this study.

Conclusion

The present study investigates the flow topology and hemodynamic variations in 44 Table 1. TAWSS distribution at different stenosis severities for curved artery with symmetrical and asymmetrical stenosis at 75 bpm.

Table 2. TAWSS distribution at different pulse rates for curved artery with symmetrical and asymmetrical stenosis of 35%.

Table 3. TAWSS distribution at different distances between stenosis and toruosity for curved artery with symmetrical and asymmetrical stenosis of 35% at 75 bpm.

Fig. 4

 4 with curved artery. It's known that TAWSS is an important WSS-based indicator to potential sites of stenosis with critical value of 0.4 Pa and lower value indicates larger possibility of plaques[START_REF] Malek | Hemodynamic shear stress and its role in atherosclerosis[END_REF]. When we focus on the case of 0%, it is noticed that low value regions of TAWSS are located at outer wall upstream and inner wall downstream along each curvature. As the influence of stenosis located before the tortuosity is limited to the near region of curvature, the zone in the black square is mainly focused in the subsequent analysis. TAWSS is greatly increased with larger stenosis severity both for symmetrical and asymmetrical stenosis focusing on the stenosis region and inner wall of tortuosity. The reason is the narrowed artery lumen brings more drastically varied velocity and stronger inertial force. Larger TAWSS at up wall downstream asymmetrical stenosis can be found compared to the symmetrical case. Because the geometrical change of stenosis is mainly at down wall for asymmetrical stenosis, stronger inertial force is almost remained near the up wall. Quantified results regarding the artery surface with TAWSS below 0.4 Pa ( TA S ) have been plotted in Fig. 5 in order to better analyze the influence of stenosis severity on the potential risks of atherosclerosis. As observed that larger stenosis severity contributes to larger value of TA S both for symmetrical and asymmetrical cases. Moreover, asymmetrical stenosis tends to more risky with larger value of TA S compared to symmetrical case. The reason is that asymmetrical stenosis brings more disturbed flow downstream the stenosis due to the uneven effects on the arterial wall radially compared to the symmetrical stenosis.

[

  Fig. 12 near hear] Spiral tortuosity as non-planar geometry makes the flow disturbance is more complicated. Compared to the curved tortuosity, both vertical and lateral curvature variations affect the blood flow for spiral artery instead of only vertical curvature variation. Thus the flow streamlines are studied in view of 3D instead of the 2D cross section compared to the planar curved artery. As shown in Table 8, streamlines colored with velocity around stenosis and tortuosity have been studied at different stenosis severities. Flow disturbance downstream stenosis and streamlines moving forward spirally along the tortuosity can be easily observed. The peak value of velocity can be obtained at the stenosis site both in symmetrical and asymmetrical cases affected by the reduced artery diameter and the peak value is increased with larger stenosis severity.

  The vortices indicating the flow disturbance level have been found affected by the curvature, and the streamlines moving forward spirally along the spiral tortuosity can be easily observed affected by the spiral structure. It is notable that when we compare the values of TA S between curved and spiral tortuosities through Fig.5-7 and Fig.10-12respectively, the obviously smaller values have been obtained under different conditions for spiral artery. This finding is consistent with the investigations by the group of X.Deng et al.[START_REF] Zhan | Effect of swirling flow on platelet concentration distribution in small-caliber artificial grafts and end-to-end anastomoses[END_REF][START_REF] Sun | Intentionally induced swirling flow may improve the hemodynamic performance of coronary bifurcation stenting[END_REF]: swirling/spiral flows could suppress platelet adhesion. G. De Nisco et al. has demonstrated the atheroprotective nature of helical flow and the helicity intensity inversely associated with the unfavorable condition of WSS[START_REF] De Nisco | The Atheroprotective Nature of Helical Flow in Coronary Arteries[END_REF][START_REF] De Nisco | The impact of helical flow on coronary atherosclerotic plaque development[END_REF]. Clinical study conducted by J.G. Houston et al. has concluded as well that spiral flow is beneficial to inhibit the suspected artery stenosis[START_REF] Houston | Spiral laminar flow in the abdominal aorta: a predictor of renal impairment deterioration in patients with renal artery stenosis?[END_REF].

Fig. 1 .Fig. 2 .

 12 Fig. 1. 3D geometrical model of curved artery (a) and spiral artery (b) with stenosis of symmetrical and asymmetrical structure (c).

Fig. 3 .

 3 Fig. 3. Inlet pulsed flow in one cycle at different pulse rates.

Fig. 4 .

 4 Fig. 4. Location definitions with curved artery coupling stenosis.

Fig. 5 .

 5 Fig. 5. Artery surface of TAWSS below 0.4 Pa at different stenosis severities for curved

Fig. 6 .

 6 Fig. 6. Artery surface of TAWSS below 0.4 Pa at different pulse rates for curved artery.

Fig. 7 .

 7 Fig. 7. Artery surface of TAWSS below 0.4 Pa at different distances between stenosis

Fig. 8 .

 8 Fig. 8. Positions of cross section selection.

Fig. 9 .Fig. 10 .

 910 Fig. 9. Location definitions with spiral artery coupling stenosis.

Fig. 11 .

 11 Fig. 11. Artery surface of TAWSS below 0.4 Pa at different pulse rates for spiral artery.

Fig. 12 .

 12 Fig. 12. Artery surface of TAWSS below 0.4 Pa at different distances between stenosis

Fig. 1 .

 1 Fig. 1. 3D geometrical model of curved artery (a) and spiral artery (b) with stenosis of symmetrical and asymmetrical structure (c).

Fig. 2 .

 2 Fig. 2. Computational mesh for curved artery (a) and spiral artery (b).

Fig. 3 .

 3 Fig. 3. Inlet pulsed flow in one cycle at different pulse rates.

Fig. 4 .

 4 Fig. 4. Location definitions with curved artery coupling stenosis.

Fig. 5 .

 5 Fig. 5. Artery surface of TAWSS below 0.4 Pa at different stenosis severities for curved

Fig. 6 .

