M A Hernandez-Shek

M Mathieux

L André

P Peultier

A Pauss

Thierry Ribeiro
email: thierry.ribeiro@unilasalle.fr

Quantifying porosity changes in solid biomass waste using a disruptive approach of water retention curves (WRC) for dry anaerobic digestion

Keywords: Water retention curve, Porosity distribution, Dry anaerobic digestion, Solid biomass, Leach-bed reactor

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

Quantifying porosity changes in solid biomass waste using a disruptive approach of water retention curves (WRC) for dry anaerobic digestion

Introduction

Dry Anaerobic Digestion (D-AD) has already proven its efficiency in the methane recovery from lignocellulosic biomass having more than 15% of Total Solids (TS) content [START_REF] Ge | Solid-state anaerobic digestion of lignocellulosic biomass: Recent progress and perspectives[END_REF][START_REF] Karthikeyan | Bio-energy recovery from high-solid organic substrates by dry anaerobic bio-conversion processes: A review[END_REF][START_REF] Rocamora | Dry anaerobic digestion of organic waste: A review of operational parameters and their impact on process performance[END_REF]. Accessibility and availability of biomass are related to the cost of collection and transportation. Biomass with higher concentration of TS involves lower transportation costs per unit of solids compared to low TS feedstocks [START_REF] Brown | Comparison of solid-state to liquid anaerobic digestion of lignocellulosic feedstocks for biogas production[END_REF]. Agricultural residues, such as cattle manure and corn stover are the most common substrates for D-AD process in France (FranceAgrimer, 2016). Furthermore, yard waste, which includes grass, is a major biowaste generated from municipalities, which has become an interesting substrate for D-AD [START_REF] Koch | Biogas from grass silage -Measurements and modeling with ADM1[END_REF].

Given its simplicity and the physical characteristics of solid biomass, Leach-Bed Reactor (LBR) operated in batch is the most common technology for the anaerobic treatment and valorization of solid biomass (Riggio et al., 2017b). In this reactor, the solid biomass is irrigated with a liquid inoculum -named leachate percolating the solid bulk until being recovered at the reactor bottom. Liquid recirculation has a positive effect on the methane production, it improves the contact between the microorganisms and the solid substrate and avoid possible failures by diluting inhibitory compounds (Degueurce et al., 2016b;[START_REF] Kusch | Effect of various leachate recirculation strategies on batch anaerobic digestion of solid substrates[END_REF][START_REF] Shahriari | Effect of leachate recirculation on mesophilic anaerobic digestion of food waste[END_REF]. Despite the positive effect of liquid recirculation on biogas production (Degueurce et al., 2016b;[START_REF] Kusch | Effect of various leachate recirculation strategies on batch anaerobic digestion of solid substrates[END_REF], there is no clear consensus between the parameters leading liquid recirculation. In general, once an operation mode is chosen (total volume, frequency, flow), this would be kept until the end of the batch operation.

Liquid percolation through the solid bed is feasible due to its porosity [START_REF] Valencia | The effect of hydraulic conditions on waste stabilisation in bioreactor landfill simulators[END_REF].

The total porosity of a matrix represents the fraction not occupied by solid and which is available for the liquid and gas phases. Porosity has been identified as a major element influencing the liquid distribution and the degradation efficiency of biomass in LBR [START_REF] Myint | Enhancing anaerobic hydrolysis of cattle manure in leach bed reactors[END_REF]. Despite the importance of biomass porosity and its evolution through D-AD process, its analysis is poorly documented in literature. The physical changes of the solid bed like the loss of permeability limit the efficiency of liquid percolation to maintain the solid degradation [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF]. Unfortunately, to our knowledge, there is no method able to efficiently describe the changes in porosity distribution of the solid bed. As consequence, daily recirculated liquid volume still being established without considering the physical evolution of the solid phase.

Pore media is frequently studied by its physical relation with water [START_REF] Gerke | A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media[END_REF]. Initially developed for the analysis of soils, two-region MIM (M-mobile/IM-immobile water) model has allowed the modeling of successive percolation and drainage operations and the presence of non-uniform flow pathways in cattle manure [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF][START_REF] Shewani | Assessment of percolation through a solid leach bed in dry batch anaerobic digestion processes[END_REF]. This model considers as mobile water the one present in the macropores and that drains rapidly into the solid bed, while water retention is assured by the micropores (immobile water). MIM model does not consider capillary region or mesopores, being this one of the highest drawbacks in its application to porous media. As a consequence, capillary effects have been responsible for differences between the experimental and numerical analysis of percolation operations in LBR treating cattle manure. Meaning the importance of considering capillary pores (mesopores) as an intermediate pore size between the macropores and the micropores.

Furthermore, thermogravimetric analysis (TGA) has been used for determining the free and bound water present in biomass [START_REF] Dumas | Effects of grinding processes on anaerobic digestion of wheat straw[END_REF][START_REF] Garcia-Bernet | Water distribution in biowastes and digestates of dry anaerobic digestion technology[END_REF]. Some other studies have focused only on the Water-Holding Capacity (WHC) of biomass without considering the pores fraction responsible for water retention [START_REF] Fernandez | Methods for the evaluation of industrial mechanical pretreatments before anaerobic digesters[END_REF][START_REF] Sanchez | Hydration of lignocellulosic biomass. Modelling and experimental validation[END_REF].

Biomass porosity distribution and its evolution through D-AD process remains an open question, limiting the D-AD process optimization and the liquid recirculation operation. Thus, new methodologies need to be adapted and developed for solid biomass analysis. The Water Retention Curve (WRC) analysis is a technique relating the soil water content with the matric suction [START_REF] Du | A novel segmental model to describe the complete soil water retention curve from saturation to oven dryness[END_REF][START_REF] Wassar | Predicted and measured soil retention curve parameters in Lombardy region north of Italy[END_REF]. This is a method frequently used to estimate the water distribution and hysteresis in soils (hygroscopic water, the capillary water and the gravitational drained water) thereby fixing water irrigation operations according to the soil type, the season and the crop water necessities. The WRC of soils is built using pressured systems as the Richards chambers or the sand pressure tables [START_REF] Darwish | Caractérisation des propriétés hydrodynamiques d'un sol de la Bekaa (Liban) sur les rives du fleuve Litani[END_REF][START_REF] Jordan | Actualización en métodos y técnicas para el estudio de los suelos afectados por incendios forestales[END_REF][START_REF] Lavelle | Biodiversity: Conserving biodiversity in agroecosystems[END_REF][START_REF] Menéndez | Use of fractal scaling to discriminate between and macro-and meso-pore sizes in forest soils[END_REF]. Hitherto, no application of WRC methodology has been documented in literature for biomass, this could be explained by the fact that existed pressured chambers do not correspond to the needed volume for biomass analysis.

The aim of this work was to present a novel adaptation of WRC methodology to quickly and efficiently determine the pore distribution of solid biomass. This approach was inspired by the analysis of soils, allowed to determine the macro, meso and micropores of porous medium [START_REF] Luxmoore | Micro-, Meso-, Macroporosity of Soil[END_REF]. It integrates a first phase of immersion / saturation (I&S) of the sample with water, followed by drainage analysis (DA) and finally the thermogravimetry analysis (TGA). In the first part of this work, WRC methodology was used to characterize the pore distribution of four of the most common lignocellulosic biomasses used as substrate in D-AD; Cattle Manure (CM), Shredded Cattle Manure (S-CM), Chopped Corn Silage (CCS) and Roadside Grass (RSG). Additionally, bulk density, WHC and permeability of biomasses were determined for each biomass. Secondly, pores distribution evolution was determined from digested CM from four LBR's of 60L started up in parallel and sacrificed at different stages of the D-AD process (10, 15, 21 and 31 day). Changes in porosity distribution, fiber content of the solid phase and permeability values were quantifying and correlated. The impact of porous changes over the management of the liquid recirculation during the batch and methane production in LBR are also discussed.

Materials and Methods

Tested materials

Biomass samples were collected in summer to avoid any variability due to seasonality following the protocol described by [START_REF] Gy | Sampling for Analytical Purposes 172[END_REF]. No conservation of samples was undertaken, these were analyzed the same collection day.

i. Cattle Manure (CM)

CM is a mixture of cow slurry with the bedding material which is in most cases wheat straw.

Two kinds of CM, non-shredded CM and Shredded CM (S-CM) were respectively collected from the farm of the Institute LaSalle Beauvais and from another farm located in Talmas (France). Non-shredded CM presented fibers of wheat straw < 20 cm. Otherwise, industrially size reduction enhanced fibers with less than 5 cm length in S-CM

ii. Chopped Corn Stover (CCS)

CCS is used as animal feed in farms. Silage fermentation of stored CCS could reduce its nutritional value, then this is considered as a farm waste needed treatment, a sample of wasted CCS was collected from the farm located in Beauvais. CCS particles have a cylindrical shape and sizes between 1.0 and 2.0 cm length.

iii. Roadside Grass (RSG)

RSG recently harvesting by cutting machines was collected in Beauvais (France). RSG was still green and fresh at the moment of collection. It was composed of fibers between 10 and 15 cm in length and <3 mm of thickness.

Analytical methods

Biomass physicochemical characterization

For all the experiments, the total solids (TS) and volatile solids (VS) of the raw and anaerobically digested biomass were determined [START_REF] Apha | Standard methods for the examination of water and wastewater, 23rd ed[END_REF]. Dry and wet bulk density was determined using the mass-volume ratio in a cylindrical shape. Total dry ( dry) and wet porosities ( wet) were measured by dividing the saturated water by the total dry and wet sample weight as following [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF]Lam et al., 2008b):

= ( ) ℎ ( ) (1)
= ( ) ℎ ( ) (2)
Van Soest fractionation allowed the determination of the hemicellulose, cellulose and lignin content [START_REF] Van Soest | Use of Detergents in the Analysis of Fibrous Feeds. II. A Rapid Method for the Determination of Fiber and Lignin[END_REF]). The biochemical methane potential (BMP) of the biomass was also measured following the methodology proposed by [START_REF] Holliger | Towards a standardization of biomethane potential tests[END_REF]. Experimental data will be presented as average values, in addition, the standard derivation of the results will be shown as well.

Water Retention Curve (WRC) Analysis

Adapted from the analysis performed using the Richard's chambers to determine the porosity distribution and the field capacity in soils [START_REF] Darwish | Caractérisation des propriétés hydrodynamiques d'un sol de la Bekaa (Liban) sur les rives du fleuve Litani[END_REF][START_REF] Klute | Water Retention: laboratory methods[END_REF][START_REF] Richards | Porous plate apparatus for measuring moisture retention and transmission by soil[END_REF]. The proposed approach integrates a first stage of immersion and water saturation of the biomass (I&S), followed by a second stage of drainage analysis (DA) and finally, the last stage of evaporation of residual water and measurement by thermogravimetry (TGA) (Fig. 1). DA and TGA allowed the quantification of water stocked in the different pores of the solid, Luxmoore, (1980) pore size classification and definitions were considered in this work, macropores would consider the pores larger than 1 mm, mesopores from 10 μm to 1 mm and micropores inferior to 10 μm. The determination of the different volumetric fractions satisfied the following equation:

%" # + %" + %" # + %% = 100% ( (3)
Pore distribution tests were performed in duplicate for each biomass, except the sample of CM which analysis was performed on four occasions to better statistical analysis and representativeness of the proposed methodology.

