Flavia Maurice

Anne Dutour

Clara Vincentelli

Ines Abdesselam

Monique Bernard

Henry Dufour

Yann Le Fur

Thomas Graillon

Frank Kober

Y Lefur

P Cristofari

E Jouve

L Pini

R Fernandez

C Chagnaud

T Brue

F Castinetti

Dr Benedicte Gaborit
email: benedicte.gaborit@ap-hm.fr

Active cushing syndrome patients have increased ectopic fat deposition and bone marrow fat content compared to cured patients and healthy subjects: a pilot 1H-MRS study

Keywords: Glucocorticoids, adverse effects -Cushing Syndrome, complications -Bone marrow fat -Adipose tissue, metabolism -Osteoporosis

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

Introduction

Chronic Glucocorticoid (GC) excess is the most frequent etiology of secondary bone loss [START_REF] Tóth | Glucocorticoid-induced osteoporosis: lessons from Cushing's syndrome[END_REF]. It induces severe bone loss via multiple and incompletely understood mechanisms [START_REF] Canalis | Glucocorticoid-induced osteoporosis: pathophysiology and therapy. Osteoporosis international: a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA[END_REF]. Indeed, GC have direct effects on bone. They impair the replication, differentiation and functions of osteoblasts, induce apoptosis of mature osteoblasts and osteocytes, and promote osteoclastogenesis. GC also have indirect effects that lead to bone loss through interference with both calcium metabolism and secretion of hormones, such as growth hormone and sex steroids. Cushing's syndrome (CS) is an interesting clinical model of endogenous GC excess. Compared to patients treated with GC, there are no confounding factors due to the underlying primary disease. CS induces major bone disorder, which is an important factor among various disease comorbidities [START_REF] Brue | The risks of overlooking the diagnosis of secreting pituitary adenomas[END_REF]. Identifying patients with increased fracture risk is challenging because of the great inter-individual variability in bone defects and because Dual-energy X-ray absorptiometry (DXA) measurements are not sufficient to predict fracture risk. Furthermore, after correction of hypercortisolism, a discordance between bone mineral density (BMD) and the risk of fracture was evidenced [START_REF] Somma | Effect of 2 years of cortisol normalization on the impaired bone mass and turnover in adolescent and adult patients with Cushing's disease: a prospective study[END_REF][START_REF] Hermus | Bone mineral density and bone turnover before and after surgical cure of Cushing's syndrome[END_REF].

Bone marrow fat (BMF), which is a unique and dynamic fat depot, has been suggested to play a pivotal role in bone metabolism [START_REF] Hardouin | Bone marrow fat[END_REF]. Sharing the same precursor in the bone marrow, mesenchymal stromal cells, osteoblasts and adipocytes have a reciprocal relationship in differentiation and function that drives bone integrity. Many studies have found that changes in BMF volume correlate with reduced BMD as well as a history of low-energy fractures in patients with osteoporosis or aging [START_REF] Griffith | Vertebral bone mineral density, marrow perfusion, and fat content in healthy men and men with osteoporosis: dynamic contrast-enhanced MR imaging and MR spectroscopy[END_REF][START_REF] Schwartz | Vertebral bone marrow fat associated with lower trabecular BMD and prevalent vertebral fracture in older adults[END_REF]. Increased BMF was also found in patients with metabolic diseases, such as obesity [START_REF] Bredella | Vertebral bone marrow fat is positively associated with visceral fat and inversely associated with IGF-1 in obese women[END_REF][START_REF] Schafer | Changes in vertebral bone marrow fat and bone mass after gastric bypass surgery: A pilot study[END_REF], diabetes mellitus [START_REF] Baum | Does vertebral bone marrow fat content correlate with abdominal adipose tissue, lumbar spine bone mineral density, and blood biomarkers in women with type 2 diabetes mellitus? Journal of magnetic resonance imaging[END_REF] and anorexia nervosa [START_REF] Bredella | Increased bone marrow fat in anorexia nervosa[END_REF].

Recent developments in magnetic resonance imaging with 1 H-spectroscopy ( 1 H-MRS) allow for direct and sensitive non-invasive quantification of BMF. GC are known to modulate adipose tissue proliferation and differentiation as well as induce a specific redistribution of body fat. However, the impact of GC on BMF is unclear. Only one study [START_REF] Geer | Body composition and cardiovascular risk markers after remission of Cushing's disease: a prospective study using whole-body MRI[END_REF] evaluated BMF changes with magnetic resonance imaging (MRI) using manual segmentation of fat after remission of Cushing's disease and showed discordant results with a modulation of pelvic BMF but no modulation of total BMF. Therefore, the purpose of this study was to evaluate BMF by 1 H-MRS in patients in remission (at least 2 years) vs. active ACTH-dependent CS in comparison with age-and sex-matched controls.

Subjects and Methods

A. Patients

Patients with ACTH-dependent CS were prospectively recruited from December 2014 to June 2017 in the Endocrinology and in the Neurosurgery departments of Marseille University Hospital, France. The active group consisted of newly diagnosed patients or patients with uncontrolled disease despite multiple treatments. The remission group included patients who were in remission for at least 2 years, but no more than 6 years, regardless of their treatment modality.

Exclusion criteria included an age below 18 years, pregnancy or breastfeeding, presence of another chronic disease known to affect bone density (renal failure, rheumatoid arthritis, hyperthyroidism, primary hyperparathyroidism, alcoholism, malabsorption syndromes, chronic liver or obstructive pulmonary disease, premature ovarian failure, prolonged immobilization, …), and contraindications for magnetic resonance imaging (MRI). ACTH-dependent CS was diagnosed according to the usual clinical and biological criteria, including: 1) elevated twenty-four-hour urinary free cortisol (UFC) for at least two times; 2) increase of basal plasma cortisol levels with a loss of the circadian pattern and inappropriate unsuppressed plasma ACTH levels; 3) lack of cortisol suppression after a low-dose dexamethasone test (0.5 mg every 6 hours for 48 hours). Patients were considered to be in remission after treatment if they presented either with secondary adrenal insufficiency based on the following criteria: low morning plasma cortisol levels after 24 hours of withdrawal of hydrocortisone or with eucortisolism based on the following criteria: 1) Twenty-four-hours UFC below or within the normal range for at least two times; 2) Basal plasma cortisol levels below or within the normal range with a restoration of physiological circadian pattern and appropriate plasma ACTH levels; 3) cortisol suppression after the overnight 1-mg dexamethasone test or if they were controlled with anti-cortisolic therapy based on the following criteria: twenty-four-hour UFC below or within the normal range at every control during follow-up for at least two years.

B. Control subjects

Control subjects were recruited through advertisements and matched with active patients for age and sex. Exclusion criteria included an age below 18 years, pregnancy or breastfeeding, contraindication for MRI, presence of a chronic disease known to affect bone density as for patients, past or actual chronic treatment with GC or other medication for osteoporosis (bisphosphonates, raloxifene, calcitonin or PTH), metabolic syndrome and a body mass index (BMI) above 25 kg/m -2 .

All the patients and volunteers gave their written informed consent, and the study protocol was

C. Study protocol

1. Clinical assessments.

BMI was calculated for each participant by dividing weight in kilograms by height in squared meters.

We recorded a history of medical conditions for all subjects as well as past and current medications and the duration of uncontrolled CS, which was defined as the period of time between symptoms onset (as determined by the patients) and inclusion in the study for patients with active CS. For the patients in remission, duration of uncontrolled disease was defined as the period of time between symptoms onset and remission of hypercortisolism after treatment.

Biochemical evaluation.

Fasting blood tests for glucose, total cholesterol, LDL-cholesterol, HDL-cholesterol, serum triglyceride, HbA1c, 25-hydroxyvitamin D, calcium, parathyroid hormone and serum C-terminal telopeptide of type I collagen (CTX-1) were taken in all the patients the day of inclusion. Control subjects were asked to perform a blood test with a fasting blood glucose and lipid unless they had one from less than a year.

The results were determined with standard analytical methods. Twenty-four-hour UFC excretion was quantified using a specific radioimmunoassay (reference: IM1841, Beckman Coulter Diagnostics France). Plasma cortisol levels and plasma ACTH levels were measured with an electrochemiluminescent immunoassay (Roche Diagnostics France). CTX-1 was quantified using ELISA assays (cross laps).

1 H-MRS spectroscopy.

All MRI acquisitions were carried out in a 3-Tesla wide-bore magnet (Magnetom Verio, Siemens Healthineers, Erlangen, Germany) equipped with a 32-element phased array coil. The participants were scanned in a head-first supine position. A spectroscopic volume of interest was positioned using a multi-slice FLASH image series with three different orientations (axial, coronal and sagittal), and a point-resolved single-voxel proton spectroscopy (PRESS) sequence was used to determine the molecular content of lipids and water. The parameters of PRESS 1 H-MRS were echo time= 35 ms, repetition time= 1000 ms, receiver bandwidth= 2000 Hz. Non-water-suppressed spectra (16 averages) were acquired to measure fat content. Full-relaxed spectra (1 excitation) were acquired to measure water content. At the lumbar spine, the voxel (voxel size 15x15x15 mm 3 ) was placed within the L3 vertebral body, whereas at the right hip, the voxel (voxel size 10x10x10 mm 3 ) was positioned within the femoral neck (Supplementary Figure 1). Spectral data were analyzed after phase, baseline and frequency shift corrections using a semi-automatic method (AMARES, Advanced Method for Accurate, Robust and Efficient Spectral fitting) implemented under an Interactive Data Language (IDL) environment (Exelis Visual Information Solutions, Inc., Boulder, Colorado, USA). Four peaks could be isolated in bone marrow spectra: unsaturated lipids (UL corresponding to olefinic protons, double bond -CH=CH-) at 5.3 ppm, water (W) at 4.65 ppm, residual lipids (RL corresponding to methylene protons, αto a double bond -CH=CHCH 2 -) at 2.03 ppm and saturated lipids (SL corresponding to bulk methylene protons, -CH 2 -) at 1.3 ppm [START_REF] Paccou | The Role of Bone Marrow Fat in Skeletal Health: Usefulness and Perspectives for Clinicians[END_REF]. We added the peaks fitted at 1.3 ppm and 2.03 ppm to represent one fat peak. It was decided not to include UL in the measurement because it was not always well-resolved. The calculations were performed as follows: BMF content (%) = Ifat/ (Ifat+Iwater) x 100, where I is the peak area under the curve.