 6 Fig. 6. Artery surface of TAWSS below 0.4 Pa at different pulse rates for curved artery.

Fig. 7 .

 7 Fig. 7. Artery surface of TAWSS below 0.4 Pa at different distances between stenosis

Fig. 8 .

 8 Fig. 8. Positions of cross section selection.

Fig. 9 .

 9 Fig. 9. Location definitions with spiral artery coupling stenosis.

Fig. 10 .

 10 Fig. 10. Artery surface of TAWSS below 0.4 Pa at different stenosis severities for spiral

Fig. 11 .

 11 Fig. 11. Artery surface of TAWSS below 0.4 Pa at different pulse rates for spiral artery.

Fig. 12 .

 12 Fig. 12. Artery surface of TAWSS below 0.4 Pa at different distances between stenosis

Table 4 ,

 4 it is found that the high value region of velocity corresponds to the stenosis throat region and higher velocity value is positively related to larger stenosis severity both for symmetrical and asymmetrical cases. The streamlines are more disturbed with increased stenosis severity especially for symmetrical case even though there is no vortice formed. However, when focusing on S2 both in symmetrical and asymmetrical cases, there is no big changes occurred to the peak value of velocity distribution with the increased stenosis severity. The streamlines on S2 is more significantly disturbed compared to S1 especially for asymmetrical case. The vortices can be observed and the vortice number is developed from 2 into 4 with increased stenosis severity. Compared to symmetrical case, asymmetrical stenosis contributes to stronger flow disturbance at the same stenosis severity. Similar phenomena can be found out with the effects of different pulse rates and distances between stenosis and tortuosity which are not shown here. The vortices are commonly found at S2 where the flow tend to be more disturbed with larger pulse rate and smaller distance especially in asymmetrical case.

  Table 7 shows the TAWSS distribution at different distances of 0 mm, 3 mm and 6 mm between stenosis and tortuosity for symmetrical and asymmetrical stenosis of 35% at 75 bpm. larger distance between stenosis and tortuosity greatly increases the low value region of TAWSS either at front view or back view. Compared to the asymmetrical stenosis case, larger low value region of TAWSS is observed at symmetrical case in the artery segment between stenosis and toruosity. The reason is that asymmetrical stenosis geometry can more maintain the inertial force after the stenosis site within regions

Table 1 .

 1 TAWSS distribution at different stenosis severities for curved artery with symmetrical and asymmetrical stenosis at 75 bpm.

	Diameter stenosis	Symmetrical stenosis	Asymmetrical stenosis
	0%
	20%
	35%
	50%

Table 2 .

 2 TAWSS distribution at different pulse rates for curved artery with symmetrical and asymmetrical stenosis of 35%.

	Pulse rate	symmetrical	asymmetrical
	75 bpm
	100 bpm
	120 bpm

Table 3 .

 3 TAWSS distribution at different distances between stenosis and toruosity for curved artery with symmetrical and asymmetrical stenosis of 35% at 75 bpm.

	Distance	Symmetrical	Asymmetrical
	0mm
	3mm
	6mm

Table 4 .

 4 Streamlines with colored velocity distribution and vectors at S1 and S2 for in curved artery of different symmetrical and asymmetrical stenosis at 75 bpm at T/2.

	Stenosis	Symmetrical stenosis	Asymmetrical stenosis
	severity	S1	S2	S1	S2
	20%
	35%
	50%

Table 7 .

 7 TAWSS distribution at different distances between stenosis and tortuosity for spiral artery with symmetrical and asymmetrical stenosis of 35% at 75 bpm.

	Distance View	Symmetrical stenosis	Asymmetrical stenosis
	front
	0 mm
	back
	front
	3 mm
	back
	front
	6 mm
	back

Table 8 .

 8 Streamlines at different stenosis severities for spiral artery with symmetrical and asymmetrical stenosis at 75 bpm at T/2.

	Stenosis severity	Symmetrical stenosis	Asymmetrical stenosis

Table 4 .

 4 Streamlines with colored velocity distribution and vectors at S1 and S2 for curved artery of different symmetrical and asymmetrical stenosis at 75 bpm at T/2.

Table 5 .

 5 TAWSS distribution at different stenosis severities for spiral artery with symmetrical and asymmetrical stenosis at 75 bpm.

Table 6 .

 6 TAWSS distribution at different pulse rates for spiral artery with symmetrical and asymmetrical stenosis of 35%.

Table 7 .

 7 TAWSS distribution at different distances between stenosis and tortuosity for spiral artery with symmetrical and asymmetrical stenosis of 35% at 75 bpm.

Table 8 .

 8 Streamlines at different stenosis severities for spiral artery with symmetrical and asymmetrical stenosis at 75 bpm at T/2.

This study was supported by China Scholarship Council. The authors would like to thank Doctor Blandine Maurel, vascular surgeon at Nantes Hospital for sharing her expertise on atherosclerosis.

Conflict of interest statement

None declared


Imane Hammad

Manuel Dornier

Adrien Servent

Patrick Poucheret

Claudie Dhuique-Mayer
email: claudie.dhuique-mayer@cirad.fr

Modulation of carotenoid/flavonoid profiles and sugar content of a potential functional citrus-based food through crossflow microfiltration

Keywords: Membrane process, lycopene, provitamin A carotenoids, citrus flavonoids, functional food

Crossflow microfiltration was implemented to enrich a clementine / pink grapefruit juice in carotenoids, flavonoids and pectins modulating its sugar content thanks to an added diafiltration step. Using tubular ceramic membrane with pore diameter of 0.2 μm at 30-40°C, a crossflow velocity of 5 m‧s -1 and a transmembrane pressure of 2.6 bar, the impact of the process was assessed focusing on bioactive compounds and physical characteristics of the concentrates. With permeate flux above 30 kg‧h -1 ‧m -2 , the process resulted in an increase of 8 to 10 times in the content of provitamin A carotenoids (33 mg‧kg -1 in the final products), lycopene (43 mg‧kg -1 ), hesperidin (3.2 g‧kg -1 ) and pectin (5.5 g‧kg -1 ) giving a unique and interesting composition profile. Moreover, diafiltration divided the sugar content by 3. This can be relevant for the product to be recommended as part of a reduced sugar diet for diabetic people. By modelling the retention of bioactive compounds, we showed that it was possible to modulate sugar, flavonoids, carotenoids and pectin contents in the concentrate that could be a key issue for the biological activity of this potential functional citrus-based food.

