Valentina Ciarla

Violaine Cahouet

C Canudas De Wit

F Quaine

Genesis of booster curves in Electric Power Assistance Steering Systems

Keywords: Steering (EPS) system, Dahl friction model, static optimization

The typical architecture of an Electric Power Assistance Steering (EPAS) system includes a static map to provide the correct amplification to the driver's exerted torque. In literature, it is generally known as booster curve. This paper concerns the study of the amplification criteria, that are commonly used to these booster curves. The basic concepts of the Electric Power Steering (EPS) systems with a realistic model for the friction contact, that acts on the wheels are discussed. A relation between the assistance and the driver's torque is provided, under the hypothesis of a position-oriented control of the movement and the Stevens' power law. Finally, the simulation results proposed at the end of this paper validate the shape of the booster curves and are in accord with the initial hypothesis.

I. INTRODUCTION

Nowadays, vehicles have been widely equipped with power steering systems and the way of providing assist torque is various. The EPAS systems have the tendency to replace the hydraulic power steering, due to better fuel consumption [START_REF] Zaremba | Control and steering feel issues in the design of an electric power steering system[END_REF], [START_REF] Wang | Modeling and simulation studies on differential drive assisted steering for ev with four-wheelindependent-drive[END_REF]. They include the mechanical model of the steering column and the power steering unit. Moreover, this last element has the aim to reduce the steering efforts to a reasonable level, to ensure the most possible road feel feedback to the driver and to improve the return-to-center performance of the steering system. The assistance provided by the electric motor of EPS systems reproduces the hysteresis cycle of the hydraulic valve, as shown in Fig. 1: the amplification torque U grows, according to the value of the driver's torque τ v and the vehicle speed V , then saturates. If the driver's torque changes in direction, we have the downhill phase of the amplification torque. During this phase, the amplification torque decreases, until reaching the lower saturation values. In literature, we can find many stationary models for the EPS system ( [START_REF] De | Fun-to-drive by feedback[END_REF], [START_REF] Canudas De Wit | Stability analysis via passivity of the lateral actuator dynamics of a heavy vehicle[END_REF], [START_REF] Claeys | Modeling and control of steering actuator for heavy duty vehicle[END_REF], [START_REF] Zhang | Modeling and characteristic curves of electric power steering system[END_REF], [START_REF] Chabaan | Optimal control and gain scheduling of electrical power steering systems[END_REF], [START_REF] Jiang | Low-pass filter based automotive eps controller and comparative full-vehicle tests[END_REF], [START_REF] Tsung Hsien | Design of control logic and compensation strategy for electric power steering systems[END_REF], [START_REF] Burton | Innovation drivers for electric power-assisted steering[END_REF], [START_REF] Hoon | Control logic for an electric power steering system using assist motor[END_REF]), where the hysteresis cycle is approximated by a single curve. Nevertheless, these investigations do not provide ground foundations (other than these curves reproduce the behaviour of the older power steering systems, based on hydraulic valves), neither evidence that they are optimal for the driver in any sense. This work aims valentina.ciarla@gipsa-lab.grenoble-inp.fr, violaine.cahouet@gipsa-lab.grenoble-inp.fr, carlos.canudas-de-wit@gipsa-lab.grenoble-inp.fr, franck.quaine@gipsa-lab.grenoble-inp.fr) Example of the booster curve, provided by the EPAS system, reported in [START_REF] De | Fun-to-drive by feedback[END_REF].

for providing some rationality to these curves and validating their optimality for the drivers. To this aim, it is interesting to refer to the literature concerning the criteria at the basis of the human coordination, that try to explain the human movement by minimizing a cost function. For example, to optimize the muscular effort during a one degree-of-freedom repetitive exercise motion, authors in ( [START_REF] Li | Control of smart exercise machines. i. problem formulation and nonadaptive control[END_REF], [START_REF] Li | Control of smart exercise machines. ii. self-optimizing control[END_REF]) choose to maximize the power spent by the user. To explain the trajectory formation in a constrained point-to-point motion, in [START_REF] Ohta | Optimal trajectory formation of constrained human arm reaching movements[END_REF] authors propose a combined criterion minimizing the variation of the hand contact force and the change of the actuating force over the course of the movement. In the case of a planar horizontal movements with one mechanical degree of freedom [START_REF] Engelbrecht | Invariant characteristics of horizontal-plane minimum-torque-change movements with one mechanical degree of freedom[END_REF], the authors find an analytical expression for the predicted minimum torque change trajectories. In [START_REF] Flash | The coordination of arm movements: An experimentally confirmed mathematical model[END_REF], the cost function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. The hypothesis at the basis of this paper is that driver's coordination provide a steering wheel movement that minimize the jerk criterion. Solving this optimization, the optimal steering wheel trajectories are derived. These trajectories allow to retrieve the driver's and the amplification torques, that model the shape of the booster curves. The paper is organized as follows: in Section II, the main equations describing the EPAS system are introduced and the amplification model is defined; in Section III, the optimization problem, that will predict the optimal booster curves, is developed. Finally, in Section IV, significant simulation results and the conclusions are discussed. The dynamical equations governing an EPS system are (see [START_REF] Illán | Oscillation annealing and driver/tire load torque estimation in electric power steering systems[END_REF], [START_REF] Canudas De Wit | Control design for an electro power steering system: Part 1 the reference model[END_REF] and [START_REF] Canudas De Wit | Control design for an electro power steering system: Part 2 the control design[END_REF]):