One patient in the remission group had a hip prosthesis and therefore did not undergo 1 H-MRS at the femur.

To evaluate inter-scan variability, 1 H -MRS was performed in five volunteers before and after repositioning. The average interscan coefficient of variation (CV) of BMF was 1.93% and 3.55% for vertebrae and femur, respectively. All femoral spectra were of good quality, while vertebral spectra in 4 cases had shimming problems and were unsuitable for analysis.

MRI assessment of abdominal adiposity

A 3D three-point Dixon volume interpolated breath-hold gradient echo sequence (VIBE) was used to acquire fat and water images of the volume between vertebrae L4 and the sacrum. The parameters of the Dixon sequence were TE=2.45/3.67 ms, TR=6.56 ms, receiver bandwidth=530/574 Hz, FOV=450 mm, Matrix size (in 3D)=225x448. Areas of abdominal adipose tissue (AT) compartments were measured with a semi-automatic method at a single axial slice at the intervertebral disc L4-L5 using inhouse software running under IDL [START_REF] Zhou | Comparison of visceral adipose tissue quantification on water suppressed and nonwater-suppressed MRI at 3.0 Tesla[END_REF]. Fascia between superficial and deep subcutaneous adipose tissue was traced manually. Total subcutaneous adipose tissue (TSCAT) was calculated by adding superficial subcutaneous adipose tissue (sSCAT) and deep subcutaneous adipose tissue (dSCAT).

The mean intra-subject CV between five repeated measurements was 3.6% for visceral adipose tissue (VAT), 4.3% for dSCAT and 4.8% for sSCAT. The mean inter-subject CV between two observers of 45 patients was 9.6% for VAT, 7.8% for dSCAT and 8.7% for sSCAT.

Dual-energy X-ray absorptiometry (DXA).

The patients underwent DXA to measure the bone mineral density (BMD) of the whole body, the right hip and the spine (L1-L4) using a GE Lunar iDXA (GE Healthcare, Waukesha, WI).The Coefficient of variation is 0.41% for lumbar spine and 1.36% for femoral neck [START_REF] Hind | In vivo precision of the GE Lunar iDXA densitometer for the measurement of total body composition and fat distribution in adults[END_REF].

D. Statistical analysis

All statistics were performed using Prism (v 7.01) software (GraphPad Software Inc., San Diego, CA, USA). All quantitative results are presented as the means ± standard error of mean (SEM) or median [25 th , 75 th percentile] when the distribution was non-Gaussian. All qualitative results are presented as numbers and percentages. A p value less than 5% was considered to be statistically significant. All qualitative datasets were compared using Fischer's test. All normally distributed quantitative datasets were compared using Student's t-test, and non-normally distributed quantitative datasets were compared using Mann-Whitney. Analyses of covariance (ANCOVA) were performed using patients' group and sex as fixed effect, age, VAT and HbA1c as covariate. Least-square means were calculated (adjusted means) and pairwise comparisons between groups where p-value adjusted using Bonferroni method. Pearson's (Gaussian distribution) or Spearman's (non-Gaussian distribution) correlations were used to evaluate associations between BMF and anthropometrical, biological and bone density parameters. A multiple linear regression analysis was performed with Statview version 5.0 among the variables correlated at the linear correlation. An ANCOVA model under JASP version 0.8.2 was used to adjust BMF to covariates (age, sex, VAT and BMD values).

Results

A. Clinical and biological characteristics

Seventeen patients in each group completed the study (Figure 1). The 3 groups did not differ in age or sex (Table 1). Subjects had a mean age of 51.6 ± 3.4, 48.3 ± 3.0 and 50.3 ± 2.1 years in the active, remission and control groups, respectively. Patients from both the active and remission groups did not differ in duration of uncontrolled disease, and all had comparable plasma midnight ACTH, cortisol levels and twenty-four-hour UFC. Fifteen patients of the active and remission group had Cushing's disease and two had an ectopic source of ACTH. Patients with ectopic CS had shorter duration of uncontrolled CS compared to patients with Cushing disease: 9.5 [2.5-13.5] months versus 25 , p=0.043. Thirteen patients of the active group had newly diagnosed CS, whereas four were uncontrolled despite multiple treatments, and they did not differ for main clinical characteristics. In the remission group, the mean duration of remission was 43 ± 4 months, and the mean duration of hydrocortisone supplementation was 39 ± 4 months. Among the 17 patients in the remission group, 13 had glucocorticoid deficiency at the time of the MRI with a mean hydrocortisone dose of 26.5 ± 1.3 mg/day (full range: 20 to 30 mg/day). One treatment modality was sufficient to achieve remission for eleven patients, whereas for the others, two to three treatments were necessary. The 3 groups did not differ in terms of estrogen deficiency, hormonal replacement therapy (estrogen and/or progestogen) and number of fragility fractures. Patients in the active and the remission groups did not differ with regards to anti-osteoporotic therapy or testosterone deficiency, which was correctly substituted in each case. Current BMI (i.e BMI at the time of inclusion in the study) did not differ between the active (27.11 ± 0.87 kg/m 2 ) and remission (26.62 ± 1.22 kg/m 2 ) groups. BMI at diagnosis (i.e BMI at discovery of CS) was also comparable between the 2 groups. As expected, controls had lower BMI, 22.14 ± 0.71 kg/m 2 , compared to patients (p<0.001). Active patients had higher fasting blood glucose levels and serum triglyceride levels than controls. Patients in the remission group had lower HbA1c and significantly lower fasting blood glucose than their active counterparts. Serum triglyceride levels displayed a tendency to be lower in the remission group compared to the active group, and they were not different from the controls.

B. Abdominal adipose tissue distribution

The mean adipose tissues (AT) areas in each abdominal compartment are shown in Table 2. Active patients had a pathological distribution of abdominal AT with higher VAT and dSCAT/sSCAT ratios than controls (p<0.001 and p=0.013 respectively). Patients in the remission group had decreased VAT compared to active patients, but VAT remained higher than in controls (p<0.05). dSCAT/sSCAT ratio was significantly lower in remission group compared to the active group, and was statistically not different from controls.

C. Bone marrow fat content and BMD

Active patients had higher BMF content (Figure 2) in their femur (82.5 ± 2.6%) and in L3 (70.1 ± 5.1%) than the controls (70.8 ± 3.6%, p=0.013 and 49.0 ± 3.7%, p=0.005, respectively). In the remission group, BMF content was not different from controls at both locations (72.3 ± 2.9% and 46.7% ± 5.3%, respectively). After adjustment to VAT, both BMF content in femurs and vertebrae were still significantly higher in the active group compared to the remission group (p=0.015 and p=0.040, respectively). Further adjustment for age, sex, and HbA1c showed that active patients remained with higher BMF at both location compared to remission patients (table 4). Exclusion of the 5 patients with anti-osteoporotic therapy (2 in the active, and 3 in the remission group) did not statistically change our results (For BMF at femur: p=0.008 between active and controls groups, p=0.019 between active and remission groups. For BMF at vertebrae: p=0.005 between active and controls groups, p=0.010 between active and remission groups. Remission and controls groups did not differ at either location.

Osteodensitometric parameters (Table 3) did not differ significantly between active and remission groups. Two patients of each group (11.8%) were considered osteoporotic. Seven from the active group (41.2%) and six from remission group (35.3%) were considered osteopenic according to WHO criteria using T-score [START_REF] Kanis | The diagnosis of osteoporosis[END_REF].

D. Correlation analysis

BMF content in L3 and femurs were positively correlated (r=0.53 p=0.002) and correlated with age (Supplementary Table 1) but not with BMI. No correlation was found with the duration of uncontrolled CS, duration of hydrocortisone supplementation or UFC levels. Both femoral and L3 BMF correlated positively with HbA 1 c but only L3 BMF correlated additionally with fasting blood glucose levels (r=0.42 p=0.042). L3 BMF also correlated with serum triglyceride levels and with VAT, whereas femoral BMF correlated only with the dSCAT/sSCAT ratio. CTX-1 was positively correlated with BMF (at femur: r=0.42 p=0.018), but not with BMD (at the same location: r=-0.29, p=0.156). In subgroup analyses, BMF remained correlated with BMD values only in the remission group (supplementary table 1). Neither HbA1c nor VAT was correlated with BMF or BMD values in the active group or in the remission group. However, L3 BMF was correlated with VAT in controls (Pearson correlation r=0.66, p=0.007), and there was a trend with femur BMF (r=0.42, p=0.09).

After performing a multiple regression analysis including L3 BMF as a dependent variable (Table 5) and VAT, age and sex as independent variables, BMF was positively associated with VAT (β=0.37; p=0.030) and age (β=0.42; p=0.012).

There was an inverse correlation between femoral BMF and BMD at the same location, and there was a similar connection between L3 BMF and total body BMD. After performing a multiple regression analysis that includes femoral BMF as a dependent variable and BMD at the same location, age and sex (known to be related to BMF content) as independent variables, femoral BMF was negatively associated with BMD (β=-0.51; p=0.003) and positively associated with age (β=0.38; p=0.018 with BMD)

After performing a multiple regression analysis with L3 BMF as a dependent variable and total body BMD, age and sex as independent variables, BMF content was negatively associated with total body BMD (β =-0.99; p=0.003). However, there were no correlations with age.

