Hua Sun

Eric Chénier

Guy Lauriat
email: lauriat@univ-mlv.fr

Keywords: Natural convection, Surface radiation, Numerical study, Unsteady flows, Bifurcations Coupled radiation and free convection

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Introduction

In this paper, the results of a numerical study of combined natural convection and surface radiation from an inner body enclosed in a cavity are reported. Relevant to the present work are engineering applications such as electronic cooling, manufacturing processes, building energy components … in which natural convection heat transfer between a gas-filled enclosure and inner bodies occurs. Considerable research has been performed for fully partitioned cavities or obstructions in the form of partial baffles centered vertically in a vertical enclosure and, for various shaped obstructions located within a rectangular cavity because the obstructions may increase as well as decrease the heat transfer. For tall cavities with multiple partitions, the numerical study by Rabhi et al. [START_REF] Rabhi | Radiation-natural convection heat transfer in inclined rectangular enclosures with multiple partitions[END_REF] demonstrates the effects of surface radiation on the overall thermal resistance of partitioned cavities.

Relevant to the geometry investigated in the present study are the work by House et al. [START_REF] House | Effect of a centered conducting body on natural convection heat transfer in an enclosure[END_REF] who considered the influence of a centered square obstruction in a differentially heated cavity, and those by Deng and Tang [START_REF] Deng | Numerical visualization of mass and heat transport for conjugate natural convection/heat conduction by streamline and heatline[END_REF], Ha et al. [START_REF] Ha | Twodimensional and unsteady natural convection in a horizontal enclosure with a square body[END_REF] and Lee et al. [START_REF] Lee | A numerical study of natural convection in horizontal enclosure with a conducting body[END_REF][START_REF] Lee | Numerical simulation of natural convection in a horizontal enclosure with a heat-generating conducting body[END_REF]. More recently Bouafia and Daube [START_REF] Bouafia | Natural convection for large temperature gradient around a square solid body within a rectangular cavity[END_REF] reconsidered this class of problem by using the low Mach number approximation [START_REF] Bouali | Radiation-natural convection heat transfer in an inclined rectangular enclosure[END_REF] for large temperature differences between a heated body within a rectangular cavity with cold vertical walls and insulated horizontal walls. This approximation allows to take density variations into account in all terms of the conservation equations, and it based on a pressure decomposition into a leading term, assumed spatially uniform, and a second-order, fluctuating term.

Studies on combined natural convection and surface radiation from heated body inside a cavity are more scarse (for an overview of recent references, see Bouali et al. [START_REF] Chenoweth | Natural convection in an enclosed vertical air layer with large horizontal temperature differences[END_REF], Lauriat and Desrayaud [START_REF] Lauriat | Effect of surface radiation on conjugate natural convection in parially open enclosures[END_REF], Mezrhab et al. [START_REF] Mezrhab | Modelling of surface radiation and natural convection in a vented « T » form cavity[END_REF]) while the interaction of natural convection and radiation in participating media was the purpose of many studies (see Colomer et al. [START_REF] Mezrhab | Computation of combined naturalconvection and radiation heat-transfer in a cavity having a square body at its center[END_REF], for example). The paper by Mezrhab et al. [START_REF] Colomer | Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method[END_REF] may be considered as the most related study to the present work.

They considered a differentially-heated cavity of square cross-section containing a conducting, centered square body. Amongst the conclusions drawn for this particular configuration, the effect of the inner body on the flow field and heat transfer was shown much important when surface radiation exchanges were taken into account. In the range of Rayleigh number considered, it is also shown that radiation augments the fluid velocities in comparison with those obtained for an empty cavity. It what follows, it will be shown that surface radiation has opposite effects for the boundary conditions considered herein, and on the stability properties of the flow.

There is still lacking information about the influence of radiation exchanges between surfaces, even when considering the simplest model based on gray, diffuse surfaces. For example, although many experimental, numerical and theoretical works are available in the archival literature, some questions remain open, in particular the relevance in comparisons between experimental data and numerical simulations when the experiments are conducted for gas-filled cavities (generally air at an average temperature close to room temperature). Up-to-date flow visualization techniques are widely used (Cesini et al. [START_REF] Cesini | Natural convection from a horizontal cylinder in a rectangular cavity[END_REF], Leplat et al. [START_REF] Leplat | Natural convection around a heated squaresection cylinder in an enclosure: visualization and dynamic characterization of instabilities by Particle Image Velocimetry[END_REF]), but the requirements are generally that two parallel walls should be transparent to laser beams in order to allow optical access to the cavity. Except for small scale experimental set-up for which glasses having high infra-red (I.R.) transmittance can be used (such as KRS-5 or KBr crystal material), the experiments are often conducted by using common glass window or polycarbonate sheets, opaque at I.R. wavelengths corresponding to room temperature. As it is well known, these materials have also a high emissivity (close to one) for this wavelength domain. Therefore, owing to the low temperature differences involved in many experimental work (typically of the order of 10 K around ambient temperature in air-filled cavities), it was assumed that radiation exchanges amongst the walls have a negligible influence on the flow and temperature fields.

Such an assumption may be justified if a great care is taken during both designs of the experimental set-up and measurements. Unfortunately, experiments are still conducted to determine routes to chaos (bifurcation phenomena) or to validate direct numerical simulations (DNS) of weakly turbulent flows without taking into account the right boundary conditions at the semi-transparent walls and, consequently, the effects of surface radiation on the critical parameters.

The purpose of this investigation is to emphasize the effect of radiation exchanges amongst surfaces on the stability properties of natural convection flows around an inner body. To this end, a numerical analysis is performed for natural convection from a single horizontal, heated solid body of square section immersed at the center of an air-filled cavity of square cross section, as shown schematically in Fig. 1. The solid body is assumed at uniform hot temperature, T h , close to ambient temperature (300 K). The vertical side walls are adiabatic while the lower and upper horizontal walls are isothermally cooled at a temperature T c , not very different from T h . We are particularly interested in the flow transitions (or bifurcations) which occur when the Rayleigh number is increased through increases in the temperature difference between the inner body and the cold horizontal surfaces (ΔT = T h -T c ) within the range [1 K, 5 K] for a square cavity whose side length is L = 10 cm, containing a body having a side length W ranging from W = 2 cm to W = 8 cm, as in the experiments conducted recently by Ménard [START_REF] Ménard | Convection naturelle dans une cavité contenant une source de chaleur[END_REF] and Leplat [START_REF] Leplat | Stabilité d'un écoulement de convection naturelle en milieu confiné[END_REF]. Since the study concerns an air-filled cavity, the Rayleigh number based on L and on physical properties of air at 298.15 K is very close to Ra L = 10 5 ΔT.

The influence of radiation exchanges amongst the surfaces on the flow field originates in the thermal boundary conditions applied at the vertical side walls. By assuming the side-walls as isothermal, radiation has no effect on the flow structure. On the other hand, noticeable interaction between convection and radiation arises if heat flux boundary conditions are applied at some parts of the cavity walls, while the emissivities of the surfaces are not close to zero. In order to reduce the heat losses at the non isothermal parts of the walls, most of the experimental set-ups were designed such that the non-isothermal walls may be assumed as adiabatic, so that the number of parameters involved is reduced. Unfortunately, the adiabatic conditions are the worst for experimental studies of natural convection in gas-filled cavities when the emissivities of the thermally insulated surfaces are high.

The present study being restricted to two-dimensional flows, the Rayleigh number should not be too high in order that this assumption may be assumed valid, as in Boufia and Daube [START_REF] Bouafia | Natural convection for large temperature gradient around a square solid body within a rectangular cavity[END_REF]. For Ra L much higher than the supercritical value corresponding to the geometric configuration investigated, the experimental and numerical results by Leplat [START_REF] Leplat | Stabilité d'un écoulement de convection naturelle en milieu confiné[END_REF][START_REF] Leplat | Numerical simulation of an unsteady confined natural convection flow[END_REF] for A = W/L = 0.4 and ΔT ≈ 9.6 K show indeed that complex 3D flows develop. We believe that the effect of surface radiation would be similar to those discussed in the present study because larger temperature differences imply also larger effects of radiation on the topology of chaotic flows. A comprehensive study of such flows is beyond the scope of the present work.

Governing equations

The dimensions of the box and of the heated inner solid body and, the temperature difference are such that the flows generated are assumed two-dimensional, incompressible, laminar and that the Boussinesq approximation can be applied with constant fluid properties. The surfaces are supposed to be gray and diffuse and, separated by a radiatively nonparticipating medium. The net radiative heat flux distributions are calculated by using the well-known radiosity-irradiation method [START_REF] Bird | Transport Phenomena[END_REF][START_REF] Modest | Radiative Heat Transfer[END_REF]. The governing equations can be written in dimensionless form as 0  .V Pr

L P Ra t           V V. V V g g (2) 2 t          V. (3)
The above equations were cast in dimensionless form by scaling length, time, velocity, pressure and temperature difference (T -T 0 ) by L, L 2 /α, V 0 = α/L, ρV 0 2 and ΔT. Therefore, the dimensionless variables in the above equations are defined as

c h T T T T L P P L y y L x x L t t        0 2 2 * * * 2 * , , , ,    (4)
where superscript « * » stands for dimensional quantities.

For the boundary conditions, no-slip velocity conditions are applied at the boundaries. When radiative interchanges among surfaces are accounted for, the thermal boundary conditions at the adiabatic walls must include the contribution of the net radiative heat flux. The net radiative heat flux distributions are axially symmetric provided that the flow is also axially symmetric.

Otherwise, the radiosity distributions being dependent on the wall temperature profiles, ( ) ( , )

j N r i i j j S j q B B K dS     j i j r r r (5)
where B i (r i ) is the dimensionless radiosity along surface S i :

4 1 ( ) ( ) (1 ) ( ) ( , ) j N i i i i j j S j B B K dS          i i j i j r r r r r (6)
where η i = T/T 0 is the dimensionless temperature used for non-dimensionalizing the radiation part of the problem. The position vectors r i and r j denote the locations of elementary surfaces dS i and dS j on surfaces S i and S j . The kernel function K is defined as

j dS dS dS dF K j i   ) , ( j i r r (7)
where dF dSi-dSj is the elementary view factor between dS i and dS j [START_REF] Modest | Radiative Heat Transfer[END_REF]. The N surfaces involved are the four walls of the cavity and the four sides of the inner body (i.e. N = 8).

