PhD Antonio Pires De Camargo

MSc Nicolás Duarte Cano

MSc Nicolás Duarte Cano

PhD Nassim Ait-Mouheb
email: nassim.ait-mouheb@inrae.fr

Gustavo Lopes Muniz

Jhonnatan Alexander

Yepes Guarnizo

Diego José

Sousa Pereira
email: dpereira@usp.br

José Antônio Frizzone
email: frizzone@usp.br

Nicolas D Cano

Antonio P Camargo

Gustavo L Muniz
email: gustavo.muniz@feagri.unicamp.br

Jhonnatan A Y Guarnizo

Diego J S Pereira

Optimisation of the filter housing dimensions of an automatic flushing strainertype filter

Keywords: filtration, CFD, screen filter, irrigation engineering, hydraulics

Filtration is essential in drip irrigation systems to remove physical contaminants carried by water that can clog the emitters, cause wear, or foul components of the system, affecting its performance and lifespan. Automatic flushing strainer-type filters initiate and terminate discrete flushing cycles that are activated automatically by means of differential pressure. The objective of this study is to investigate the hydraulic performance and flow behaviour of an automatic flushing strainer-type filter operated with clean water, using experimental and numerical approaches, to optimise the dimensions of its filter housing and to increase the range of operating flow rates. Pressure drop curves were determined for the filter housing and the filter system equipped with five models of filter elements (woven and non-woven elements). Excessive pressure drop in the filter housing and low filtration rates were identified as the main drawbacks of the original filter system. Numerical simulations enabled the identification of the most critical regions in terms of pressure losses near the transitions between the inlet and outlet segments of the pipe. Four designs of filter housing were simulated to evaluate the possibilities of optimising the filter housing dimensions using a constant filtering area. Larger inlet and outlet diameters combined to a filter housing shorter and wider were improvements in the filter housing dimensions that enabled to decrease the pressure drop in the filter and/or increase the range of operating flow rates. The results provided useful information for enhancing the hydraulic performance of the filtration system.

Abstract: Filtration is essential in drip irrigation systems to remove physical contaminants carried by water that can clog the emitters, cause wear, or foul components of the system, affecting its performance and lifespan. Automatic flushing strainer-type filters initiate and terminate discrete flushing cycles that are activated automatically by means of differential pressure. The objective of this study is to investigate the hydraulic performance and flow behaviour of an automatic flushing strainer-type filter operated with clean water, using experimental and numerical approaches, to optimise the dimensions of its filter housing and to increase the range of operating flow rates. Pressure drop curves were determined for the filter housing and the filter system equipped with five models of filter elements (woven and non-woven elements). Excessive pressure drop in the filter housing and low filtration rates were identified as the main drawbacks of the original filter system. Numerical simulations enabled the identification of the most critical regions in terms of pressure losses near the transitions between the inlet and outlet segments of the pipe. Four designs of filter housing were simulated to evaluate the possibilities of optimising the filter housing dimensions using a constant filtering area. Larger inlet and outlet diameters combined to a filter housing shorter and wider were improvements in the filter housing dimensions that enabled to decrease the pressure drop in the filter and/or increase the range of operating flow rates. The results provided useful information for enhancing the hydraulic performance of the filtration system. Filtration involves the physical separation of one or more components from a suspension in a fluid by passage through or across a barrier (filter medium) that is permeable only to some of these components [START_REF] Purchas | Handbook of Filter Media[END_REF]. In irrigation systems, particularly in microirrigation, filtration is important to prevent the intake of particles and sediments that can accumulate along pipes and other components, resulting in the clogging of emitters. Under typical irrigation conditions, complete removal of all suspended particles cannot be achieved (ISO9912-1, 2004).

Practical and economic limitations only allow for the removal of larger particles, and consequently, sediments can be found in irrigation lines [START_REF] Oliveira | Clogging of drippers caused by suspensions of kaolinite and montmorillonite clays[END_REF][START_REF] Puig-Bargués | Effect of Flushing Velocity and Flushing Duration on Sediment Transport in Microirrigation Driplines[END_REF][START_REF] Ravina | Control of emitter clogging in drip irrigation with reclaimed wastewater[END_REF] Strainer-type, or screen filters, are devices that contain one or more filter elements. The strainer-type filter elements consist of a perforated plate, screen, mesh, or a combination of these, intended to retain suspended solids larger than the aperture size specified by the manufacturer. The screen can be made of steel, nylon, polypropylene, or nonwoven materials. The material and characteristics of the screen directly affect the fluid flow and performance of the filter [START_REF] Sparks | Filters and filtration handbook[END_REF][START_REF] Sutherland | Filters and filtration handbook[END_REF]. In irrigation applications, the filter performance mainly refers to hydraulic performance (i.e., pressure drop, filtration rate), removal efficiency of suspended particles, resistance to corrosion, and backwash effectiveness when automatic mechanisms are part of the filtration system. For woven wire cloths, the filtration performance is influenced by filter cloth specifications such as wire diameter, shape and material, type of weave (e.g., plain Dutch weave, twill Dutch weave, reverse Dutch weave), aperture size, and mesh count. The performance of nonwoven fabrics is influenced by the material, porosity, permeability, thickness, pore size, and mass per unit area of the fabric [START_REF] Ribeiro | Performance of non woven synthetic fabric and disc filters for fertirrigation water treatment[END_REF][START_REF] Ribeiro | Comparison Between Disc and Non-Woven Synthetic Fabric Filter Media to Prevent Emitter Clogging[END_REF]. For media filters, the requirements for evaluating several characteristics related to filter performance are standardized in ASAE S539 [START_REF] Asabe | Media filters for irrigation -Testing and performance reporting[END_REF].

The filtration for irrigation systems may consist of primary and secondary filters. The primary filter may serve several plots and consist of a media filter, screen or disc filter, most often incorporating a self-cleaning mechanism. Screen or disc filters manually cleaned, can be installed as secondary downstream safety filters at the inlet of plots [START_REF] Pizarro Cabello | Riegos localizados de alta frecuencia[END_REF][START_REF] Ravina | Control of clogging in drip irrigation with stored treated municipal sewage effluent[END_REF]. Screen filters are suitable for removing suspended solid particles, but problems may arise when algal debris are part of the contaminants. Algal material tends to intertwine between the screen mesh and removal is difficult when the packing becomes dense [START_REF] Nakayama | Maintenance[END_REF]. If the irrigation water contains a high concentration of suspended solid particles, sand separators or settling basins should be installed upstream of the filtration system [START_REF] Keller | Sprinkle and Trickle Irrigation[END_REF].

Some screen filters have flushing cycles that are automatically activated, and they are called automatic flushing strainer-type filters (ISO9912-3, 2013). Automatic flushing filters initiate and terminate discrete flushing cycles that are activated automatically by means of differential pressure or at regular intervals of time or filtered volume [START_REF] Nakayama | Maintenance[END_REF].

Several studies have emerged in recent years with the intention of improving designs for energy consumption, and understanding the flow behaviour and performance of filters, mainly media filters [START_REF] Arbat | Using Computational Fluid Dynamics to Predict Head Losses in the Auxiliary Elements of a Microirrigation Sand Filter[END_REF][START_REF] Bové | Development of a new underdrain for improving the efficiency of microirrigation sand media filters[END_REF]Bové, Arbat, Pujol, et al., 2015;[START_REF] Mesquita | Characterization of flow lines generated by pressurized sand filter underdrains[END_REF][START_REF] Mesquita | Design and hydrodynamic performance testing of a new pressure sand filter diffuser plate using numerical simulation[END_REF][START_REF] Pujol | Effect of wand-type underdrains on the hydraulic performance of pressurised sand media filters[END_REF][START_REF] Solé-Torres | Effect of underdrain design, media height and filtration velocity on the performance of microirrigation sand filters using reclaimed effluents[END_REF]. Many studies have used computational fluid dynamics (CFD) to investigate, design, and improve irrigation equipment [START_REF] Camargo | Applications of computational fluid dynamics in irrigation engineering[END_REF]. Although experimental data will always be necessary for the validation of numerical simulations and to confirm the performance of irrigation equipment, numerical simulations can be useful to reduce resources related to development costs.