Discussion

We have demonstrated for the first time with 1 H-MRS that patients with active ACTH-dependent CS have increased BMF content in the right femoral neck and in the lumbar spine compared to age and sex-matched normal-weight controls. Furthermore, in cured ACTH-dependent CS patients we found that BMF content was similar to controls at either site after 43 months of remission.

Our work confirms and follows results from previous preliminary studies on exogenous glucocorticoids, including one study that involved pre-menopausal women treated with GC for lupus that showed with MRI that there was a high percentage of marrow to fat conversion in the proximal femur [START_REF] Berg | Fat conversion of femoral marrow in glucocorticoid-treated patients: a cross-sectional and longitudinal study with magnetic resonance imaging[END_REF].

However, inflammatory connective tissue pathology could directly influence bone marrow adipocytes.

Furthermore, inflammatory diseases are known to be associated with bone loss.

Small sample sized studies did not find significant variation of marrow adiposity in CS patients versus healthy volunteers using dual energy CT scanning [START_REF] Mayo-Smith | Intravertebral fat measurement with quantitative CT in patients with Cushing disease and anorexia nervosa[END_REF]. However, only 4 patients with Cushing disease were included in this study. Besides, CT is limited by the long acquisition times, high radiation dose, and is related to the linear attenuation coefficient. Single-voxel proton magnetic resonance spectroscopy ( 1 H-MRS) remains the gold standard for the quantification of marrow adipose tissue in humans [START_REF] Singhal | Marrow adipose tissue imaging in humans[END_REF].

The study of Geer et al. [START_REF] Geer | Body composition and cardiovascular risk markers after remission of Cushing's disease: a prospective study using whole-body MRI[END_REF], found a decrease in pelvic BMF after 20.1 months of remission but not when total BMF was considered. However, their study design had no control patients and used quantification methods that are not widely used. Our results showed a significant difference between active and remission patients with regards to both femoral neck and L3 BMF; furthermore, we found that L3 BMF and osteodensitometric parameters were negatively associated, even after controlling for age and sex. However, osteodensitometric parameters were not significantly different between active and remission patients. Moreover, in subgroup analyses, BMF remained correlated with BMD values only in the remission group, confirming that BMD is not a surrogate marker for BMF. This could be explained by the remission time being too short. Indeed, a study by Kristo et al. [START_REF] Kristo | Restoration of the coupling process and normalization of bone mass following successful treatment of endogenous Cushing's syndrome: A prospective, long-term study[END_REF], found a significant increase in BMD measurements only after 71 months of remission and not earlier.

Therefore, our results showed discordance between variation of BMF with a significant decrease in remission patients and a lack of BMD value variation. Data of epidemiological studies found that fracture risk waned rapidly after remission in patients with CS [START_REF] Vestergaard | Increased risk of osteoporotic fractures in patients with Cushing's syndrome[END_REF] as well as after stopping glucocorticoid treatment in a large study including patients with exogenous hypercortisolism [START_REF] Van Staa | Use of oral corticosteroids and risk of fractures[END_REF].

BMF content seems to better reflect this brief risk improvement after remission than BMD values. Furthermore, in hypercortisolism secondary fractures with normal or only slightly decreased BMD have been described [START_REF] Tóth | Glucocorticoid-induced osteoporosis: lessons from Cushing's syndrome[END_REF], which can be explained by the qualitative and not the quantitative deterioration of bone tissue. Indeed, GC excess is known to induce alterations in trabecular microarchitecture rendering the trabecular bone specifically more fragile [START_REF] Vinolas | Assessment of vertebral microarchitecture in overt and mild Cushing's syndrome using trabecular bone score[END_REF]. BMF could be a marker of bone quality, more sensitive than BMD to predict risk fracture in CS patients either during active disease or after remission. However, long-term prospective studies with fracture evaluation are needed to test this hypothesis.

Patients with an important clinical and biological impact of their hypercortisolism in our cohort also had a more severe accumulation of BMF. Interestingly, we also found a significant correlation between BMF content and markers of severity of hypercortisolism, such as abnormalities in abdominal fat distribution (increased VAT and dSCAT/sSCAT ratio) and certain biological markers, i.e., HbA 1 c. However, in subgroup analysis VAT was significantly correlated with BMF only in the control group, suggesting that in CS patients, VAT is probably not the main driver of marrow adiposity. Duration of uncontrolled CS, which is a subjective parameter determined by patients, was not correlated with BMF content, nor was the level of UFC. Other groups have found no correlation between BMD and these two parameters [START_REF] Fütő | Skeletal differences in bone mineral area and content before and after cure of endogenous Cushing's syndrome[END_REF]. Polymorphisms in the GC receptor gene, which may increase or decrease GC sensitivity could explain these results [START_REF] Shen | MRI-measured bone marrow adipose tissue is inversely related to DXA-measured bone mineral in Caucasian women. Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA[END_REF]. Our study demonstrates a correlation between VAT volumes and BMF content, but the impact of hypercortisolism on BMF was statistically significant even after adjusting for VAT volumes. Studies with normal-weight and obese patients have also found a positive association between VAT and BMF content [START_REF] Bredella | Vertebral bone marrow fat is positively associated with visceral fat and inversely associated with IGF-1 in obese women[END_REF][START_REF] Shen | MRI-measured bone marrow adipose tissue is inversely related to DXA-measured bone mineral in Caucasian women. Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA[END_REF], whereas another study on anorexia nervosa [START_REF] Bredella | Increased bone marrow fat in anorexia nervosa[END_REF] found a negative correlation between these parameters. It seems that BMF is an independent fat depot, which can be modulated differently than other fat depots depending on the underlying pathologies. We can therefore consider higher VAT volumes as a reflection of severity of hypercortisolism, rather than a potential actor in BMF accumulation.

Increased BMF content and decreased BMD in hypercortisolism could be the result of an imbalance between stromal progenitor cell commitment down the osteogenic and adipogenic lineages in bone marrow [START_REF] Georgiou | Regulatory pathways associated with bone loss and bone marrow adiposity caused by aging, chemotherapy, glucocorticoid therapy and radiotherapy[END_REF]. Peroxisome proliferator activated receptor-gamma (PPAR-γ), which represses osteogenic transcription factors (runt-related transcription factor 2 and osterix) and stimulates expression of adipogenic genes in bone marrow, was already found to be modulated by hypercortisolism in VAT [START_REF] Lindroos | Human but not mouse adipogenesis is critically dependent on LMO3[END_REF]. Glucocorticoids can also dysregulate Wnt/β catenin signaling, which is a key regulator of the two lineages, by stimulating Wnt antagonists (sclerostin and dickkopf-1), as shown in studies conducted in humans and mice [START_REF] Gifre | Effect of glucocorticoid treatment on Wnt signalling antagonists (sclerostin and Dkk-1) and their relationship with bone turnover[END_REF][START_REF] Beier | Sclerostin activity plays a key role in the negative effect of glucocorticoid signaling on osteoblast function in mice[END_REF][START_REF] Belaya | Effects of endogenous hypercortisolism on bone mRNA and microRNA expression in humans. Osteoporosis international: a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA[END_REF].

One strength of our study is that we used the best available method to measure BMF, which is 1 H-MRS, as it allows to quantify BMF compared to water quantity with good reliability and reproducibility [START_REF] Li | Quantification of vertebral bone marrow fat content using 3 Tesla MR spectroscopy: reproducibility, vertebral variation, and applications in osteoporosis[END_REF]. Our team has a long experience with 1 H-MRS quantification of myocardial, hepatic and pancreatic triglyceride contents [START_REF] Dutour | Exenatide decreases Liver fat content and Epicardial Adipose Tissue in Patients with obesity and Type 2 Diabetes: A prospective randomised clinical trial using Magnetic Resonance Imaging and Spectroscopy[END_REF][START_REF] Gaborit | Effects of bariatric surgery on cardiac ectopic fat: lesser decrease in epicardial fat compared to visceral fat loss and no change in myocardial triglyceride content[END_REF][START_REF] Abdesselam | Time Course of Change in Ectopic Fat Stores After Bariatric Surgery[END_REF]. We measured BMF content at two sites: the femoral neck and the corpus of vertebrae L3, which allowed us to study different kinetics of BMF evolution with aging. Indeed, red marrow is gradually being replaced by BMF throughout aging, and it extends from the appendicular skeleton up to the axial skeleton [START_REF] Hardouin | Bone marrow fat[END_REF]. Another strength of our study is that we did not include hypercortisolism with adrenal etiology to eliminate possible confounding from other cosecreted steroids from adrenal glands. Nevertheless, one study found no difference in BMD between the etiologies of hypercortisolism [START_REF] Tauchmanovà | Bone demineralization and vertebral fractures in endogenous cortisol excess: role of disease etiology and gonadal status[END_REF]. There are several limitations in our study. The major one is the retrospective nature of our study with a small sample size. However, CS is a very rare disease with an incidence of 0.7-2.4 per million people per year that makes the feasibility of a large-scale prospective analysis not applicable [START_REF] Lindholm | Incidence and Late Prognosis of Cushing's Syndrome: A Population-Based Study 1[END_REF][START_REF] Pivonello | Complications of Cushing's syndrome: state of the art[END_REF] given the high-precision techniques used in our center, and not available in the majority of the centers dealing with hypercortisolism. The majority of our patients were treated by hydrocortisone, and this treatment is assumed to impact bone turnover and density at supraphysiological doses [START_REF] Schulz | Reduction in daily hydrocortisone dose improves bone health in primary adrenal insufficiency[END_REF]. However, corticotroph deficiency is now considered as the best prognosis marker to consider that the patients are in remission, and it would have been difficult to evaluate patients in remission if they had not been ACTH deficient for a long period of time after surgery. Moreover, Schulz et al., clearly demonstrated that patients substituted with a dose of hydrocortisone of 25.2 +/-8.2 mg/day (similar to our study) had normal BMD that did not change after two years, suggesting that exogenous replacement therapy within this range of hydrocortisone dosing has no significant impact on BMD. The improvement of diabetes or hypertriglyceridemia could also have an impact on BMF after remission of CS. Anti-osteoporotic therapies taken by some of our patients, could also have modified BMF: however, these treatments were evenly distributed in both the active and remission groups. Finally, we could not calculate fat unsaturation, which could have been interesting as saturated lipids could directly influence osteoblasts [START_REF] Philippe | GPR40 mediates potential positive effects of a saturated fatty acid enriched diet on bone[END_REF]. As other teams have also reported [START_REF] Dutour | Exenatide decreases Liver fat content and Epicardial Adipose Tissue in Patients with obesity and Type 2 Diabetes: A prospective randomised clinical trial using Magnetic Resonance Imaging and Spectroscopy[END_REF][START_REF] Liney | Age, gender, and skeletal variation in bone marrow composition: A preliminary study at 3.0Tesla[END_REF] we found at 3 Tesla that the spectroscopic peak at 5.3 ppm was sometimes confounded with the water peak and could not be isolated.