The thermal boundary conditions are: θ= 0.5 at the inner body surface (8a) θ= -0.5 at the bottom and top horizontal surfaces at y=-0.5 and 0.5

(8b) , () i r r i i y N q y x    
at the adiabatic cavity side walls at x=-0.5 and 0.5 (8c)

where N r = σT 0 4 L/kΔT is the radiation number. Whatever the N r -value, the radiation effects may be discarded provided that the wall emissivity is very small.

The local Nusselt number along the walls is defined as:

, ( ) . ( )
( ) ( ) i i i r r i i cv i r i Nu N q Nu Nu        r n r r r ( 9
)
where n i is the outward unit normal to wall "i". Nu cv and Nu r are the local convective and radiative Nusselt number, respectively. The average Nusselt number along a side wall is obtained by integration along the wall.

Numerical methods

Calculations were carried-out using the control volume code ANSYS FLUENT (Ansys Fluent 12 User'Guide [START_REF]Ansys Fluent 12 User'Guide[END_REF]). Results of the simulations were collected and processed by employing inhouse softwares.

Collocated, rectangular, structured and weakly non-uniform grids were used on account of the expected flow structures. The Quadratic Upwind Interpolation for Convective Kinematics scheme (QUICK) was used for the advective and transport terms in order to compute third-order truncation error of the convected variables [START_REF] Leonard | A stable and accurate convection modelling procedure based on quadratic upstream interpolation[END_REF]. The velocity-pressure coupling was solved with the Pressure-Implicit with Splitting of Operators algorithm (PISO [START_REF] Issa | Solution of the implicitly discretized fluid-flow equations by operator-splitting[END_REF]) since transient computations were carried out, and the pressure was calculated with a body-force weighted scheme which is well adapted for natural convection flows.

The governing equations were solved either in their transient form, sequentially, with a secondorder decoupled implicit scheme (segregated solver) or using the implicit coupled scheme for purely steady approaches. In both cases, the implicit treatment of the equations was achieved using an iterative solver with a convergence criterion of 10 -6 and 10 -10 for unsteady and steady problems, respectively. The radiation fluxes were updated once every 10 iterations of the iterative solver ensuring the implicit coupling of all the variables and the radiosity field was assumed converged when its maximum normalized changes from one sweep to the next was less than 10 -6 .

Validations of the results for pure natural convection flows were carried out by comparison of our results with those reported in Leplat [START_REF] Ménard | Convection naturelle dans une cavité contenant une source de chaleur[END_REF]. A mesh study for uniform grids was also conducted using a steady approach and the dependences of the wall heat fluxes on the grid resolution are reported in Table 1. Comparison of these results with those obtained with a 150×150 weakly non-uniform grid (see Tab. 2 for ε c = ε s =0) shows a good agreement and justifies the use of this latter mesh which presents a good compromise between accuracy and computational loads.

The computational costs depend strongly on the flow regime. For steady flows, at Ra L ≤ 2.10 5

for pure natural convection with a 150×150 grid, for example, the CPU-time is about 2900 s to reach convergence on a workstation with a mono-processor (2.8GHz) and 4GB of RAM. With radiation taken into account, the CPU-time is increased up to about 3500 s. For unsteady flows, one thousand time-steps requires about 7 hours for pure natural convection and more than 8 hours with radiation

Results

All the computations were carried out for a square cavity of L = 10 cm side-length, containing a centered, square body made in aluminum, having a side length ranging from W = 2 cm to W = 8 cm. The average temperature of air was kept fixed at T 0 = 298.15 K (α = 2.15 10 -5 m 2 /s, Pr = 0.71). The temperature difference between the hot inner body and the cold horizontal surfaces (ΔT = T h -T c ) was varying between 2 K and 4 K. The emissivity of the inner body surface was ε h =0.05 for all of the cases investigated. The reference heat flux used for the dimensionless heat flux is thus q ref = 0.2607 ΔT (W/m 2 ) and the radiation number is N r = 1718/ΔT.

Case A = 0.4: steady flows

In that case, the flow is stable up to a Rayleigh number very close to Ra c = 2.10 5 (i.e. ΔT ≈2 K) when neglecting radiant interchanges among the surfaces. Below this Rayleigh number, the flow is steady and symmetric about the vertical centerline of the cavity (reflection symmetry, Boufia and Daube [START_REF] Bouafia | Natural convection for large temperature gradient around a square solid body within a rectangular cavity[END_REF]).

Pure natural convection

The isothermal patterns and streamlines displayed in Fig. 2a for Ra L = 2.10 5 and A = 0.4 show that the flow structure consists in two symmetric, counter-rotating, Rayleigh-Bénard type cells at the upper part of the cavity delimited by two large cells rotating in opposite directions along the vertical walls (clockwise at the right-hand side). These side-cells extend up and penetrate into the thermally stratified fluid layer below the inner body. For this case, the Rayleigh numbers based on the distance between the cavity and inner solid walls (e = 3 cm) are Ra t = 5400 for the bottom and upper parts of the cavity. Therefore, Ra t being larger than 1708, potentially unstable flows occur within the horizontal upper part of the cavity (note that Ra t = 1708 for ΔT =0.63 K). From our computations and those reported in Leplat [START_REF] Leplat | Stabilité d'un écoulement de convection naturelle en milieu confiné[END_REF], the flow undergoes a bifurcation leading to a periodic motion as it will be discussed in the next section. About the fluid layers along the vertical sides, the effective Rayleigh numbers, Ra s , could be evaluated from a characteristic temperature difference ΔT s = T h -T side , where T side is the average temperature of the parts A"B" or C"D" (see Fig. 1) of the adiabatic walls facing the inner body (Ra s = 2700 ΔT s ). These parts being obviously the hottest parts of the side walls, Ra s is smaller than Ra t as can be seen in Fig. 3 from which it is found that Ra s ≈ 2295 (ΔT s ≈ 0.85 K) when neglecting surface-to-surface radiation exchanges (ε c = ε s = ε h = 0).

Effects of surface radiation

The effects of radiation were considered for four cases: first, the asymptotic case of four black surfaces of the cavity (ε c = ε s = 1). This case corresponds to the emissivities of the wall surfaces in the experimental set-up used in Ménard [START_REF] Ménard | Convection naturelle dans une cavité contenant une source de chaleur[END_REF] and Leplat [START_REF] Leplat | Stabilité d'un écoulement de convection naturelle en milieu confiné[END_REF], i.e. black cold horizontal walls, side walls made of double-glazing windows. Second, the isothermal, cold horizontal surfaces made in copper could have been polished instead of being painted in black. In that case, we assumed that their emissivities could be close to ε c = 0.05 while double-glazing windows are still used to allow flow visualization (ε s = 1). Third, we considered that the four side walls have the same emissivity ε c = ε s = 0.05 (insulated vertical walls covered with aluminum sheets, for example). Fourth, we assumed that the four cavity walls were slightly oxidized (ε c = ε s = 0.1).

The averaged convective Nusselt numbers at the various surfaces shown in Fig. 1 are reported in Table 2 for these four cases. Due to space limitation, the streamlines and isothermal patterns are plotted in Fig. 2b and2c for the cases (ε c = 0.05, ε s = 1) and (ε c = ε s = 1) only.

Comparisons between Figs. 2a (pure natural convection) and 2b shows a rather small effect of radiation exchanges on the flow field, and effects of radiation restricted to small fluid layers along the vertical adiabatic walls where the impingements of the isotherms are not perpendicular to the black surfaces. The largest effects of radiation are seen at the bottom part of the cavity where the thermal stratification differs. However, these effects of radiation may be assumed to have a small influence on the main flow circulations, and thus on the bifurcation path to unsteady flows. The reason is that the temperature distribution along the vertical walls does not differ much from that for pure natural convection, as can be seen in Fig. 3.

When the cold horizontal walls are recovered with a black paint (ε c = 1), a comparison between Fig. 2a (no radiation) and 2c shows that the fluid recirculations in the vertical side layers are noticeably increased (about 30%). The explanation can be found in the decrease in the adiabatic wall temperatures, as can be seen in Fig. 3. It is found that Ra s increases then up to 4185 due to the reduction of about 1.3 K in the mean temperature of segment A"B". Since the emissivity of the hot inner body is very small (ε h = 0.05), the heating of the adiabatic walls by radiation is insignificant. On the other hand, the view factors between the horizontal cold surfaces and the vertical wall surfaces being quite large (F c,a ≈ 0.46 as a rough approximation) due to the relatively small size of the inner body, the radiation exchanges between the vertical sides and the cold horizontal surfaces lead to significant decreases in the temperatures of the adiabatic walls.

Radiation has a rather weak effect on the Rayleigh-Bénard cells because the two horizontal, top surfaces BC and B'C' are isothermal.

Finally, since the effect of the radiation exchanges amongst the cold and adiabatic surfaces are to decrease the adiabatic surfaces temperature, it could be assumed that the case of a cavity with four cold walls at T c = 297.15 K is an asymptotic configuration. In that case, surface radiation has no effect. Through comparisons between Fig. 2a, 2c and 2d, it can be deduced that the flow structure predicted for isothermal, cold vertical walls (Fig. 2d) is closer to the experimental conditions than that for pure natural convection in a cavity with two adiabatic, non-radiating vertical surfaces (Fig. 2a). The values of the convective Nusselt number at the surfaces of the inner body, reported in Table 2, support this observation. The stabilizing influence of radiation can be indeed exemplified by the increase in the fluid recirculations produced within the vertical layers which, in turn, leads to higher convective heat flux at surfaces A'B' and C'D'.

The increases in fluid recirculations along the side walls caused by radiation can be depicted by the variation of the maximum value of the streamfunction (Fig. 4). It was found that the flow rate increases almost linearly with the emissivity according to the smoothed law: ψ max = 1.464 + 0.339 ε for A = 0.4, ε = ε c = ε s and Ra L = 3.10 5

The question is whether two-dimensionality of the flow field may be invoked. In order to check this assumption, 3D simulations were carried out for a 18 cm-depth cavity, i.e. the length of the experimental set-up in [START_REF] Leplat | Stabilité d'un écoulement de convection naturelle en milieu confiné[END_REF]. Isothermal patterns are displayed in Fig. 5a for pure natural convection and in Fig. 5b in the case of four black walls. These patterns for the middle plane section (z* = 0) and two symmetrical sections (z*=-4.5 cm and z* = 4.5 cm) clearly show that 3D effects can be neglected over most of the cavity depth for Ra = 2.10 5 . The influence of surface radiation does not differ from that found through 2D-simulations.