Mathematical models based on dimensional analysis have been developed to predict head losses of filters for irrigation systems operated with tap water [START_REF] Yurdem | Development of a mathematical model to predict head losses from disc filters in drip irrigation systems using dimensional analysis[END_REF][START_REF] Yurdem | Development of a mathematical model to predict clean water head losses in hydrocyclone filters in drip irrigation systems using dimensional analysis[END_REF], water with suspended solids, and effluents [START_REF] Duran-Ros | Assessment of head loss equations developed with dimensional analysis for micro irrigation filters using effluents[END_REF][START_REF] Puig-Bargués | Development of Equations for calculating the Head Loss in Effluent Filtration in Microirrigation Systems using Dimensional Analysis[END_REF][START_REF] Zong | Development of head loss equations for self-cleaning screen filters in drip irrigation systems using dimensional analysis[END_REF]. Some of these models can describe filter clogging as a function of the characteristics of the filter, water, and flow. CFD was used to estimate fluid flow characteristics and pressure losses in different parts of sand filters, as well as to propose improvements in the design of filter components aiming for better hydraulic performance [START_REF] Arbat | Using Computational Fluid Dynamics to Predict Head Losses in the Auxiliary Elements of a Microirrigation Sand Filter[END_REF]Bové, Arbat, Pujol, et al., 2015;[START_REF] Mesquita | Characterization of flow lines generated by pressurized sand filter underdrains[END_REF][START_REF] Mesquita | Design and hydrodynamic performance testing of a new pressure sand filter diffuser plate using numerical simulation[END_REF]. CFD studies on strainer-type filters are scarce in the literature on irrigation engineering.

The objective of this study was to investigate the hydraulic performance and flow behaviour of an automatic flushing strainer-type filter operated with clean water, using experimental and numerical approaches, to optimise the dimensions of its filter housing and to increase the range of operating flow rates.

Material and methods

Filter

The automatic flushing strainer-type filter model FA-20 manufactured by Iavant Filtering Systems, Brazil, was investigated (Fig. 1). The filter housing is made of steel, and an electrostatic powder coating is applied over its inner and outer surfaces. The inlet and outlet internal diameters are 80 mm, and the total surface area of the filtration element is 272,376 mm 2 .

This filtration system operates differently from other automatic flushing strainer-type filters. In this filter, the operating water flows from the outer to the inner surface of the filter element; thus, residues gradually accumulate over the external surface of the element. The automatic flushing mechanism is activated by a differential pressure threshold with a default value of 50 kPa. When the flushing routine is activated, the flushing valve is opened, and the electric motor coupled to a gearbox rotates the filter element. When the filter element rotates, its outer surface rubs against the brushes, which facilitates the detachment of solid material accumulated during the filtration routine. Parallel to the brushes, there is a narrow cavity that is connected to a flushing pipe. The differential pressure between the inside of the filter and the atmosphere is converted into a high velocity through the flushing pipe, which removes the material accumulated over the external surface of the filter element.

[Fig. 1]

A technical description of the five models of the filter elements evaluated is presented in Table 1. According to the filter manufacturer, stainless steel (SS-120 and SS-150) and polypropylene (PP-120) models are used in several applications (e.g., irrigation, wastewater, water supply, and industry), whereas non-woven models (NW-500 and NW-2500) are usually required for industrial purposes. Fig. 2 shows images of the woven and non-woven meshes obtained using a Leica M125C stereo microscope. The pressure drop curves as a function of flow rate were determined in the test bench, as illustrated in Fig. 3 using clean tap water. The hydraulically closed circuit consisted of a 25 m 3 water tank, a 18.6 kW centrifugal pump (maximum flow rate of 70 m 3 h -1 at 400 kPa), an orifice plate flow meter equipped with a differential pressure transmitter, calibrated in the range from 20 to 65 m 3 h -1 (maximum error of 5% from the measured value), a gate valve installed upstream of the filter to set the testing pressure, a temperature transmitter PT100 (0 to 50 ºC, maximum error of 0.5 ºC), a pressure transmitter (0 to 500 kPa, maximum error of 0.5% of the full scale), a differential pressure transmitter (0 to 100 kPa, maximum error of 0.5% of the full scale), the filter under test, and a gate valve installed downstream of the filter to adjust the test flow rate.

The pressure tap distance was 5 𝐷 at the filter inlet and 10 𝐷 at the filter outlet [START_REF] Asabe | Media filters for irrigation -Testing and performance reporting[END_REF]ISO9644, 2008).

[Fig. 3]

All sensors provided an analogue output signal that ranged from 4 to 20 mA, which varied linearly with the measured quantity. The data acquisition of all measurement instruments was performed using an electronic system equipped with a 16-bit analogueto-digital converter to acquire analogue signals within the range of 4 to 20 mA and a resolution of 625 nA. The differential pressure was measured increasing and decreasing conditions of flow rate. For each test condition, 100 records of the sensor readings. were sampled at a 1 s acquisition interval. Data was gathered in three replications evaluating one unit of each filter element model.

Pressure drop curves as a function of flow rate were determined for the filter housing without filter elements, as well as for the filter system equipped with each of the filter elements shown in Table 1. The pressure drop in the filter was measured at flow rates varying from 25 to 65 m 3 h -1 . The pressure at the filter inlet ranged from 350 to 400 kPa, and the average water temperature was 21.5 ºC (20.7 and 22.5 °C were the extreme values). The automatic flushing mechanism was disabled during the experiments because it was not part of the purpose of this study.

Simulations evaluating the original filter housing

CFD simulations were performed to estimate the pressure drop of the original filter housing operated with clean water. In this stage, experimental data of pressure drop as a function of flow rate was available for comparison. Numerical simulations including filter elements were not included in this study.

The CFD module of COMSOL Multiphysics V. 5.4. was used to draw the threedimensional solids representing the filter housing and running the numerical simulations. Simulations assumed an incompressible Newtonian fluid (i.e., water) and steady state conditions.

The realisable k-ε model was used to solve the turbulent flow. This model is an extension to the standard k-ε model which is used for simulating incompressible and single-phase flows at high Reynolds numbers (COMSOL Multiphysics, 2016).

Comparison of turbulence models was not part of the study. Log-law wall functions were applied to approximate the flow velocity profile inside the boundary layer, serving to bridge the velocity profile from the wall to the main flow. The no-slip condition was assumed.

Simulations were performed for three flow rates corresponding to some of the conditions in which experimental data was available: 35.7, 49.5 and 62.8 m 3 h -1 . Taking the inlet diameter as a reference dimension, the Reynolds number varied from 162,099 to 285,149, indicating turbulent flow conditions in all simulations. The mean flow velocity corresponding to each flow rate was set as a boundary condition at the filter inlet, and the pressure was set to 400 kPa as a boundary condition at the filter outlet.

The mesh was generated based on the free tetrahedrals, including a boundary layer mesh (i.e., inflation or prism layer) near the walls (Fig. 4). The default values were kept for the boundary layer mesh (number of layers = 5; stretching factor = 1.2; thickness of first layer = automatic; thickness adjustment factor = 2.5).

[Fig. 4]

The mesh quality was examined based on minimum and average element quality (skewness). Mesh independence analysis was performed to validate the simulations.

Velocity profiles were plotted at four flow sections (inlet pipe, middle of the filter housing, outlet of the filter housing, and outlet pipe) and results of pressure drop in the filter were analysed to prove the results were mesh independent.

Simulations for optimizing the filter housing dimensions

Excessive pressure drop in the filter housing and low filtration rates were identified as the main drawbacks in the original filter system; hence, simulations focused on evaluating possibilities for optimizing the filter housing dimensions.

Four designs of the filter housing were simulated (Fig. 5). The total surface area of the filtration was kept constant in all the designs (𝐴 = 272,376 mm 2 ). The inlet and outlet diameters of the filter housing were the basic dimensions of the new designs and were set according to the commercial diameters of the steel pipes (80, 100, 125, and 150 mm).

The steps to obtain the main dimensions of the filter housing were as follows: For a total surface area of 272,376 mm 2 , the corresponding flow rate for the automatic flushing strainer-type filter was 102.1 m 3 h -1 . Therefore, a pressure of 400 kPa at the filter outlet and the flow rate of 100 m 3 h -1 were set as boundary conditions for CFD simulations. Also, pipes of 150 mm diameter and reducing adapters were included at the filter inlet and outlet in these simulations to keep flow velocities lower than 2 m s -1 in the pipeline, as recommended in most of practical applications [START_REF] Azevedo Netto | Manual de hidráulica[END_REF]. Including the reducing adapters in the simulations enables to consider minor losses caused by these fittings.

RESULTS AND DISCUSSION

Pressure drop curves -Experimental data

Figure 6 shows the pressure drop curves of the filtering system with and without the filter elements. The pressure drop curve in filters is influenced by the geometric characteristics of the filter housing and filter elements, as well as the filtering water characteristics [START_REF] Wu | A new model for head loss assessment of screen filters developed with dimensional analysis in drip irrigation systems[END_REF]. In this stage, the filter housing and filtering water quality were the same for all evaluations.