In conclusion, our data demonstrated that BMF content is increased by CS at various localizations and did not differ from normal-weight controls after 43 months of remission. Moreover, the degree of BMF accumulation was positively correlated with markers that reflect the biological and clinical impacts of hypercortisolism. We provide the first study evaluating bone marrow adiposity with 1 H-MRS in such patients. It would be interesting to study further the link between BMF and bone microarchitecture in hypercortisolism.

Declaration of interest

The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported. 12.

Funding

  approved by the local ethics committee (Marseille, Comité de Protection des Personnes, Sud-Méditerranée II identification 2014-A01302-45 and 2016-A00026-45, clinical trial identification: NCT02335996 and NCT02848703).

1 )

 1 This work was supported by ARARD (Association d'Assistance médico-Technique à Domicile), Conception and design or analysis and interpretation of data, or both: FM, AD, CV, IA, LP, YL, RF, CC, AD, TB, FC, BG, PC 2) Drafting of the manuscript or revising it critically for important intellectual content: FM, BG, MB, HD, TG, FK, AD, FC, TB 3) Final approval of the manuscript submitted: all the authors.

Figure 1 Figure 2 1 H 1 Figure 2

 12112 Figure 1 Flow chart of the study

Table 3

 3 BMD parameters measured by DXA of active and remission groups

		Active group	Remission group	p value
	Lumbar spine BMD, g/cm 2	1.045±0.041	1.067±0.040	0.720
	Lumbar spine BMD T-score	-1.125±0.354	-0.500±0.361	0.240
	Femoral neck BMD, g/cm 2	0.842±0.033	0.941±0.040	0.085
	Femoral neck BMD T-score	-1.231±0.276	-0.725±0.284	0.218
	Total body BMD, g/cm 2	1.091±0,035	1,104±0.035	0.822
	Total body BMD T-score	-0.187±0.298	-0.069±0.301	0.806
	Notes: Data presented as mean ± SEM

Table 4

 4 Adjusted means with 95% confidence interval of bone marrow fat content 1) adjusted means of BMF for age and sex 2) adjusted means for age, sex, and HbA1c 3) adjusted means for age, sex, and VAT

		Active	Remission group	Controls	p
		group
	1) L3 BMF
	Adjusted for age	70.3 ± 4.8 b	39.4 ± 4.4 a	50.2 ± 3.2	<0.0001
	and sex
	2) L3 BMF
	Adjusted for age	80.0 ± 11.7	38.9 ± 4.2 a	47.9 ± 4.5	0.003
	sex and HbA1c
	3) L3 BMF
	Adjusted for age	65.6 ± 6.3	38.4 ± 4.4 a	51.8 ± 3.5	0.002
	sex and VAT
	1) Femur BMF
	Adjusted for age	84.9 ± 2.7	73.1 ± 2.9 a	75.6 ± 2.9	0.01
	and sex
	2) Femur BMF
	Adjusted for	86.6 ± 5.2	68.8 ± 3.6 a	73.6 ± 3.5	0.028
	age, sex and
	HbA1C
	3) Femur BMF
	Adjusted for age	88.6 ± 3.0 b	74.0 ± 2.8 a	73.1 ± 3.0	0.001
	sex and VAT
	p for the difference between groups was calculated using an ANCOVA model, pairwise
	comparisons were adjusted using Bonferroni method.
	a p< 0.05 between active and remission group
	b p<0.05 between active group and controls

Table 5

 5 Multiple regression analysis

	Independent variables

Acknowledgements

We thank the Association pour le Développement des Recherches Biologiques et Médicales (ADEREM) and the Association d'Assistance médico-Technique à Domicile (ARARD) for their financial support. We are also grateful to the patients who participated in the study. We also thank the study staff for their help in recruiting patients and analyzing the data.


Citra Yanto

Ciki Purba

Guillaume Pot

Joffrey Viguier

Julien Ruelle

Louis Denaud

The influence of veneer thickness and knot proportion on the mechanical properties of laminated veneer lumber (LVL) made from secondary quality hardwood

The influence of veneer thickness and knot proportion

on the mechanical properties of laminated veneer lumber (LVL) made from secondary quality hardwood

Introduction

Hardwood dominates both the surface area and standing stock of French forests (IGN 2016). In contrast, the wood harvested and the timber produced are dominated by softwood (Ministère de l'Agriculture et de l'Alimentation-Agreste 2017). Forests cannot produce high-quality wood without also producing a large quantity of low-grade wood. Moreover, the new forest management systems based on intensive silviculture generally produce low-quality wood. Young thinnings, top wood and early harvested wood are secondary resources that have great potential for high-value applications [START_REF] Eckelman | Potential uses of laminated veneer lumber in furniture[END_REF][START_REF] Marchall | Une alternative pour les bois feuillus de qualité secondaire: les LVL (laminated veneer lumber), lamelles-colles de placages. (An alternative for secondary quality hardwoods: LVL (laminated veneer lumber), glued laminated veneer)[END_REF][START_REF] Mckeever | Engineered wood products: a response to the changing timber resource[END_REF][START_REF] Knudson | Properties of veneer and veneer-based products from genetically improved white spruce plantations[END_REF]).

The presence of various wood defects such as knots, grain deviation, juvenile wood and reaction wood restricts the utilization of secondary quality hardwood for structural materials. The presence of knots and knotholes in timber induces zones with weaker strength where defects will most likely start. Knots also create a larger area around the knot that has high grain angle deviation [START_REF] Viguier | Improving strength grading of timber by grain angle measurement and mechanical modeling[END_REF](Viguier et al. , 2017a)). In addition, young trees are usually characterized by a high proportion of juvenile wood [START_REF] Bendtsen | Properties of wood from improved and intensively managed trees[END_REF][START_REF] Kretschmann | Effect of various proportions of juvenile wood on laminated veneer lumber[END_REF]. Juvenile wood is a zone close to the pith created at the beginning of the radial growth that can be characterized by lower mechanical properties compared to mature wood [START_REF] Moore | Effects of early re-spacing on the physical and mechanical properties of Sitka spruce structural timber[END_REF][START_REF] Zobel | Juvenile wood in forest trees[END_REF]. Finding an alternative use for these abundant resources is essential. These resources have been insufficiently explored and commonly used only for firewood and wood composite (fiber and particleboard). The valorization of this resource as structural material requires better characterization of its mechanical properties and better knowledge of the effect of the defects on mechanical properties.

Laminated veneer lumber (LVL) is an engineered wood product made from rotary peeled veneer glued together with the grain generally oriented parallel to the panel length. LVL is usually used for structural and nonstructural applications such as flooring, furniture and construction [START_REF] Ozarska | A review of the utilisation of hardwoods for LVL[END_REF][START_REF] Lam | Modern structural wood products[END_REF]). Compared to solid wood, LVL has dispersed defects due to the production process, better dimensional stability, is available in large dimensions, and provides higher modulus of elasticity (MOE) and modulus of rupture (MOR) [START_REF] Ebihara | Shear properties of laminated-veneer lumber (LVL)[END_REF][START_REF] Youngquist | End jointing of laminated veneer lumber for structural use[END_REF].

Previous studies reported that veneer quality influences the mechanical properties of LVL [START_REF] Daoui | Influence of veneer quality on beech LVL mechanical properties[END_REF][START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF]Viguier et al. 2017b[START_REF] Viguier | An innovative method based on grain angle measurement to sort veneer and predict mechanical properties of beech laminated veneer lumber[END_REF]. Generally, LVL mechanical strength increases with the number of veneers inside the LVL [START_REF] Schaffer | Feasibility of producing a high-yield laminated structural product: general summary[END_REF][START_REF] Hoover | Material design factors for hardwood laminated-veneer-lumber[END_REF][START_REF] Kilic | Effect of machining on surface roughness of wood[END_REF]. Thinner veneer distributes the defects (knots, knotholes, split and slope of grain) better than thicker veneer and improves the LVL strength [START_REF] Ebihara | Shear properties of laminated-veneer lumber (LVL)[END_REF]. On the other hand, increasing the number of veneers inside the LVL demands much more glue and more numerous steps for its production. Moreover, other studies also reported that the increase in veneer thickness decreases the shear strength and shear modulus of LVL, especially in the edgewise direction [START_REF] Ebihara | Shear properties of laminated-veneer lumber (LVL)[END_REF][START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF]. Rotary peeling creates lathe checks on the loose side of the veneer surface [START_REF] Thibaut | Le processus de coupe du bois par déroulage (The cutting process of wood by peeling)[END_REF]. Veneer lathe check properties are commonly characterized by the lathe check depth and lathe check interval. Under the same cutting conditions, higher peeling thickness produces veneer with deeper lathe checks and a greater distance between two consecutive checks [START_REF] Denaud | Online control of wood peeling process: acoustical and vibratory measurements of lathe checks frequency[END_REF][START_REF] Pałubicki | A Method of lathe checks measurement; SMOF device and its software[END_REF]. According to [START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF], the decrease in shear modulus with the increase in veneer thickness in the edgewise direction is caused by the presence of lathe checks, which are almost perpendicular to the veneer surface and, consequently, more penalizing in the edgewise than in the flatwise direction. Nevertheless, the quoted authors` report was based on numerical studies and has not yet been clarified on a large number of experimental measures.