Introduction

Citrus fruits and their juices represent important sources of phytochemical bioactive compounds such as carotenoids (β-cryptoxanthin: βcx, β-carotene: βc, lycopene: Lyc) and flavonoids (hesperidin: Hes, naringin: Nar) which can contribute with certain key micronutrients such as vitamins (C, folate), minerals and fibers (pectins) to their beneficial effects on health including anti-oxidant activity, cardiovascular desease prevention and obesity control [START_REF] Lv | Citrus fruits as a treasure trove of active natural metabolites that potentially provide benefits for human health[END_REF].

With regards to phytochemicals, the health properties of citrus flavonoids such as Hes and Nar are largely described in the literature. They include antioxidant anti-inflammatory, anticarcinogenic, anti-diabetic and anti-hypertensive effects (Mahmoud, Hernandez Bautista, Sandhu, & Hussein, 2019). Hes was mainly found in orange and mandarin, and Nar in grapefruit (Dhuique-Mayer, Caris-Veyrat, Ollitrault, Curk, & Amiot, 2005;[START_REF] Fanciullino | Carotenoid Diversity in Cultivated Citrus Is Highly Influenced by Genetic Factors[END_REF]. Other citrus phytochemicals of interest are carotenoids. The health effects of carotenoids are associated with their antioxidant properties, which reduce the risk of lowdensity lipoprotein oxidation, heart disease, eye disease, as well as cancer [START_REF] Ciccone | Dietary intake of carotenoids and their antioxidant and anti-inflammatory effects in cardiovascular care[END_REF][START_REF] Karn | Potential role of Citrus Carotenoids on Human Health[END_REF]). Among the major carotenoids identified in citrus, the pro-vitamin A carotenoids mainly βcx and βc have a primordial role for human health, especially for eyesight, growth, development and immune response [START_REF] Burri | Beta-cryptoxanthin as a source of vitamin A[END_REF]. Moreover, in vivo, animal and human studies have showed that βcx plays an important role in bone homeostasis (Yamaguchi, 2012). Lyc, another carotenoid found in pink grapefruits has attracted much interest with regard to health benefits mainly for its role in antioxidative, anti-atherogenic and anticarcinogenic activities (Camara et al., 2013). Citrus juices are part of healthy diet and contribute to a healthy lifestyle. European guidelines (NHS National Health Service, PNNS Plan National Nutrition et Santé) recommends a maximum of one glass of 150-200 mL of fruit juice daily as part of the 5 fruits and vegetable a day campaign [START_REF] Braesco | Jus de fruits et nectars[END_REF]. This recommendation is in line with limiting the intake of free sugars recently reduced to less than 5% of total daily energy intake (25g) (WHO, 2015). Knowing that a glass of 250 mL of 100% orange juice contains 20 g of sugars, it would be preferential to consume high fibers foods that promote reduced sugar absorption [START_REF] Silva | Fiber intake and glycemic control in patients with type 2 diabetes mellitus: a systematic review with meta-analysis of randomized controlled trials[END_REF]. Thus, citrusbased products enriched in nutrients of interest with less or no sugars could meet consumer demands for food offering health benefits and provide an alternative to regular citrus juice consumption.

Crossflow microfiltration (CMF) can be used to produce new citrus based products especially enriched in phytochemicals such as carotenoids and certain flavonoids as well as in pectin without heating [START_REF] Polidori | Crossflow microfiltration coupled with diafiltration to concentrate and purify carotenoids and flavonoids from citrus juices[END_REF][START_REF] Gence | Pectin structure and particle size modify carotenoid bioaccessibility and uptake by Caco-2 cells in citrus juices vs. concentrates[END_REF]. This membrane process mainly used to clarify or to stabilize fruit juices was used to concentrate insoluble phytochemicals. Carotenoids and flavonoids are often retained by the porous membrane and thereby concentrated in the retentate. Moreover, the process can be used to modulate and control the concentration in bioactive compounds as well as the proportion between insoluble and soluble solids such as sugars in the concentrate depending on the objective. Indeed, a diafiltration step can be added to a microfiltration step in order to remove soluble compounds especially sugars, for health benefits purposes. This step is used in industrial processing for example to reduce bitterness (grapefruit juice) associated to such as Nar and limonoids in order to make a product more desirable by consumers [START_REF] Ilame | Application of Membrane Separation in Fruit and Vegetable Juice Processing: A Review[END_REF]. Therefore it is of great interest to focus on the advantage of concentrating bioactive compounds (carotenoids and flavonoids) as well as on removing a high part of sugars.

The aim of this work was to modulate the nutritional quality of citrus-based products obtained by crossflow microfiltration (CMF). These citrus-based products can be considered as potential functional foods because they can be enriched in carotenoids, flavonoids, pectins and possibly made with or without sugar. In order to better know their nutritional quality before carrying out a detailed nutrition-health study, two products were obtained with or without a diafiltration step allowing the sugar content to vary. They were characterized through their bioactive compounds (βcx, βc, Lyc, Hes, Nar, and Nat) and pectin content. The impact of the membrane process was evaluated on bioactive compounds by pointing out the correlations with physico-chemical properties of the citrus-based food. Finally, a simple predictive model was proposed in order to forecast composition profiles as a function of operating conditions.

Materials and methods

2.1.Citrus juices

Commercial flash-pasteurized 100% pure clementine (Citrus clementina Hort. Ex. Tan) and pink grapefruit (Citrus paradisi Macf.) juices were purchased from a local food supplier (Carrefour, Montpellier, France). Juices were kept at 4°C between 4 and 5 days until processing. Then, the initial citrus juices were formulated by mixing 60/40% clementine juice/pink grapefruit juices (v/v) using juices from 4 different 15 L batches.