[Fig. 6]

The pressure drop curves of the woven filter elements SS-120, SS-150, and PP-120 were similar. These three models offer similar resistance to flow, although Table 1 indicates differences in aperture size, wire diameter, wire material, and type of weave of these filter elements. [START_REF] Testezlaf | Sistema automatizado para determinação de perda de carga em filtros de tela e disco usados na irrigação localizada[END_REF] also found that the differences between pressure drop curves of 125-and 100-µm screen filters were not significant because of their similar permeability.

The pressure losses of 15 types of screen filters with plain weave woven wire cloth were analysed by [START_REF] Wu | A new model for head loss assessment of screen filters developed with dimensional analysis in drip irrigation systems[END_REF]. The plain weave filter cloth is one of the simplest weave patterns, in which single wires (i.e., weft and warp wires) have the same diameter and are woven together to form rectangular or square apertures. [START_REF] Wu | A new model for head loss assessment of screen filters developed with dimensional analysis in drip irrigation systems[END_REF] developed an empirical model based on dimensional analysis to predict pressure losses in screen filters was proposed. In their experiments, the filter pore and the wire diameters ranged from 120.4 to 195.6 µm and 64.5 to 208.5 µm, respectively. For screen filters with 64.5 µm wire diameter, [START_REF] Wu | A new model for head loss assessment of screen filters developed with dimensional analysis in drip irrigation systems[END_REF] identified that the pressure drop increased when the mesh count was increased from 80 mesh to 140 mesh (i.e., the aperture size decreased from 200 to 115 µm), but the differences in pressure drop due to mesh count were not statistically significant. Also, for a given mesh count, the increase in wire diameter reduced the pore size and filter permeability and increased the pressure drop in the filters. Given a fixed flow range and mesh count, a larger inlet/outlet diameter and a thinner wire diameter of the screen reduced the inlet flow velocity and average filter flow velocity minimising both head loss caused by pipeline turbulence and local head loss caused by streams [START_REF] Wu | A new model for head loss assessment of screen filters developed with dimensional analysis in drip irrigation systems[END_REF].

The pressure drop in a clean strainer-type filter ranges from 10 to 30 kPa, and the filter element should be cleaned when ∆𝑝 reaches 40-60 kPa [START_REF] Pizarro Cabello | Riegos localizados de alta frecuencia[END_REF]. In this study, the nominal flow rate (𝑄 𝑛 ) for a clean filter was calculated assuming a midrange value of ∆𝑝, which was 20 kPa. The nominal flow rate ranged from 59.1 to 60.7 m 3 h -1

for the elements SS-120, SS-150, and PP-120 (Table 2). The difference in 𝑄 𝑛 values among these elements was less than 5%.

The pressure drop curves of the non-woven filter elements (i.e., NW-500 and NW-2500) were stepper than those of the woven filter elements (i.e. SS-120, SS-150, and PP-120), which is expected because the non-woven elements presented lower permeability and offer higher resistance to flow than the woven elements. The lower permeability of the non-woven elements also led to nominal flow rates that were approximately 20% smaller than those of the woven elements. Comparing the nonwoven filter elements, the difference in 𝑄 𝑛 was approximately 8%, although the air permeability of NW-500 was more than three times that of NW-2500.

At the nominal flow rate, the pressure drop due to the filter housing in the woven elements (i.e., SS-120, SS-150, and PP-120) was dominant and represented more than 87% of the total pressure drop in the filtering system (Table 2). In the non-woven filter elements operating at the nominal flow rate, the pressure drop due to the filter housing was more than 60% of the total pressure drop in the filtering system.

The percentages of pressure drop caused by the filter housing (Table 2) suggest that enhancements in the filter housing design could improve energy efficiency aspects and, perhaps, it could allow the filtering system to operate at higher flow rates [START_REF] Demir | Determination of the head losses in metal body disc filters used in drip irrigation systems[END_REF][START_REF] Wu | A new model for head loss assessment of screen filters developed with dimensional analysis in drip irrigation systems[END_REF]. Table 2 presents the pressure drop equations for each filter element. These equations were estimated by the difference between the results of the total pressure drop in the filtering system and the pressure drop caused by the original filter housing. In irrigation, the filtration rate of strainer-type filters with elements made of steel woven wire mesh usually range from 446 to 1004 m 3 m -2 h -1 [START_REF] Pizarro Cabello | Riegos localizados de alta frecuencia[END_REF]. The flow rate can be obtained by multiplying the filtration rate by the total surface area of the filter element. For the stainless-steel elements evaluated (i.e., SS-120 and SS-150), the filtration rate at 𝑄 𝑛 ranged from 217.0 to 222.9 m 3 m -2 h -1 . The filtration rate values indicated in Table 2 are smaller than the values reported in the literature, which suggests that the filtering system could operate at higher flow rates if the filter housing design was improved to reduce the pressure drop. Based on the values presented by Pizarro [START_REF] Pizarro Cabello | Riegos localizados de alta frecuencia[END_REF] for steel woven wire mesh, the flow rate values can vary from 121.5 to 273.5 m 3 h -1 (i.e., 446 to 1004 m 3 m -2 h -1 ).

If an increase in the flow rate does not interfere with the removal efficiency of solid particles, improvements in the filter housing design could contribute to enlarge the range of operating conditions of the filtration system, to reduce pressure losses and energy consumption. As examples to encourage further investigation on these aspects, the 4" automatic vertical screen filter Netafim Screenguard™ exhibits a filtration surface area of 0.2 m 2 and maximum recommended filtration rate of 375 m 3 m -2 h -1 (NETAFIM, 2022); the 4" Azud Luxon MFH 2400 M/4 has a filtration surface area of 0.24 m 2 and maximum recommended filtration rate of 375 m 3 m -2 h -1 (AZUD, 2022); and the 4" Filtomat M104C exhibits a filtration surface area of 0.212 m 2 and maximum recommended filtration rate of 377 m 3 m -2 h -1 (AMIAD, 2022). The maximum filtration rates recommended by the manufacturers of automatic flushing strainer-type filters are lower than the values proposed by Pizarro Cabello (1996). Regardless of the type of filter, lower filtration rates are recommended for low-quality water [START_REF] Ravina | Control of clogging in drip irrigation with stored treated municipal sewage effluent[END_REF].

Simulated and experimental pressure losses of the original filter housing

Simulations of the original filter housing were performed at flow rates of 35.7, 49.5 and 62.8 m 3 h -1 . Mesh independence analyses were performed to validate all conditions simulated. Figure 7 shows velocity profiles plotted at four flow sections (I, II, III and IV) and results of pressure drop in the filter operating at 62.8 m 3 h -1 , which corresponds to 3.47 m s -1 at the filter inlet. The influence of mesh size in the velocity profiles and values of pressure drop in the filter housing is clearly demonstrated in Fig. 7. Mesh independence was confirmed when the mesh size was increased from 4,053,468 (e) to 4,684,543 (f) elements. In these mesh sizes (e and f ), the velocity profiles are practically matching at the four flow sections evaluated, and the pressure drop in the filter housing was 29.8 and 29.7 kPa, which represents a difference smaller than 0.5%.

Although not shown here, the same procedure was used for proving the results were mesh independent in all CFD simulations.

Figure 7 also shows values of 𝑦 + for the simulation at 62.8 m 3 h -1 using mesh size f, in which mesh independence was identified. The distance between the first grid cell and wall (𝑦 + , dimensionless wall distance) should be lower than an upper limit, which depends on the Reynolds number [START_REF] Pope | Turbulent flows[END_REF]. Log-law of wall provides a function for velocity to match the inner sub-layer to the outer layer and is extensively verified experimentally. The log-law wall functions are known to be valid for 30 < 𝑦 + < 1,000 [START_REF] Tabatabaian | CFD Module: Turbulent Flow Modeling[END_REF]. In COMSOL, log-law is used for wall functions up to 𝑦 + = 11.06

for the k-ε model and 𝑦 + is designated by 𝛿 𝑤 + in the software documentation (COMSOL Multiphysics, 2016;[START_REF] Tabatabaian | CFD Module: Turbulent Flow Modeling[END_REF].

In all simulations, the minimum element quality ranged from 0.065 to 0.1, and the average element quality varied between 0.68 to 0.72. In COMSOL, the mesh quality of 1 represents an optimal element quality, while minimum element qualities below 0.01 are very low quality and should be avoided to prevent convergence problems.

[Fig. 7]

Figure 8 shows the experimental and simulated values of the pressure drop for the original filter housing evaluated under mean flow velocities at the filter inlet 1.97, 2.73 and 3.47 m s -1 , which corresponds to flow rates of 35.7, 49.5 and 62.8 m 3 h -1 , respectively. Simulations overestimated the pressure drop in the filter housing as the flow velocity was increased. Differences between measured and simulated values can be attributed to the simplifications in the three-dimensional model, inaccuracies of the turbulence flow model, and experimental data measurement uncertainty [START_REF] Pope | Turbulent flows[END_REF].