The conclusion which could be drawn is that the experiments conducted for four black walls, two adiabatic vertical walls and two cold isothermal walls, lead to measurements far from those expected for pure natural convection. The two large lateral circulation cells have thus a stabilizing effect on the Rayleigh-Bénard convection above the heated inner body.

Case

When the temperature difference is increased up to ∆T ≈ 2 K, the Rayleigh number is beyond the critical value deduced from the linear stability theory. For larger ∆T, the steady flow displayed in Fig. 2a becomes unstable through a growing oscillatory disturbance and, finally, reaches a mono-periodic regime. Before describing the behavior of the flow as a function of time, let us first notice that the Rayleigh number based on the height between the hot and cold horizontal surfaces is equal to about Ra t = 5400 for ∆T = 2 K, a value much smaller than Ra c ≈ 3 10 4 , which is the critical value for the onset of oscillations for 2D Rayleigh-Bénard flows between infinite horizontal plates (Shan [START_REF] Bird | Transport Phenomena[END_REF]). Thus, the transition in the present problem is probably not explained through classical Rayleigh-Bénard instability theories. When the Ra-number is increased, the intensities of the cells are strengthened, but proportionally more for the Rayleigh-Bénard cells than those for the lateral circulations. As a result, the lateral cells cannot restrain the size of the cells below the top cold wall.

Let us assume that a small perturbation amplifies the horizontal stretching of the left Rayleigh-Bénard cell with respect to the right one. This left cell (LHS) tends to recover its natural extension just above the heated body at the expense of the right cell (RHS). Because the right circulation flow is not strong enough to prevent displacement of the RHS Rayleigh-Bénard cell, this cell is shifted above the inner body toward the right upper corner of the cavity (Fig. 6a).

Consequently, the size and intensity of the side circulation are considerably reduced. On the other hand, the circulation cell along the left wall being not blocked by the top Rayleigh-Bénard cell, it grows until the occurrence of an overall circulation around the heated body (Fig. 6b).

Finally, the top RHS cell comes back above the inner body and ejects the left cell in the LHS upper corner (Fig. 6c).

While the oscillatory flow breaks the natural symmetry of the problem, this property may be recovered by averaging the flow field over an oscillation period. It should be noticed that this average solution is nevertheless different from the unstable steady flow (i.e. before the growth of the disturbances). The temporal variations of the vertical velocity component v 1 (t) and v 2 (t) at locations P 1 (-0.22, 0.35) and P 2 (0.22,0.35), shown in Fig. 1, were recorded and then used to compute the difference v 1 (t) -v 2 (t). This signal centered upon zero can be viewed as a local symmetry indicator.

Effects of radiation

As depicted previously for stable steady flows, increases in the effect of surface radiation lead to strengthen the intensity of the circulation cells along the vertical walls owing to the decrease in wall temperatures. Therefore, the circulation cells along the vertical walls increase with the wall emissivity and prevent the top cells from periodically moving from one side of the cavity to the other side. It can be concluded that surface radiation leads to larger critical Rayleigh numbers for the onset of the first bifurcation, as shown in Fig. 10 for emissivites of the cavity walls set to ε c = ε s = 0.1. The transitions between steady and oscillatory flows are shifted from Ra c1 =2 10 5 and 1.7 10 5 < Ra c2 < 1.75 10 5 for pure natural convection (Fig. 9) to Ra c1 =3.15 10 5 and to 2.85 10 5 < Ra c2 < 2.9 10 5 for ε c = ε s = 0.1 (Fig. 10), namely an increase of 50% in the stability threshold values.

Effects of the inner body size

Changes in the size of the inner body lead to large modifications in the flow structure. For a small body size, say A ≤ 0.2, Rayleigh-Bénard cells cannot develop above the top side and the flow turns into buoyant plume convection with interaction with the boundaries: for small enough Rayleigh numbers, the flow pattern is characterized by two counter-rotating, recirculating flows spreading over most of the flow domain, and separated by an ascending thermal plume which raises above the top wall. The results are thus similar to those discussed in Desrayaud and

Lauriat [START_REF] Desrayaud | Unsteady confined buoyant plumes[END_REF] and Bouafia and Daube [START_REF] Bouafia | Natural convection for large temperature gradient around a square solid body within a rectangular cavity[END_REF], with transition to unsteady flows beyond a critical value of the Rayleigh number. On account of the value of the Rayleigh number considered here (Ra L = 2. 10 5 ), the flow is unsteady for A = 0.2 because Ra t = 12,800. The breaking of the reflection symmetry induces a swaying motion of the thermal plume which oscillates horizontally.

Increases in the inner body size lead to smaller effective top and side Rayleigh numbers (Ra t and Ra s ). Therefore, the fluid motions decrease along the side walls as well as in the top part of the cavity. The computations carried out for 0.3 ≤ A ≤ 0.8 confirmed these predictions. For A = 0.3, the flow exhibits a periodic behaviour. On the other hand, an almost pure conductive régime is obtained for A = 0.8 since Ra t = 200. In that case, Figure 11a shows that the fluid is fully thermally stratified below and above the inner body, and it is almost uniformly hot along the side walls.

When the effects of surface radiation are taken into account (in the case of a cavity with four black walls as in the experimental set-up used by Ménard [START_REF] Ménard | Convection naturelle dans une cavité contenant une source de chaleur[END_REF] and Leplat [START_REF] Leplat | Stabilité d'un écoulement de convection naturelle en milieu confiné[END_REF]), the view factors between the horizontal and vertical black walls are reduced by increasing A, and the effect of radiation exchanges amongst these surfaces decreases. On the other hand, the view factors between the hot vertical surfaces of the inner body and the cavity walls increases. However, the inner body emissivity being ε h = 0.05, the radiation exchanges between the adiabatic walls and the hot vertical surfaces have a rather weak influence on the flow field. The overall result is that the side recirculation cells are strengthened whatever the aspect ratio provided that A ≥ 0. The averaged heat flux density at the inner body surfaces is reported in Table 3 for 0.3 ≤ A ≤ 0.8, with and without radiation taken into account. For A = 0.3 without radiation, the value reported in Table 3 is a time averaged heat flux obtained by integrating instantaneous data over one period. The increase in heat flux due to radiation is about 50% for A = 0.3 and 30% for A = 0.8.

That is due in part to the radiation exchanges between the surfaces of the inner body and the cavity walls. However, the most significant result to be considered is the increase in the convective heat flux induced by the decrease in the temperatures of the adiabatic walls. The third line of Table 3 shows that effects of radiation on the increase in the convective part of the Nusselt number are reduced as the size of the inner body is increased, because the view factors between the cold horizontal walls and the vertical walls become smaller. However, it is clear that there is a critical aspect ratio above which the conductive heat transfer becomes dominant, as it is for A = 0.8.

The above results show that surface radiation exchanges strengthen the recirculation cells along the vertical side walls which, in turn, stabilize the flow fields. However, it should be underlined that these results are valid for the specific configuration studied here. By just changing the thermal boundary conditions, radiation exchanges could produce opposite effects (Mezrhab et al.

[12]).

Conclusion

A numerical study of combined natural convection and surface radiation has been carried out with the aim at demonstrating the influence of radiation on the first transition to periodic flows which occurs in air-filled cavities when the Rayleigh number is increased. To this end, we have modeled an experimental set-up recently used to study the flow and heat transfer characteristics in a square cavity with an inner heated body. For this particular case, the stabilizing effect of radiation has been clearly demonstrated.

This work underlines that discrepancies between experimental and numerical results for gasfilled cavities may be explained just by having neglected the influence of surface radiation. We can conclude that it is highly difficult to properly interpret experimental results for gas-filled cavities with non isothermal boundary conditions. We believe that the present results can be extended for 3D flows as well as for turbulent natural convection flows (Ampofo and Karayiannis [START_REF] Ampofo | Experimental benchmark data for turbulent natural convection in an air filled square cavity[END_REF]).

Table captions

Table 1 Effect of the grid resolution on the average Nusselt numbers at the isothermal surfaces (see Fig. 1) in the case A = 0.4, Ra = 2.10 5 for pure natural convection.

Table 2 Average convective Nusselt numbers at the various surfaces (see Fig. 1) in the case A = 0.4, Ra = 2.10 5 for pure natural convection and for combined natural convection and radiation. The last column is for cold isothermal side walls.

Table 3 Effect of the body size on the average Nusselt number at the inner body surface in the case Ra = 2.10 5 (ΔNu cv is the increase in the convective Nusselt number due to surface radiation). 1 Effect of the grid resolution on the average Nusselt numbesr at the isothermal surfaces (see Fig. 1) in the case A = 0.4, Ra = 2.10 5 for pure natural convection.

Figure captions

Emissivity

ε c = ε s =0 =0 ε c = ε s = 0.05 =00.5 ε c = ε s = 0.1 ε c = 0.05, ε s = 1 ε c = ε s = 1 T s = T c Side A'B'

  Effect of surface radiation on the breakdown of steady natural convection flows in a square, air-filled cavity containing a centered inner body H. Sun, Eric Chénier, Guy Lauriat To cite this version: H. Sun, Eric Chénier, Guy Lauriat. Effect of surface radiation on the breakdown of steady natural convection flows in a square, air-filled cavity containing a centered inner body. Applied Thermal Engineering, 2011, 31, pp.1252-1262. 10.1016/j.applthermaleng.2010.12.028. hal-00691303 Effect of surface radiation on the breakdown of steady natural convection flows in a square, air-filled cavity containing a centred inner body Nomenclature A aspect ratio of the inner body, A = Wsides of the inner body (m) (x, y, z) Cartesian coordinates with the origin at cavity center.

4 .

 4 dissymmetry in the flow field implies different radiative heat flux distributions at the vertical walls. In what follows, the scale for the radiative flux and radiosity is σT 0 The net radiative flux density along the surfaces of the diffuse-gray and opaque, vertical walls is written in the following dimensionless form: , 1

4 (

 4 A = 0.4: unsteady flows 4.2.1. Pure natural convection As described in the previous sections, the flow structure consists in two symmetric counterrotating Rayleigh-Bénard cells above the heated body, delimited by two large circulation flows along the vertical walls. In the classical Rayleigh-Bénard problem between infinite plates, the natural dimensionless wavelength based on the fluid thickness is 2/3.117 ≈ 2 at the conduction/convection transition, and then increases with Ra. In the present configuration, the Rayleigh-Bénard cell stretching is limited from below by the size of the inner body (W = 4 cm) and also by the distance between the heated body and the cold horizontal surfaces (e = 3 cm). Since W/e = 1.33, this distance is smaller than the natural wavelength. If the two large circulation flows located on both sides of the solid body are suppressed, for example by changing the adiabatic boundary conditions into hot wall temperature boundary conditions for Ra L = 7.5 10 ∆T ≈ 0.75 K) the two upper cells become unstable (Ra t = 2025), and a new steady flow configuration takes place which is characterized by an overall circulation around the inner body.