Sample preparation

The medium to be analyzed is gently placed in a cylindrical plastic laboratory constructed permeameter (internal diameter 0.26 m, total height 0.25 m) until reaching about 0.2 m solid height. In order to avoid sample volume changes during the next step, the initial sample volume was fixed using a metallic aperture grill on the top of the sample.

Immersion and Saturation (I&S)

Tap water was gently injected from the bottom until the solid bed was completely filled with water. When water levels decreased for biomass absorption, more water was added until the top grill. At this stage wet porosity was determined using Eq. 2. The system was maintained closed for two hours to make the wetting and saturation process more efficient [START_REF] Fernandez | Methods for the evaluation of industrial mechanical pretreatments before anaerobic digesters[END_REF][START_REF] Shewani | Assessment of percolation through a solid leach bed in dry batch anaerobic digestion processes[END_REF]. At this stage, it is assumed that total biomass porosity was completely filled with water, and biomass achieved the maximum WHC.

Draining analysis (DA)

Once the submerged time ended, water was gravitationally drained from the permeameter bottom for 24 h. Drained water mass was measured using a HD150 balance (My Weigh, United

States, precision ± 20 g). The weight values were taken every 5 seconds during the first minute and then every minute until completing the first 10 minutes of DA. From this moment, data was registered each 10 min until the first hour and from there each hour to the end of the DA.

Disruption of linear behavior of recovered water with time in the DA indicated the limit between the macropores and the rapid mesopores. According to [START_REF] Luxmoore | Micro-, Meso-, Macroporosity of Soil[END_REF] in macropores drainage may occur very rapidly with the presence of surface ponding or perched water, while rapid mesopores or capillary flow may occur without the of theses last. Thus, once the slope of drainage drastically changed, the recovered water concerned rapid mesopores flow.

Thermogravimetric analysis (TGA)

Once the previous test was achieved, 20 g of remaining solid was collected and placed on an aluminum pan (diameter 10 cm). Then, the sample was introduced into a moisture weight Mark 160Top-Ray (BEL Engineering). Water evaporation was carried on at 105°C and sample weight loss data were registered each second using a RS232 port connected to a PC [START_REF] Dumas | Effects of grinding processes on anaerobic digestion of wheat straw[END_REF][START_REF] Garcia-Bernet | Water distribution in biowastes and digestates of dry anaerobic digestion technology[END_REF]. Samples weight data was analyzed using the moisture derivation of the Savitzky-Golay filter in Scilab 6.0 [START_REF] Savitzky | Smoothing and Differentiation of Data by Simplified Least Squares Procedures[END_REF]. This derivation allowed to identify the limit between the water present in mesopores and water present in the micropores of biomass. The Savitzky-Golay filter derivative of the resulted curve from the evaporation test of the RSG sample is illustrated in Fig. 2. At first, a period of increasing temperature is depicted until α, this is succeeded by a constant water evaporation until β, the fraction of water evaporated since the beginning of the test until β refers to water presented in capillary or mesopores.

Water mass balance in WRC analysis

Draining and evaporation test results allowed the construction of the experimental WRC for each biomass; DA allowed the quantification of water present in macropores and in rapid mesopores, whereas the TGA allowed the quantification of water stocked in capillaries (mesopores) and water very attached to the biomass, these pores spaces were considered as micropores. Water mass balance analysis was used to validate the results of WRC methodology using the following equations:

% ) *# ( "+): -* (-) + % * * (% ) * ( . ) + ( / 0 1& ) (4

Determination of Mobile and immobile water volume fractions

In this work mobile (θmobile) and immobile (θimmobile) water volume fractions were determined from the previous mass balance. These fractions have been determined from the total and added water to achieve I&S.

3 40567 3 / = - / 0 1& * 100 (5)
3 6440567 3 / = / 0 1& -- / 0 1& * 100 (6) 3 40567 3 0 /7 = - / 0 1& + . * 100 ( 7
)
3 6440567 3 0 /7 = % / 0 1& + . * 100 (8)

Hydraulic conductivity

The permeameter described in section 2.2.2 was used to determine the permeability of each sample. The same procedure of filling was performed and tap water was added until the permeameter limit (0.25 m), then, water was allowed to percolate the sample and the changes in water level with time were recorded using a cell phone (one plus 6.0). Video was analyzing using DaVinci software in order to better estimate the time of the water descent. The following equation allowed the determination of the water permeability (m s -1 ).

: = ; 5604/<< * =* > ℎ 0_ / ℎ @_ / A (9)
Where Hbiomass is the biomass height (m), t is the recorded time (s), ho_water and hf_water were the initial and the final water height respectively (m).

Inoculum characterization

Liquid inoculum was obtained from a previous D-AD cycle in a 500L batch digester fed with CM operated under mesophilic temperature (37°C) for two months. Thereafter, it was stored in drums at room temperature for one week. Before sampling for D-AD experiments, the inoculum was homogenized. TS content was measured at 1.9% and the VS averaged 42.5%TS. The initial pH was 8.4 and the VFA/alkalinity ratio was measured at 0.125.

Dry Anaerobic Digestion of CM in Sacrificed LBR's

Given its highlighted importance in agricultural methane production, CM was chosen as a substrate for D-AD process to validate and compare the results of this study with literature. In order to follow physical changes of biomass with the already proposed WRC method. Four batch reactors with liquid recirculation were started in parallel, and each was sacrificed at different stages of degradation according to the typical biogas flow behavior in a batch D-AD digester treating CM [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF]. The first batch reactor corresponded to the initial conditions of the CM before anaerobic digestion (day_0). The second reactor corresponds to the first peak of methane production (day_10), third reactor corresponds to the methane production valley founded between days (day_15), the fourth reactor was sacrificed once reaching the second peak of methane production (day_21) and finally, the fifth reactor was sacrificed when biogas flow would decrease until the batch end (day_31).

The four reactors used in this study were made of polyethylene; the internal diameter and the total height were 39 cm and 50 cm, respectively, for a total volume of approximately 60 L. A mesh (5 mm holes) placed at the bottom avoided solid blockage of liquid phase pipes recirculation. Twenty-one kilograms of CM were gently placed in the reactor using hands, subsequently, 22 kg of inoculum (liquid phase) was added obtaining a ratio Inoculum/Substrate (I/S) of VS content equal to 0.05.

Loaded reactors were hermetically sealed and a thermostatically controlled water bad allowed to keep mesophilic temperature (37°C) during all the batch duration. Approximately 40 L of the liquid phase was daily recirculated (2 min each 2 h with a flow rate of 100 L h -1 ) using MasterFlex peristaltic pumps. A valve in the liquid phase circuit enabled samples to be taken for analysis. Biogas production was continually measured using drum gas meter TG5 (Ritter, Germany), biogas composition (CH4, CO2 and H2) was monitored daily by a MGA300 multi-gas analyzer (ADC Gas Analysis Ltd, Hoddesdon, United Kingdom).

In order to follow and control the anaerobic digestion process, the liquid phase was sampled and analyzed on a daily basis. The pH and the conductivity were measured using Mettler Toledo (Switzerland) SevenEasy TM S20. The buffer capacity and the volatile fatty acid concentration (VFA) were determined by two acidification steps using sulphuric acid. The first acidification down to pH 5.0 allowed the buffer capacity to be determined, and the second acidification down to pH 4.4 allowed the quantity of volatile fatty acids to be determined. These analyses were carried by means of an automatic titrator T50 (Mettler Toledo, Switzerland).

Once each reactor was sacrificed, physical characterization of the solid phase was performed according section 2.2.1. In order to minimize any structural changes of the samples for WRC analysis, similar core drilling procedure performed in soils was used, representative sampling amount (around 3 kg) of the solid was taken using a sharpened cylinder and carefully introduced into the permeameter. Finally, Pearson linear correlation analysis was performed to assess the significance and correlation between the pore distribution with TS content, VS content, the fiber content, the bulk density and permeability. Results and Discussion

Biomasses physical characterization

Physical properties of four of the most common biomasses treated by D-AD process were measured in this section (Table 1). Physical properties such as the TS, the VS and the bulk density are essential parameters for D-AD because they determine the loading of biomass, and consequently the methane yield per volume of reactor [START_REF] Caicedo | Effect of initial bulk density on high-solids anaerobic digestion of MSW: General mechanism[END_REF][START_REF] Møller | Feces composition and manure derived methane yield from dairy cows: Influence of diet with focus on fat supplement and roughage type[END_REF].

For tested biomass, TS values ranged from 14.5 and 20.1 % except for corn silage with 37.7% TS (Table 1). These values of TS are in the range of lignocellulosic biomass treated by D-AD process [START_REF] Brown | Comparison of solid-state to liquid anaerobic digestion of lignocellulosic feedstocks for biogas production[END_REF][START_REF] Rocamora | Dry anaerobic digestion of organic waste: A review of operational parameters and their impact on process performance[END_REF][START_REF] Sawatdeenarunat | Anaerobic digestion of lignocellulosic biomass: Challenges and opportunities[END_REF]. Biomass is considered as a spongy material; it means that according to their particle size, biomass can integrate and absorb high water quantities inside the vegetal tissues, hence, dry biomass is frequently used as bedding by livestock activities. Biomass WHC increase with size reduction due to an increase of the contact surface of biomass [START_REF] Dumas | Effects of grinding processes on anaerobic digestion of wheat straw[END_REF][START_REF] Fernandez | Methods for the evaluation of industrial mechanical pretreatments before anaerobic digesters[END_REF].

This fact was observed when comparing CM with S-CM, the WHC were 6.7 ± 0.2 and 7.4 ± 0.2 gwater gDM -1 respectively.

Bulk density and porosity depend on the particle shape, size and orientation, the particle specific density, the particles size distribution, the moisture content and the applied pressure (Lam et al., 2008a). In shredded CM, the fibers size reduction and a larger presence of feces increased the humidity, as a consequence, higher wet and dry bulk density values compared to non-shredded CM (Table 1). Initial bulk density has been identified as a key factor in the anaerobic treatment of municipal solid waste in LBR, indeed, over 1000 kg m -3 inhibition of methane production was observed [START_REF] Caicedo | Effect of initial bulk density on high-solids anaerobic digestion of MSW: General mechanism[END_REF]. Degueurce et al., 2016a have reported similar values of non-shredded CM bulk density for samples collected during the winter, they have used the "Schaub-Szabo" device to measure the evolution of the bulk density with the material height from 0.2 to 2.2 m, their results suggests an increase in bulk density from 311 to 577 kg m -3 with the material deep, meaning an increase of 85% of the bulk density.