Ilker and Sorgun (2020) observed errors of up to 20% evaluating the performance of different flow turbulence models for single-phase and liquid-solid slurry flows in pressurized pipe systems. [START_REF] Movahedi | Experimental and CFD simulation of slurry flow in the annular flow path using two-fluid model[END_REF] evaluated the accuracy of different turbulence models for the prediction of pressure drop along with an annular pipe and reported errors of up to 25% according to the model employed. For practical purposes, to estimate how changes in the filter housing dimensions will influence the filter pressure drop, we can assume the prediction errors are acceptable and useful.

[Fig. 8]

Part of the pressure drop found in filters is produced by the filter medium itself and cannot be avoided. However, a large part of the pressure drop may be caused by the filter housing design and by auxiliary elements of the filter, and this could potentially be reduced without reducing the effectiveness of the filtration process (Bové et al., 2015).

From the CFD simulations, the velocity streamlines and pressures were analysed to identify which regions of the filter housing caused most of the pressure drop. Figure 9 shows the results of the original filter housing simulated at 62.8 m 3 h -1 (i.e., mean flow velocity at the inlet = 3.47 m s -1 , outlet pressure = 400 kPa). Eight lines were positioned in the three-dimensional model, and the average pressure at each location was plotted (Fig. 9A). The most critical regions in terms of pressure losses (i.e., regions i and ii) are near the transitions between the inlet and outlet segments of the pipe (red dashed rectangles in Fig. 9A). These regions present sudden expansion (i) and sudden contraction (ii) of streamlines combined with the highest flow velocities (Fig. 9B). For the simulated condition, 37.6% and 46.2% of the pressure drop in the filter housing occurred from locations 2 to 3 (i.e., region i) and 5 to 6 (i.e., region ii), respectively (Fig. 9A). Thus, 83.9% of the total pressure drop in the filter housing occurred at regions i and ii. Improvements in filter housing seeking to reduce pressure losses should focus on changing the dimensions near regions i and ii. Bové et al. (2015) showed the importance of improving inlet/outlet regions and auxiliary elements of media filters.

These authors proposed a new underdrain design and a packing strategy that could reduce the overall pressure drop in the filter by 35%.

[Fig. 9]

The filter inlet is left aligned in the filter housing, which leads to the vorticity and circulation of water around the filter element. This position is important to avoid excessive strain on a small region of the screen and to allow a better distribution of impurities over the filtration element. A similar design of filter inlet was found for the 2" Spin Klin® disc filters -Amiad company (AMIAD, 2021).

In the current design of the filter housing, the highest flow velocities occurred at the inlet and outlet of the filter housing (Fig. 9B), leading to most of the pressure losses.

The inlet and outlet sections should be enlarged to allow the filter to operate at higher flow rates with feasible pressure losses.

While sizing pipelines for irrigation applications, mean flow velocities higher than 2.0 -2.5 m s -1 are not recommended for operation of pressurized systems [START_REF] Azevedo Netto | Manual de hidráulica[END_REF][START_REF] Frizzone | Irrigação por aspersão: sistema pivô central[END_REF][START_REF] Lamm | Microirrigation for crop production: design, operation and management[END_REF], but high velocities may occur in short segments of pipes and in its components. In general, excessive flow velocities increase pressure losses and energy waste, cause premature wear of components, and lead to more intense pressure surges in the case of water hammer events [START_REF] Porto | Hidráulica básica[END_REF].

Optimization of the filter housing dimensions

The pressure losses in the filter housing designs simulated (Fig. 5) at 100 m 3 h -1 were: A (80 mm) = 57.6 kPa; B (100 mm) = 35.8 kPa; C (125 mm) = 25.8 kPa; D (150 mm) = 13.3 kPa. Following the same schema of locations illustrated in Fig. 9, the pressure losses were quantified for each of the proposed designs (Fig. 10). Increasing the dimensions at the inlet and outlet segments of the pipe (i.e., at the critical regions i and ii) effectively decreased the pressure drop in the filter housing. Because the allowable pressure drop in a clean strainer-type filter should be lower than 30 kPa [START_REF] Pizarro Cabello | Riegos localizados de alta frecuencia[END_REF], only designs C (125 mm) and D (150 mm) comply with the allowable pressure drop criterion at the target flow rate of 100 m 3 h -1 (𝑞 = 375 m 3 m -2 h -1 ).

[Fig. 10]

A slight increase in pressure was observed between location 6 to 7 (Fig. 10). Although such small values are not relevant for practical purposes, it is known that pressure recovery downstream a 90º bend can be related to conversion between kinetic head and pressure head. A bend or curve in a pipe, as in the filter outlet, induces a pressure loss due to flow separation on the curved walls and a swirling secondary flow arising from the centripetal acceleration [START_REF] White | Fluid Mechanics[END_REF].

Filter housing designs combined with filter elements

CFD simulations combining filter housing designs with woven and non-woven filter elements were not possible in our current facilities. The arrangement, shape, and dimensions of the fibres in each type of filter element would result in a highly complex three-dimensional model that could not be simulated using the CFD module of COMSOL Multiphysics. Further investigation may take advantage of simulation tools such as GeoDict® filtration package, which has been developed particularly for the simulation of air and liquid filtration processes using woven and non-woven fabrics and meshes.

The experimental pressure drop equation shown in Table 2 assumes that the flow pattern obtained without the filter element (i.e., only the filter housing) is the same than that including it. But from Fig. 1, the installation of the filter element will modify the flow pattern, mainly at the filter inlet. Although flow behaviour and minor losses are influence by the presence of the filter element, the screen characteristics can be assumed to be the dominant factor when summing the pressure drop of the filter housing and filter element. A feasible method for approximating the pressure drop of the proposed filter designs and the existing filter elements consists of summing the pressure drop of each filter housing obtained from CFD with the pressure drop calculated from the equations of filter elements shown in Table 2. At this stage, simplifications and approximations must be performed to provide useful information before building new prototypes of the filter.

The best size of the filter housing depends on which is the target nominal flow rate defined by the manufacturer according to market strategies. Assuming a target flow rate of 100 m 3 h -1 , Table 3 presents estimated operational characteristics of the filter housing designs equipped with the filter elements. The total pressure drop (∆𝑝 𝑡𝑜𝑡𝑎𝑙 ) was estimated by summing the pressure drop caused by the filter element (∆𝑝 𝑓 ) and the pressure drop in the filter housing, which was obtained from the CFD simulations. Model A (80mm) corresponds to the original filter housing coupled to inlet and outlet pipes of 150 mm diameter by reducing adapters (Fig. 5A). From Table 3, improvements in terms of pressure drop reduction for operation at 100 m 3 h -1 can be observed. Taking the model A as the reference for comparisons, for the filter equipped with the element SS-120, the decrease in pressure drop was 33.3, 48.5 and 67.6% for the designs B, C and D, respectively. For NW-2500, which presents the smallest permeability among the evaluated elements, the decrease in pressure drop was 27.6, 40.3 and 56.1% for the designs B, C and D, respectively.

Graphical Abstract

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  Keywords: filtration; CFD; screen filter; irrigation engineering; hydraulics Nomenclature 𝐴 Total surface area of filtration (mm 2 ) 𝑎, 𝑏 Fitted coefficients of the pressure drop equation CFD Computational fluid dynamics 𝐷 Inlet diameter of the filter (mm) the original filter housing, obtained experimentally (kPa) ∆𝑝 𝑓 Differential pressure of the filter element (kPa) ∆𝑝 ℎ𝑜𝑢𝑠𝑖𝑛𝑔 Differential pressure of the filter housing (kPa)

  Wire diameter: 0.64 mm; Mass per unit area: 300 g m -2 ; Air permeability: 80 m 3 m -2 min -1 at 200 Pa NW-500 Polypropylene 500 25 Non-woven, needlona® PP/PP 601 Air permeability: 13 m 3 m -2 min -1 at 200 Pa NWTests were carried out at the Hydraulics and Irrigation Laboratory (LHI/FEAGRI/ UNICAMP), Campinas, SP, Brazil.

[Fig. 5 ]

 5 1) Define the inlet diameter (𝐷); 2) Filter element diameter (𝐷 𝑒𝑙 ) = 𝐷 + 90; 3) Filter housing diameter (𝐷 ℎ𝑜 ) = 𝐷 𝑒𝑙 + 40; 4) Filter element height (ℎ 𝑒𝑙 ) = 𝐴 𝜋 𝐷 𝑒𝑙 ; 5) 5: Filter housing height (ℎ ℎ𝑜 ) = ℎ 𝑒𝑙 + 160. The values summed to each of the variables were based on the dimensions measured in the original filter housing. Model A (80 mm) corresponded to the original filter housing dimensions, but inlet and outlet pipes were changed to 150 mm and reducing adapters were added, as explained below.For optimising the filter housing dimensions, the maximum filtration rate 375 m 3 m -2 h -1 found in commercial automatic flushing strainer-type filters (AMIAD, 2022; AZUD, 2022; NETAFIM, 2022) was assumed as the target value (see discussion in section 3.1).