Figure 7

 7 shows its time variation for Ra L = 2.15 10 5 : the amplitude of the oscillation growths exponentially at first, and becomes constant for t > 8.5, showing an unsteady, asymptotic mono-periodic flow. It should be noted that the dimensionless frequency of this solution is equal to 15.9 (0.0342 Hz), about half of the values measured during the exponential growth, i.e. 32.1 (0.0690 Hz). The amplitudes of the oscillations are then extracted and drawn for unsteady flows at various Rayleigh numbers (Ra L = 2.15 10 5 in Fig.8). The exponential development of a perturbation is clearly highlighted with a linear growth rate, obtained by a least mean square fit of the logarithm of the amplitudes, equal to 1.68. At dimensionless times t > 8.5, the amplitudes of the oscillations become constant (a(t) = a ∞ ). Similar amplitude analyses performed for various Rayleigh numbers allow the time variation of the growth rates in the exponential regime to be plotted (Fig 9, left axis) and the amplitudes of the oscillations for the asymptotic flows (Fig 9, right axis) as a function of Ra L . The positivegrowth rates were obtained by starting the computations for a fluid initially at rest and at the uniform temperature T 0 , whereas oscillatory solutions were used to initialize the computations and calculate the negative values. From the growth rate analysis, the linear stability threshold Ra c1 for the steady symmetric flow is found to be slightly greater than Ra L = 2 10 5 . On the other hand, numerical simulations indicate that oscillatory solutions are also predicted for Ra L < Ra c1 , until Ra L = 1,75 10 5 . For Ra L ≤ 1.7 10 5 , the flow always converges toward a symmetrical, steady solution. From this study, it can be concluded that the steady solution is stable for finite amplitude perturbations if Ra L ≤ Ra c2 , a critical Rayleigh number value located within the range [1.7 10 5 -1.7510 5 ]. For Ra c2 < Ra L < Ra c1 , two established flows (periodic or steady) are thus possible according to the choice of the initial conditions. A hysteretic behavior for the fluid flow is therefore expected. It should be noted that the asymptotic mono-periodic regime is characterized by a dimensionless frequency which decreases linearly from 15.7 (0.0338Hz) at Ra L = 2.5 10 5 to 14.4 (0.0310Hz) at Ra L = 3.5 10 5 .

  [START_REF] Deng | Numerical visualization of mass and heat transport for conjugate natural convection/heat conduction by streamline and heatline[END_REF]. For A = 0.3, a complex unsteady flow was predicted without radiation: the Rayleigh-Bénard cells oscillate and then merge into one or the other of the two side cells to produce a periodic fluid circulation around the inner body. A Fourier analysis of the signals at point P 1 (-0.22, 0.35) yields a fundamental frequency of this periodic flow equal to f = 5.11 (0.011 Hz) with numerous harmonics. When surface radiation is taken into account, the flow is steady and exhibits then a symmetric motion about the vertical centerline of the cavity with two stable Rayleigh-Bénard cells below the top wall. Figure11bshows the effect of surface radiation on the conductive regime predicted for the largest aspect ratio considered (A = 0.8): the small temperature differences between the vertical walls produce weak recirculation cells. The largest effects of radiation occur at the four corner regions where the decreases in the adiabatic wall temperatures are the origin of the vertical fluid motion.

Figure 1

 1 Figure 1 Schematic of the system of interest: a square, heated inner-body centred within a square cavity.

Figure 2

 2 Figure 2 Comparisons between streamlines and isothermal patterns for pure natural convection at Ra L = 2.10 5 (a), combined convection and surface radiation [(b) ε c =0.05, ε s =1 and (c) ε c = ε s =1] and for cold vertical side walls (d). Isotherms and streamlines equally spaced (Ψ n =0.3856 + n×0.7713 for the streamline contours, the dashed lines indicate clockwise circulations).

Figure 3

 3 Figure 3 Effect of surface radiation on the dimensionless temperature distributions along the vertical, adiabatic side-walls at Ra L = 2.10 5 .

Figure 4

 4 Figure 4 Variation of the maximum streamfunction for the side wall circulations as a function of emissivity of the cavity walls (ε c = ε s = ε) at Ra L = 3.10 5 . The continuous line is for steady, symmetric flow structures.

Figure 5

 5 Figure 5 3D-isothermal patterns (T h = 299.15 K in red, T c =297.15 K in dark blue) for three cross sections (z* = -4.50 cm, z* = 0, z* = 4.5 cm) of the parallelepipedic cavity (10 cm ×10cm ×18 cm) at Ra L = 2.10 5 (a): pure natural convection, (b): combined convection and surface radiation (ε c = ε s =1).

Figure 6

 6 Figure 6 Characteristic flows and temperature patterns over a period for supercritical pure natural convection (A = 0.4, Ra L = 2.15 10 5 ) Isotherms and streamlines equally spaced (Ψ n =0.3856 + n×0.7713 for the streamline contours, the dashed lines indicate clockwise circulations).

Figure 7

 7 Figure 7 Time variation of the difference between the vertical velocity components at point P 1 and P 2 shown in Fig. 1 (Ra = 2.15 10 5 , A = 0.4, pure natural convection).

Figure 8

 8 Figure 8Variation of the logarithm of the amplitude disturbance, a(t), versus dimensionless time for Ra L = 2.15 10 5 and A = 0.4 (pure natural convection). τ g is the linear growth rate and a ∞ the amplitude of the asymptotic periodic flow. Open circles denotes numerical results, the full line is the least mean square fit.

Figure 9

 9 Figure 9Linear growth rate of the disturbances (left axis, filled square) and amplitude of the disturbance for the asymptotic flow (right axis, cross-symbols) versus the Rayleigh number for pure natural convection.

Figure 10

 10 Figure 10Linear growth rate of the disturbances (left axis, filled square) and amplitude of the disturbance for the asymptotic flow (right axis, cross-symbols) versus the Rayleigh number for combined surface radiation and natural convection (ε c = ε s = 0.1).

Figure 11

 11 Figure 11 Comparisons between streamlines and isothermal patterns for pure natural convection in the case A = 0.8 and Ra L = 2.10 5 (a), combined convection and surface radiation for ε c = ε s = 1 (b) (Ψ 1 = + 0.07713 for the streamline contours, the dashed lines indicate clockwise circulations).

FIGURESFigure 1

 1 FIGURES

Figure 2

 2 Figure 2 Comparisons between streamlines and isothermal patterns for pure natural convection at Ra L = 2.10 5 (a), combined convection and surface radiation [(b) ε c =0.05, ε s =1 and (c) ε c = ε s =1] and for cold vertical side walls (d). Isotherms and streamlines equally spaced (Ψ n =0.3856 + n×0.7713 for the streamline contours, the dashed lines indicate clockwise circulations).

Figure 3

 3 Figure 3 Effect of surface radiation on the dimensionless temperature distributions along the vertical, adiabatic side-walls at Ra L = 2.10 5 .

Figure 4

 4 Figure 4 Variation of the maximum streamfunction for the side wall circulations as a function of emissivity of the cavity walls (ε c = ε s = ε) at Ra L = 3.10 5 . The continuous line is for steady, symmetric flow structures.

Figure 5

 5 Figure 5 3D-isothermal patterns (T h = 299.15 K -red, T c =297.15 K -dark blue) for three cross sections (z* = -4.50 cm, z* = 0, z* = 4.5 cm) of the parallelepipedic cavity (10 cm ×10cm ×18 cm) at Ra L = 2.10 5 (a): pure natural convection, (b): combined convection and surface radiation (ε c = ε s =1).

Figure 6

 6 Figure 6 Characteristic flows and temperature patterns over a period for supercritical pure natural convection (A = 0.4, Ra L = 2.15 10 5 ) Isotherms and streamlines equally spaced (Ψ n =0.3856 + n×0.7713 for the streamline contours, the dashed lines indicate clockwise circulations).

Figure 7

 7 Figure 7 Time variation of the difference between the vertical velocity components at point P 1 and P 2 shown in Fig. 1 (Ra = 2.15 10 5 , A = 0.4, pure natural convection).

Figure 8

 8 Figure 8Variation of the logarithm of the amplitude disturbance, a(t), versus dimensionless time for Ra L = 2.15 10 5 and A = 0.4 (pure natural convection). τ g is the linear growth rate and a ∞ the amplitude of the asymptotic periodic flow. Open circles denotes numerical results, the full line is the least mean square fit.

Figure 9

 9 Figure 9 Linear growth rate of the disturbances (left axis, filled square) and amplitude of the disturbance for the asymptotic flow (right axis, cross-symbols) versus the Rayleigh number for pure natural convection.

Figure 10

 10 Figure 10 Linear growth rate of the disturbances (left axis, filled square) and amplitude of the disturbance for the asymptotic flow (right axis, cross-symbols) versus the Rayleigh number for combined surface radiation and natural convection (ε c = ε s = 0.1).

Figure 11

 11 Figure 11 Comparisons between streamlines and isothermal patterns for pure natural convection in the case A = 0.8 and Ra L = 2.10 5 (a), combined convection and surface radiation for ε c = ε s = 1 (b) (Ψ 1 = + 0.07713 for the streamline contours, the dashed lines indicate clockwise circulations).

Table 2

 2 Average convective Nusselt numbers at the various surfaces (see Fig.1) in the case A = 0.4, Ra = 2.10 5 for pure natural convection and for combined natural convection and radiation. The last column is for cold isothermal side walls.

	or C'D'	3.7174	3.7601	3.9955	4.1719	6.2773	8.2144
	Side A'D' (bottom)	5.6347	5.6876	5.9172	6.0218	8.0667	11.0136
	Side B'C' (top)	9.4614	9.4726	9.4807	9.5454	9.4448	9.3594
	Bottom wall (AD)	2.5346	2.5738	2.4910	2.9873	1.4540	0.6020
	Top wall (BC)	6.4778	6.4875	6.4770	6.6339	6.3673	6.1314
	Side Wall	0	-5.4 10 -3	-0.1937	+0.0288	-2.1026	3.7373

Table 3

 3 Effect of the body size on the average Nusselt number at the inner body surface in the case Ra = 2.10 5 (ΔNu cv is the increase in the convective Nusselt number due to surface radiation).