2.2.Crossflow microfiltration process

The process of crossflow microfiltration (CMF) was performed at laboratory scale using a TIA device (Bollène, France) already described in details by [START_REF] Polidori | Crossflow microfiltration coupled with diafiltration to concentrate and purify carotenoids and flavonoids from citrus juices[END_REF]. The system was equipped with a 3 L feed tank, a positive-displacement Moineau pump that allowed to feed the 1 L circulation loop under pressure at high velocity and 4 Pall-Exekia ceramic tubular membranes (Bazet, France) of 0.2 μm average pore diameter and 55 cm 2 filtering area each. Two concentrates were obtained by recovering the retentate up to a mass reduction ratio MRR (Eq. 1) between 8 and 9 with or without a final diafiltration step.

= +

(1)

With mp, mass of permeate (kg), and mr mass of retentate (kg).

During the concentration process, the mass of retentate was maintained constant in the circuit by adding the same mass of fresh juice into the feeding tank to compensate the extracted permeate. The concentration factor of the compound i (CFi ) in the retentate was calculated using Eq. 2.

= (2)

with Ci, final concentration of compound i in the retentate and Ci0, initial concentration of compound i in the feed.

The diafitration step was carried out at the end of the concentration phase without modifying the filtration conditions. It consisted in adding distilled water to the system in order to remove the water soluble compounds. The addition of distilled water meant that the mass of retentate remained constant by compensating the mass of extracted permeate up to a diamass ratio DMR of 1 (Eq. 3). From the initial and final purities of the retained compound i calculated on the basis of total dry matter content (TDM), pi and pi0 (Eq. 4), the purification factor of the compound i, PFi was calculated according to Eq. 5.

= (3)

with mw, mass of added water (kg) and mr, mass of retentate (kg).

= (4) = (5)
The citrus concentrate obtained by microfiltration without a diafiltration step was labelled (DF0) and the concentrate from microfiltration coupled with diafiltration up to DMR 1 was labelled (DF1). These concentrates were stored in amber sealed bottles under nitrogen and kept frozen (-20°C) until physico-chemical and biochemical analyses. Assuming retentions Ri (Eq. 6) are constant, mass balances are correct (no losses), the retentate compartment is perfectly stirred and changes in product density during the process can be neglected (density differences below 3.10 -2 kg L -1 ), CFi in the retentate can be evaluated thanks to the Eq. 7 from MRR and DMR [START_REF] Polidori | Crossflow microfiltration coupled with diafiltration to concentrate and purify carotenoids and flavonoids from citrus juices[END_REF].

= 1 - (6)
with Cip and Cir, the concentrations of the compound i in the permeate and the retentate respectively.

= ( ) (7)
The purification factor of the compound i compared to TDM can then be expressed as Eq. 8.

= (8)

Macroanalyses and physical characterization

Total soluble solids (TSS) were measured with a digital refractometer Pal3 Pocket Atago (Tokyo, Japan) at 25°C and total dry matter (TDM) was measured by drying 2.0 g of sample in an oven at 70°C under vacuum (100 mbar) for 24 h. pH was assessed using TitroLine pHmeter (Schott instruments, Mainz, Germany) at 20°C. Titratable acidity (TA) was measured with the same equipment, by titration with 0.1 mol•L -1 NaOH solution. Suspended insoluble solids (SIS) were determined by centrifugation at 3000 x g for 20 min [START_REF] Gence | Pectin structure and particle size modify carotenoid bioaccessibility and uptake by Caco-2 cells in citrus juices vs. concentrates[END_REF]. The rheological analyses were measured using a constrained strain Physica MCR301 rheometer (Anton Paar GmbH, Graz, Austria). The experimental results were analysed by the apparent viscosity representation η (mPa•s) as a function of shear rate. Rheological measurements allowed the calculation of a flow index in order to determine whether the samples rheofluidifyed, rheo-thickened, or were Newtonian by the classical power law.

Particle size was determined according to [START_REF] Gence | Pectin structure and particle size modify carotenoid bioaccessibility and uptake by Caco-2 cells in citrus juices vs. concentrates[END_REF] coordinates obtained, the hue angle (h*) and color difference from the initial juice (ΔE*) were also calculated

Macronutrients analysis

Simple soluble sugars were analyzed by HPLC according to [START_REF] Gies | Incorporation and stability of carotenoids in a functional fermented maize yogurt-like product containing phytosterols[END_REF]. Briefly, 2 g of sample was twice extracted with 8 mL ethanol (80%), then the mixture was heated at 80°C for 10 min. After homogenization and centrifugation (5000 x g, 10 min, 10°C, Beckman Coulter, USA), the supernatant was filtered through a 0.45 µm membrane before injection in UPLC. Samples were analyzed using an UPLC -1290

System Infinity II (Agilent, USA) equipped with a refractometer detector. A SHODEX SH1011 column 300x8 mm (Tokyo, Japan) was used with an isocratic system of water with H2SO4 (0.01 %) and a flow rate of 0.7 mL‧min -1 . Temperature was set at 30°C, injection volume at 10 µL and spectrophotometric detection at 210 and 245 nm. External calibration was established for each standard sugar for concentrations from 0 to 10 g•L -1 . The pectin content is determined from alcohol-insoluble residue (AIR) and then extracted in acidified water, that was adjusted to pH 1.5 with nitric acid prior to acetone precipitation and drying according to the method reported by De Roeck, Mols, Duvetter, Van Loey, & Hendrickx (2010).