Biomass porosity values are shown in Table 1, the dry porosity concerns the total porosity after drying the sample at 105°C, whereas the wet porosity refers to the total available porosity of the sample at the moment it was collected. Total dry porosity values were around 90% for all biomass, according to Jordan and Cerdá (2010), total porosity is very high over 60% and too low under 30%. Similar values of dry bulk density and dry porosity have been presented by [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF] treating non-shredded CM, however, values of dry porosity barely changed between the initial CM and the digestate. In consequence, total dry porosity by itself does not represent the physical changes of CM treated in D-AD.

Wet porosity values showed higher variability than dry, meaning that water presence and its distribution may play an important role in the porosity volume of biomass and in the hydraulic behavior. Initial moisture in biomass samples indicates that a portion of porosity is already water filled. Comparing S-CM with non-shredded CM, size reduction enhanced important physical changes in the biomass, reducing wet porosity values from 51.7 ± 1.3% to 18.6 ±1.7%.

Moreover, despite the differences in particle size and shape and TS content, CCS and RSG presented similar values of porosity and bulk density, both dry and wet. Based on the previous results, it appears that physical parameters present a high variability given their interdependent correlation, more research should be performed in order to establish detailed physical models than the existed ones to easily determine the potential biomasses that could be treated in LBR for methane recovery.

WRC analysis of biomass for pores distribution determination

As describe before, total porosity can be distinguished according to its function and relation with water (Fig. 1); macropores are the larger ones and allow the rapid percolation of water and the presence of a gas phase in the biomass. Next, the mesopores ensure the presence of capillary water, they can be divided into rapid and slow mesopores. Finally, the micropores water volume concerns vicinal or bound water. Water stocked in mesopores can be removed by mechanical dewatering, whereas the water in the micropores can be only withdrawn using heat. Fig. 3 illustrates the experimental WRC for each tested biomass, this analysis is composed of two subsequential analyses; the DA and the TGA giving as result the porosity distribution for each biomass, macro-, meso-, micropores and solid percentages of the total biomass bulk volume.

Macropores were represented with green color, mesopores with yellow, micropores in blue and solid fraction in gray.

DA: Macropores and rapid mesopores volumes

According to the proposed WRC methodology, the water volume present in macropores channeling would flow with a linear behavior in the first seconds of the DA, a change in this linear behavior indicates the macropores water stock depletion, from this point, recovered water in the next hours for DA concerns the water stocked in rapid mesopores channeling (dash yellow line). According to [START_REF] Luxmoore | Micro-, Meso-, Macroporosity of Soil[END_REF], macropores drainage occurs very rapidly once DA start, while, rapid mesopores drainage includes slow capillary water flow without the presence of pounding or perched water in the solid. The DA was maintaining for 24 hours in order to ensure maximal water recovery from rapid mesopores. Time log-scale was useful to represent the draining behavior since higher changes are expected in the first minute of the test.

Similar values of macropores volume for CCS and RSG were measured, 58.0% and 62.0% respectively (Fig. 3a andb). However, the draining was faster for the RSG than for the CCS, this explains the slight difference between the macropores slopes of these two biomasses. Even if these samples have similarities in their physical properties, the solid particle shape is different affecting the shape of pores, as a consequence, differences in the drainage velocity have been observed. Further research is necessary in order to fully determine the effect of particles shape on the pores shape structure for solid biomass. Otherwise, WRC results of S-CM presented low macropore volume (1.1%) affecting the amount of water recovered in DA (Fig. 3d). Contrary to S-CM (Fig 3c), non-shredded CM had better macropores structure with 30.4%. As indicated before, rapid mesopores volume was determined after the linear macropores draining for each biomass, for RSG, CCS and CM, the rapid mesopores volume was 7.9%, 8.43% and 5.32%

respectively, whereas for S-CM only had 0.31% for this type of pore channeling.

The presence of macropores is linked with the permeability values of matter (Table 1). In biomasses with lower values of macropores, lower values of permeability have been observed.

Considering the S-CM, the measured permeability value (Table 1) was only 1.2 •10 -8 m s -1 , this was very low compared to the other tested biomass with values from 8.6 • 10 -4 to 1.3 •10 -3 m s -1 .

Concentrated biomasses with lower values than 10 -4 as the S-CM could not be an indicated substrate for D-AD process with liquid recirculation, because water can barely infiltrate the biomass and very low percolation rate is observed. This kind of biomass could be subject better of a reactor type different from LBR.

Finally, the DA allowed the determination of the WHC at 24 h of drainage of biomasses.

Compared to other biomasses, S-CM was the biomass with higher WHC value with (7.4 ± 0.2 g water /g TS) (Table 1). WHC values for CM, RSG and CCS were 6.74, 7.35 and 4.08 g water /g

TS respectively. [START_REF] Fernandez | Methods for the evaluation of industrial mechanical pretreatments before anaerobic digesters[END_REF] showed similar results of WHC for samples of CM before and after industrial size reduction. Consequently, biomass WHC is affected by the same parameters determining physical properties described before.

TGA: Slow mesopores and micropores volumes

The next step in the proposed methodology concerns the TGA, here a sample of the remained solid of DA was analyzing using a thermogravimetric balance in order to quantifying the slow mesopores and the micropores volume. Whilst the former refers to water trapped inside crevices and interstitial spaces, the latter made emphasis on the hydration water (water chemically bound to the particles) and the vicinal or surface water (monolayer and multilayer) [START_REF] Garcia-Bernet | Water distribution in biowastes and digestates of dry anaerobic digestion technology[END_REF]. The limit between mesopores and micropores for RSG sample is depicted in Fig 2.

The fraction of water evaporated since the beginning of the test until β refers to water presented in capillary or mesopores which is less influenced by the solid particles. This fraction of water plays a key role in D-AD since it determines the available water for microorganisms [START_REF] Garcia-Bernet | Water distribution in biowastes and digestates of dry anaerobic digestion technology[END_REF]. As can be seen, β mark a sudden change of the water evaporation derivative at time 480 seconds, it means that the constant water rate evaporation ended and from this point the remaining humidity is harder to evaporate, thus a reduction in the evaporation rate indicating the limit between mesopores and micropores. Water evaporated from β to ψ is considered as micropores volume water, given its strong relation with the solid, this water fraction is not available from metabolic activities of microorganisms [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF][START_REF] Garcia-Bernet | Water distribution in biowastes and digestates of dry anaerobic digestion technology[END_REF].

The results of TGA for each biomass are also depicted in Fig. 3. Total mesopores volume fraction concerns the sum of the volume of rapid mesopores determined in DA and the slow mesopores quantifying using the TGA. Similar values were obtained for the mesopores volume of RSG and CCS with 26.4 ± 0.8% and 25.2 ± 0.3% respectively. In contrast, CM samples presented more significant number of mesopores and micropores than RSG and CCS, the presence of animal slurry would be responsible for these higher values. S-CM achieved 64.9 ± 3.6 of mesopores volume, while for CM this fraction represented 44.4 ± 3.4% of the total porosity. As can be seen, in S-CM the macropores volume was transformed in mesopores volume due to the size particles reduction. Mesopores volume could include dead-end pores and isolated or closed pores of the solid volume [START_REF] Nishiyama | Permeability of porous media: Role of the critical pore size[END_REF][START_REF] Yokoyama | Porosimetry of vesicular volcanic products by a water-expulsion method and the relationship of pore characteristics to permeability[END_REF], in these pores water and gas could be stocked and limited mass transfer may enhance local inhibition of D-AD process .

Similarities between the values of solid and micropores volumes percentages for all biomasses were observed (Fig 2), this could be explained due to micropores are inside the solid fraction and on its walls surface; indeed, SEM images have already allowed the observation of the internal micropore structure of wheat straw fibers [START_REF] Han | Alkali pretreated of wheat straw and its enzymatic hydrolysis[END_REF]. In S-CM, size reduction increased the microporosity volume by the creation of more surface of solid, thus higher WHC.

Otherwise, compared with the other tested biomasses, RSG obtained the lower value of micropores 6.8% and solid volume fraction 4.8%, this could be due to that sample was analyzed fresh and green, just after harvesting; thus, the vegetal structures were not degraded and were naturally filled with water and less water absorption took place while the test was performed. It seems that biomass sponginess increases by drying due to a partial irreversible collapse of pores and the creation of larger water absorption pores [START_REF] Meng | Determination of porosity of lignocellulosic biomass before and after pretreatment by using Simons' stain and NMR techniques[END_REF].

WRC analysis Vs MIM model

In the double porosity MIM model, the volumetric water content is assumed to be divided into two distinct volumetric regions; mobile (θmobile) also called macropores and immobile (θimmobile) known as micropores. In order to compare WRC analysis with previous works using double porosity model and setting the advantages of the proposed methodology, mobile (θmobile) and immobile (θimmobile) water volume fractions have been determined from the total water and the added water to achieve I&S. θmobile/θadded refers to the drained water after 2 hours over the added water, thus the sum of macropores and rapid mesopores volume, controversy, θimmobile/θadded indicate the stagnant water fraction stocked in slow mesopores and microporosity over the added water.

Analysis of CM gave as results 60.0 ± 3.6% of θmobile/θadded and 40.0 ± 3.6% of θimmobile/θadded; similar values were reported by [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF] as macro and microporosity, 64% and 36 % respectively, using modeling of tracer tests. MIM model limitations have been observed since it does not consider the initial absorbed water by the sample before the test in which diffusion and convection of the tracer is more difficult. As a consequence, inconsistent results in the first 21 days of D-AD process indicates difficulties in determining the pore distribution of digested samples of CM. In WRC analysis, the initial volumetric was including in the mesopores and micropores volume calculation, this could represent an advantage over MIM model.

In another work, [START_REF] Shewani | Assessment of percolation through a solid leach bed in dry batch anaerobic digestion processes[END_REF] using double region porosity model have measured values from 18 to 50% for macroporosity, 42 to 70% for microporosity and 8 to 12% for the solid volume of CM with different compaction levels. In this work, using the same calculation proposed by the previous authors for CM with 18.59 ± 0.43 %TS, values in the same range of measure were determined at 30.5 %, 60.5% and 9% respectively for macroporosity, microporosity and solid volume, Even though [START_REF] Shewani | Assessment of percolation through a solid leach bed in dry batch anaerobic digestion processes[END_REF] have for the first time given values for macropores, micropores and solid volume, their method for porosity distribution does not consider the mesopores or capillary volumes. Consequently, this fraction of pores was responsible for differences between experimental and calculated drainage results using Computational Fluid Dynamic (CFD) tool. The proposed WRC analysis included the mesopores or capillary volume and offer a better pore distribution information for future studies of these kinds of porous media.