Regina C Betz
email: regina.betz@uni-bonn.de

Lina M Forstbauer

Felix F Brockschmidt

Valentina Moskvina

Christine Herold

Silke Redler

Alexandra Herzog

Axel M Hillmer

Christian Meesters

Stefanie Heilmann

Florian Albert

Margrieta Alblas

Sandra Hanneken

Sibylle Eigelshoven

Kathrin A Giehl

Dagny Jagielska

Ulrike Blume-Peytavi

Natalie Garcia Bartels

Jennifer Kuhn

Hans Christian Hennies

Matthias Goebeler

Andreas Jung

Wiebke K Peitsch

Anne-Katrin Kortüm

Ingrid Moll

Roland Kruse

Gerhard Lutz

Hans Wolff

Bettina Blaumeiser

Markus Böhm

George Kirov

Tim Becker

Markus M Nöthen

Prof. Regina C Betz

Genome-wide pooling approach identifies SPATA5 as a new susceptibility locus for alopecia areata

Keywords: Alopecia areata, genome-wide association study, autoimmunity, hair loss

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Introduction

Alopecia areata (AA) is a common hair loss disorder which affects approximately 1-2 % of the general population. It affects both sexes and all age groups. [START_REF] Safavi | Incidence of alopecia areata in Olmsted County, Minnesota, 1975 through 1989[END_REF] Affected individuals present with a non-scarring, circumscribed hair loss which has a sudden onset and a recurrent course. The scalp is the most commonly affected site, although all hair-bearing areas of the skin may be involved. Episodes of hair loss typically start with isolated hairless patches. These extend centrifugally and may coalesce. AA is divided into three main clinical types on the basis of the degree of hair loss and the sites affected: (i) patchy AA; (ii) AA totalis (AT), affecting the whole scalp; and (iii) AA universalis (AU), affecting the whole body. Individuals with AA may experience complete remission, a chronic course, or progression towards AT or AU. Familial AA also occurs, and recurrence risks of 5-6% have been reported for the children of affected individuals. [START_REF] Blaumeiser | Familial aggregation of alopecia areata[END_REF][START_REF] Jackow | Alopecia areata and cytomegalovirus infection in twins: genes versus environment?[END_REF] The pattern of familiality and a limited twin study which reports a concordance rate in monozygotic twins of 55% [START_REF] Jackow | Alopecia areata and cytomegalovirus infection in twins: genes versus environment?[END_REF] suggest that multiple genetic factors and environmental factors are involved in the pathology of AA. Nevertheless, the etiopathogenesis of AA remains poorly understood. One hypothesis is that AA is a tissue-specific autoimmune disease of the hair follicle. [START_REF] Tobin | Characterization of hair follicle antigens targeted by the anti-hair follicle immune response[END_REF] This is supported by reports of association between AA and specific HLA alleles. [START_REF] Entz | Investigation of the HLA-DRB1 locus in alopecia areata[END_REF][START_REF] Colombe | The genetic basis of alopecia areata: HLA associations with patchy alopecia areata versus alopecia totalis and alopecia universalis[END_REF][START_REF] Xiao | Association of HLA class I alleles with aloplecia areata in Chinese Hans[END_REF][START_REF] De Andrade | Alopecia areata in families: association with the HLA locus[END_REF] Association has also been reported between AA and the W620 variant of the PTPN22 gene (protein tyrosine phosphatase, nonreceptor type 22), which has been implicated in several autoimmune disorders. [START_REF] Betz | The R620W polymorphism in PTPN22 confers general susceptibility for the development of alopecia areata[END_REF][START_REF] Kemp | The non-synonymous C1858T substitution in the PTPN22 gene is associated with susceptibility to the severe forms of alopecia areata[END_REF] To date, only one systematic genome-wide linkage study of AA has been performed in humans. This identified four susceptibility loci on chromosomes 6, 10, 16, and 18, respectively. [START_REF] Martinez-Mir | Genomewide scan for linkage reveals evidence of several susceptibility loci for alopecia areata[END_REF] The pattern of familiality and a limited twin study which reports a concordance rate in monocygotic twins of 55%

To identify new genetic variants and thus further elucidate the genetic basis of AA, we performed a genome-wide association (GWA) study in 729 AA cases and 656 controls using the strategy of pooled DNA genotyping. The top 61 single nucleotide polymorphisms (SNPs) were selected for individual genotyping in the initial sample of the pooling approach for the purpose of confirmation. We further analyzed these SNPs in an independent replication sample. The best association finding was then analyzed in a second independent replication sample. The strongest association was found for variants in the HLA region. These results thus confirm the validity of the pooling-based approach to DNA genotyping. Borderline significance was found for rs304650 in the SPATA5 (spermatogenesis-associated protein 5) gene, which may therefore represent a new susceptibility gene locus for AA.

During the final stages of the present study, a GWA study of an AA sample from the US was published by Petukhova et al.. 12 This identified eight gene loci for AA, most of which are implicated in autoimmunity. Although SPATA5 was not among these loci, six SNPs in SPATA5, of all which show evidence for linkage disequilibrium with rs304650, were reported with a P-value < 10 -4 .

Materials and Methods

DNA samples

The analyses involved 1 720 individuals with AA (cases) and 2 677 controls. For cases, the inclusion criterion was a dermatologist-assigned diagnosis of AA. Patients with Down syndrome or Turner syndrome were excluded. The cases were recruited from: (i) outpatient clinics in Belgium (University Hospitals of Antwerp and Gent) and Germany (University Hospitals of Munich, Münster, Düsseldorf, Berlin, Bonn, Gießen, Hamburg and Mannheim); (ii) a private dermatology practice (Wesseling, Germany); and (iii) AA self-help support groups (Germany, Netherlands).

All cases were asked whether or not they had a positive family history of AA. This was defined as a history of at least one first-or second-degree relative with any form of the disorder. The controls were drawn from the general population, and were therefore not specifically screened for the absence of AA. They were healthy unrelated blood donors from the University Hospital of Bonn (n = 1 313) or participants in one of three population-based epidemiological studies: (1) PopGen [START_REF] Krawczak | PopGen: population-based recruitment of patients and controls for the analysis of complex genotype-phenotype relationships[END_REF] (n = 490); (2) KORA [START_REF] Wichmann | KORA-gen--resource for population genetics, controls and a broad spectrum of disease phenotypes[END_REF] (n = 490); and (3) HNR [START_REF] Schmermund | Assessment of clinically silent atherosclerotic disease and established and novel risk factors for predicting myocardial infarction and cardiac death in healthy middle-aged subjects: rationale and design of the Heinz Nixdorf RECALL Study. Risk Factors, Evaluation of Coronary Calcium and Lifestyle[END_REF] (n = 384). All cases and controls were of central European origin.

Ethical approval was obtained from the respective ethics committees, and all participants provided written informed consent prior to blood sampling. The DNA of patients and blood donors was extracted from peripheral blood leukocytes. This was achieved by salting out with saturated NaCl solution according to standard methods, or through the use of a Chemagic Magnetic Separation Module I (Chemagen, Baesweiler, Germany) in accordance with the manufacturer's instructions. The DNA was stored in liquid nitrogen until use. For the controls from the three population-based epidemiological studies, the genotypes were taken from previously generated genomewide association data sets. The PopGen and KORA datasets were generated within the German National Genome Research Network to serve as a national research resource.

The HNR data set was generated as part of a collaboration to generate a set of universal controls for genetic studies.

DNA Pooling

The DNA samples of 729 AA cases and 656 blood-donor controls were selected at random. These samples were then used to generate a control pool and two AA case pools. The first AA case pool consisted of the DNA of all 729 AA cases (including the 224 AA cases with a positive family history). The second AA case pool consisted of the DNA of 'positive family history' AA patients only (n = 224). To ensure equal amounts of DNA in each pool, each individual DNA sample was subjected to a series of dilution steps (above 100ng/µl to 20ng/µl, and so on to a final concentration of 10ng/µl). Each DNA sample was double-quantified using a NanoDrop device (PEQLAB Biotechnologie GmbH, Erlangen, Germany) and adjusted to +/-10% of the required concentration. For the 10ng/µl dilution, a broader range of -60% to +80% was used to reflect the measurement error of the NanoDrop device at low DNA concentrations. Equimolar amounts of each DNA sample (100ng) were pipetted manually into a large tube to form the pool. Each pool was then concentrated to 60ng/μl using the Microcon YM-100 Centrifugal Filter Device (Millipore GmbH, Schwalbach, Germany), and then requantified with the NanoDrop device.

Genotyping of the pooled DNA and data analysis

The Illumina Sentrix HumanHap550v3 genotyping BeadChips were used. These contain more than 550 000 tag SNPs (Illumina Inc.,San Diego, CA). To avoid inter-experimental variation, each pool was genotyped on five chips in accordance with the manufacturer's recommendations for individual samples. SNP allele frequencies were estimated using data from the BeadArray TM Reader imaging (Illumina Inc.,San Diego, CA) and Illumina's genotyping software Bead Studio 2.0 (Illumina Inc.,San Diego, CA). Three analyses were performed on the basis of the allele frequency estimates obtained from the genotyping experiment: (i) 729 cases vs. 656 controls; (ii) 224 cases with a positive family history vs. 656 controls; and (iii) a sliding window analysis using the dataset of 729 cases vs. 656 controls, in accordance with recommendations described elsewhere. [START_REF] Papassotiropoulos | Common Kibra alleles are associated with human memory performance[END_REF] For each replicate, the following approximation of allele frequencies in cases and controls was performed on the basis of the raw data: f i = Xraw/(Xraw+Yraw), where Xraw and Yraw are the intensities of the two dyes (Cy5 and Cy3) used to genotype SNPs on the Illumina platform, and i is the replicate number. The obtained allele frequency was then averaged over the number of replicates of each pool f=(f 1 +...+f M )/M (where M is the number of replicates) and corrected for unequal amplification using the formula f corrected =f/(f+k•(1-f)). [START_REF] Moskvina | Streamlined analysis of pooled genotype data in SNP-based association studies[END_REF] For each SNP, the correction factor k was estimated using HapMap CEPH data (http://hapmap.ncbi.nlm.nih.gov/) and the formula k=(f con -

f con •f CEPH )/(f_ CEPH -f con •f CEPH )
, where f cont is the allele frequency in controls obtained from the pooling experiment and f CEPH is the allele frequency calculated from HapMap CEPH data.

The correction factor k was used as the quality control measure as it provides an indication of how close the estimated allele frequencies in controls are to those of the CEPH data. SNPs were excluded from the further analysis when k was >4 or <0.25.