Fig. 1 .Fig. 2 .

 12 Fig. 1. Automatic flushing strainer-type filter model Iavant FA-20. (1: electric motor; 2:

Fig. 2 Fig. 3 .

 23 Fig. 2 Click here to access/download;Figure;Fig. 2.docx

Fig. 3 Fig. 4 .

 34 Fig.3 Click here to access/download;Figure;Fig. 3.docx

Fig. 4 Fig. 5 .Fig. 7 .Fig. 8 .

 4578 Fig. 4 Click here to access/download;Figure;Fig. 4.docx

Fig. 8 Fig. 9

 89 Fig. 8 Click here to access/download;Figure;Fig. 8.docx

  Fig. 10 Click here to access/download;Figure;Fig. 10.docx

Table 1 .

 1 Specifications of the filter elements provided by the mesh manufacturers.

	Model	Material	Mesh count	Aperture size (µm)	Type of weave	Additional specifications
						Wire diameter: 0.38 mm (warp) and 0.26 mm
	SS-120	Stainless steel	120	125	Plain Dutch weave	(weft); Number of apertures per inch: 24 (warp) and 110 (weft). Number approx. of
						apertures per cm 9 (warp) and 43 (weft)
						Wire diameter: 0.23 mm (warp) and 0.18 mm
	SS-150	Stainless steel	150	100	Plain Dutch weave	(weft); Number of apertures per inch: 30 (warp) and 150 (weft). Number approx. of
						apertures per cm 12 (warp) and 59 (weft)
					Satim weave,
	PP-120	Polypropylene	120	125	calendered,
					monofilament

Table 2 .

 2 Nominal flow rate, filtration rate and percentage of pressure drop caused by the original filter housing when the filtering system is operating at the nominal flow rate, and pressure drop equation of each filter element.

	Model	𝑄 𝑛 (m 3 h -1 )	𝑞 (m 3 m -2 h -1 )	% of pressure drop caused by the filter housing at 𝑄 𝑛	Pressure drop equation of the filter element = 𝑎 𝑄 (𝑚 3 ℎ -1 ) 𝑏 ∆𝑝 𝑓 (𝑘𝑃𝑎) 𝑎 𝑏 𝑅²
	SS-120	60.7	222.9	91.0	2.07E-5	2.79	0.992
	SS-150	59.1	217.0	87.8	1.35E-4	2.41	0.997
	PP-120	59.8	219.4	89.1	3.40E-4	2.15	0.999
	NW-500	48.0	176.1	66.6	4.21E-2	1.31	0.999
	NW-2500	44.4	162.8	60.0	8.08E-2	1.21	0.999
	𝑄

𝑛 is the filtering system nominal flow rate predicted considering 20 kPa differential pressure; 𝑞 is the filtration rate considering the total surface area of filtration and 𝑄 𝑛 ; ∆𝑝 𝑓 is the pressure drop of the filter element alone; 𝑄 is the flow rate; 𝑅 2 is the coefficient of determination.

Table 3 .

 3 Estimated operational characteristics of the filter housing designs equipped

	with filter elements operating at 100 m 3 h -1
				Model of filter housing
	Filter element ∆𝑝 𝑓 (kPa)	A (80 mm) B (100 mm) C (125 mm) D (150 mm)
				∆𝑝 𝑡𝑜𝑡𝑎𝑙 (𝑘𝑃𝑎)
	SS-120	7.9	65.5	43.7	33.7	21.2
	SS-150	8.9	66.5	44.7	34.7	22.2
	PP-120	6.8	64.4	42.6	32.6	20.1
	NW-500	17.6	75.2	53.4	43.4	30.9
	NW-2500	21.3	78.9	57.1	47.1	34.6

In general, the woven wire filter elements (i.e., SS-120, SS-150, and PP-120) mounted within the filter housing D (150 mm) could operate at flow rates up to 100 m 3 h -1 with pressure drop lower than 30 kPa, which is a threshold mentioned by Pizarro Cabello (1996). Even the model C (125 mm) could be suitable since its values of ∆𝑝 𝑡𝑜𝑡𝑎𝑙 are near 30 kPa. Although the evaluation of the efficiency of suspended solids removal is not part of this research, the filtration efficiency is acceptable because the filtration rate values are matching the thresholds of commercial screen filters.

The obtained results provide useful information for planning enhancements of the filtration system and for building prototypes for further experimental evaluation.

CONCLUSIONS

The hydraulic performance and flow behavior of an automatic flushing strainer-type filter operated with clean water were investigated using experimental and numerical approaches. For the original filtration system equipped with woven elements, the experimental results indicated that the pressure drop due to the filter housing was dominant and represented more than 86% of the total pressure drop in the filtering system. Similarly, for non-woven elements, more than 53% of the total pressure drop was caused by the filter housing. Excessive pressure drop in the filter housing and low filtration rates were identified as the main opportunities for improving the original filtration system. CFD simulations were performed to predict values of pressure drop of the original filter housing operated with clean water. Numerical simulations enabled the identification of the most critical regions in terms of pressure losses near the transitions between the inlet and outlet segments of the pipe.

Keeping the filtering area constant, four designs of filter housing were simulated to evaluate possibilities for optimizing the filter housing dimensions. Larger inlet and outlet diameters combined to a filter housing shorter and wider were improvements in the filter housing dimensions that enabled to decrease the pressure drop in the filter and/or increase the range of operating flow rates. When comparing the proposed models of filter housing (models B, C and D) against the original design (model A) at the flow rate of 100 m 3 h -1 (i.e., filtration rate of 375 m 3 m 2 h -1 ), the decrease in pressure drop varied from 27.6% to 67.6% according to the combination of filter element and model of filter housing.

The CFD simulations indicates that the filter housing design of an existing automatic strainer-type filter can be improved to reduce pressure loss and/or increase the range of operating flow rates. The obtained results provide useful information for planning enhancements of the filtration system and for building prototypes for further experimental evaluation. The best size of the filter housing depends on the target nominal flow rate, which is defined by the manufacturer according to their market strategies. For development purposes, numerical simulations may reduce the number of prototypes manufactured for preliminary evaluations, thereby decreasing investment, time, and labour requirements.

ACKNOWLEDGEMENT

The authors would like to thank the Fundação de Amparo à Pesquisa do Estado de São


B Gibaud

S Garlatti

C Barillot1

E Faure2

Methodology for the Design of Digital Brain Atlases

This paper deals with the development of computerized brain atlases addressing both research and clinical needs. The authors analyze in detail the potentialities of these systems and discuss the capabilities and limitations of the digital atlases currently being developed around the world. The authors propose to reconsider the concept of a brain atlas, regarding both its content, and the way it has to be used and managed in order to set up a more effective cooperation between the user and the system. Particular emphasis is put on the evolutivity and reuse issues, which are critical in this rapidly evolving field. These orientations result from both the authors' experience and the analysis of current trends in the field of neuroimaging. The general methodology is illustrated with examples related to computer aided surgical planning.

1.

Introduction

The role of medical imaging in the neurological and neurosurgical practice, as well as in neuroscience in general, is becoming increasingly important. Indeed, the interpretation of the images plays a prominent role in diagnostic and therapeutic decisions, and quantitative image analysis is a major research issue in neuroimaging. Brain atlases [e.g. l, 2, 3, 4) aim at assisting the interpretation of brain images by providing a priori knowledge about brain anatomy by means of anatomical plates obtained from post-mortem brains or in vivo images. These plates provide the anatomical substrate, from which more details about brain features (e.g. morphology, relationships with surrounding anatomical structures, function, variability) are accessible in textual or graphical form.