In order to measure the applicability and accuracy of WRC analysis to determine the water distribution in biomass samples, water mass balances (WMB) were performed using Eq. 4 (see Table 1) obtaining higher values than 96.7 ± 0.1%. WRC methodology coupled with tracer tests and digital volumetric imaging could be powerful tools in the understanding of the pore distribution network evolution of treated biomass in D-AD. Finally, the effect of pore distribution, tortuosity and preferential flow pathways on liquid recirculation could be fully simulated using CFD [START_REF] Vallabh | Modeling tortuosity in thin fibrous porous media using computational fluid dynamics[END_REF].

Dry Anaerobic Digestion of CM in Sacrificed LBR

In the previous section, the use of WRC analysis has successfully quantifying the pores distribution of several biomasses. This section presents the results of the changes in porosity distribution of anaerobically digested CM from days 10, 15, 21 and 31 have been sampled from 60 L sacrificed LBR's. Reactor mass balances between the inlet and the outlet ranged from 93.28% to 99.62% indicating a good D-AD experimental performance. The BMP value of CM was measured at 222.8 ± 4.4 NmL CH4 gVS -1 , this BMP was recovered at 98.66% on day 31.

Monitoring of the volatile fatty acids, pH and buffer capacity did not evidenced inhibition problems during the D-AD process.

Biogas Production

Similar behavior on methane production was observed for the four LBR compared with literature (Degueurce et al., 2016c;Riggio et al., 2017a), Fig. 4a presents the biogas and methane flow of the last reactor sacrificed at day 31. The first gas peak was observed around day 3, this was mainly carbon dioxide produced by aerobic digestion of rapid fermentative matter partially given the initial oxygen present in matter before the reactor sealing. Second gas peak production was achieved for all reactors between days 9 and 11. The valley between peaks 2 and 3 mark the slack on methane production. The third and last gas production peak was observed at day 16.5 ± 1.5 for the two remaining reactors. The cumulated methane for all reactors and the average production at the sacrificed days of still working reactors is depicted in (2015) using recirculation each 2 h during 2 min with 100 L h -1 of flow.

Cattle Manure Physical Characterizations at Different Stages of D-AD

Physical characterization of cattle manure at different stages of D-AD process included the TS content, VS content, dry and wet bulk density and porosity and the WHC (Table 2). TS content decreased from 18.59 ± 0.43% to 11.10 ± 0.51% between the initial CM and the digestate at 31 days. VS consumption presented a linear behavior with time, probably matter degradation would have continued for some days more after day 31. Water impregnation and solid degradation enhanced the augmentation of wet bulk density from 407.8 ± 14.1 to 914.2 ± 10.9 kg m -3 , in contrast, wet porosity values decreased from 51.7 ± 1.3 to 10.2 ± 1.5 % with time proving the bulk compaction with D-AD process with liquid recirculation. Dry values of bulk density and porosity did not present important changes as wet values (Table 2), thus water in samples plays an important role in physical characterization of CM and digestates. Similar results were obtained comparing the values of TS, VS, dry bulk density and dry porosity with the reported values by [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF]. Otherwise, similarities between the values of the wet bulk density determined at the 60 L LBR's (data not shown) and those determined with the permeameter for WRC methodology were observed, meaning that the use of a 13 L permeameter did not inflect important changes in the structure of the digested biomass once this was sampled and placed in the permeameter.

WRC and porosity distribution of CM at different stages of D-AD in sacrificed LBR

The WRC of CM and digested samples recovered at days 0, 10, 21 and 31 are depicted in Fig. 5a. In DA, the slope determining macropores in D-DA decreases with the anaerobic degradation of the solid medium. Initially, the macropores slope value in DA was -0.09, this value gradually decreased with the solid degradation, on day 10 the slope value was -0.059, at day 15 this was determined at -0.056, at day 21 was -0.029 and finally at day 31 the slope value was reduced until -0.006. Rapid mesopores (dashed yellow line) slopes presented lower variability than macropores slopes, they changed from -0.006 and -0.004 from days 0 to 31. TGA's results are also shown in Fig. 5a, as can be observed, the time of the test was slightly different for all samples even if the sample amount was the same in all performed TGA. In samples at day 0, the total humidity was removed in average 2865 seconds, this time increased at days 10 to 3150 seconds, degraded mater was able to hold more water, thus micropores volume increased from 16.2 ± 3.6% to 21.1 ± 3.9 in the first 10 days. (3). Table 3 shows the slope (m) and the y-intercept which represent the initial percentages of macro, meso and micropores of CM. The use of these equations can allow the estimation of pores distribution changes of anaerobically digested CM between 0 and 31 days in 60 L LBR.

Effect of fiber degradation on pore distribution evolution and the permeability of the solid bed

In this section the structural changes of the solid phase were related with fibers biological degradation. As defined before, CM is a mixture between cow feces and the wheat straw used as bedding material. The presence of wheat straw fibers gives a solid structure and high porosity values allowing the liquid percolation in LBR in the first days of batch. As a vegetal material, wheat straw is composed of fibers of cellulose, hemicellulose and lignin. Fiber content has been determined for samples from sacrificed D-AD reactors (Fig. 6a). Hemicellulose decreased from 27.2 ± 0.2 to 17.2 ± 0.6 %TS, whilst cellulose decreased from 31.9 ± 1.2 to 22.9 ± 1.0 % TS. The lignin is a non-degradable molecule by D-AD, thus, increase of the lignin content in the solid fraction was observed from 7.4 ± 0.2 % to 10.8 ± 0.5 % TS. Table 3 depicts the linear regression parameters determining the kinetic degradation of hemicellulose and cellulose respectively, similar patterns of biological degradation were observed for both.

According to the Pearson correlation results between the pore distribution changes with fiber degradation and loss of permeability, macropores volume and the mass height were linearly related to the degradation of cellulose and hemicellulose content of the biomass. Strong correlations between these parameters were observed. Macropores reduction was correlated with hemicellulose and cellulose degradation in 0.98 and 0.93 respectively with p-values inferior to 0.05 (Table 4). Moreover, fiber degradation was found responsible for the loss of solid permeability from 2.5 ± 0.2 • 10 -3 to 6.1 ± 0.7 • 10 -5 m s -1 (Fig 6b). The permeability was reduced in 97.6%, which is a very approximate value of the macropores reduction of 94.3% in 31 days of D-AD treatment of CM. Similar permeability reduction behavior was observed by [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF] in quantifying non-uniform flow using tracer experiments.

Methane production was well correlated with solid physical changes and fiber degradation with

Pearson coefficient values higher than 0.79. Macropores volume reduction was strongly related to the settlement and compaction of the biomass with correlation coefficient of 0.98 (Table 4), indeed, the CM height was reduced from 42 ± 2 to 18.0 ± 0.4 cm in LBR between days 0 to 31, meaning height reduction of 57.1%. Hence, solid height decrease can be used as an indicator of macropores and permeability reduction. This consideration is important since at the industrial scale, following of the solid height would be easier than macropores and permeability; additionally, this does not entail the reactor sacrifice necessarily for solid sampling.

Implication of macropores reduction on the liquid recirculation operation in D-AD process

In literature the positive effect of liquid recirculation on biogas production in LBR is well known (Degueurce et al., 2016b;[START_REF] Kusch | Effect of various leachate recirculation strategies on batch anaerobic digestion of solid substrates[END_REF]. However, there is no clear consensus between the parameters leading liquid recirculation. In general, an operation mode is chosen once (total volume, frequency, flow) and is kept until the end of the batch operation without considering the physical changes occurred on the solid bed. [START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF] has reported poor percolation through the digestate on day 32, instead, liquid flow occurs at the reactor boundary, which is useless to keep moisture content inside the solid bed and to maintain solid degradation.

Since liquid percolation is possible due to the presence of macropores, the recirculated liquid volume should be adjusted according to the macropores reduction. This could enhance important

Conclusion

D-AD using LBR system is often used in practice, while leaching pattern and strategy are not well understood. Therefore, characterization of the pore in the digestion medium is required.

WRC analysis was useful to quantify the pore distribution of various raw solid biomasses into macro, meso and micropores. Solid compaction and loss of permeability during CM batch fermentation were related with the linear decrease of macropores and structural changes due to lignocellulosic fiber degradation. As macropores are essential to ensure percolation of the liquid,

  M.A. Hernández-Shek, M. Mathieux, Laura André, P. Peultier, A. Pauss, Thierry Ribeiro To cite this version: M.A. Hernández-Shek, M. Mathieux, Laura André, P. Peultier, A. Pauss, et al..Quantifying porosity changes in solid biomass waste using a disruptive approach of water retention curves (WRC) for dry anaerobic digestion. Bioresource TechnologyReports, 2020Reports, , 12, pp.100585. 10.1016Reports, /j.biteb.2020.100585. hal-03246805 .100585. hal-03246805

  : initial water weight in the sample determined by multiplying the initial biomass weight by the humidity. ( / 0 1& ): added water to achieve immersion and saturation of the sample -* (-): drained water weight once DA is complete (Macropores and rapid mesopores volume) water present in the samples after DA determined by multiplying the remaining mass by the humidity determined by TGA (Slow mesopores and micropores volume)

Fig. 4b .

 4b Fig. 4b. Differences in methane production were attributed to the starting-up of the heating baths at the first moment of the experiment and to the experimental uncertainties. The results of methane production of these four LBR's were similar to the results presented by André et al.

  reductions of energy consummation by recirculation pumps and extend their useful life period in industrial biogas production. In this work, approximately 40 L of liquid was discontinuously recirculated daily (2 minutes each 2 hours with flow 100 L/h), this recirculation mode was chosen for several reasons: the first 40 L was the initial solid working volume in the reactor, secondly, this recirculation mode has shown good D-AD performance for CM in previous research works[START_REF] André | Methane production improvement by modulation of solid phase immersion in dry batch anaerobic digestion process: Dynamic of methanogen populations[END_REF][START_REF] André | Quantifying physical structure changes and non-uniform water flow in cattle manure during dry anaerobic digestion process at lab scale: Implication for biogas production[END_REF]. An alternative pattern of recirculation is shown in Fig 6c, here the daily recirculated volume is reduced considering the loss of macropores. Hitherto, none study about the effects of decreasing recirculation volume over D-AD has been found in literature. In this type of recirculation, only the liquid volume able to pass through the solid bed would be irrigated, avoiding excessive recirculation and liquid flow on the reactor boundary. Thus, the recirculated volume could be reduced in 50% in around 15 days (Fig 6c), and completely suppressed at day 31 in the treatment of CM.