Carotenoid analysis

Carotenoids extraction was carried out in triplicate according to [START_REF] Gies | Incorporation and stability of carotenoids in a functional fermented maize yogurt-like product containing phytosterols[END_REF]. A quantity of 2 g of juice, or 0.5 g of concentrate with 0.5 mL distilled water added, was weighed in a glass tube, mixed with 2 mL of pyrogallol 1% in ethanol and was homogenized 30 s on a vortex. Then the tube was placed for 3 min in a water-bath at 70°C. After cooling, 2 mL of 12 mol•L -1 KOH was added and the tube was set in a water-bath 30 min at 70°C for saponification. After cooling in an ice-bath, 2 mL of distilled water was added, in order to help for phase shifting. Then, samples were extracted twice with 5 mL of n-hexane. The organic phases were pooled and evaporated under nitrogen. The residue was dissolved in 500 µL of CH2Cl2 and 500 µL of MTBE/MeOH (4:1, v/v), transferred to an amber vial before injection into the HPLC system.

Carotenoids were analyzed by HPLC using the Agilent 1100 system (Agilent, Massy, France) with a diode array detector. Carotenoids were separated along a C30 column 250 x 4.6 mm i.d.,5 µm (YMC, Tokyo, Japan). The mobile phases were H2O as eluent A, methanol as eluent B, and MTBE (methyl-tert-butyl-ether) as eluent C with the gradient used by [START_REF] Poulaert | Grapefruit Juices Impair the Bioaccessibility of β-Carotene from Orange-Fleshed Sweet Potato but Not Its Intestinal Uptake by Caco-2 Cells[END_REF]. The flow rate was fixed at 1 mL•min -1 . The column temperature was set at 25°C and the injection volume was 20 µL. The absorbance was measured at 470 and 450 nm. Chromatographic data and UV-Visible spectra were treated using the Agilent Chemstation Plus software. Quantification of carotenoids was achieved using calibration curves with 5 concentration levels from 2 to 15 mg•L -1 for the βc standard, from 10 to 40 mg•L -1 for βcx and from 7 to 50 for Lyc.

Flavanone glycoside analysis

The flavanone glycosides hesperidin (Hes), naringin (Nar) and narirutin (Nat) were determined according to the method described in Dhuique-Mayer et al. (2005). Briefly, 5 g of juice or 1 g of concentrate were extracted with 10 mL dimethylformamide and 10 mL ammonium oxalate 0.05 mol‧L -1 (1:1 v/v) in tightly Pyrex tube. Then, the tubes were heated in an oil bath at 90°C for 10 min. After cooling, the volume were adjusted to 50 mL with distilled water. After centrifugation, the supernatant was filtered through a 0.45 µm membrane and analyzed by HPLC-Agilent 1100 system (Agilent, Massy, France). The isocratic solvent system was made of water/acetonitrile/THF/acetic acid (80:16:3:1, v/v/v/v).

Quantification was carried out at 280 nm. The flow rate was fixed at 1 mL•min -1 and the injection volume was 20 µL. Flavanone glycoside concentrations were determined using an external calibration method. Standard solutions of Hes, Nat and Nar were diluted in DMF/water (2:1, v/v) to reach maximum concentration of 151 and 158 and 160 mg•L -1 respectively.

Statistical analysis

All statistical analyses were performed using XLSTAT software version 2019.4.1 (Addinsoft, Paris, France). All data were reported as mean and standard deviation from 3 replicates of each experiment. Data were analyzed statistically using one-way analysis of variance (ANOVA) in order to determine significant differences (p < 0.05). Tukey's multiple comparison method was used to further examine any significant difference between results.

Results and discussion

Nutritional quality of the initial citrus juices

The initial citrus juice was formulated with 60/40% C. clementina / C. paradisi juices in order to optimize carotenoid and flavonoid profile. Three main carotenoids were found in this initial citrus juice: βcx and βc, the pro-vitamin A carotenoids coming from clementine juice and lycopene, the well-known antioxidant carotenoid representing the major carotenoid in pink grapefruit juice. Lyc was the major carotenoid of this formulated juice for lots A and B (4.47 mg‧kg -1 ) followed by βcx (2.68 mg‧kg -1 ) and βc (1.08 mg‧kg -1 ) (Table 1). The main flavanone glycosides identified in this initial citrus juice was Hes related to clementine juice and displaying the highest concentration (376.2 mg‧kg -1 ). Nat was the minor flavanone glycoside from clementine juice with a content 5 times lower than Hes (71.5 mg‧kg -1 ). Finally, Nar was the main flavanone from pink grapefruit (259.6 mg‧kg -1 ). Together, these bioactive compounds of nutritional interest with pectin and sugars contained in initial juices (Table 2) can be concentrated or modulated in a same functional citrus-based product by CMF. Note that citrus juices from lot C and D had lower levels of βcx and Hes presenting a less interesting nutritional profiles (Table 1).

Crossflow microfiltration process

The permeate flux (Jp) decreased (30%) with the MRR (between 1 and 9) for both concentrates (DF0 and DF1) to reach a value between 30 and 40 kg‧h -1 ‧m -2 at MRR of 8-9, with a sudden drop (MRR of 1 to 3) and then with a pseudo-stabilization from 4 to 9 MRR (Figure . 1). This typical behavior is mainly associated with the increase of the viscosity and of the fouling power of the retentate during concentration, which contributes to decreasing the permeability of the filtration system [START_REF] Jesus | Orange (Citrus sinensis) juice concentration by reverse osmosis[END_REF]. The permeate flux was quite similar to that obtained by [START_REF] Polidori | Crossflow microfiltration coupled with diafiltration to concentrate and purify carotenoids and flavonoids from citrus juices[END_REF] during concentration of different orange juices (from 20 to 80 L‧h -1‧ m -2 ). For DF1 concentrate, Jp increased a little during the diafiltration step from 30 to 40 L‧h -1‧ m -2 . This could probably be explained by the decrease in viscosity of the permeate due to the solute dilution by adding distilled water. These results showed good repeatability for the flux at high MRR (variation coefficient between 6-15%) except for lot D.

Conversely, flux was less repeatable at low MRR and this was probably due to the different batches or to slight temperature variation between filtration trials.