Increasing veneer thickness helps to decrease glue consumption and production time. More recent studies in LVL made of hardwood species reported that increasing veneer thickness resulted in minor weakening of the MOE and MOR of LVL [START_REF] Daoui | Influence of veneer quality on beech LVL mechanical properties[END_REF][START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF][START_REF] Rahayu | Ten new poplar cultivars provide laminated veneer lumber for structural application[END_REF]. The first objective of this study was to better understand the relationship between veneer properties and mechanical properties of LVL made of secondary quality hardwood. Most of the previous studies in hardwood LVL were performed using LVL made of knot-free veneer. [START_REF] Viguier | An innovative method based on grain angle measurement to sort veneer and predict mechanical properties of beech laminated veneer lumber[END_REF] reported the influence of grain angle and its deviation around the knot on the MOE and the MOR of LVL but none have quantified the relationship with the proportion of knots. Lathe check properties and knot proportion were used to characterize the quality of veneer, taking into account the radial variation of the veneer inside the tree trunk that provides different wood properties, i.e., internal and external position. The second objective of this paper was to study the effect of veneer thickness on LVL mechanical properties and propose an adapted veneer thickness that provides optimum mechanical properties. It was expected that a compromise would have to be made between lathe check properties generated during wood peeling and wood knot proportion.

Materials and methods

Wood material

Beech (Fagus sylvatica L.) and oak (Quercus petraea Liebl.) were used for this study. They are the two major hardwood species in Europe and particularly in France (IGN 2016). Twelve logs were gathered during the thinning of tree stands in a local forest in Lorraine, France. The log diameters varied between 21 and 30 cm, with a length of 150 cm. Oak tree age ranged between 61 and 90 years, whereas beech age varied between 57 and 84 years. Each log was extracted from the upper part of the tree (above 5 m from the ground) and generally contained knots.

Veneer preparation

To minimize veneer lathe checks, all logs were soaked in hot water (60 °C) for 24 h. They were then cut into veneers using a rotary veneer lathe. Three classical veneer thicknesses for LVL and plywood products (2.1 mm, 3 mm, 4.2 mm) were used. The angular pressure bar of the rotary peeling machine was maintained at 5% for all thicknesses (the gap between the knife and pressure bar was 5% lower than the expected veneer thickness). These settings, which take log quality (relatively high density, knots, limited log diameter) into account, were used to produce moderately checked veneers. Each log was peeled to produce one particular veneer thickness. The veneers were numbered and clipped in 0.6 × 0.5 m 2 sheets and dried using a vacuum drying device to reduce veneer moisture content (MC) to 18% and then air-dried to about 10% MC at the same time to limit drying time and drying cracks.

Measurement of veneer lathe checks and weighted knot proportions

The quality of fresh veneers was assessed by measuring lathe check depths and lathe check intervals (distance between two adjacent lathe checks). The measurement was performed on 10-cm-wide bands of fresh-cut veneer with a length of 20-60 cm. These veneer bands were taken from the edge of the veneers right after the peeling process ended. Lathe check depths and intervals were immediately measured using a Systeme de Mesure d'Ouverture des Fissures (SMOF) device to characterize the green veneer [START_REF] Pałubicki | A Method of lathe checks measurement; SMOF device and its software[END_REF]. These two parameters were measured on a large proportion of veneers (around 40% of veneer from each veneer thickness). Approximately 11,500 lathe checks were used for this study.

A photograph of each dry veneer was taken before being laminated. The images of the veneer surface were analyzed using Image-J software to measure the weighted knot proportion. The percentage of knot surface to the total veneer surface was calculated and defined as knot proportion. The position of each knot on the veneer surface was also recorded. The veneer weighted knot proportion was calculated by multiplying the knot proportion by a factor of correction based on the knot position along the veneer length (parallel to the fiber direction). This factor of correction was determined according to the variation of the bending moment along a beam subjected to a 4-point bending test. Factor correction 1 was used for the section with the maximum bending moment, which lies in the middle area of the tested beam. Factor corrections 0.5 and 0 were used for the second section and the section closer to the support, respectively, as presented in Fig. 1.

LVL production

Veneers from each log were divided into two categories by their radial positions inside the trunk, i.e., internal and external veneer. The internal veneers originated from the zone closer to the center of the trunk, whereas the external veneers were closer to the periphery. The limit between the two zones was the midpoint between the first and the last peeled veneer. This separation gives two groups with different mechanical properties, even if this could not be considered as a limit between mature and juvenile wood.

The veneers were glued together with the grain oriented parallel to the panel length using PVAc (polyvinyl acetate) as an adhesive. The glue spread of each glue line was 180 g/ m 2 . Glued veneers were pressed under a pressure of 0.8 MPa for about 60 min at ambient temperature. For each combination of treatment (wood species, veneer position inside the tree trunk and veneer thickness), four LVL panels were prepared (Table 1). All together, 48 LVL panels were used for this study. The final dimensions of the LVL panel were 500 × 250 × 21 mm 3 . After gluing and pressing, the LVL panels were stacked and stabilized for 2 weeks prior to mechanical tests.

Measurement of LVL mechanical properties

Nine test specimens were prepared with a dimension of 500 × 21 × 21 mm 3 from each LVL panel. The MC of the LVL specimens was determined prior to the mechanical tests. The mean MC values obtained were 10.81% for oak LVL and 10.77% for beech LVL with a standard deviation of 0.18% and 0.2% respectively. Destructive tests and nondestructive tests based on the vibration method were used for measuring the LVL mechanical properties. Two loading directions were studied, i.e., flatwise and edgewise. For the flatwise bending test, the load direction was perpendicular to the glue lines, whereas for the edgewise test, the load direction was parallel to the glue lines. The dynamic MOE and shear modulus were measured in both loading directions using a nondestructive test called Bing [START_REF] Brancheriau | Natural vibration analysis of clear wooden beams: a theoretical review[END_REF][START_REF] Brancheriau | Bing-beam identification by non-destructive grading (Cirad)[END_REF].

For the destructive tests, half of the samples was used for the flatwise bending test and the other half for the edgewise bending test. These 4-point bending tests made it possible to measure the MOE and the modulus of rupture (MOR). A local MOE and a so-called global MOE were calculated from the same test. The specific modulus was also calculated by dividing the measured modulus by the LVL density. The test arrangement is described in Fig. 2.

The local MOE is the MOE computed between the two central loading heads, in a zone of pure bending. It was calculated using this formula:

where a = distance between a loading position and the nearest support in a bending test (129 mm here), l 1 = gauge length for the determination of the local MOE (120 mm in this case), I = the second moment of inertia (mm 4 ), F 2 -F 1 = the increment of load on the regression line with a correlation coefficient of 0.99 or better (N), and w 2w 1 = the increment of local deflection corresponding to F 2 -F 1 (mm).

The global MOE was computed from the deflection of the whole beam and not just the pure bending zone. Deflection was calculated based on the movement of the loading tools. Equation 2 shows how the global MOE is computed. Shear effects, punching under the loading heads, and deformations

(1) E m,l = al 2 1 (F 2 -F 1 ) 16I(w 2 -w 1 )
of the loading machine are not taken into account using this calculation method. However, this so-called global MOE provides valuable information that takes the whole specimen deformation into account, which is of interest for such heterogeneous material, whereas the local MOE may be too local:

where l = length of the test piece between the testing machine grips (mm), V 2 -V 1 = the increment of displacement of the loading tools corresponding to F 2 -F 1 (mm), and the other parameters are the same as those in Eq. 1.

Data analysis

To evaluate the influence of different wood species, veneer thickness, veneer position and loading direction on the LVL mechanical properties, multi-factor analysis of variance (ANOVA) and Tukey's HSD (Honestly Significant Difference) multiple comparison tests were carried out. All of the statistical analysis was performed at a level of significance of 0.05 using R-software. The coefficient of correlation and the coefficient of determination were used to evaluate the relationship between measured parameters. Paired t-tests were used to analyze the influence of veneer position on LVL mechanical properties.

Results and discussion

Veneer quality

Lathe check depth and lathe check interval

Mean lathe check depth and lathe check interval for each veneer thickness and wood species are presented in Table 2. Both the lathe check depth and the lathe check interval were affected by the veneer thickness. Statistical analysis showed that the difference in lathe check depth and lathe check interval among veneer thickness was statistically significant (p < 0.05). From the thinnest to the thickest veneer, there was an increase in lathe check depth of 40% and 57%

(2) 54.9 a (2.7) 67.7 c (6.3) 76.9 d (3.8) 46.3 b (5.3) 63.8 c (4.2) 72.9 d (3) Mean lathe check interval (mm) 1.9 a (0.2) 2.6 c (0.2) 3.7 d (0.3) 1.7 b (0.2) 2.5 c (0.1) 3.7 d (0.3) for oak and beech, respectively. Correspondingly, the lathe check interval on the thickest veneer rose sharply by 95% and 118% for oak and beech, respectively. Oak had deeper lathe checks and higher lathe check intervals than beech for veneer with a 2.1-mm thickness. This difference was statistically significant at the 0.05 level. The lathe check depth and the lathe check interval were relatively the same for both species for veneer with a 3-mm and 4.2-mm thickness. The results obtained for oak are interesting. Indeed, this species is less homogenous than beech (larger rays and a big difference between earlywood and latewood density), but shows similar behavior. The lathe check properties of oak veneers have never been reported before. Unlike oak, beech lathe check properties have been studied more extensively [START_REF] Denaud | Online control of wood peeling process: acoustical and vibratory measurements of lathe checks frequency[END_REF][START_REF] Pałubicki | A Method of lathe checks measurement; SMOF device and its software[END_REF][START_REF] Daoui | Influence of veneer quality on beech LVL mechanical properties[END_REF][START_REF] Rohumaa | Lathe check development and properties: effect of log soaking temperature, compression rate, cutting radius and cutting speed during peeling process of European beech (Fagus sylvatica L.) veneer[END_REF].