FiguresFig. 1

 1 Figures

Fig. 2

 2 Fig. 1 (a) Schematic pores structure of the biomass and definitions of pores function (b) Theoretical WRC with the test phases: Immersion and saturation (I&S), Drainage analysis (DA) and Thermogravimetric analysis (TGA)

  After this point, micropores volume remains almost similar until the end of the experiment on day 31. Evaporation time was inferior on days 31 and 21, with 2670 and 2250 seconds, respectively. Moreover, water mass balance (Eq. 4)

	values obtained for WRC analysis ranged from 88.3 ± 1.3 to 98.5 ± 2.2 % (Table 2), meaning a
	good WRC analysis performance.
	Volume porosity distribution changes are depicted in Fig 5b. Macropores decreased linearly
	from 30 ± 3 on days 0 to 1.7 ± 0.3% on day 31, meaning a reduction of 94.3%. Macropores were
	converted into mostly mesopore volume which increased linearly from 44.4 ± 3.4 to 65.4 ±
	0.2%. Moreover, micropores volume slightly increased from 16.2 ± 3.6 to 22.9 ± 0.3%. Previous
	results drive to a group of linear regression equations able to estimate the volumetric fractions of
	CM related in Eq.

Table 1 .

 1 Biomass characterization

	Biomass	RSG	CCS	S-CM	CM
	Particle shape	Plate	Angular	Plate	Cylindrical
	Particle size	Length: 10-15 cm Thickness: <2 mm	1-2 cm	Length: <5 cm Thickness: <2 mm	Length: 10-20 cm Diameter: <5 mm
	TS (%)	22.6 ± 0.6	37.9 ± 0.6	14.5 ± 1.7	18.6 ± 0.4
	VS (%TS)	85.3 ± 0.6	95.8 ± 0.7	79.4 ± 1.5	86.4 ± 0.1
	ρwet (kg m -3 )	174.1 ± 4.5	166.2 ± 0.7	797.8 ± 11.4	407.8 ± 14.1
	ρdry (kg m -3 )	39.4 ± 1.0	63.0 ± 0.3	115.6 ± 1.7	75.8 ± 2.6
	εwet (%)	78.7 ± 0.1	77.9 ± 0.4	18.6 ± 1.7	51.7 ± 1.3
	εdry (%)	95.2 ± 0.1	91.6 ± 0.1	88.2 ± 0.3	91.0 ± 0.2
	θmobile/ θadded (%)	76.1 ± 0.8	73.7 ± 2.3	5.5 ± 1.0	60.0 ± 3.6
	θmobile/ θtotal (%)	62.9 ± 0.6	62.6 ± 2.2	1.2 ± 0.1	33.5 ± 2.7
	WHC (gwater gDM -1 )	7.4 ± 0.1	4.1 ± 0.2	7.4 ± 0.2	6.7 ± 0.2
	WMB (%)	96.7 ± 0.1	99.0 ± 0.8	99.0 ± 0.2	98.5 ± 2.2
	K (m s -1 )	1.3 ± 0.3 • 10 -3	8.6 ± 0.6 • 10 -4	1.2 ± 0.2 • 10 -8	2.5 ± 0.2 • 10 -3

Table 2 .

 2 Physical characteristics evolution of digested CM

	Event	CM_Day 0	CM_Day 10	CM_Day 15	CM_Day 21	CM_Day 31
	TS (%)	18.6 ± 0.4	11.7 ± 0.1	13.9 ± 0.1	10.5 ± 0.3	11.1 ± 0.5
	VS (%TS)	86.4 ± 0.1	82.7 ± 0.2	82.1 ± 0.3	78.6 ± 0.2	76.0 ± 0.3
	ρwet (kg m -3 )	407.8 ± 14.1	556.0 ± 4.0	594.6 ± 13.8	766.2 ± 15.3	914.2 ± 0.9
	ρdry (kg m -3 )	75.8 ± 2.6	64.8 ± 0.5	82.9 ± 1.9	80.6 ± 1.6	101.5 ± 1.2
	εwet (%)	51.7 ± 1.3	29.8 ± 3.2	28.4 ± 0.2	23.9 ± 1.1	10.2 ± 1.5
	εdry (%)	91.0 ± 0.2	91.8 ± 0.4	90.0 ± 0.1	92.0 ± 0.1	90.0 ± 0.2
	WHC (gwater gDM -1 )	6.7 ± 0.2	8.9 ± 0.1	7.5 ± 0.3	10.4 ± 0.3	8.9 ± 0.2
	WMB (%)	98.5 ± 2.2	95.1 ± 0.1	95.3 ± 4.6	88.3 ± 1.3	96.6 ± 0.7

the recirculated volume could be progressively reduced considering the kinetics of macropores volume decrease.

Supplementary material

Visual aspect of studied biomasses, liquid phase monitoring, reactor mass balances and Pearson correlation coefficients can be consulted as supplementary material.

Acknowledgments

The authors wish to thank the Agence Nationale Recherche Technologie (ANRT) for the financial support of this work and for the Ph.D. grant of Manuel HERNANDEZ-SHEK (CIFRE n° 2017/0352).

LBR's


Pierre-Edouard Fournier

Christine Zandotti

Laetitia Ninove

Elsa Prudent

Philippe Colson

Céline Gazin

Matthieu Million

Hervé Tissot- Dupont

Florence Fenollar
email: florence.fenollar@univ-amu.fr

Contribution of VitaPCR SARS-CoV-2 to the emergency diagnosis of COVID-19

Keywords: SARS-CoV-2, COVID-19, diagnosis, rapid diagnostic test, point-of-care

Background: With the persistent COVID-19 pandemic, there is an urgent need to use rapid and reliable diagnostic tools for highly urgent cases. Antigen tests are disappointing with their lack of sensitivity. Among molecular tools allowing a diagnosis in less than an hour, only one, the Cepheid Xpert Xpress SARS-CoV-2 assay, has exhibited a good sensitivity. However, we are also facing a global shortage of reagents and kits. Thus, it is imperative to evaluate other point-of-care molecular tests.

Methods:

We evaluated the VitaPCR TM RT-PCR assay, whose sample analysis time is of approximately 20 minutes, in nasopharyngeal secretions from 534 patients presenting to our Institute, for the diagnosis of COVID-19, and compared it to our routine RT-PCR assay.

We also compared the two assays with tenfold dilutions of a SARS-CoV-2 strain.

Results: Compared to our routine RT-PCR and the previous diagnosis of COVID-19, the sensitivity, specificity, positive and negative predictive values of VitaPCR TM can be evaluated to be 99.3% (155/156), 94.7% (358/378), 88.6% (155/175) and 99.7% (358/359), respectively. Tenfold dilutions of a SARS-CoV-2 strain show that the VitaPCR TM was more sensitive that our routine RT-PCR assay.

Conclusion:

The VitaPCR TM SARS-CoV-2 is an accurate rapid test, suitable for clinical practice that can be performed as part of a point-of-care testing, for the rapid diagnosis of COVID-19.

INTRODUCTION

The onset of the coronavirus disease 2019 (COVID-19) pandemic in March 2020 initiated a race to develop rapid detection tools for the causative virus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in order to optimize the management and triage of patients [START_REF] Dinnes | Cochrane COVID-19 Diagnostic Test Accuracy Group. Rapid, point-of-care antigen and molecular-based tests for diagnosis of SARS-CoV-2 infection (Review)[END_REF][START_REF] Pabbaraju | A public health laboratory response to the COVID-19 pandemic[END_REF][START_REF] Corman | Detection of 2019 novel coronavirus (2019-nCoV) by realtime RT-PCR[END_REF][START_REF] Ransom | Comparison of Extraction Methods and Thermocyclers for SARS-CoV-2 Molecular Detection Using Clinical Specimens[END_REF]. The congestion of emergency departments also required that we could offer an accurate point-of-service test that could be performed directly there. Antigen tests are easy to perform and can provide rapid diagnosis, but lack sensitivity, which makes them unreliable for the diagnosis of COVID-19 [START_REF] Dinnes | Cochrane COVID-19 Diagnostic Test Accuracy Group. Rapid, point-of-care antigen and molecular-based tests for diagnosis of SARS-CoV-2 infection (Review)[END_REF]. Therefore, RT-PCR assays remain the gold standard for the diagnosis of COVID-19. Several molecular tools allowing a diagnosis in less than an hour have been evaluated. Of these, the fastest two (the Abbott ID NOW and the Mesa Accula) with less than 30 minutes of delay between sampling and answer accumulated evidence of poorer diagnostic performance with a lack of sensitivity [START_REF] Hogan | Comparison of the Accula SARS-CoV-2 Test with a Laboratory-Developed Assay for Detection of SARS-CoV-2 RNA in Clinical Nasopharyngeal Specimens[END_REF][START_REF] Hogan | Fiveminute point-of-care testing for SARS-CoV-2: Not there yet[END_REF]. Only the Cepheid Xpert Xpress SARS-CoV-2 assay has shown to be a valuable tool with a run-time of 45-50 minutes with hands on time limited to 2-3 minutes [START_REF] Wolters | Multi-center evaluation of cepheid xpert® xpress SARS-CoV-2 point-of-care test during the SARS-CoV-2 pandemic[END_REF]. However, due to the pandemic, we are also facing a global shortage of reagents and kits and uncertainty over the availability of Xpert Xpress cartridges [START_REF] Hogan | Comparison of the Accula SARS-CoV-2 Test with a Laboratory-Developed Assay for Detection of SARS-CoV-2 RNA in Clinical Nasopharyngeal Specimens[END_REF]. It is therefore imperative to evaluate other point-of-care molecular tests for emergency diagnosis.

In this context, we evaluated the VitaPCR TM RT-PCR assay (Credo Diagnostics Biomedical, Singapore), whose sample analysis time is of approximately 20 minutes.

MATERIAL AND METHODS

From September 28 th to October 1 st , 2020, 534 patients presenting to the Mediterranee Infection Institute (Marseille, France), for the diagnosis of COVID-19, were included in the study. Each patient benefited from two naso-pharyngeal swab samplings, one per nostril.

VitaPCR TM SARS-CoV-2 was systematically compared to our routine in-house real-time RT-PCR as reference method [START_REF] Amrane | Rapid viral diagnosis and ambulatory management of suspected COVID-19 cases presenting at the infectious diseases referral hospital in Marseille, France, -January 31st to March 1st, 2020: A respiratory virus snapshot[END_REF][START_REF] Mediannikov | Coxiella burnetii in humans and ticks in rural Senegal[END_REF]. The VitaPCR TM assay includes three detection systems: (1) one targeting the human βglobin gene, to check the quality of DNA extracts; (2) a second targeting a specific sequence on the nucleocapside N-encoding gene; (3) a third targeting a conserved sequence common to SARS-CoV-2, SARS-CoV, and SARS-like bat coronavirus, also located on the N-encoding gene. We strictly followed the manufacturer's instructions for VitaPCR TM SARS-CoV-2 assay (Credo Diagnostics Biomedical, Singapore). For virus lysis and inactivation, the swab was discharged in the kit-provided collection buffer by stirring it 15 times. We allowed the lysis buffer to act for 5 minutes. Thirty µL of lysate were transferred to the tube containing the lyophilized PCR reagents. They were mixed well by pipetting. We avoided bubbles during all the process. The tube was then introduced into the apparatus in order to perform the analysis by RT-PCR, and then the latter returned the results in 20 minutes.