From an historical point of view, atlases were developed to overcome the limitations of the in vivo imaging techniques. However, in spite of the availability of modem and powerful imaging techniques such as Magnetic Resonance Imaging (MRI), atlases are still necessary for three major reasons: ( 1) The spatial resolution and the contrast of the images are limited: for example the different nuclei composing the thalamus cannot be distinguished on MRI images; (2) Through the anatomical substrate, it is often the function of the different brain areas that is relevant to the surgeon in order to select the best surgical approach. In most cases this information is not available (functional imaging modalities are not so widespread) and this information has to be retrieved from an atlas;

(3) Brain atlases are still commonly used in the neuroimaging community, especially by people working on the mapping of human brain functions [START_REF] Seitz | Accuracy and precision of the computerized brain atlas programme for focalization and quantification in Positron Emission Tomography[END_REF][START_REF] Evans | Mri-Pet Correlative Analysis Using A Volume Of Interest (Voi) Atlas[END_REF]. A first explanation is related to the low spatial resolution of functional imaging techniques like Positron Emission Tomography (PET): indeed, the registration with patient anatomy (through MRI) cannot be very precise, so it may be more simple to relate functional information to anatomy by means of a reference atlas (e.g. Talairach) rather than the patient MRI data itself. A second explanation arises from the fact that PET experiments cannot be repeated many times on the same individual due to the use of radiopharmaceuticals. Therefore PET studies must be conducted onto several individuals in order to provide statistically significant results: registration to a common atlas is a simple way to merge results from different patients in a standardized way.

The digital nature of in vivo imaging techniques brings new capabilities to represent anatomical information in an atlas and to access to related knowledge. We have experienced some of them during the last decade. Our interest in the mid-80s was primarily focused on 3D representation of brain anatomy [START_REF] Barillo | Three dimensional reconstruction of cerebral blood vessels[END_REF][START_REF] Barillot | Computer graphics in medicine: a survey[END_REF], then on the registration of images between different patients [START_REF] Lemoine | An anatomical-based 3D registration system of multimodality and atlas data in neurosurgery[END_REF][START_REF] Barillot | Data fusion in medical imaging: merging multimodal and multipatient image, identification of structures and 3D Display aspects[END_REF]. More recently we have studied how knowledge about the major anatomical features could be represented in a more explicit way (e.g. atlas plates, symbolic objects represented by frames, illustrations) [START_REF] Montabord | An Hypermedia System to Manage Anatomical Knowledge about Brain[END_REF][START_REF] Barillo | An Information System to Manage Anatomical Knowledge and Image Data about Brain[END_REF], and how access to this information could be managed in a way taking into account contextual information (domain of interest and task of the user) [START_REF] Montabord | HYPER-Y AKA: Hypermedia et base de connaisances sensible au contexte[END_REF]. Finally some aspects of the evolutivity of such systems have been studied, especially regarding schema evolution capabilities in Object Oriented databases [START_REF] Yapi | Evolution de schema et migration d'instances. Prise en compte des besoins d'une application medicale[END_REF].

These works, as well as the analysis of general trends concerning the management of information in the neuroimaging community have led us to reconsider the concept of a brain atlas, regarding both its content, and the way it has to be used and managed. This is the major subject of this paper. Section 2 analyzes in more details new capabilities induced by the digital nature of the images, and discusses the major trends arising from the recent literature on brain atlases. Section 3 presents our approach to this problem, with particular emphasis on the evolutivity and reuse issues. These two constraints strongly influence both the content of the atlas and the way it is used and managed. Finally, section 4 summerizes this general approach, and underlines some difficulties in putting this methodology into practice.

Current Status of Digital Atlases

Before analyzing the potentialities and added value of digital brain atlases, and reviewing current works in this field, it is useful to briefly recall the basic function of an atlas. The utilization of an atlas involves 3 steps (Fig. 1): (I) sp atial registration between the image data to interpret and the anatomy of one or several individuals displayed on atlas plates;

(2) identification of anatomical structures of the subject from the outlines and labels of the same structures within the atlas plates; (3) access to the knowledge associated to the anatomical structures. Atlases are usually printed and thereby have severe limitations. Digital atlases offer a wide range of capabilities, which overcome these limitations.

• The first concerns image display. Brain anatomy is 3D, so the understanding of 3D data sets makes it necessary to use both surface representation and volume representation (cut planes in the three major directions of space). Printed atlases obviously cannot offer this flexibility (limited to 2D display, no possibility to redefine viewing angles).

• The second concerns inter-individual variability. The matching between two brains assumes that some warping model can be applied. Printed atlases impose warping models to be very simple (for example Talairach [I]). Computer-based atlases allow much more complex models to be used (e.g. non-linear rather than linear), leading to simpler use and better accuracy.

• The third is related to extensibility. As opposed to printed atlases, a digital atlas can be extensible: i) the number of atlas plates can be increased (which helps to overcome the inter-individual variability problem); ii) new warping models can be added; iii) the corpus of accessible knowledge can be extended.

•The fourth concerns the flexibility of navigation within the associated knowledge corpus; this allows for taking into account the goals and tasks of the user in order to guide the navigation towards the more pertinent information.

• The last concerns the possible utilization of this knowledge by artificial cognitive agents for decision-making. This is obviously not feasible with classical atlases and permits to free the user from computing tasks that computers do more efficiently than humans.

The development of computer-based atlases is motivated by this potential added value; three major categories of systems have been or are being developed.

(1) The first category is basically a transposition of paper-atlases, and may be called computerised maps. Some of these systems put emphasis on gathering encyclopaedic knowledge from neuroscience sub-areas. For example Toga has developed a 3D anatomical and functional atlas of the rat brain [START_REF] Toga | A Three-Dimensional atlas of structure/function relationships[END_REF]. Other systems propose the integration of data from various atlases, such as the system developed by Nowinski: this system provides atlas plates from the Talairach et Tournoux, Schaltenbrand/Wahren and Ono atlases [START_REF] Nowinski | Schaltenbrand-Wharen/Talairach-Tournoux brain atlas registration[END_REF]. Finally, some systems are organized around 3D display tools: for example the system called "Digital Anatomist", proposed by Brinkley, provides 3D display of the anatomical features by means of both still and moving images, and offers designation facilities allowing their naming [START_REF] Brinkley | Knowledge-based client-server approach to structural information retrieval: the digital Anatomist Browser[END_REF]. The "Voxel-Man" system developed by Hohne is based on the same concept with more enhanced facilities for editing the 3D model and retrieving related symbolic information [START_REF] Hiihne | A volume based anatomical atlas[END_REF]. These systems are more and more edited and distributed on CD-ROM; demonstrations are sometimes possible through Internet.

(2) The second category focuses on modeling the morphological inter-subject variability and on the design of warping models. The general principle consists of labelling precisely 3D data sets of one (or several) brains, and to estimate a displacement field between this reference brain and the particular brain to be matched, in order to assign the reference brain labels to the voxels of the unknown brain. The major issue is to make sure that this transformation guarantees the conservation of topological relationships between the labelled regions. Many methods have been developed, for example: [START_REF] Bajcsy | Multiresolution Elastic Matching[END_REF][START_REF] Bookstein | Thin-Plate Splines And The Atlas Problem For Biomedical Images[END_REF][START_REF] Evans | An MRI-based stereotactic atlas from 250 young normal subjects[END_REF][START_REF] Gee | Matching Structural Images of the Human Brain using Statistical and Geometrical Image Features[END_REF][START_REF] Collins | Automatic 3D segmentation of neuro anatomical structures from MRI[END_REF][START_REF] Christensen | Topological properties of smooth anatomic maps[END_REF][START_REF] Subsol | Une methode generale pour construire automatiquement des atlas anatomiques morphometriques a partir d'images medicales tridimensionnelles : application a un atlas du crane[END_REF].

(3) Finally, many atlas systems have been developed to support the automatic interpretation of anatomical images. They generally include symbolic knowledge about anatomy or imaging techniques in order to assist the delineation and labelling of these features within morphological or functional images, for example: [START_REF] Sokolowska | Multi-Layered Image Representation: Structure and Application in Recognition of Parts of Brain Anatomy[END_REF][START_REF] Zachmann | Interpretation of cranial MR images using a digital atlas of the human head[END_REF][START_REF] Lc. Carlsen | Knowledge based Interpretation of cranial MR images[END_REF][START_REF] Natarajan | A knowledge based system paradigm for automatic interpretation of CT scan[END_REF][START_REF] Lehmann | Computer aided interpretation of SPECT images of the brain using an MRI derived 3D neuro anatomical atlas[END_REF][START_REF] Staemmler | SAMMIE -Software applied to multimodal images and education[END_REF][START_REF] Robinson | Model-Based Recognition of Anatomical Objects from Medical Images[END_REF].

It is also important to mention collaborative efforts carried out in the context of the american Human Brain Project. Mazziota proposed the constitution of a multi-centric database, in order to build a probabilistic brain atlas [START_REF] Mazziotta | A Probabilistic Reference System for the Human Brain[END_REF][START_REF] Mazziotta | A Probabilistic Atlas of the Human Brain: Theory and Rationale for its development[END_REF]. The "BrainMap" system developed by Fox at the University of Texas is accessible through the Internet and gathers many experimental results concerning cognitive studies from many laboratories (activation protocols, localization in the Talairach space, references of publications).