The coefficient of variation was also used as a quality control measure for each SNP in each pool. This was calculated using the formula sqrt(var e )/f, where var e is the experimental variance estimated from the replicates data. This indicates how close the SNP is to the replicates, while taking into account allele frequencies and the number of replicates per pool. SNPs were excluded from further analysis when the coefficient of variation was >1 (upper boundary of the 95% confidence interval) in at least in one of the three pools (i.e. cases, controls, familial cases).

For the remaining 487 932 SNPs, association analyses were performed to compare 729 cases and 224 familial cases with 656 controls. Modified Z-statistics were used, as described by Abraham et al. [START_REF] Abraham | A genome-wide association study for late-onset Alzheimer's disease using DNA pooling[END_REF] These take into account both the experimental variance (see above) and the sampling variance.

A signal processing analysis technique was used to interpret the results of the casecontrol association analysis. This enables the detection of genetic association with disease, while taking into account the significance of several subsequent genetic markers in a sliding window. Moskvina has described a theoretical approach to calculating the probability of at least one false alarm being flagged by the detection statistic under the Null hypothesis of no signal (association). [START_REF] Wichmann | KORA-gen--resource for population genetics, controls and a broad spectrum of disease phenotypes[END_REF] This is equivalent to the probability of type I error when taking the number of comparisons in the window into account, and thus provides a "genome-wide window-based" significance level. 19 SNP selection, confirmation of pooling results, and independent replication A number of SNPs were selected to confirm the pooling results on an individual genotyping level.

A replication step was performed in two independent case-control samples (for an overview see Fig. 1). The following SNPs were selected from the three pooling-based analyses: (i) the top 50 SNPs from the analysis '729 cases vs. 656 controls'; (ii) the top 20 SNPs from the analysis '224 cases with a positive family history vs. 656 controls'; and (iii) the top 35 SNPs from the 'sliding window analysis'. All selected SNPs had

shown P-values of < 1x10 -4 in the respective pooling analysis. As SNPs from the previously known HLA region were highly overrepresented, all but three of these SNPs were excluded. The three remaining HLA SNPs, rs3115553 (chr. 6: 32 353 805bp), rs9275141 (chr. 6: 32 759 095bp), and rs9275572 (chr. 6: 32 786 977bp), were selected since they were the best findings in the HLA region in the 'sliding window analysis'. 95% call rate was required for each of the samples used in the confirmation and replication steps. In the confirmation step (step 2), DNA samples from eight AA cases and 11 controls failed to fulfil the quality criteria and were excluded from the analysis, and thus 721 AA cases and 645 controls remained for the analyses. In the independent replication step (step 2), four DNA case-samples failed to fulfil the quality criteria, and thus 450 cases and 1 364 controls remained for the analyses. Of the 61 selected SNPs, six SNPs (rs12493901, rs30117, rs41515, rs4777450, rs7246435, and rs9520256) were technical failures, and five SNPs (rs10123149, 11098149, rs6700586, rs7099812, and rs724841) had to be excluded as they did not reach the required call rate of ≥95% in one or more of the confirmation and/or replication samples. The SNP rs7334982 was not biallelic in the present samples and was therefore excluded from further analysis. Thus, a set of 49 SNPs remained for further analysis.

Statistical analyses of individual genotyping data

The FAMHAP software package [START_REF] Herold | Genetic association analysis with FAMHAP: a major program update[END_REF] was used for the association and haplotype analyses. The Armitage trend test was used for the single marker analyses. [START_REF] Armitage | Tests for linear trends in proportions and frequencies[END_REF] All SNPs met the following quality criteria: minor allele frequency > 1%, P HWE in cases > 0.001, and P HWE in controls > 0.05. The resulting P-values were corrected for multiple testing according to the number of SNPs successfully analyzed on the individual genotyping level (n = 49).

Expression analyses We used the forward primer 5'-CCTTCAAACCGACGCATACT- was included as a negative control.

Results

Step 1: Pooling-based approach

The genome-wide pooling-based approach involved three DNA-pools: Markers were excluded if the coefficient of variation was >1 in at least one of three DNA-pools, or if the correction factor k was >4 or <0.25. The remaining 487 932 SNPs were corrected for k, and SNPs with minor allele frequencies of <5% in controls were filtered out. The remaining 468 389 SNPs were tested for association using modified Zstatistics. [START_REF] Abraham | A genome-wide association study for late-onset Alzheimer's disease using DNA pooling[END_REF] Separate comparisons with controls were made for cases and familial cases.

The results of the case-control comparison were further analyzed in a sliding window.

The best markers from the top regions identified by the sliding window analysis 19 were selected for replication. Thus, three different analyses were performed: (I) 729 AA cases vs. 656 controls; (II) 224 AA cases with a positive family history vs. 656 controls; and

(III) a sliding window analysis (Fig. 1). These analyses identified 31 SNPs with Pvalues < 5 x 10 -7 (supplement table 1), resulting in a total of 18 SNPs after the exclusion of duplicates and triplicates. Of these 18 SNPs, eight SNPs were localized in the HLA region, and ten SNPs were localized elsewhere in the genome. The best SNP of all three analyses was rs9952976 (chr. 18: 42,561,717bp) which had a P-value of 6.48 x 10 -14 in analyses I and III (supplement table 1). The best SNP in analysis II was rs9275572, which is localized in the HLA region (P = 1.87 x 10 -8 ). This SNP was also the best HLA-SNP in analyses I (P = 1.00 x 10 -11 ) and III (P = 5.67 x 10 -12 ) (supplement table 1). When the best SNPs from each analysis were considered (see selection criteria in Materials and Methods), three SNPs (rs9275141 (chr. 6: 32 759 095); rs9275572 (chr.

6: 32 786 977); and rs9952976 (chr. 18: 42 561 717)) appeared in all three analyses.

Two of these SNPs (rs9275141 and rs9275572) are localized in the HLA region (supplement table 1).

Step

2: Individual confirmation and independent replication

The top 50 SNPs from analysis I, the top 20 SNPs from analysis II, and the top 35 SNPs from analysis III were selected for further analysis (Fig. 1). The elimination of duplicates and triplicates resulted in a total of 61 SNPs (see Materials and Methods and supplement table 1). To confirm the association findings of the 61 selected SNPs in the pooling approach, individual genotyping was performed in the previously pooled discovery sample of 729 AA cases and 656 controls. An independent replication step involved 454 AA cases and 1 364 controls. Following quality control, 49 SNPs remained for analysis (see Materials and Methods). With the exception of five SNPs, this analysis confirmed the pooling results at a nominal level of significance, and thus demonstrated the validity of the DNA pooling approach. The strongest association was found for the three HLA-SNPs (rs3115553, rs9268528, and rs9275572). The SNP rs9275572 showed the strongest association with P = 2.50 x 10 -10 (OR = 1.65 [1.41 -1.94]) (Table 1). These were the only SNPs to withstand correction for multiple testing using the previously suggested threshold of P = 5 x 10 -7 . [START_REF]TWTCC: Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls[END_REF] The remaining SNPs failed to show strong association. The best association finding outside of the HLA region was for rs2110597 (chr. 12: 12 832 280bp) with P = 1.42 x 10 -5 (OR = 1.44 [1.22 -1.68]). The best finding from the pooling-based analysis, rs9952976 (chr. 18: 42 561 717 bp),

showed only borderline significance on the level of individual genotyping, with P = 0.034 (OR = 1.20 [1.01 -1.43]). This was one of the weakest association findings in this confirmation step (Table 1).

In the independent replication step, the strongest association was again found for the three HLA SNPs. The SNP rs9275572 was the most strongly associated SNP (P = 7.94

x 10 -11 (OR = 1.71 [1.46 -2.01]). Twenty-seven SNPs showed the same risk alleles as in the discovery sample. Only one SNP outside of the HLA region (rs304650; chr. 4:

124,303,368bp) showed significant association (P-value of 0.001 (OR = 1.31 [1.12 -1.53])). Following Bonferroni-correction for the number of SNPs tested (n = 49), only the three HLA SNPs and rs304650 (P = 0.049) remained significant (Table 1).

Step

3: Follow-up analysis of the top finding

A second independent sample of 537 cases and 657 controls was then used to investigate the association finding for rs304650 further (Fig. 1). Genotyping of rs304650 failed in one case and two controls, and thus 536 cases and 655 controls remained. In this analysis, rs304650 could not be replicated at a significant level (P = 0.127) (Table 2). However, the risk allele remained the same. A combined analysis was therefore performed using all AA cases and controls from the independent replication and follow-up steps (a total of 985 cases and 2,014 controls were successfully genotyped for this SNP) (data not shown). Here, rs304650 showed stronger association, with P = 3.43 x 10 -4 (OR = 1.24 [1.10 -1.39]). After combining all cases and controls, we obtained a P-value of 1.58 x 10 -5 ; OR = 1.23 [1.12 -1.35]. Interestingly, SPATA5 expression was observed in hair follicles and skin, which confirms the importance of this gene in terms of hair biology.

wide significant P-values. This was also the case in the independent replication step.

This indicates that the DNA pooling approach can reliably detect SNPs that have shown genome-wide significance in association studies. Furthermore, pooling detects highly significant results, and it is therefore very unlikely that any genes beyond the HLA region are more significant. However, our strategy carries a risk of false-negative findings in the case of smaller genetic effects. DNA pooling adds extra experimental error (e.g. pipetting for pool construction) to the allele frequency measurement that directly influences the power to detect small effect sizes. [START_REF] Bosse | Identification of susceptibility genes for complex diseases using pooling-based genome-wide association scans[END_REF] Furthermore, only 61 top hits from the GWAS step were pursued in individual samples, with the great majority of nominally significantly associated markers having been excluded from the subsequent analyses. These are the two most likely explanations as to why the present study may have missed previously reported association findings 12 Therefore, the reliable detection of genes with smaller effects requires larger sample sizes and individual genotyping.

The only other SNP to reach experiment-wide significance in the combined analysis was rs304650 in the SPATA5 gene on chromosome 4q27-q28. Joint analysis of the replication samples used in steps 2 and 3, which included a total of 985 cases and 2,014 controls who were successfully genotyped for this SNP, revealed a significant association between this variant and AA, with a P-value of 3.43 x 10 -4 (OR = 1.24 [1.10 -1.39]). A joint analysis of all of the investigated samples revealed a significant association between this variant and AA, with a P-value of 1,58 x 10 -5 (OR = 1.23 [1.12 - 1.35]). The SNP rs304650 maps to an intronic region of the SPATA5 transcript. At the time of writing, the functional aspects of this protein are unknown. However, one study identified SPATA2, another member of the spermatogenesis associated protein family, as a susceptibility gene for the autoimmune disorder psoriasis [START_REF] Capon | Identification of ZNF313/RNF114 as a novel psoriasis susceptibility gene[END_REF] .