For our routine assay, automated nucleic acid extraction was performed using a KingFisher TM Flex system (Thermo Fisher Scientific), following the manufacturer's instructions. Our routine SARS-CoV-2 RT-PCR assay, that targets the envelope protein Eencoding gene, was performed as previously reported [START_REF] Amrane | Rapid viral diagnosis and ambulatory management of suspected COVID-19 cases presenting at the infectious diseases referral hospital in Marseille, France, -January 31st to March 1st, 2020: A respiratory virus snapshot[END_REF]. Besides, PCR targeting the human β-actin gene was performed to check the quality of DNA extracts [START_REF] Mediannikov | Coxiella burnetii in humans and ticks in rural Senegal[END_REF]. In routine, the cycle threshold (Ct) to conclude that an analysis is positive using our RT-PCR is less than or equal to 35 Ct. In parallel, we also assessed the impact of delayed testing on Ct values using VitaPCR TM assay for twelve positive samples tested directly and 3 hours later.

Besides, we also determined the level of detection of the two molecular assays by analyzing tenfold dilutions of a suspension of Vero E6 cell-cultured SARS-CoV-2 IHUMI-3 strain [START_REF] Jaafar | Correlation between 3790 qPCR positive samples and positive cell cultures including 1941 SARS-CoV-2 isolates[END_REF]. This strain was obtained from a nasopharyngeal swab of an RT-PCR positive patient, as previously reported [START_REF] Jaafar | Correlation between 3790 qPCR positive samples and positive cell cultures including 1941 SARS-CoV-2 isolates[END_REF].

RESULTS

By analyzing tenfold dilutions of IHUMI-3 strain, from 780 x 10 6 copies/ml at a dilution of 10 -1 to 1,484 copies/ml at a dilution of 10 -6 , the Ct values were 16 and 34 for the highest (10 -1 ) and lowest (10 -6 ) using the VitaPCR TM and 20 and 36, respectively, using our routine PCR assay (Figure 1). Among the 534 analyzed samples, 119 were positive and 358 negative using both assays (Supplementary Figure ). One from recent diagnosis of COVID-19 was positive only with our routine RT-PCR. Fifty-six were positive only with the VitaPCR TM . Among them, nine were negative for β-actin PCR showing thus the poor quality of the DNA extracts and the impossibility of interpreting the SARS-CoV-2 results obtained by routine RT-PCR; in contrast, β-globin was correctly detected from the naso-pharyngeal swabs from these patients interpreted using VitaPCR TM . Eighteen exhibited a cycle threshold (Ct) value from 35 to 38 using our routine RT-PCR (including 6 from patients with a recent diagnosis of COVID-19).

In our laboratory, a threshold of Ct 35 was selected in order to prioritize diagnoses of putatively contaminant patients. Nine were also from recent diagnosis of COVID-19, including 6 with a Ct value greater than 31 with VitaPCR TM . Overall, these data support false negative results from our routine RT-PCR due to a biased threshold or at least a lower sensitivity. Finally, among the other twenty patients, two were asymptomatic whereas eighteen exhibited clinical and biological data highly evocative of COVID-19, such as fever, cough, anosmia, ageusia, and eosinopenia (Table 1) [11]. Compared to our routine RT-PCR with a Ct less than or equal to 38 and the previous diagnosis of COVID-19, the sensitivity, specificity, positive, and negative predictive values of VitaPCR TM can be evaluated to be 99.3% (155/156), 94.7% (358/378), 88.6% (155/175) and 99.7% (358/359), respectively.

Finally, a 3-hour delayed testing using VitaPCR TM assay has an impact on Ct values with an increase in these (Table 2).

DISCUSSION

Our study shows that the VitaPCR TM assay exhibits a high sensitivity for SARS-CoV-2 detection in nasopharyngeal samples. Moreover, the apparent lack of specificity must be heavily weighted with the patient data which suggests a potential lack of sensitivity of our routine RT-PCR. Of note, the manufacturer has reported no cross-reactivity with human coronavirus 229E, human adenovirus 1, influenza A virus (H1N1, H2N3), influenza B virus, and respiratory syncytial virus A. The assay is not only fast but also easy to handle. After the nasopharyngeal sampling, the swab is discharged into a specific lysis buffer and tested directly using ready-for-use reagents, stored at room temperature. The results are automatically interpreted, limiting human interpretation bias. The training required for operators is simple and does not last long. It required us an hour to train technicians, medical students and pharmacy students from collecting the sample to analyzing it. The device is not bulky and can therefore be installed in a delocalized laboratory, close to patients to be tested. Finally, the system is secure as the virus is inactivated by the kit-provided collection buffer.

Legend Figure 1 .

 1 Potential limits are that only one sample is processed by apparatus at a time(3 tests per hour) but several devices can be used concomitantly by a single person. Besides, extracted viral RNAs in lysis buffer is rapidly degraded, which prevents delayed testing. Overall, the VitaPCR TM is a highly sensitive test that enables to deliver results in less than half an hour and to decentralize testing for SARS-CoV-2 in acute-care hospital or emergency departments where rapid triage decisions are required for the establishment of specific isolation for contagious patients, the use of adequate personal protective elements for the healthcare workers, and for the management of the patient. The VitaPCR TM can therefore be included in point-of-care tests. IHU COVID-19 Task force. Outcomes of 3,737 COVID-19 patients treated with hydroxychloroquine/azithromycin and other regimens in Marseille, France: A retrospective analysis. Travel Med Infect Dis. (2020) 36:101791. https://doi.org/10.1016/j.tmaid.2020.101791 Evaluation of the in vitro sensitivity of VitaPCR TM SARS-CoV-2 assay by comparison with our routine RT-PCR using tenfold dilutions of a suspension of Vero E6 cellcultured SARS-CoV-2, IHUMI-3 strain.

Figure 1 .

 1 Figure 1. Evaluation of the in vitro sensitivity of VitaPCR TM SARS-CoV-2 assay by

Table 1 .

 1 Clinical and biological data for the twenty patients positive only with the VitaPCR TM and without previous diagnosis of COVID-19.. 216

			Date of	Date of
	Patients Sex, age	sample	symptoms onset Clinical and biological data
	1	F, 20 y	sept	None	Asymptomatic (another sample collected on 09/28 was negative by both techniques)
	2	M, 83 y	sept	None	Asymptomatic (another sample collected on 09/30 was negative by both techniques)
					Cough, aches, asthenia, leucopenia (3.6 Giga/l), eosinopenia (0.03 Giga/l), lymphopenia (0.87
	3	M, 31 y	sept	23 sept	Giga/l)
					Fever, cough, anosmia, ageusia, thoracic pain, rhinitis, diarrhea, eosinopenia (0 Giga/l), elevated
					CRP (42.1 mg/l), elevated ferritin (660 µg/l), elevated γGT (41 UI/l), elevated transaminases
	4	F, 47 y	sept	20 sept	(ALT [45 UI/l] and AST [43 UI/l]), elevated LDH (272 UI/l), elevated fibrinogen (5.4 g/l)
	5	F, 40 y	sept	28 sept	Cough, headache, leucopenia (3.8 Giga/l), lymphopenia (0.63 Giga/l)
					Fever, cough, anosmia, ageusia, diarrhea, headache, eosinopenia (0.02 Giga/l), elevated ferritin
					(943 µg/l), elevated CRP (21.8 mg/l), elevated transaminases (ALT [72 UI/l] and AST [63 UI/l]),
	6	M, 40 y	sept	19 sept	elevated LDH (301 UI/l)
					Fever, anosmia, ageusia, headache, leucopenia (3.6 Giga/l), eosinopenia (0.08 Giga/l),
	7	F, 39 y	sept	25 sept	thrombocytopenia (134 Giga/l), elevated fibrinogen (4.15 g/l), elevated d-dimers (3 µg/ml)
					Anosmia, ageusia, leucopenia (3.9 Giga/l), neutropenia (1.9 Giga/l), eosinopenia (0.02 Giga/l),
	8	M, 24 y	sept	18 sept	elevated CRP (22.2 mg/l), elevated LDH (223 UI/l), elevated ferritin (10.8 µg/l)
					Fever, diarrhea, aches, abdominal pain; leucopenia (2,9 Giga/L), neutropenia (1.7 Giga/l),
					eosinopenia (0.03 Giga/l), lymphopenia (0.79 Giga/l), thrombocytopenia (129 giga/l), elevated
					CRP (16.3 mg/l), elevated ferritin (1400 µg/l), elevated fibrinogen (5.15 g/l), elevated LDH (242
	9	M, 62 y	oct	26 sept	UI/l)
					Fever, cough, headache, leucocytosis (23 Giga/l), neutrophilic leucocytosis (20 Giga/l),
	10	M, 43 y	sept	14 sept	eosinopenia (0.04 Giga/l), elevated CRP (33 mg/l), elevated γGT (90 UI/l)
					Ageusia, headache, asthenia, aches, eosinopenia (0.02 Giga/l), elevated CRP (13.5 mg/l), elevated
	11	M, 35 y	sept	26 sept	fibrinogen (4.6 g/l)
	12	M, 19 y	sept	21 sept	Cough, ageusia, headache, asthenia, no biological abnormalities reported
	13	M, 23 y	sept	21 sept	Rhinorrhea, headache, asthenia, eosinopenia (0.05 Giga/l)
	14	F, 43 y	sept	22 sept	Cough, anosmia, rhinitis, aches, diarrhea, eosinopenia (0.01 Giga/l), elevated ferritin (212 µg/l)
					Fever, anosmia, ageusia, headache, diarrhea, rhinitis, chest pain, aches, eosinopenia (0.02 Giga/l),
	15	F, 41 y	sept	22 sept	elevated LDH (222 UI/l)
	16	M, 43 y	sept	20 sept

Anosmia, ageusia, eosinopenia (0.08 Giga/L), elevated ALAT (54 UI/l), elevated γGT (173 UI/l)

Table 2 .

 2 Cycle threshold values obtained using VitaPCR TM assay when analyses were 218 performed directly after the sampling and 3 hours later.

	219
	220
		VitaPCR TM cycle threshold values
	Patients	Directly performed	Performed 3 hours later
	1	22	22
	2	30	32
	3	19	20
	4	17	25
	5	16	27
	6	28	30
	7	25	31
	8	19	20
	9	28	30
	10	20	22
	11	27	30
	12	22	26
	221

Transparency declaration

This study was supported by the Méditerranée-Infection Foundation and the French Agence Nationale de la Recherche under the program "Investissements d'Avenir", reference ANR-10-IAHU-03.

The authors declare no conflict of interest in relation to this research.

The patients gave an informed consent for this study.

Authors' contributions

PEF and FF conceptualized and supervised the study. CZ, EP, LN, MM, HTD, and PC performed the investigations and experiments. PEF and FF wrote the initial draft of the manuscript. All authors agreed to the publication of this version of the manuscript.