E m,g = - a 2 (F 2 -F 1 ) 6I(V 2 -V 1 ) (3l -4a)

Knot proportion

Knot proportion on veneer surface of secondary quality oak and beech

Figure 3 compares the veneer knot proportion (unweighted) on different positions in the log and different veneer thicknesses. The aim was to determine the influence of veneer radial position inside the trunk on knot proportion. Knot proportion is important since it demonstrates the quality of the veneer used in this study and highlights the possible variations in the mechanical properties of the different veneers according to their position in the log or thickness. The highest knot proportion on oak veneer was found on 4.2-mm-thick veneer in the internal position, whereas the minimum was for the veneers of the same thickness, but in the external position. The knot proportion for oak veneer with a 2.1-mm and 3-mm thickness was fairly similar. On the other hand, the highest knot proportion on beech veneer was found for the thinnest veneers and the lowest for the thickest veneers. Of course, veneer thickness has no influence on the knot proportion, but this result is interesting to take into account when discussing the mechanical properties measured below. In particular, beech veneers with a 4.2-mm thickness present a much lower knot proportion than other veneers (below 0.5%). Figure 3 also demonstrates that the veneer knot proportion was generally higher on the surface of veneer peeled from the internal part of the tree than the external part except for beech veneers with a 4.2-mm thickness. Trimmed knots on the edge of the veneer in the internal position may have caused one peeled 4.2-mm-thick log to reveal a higher knot proportion in the external position.

Figure 4 compares the mean knot size and frequency between the internal and external position on the two wood species. It describes the increase in knot frequency and the decrease in knot diameter from the periphery to the center of the trunk. During peeling, the outer part of the log was cut first and then followed by the inner part. Knot diameter is bigger at the position closer to the periphery and becomes smaller towards the inside. Since log diameter is bigger on the outer side and knot diameter is also bigger, peeled veneer from the external position only contained a small number of big knots. Bigger log diameter leads to a greater distance between knots related to wood peeling. When the peeling As a result, since the distance between knots is closer, peeled veneer in the internal position contains a higher number of knots. As a consequence of the higher number of knots, internal veneers contain a higher knot proportion than the external veneers. The increase in knot proportion from the veneer periphery to the center of the log has also been reported on a white spruce veneer [START_REF] Knudson | Properties of veneer and veneer-based products from genetically improved white spruce plantations[END_REF]). Furthermore, [START_REF] Mcgavin | Variation in rotary veneer recovery from australian plantation Eucalyptus globulus and Eucalyptus nitens[END_REF] reported that the higher proportion of knots in addition to less mature wood properties (e.g., lower wood density) produced lower MOE compared with veneer sheets recovered from the periphery of eucalyptus, which generally yields higher MOE. In addition, lower MOE on LVL made of juvenile wood has also been reported in poplar [START_REF] Rahayu | Ten new poplar cultivars provide laminated veneer lumber for structural application[END_REF].

The influence of veneer radial position on LVL mechanical properties

In Table 3, the density and mechanical properties of internal and external positions measured using destructive tests are compared. For oak, the LVL made of internal veneer has a relatively higher density than the LVL made of external veneer. The difference was statistically significant at the 0.05 level. A previous study reported that oak ring density and ring width decrease with the increase in the distance to the pith [START_REF] Nepveu | Les facteurs influencant la qualite du bois de chene (Chene rouvre, Chene pedoncule). (Factors influencing the quality of oak wood (Chene rouvre, Chene pedoncule))[END_REF]). This decrease in oak ring density by cambial age explains the difference of the LVL density between both veneer positions. Nevertheless, for beech LVL, the difference of LVL density between both positions was insignificant at the 0.05 level. On the contrary, MOE and MOR were significantly higher on beech LVL made of external veneers. For oak, the differences are not significant at the 0.05 level. These results showed that, generally, LVL made of veneers closer to the pith (internal) produce lower mechanical properties compared to the external veneers. This difference was due to the variation explained above of knot proportion on these two positions where the external veneer contains a lower knot proportion compared to the internal veneer, thus providing better mechanical properties. The higher knot proportion on the surface of internal veneer may be related to natural pruning. [START_REF] Knudson | Properties of veneer and veneer-based products from genetically improved white spruce plantations[END_REF] reported that the number of knots in spruce veneers increases from sapwood to heartwood. This author explained that more natural pruning occurred on older trees. Lower mechanical properties on the internal veneer of beech may also be caused by the presence of a small part of juvenile wood. Mature wood on the external position may provide greater strength on oak LVL.

Knot size external posiƟon

The influence of veneer thickness on mechanical properties of LVL made of secondary quality hardwood

Table 4 presents the mechanical properties of oak and beech LVL measured using destructive tests. In addition, it also provides the specific modulus of elasticity (SMOE) for both local and global measurements. The objective of using specific modulus was to precisely compare the effect of veneer thickness on the mechanical properties of LVL without any distortion due to the different wood densities. There was no significant influence of testing direction on the mechanical properties for either species. Previous studies show contrasting results on the effect of the loading direction on LVL mechanical properties. Nevertheless, the results in this study are similar to previous reports on beech, poplar and pine [START_REF] Burdurlu | The effects of ply organization and loading direction on bending strength and modulus of elasticity in laminated veneer lumber (LVL) obtained from beech (Fagus orientalis L.) and lombardy poplar (Populus nigra L.)[END_REF][START_REF] Daoui | Influence of veneer quality on beech LVL mechanical properties[END_REF][START_REF] Souza F De | Material properties and nondestructive evaluation of laminated veneer lumber (LVL) made from Pinus oocarpa and P. kesiya[END_REF][START_REF] Rahayu | Ten new poplar cultivars provide laminated veneer lumber for structural application[END_REF].

As expected, global MOE and SMOE are generally lower than local ones, which can be explained by the punching under the loading heads, the disregard of shear effects, and deformations of the loading machine. Generally, the relationships between LVL made of different veneer thicknesses are maintained, regardless of whether global or local MOE are considered, showing the relative homogeneity of mechanical behavior along the length of an LVL beam.

For oak, the highest local and global SMOE were found for LVL made from 3-mm-thick veneers. The oak LVL made from 2.1-mm-and 4.2-mm-thick veneer showed relatively similar values of local and global SMOE. The highest SMOE values for beech were found for LVL made from 3-mm-or 4.2-mm-thick veneers, which are not significantly different (p < 0.05). It should be recalled, however, that 4.2-mm-thick beech veneers presented a lower knot proportion. The highest mean MOR value for both species was found on LVL made of 3-mm-thick veneer, whereas the lowest was on the LVL made of the thickest veneer. However, the differences are not significant for beech at the 0.05 level.

The standard deviation of local and global SMOE rises with the increase in veneer thickness. The increase in the standard deviation of both local and global SMOE may be related to the effect of the distribution of defects. Since the defects are better distributed in the LVL made of thinner veneer, the variation of SMOE tends to be lower compared to the LVL made of thicker veneer. For LVL with thicker veneer, the defects are more concentrated and therefore generate more variations of SMOE. These results are consistent with previous reports on poplar [START_REF] Rahayu | Ten new poplar cultivars provide laminated veneer lumber for structural application[END_REF].

Based on the three mechanical parameters compared and its standard deviation, 3-mm-thick veneer generally produced the optimum LVL mechanical properties. This veneer thickness complies with the common veneer thickness used to produce LVL, i.e., 3-3.5 mm [START_REF] Pollmeier | Declaration of performance[END_REF]. According to the literature, the thinnest veneer should provide the best mechanical properties since more veneer layers inside the LVL should give a better distribution of defects and, consequently, better mechanical properties. This contradiction may be explained by the different wood quality used in this research. In general, the previous study used knot-free or much less defective veneer to produce LVL. It appears that in the present study, the lowest veneer thickness had the highest knot proportion (Fig. 3) and could thus have influenced the results. It is, however, difficult to separate the effect of knots from the effect of veneer thickness and lathe checks in this case.

As expected, the MOE and MOR of beech LVL made of secondary quality beech in this study are much lower than those in a previous study using knot-free LVL [START_REF] Aydın | A comparative study on some physical and mechanical properties of Laminated Veneer Lumber (LVL) produced from Beech (Fagus orientalis) and Eucalyptus (Eucalyptus camaldulensis) veneers[END_REF][START_REF] Burdurlu | The effects of ply organization and loading direction on bending strength and modulus of elasticity in laminated veneer lumber (LVL) obtained from beech (Fagus orientalis L.) and lombardy poplar (Populus nigra L.)[END_REF][START_REF] Daoui | Influence of veneer quality on beech LVL mechanical properties[END_REF][START_REF] Knorz | Development of a high-capacity engineered wood product-LVL made of European beech (Fagus sylvatica L.)[END_REF]. [START_REF] Burdurlu | The effects of ply organization and loading direction on bending strength and modulus of elasticity in laminated veneer lumber (LVL) obtained from beech (Fagus orientalis L.) and lombardy poplar (Populus nigra L.)[END_REF], who studied the (2011), the mean MOE value is also more than 25% lower, but the MOR value is only about 30% lower. Nevertheless, the MOE of LVL made of the secondary quality oak and beech in the present study are comparable or even higher than the MOE of LVL made of other hardwood species such as eucalyptus, maple, aspen and poplar [START_REF] Aydın | A comparative study on some physical and mechanical properties of Laminated Veneer Lumber (LVL) produced from Beech (Fagus orientalis) and Eucalyptus (Eucalyptus camaldulensis) veneers[END_REF][START_REF] Shukla | Properties of laminated veneer lumber (LVL) made with low density hardwood species: effect of the pressure duration[END_REF][START_REF] Rahayu | Ten new poplar cultivars provide laminated veneer lumber for structural application[END_REF]. Although the mechanical properties of LVL made from secondary quality beech and oak are acceptable, further studies are needed to assess its suitability for the manufacture of commercially acceptable LVL with regard to the recovery rates and production costs.