Interestingly, although SPATA5 was not among the eight loci with genome-wide significance reported by Petukhova et al., the authors reported 6 SNPs in SPATA5 with a P-value < 10 -4 in their supplementary material. Although not very strong, there is evidence for LD between rs304650 and the Pethukova et al. SNPs (ranging between r² = 0.29 for rs11735364 and r 2 = 0.46 for rs2201997). Although this might be viewed as supportive evidence, a more detailed workup of the region in very large samples is required to allow more definitive conclusions to be drawn. It is also interesting that the SPATA5 gene is located only 320kb distal to rs7682241, a genome-wide significant marker in the study of Petukhova et al., which strongly suggests the involvement of the IL2/IL21 gene locus. Data from the CEU HapMap sample, however, show that rs304650 is not in LD with the best variants of the IL2/IL21 gene locus. Thus, the two loci probably confer their risk independently of each other. It remains theoretically possible, however, that the true causal variant for AA may be a functional variant that is in moderate LD to the variants reported in both analyses and which is located between the IL2/IL21 and SPATA5 regions." Expression analysis of mRNA of SPATA5. SPATA5 was found to be expressed in human hair follicle, skin, kidney, and lung (samples displayed from left to right). The final lane shows a negative control. [START_REF] Safavi | Incidence of alopecia areata in Olmsted County, Minnesota, 1975 through 1989[END_REF] Position in base pairs based on NCBI build 36. 2 MAF = Minor allele frequency with minor allele in parentheses. [START_REF] Jackow | Alopecia areata and cytomegalovirus infection in twins: genes versus environment?[END_REF] OR = odds ratio; CI = confidence interval. OR-calculation based on the risk allele deriving from the initial pooling confirmation step. [START_REF] Tobin | Characterization of hair follicle antigens targeted by the anti-hair follicle immune response[END_REF] Nominal P-value was corrected for the number of SNPs finally investigated (n = 49) in the initial pooling-based confirmation step.

3 '

 3 and the reverse primer 5'-GCAGCCCACTCTTCTCTTGA-3' to analyse the expression of SPATA5 in human hair follicle and skin samples (expected product size: 197bp). As SPATA5 expression has been proven in human kidney and lung (http://www.genecards.org/cgi-bin/carddisp.pl?gene=SPATA5&search=SPATA5), these tissues were included as positive controls. Total RNA was extracted from human hair follicles and skin using the the RNeasy® Micro Kit (Qiagen), and single strand cDNA was synthesized from a total of 400ng RNA using the Super Script III First Strand Synthesis System (Invitrogen). Single strand cDNA from kidney and lung was obtained from the Human Multiple-Tissue cDNA (MTC) Panel Human MTC™ Panel I (LOT Nr. 6060248; Clontech). A negative reverse transcription reaction (no enzyme)

  (1) 729 AA cases (including the 224 cases with a positive family history), (2) 224 AA cases with a positive family history, and (3) 656 controls. Each pool was genotyped on five replicates of the Illumina Sentrix® HumanHap550v3 genotyping BeadChip. Pool 1 was successfully analyzed in all five replicates. Pool 2 was successfully analyzed in four replicates. Two of the five control chips were excluded following quality control filtering. Quality control measures and allele frequencies were estimated for all 504 931 SNPs. The quality control measures used were: (i) the coefficient of variation of each SNP in each pool, which reflected how close the SNP was to the replicates while taking into account allele frequencies and the number of replicates per pool; and (ii) correction factor k as an indicator of the closeness of the allele frequency estimates in the control pool to the allele frequencies in the CEPH sample from HapMap (for details see the Methods section).

Fig. 1

 1 Fig. 1 Overall workflow. The study was conducted in three steps: (a) pooling-based analyses using three different approaches ((I) all cases vs. all controls, (II) cases 'positive family history' vs. all controls and (III) a sliding window analysis; (b) confirmation of selected best pooling-based findings through individual genotyping in previously pooled caseand control samples; (c) independent replication and follow-up analyzes in additional samples of cases and controls.

Fig. 2

 2 Fig.2

  SNPs from the HLA region and SNPs appearing in more than one of the analyses (doubles and triples), it was possible to reduce the SNP set for the confirmation and

	replication step (step 2) from 105 to 61 SNPs. Individual genotyping was performed on
	the Illumina platform. For the DNA samples from the HNR-, KORA-and Popgen
	controls (n = 1 364), HumanHap550v3 genotyping BeadChips (Illumina Inc.,San Diego,
	CA) were used. For all other DNA samples, Sequenom's Compact MALDI-ToF Mass
	Array system and iPLEX Gold reagents (Sequenom GmbH, Hamburg, Germany) in
	multiplex reactions were used. Primer sequences and Sequenom's standard assay
	These were used as positive controls in subsequent analyses. Regrettably, rs9275141
	failed during the assay design of the Sequenom iPlex reaction (Sequenom GmbH,
	Hamburg, Germany). It was therefore replaced by the next best SNP in the HLA region

from the 'sliding window analysis', rs9268528 (chr. 6: 32 491 086bp). By excluding other conditions are available upon request. All primers were checked by MALDI-ToF. For quality reasons, a success rate of at least 95% was required for all analyzed SNPs. A

Table 1 : Association between alopecia areata and selected markers in the case- control confirmation-and case-control replication analyses Cases-control confirmation analysis Cases-control replication analysis MAF 2