All these works have brought out significant contributions to the various aspects of brain atlas conception and use (more accurate models of the brain variability, 3D display and editing tools, computer-aided image interpretation techniques). Besides, projects like the Human Brain Project highlighted the interest of collaboration across disciplinary and geographic boundaries for brain research. Nevertheless, although claimed as important [START_REF] Mazziotta | A Probabilistic Atlas of the Human Brain: Theory and Rationale for its development[END_REF], evolutivity and reuse issues have not really been addressed yet. Finally, potentialities concerning the utilization of knowledge available from an atlas for automatic or assisted problem resolution (for example surgery planning) have not been really investigated yet. Projects like SAMMIE have tried to go into this direction, in particular for assisting the interpretation of Electroencephalography (EEG) or Magnetoencephalography (MEG), but achievements are still in their infancy [START_REF] Staemmler | SAMMIE -Software applied to multimodal images and education[END_REF].

This situation requires a more thorough analysis of the way knowledge is used by humans for the resolution of medical problems concerning the brain. Experiments carried out by Boshuizen and Schmidt [START_REF] Schmidt | On Acquiring Expertise in Medecine[END_REF] have shown that physicians make use of several kinds of knowledge, including both general knowledge (called biomedical knowledge) and situated knowledge derived from previous experiences. They also demonstrated that novices use more biomedical knowledge than experts do. However, in difficult cases where usual reasoning schemes may fail, experts use general knowledge as well. These works are very interesting with respect to our atlas problem. First, they reinforce the need of associating in an atlas several kinds of knowledge, namely general knowledge, and situated knowledge. Second, they suggest that the system should be designed in such a way that: (1) it provides the user with the most relevant knowledge, depending on the user's task and expertise level, and (2) it supports the emergence of new biomedical knowledge from the experience of past cases. This is the general orientation described hereafter.

Design and Use of Atlases

The general approach described here emphasizes the evolutivity and reuse issues. This concern tends to be more and more critical in the design of Information Systems in general, and are particularly relevant in the context of the management and use of brain related knowledge. Indeed, neuroscience is a very active research field [START_REF] Mazziotta | A Probabilistic Atlas of the Human Brain: Theory and Rationale for its development[END_REF], and many disciplines try to elucidate brain structure and functioning from different perspectives (e.g. anatomy, physiology, psychology, behaviour), which leads to an extreme fragmentation of knowledge. However it is generally admitted that multi-disciplinary research is very effective and fruitful, which assumes that knowledge and results must be shared in an appropriate way. Brain research is also very productive which means that this knowledge must be able to be easily updated, which obliges to consider evolutivity as a major concern in the design of brain knowledge management systems. The same arguments apply regarding clinical applications, since clinical processes and medical decisions oblige to integrate many components (patient specific anatomy, physiology, age, medical history, social condition) each of which referring to specific knowledge, and involving references to previous cases.

This approach articulates around three axes: (1) the first deals with the content of atlases (knowledge sources), (2) the second with the general organization of information processing (Decision-making and knowledge acquisition processes) and (3) the third with the way multi-disciplinary knowledge can be managed.

3.1

Knowledge Sources

Before describing in detail the different kinds of information a digital atlas should manage, it is necessary to introduce the terminology we are going to use in the following. The term data refers to any signifying entity used by an information processing agent. The term information refers to the meaning attached to a particular datum, which thereby depends on the cognitive background of the agent which interprets this datum [START_REF] Prince | Vers une informatique cognitive dans /es organisations, le role central du langage[END_REF]. The term knowledge is (as usual) more difficult to define: we will consider as knowledge any information allowing data to be interpreted and to which one wishes to attach a particular worth; this worth may arise from several origins: (I) abstraction level and capacity to synthesize a set of information; (2) level of consensus a piece of information is gathering;

(3) applicability of a piece of information in a given context (solving power) and potential of reuse in other contexts.

These notions are very important with respect to evolutivity and reuse: the level of abstraction, applicability and degree of confidence play a major role in reuse. Moreover broadly accepted knowledge is likely to be more stable in time than uncertain one.

An atlas involves two fundamentally different kinds of information:

(1) biomedical knowledge concerning brain, characterizing the properties which are shared by most individuals, or within meaningful categories of individuals (such as right handed people).

(2) Situated knowledge (cases): this information characterizes particular individuals, about which data have been recorded (e.g. images, physiological signals) and interpreted, in order to make their specific characters explicit.

One may feel appropriate to speak about these two kinds of information in terms of knowledge base and database. We prefer avoiding to do so in order to emphasize the conceptual difference between the two, rather than focusing on implementation issues.

Biomedical Knowledge

This general biomedical knowledge includes four major kinds of knowledge:

-Conceptual knowledge about one or more brain disciplines: it is usually organized in ontologies describing abstract brain entities (e.g. anatomical structures, functional systems, neurochemicals) or relationships between these entities (e.g. spatial relationships, neural connections, part-whole relationships). These entities are generally represented by means of object oriented models or frames.

-Illustrations (such as drawings or schemata) aim at making more explicit the meaning to be associated to the previous brain abstract entities. By definition they are indented to humans rather than artificial agents.

-Numerical data, functions of sp ace or time: for example 3D probability maps represent the probability that a point belongs to a particular anatomical structure.

-Decision models include inference mechanisms or algorithms capable of deriving new information from existing one: for example a warping model which allows a brain to be mapped onto another, or an image segmentation algorithm, consisting of successive image processing operations, aiming at delineating and labelling a particular structure.

Situated Knowledge

This information depicts various aspects of the brain of particular subjects: anatomy, physiology, behaviour of the subject, characteristics of the individual himself (for example sex, manual dominance, age, pathology, if any). It may have been obtained in vivo, by means of imaging techniques (e.g. CT scanner, MRI, functional MRI, PET) or neurophysiological techniques (e.g. EEG, Depth electrodes recordings, MEG), or from cadavers (photographs of brain cryosections, histological or histochemical data).

This information about individual brains can take several forms:

-numerical data, functions of space or time: e.g. images or physiological signals.

instances of brain abstract entities, whose attributes describe the specific characters of each brain (e.g. length and depth of a cortical sulcus, volume of grey matter within a gyms), or relationships between these entities for example spatial relationships between anatomical structures. These objects describe in an explicit way some properties which are shown by images or signals, as a result of a manual or automatic interpretation process.

-instances of application of a decision model, for example describing the successive steps of an image processing procedure resulting in the labelling of a particular anatomical structure (interpretation process). This information can be considered as knowledge, because according to previous definitions, one assigns a worth to it, and therefore wishes to keep it, in order to refer to it and reuse it. This value arises from several factors:

-a particular brain feature may be typical or atypical; -some information may be difficult to obtain for technical or medical reasons: for example depth electrodes recordings can be obtained in very few patients (e.g. patients suffering some form of epilepsy requiring surgery). This kind of information is very precious although a very small part of it can be understood yet: indeed it provides a view of what is really happening inside the brain.

-complexity level of the description: the delineation, identification and labelling of brain features on images or signals bring a significant added value to the data because it establishes explicit relationships between this data and abstract brain entities. This added value is manifold and brings potentialities of reuse: (1) the result of this delineation may help another user or expert to achieve a similar task; (2) the description itself provides many ways for accessing the images (indexation of the data); the more complex the description is, the more various and specific these ways are; (3) it allows multivariate analysis to be done in the future in order to put in light interesting correlations.

-level of consensus they gather: an interpretation may always be wrong or uncertain. Validation by several experts increases the confidence one may have, and thereby augments the chances of reuse.

A major issue is to be able to clearly distinguish, each time it is feasible, the raw data (which are relatively objective) and the interpretations one may wish to record (which are necessarily subjective). Digital atlases allow to do that, whereas it is much more difficult with classical printed ones (for example on paper, the delineation of a region on an image generally hides the initial information, e.g. pixels values in an MRI image). This issue is also very important with respect to the system evolutivity: in effect, one may be able to interpret or re-interpret data, using some new knowledge appeared in the meantime: in a such case it is important to be able to use the original data, rather than processed ones.

Relationships Between Situated and Biomedical Knowledge

Biomedical knowledge and situated knowledge are complementary. As previously mentioned, the descriptions of particular subjects' brains refer to abstract brain entities, which have to be defined in a non-ambiguous way (notably to allow correct interpretation and reuse in other contexts). Conversely, situated knowledge explain general concepts by providing real world examples.

Decision and Knowledge Acquisition Processes

We are now presenting our general framework for managing information and knowledge in computerized brain atlases. It details the decision-making processes in which data are interpreted, leading to the production of new information, and the knowledge acquisition processes by which information (situated knowledge) is transformed into new biomedical knowledge. The analysis of decision-making processes will particularly focus on human computer cooperation and on the management of multi-disciplinary knowledge.