Dynamic shear modulus

Table 5 provides the dynamic MOE and shear modulus measured using the vibration method. The highest dynamic SMOE for both species was found on the LVL made of 3-mm-thick veneer. These results are consistent with the trend on global SMOE previously observed. However, the dynamic MOE was always higher than that found in previous studies [START_REF] Daoui | Influence of veneer quality on beech LVL mechanical properties[END_REF][START_REF] Souza F De | Material properties and nondestructive evaluation of laminated veneer lumber (LVL) made from Pinus oocarpa and P. kesiya[END_REF][START_REF] Rahayu | Ten new poplar cultivars provide laminated veneer lumber for structural application[END_REF]. Nevertheless, these results are important since they measure the MOE along the specimen, unlike the local MOE, while also confirming the computation used for the global MOE.

For the edgewise test, the LVL made of the thinnest veneer generated the highest shear modulus for both species at the 0.05 level. The thicker the veneer is, the lower the shear modulus will be. The decrease in the shear modulus for the edgewise direction with thicker veneer in this study confirmed the previous report by [START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF] who studied the effect of veneer lathe checks on beech MOE using a numerical approach. In addition, Melo and Menezzi (2014) also reported the decrease in shear strength by the increase in veneer thickness in LVL made of Parica (Schizolobium amazonicum). However, the correlation between lathe check and shear modulus could be biased by the direction of the lathe checks. [START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF] explained that the lathe check is more penalizing in the edgewise direction because it is almost perpendicular to the veneer surface.

The relationship between veneer quality and LVL mechanical properties

Influence of lathe check properties on LVL specific shear modulus and MOR

To understand the effect of lathe check on LVL mechanical properties, the correlations among the measured parameters were analyzed and are presented in Table 6. In agreement with the literature, these results demonstrate the positive correlation between lathe check depth and lathe check interval [START_REF] Pałubicki | A Method of lathe checks measurement; SMOF device and its software[END_REF]. Deeper lathe check increases the distance between two lathe checks and lowers the check frequency. The correlation between lathe check depth and lathe check interval in oak (r = 0.99) was better than beech (r = 0.77). Specific shear modulus and MOR showed negative correlations with lathe check depth and check interval except for flatwise tested oak. An increase in lathe check depth and lathe check interval tended to lower the specific shear modulus in the edgewise direction, as mentioned before. The correlation between both parameters was better in the edgewise than in the flatwise test. Contrary to specific shear modulus, MOR has a better correlation with lathe check properties in the flatwise direction. Increased lathe check depth and check interval decreased the LVL strength.

The negative correlation between lathe check depth and shear modulus supported previous reports by [START_REF] Ebihara | Shear properties of laminated-veneer lumber (LVL)[END_REF]. In addition, this author also reported that shear strength parallel to the grain direction on both edgewise and flatwise LVL decreases when the veneer thickness increases. A more recent study by [START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF] proposes a numerical model able to explain this trend. No correlation was found between lathe check properties and MOE. These results were also in accordance with previous reports on the effect of lathe check and veneer thickness on the MOE [START_REF] Ebihara | Shear properties of laminated-veneer lumber (LVL)[END_REF][START_REF] Hoover | Material design factors for hardwood laminated-veneer-lumber[END_REF][START_REF] Pot | Numerical study of the influence of veneer lathe checks on the elastic mechanical properties of laminated veneer lumber (LVL) made of beech[END_REF].

Influence of weighted knot proportion on global SMOE

The correlation between weighted knot proportion and global SMOE is presented in Table 7. Two types of weighted knot proportions were used for the analysis. The first used the weighted knot proportion of all of the veneer layers that constituted the LVL. The second weighted knot proportion was calculated using the data from the two outer veneers only.

Both weighted knot proportions revealed negative correlations with SMOE. These negative correlations could be seen on both hardwood species and the two test directions. The increase in weighted knot proportion on the veneer surface decreases the global SMOE on oak and beech LVL. The correlations in the edgewise direction are better using weighted proportions from all of the veneer. Flatwise tested oak was better correlated with the weighted knot proportion of the outer veneer. Beech revealed better correlation than oak for both weighted knot proportions. For the edgewise direction, the LVL MOE is determined by the sum of the MOE of each veneer. The contribution of each layer to the LVL MOE is equal. This explains the better correlation using the weighted knot proportion of all the veneers in the edgewise direction compared to the use of outer veneers.

For the flatwise direction, the location of each veneer determines their contribution to the LVL MOE. This different contribution of each layer is due to the different stresses faced by the outer layers in comparison to the central layers [START_REF] Girardon | Modelling the effects of wood cambial age on the effective modulus of elasticity of poplar laminated veneer lumber[END_REF], which can explain why correlations with flatwise SMOE were better (or similar) for beech using the data from outer veneers.

Effect of the weighted knot proportion on SMOR

The correlations between the two types of weighted knot proportions and SMOR are presented in Table 8. Low negative correlations were found between both parameters on both species and the two loading directions. The correlations of weighted knot proportion with LVL MOR were lower compared to the LVL SMOE. For both species, the correlation between the weighted knot proportion of all of the veneers was better in the edgewise than the flatwise direction. For both test directions, the correlations were better using the weighted knot proportions of all of the veneer except for flatwise beech that was slightly better correlated with the weighted knot proportion of the outer veneer.

Conclusion

High knot proportions were found on the surface of veneer prepared from secondary quality hardwood. Veneer lathe check depth and interval increase with the increase in veneer thickness. For both species, the 3 mm thick veneer provided the optimum mechanical properties for LVL. The testing direction had no significant influence on the mechanical properties of either species. The average MOE values obtained were 13.2 GPa for beech LVL and 13.3 GPa for oak LVL, whereas the MOR was 72.0 MPa and 63.4 MPa, respectively, in the flatwise direction. Such mechanical properties are comparable to those of LVL manufactured from other species of hardwood. The increase in weighted knot proportion provided lower MOE and MOR on LVL. The weighted knot proportion can better predict the LVL MOE. Deeper lathe checks and higher lathe check intervals generated lower shear modulus in the edgewise direction for both species. No correlation was found between lathe check properties and LVL MOE. The radial position of veneer inside the tree trunk influences the physical and mechanical properties of LVL. Internal veneer produced higher LVL density but provided lower mechanical properties than external veneer. These lower mechanical properties were due to a higher knot proportion on the internal veneer surface than on the veneer from external position.

Fig. 1

 1 Fig. 1 Scheme of the factor of correction applied to knot proportion according to the knot position along the veneer

Fig. 2

 2 Fig. 2 Test arrangement for the 4-point bending test to measure local MOE

Fig. 3

 3 Fig. 3 Knot proportion of a oak veneer and b beech veneer according to different peeling thicknesses and veneer position inside the trunk

Fig. 4

 4 Fig. 4 Mean knot size and frequency of a oak veneer and b beech veneer according to different peeling thicknesses and veneer positions inside the trunk

Table 1

 1

	Peeling setup, number specimens prepared for the of panels, and number of test	Wood species	Veneer position	ness Veneer thick-	veneer layers Number of	Panel	Test specimen
	mechanical test of LVL made of secondary quality hardwood	Oak	Internal	2.1 3.0	10 7	4 4	32 32
				4.2	5	4	32
			External	2.1	10	4	32
				3.0	7	4	32
				4.2	5	4	32
		Beech	Internal	2.1	10	4	32
				3.0	7	4	32
				4.2	5	4	32
			External	2.1	10	4	32
				3.0	7	4	32
				4.2	5	4	32

Table 2

 2

	Effect of peeling thickness on the mean lathe	Species	Oak			Beech
	check depth and lathe check interval on oak and beech veneer surfaces	Veneer thickness (mm) Mean lathe check depth (%)	2.1	3	4.2	2.1	3	4.2
		Different letters above the numbers signify statistically different populations, based on Tukey's post hoc
		HSD tests (p < 0.05). Values in parentheses are standard deviations

Table 3

 3 Comparing density, MOE and MOR of LVL made of internal veneer and external veneer f m modulus of rupture (MOR), E m,g global modulus of elasticity (global MOE) Different letters above the numbers signify statistically different populations, based on Tukey's post hoc HSD tests (p < 0.05). Values in parentheses are standard deviations of ply organizations and loading direction on beech LVL MOE and MOR, reported that beech mean MOE in the flatwise and edgewise directions was 12,679.6 MPa and 13,235.10 MPa, respectively, whereas the mean MOR was 152.36 MPa and 148.30 MPa, respectively. Compared to knot-free beech LVL, the mean MOE measured in the present study is more than 25% lower, whereas the mean MOR is more than 50% lower. Furthermore, compared to the mechanical properties of beech LVL reported by Daoui et al.