Effect of CMF on physical properties and main constituents of citrus concentrates

The physical characteristics as well as pectin and sugar contents of initial citrus juices and both concentrates are reported in Table 2. The viscosity of concentrates increased comparatively with juices because the membrane process concentrated insoluble solids and pectin almost 10 times [START_REF] Cho | Concentration and purification of soluble pectin from mandarin peels using crossflow microfiltration system[END_REF]. The progressive decrease of soluble compounds (e.g. decrease of 67% of sugars), due to the addition of water during the diafiltration step. explained the final lower viscosity (p < 0.05) of DF1 compared with DF0.

Particle size distribution indicated that both concentrates were very close to each other (Figure 2). CMF reduced the size of the particles (40%) and this agreed with previous studies carried out on fruit juice and orange juice [START_REF] Dahdouh | Sizecartography of orange juices foulant particles: Contribution to a better control of fouling during microfiltration[END_REF]Sentandreu, Gurrea, Betoret, & Navarro, 2011). [START_REF] Gence | Pectin structure and particle size modify carotenoid bioaccessibility and uptake by Caco-2 cells in citrus juices vs. concentrates[END_REF] also reported that the membrane process led to the mechanical disruption of particles by high shear-rate in the circulation loop. The pulp content or suspended insoluble solids (SIS), which represented a small mass fraction of the TDM, was higher for DF0 than DF1 and was correlated to turbidity (Tamba, Servent, Mertz, Cisse, & Dornier, 2019). The higher pulp content in DF0 was due to retention of insoluble solids of initial juice because DF0 had a higher MRR (MRR = 9) than DF1 (MRR= 8). [START_REF] Dahdouh | Sizecartography of orange juices foulant particles: Contribution to a better control of fouling during microfiltration[END_REF] showed that there was a relationship between turbidity and SIS content for fruit juices.

Total dry matter (TDM), total soluble solids (TSS), titrable acidity, as well as sugars were lower for DF1 compared to DF0. The cause of this significant difference (p < 0.

Effect of CMF on carotenoids and flavonoids

Similar effects of CMF on carotenoids and flavonoids were observed whatever the lot of initial juice even if the carotenoids/flavonoids profiles of juices C and D were slightly less nutrionnally pertinent in term of composition in bioactive compounds. The two types of carotenoids xanthophylls and carotenes of which βcx, βc and Lyc, were similarly concentrated by approximately 9-fold, the corresponding concentration being 25.9 mg‧kg -1 ; 10.5 mg‧kg -1 and 47.2 mg‧kg -1 respectively in average for lot A and B. This unique profile made the citrus-based product nutritionally interesting because no vegetables nor fruits were equivalent to these carotenoids levels and profile. Among fruit rich in βcx, butternut squash represents the higher content with 34.7 mg‧kg -1 but all the others ranged from 1.16 to 13.4

mg‧kg -1 [START_REF] Burri | Absorption, metabolism, and functions of betacryptoxanthin[END_REF]. Lycopene from fresh tomato displayed a content of 17.4 mg‧kg -1 [START_REF] Karakaya | Lycopene content and antioxidant activity of fresh and processed tomatoes and in vitro bioavailability of lycopene[END_REF]. Pink grapefruit juices, considered rich in Lyc and βc, displayed a content of 13.4 mg‧kg -1 and 3.8 mg‧kg -1 respectively [START_REF] Achir | Pasteurization of citrus juices with ohmic heating to preserve the carotenoid profile[END_REF].

Moreover, Hes the more hydrophobic flavanone glycoside was also concentrated 8.5-fold

showing that this compound, like carotenoids, was completely retained by the membrane.

Conversely, Nat and Nar were either incompletely or not retained at all by the membrane and were recovered in permeate fraction. Their concentration factor ranged from 1.3 to 2.8 respectively for Nar and Nat. These results were consistent with previous work on CMF of citrus juices where Nat was less retained by membranes [START_REF] Polidori | Crossflow microfiltration coupled with diafiltration to concentrate and purify carotenoids and flavonoids from citrus juices[END_REF]. The different solubility of the major flavanone glycosides (0.02 g‧L -1 for Hes and 0.6 g‧L -1 for Nar) can explain their different behaviors. Probably the number, localization and nature of the substituents on the flavonoid skeleton, as well as the conformation of bound glucosides greatly influenced their solubility. Carotenoids and Hes were associated with the insoluble fraction, and their concentration factors are approximately the same (and very close to MRR) than those reported by [START_REF] Gence | Pectin structure and particle size modify carotenoid bioaccessibility and uptake by Caco-2 cells in citrus juices vs. concentrates[END_REF] or [START_REF] Polidori | Crossflow microfiltration coupled with diafiltration to concentrate and purify carotenoids and flavonoids from citrus juices[END_REF]. Adding a diafiltration step to crossflow microfiltration helped to better purify the bioactive compounds. Carotenoids and Hes were purified from 12 to 16-fold whereas Nat was purified only 3 times and Nar almost not in accordance with the much lower retention of these last two flavonoids.

Correlations between physico-chemical characteristics and bioactive compounds

Principal component analysis (PCA) was used to differentiate the two citrus concentrates based on nutritional and physico-chemical criteria (Figure 3). The two concentrates were quite distinct from each other and from their initial juice. The main information was explained by axis F1 (69%). Strong correlations (Pearson) were observed between carotenoids (βcx/ Lyc) and colour (0.996), flavonoids (Hes) (0.996), turbidity, viscosity, pulp and pectin (0.967, 0.987, 0.978, and 0.994). These correlations were explained by the fact that carotenoids and flavonoids were hydrophobic molecules (except Nar, the only flavonoid not retained by the membrane) bound to the pulp which lead to a higher viscosity and turbidity as well as a darker color of the concentrates compared to the initial juices. Opposite and negative correlations were observed for the hydrosoluble fraction mainly sugars and Nar and for granulometry.

These characteristics corresponded to the initial juices group.

Retention evaluation and modelling

The retentions of all the compounds Ri were evaluated in both concentrates from the measured concentration factors rearranging Eq. 7 to obtain Eq. 12.