Benoit Lucereau

Foued Koffhi

Anne Lejay

Yannick Georg

Bernard Durand

Fabien Thaveau

Frédéric Heim

Nabil Chakfe
email: nabil.chakfe@chru-strasbourg.fr

Compliance of Textile Vascular Prostheses Is a Fleeting Reality

Keywords: Compliance, Compliance evolution, Compliance mismatch, Vascular graft

Compliance is considered to be a major property influencing the long term performances of synthetic vascular substitutes that could play a role in anastomotic false aneurysm and intimal hyperplasia stenosis onset. In this in vitro model, it was shown that polyethylene terephthalate textile graft compliance already decreases significantly within 3 hours. The rapid loss of compliance identified in this experimental study helps explaining the mismatch mentioned in clinical observations. This study informs vascular surgeons about how

INTRODUCTION

Synthetic vascular grafts (VGs) were introduced about 50 years ago. [START_REF] Chakfé | Vascular graft prosthesis[END_REF] Since then, researchers and manufacturers have attempted to develop generations of materials which could mimic native arteries in terms of thrombogenicity and mechanical properties. [START_REF] Rosset | Viscoelastic properties of human arteries. Methodology and preliminary results[END_REF] One critical mechanical property of a VG is compliance, which corresponds to its ability to expand over the systolic-diastolic loading cycle. Compliance can be described as the link between intraluminal pressure and arterial wall deformation. [START_REF] Patel | A review on atherosclerotic biology, wall stiffness, physics of elasticity, and its ultrasound-based measurement[END_REF] It corresponds to the capacity of a vascular structure to absorb cardiac ejection. Over the years, different materials and designs have been considered for the construction of vascular substitutes, without strong recommendation on which synthetic material to favour in absence of suitable autologous material. [START_REF] Aboyans | Editor's Choice -2017 ESC Guidelines on the Diagnosis and Treatment of Peripheral Arterial Diseases, in collaboration with the European Society for Vascular Surgery (ESVS)[END_REF][START_REF] Conte | Global Vascular Guidelines on the Management of Chronic Limb-Threatening Ischemia[END_REF] Expanded polytetrafluoroethylene (ePTFE) and textiles obtained from polyethylene terephthalate (PET) are the technologies of choice used by surgeons today. [START_REF] Guidoin | Aneurysmal deterioration of vascular substitutes[END_REF] Textile PET VG are used in particular for the reconstructions involving middle-sized and large diameter vessels. These devices, which are made from woven or knitted fabric, present some limitations as they fail to mimic the mechanical properties of arterial vessels. Basically, VGs are in general not deformable enough to prevent compliance mismatch, [START_REF] Kinley | Compliance: a continuing problem with vascular grafts[END_REF][START_REF] Abbott | Effect of compliance mismatch on vascular graft patency[END_REF][START_REF] Weston | Compliance and diameter mismatch affect the wall shear rate distribution near an end-to-end anastomosis[END_REF][START_REF] Tai | Compliance properties of conduits used in vascular reconstruction[END_REF] especially at the level of the anastomoses. This mismatch can be responsible for pathologies such as false aneurysm, [START_REF] Downs | Etiology of prosthetic anastomotic false aneurysms: pathologic and structural evaluation in 26 cases[END_REF][START_REF] Gaylis | Anastomotic aneurysms: facts and fancy[END_REF][START_REF] Chakfé | In vitro approach to the dilative behavior of knitted vascular prosthetic grafts[END_REF][START_REF] Mehigan | Is compliance mismatch the major cause of anastomotic arterial aneurysms? Analysis of 42 cases[END_REF] intimal hyperplasia and anastomotic stenosis. [START_REF] Okuhn | Does compliance mismatch alone cause neointimal hyperplasia?[END_REF][START_REF] Abbott | Does compliance mismatch alone cause neointimal hyperplasia (letter)?[END_REF][START_REF] Hasson | Increased compliance near vascular anastomoses[END_REF][START_REF] Sarkar | The mechanical properties of infrainguinal vascular bypass grafts: their role in influencing patency[END_REF] All these issues lead to VG failure. [START_REF] Chakfé | Longitudinal ruptures of polyester knitted vascular prostheses[END_REF][START_REF] Chakfé | Impregnated polyester arterial prostheses: performance and prospects[END_REF] In order to optimise the VG performances, their mechanical behaviour has already been studied by several groups. [START_REF] Hasegawa | Mechanical properties of synthetic arterial grafts[END_REF][START_REF] Lee | Anisotropic tensile viscoelastic properties of vascular graft materials tested at low strain rates[END_REF][START_REF] Salacinski | The mechanical behavior of vascular grafts: a review[END_REF] Moreover, standards have been defined to better characterise these devices. [START_REF]International standard ISO/DIS 7198: 1998 -Cardiovascular implants -tubular vascular prostheses[END_REF][START_REF]International standard ISO/DIS 7198 : 1998 -Cardiovascular implants -Tubular vascular prostheses[END_REF] However, not much is really known about the effective compliance of commercial devices. In particular, how the compliance evolves with time has not been studied much yet. The goal of this paper was to test the compliance of various VGs on a specific equipment already described previously in literature [START_REF] Khoffi | A development of a technique for measuring the compliance of the textile vascular prostheses[END_REF][START_REF] Lucereau | Relation between tensile tests and compliance in polyester textile vascular graft[END_REF][START_REF] Khoffi | Compliance properties of collagen-coated polyethylene terephthalate vascular prostheses[END_REF] in order to measure the compliance evolution over time under cyclic loading conditions.

MATERIALS AND METHODS

Vascular graft samples considered in the study

Three different models of commercially available knitted VGs (P1, P2, and P3) obtained from polyethylene terephthalate (PET) material were studied. Models and brands were kept anonymous in order to avoid irrelevant marketing interpretation since no exhaustive evaluation of all the models commercially available was performed. The samples were all knitted, crimped, and divided in two groups: non-coated and collagen coated. All specimens were 80 mm long and their characteristics are given in Table 1.

It is to be noted that P1 was characterised by a crimp configuration obtained from independent circular grooves, while and P2 and P3 were characterised by one unique helical groove running all along the prosthesis. Before tests were carried out, all these VGs were conditioned for implantation and available in their coated configuration. In order to assess if the coating would tend to rigidify the prosthesis by increasing the modulus on one side and reducing the compliance on the other, uncoated samples were also considered. These latter were obtained by removing the coating with successive baths of sodium hypochlorite 2.6% according to the laboratory protocol. [START_REF] Abbott | Does compliance mismatch alone cause neointimal hyperplasia (letter)?[END_REF] Finally, for each VP model, two diameters (6 and 8 mm) were considered. Figure 1 summarises the configurations tested for each model. Moreover, in order to consider the influence of the extension undergone by the graft when implanted, two longitudinal loading configurations were considered: (1) with no load and (2) with a 0.4 N pre-load (value defined by the ISO7198 standard).

Compliance measurement

The three different groups of VG (P1, P2, P3) were tested under a 60 -140 mmHg pulsed pressure range (2 Hz) at 37°C. The testing bench used is represented in Figure 2. In order to assess the compliance of the samples over cycling, diameter variations were measured using a camera (Stingray, Allied Vision, Exton, USA). Images were analysed with a dedicated software (Image J, NIH Image, USA). Moreover, four angular positions were considered over the whole circumference of the samples (0°, 90°, 180°, and 270°) in order to account for specimen variability. Diameters were measured in six locations along the length of the VG for the same reasons. Average diameter values were then calculated and variation coefficients were assessed (percentage). In order to assess the influence of time on the compliance evolution, measurements were made at time 0, and after 3, 6, and 24 hours.

Compliance was considered and calculated at three levels: radial (Cr), longitudinal (Cl) and volume (Cv) for each sample according to the formula: C = 100 . ∆X/∆P, where C = compliance in %/mmHg; ΔX = X140-X60; X = D: outside diameter (mm), or L: length (mm), or V: volume (mm3); ΔP = pressure variation Statistical analysis was based on a Student t-test (p = .050) and variables were described by mean and variation coefficients.

RESULTS

Evolution of the compliance with time

Figure 3 shows the results observed for P1 (6 mm, non-coated, no pre-load) regarding the compliance evolution (radial, longitudinal and volume) at the various considered time intervals (begin H0, 3 hours H3, 6 hours H6, 24 hours H24).

One can observe a significant compliance loss already 3 hours after the start of the experiment for every compliance pattern: 39% (from 0.081 to 0.05), 35% (from 0.056 to 0.036), and 37% (from 0.073 to 0.047) respectively for Cr, Cl, and Cv. Moreover, after 24 hours, the compliance drops drastically: up to 63%, 60.5% and 61% respectively for Cr, Cl and Cv.

Influence of the diameter

Figure 4 compares the results obtained for P1 (non-coated, no pre-load) for both diameters 6 and 8 mm. At the beginning of the test, the radial compliance was nearly twice as large for the 8mm diameter sample (0.021 vs. 0.008) while no difference could be observed longitudinally. Results demonstrate that after 3, 6 and 24 hours of cycling, the compliance drops more significantly for the larger diameter (100% from 0.021 to 0 vs. 65% from 0.008 to 0.003).

Influence of the design

When comparing the three VG designs (P1, P2, and P3 non-coated and no pre-load) it can be observed in Figure 5 that the radial compliance evolves in a similar way for P1 et P2. Values decrease respectively from 0.0081 and 0.0186 down to low values for these samples (0.03 and 0.0016 respectively). Conversely, with respect to P3, the compliance value is already larger when the experiment starts (0.025) and remains significant after 24 hours cycling (0.008).

The compliance drop was accompanied by a drop in the crimp frequency (number of ridges per centimetre over the graft length) for all samples. P1, P2, and P3 were characterised respectively by 3.9, 6.8, and 4.2 crests/cm before starting the experiment.

After cycling values went down to 3.3, 5, and 3.4 crests/cm corresponding to respectively 15.4%, 26%, and 19% crimp frequency loss (decrease in the number of ridges per centimetre).

Regarding the evolution of the longitudinal and volume compliances after 24 hours cycling time, average results are summarised in Table 2.

While P2 is globally more compliant at the beginning of the test, differences become less significant after 24 hours of cycling.

Influence of the coating

According to Figure 6, which compares the compliance of a coated and a non-coated P2 VG (6 mm, no pre-load), the coating seems to help maintain the radial compliance up to 24 hours. Actually, after 24 hours, the coated sample keeps around 70% of its initial compliance (0.01 at H24 vs. 0.015 at test begin) while the uncoated sample undergoes a 90% compliance drop (from 0.018 to 0.0016).

Regarding the evolution of the longitudinal and volume compliances for P2, results

show that coated and non-coated VG behave in a similar way (Table 3). Both samples show up to over at least 75% compliance loss after 24 hours of cycling.

Influence of the pre-load

Figure 7 shows that with a pre-load applied on P1 (8 mm, non-coated), some compliance remains after 24 hours cycling compared with a free end configuration (20% vs. 0%).

Evolution of the VG diameter over cycling

The loss of compliance observed for all models of VG was in correlation with an increase in diameter over cyclic loading. Actually, the textile construction tended to get loose after 24 hours in all samples, which led to diameter increase by 1.74%, 2.98%, and 3.72% for P1, P2, and P3 respectively.