Modeling of the General Approach

The general process of using and evolving an atlas is presented on (1) Decision processes (Fig 2 -Left) usually consist of analyzing brain-related data acquired for clinical or research purposes, and interpreting them. These interpretations (for example in which anatomical structure a particular depth electrode is located) may be part of the resolution of a more global and more complex problem (in this case, locating an epileptogenic focus, in order to remove it by surgery). Such processes make use of:

brain-related information concerning a particular individual (such as a 3D MRI dataset, neurophysiological data),

-general biomedical knowledge (brain abstract entities, decision models),

-information concerning previous cases (situated knowledge), which present similarities with the current problem.

These decision processes are active processes making connections between situated knowledge and the global framework and produces new information (interpretation) which becomes part of the information patrimony of the atlas. -classification into categories (for example cortical sulci having similar structural and morphological characteristics), -numerical models as probability maps (probability that a point belongs to a particular anatomical structure), -deformable models resuming the morphological properties of a particular anatomical structure.

Of course, the validity of this new information has to be assessed. In particular it should not be contradictory with previous knowledge. Eventual conflicts must be detected and solved in one way or another. This new knowledge may authorize or require to update previous knowledge (and concern both general biomedical knowledge and situated knowledge). For this reason, schema evolution capabilities must be provided in order to achieve these modifications.

Decision-making Processes and Human/Computer Cooperation

The decision-making processes requiring use of a medical atlas cannot be formalised, they are what Simon calls "unstructured decisions". This means that the processes leading to the decision may be unknown to the user himself: they are usually very heuristic and progressive, and may require backtracking stages. Decision support systems address this kind of needs by providing multiple decision models (knowledge-based systems, image tools) and human computer interaction tools, allowing the most appropriate solution to be chosen interactively, case by case.

Tasks distribution between natural and artificial cognitive agents

Current digital atlases are purely reactive systems, limited to the supplying of the information requested by the user. A more fruitful approach is to design an active environment capable of augmenting his skills. Then, the interaction between the user and the system is based on a mixed approach. Users should be able to question the system and the system can offer hints to the user as well. The tasks and the control are distributed among the user and the system in an adaptive manner. This distribution must be flexible and evolutive. Let us take an example, in order to show how the system contribution can be smoothly augmented. In this example four stages of development of the system are considered, in order to assist the identification of a given anatomical structure in a 3D MRI data set: 1. the system allows for the retrieval of other individuals' 3D MRI data sets ; 2. the system allows for the retrieval of those 3D MRI data sets in which the anatomical structure of interest has been delineated and labelled; 3. the system actually performs the superposition of a probability map concerning the anatomical structure of interest on the new 3D MRI data set; 4. finally, the system controls a segmentation algorithm which makes use of the probability map in order to achieve the delineation. This example suggests how the boundary between automatic and human-controlled tasks can be shifted. The system architecture must be designed in such a way that this boundary can be moved very easily in order to enhance progressively the performances of the system (evolutivity).

Organization of cooperation

This cooperation should be organized in a way which is both flexible and natural to the user, allowing him to assess his reasoning, and validate his assumptions. It should allow him to interrupt the system's resolution process, choose another decision model, or do the resolution himself. The system would primarily be used for executing calculations within well-known and well-formalized tasks. However, artificial agents may also be involved to provide the user with the information he needs or even play a part in determining the appropriate cooperation level, taking into account the distribution of skills in the context of a specific problem. This imposes that the relevance of available information should be explicitly and continuously assessed, which can be achieved by means of a task model [START_REF] Mittal | Context: indentifying its elements from the communication point of view[END_REF]. The precision and the sophistication of this model depend on the kind of support the system is supposed to offer. Supporting the retrieval of relevant general biomedical knowledge and relevant previous cases can be achieved in a relatively simple way, relating this information with the general concepts involved in the user's task. If the system must contribute more effectively in solving sub-problems or be involved in the control of the cooperation, then it is necessary to develop much more complex models of the tasks and the skills of the (natural and artificial) agents involved (e.g. a priori distribution schemes, decomposition of tasks into sub-tasks) [START_REF] Willamowski | Modelisation de taches pour la resolution de problemes en cooperation systeme utilisateur[END_REF].

3.3

Managing Multi-disciplinary Knowledge

The necessity to manage multi-disciplinary knowledge has been underlined previously. A major issue is that knowledge production and maintenance is generally organized vertically (according to more and more specialized research fields), whereas utilization is primarily organized horizontally (i.e. multi-disciplinary). These two organization schemes lead to contradictory constraints: taking into account evolutivity constraints would lead to organize knowledge in separate ontologies, whereas multi-disciplinarity may orient to a more ad-hoc (specific problem driven) knowledge management.

Our approach to this problem takes into account the concern of evolutivity and reuse, and recommends to organize the knowledge base by means of multiple knowledge sources [START_REF] Simmons | The Role of Knowledge and Representation in Problem Solving[END_REF][START_REF] Garlatti | A methodological approach for object knowledge bases[END_REF] which can be partitioned by type (for instance, knowledge about tasks, methods and domains) and by level of abstraction (in our framework: neuroanatomy, neurology, neurophysiology, etc).

Discussion and Conclusion

We have proposed a general methodology for building and managing knowledge in digital brain atlases, in a way which guarantees evolutivity and facilitates reuse in different contexts: it can be summerized by a number of basic principles.

1. Information concerning particular brain instances is a form of knowledge, which is complementary to general knowledge (called biomedical knowledge). One should clearly distinguish several levels of interpretation of the data acquired about each brain instance, in order to allow these interpretations to be refined in the future, in the light of some new knowledge.

2. General biomedical knowledge should be organized in a vertical way (scientific disciplines). In effect, it is difficult (almost impossible) to design a single ontology that includes every aspect required to model the world. Dividing the world into distinct knowledge sources makes it easier to understand, to reuse and to update.

Knowledge based decision-making processes involve multi-disciplinary knowledge;

it is therefore necessary to establish cross-speciality relationships.

4. Applications should as far as possible reuse existing knowledge rather redevelop it from scratch. This could save time and energy, and facilitate the maintenance and the evolution of this knowledge. Moreover it would allow the knowledge corpus to be built in an incremental way.

5. Cooperation between the user and the system should be user-centered because the decision-making processes are complex and not fully understood by the users themselves. The boundary between automatic and human-controlled tasks must be very flexible to upgrade progressively the system performance (evolutivity), and to achieve an optimal way of cooperation adapted to each situation (optimal reuse of available knowledge). These principles provide general orientations. However putting them into practice raises many unsolved issues that one should not ignore. Evolving and reusing knowledge leads to face difficulties at four different levels: (l) at a geographical level, (2) at an organizational level, (3) at a semantic level, and finally (4) at a strategic level. Whereas the two first ones can be easily overcome, the two latter are far more fundamental.

• In the field of brain atlases, more and more information can be obtained in digital form, thus facilitating their communication between research labs or within the Healthcare System, through local and global networks (Internet).

•

The second level is organizational. Indeed, in order to communicate or to share information, communicating parties have to share common objectives, in order to define the intention of communication and how it should take place. Regarding this issue, we can notice that many initiatives have been launched in the field of brain research to set up common frameworks between research labs (e.g. European projects such as SAMMIE, Human Brain Mapping project in the USA).

• The third obstacle arises from the various scientific disciplines concerned by brain research. Modeling brain related concepts within a given discipline is already a difficult task (due to the brain intrinsic complexity). Establishing models which are understood and valid across several disciplines is probably not feasible. In practice, trying to describe explicitly those concepts by means of multiple forms of representation (symbolic objects, illustrations, cases) should facilitate the understanding and the reuse by both natural and artificial cognitive agents in various research or clinical environments, or at least facilitate the detection of contradictions and mismatches. Setting up explanation mechanisms may be a good way to satisfy both the needs for concision (e. g. referring to the concepts rather than detailing them when both parties share a common understanding) and semantical accuracy (e.g. control that the associated semantics are not contradictory).

• Finally, one must be able to assess and manage the value and relevance of knowledge with respect to the goals of each organization. It becomes more and more difficult, because global networks considerably increase the possibilities of accessing existing knowledge. The problem is to find efficient ways of appropriation of this knowledge, which is particularly challenging in a multi-disciplinary context like brain research.

5.

Bibliography

Fig. 1 :

 1 Fig. 1: Process of utilization of an atlas

Fig 2 .Fig. 2 :

 22 Fig. 2 : General framework -Decision processes and knowledge acquisition processes

( 2 )

 2 Knowledge Acquisition Processes (Fig 2 -Right) aim at formalising new biomedical knowledge from available information (more abstract or more synthetic models):