= !" # $%&' !" &''$%&' (12)
As expected, on one hand the retentions of carotenoids, hesperidin and SIS were complete with Ri close to 1. The retention of pectins was very high but a small amount of these compounds passed through the membrane, probably their soluble fraction (Ri = 0.96). On the other hand, sugars and organic acids were not retained by the membrane (Ri ≈ 0). The retention of Nat was intermediate (Ri = 0.47) and only 0.09 for Nar. These results are in accordance with [START_REF] Polidori | Crossflow microfiltration coupled with diafiltration to concentrate and purify carotenoids and flavonoids from citrus juices[END_REF] who observed 97% retention for hesperidin and 63%

for Nat during the microfiltration of orange juice in similar conditions. Refractometric measurements showed 15% retention of TSS indicating one part of the soluble fraction was stopped when crossing the porous media, probably by adsorption. Nevertheless, this assumption has to be confirmed through more in depth investigations of the pool of solutes.

TDM was logically retained at 17%, this indicator combining TSS and SIS.

As shown in Figure 4 that compares experimental and calculated concentration and purification factors, model accuracy was good in many cases (coefficient of variation below 15%), except for some carotenoids, especially lycopene, in the concentrates obtained with diafiltration. For this carotenoid, the model underestimated both factors. This gap was possibly explained by isomerizations which influenced the response factor in the quantitative analysis of this carotenoid.

In spite of this shortcoming, the model can reasonably be used to predict the compositional profile of final concentrates that could be obtained using other mass reduction and diamass ratios. As an example, Figure 5 can be generated to compare carotenoid, flavonoid and macrosolute profiles of an initial juice with those of concentrates obtained using different MRR (from 8 to 12) and DMR (from 0 to 3). As expected, varying MRR allows to control carotenoids, hesperidine and pectin contents whereas DMR mainly allows to modulate total soluble solids (sugars), titratable acidity and also naringine/narirutine concentrations. So this model can be considered as an interesting simulation tool for selecting operating conditions to be used in order to reach a composition profile target.

Conclusion

In summary, this study investigated the possibility of modulating the nutritional properties of a potential functional citrus-based food obtained by membrane technology. The two citrusbased foods were enriched in bioactive compounds such as carotenoids, as well as some flavonoids and pectins but were differentiated by sugar/acid contents. Provitamin A carotenoids, Lyc, Hes and pectins were approximatively cold-concentrated from 8 to 10-fold giving a unique interesting profile to the citrus products. The originality of the product lays in the fact that the high content of bioactive compounds, which is comparable to natural food products, is naturally incorporated in the food matrix. This specific product could be consumed directly as a healthy citrus based-food. Moreover, diafiltered concentrate can be of interest if the product is recommended as part of a reduced sugar diet for diabetic people for instance. By modelling the retention of bioactive compounds, we showed that it was possible and easy to modulate sugar and flavonoid contents in the concentrate that could be a crucial issue for its biological activity. Likewise, carotenoids and pectins contents could be regulated in the same way. Further studies are necessary to validate in vivo the functionality of the product in order to confirm a potential beneficial protective effect against several lifestylerelated-diseases and especially diabetes.

  by LASER diffraction using a Mastersizer 3000 (Malvern Instruments Limited, Worcestershire, UK). The statistical diameter Dx 50 which corresponds to the diameter for which 50% of particle volume of the suspension has a diameter less than the value indicated, as well as the surface area mean diameter (D [3,2]) were derived from the measured distribution. Turbidity was measured using a Hanna LP 2000 turbidimeter (Hanna Instruments, Woonsocket, USA). The color was determined using a chromameter CR-410 (Minolta, Tokyo, Japan). From the CIE (L*, a*, b*)

  05) was mainly due to the elimination of the soluble fraction in permeate during the diafiltration step. Sugars constituted the majority of TDM in the initial juice and the diafiltration led 73% of TSS in DF1 being removed, of which 67% were soluble sugars. CMF membranes only retain the insoluble fraction. Solutes are logically not retained by the membrane because of their low molar mass between 180 and 192 g‧mol -1 (Tamba et al , 2019). All concentrates presented a bright orange color, which was due to the concentration of carotenoids by the membrane process. Only a slight difference was observed for the color parameter (L* and b*) indicating that DF1 was slightly darker than DF0 probably caused by the diafiltration step which increased the purity of all carotenoids, making the product darker.

Figure captions Figure 1 :

 captions1 Figure captions

Figure 2 :

 2 Figure 2: Particle size distribution in the initial juices (lot A and lot B) and their respective concentrates (DF0 and DF1).

Figure 3 :

 3 Figure 3: (A) Results of applying PCA to the data related to the nutritional composition and physico-chemical properties and (B) differentiation using PCA of citrus products.

Figure 4 :

 4 Figure 4: Comparison between experimental and calculated concentration and purification factors for the different compounds analyzed in concentrates without diafiltration (DF0) and with diafiltration (DF1).

Figure 5 :

 5 Figure 5: Forecasted impact of the mass reduction and diamass ratios (MRR and DMR) used during the microfiltration of a citrus juice on the profiles of carotenoids, flavonoids and macrosolutes in the final concentrate.

  Figure 1.

Table 1 :

 1 Carotenoid and flavonoid contents, purity of citrus juice and concentrates (without diafiltration DF0 and with diafiltration DF1) and concentration/purification factors (CF, PF) Different letters on the same line indicate significant differences (p < 0.05).