DISCUSSION

The results presented in this study bring out significant data about the evolution of compliance in VG solicited under cyclic pressure loading.

The analysis shows that whatever sample configuration was tested, all prostheses underwent drastic compliance loss after 24 hours of cyclic loading. When applying cyclic pressure on a knitted tubular fibrous construction, yarns tend to rearrange within the fabric in an irreversible way towards diameter increase. In knitted constructions, yarns are less tightly bound to each other than in a woven ones. [START_REF] Guidoin | Aneurysmal deterioration of vascular substitutes[END_REF][START_REF] Kinley | Compliance: a continuing problem with vascular grafts[END_REF] Under stress, yarn movements are possible that tend to change the global arrangement. Once the diameter is larger, new zones of contact between yarns are created where the applied friction forces prevent the material from going back to its initial configuration. A balanced irreversible arrangement is reached when the diameter enlarges. In that final configuration, the deformability of the fabric is reduced as yarns are more straight in the construction. Compliance is consequently limited after cycling.

The phenomenon is amplified when the VG diameter is larger as can be observed in Figure 4. Compliance drops by nearly 100% for the 8 mm VG and 65% for the 6 mm.

Basically, from a mechanical point of view, the radial stress on the VG wall is proportional to the diameter. Thereby, larger radial deformation occurs in the 8 mm samples. Regarding the longitudinal compliance no significant differences could be observed as the longitudinal stress is half as important as the radial stress. It means that efforts to create more compliant VG designs should focus on small diameters VG, those that actually require improvements.

With respect to the VG models (Fig. 5), large differences could be observed. These can be directly related to the differences observed in the textile construction design as well as in the crimping pattern. P3 appeared to be the radially most deformable sample while P1 was the least. Basically, the knitted structure is less tight in P3 as is confirmed by the respective extension modulus values (6.5 MPa for P3 vs. 7.6 MPa for P2 and 13.1 MPa for P1). The more compliant P3 sample is characterised by looser and more deformable yarn arrangement. The tighter is the fibrous construction, the less deformable is the VG, which is the case for P1 and P2.

Moreover, the crimping pattern can also be considered as having some influence on the compliance property lifetime. When comparing P1 and P2, both characterised by a circular crimping geometry while the ridge density was larger for P2 (6.8 vs. 3.9), no significant difference can be observed regarding the compliance drop. The P2 VG was more radially deformable at the start due to larger ridge density. However, after being cycled, the textile construction relaxes towards a balanced irreversible yarn arrangement as described previously. The initially curved yarns become more straight in the knit of both P1 and P2, and no additional deformation is possible. The crimping ridges become flattened with time in both samples. Conversely, P3 appears to be more compliant than P1 (30% compliance left,) after 24 hours despite similar ridge density (4.2 vs. 3.9 respectively). This can be explained by the helical geometry of the crimp in P3, while for P1 the crimping is circular.

When P1 is under pressure, circular crimps behave independently and move away from each other and the VG extends while the crimping level goes down with time. Conversely, helical crimping generates some coupling effect between the crimps along the VP. The unique helical crimp groove tends to extend when the pressure is applied. However, all the apparent local crimps being related to neighbour crimps in the same helical geometry, it is more difficult for them to move away from each other. This generates a spring back effect and makes the material more compliant even if the compliance drop cannot be avoided.

When considering the longitudinal compliance, one could observe that P2 was characterised by better deformability than P3. Actually, the circular crimping in P2 is more deformable than the helical crimping in P3. Moreover, the larger number of ridges in P2 (6.8 vs. 4.2 for P3) contributes also to larger deformability. However, longitudinal compliance doesn't have much significance in vivo. The VG being attached on both sides and sheathed in fibrotic tissue, the main role of crimping is to prevent kinking. These results demonstrate that the fabric structure and the design of the crimping can influence the properties of a specific VG and that vascular surgeons should be more aware on that before choosing a specific device.

Another significant observation could be made regarding the effect of the coating on the compliance evolution (Fig. 6). Coated samples remained more compliant after 24 hours of cycling (0.01% vs. 0.0016% for the non-coated). It seems that the coating plays a spring back effect on the textile structure to a certain level as it prevents irreversible yarns sliding movements, making the textile construction more elastic. This point is very important to take into account since impregnation matrices are biodegradable and that the speed of degradation as well as the type of coating (surface coating versus impregnation) can modify the speed of rearrangement of the textile structure depending on the porosity of the uncoated structure. A highly porous structure could be more prone to dilatation without any more compliance once the coating is degraded.

At last, the results showed that the long-term compliance is improved when a VG sample is under pre-load (Fig. 7). Actually, in that configuration, the longitudinal deformation becomes limited. Thereby, radial deformations, which occur over cyclic loading are more elastic as yarns oriented in the VG axis direction are already under slight tension, and consequently less deformable. However, even in that configuration, the final deformability after 24 hours remains limited (0.008%/mmHg). Vascular surgeons always apply tension to the graft to try to reach the property of usable length given in the standards. Here it was decided to arbitrarily use no tension or the tension proposed by the standards. However, the data suggest that this ideal tension to apply to a VG to get its optimal performance once implanted, is probably different depending on the textile structure as well as the crimping.

Results show globally a significant loss of compliance (radial, longitudinal and volume) which is difficult to limit whatever the design parameters that are modified. Nevertheless, a coated circular crimped prosthesis under tension seem to present an advantage based on this study. Of course, once the coating is degraded the textile structure can be infiltrated by the healing response. This infiltration will also modify the compliance properties at mid and long-term. These results help explaining the effect of compliance mismatch mentioned by several authors in literature. Nappi et al. studied in silico the influence of compliance mismatch on stress generation in the VG environment. [START_REF] Nappi | Compliance mismatch and compressive wall stresses drive anomalous remodelling of pulmonary trunks reinforced with Dacron grafts[END_REF] Results were compared with histological and surgical data related to an experimental animal campaign conducted by performing pulmonary artery transpositions in 30 two month old growing lambs. The in vivo observations demonstrated the effectiveness of the proposed model. In particular, the authors highlighted the crucial role played by stress fields generated by compliance mismatch and kindled in the vessel walls and around suture regions. The phenomenon has also been studied from a fluid mechanical point of view by Stewart et al. [START_REF] Stewart | Effects of a vascular graft/natural artery compliance mismatch on pulsatile flow[END_REF] The authors showed with flow visualisation experiments that compliance mismatch caused stagnant zones which may contribute to the intimal hyperplasia and thrombosis seen in failed grafts.

In another work published by Weitzel et al., the authors pointed out the link between anastomotic stenosis and vessel rigidity. [START_REF] Weitzel | High-resolution ultrasound speckle tracking may detect vascular mechanical wall changes in peripheral artery bypass vein grafts[END_REF] They underlined how lack of compliance tends to increase the risk of restenosis. All these results are in correlation with those presented in a review written by Patel et al., which confirms the role of vessel stiffness in atherosclerotic plaque formation. [START_REF] Patel | A review on atherosclerotic biology, wall stiffness, physics of elasticity, and its ultrasound-based measurement[END_REF] On the other land, the search for a compliant structure can lead to favour very light textiles whose long-term durability and stability could be questionable and lead to the risk of degradation, dilatation, or rupture. [START_REF] Lejay | Explanted Vascular and endovascular graft analysis: where do we stand and what should we do?[END_REF]

CONCLUSIONS

In this study, the compliance evolution over time of three different models of VG has been assessed. Compliance values have been measured over dynamic loading conditions after 3, 6, and 24 hours of cyclic physiological pressure stress. Results brought out a significant compliance loss (around 40% for all makes) already 3 hours after the start of the experiment for every compliance pattern. After 24 hours, the drop reaches over 60%. However, the phenomenon depends on the textile construction and the crimp. A less tight knitted structure characterised by a helical crimp presents an advantage according to the results obtained. Moreover, larger diameter, which undergo larger stress lose compliance properties more rapidly. Regarding the influence of the coating, impregnation tends to stabilise the knitted construction and makes it more elastic and compliant over time.

Furthermore pre-load applied longitudinally on a VG helps keeping the compliance over a longer period of time as well. Unfortunately, overall observations show that VG compliance in general disappears very rapidly after cyclic loading of the graft. Whatever the VG configuration, deformability vanishes after 24 hours. This compliance mismatch may explain the clinical complications observed after implantation.

Figure 1 .

 1 Figure 1. Summary of tested configurations of the three commercially available textile polyethylene

Figure 2 .

 2 Figure 2. Diagram of the experimental set up for measuring the radial, longitudinal, and volumetric

Figure 3 .

 3 Figure 3. Average change in radial (Cr), longitudinal (Cl), and volume (Cv) compliance of an uncoated,

Figure 4 .

 4 Figure 4. Average radial compliance (Cr) of an uncoated, unloaded, commercially available textile

Figure 5 .

 5 Figure 5. Average radial compliance (Cr) of three uncoated, commercially available textile

Figure 6 .

 6 Figure 6. Average radial compliance (Cr) of an unloaded , commercially available textile polyethylene

Figure 7 .

 7 Figure 7. Average radial compliance (Cr) of an uncoated, commercially available textile polyethylene

Table 1 .

 1 Main characteristics of the three commercially available textile polyethylene terephthalate (PET) vascular grafts (P1, P2, and P3) evaluated for their compliance.

		P1	P2	P3
	Diameter -mm	6 and 8	6 and 8	6 and 8
	Wall thickness -mm	0.9	0.8	0.32
	Crimping geometry	Circular	Helical	Helical
	Crimp frequency -	3.9	6.8	4.2

Table 2 .

 2 Volume and longitudinal compliance (C) in %/mmHg of the three commercially available textile polyethylene terephthalate (PET) vascular grafts (P1, P2, and P3) as function of the graft model at the initial stage and after 24 hours under a 60-140 mmHg pulsed pressure range.

	Time point	P1		P2		P3
		Longitudinal C	Volume C	Longitudinal C	Volume C	Longitudinal C	Volume C
	Initial	0.06	0.07	0.12	0.16	0.03	0.08
	After 24 h	0.023	0.028	0.018	0.02	0.013	0.03

Table 3 .

 3 Volume and longitudinal compliance (C) in %/mmHg of the three

	commercially available textile polyethylene terephthalate (PET) vascular
	grafts (VG) as function of the coating at the initial stage and after 24 hours
	under a 60-140 mmHg pulsed pressure range. For uncoated VGs, the
	original coating was removed.
	Time point	Coated VG	Uncoated VG
		Longitudinal	Volume C	Longitudinal	Volume C
		C		C
	Initial	0.15	0.19	0.12	0.17
	After 24 h	0.03	0.05	0.017	0.02

FUNDING

Partially funded by a grant of the Société Francaise de Chirurgie Vasculaire et Endovasculaire.

CONFLICT OF INTEREST

None.