	Species	Test direction	Parameters	Internal	External
				Mean	Mean
	Oak		LVL density (Kg/cm 3 )	751.44 b (37.7)	742.2 a (33.2)
		Flatwise	E m,g (GPa)	9.4 a (2)	9.7 a (1.4)
			f m (Mpa)	57.7 a (14.6)	58.8 a (12)
		Edgewise	E m,g (GPa)	9.8 a (1.6)	10.3 a (1.1)
			f m (Mpa)	58.8 a (13.4)	63.3 a (9.4)
	Beech		LVL density	740.3 a (38.4)	731.4 a (68.1)
		Flatwise	E m,g (GPa)	9.8 a (1.4)	10.5 b (1.3)
			f m (Mpa)	65.9 a (10.9)	72.1 b (11)
		Edgewise	E m,g (GPa)	9.4 a (1.1)	10.1 b (1.6)
			f m (Mpa)	63 a (9.1)	71.8 b (17.7)

effect

Table 4

 4 Comparing local MOE, global MOE and the specific MOE measured using destructive tests on beech and oak LVL made of different veneer thicknesses Values followed by a different letter within a column are statistically different at p = 5% (ANOVA and Tukey's HSD test). Values in parentheses are standard deviations

	Global SMOE (MNm/kg)	Ew Fw		(2.2) 13.2 ac (1.6) 12.3 a	(2.5) 14.7 c (1.7) 14.1 bc	(3.3) 12.9 ac (1.9) 11.6 a		(1.2) 12.1 a (1.2) 12.7 abc	(2.3) 13.6 bd (3.1) 14.8 d	(1.3) 13.7 ad (0.8) 13.8 bd	Table 5 Comparing the mechanical properties measured using a non-destructive test according to different veneer thicknesses and loading direction Veneer thickness (mm) Dynamic SMOE (MN m/kg) Shear SMOE (MN m/kg) Fw Ew Fw Ew Oak LVL 2.1 17.3 b (1.8) 16.6 a (1.9) 0.9 a (0.3) 1.1 b (0.2) 3 18.8 c (1.2) 18.8 b (1.4) 0.9 a (0.2) 0.8 a (0.2)
				(2.3)	(2.8)	(4.1)		(1.8)	(3.7)	(6.5)	4.2 Beech LVL	15.9 a (2)	16.5 a (1.9) 1.2 b (0.4) 0.8 a (0.2)
	Local SMOE (MNm/kg)	Fw Ew		14.0 a (2.6) 14.1 a	17.8 bc (2.6) 18.1 c	13.9 a (4.7) 15.4 ab		14.3 a (1.8) 13.7 a	17.7 b (3.4) 16.4 ab	18.8 b (5.8) 18.4 b	Values followed by a different letter within a column are statistically different at p = 5% (ANOVA and Tukey's HSD test). Values in paren-theses are standard deviations 2.1 15.5 a (1.3) 14.9 a (1.3) 1.1 a (0.2) 0.9 b (0.2) 3 17.7 b (2.4) 17.9 b (3.8) 1.3 b (0.3) 0.9 b (0.1) 4.2 17.0 b (1.2) 17.2 b (0.7) 1.1 a (0.3) 0.7 a (0.1)
				(9.3)	(10.2)	(11.3)		(8.4)	(20.2)	(5.7)
		Ew		61.9 bc	68.2 c	53.3 ab		62.9 a	72.2 ab	65.0 ab
	MOR (MPa)	Fw		59.3 ac (12.2)	63.4 c (14.1)	51.1 a (11.1)		68.4 ab (9.2)	72.0 ab (12.1)	64.2 ab (11.8)
				(1.1)	(1.1)	(1.3)		(0.9)	(1.6)	(0.6)
	Global MOE (GPa)	Fw Ew		9.2 a (1.5) 9.8 ab	10.6 bc (1.8) 11.1 c	8.9 a (1.4) 9.3 a		9.3 a (0.8) 8.8 a	11.0 c (1.6) 10.6 bc	9.7 ab (0.7) 9.6 a
				(1.6)	(1.8)	(2.5)		(1.5)	(1.9)	(1.7)
	Local MOE (GPa)	Fw Ew		10.5 a (1.8) 10.5 a	13.3 bc (1.8) 13.6 c	10.6 a (2.5) 11.1 ab		10.6 a (1.4) 10.1 a	13.2 bc (2.3) 12.8 b	13.8 cd (2.6) 13.9 d
	Veneer thick-	ness (mm)	Oak LVL	2.1	3	4.2	Beech LVL	2.1	3	4.2

Table 6

 6

	Correlation between lathe check properties and	Species	Parameter	Check depth	Check interval	Shear specific	MOR
	LVL mechanical properties in flatwise (lower triangle and black color) and edgewise (upper triangle and gray color)	Oak	Check depth Check interval Shear specific	0.99*** 0.43	0.99*** 0.45	-0.57* -0.60**	-0.43 -0.46 -0.14
	direction		MOR	-0.57*	-0.60*	-0.28
		Beech	Check depth		0.77**	-0.82**	-0.13
			Check interval	0.77**		-0.51	-0.08
			Shear specific	-0.49	-0.36		-0.01
			MOR	-0.54*	-0.31	0.43
		*Correlation is significant at the 0.05 level
		**Correlation is significant at the 0.01 level
		***Correlation is significant at the 0.001 level

Acknowledgements

The authors are grateful for the financial support of GDR 3544 Science du Bois and the Indonesia Endowment Fund for Education. We also wish to thank our partners and funders of the Xylomat Technical Platform from the Xylomat Scientific Network funded by the ANR-10-EQPX-16 XYLOFOREST project and the Bourgogne Franche Comté Region.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


Rouae Ben Dhia

Denis Martinand

Nils Tilton

Dynamics and transport of a solute in Taylor-Couette flow bounded by permeable walls

Performances of filtration techniques are known to deteriorate with the accumulation of retained materials near the semi-permeable membranes. In the case of a solution considered here, the osmotic pressure induced by the concentration boundary layer forming near the membrane tends to cancel out the operating pressure driving the permeate flux accross the device. Dynamic filtration devices make use of hydrodynamic instabilities to mix the solution and abate the concentration boundary layer. However, no quantitative results exist to assess the couplings between mixing, osmotic pressure and instabilities, the effectiveness of dynamic filtration and how to optimize it. This study adresses those couplings in a controled fashion by considering a Taylor-Couette cell, with a fixed outer cylinder and a rotating inner one. Moreover, the gap is filled with a solution and both cylinders are semi-permeable membranes totally rejecting the solute. Imposing an operating pressure accross the gap drives a radial in-or outflow and the transmembrane flow of pure solvent builds up a concentration boundary layer near the inner or outer cylinder. The osmotic pressure related to the concentration increase at the membrane then opposes the operating pressure and reduces the radial flow. For fixed operating conditions, a stationary state can be obtained analytically(figure 1a). As the rotation rate of the inner cylinder is increased, centrifugal instabilities emerge in the form of toroidal vortices. These instabilities are studied both analytically (figure 1b), using the previous stationary state as a base state, and numerically, using dedicated Direct Numerical Simulations implementing accurate boundary conditions for the transmembrane flow and pressure. Osmotic pressure is found to promote these centrifugal instabilities as a result of an original self-sustained mechanism coupling the advection of the concentration boundary layer by the vortices, molecular diffusion and osmotic pressure driving a transmembrane flow fostering the vortices. This mechanism can induce a substantial reduction of the critical rotation rate above which vortices are observed.

Figure 1 :

 1 Figure 1: Figure of studied situation: a) Configuration and sketch of the base state (U,V : radial and azimuthal velocity components, C : concentration profile), b) Perturbation to this base state in a meridional plane.


Denis Martinand

Nils Tilton

Global modes in Taylor-Couette-Poiseuille flow with a permeable inner cylinder

Variations in the local stability of the flow in a Taylor-Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with the a weakly permeable inner cylinder through which the radial flow is governed by Darcy's law. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for obtaining global, synchronized, modes of centrifugal instability.

b 1 r r 1 2 Cylindrical cavity (a) (b)

A two-pronged approach is adopted. First, building on the existing convective/absolute stability analysis in the axially invariant TCP flow with impermeable cylinders [START_REF] Martinand | Absolute and convective instabily of cylindrical Couette flow with axial and radial flows[END_REF], the analytical frameworks of linear and non-linear global modes are used to obtain the critical conditions and characteristics of the instabilities in the axially varying flow with a permeable inner cylinder. These analyses are based on the selection of a specific axial location that acts as a wavemaker and imposes its unstable dynamics and frequency to the rest of the perturbation. Then, Direct Numerical Simulations using a dedicated pseudospectral method implementing the Darcy's condition on the permeable cylinder [START_REF] Tilton | A 3D pseudospectral algorithm for fluid flows with permeable walls. Application to filtration[END_REF] are performed to shed new light on the validity of the analyses in global modes. Guided by application to filtration devices, we consider a set-up where fluid extraction occurs along the full length of the inner cylinder. As one moves downstream, the mean axial flow decreases and so does the local stability of the base flow. Close to critical conditions, the global mode is governed by a linear wavemaker located at the outlet, in agreement with the wavepacket of toroidal vortices obtained in the DNS shown in Figure 2(a). As the rotation rate is increased, the linear global mode evolves to a non-linear global mode governed by wavemaker located at the boundary between the convectively and absolutely unstable regions, in agreement with the DNS shown in Figure 2(b). The global mode analyses do not fully explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wave-packets, as observed in Figure 2(b), characterized by step-downs of the temporal frequency.

Figure 1 :

 1 Figure 1: (a) Radial and axial velocities of the laminar Taylor-Couette-Poisuille (TCP) flow. The outer cylinder is impermeable while fluid flows across the inner permeable cylinder, according to Darcy's law, leading to a base flow varying along the axial direction. (b) shows the azimuthal velocity of the base flow in an equatorial plane.

Figure 2 :

 2 Figure2: Direct Numerical Simulation TCP flow with a permeable inner cylinder: radial velocity at mid-gap, as a function of the axial coordinate z. The rotation rate of the inner cylinder is 0.6% (a) and 16% (b) above its analytical critical value. The stable, convectively unstable and absolutely unstable regions are denoted by blue S, CU and AU, respectively.