	Operating Conditions	Concentration (MRR = 9.2 ; DMR = 0 ; 30°C)		Concentration and purification (MRR = 7.9 ; DMR = 1 ; 34°C)
		Initial						Initial
		juice Lot A	Purity	DF0 Content	Purity	CF	PF	juice Lot B	Purity	DF1 Content	Purity	CF	PF
		Content						Content
	Carotenoids
	(mg‧kg -1 )
	βcx	2.48	22.4	23.63 159.8 9.54 7.13	2.88	27.7		28.29	338.1	9.82 12.21
		(0.14) c (1.6) (0.52) b (5.3)			(0.08) c (0.8)		(0.46) a	(7.4)
	βc	1.03	9. 3	9.42	63.8 9.17 6.86	1.13	10.9		11.52	137.7	10.2 12.69
		(0.06) c (0.6) (0.25) b (2.4)			(0.03) c (0.4)		(0.12) a	(1.2)
	Lyc	4.45	40.6	42.80 289.8 9.70 7.19	4.50	43.3		51.74	625.4	11.6 14.29
		(0.12) b (0.8) (0.90) a (7.6)			(0.20) b (2.1)		(2.21) a	(23.3)
	Flavonoids
	(mg‧kg -1 )
	Nat	74.3	669	198	1337 2.67 1.99	68.9	662		174	2084	2.53 3.15
		(0.6) c	(8)	(2) a	(30)			(1.3) d	(14)		(1) b	(15)
	Hes	384.6	3476	3180 21518 8.27 6.19	367.9	3537		3431	41005	9.33 11.61
		(1.6) c	(62)	(18) b	(370)			(3.9) c	(33)		(16) a	(364)
	Nar	265.4	2399	339	2296 1.27 0.96	253.8	2440		122.1	1455	0.48 0.60
		(2.6) b	(46)	(2) a	(43)			(5.7) b (48)		(0.1) c	(624)
	Operating Conditions	Concentration (MRR = 7.9 ; DMR = 0 ; 31°C)		Concentration and purification (MRR = 7.7 ; DMR = 1 ; 39°C)
		Initial						Initial
		juice Lot C	Purity	DF0 Content Purity	CF	PF	juice Lot D	Purity		DF1 Content Purity	CF	PF
		Content						Content
	Carotenoids
	(mg‧kg -1 )
	βcx	2.08	18.6	17.69	126.3 8.51 6.77	1.52	13.6		14.99	206.2	9.85 15.12
		(0.11) c	(0.9)	(0.30) a	(2.0)			(0.04) d	(0.4) (0.15) b	(3.1)
	βc	1.85	16.6	15.44	110.3 8.35 6.65	1.34	12.0		13.59	186.8	10.10 15.52
		(0.05) c	(0.4)	(0.29) a	(2.1)			(0.03) d	(0.3) (0.14) b	(2.2)
	Lyc	5.57	49.9	49.03	350.1 8.80 7.01	4.16	37.3		44.74	615.4	10.80 16.50
		(0.07) c	(0.2)	(1.16) a	(8.3)			(0.15) c	(1.4) (1.46) b	(26.6)
	Flavonoids
	(mg‧kg -1 )
	Nat	64.8	581	133	951	2.06 1.64	60.5	542		89	1222	1.47	2.25
		(2.4) c	(19)	(3) a	(24)			(0.4) c	(5)		(2) b	(18)
	Hes	244.6	2193	1884	13454 7.70 6.14	263.5	2360	1864	25635	7.07 10.85
		(3.2) b	(26)	(16) a	(127)			(2.5) b	(28)		(11) a	(464)
	Nar	246.5	2210	287	2049 1.17 0.93	251.3	2250	113	1554	0.45	0.68
		(9.7) b	(97)	(5) a	(43)			(2.4) b	(18)		(18) c	(262)

Table 2 :

 2 Physico-chemical characteristics and macronutrient content of citrus juice and concentrates

	Treatment and operating	Concentration		Concentration / diafiltration
	condition	MRR = 9.19 / DMR = 0	MRR = 7.88 / DMR = 1
	Raw material	Initial juice (Lot A)	Concentrate DF0	Initial juice (Lot B)	Concentrate DF1
	Rheological measures
	Flow index	0.29 (0.02) c	0.36 (0.01) b	0.31 (0.01) c	0.41 (0.01) a
	Consistency index	326.23 (59.22) c	5060.8 (104.6) a	303.59(24.02) c 3484.9 (24.22) b
	Limit viscosity at 1000 s -1
	(mPa.s)	3.46 (0.15) c	71.57 (0.68) a	2.55 (0.23) c	67.53 (0.5) b
	Granulometry
	D [3,2] (µm)	98.09 (0.45) b	42.05 (1.07) d	123.94 (2.54) a	48.5 (0.43) c
	Dx (50) (µm)	750.9 (11.5) b	139.9 (0.5) c	1105.7 (20.8) a	109.2 (0.6) c
	Colour
	L*	49.04 (0.51) c	56.3 (0.09) b	-	57.67 (0.18) a
	a*	4.28 (0.01) b	17.59 (1.81) a	-	17.43(0.03) a
	b*	40.35 (0.34) c	53.43 (0.27) b	-	55.48 (0.17) a
	h*	83.93 (0.07) c	71.79 (1.7) b	-	72.55 (0.03) a
	(E		20.06 (1.16) b		21.82 (0.27) a
	TDM (g.kg -1 )	110.66 (2.08) b	147.83 (1.76) a	104 (0.30) c	83.69 (0.47) d
	TSS (g.kg -1 )	106.0 (0. 3) b	140.7 (0.6) a	107.3 (0.6) b	67.0 (1) c
	TA (g.kg-1 )	8.69 (0.10) a	7.15 (0.34) b	9.24 (0.15) a	5.52 (1.02) c
	pH	3.31 (0.02) b	3.24 (0.18) b	3.59 (0.02) a	3.67 (0.06) a
	SIS (g.kg -1 )	3.78 (0.09) c	34.5 (0.83) a	3.39 (0.17) c	31.7 (0.33) b
	Turbidity (NTU)	2326 (46) c	17697 (356) a	2106 (11) c	15386 (215) b
	Pectins (g.kg -1 )	0.66 (0.02) c	5.50 (0.40) b	-	7.43 (0.35) a
	Sugars (g.kg -1 )
	Glucose	23.0 (0.6) a	21.8 (1.1) a	-	7.3 (0.1) b
	Fructose	23.5 (0.7) a	22.8 (0.5) a	-	7.9 (0.1) b
	Sucrose	52.6 (1.5) a	56.4 (2.6) a	-	19.0 (0.2) b

orange juice characteristics due to homogeneization and centrifugation. Journal of Food Engineering, 105, 241-245. Tamba, A., Servent, A., Mertz, C., Cissé, M., & Dornier, M. (2019)