 1

							Risk			MAF 2	Risk
	SNP	Chr	Position 1	Allele	Cases	Controls	Allele	P	OR (95% CI) 3	Cases	Controls	Allele	P	Pcorr. 4	OR (95% CI) 3
	rs3099624	1	11 419	T/C	0.419 (T)	0.477 (T)	C	0.002	1.27 (1.09 -1.47)	0.451 (T)	0.459 (T)	C	0.7	1	1.03 (0.89 -1.20)
	rs304303	1	43 950	G/T	0.241 (T)	0.311 (T)	G	5.79 x 10 -5	1.42 (1.20 -1.69)	0.269 (T)	0.275 (T)	G	0.761	1	1.03 (0.87 -1.22)
	rs4660260	1	43 967	T/C	0.245 (T)	0.313 (T)	C	9.22 x 10 -5	1.40 (1.18 -1.66)	0.278 (T)	0.281 (T)	C	0.838	1	1.02 (0.86 -1.20)
	rs12403551	1	101 636	G/A	0.472 (A)	0.492 (G)	G	0.06	1.15 (0.99 -1.34)	0.472 (A)	0.478 (A)	G	0.97	1	1.00 (0.86 -1.17)
	rs2345724	2	18 548	G/A	0.052 (G) 0.029 (G)	G	0.003	1.84 (1.23 -2.75)	0.052 (G)	0.042 (G)	G	0.185	1	1.27 (0.90 -1.80)
	rs2666138	2	36 184	C/T	0.163 (C)	0.116 (C)	C	5.92 x 10 -4	1.48 (1.19 -1.84)	0.139 (C)	0.150 (C)	T	0.42	1	0.91 (0.74 -1.13)
	rs13409979	2	184 062	A/G	0.131 (A)	0.103 (A)	A	0.024	1.31 (1.03 -1.66)	0.109 (A)	0.110 (A)	G	0.983	1	1.00 (0.78 -1.27)
	rs1692617	3	23 438	T/C	0.399 (T)	0.463 (T)	C	0.001	1.30 (1.11 -1.51)	0.463 (T)	0.440 (T)	T	0.219	1	0.91 (0.78 -1.06)
	rs6414541	3	173 403	C/T	0.119 (C)	0.092 (C)	C	0.023	1.33 (1.04 -1.71)	0.101 (C)	0.116 (C)	T	0.257	1	0.87 (0.68 -1.11)
	rs4130791	4	1 404	A/G	0.105 (A)	0.064 (A)	A	2.16 x 10 -4	1.71 (1.29 -2.26)	0.107 (A)	0.099 (A)	A	0.436	1	1.10 (0.86 -1.41)
	rs16873952	4	23 241	A/G	0.148 (A)	0.108 (A)	A	0.001	1.44 (1.15 -1.81)	0.107 (A)	0.129 (A)	G	0.072	1	0.81 (0.63 -1.02)
	rs17023881	4	96 581	T/C	0.060 (T)	0.037 (T)	T	0.007	1.66 (1.15 -2.40)	0.052 (T)	0.047 (T)	T	0.438	1	1.15 (0.81 -1.61)
	rs7657799	4	105 594	G/T	0.031 (G) 0.016 (G)	G	0.014	1.98 (1.16 -3.38)	0.022 (G)	0.022 (G)	G	0.88	1	1.04 (0.62 -1.74)
	rs7664318	4	123 818	G/A	0.177 (G) 0.125 (G)	G	1.57 x 10 -4	1.51 (1.22 -1.87)	0.152 (G)	0.146 (G)	G	0.574	1	1.06 (0.86 -1.31)
	rs304650	4	124 303	G/A	0.328 (G) 0.272 (G)	G	0.001	1.31 (1.11 -1.54)	0.360 (G)	0.301 (G)	G	0.001	0.049	1.31 (1.12 -1.53)
	rs9997120	4	147 312	T/C	0.234 (T)	0.289 (T)	C	0.001	1.33 (1.12 -1.58)	0.240 (T)	0.266 (T)	C	0.162	1	1.13 (0.95 -1.35)
	rs2125856	5	122 073	C/T	0.325 (C)	0.268 (C)	C	0.002	1.32 (1.11 -1.55)	0.299 (C)	0.291 (C)	C	0.379	1	1.08 (0.91 -1.27)
	rs3115553	6	32 353	A/G	0.137 (A)	0.217 (A)	G	7.11 x 10 -8	1.74 (1.42 -2.12)	0.139 (A)	0.208 (A)	G	6.27 x 10 -6	3.07 x 10 -4	1.63 (1.32 -2.01)
	rs9268528	6	32 491	G/A	0.477 (G) 0.381 (G)	G	2.52 x 10 -7	1.48 (1.27 -1.73)	0.499 (A)	0.391 (G)	G	6.82 x 10 -9	3.34 x 10 -7	1.56 (1.34 -1.82)
	rs9275572	6	32 786	A/G	0.304 (A)	0.420 (A)	G	2.50 x 10 -10 1.65 (1.41 -1.94)	0.303 (A)	0.430 (A)	G	7.94 x 10 -11	3.89 x 10 -9	1.71 (1.46 -2.01)
	rs916305	6	117 986	T/C	0.123 (T)	0.107 (T)	T	0.195	1.17 (0.93 -1.49)	0.107 (T)	0.122 (T)	C	0.246	1	0.87 (0.68 -1.10)
	rs505532	7	29 050	T/C	0.320 (T)	0.260 (T)	T	5.20 x 10 -4	1.34 (1.13 -1.58)	0.300 (T)	0.276 (T)	T	0.166	1	1.12 (0.95 -1.33)
	rs718121	8	3 146	T/C	0.331 (T)	0.408 (T)	C	4.73 x 10 -5	1.39 (1.19 -1.63)	0.401 (T)	0.372 (T)	T	0.122	1	0.88 (0.76 -1.03)
	rs2979742	8	25 451	T/C	0.332 (T)	0.374 (T)	C	0.02	1.20 (1.03 -1.41)	0.360 (T)	0.349 (T)	T	0.54	1	0.95 (0.81 -1.11)
	rs10503991	8	36 539	G/A	0.126 (G) 0.102 (G)	G	0.04	1.28 (1.01 -1.62)	0.107 (G)	0.116 (G)	A	0.457	1	0.91 (0.72 -1.16)
	rs4738296	8	74 020	C/A	0.041 (C)	0.018 (C)	C	8.62 x 10 -4	2.33 (1.43 -3.79)	0.032 (C)	0.039 (C)	A	0.388	1	0.83 (0.55 -1.26)
	rs7022183	9	13 006	C/T	0.092 (C)	0.066 (C)	C	0.013	1.44 (1.09 -1.91)	0.070 (C)	0.065 (C)	C	0.626	1	1.08 (0.80 -1.45)
	rs7036795	9	70 358	C/T	0.214 (C)	0.181 (C)	C	0.03	1.23 (1.02 -1.49)	0.181 (C)	0.197 (C)	T	0.628	1	0.95 (0.78 -1.16)
	rs10512241	9	97 977	A/G	0.346 (A)	0.405 (A)	G	0.002	1.28 (1.10 -1.50)	0.350 (A)	0.377 (A)	G	0.142	1	1.13 (0.96 -1.32)
	rs17479692	10	91 278	G/T	0.157 (G) 0.109 (G)	G	3.52 x 10 -4	1.52 (1.21 -1.91)	0.108 (G)	0.135 (G)	T	0.068	1	0.80 (0.63 -1.02)
	rs9419187	10	133 761	T/C	0.318 (T)	0.373 (T)	C	0.002	1.28 (1.09 -1.50)	0.368 (T)	0.340 (T)	T	0.121	1	0.88 (0.76 -1.03)
	rs16928055	11	35 870	C/T	0.151 (C)	0.104 (C)	C	2.54 x 10 -4	1.55 (1.22 -1.95)	0.116 (C)	0.113 (C)	C	0.557	1	1.07 (0.85 -1.36)
	rs1216476	11	99 915	G/A	0.230 (G) 0.177 (G)	G	6.13 x 10 -4	1.39 (1.15 -1.68)	0.206 (G)	0.216 (G)	A	0.539	1	0.94 (0.78 -1.14)
	rs11224294	11	99 954	C/T	0.098 (C)	0.063 (C)	C	9.34 x 10 -4	1.62 (1.22 -2.15)	0.078 (C)	0.091 (C)	T	0.24	1	0.85 (0.64 -1.12)
	rs11600229	11	130 998	G/A	0.042 (G) 0.057 (G)	A	0.068	1.38 (0.97 -1.95)	0.052 (G)	0.039 (G)	G	0.091	1	0.74 (0.52 -1.05)
	rs11223339	11	132 423	T/G	0.217 (T)	0.163 (T)	T	4.02 x 10 -4	1.42 (1.17 -1.73)	0.199 (T)	0.203 (T)	G	0.783	1	0.97 (0.81 -1.18)
	rs10791360	11	133 807	C/A	0.072 (C)	0.084 (C)	A	0.25	1.18 (0.89 -1.56)	0.078 (C)	0.073 (C)	C	0.607	1	0.93 (0.70 -1.23)
	rs2270797	12	128	A/G	0.054 (A)	0.031 (A)	A	0.003	1.81 (1.22 -2.68)	0.029 (A)	0.038 (A)	G	0.242	1	0.77 (0.50 -1.19)
	rs2110597	12	12 832	G/A	0.381 (G) 0.300 (G)	G	1.42 x 10 -5	1.44 (1.22 -1.68)	0.362 (G)	0.332 (G)	G	0.101	1	1.14 (0.97 -1.34)
	rs10506012	12	26 918	A/G	0.150 (A)	0.189 (A)	G	0.007	1.32 (1.08 -1.61)	0.172 (A)	0.189 (A)	G	0.262	1	1.12 (0.92 -1.37)
	rs12228387	12	117 886	A/G	0.059 (A)	0.036 (A)	A	0.005	1.70 (1.18 -2.45)	0.054 (A)	0.060 (A)	G	0.532	1	0.90 (0.65 -1.25)
	rs12430	17	71 453	T/C	0.114 (T)	0.086 (T)	T	0.017	1.36 (1.06 -1.76)	0.103 (T)	0.102 (T)	T	0.821	1	1.03 (0.80 -1.32)
	rs7228576	18	10 398	T/C	0.144 (T)	0.114 (T)	T	0.024	1.30 (1.04 -1.63)	0.149 (T)	0.129 (T)	T	0.115	1	1.19 (0.96 -1.48)
	rs9954649	18	18 867	G/A	0.384 (G) 0.331 (G)	G	0.004	1.26 (1.08 -1.47)	0.340 (G)	0.356 (G)	A	0.387	1	0.93 (0.80 -1.09)
	rs1431704	18	35 107	C/T	0.080 (C)	0.047 (C)	C	4.56 x 10 -4	1.79 (1.30 -2.47)	0.069 (C)	0.059 (C)	C	0.281	1	1.18 (0.87 -1.60)
	rs9952976	18	42 561	G/A	0.241 (G) 0.277 (G)	A	0.034	1.20 (1.01 -1.43)	0.286 (G)	0.284 (G)	G	0.829	1	0.98 (0.83 -1.16)
	rs11666141	19	15 295	C/T	0.227 (C)	0.163 (C)	C	3.18 x 10 -5	1.51 (1.24 -1.83)	0.186 (C)	0.170 (C)	C	0.3	1	1.11 (0.91 -1.35)
	rs2766671	20	51 617	T/C	0.126 (T)	0.107 (T)	T	0.123	1.20 (0.95 -1.53)	0.120 (T)	0.112 (T)	T	0.479	1	1.09 (0.86 -1.38)
	rs9982439	21	42 622	C/T	0.055 (C)	0.030 (C)	C	0.001	1.88 (1.27 -2.78)	0.040 (C)	0.037 (C)	C	0.725	1	1.07 (0.73 -1.58)

Table 2 : Follow-up analysis of rs304650 in an additional independent sample of 536 AA cases and 655 controls.

 2 Position in base pairs based on NCBI build 36. 2 MAF = Minor allele frequency with minor allele in parentheses.[START_REF] Jackow | Alopecia areata and cytomegalovirus infection in twins: genes versus environment?[END_REF] OR = odds ratio; CI = confidence interval. OR-calculation based on the risk allele deriving from the initial pooling confirmation step.

						MAF 2	Risk
	SNP	Chr	Position 1	Allele Cases Controls Allele	P	OR (95% CI) 3
	rs304650	4	124 303 368 G/A	0.347	0.316	G	0.127 1.15 (0.97 -1.36)
	1

Acknowledgements

The authors thank all patients and controls for participating in this study. The Heinz-Nixdorf Recall cohort (HNR) was established with the support of the Heinz Nixdorf Foundation (Germany). Silke Redler is a past recipient of a BONFOR fellowship from the Medical Faculty of the University of Bonn. Markus M. Nöthen is recipient of a grant from the Alfried Krupp von Bohlen und Halbach-Stiftung. Regina C. Betz is a past recipient of an Emmy-Noether fellowship and is a recipient of a Heisenberg Professorship (both German Research Foundation (DFG)).

Discussion

The present GWA study of AA is the first to have used pooled DNA. The analysis was performed in several stages to avoid the high costs of performing a GWA study in large individual samples. Genotyping of DNA pools was performed on 15 Illumina HumanHap550 arrays of patients and controls. A limitation of pooling studies in comparison to individual genotyping approaches is that allele frequencies are estimates deriving from DNA-pools, which are inherently imprecise. In view of this and the fact that the generally used quality control measures cannot be applied, the pooling-based approach was used as the discovery step (step 1; Fig. 1). In the second step, the top SNPs were confirmed using individual genotyping of the previously pooled case and control samples and replicated through individual genotyping in an independent sample of cases and controls (step 2; Fig 1). In the third step, the best SNP was followed up in a further independent replication sample (Fig. 1).

The major histocompatibility complex on chromosome 6p21.3 was identified as a major risk locus for AA. Previous research by our group and others has implicated various HLA alleles in AA susceptibility. The best replicated findings have been for alleles of the DRB1 and DQB1 loci. [START_REF] Entz | Investigation of the HLA-DRB1 locus in alopecia areata[END_REF][START_REF] Colombe | The genetic basis of alopecia areata: HLA associations with patchy alopecia areata versus alopecia totalis and alopecia universalis[END_REF][START_REF] De Andrade | Alopecia areata in families: association with the HLA locus[END_REF][START_REF] Petukhova | Genome-wide linkage analysis of an autosomal recessive hypotrichosis identifies a novel P2RY5 mutation[END_REF][START_REF] Barahmani | Human leukocyte antigen class II alleles are associated with risk of alopecia areata[END_REF][START_REF] Colombe | HLA class II antigen associations help to define two types of alopecia areata[END_REF] The present highly significant findings for variants in the HLA region demonstrate that the pooling-based strategy is a valid alternative to individual genotyping in complex disorders. [START_REF] Pearson | Identification of the genetic basis for complex disorders by use of pooling-based genomewide singlenucleotide-polymorphism association studies[END_REF] Although the pooling-based results for the HLA locus were not followed up systematically (step 1), the best three variants from the sliding window analysis were genotyped in the discovery and independent replication samples to confirm the initial pooling-based results (step 2). As expected, all three variants were confirmed on the individual genotyping level and reached genome-

Conflict of interest

The authors have no conflicts of interest to declare.