J v θv = τ v -k(θ v -θ s ) -B v θv (1)
J T θs = -k(θ s -θ v ) -N 2 2 B m θs -σ 2 θs N 2 1 - τ a N 1 +U (2)
with

J T = J c + N 2 2 J m + J w N 2 1
, U = N 2 u and θ v , θ s and θ m are, respectively, the steering wheel, the motor-shaft and the motor angles. The constants of the model are defined in Table I.

Let make the hypothesis that the stiffness k of the steering column is infinity or that its effect can be compensated as proposed in [START_REF] Illán | Oscillation annealing and driver/tire load torque estimation in electric power steering systems[END_REF]. In this case, it is possible to neglect the torsion of the column: i.e. θ vθ s = 0 and consider the equivalent steering wheel angle θ v = θ s = θ . Summing Eq. (1) with Eq. (2), it is possible to obtain:

J θ + B θ + τ a N 1 = τ v +U (3)
where

J = J v + J T and B = B v + N 2 2 B m + σ 2 N 2 1
are, respectively, the total inertia and the total viscosity of the system at the steering wheel level. From Eq. ( 3) arises that at stand hill, (or very low vehicle speeds, that is the common situation where the assistance acts), the most influencing torque, that opposes to the driver's torque, is the friction contact torque. For this reason, it is mandatory to have a realistic model of it and the following paragraph will be dedicated to the description of the adopted friction contact torque.

A. Friction contact torque at stand-still

The load torque τ a is described by the Dahl's model ( [START_REF] Dahl | Dynamic hysteresis modeling[END_REF], [START_REF] Dahl | A solid friction model[END_REF], [START_REF] Dahl | Solid friction damping of mechanical vibrations[END_REF]), given by the following differential equation:

dF dθ 1 = σ 0 1 - F F c sgn θ1 (4)
where σ 0 is the rubber longitudinal stiffness coefficient, F c is the Coulomb friction force and θ 1 = θ /N 1 is the steering wheel angle projected at the tire level. The friction force |F| will never be larger than

F c , if its initial value is |F(0)| < F c .
To obtain a time-domain model, the following change of coordinates is required:

dF dt = dF dθ 1 dθ 1 dt = dF dθ 1 θ1 = σ 0 1 - F F c sgn( θ1 ) θ1 (5)
The load torque τ a in Eq. ( 3) is:

τ a = F n LF (6)
where F n and L are, respectively, the normal force and the patch length.

For a constant speed θ1 = θ1 , it is possible to obtain the following steady-state friction force F:

F = σ 0 z = F c sgn( θ1 ) (7)
This model is a first-order dynamic system, whose steadystate behaviour gives the Coulomb friction force, as shown in Eq. ( 7). For this model, it is possible to compute the solution of its differential equation in closed form for a sign-changing speed signal. Let consider a time interval t ∈ [0,t 1 ], where the speed signal is positive and the system starts with the initial conditions, i.e. F(θ 0 ) = 0 and θ (0) = θ 0 , the solution is:

F(t) = F c 1 -e - σ 0 Fc θ (t)-θ 0 N 1 (8)
If the speed signal becomes negative during a time interval t ∈ [t 1 ,t 2 ], then the solution is:

F(t) = F c -1 + 2e σ 0 Fc θ (t)-θ (t 1 ) N 1 -e σ 0 Fc θ (t)-2θ (t 1 ) N 1 (9)
Note that this solution is evaluated starting from initial conditions, that guarantee the continuity of the solution at the time instant t 1 , when the sign change of the speed happens. Finally, if the speed changes again in sign, during the time interval t ∈ [t 2 , T ], the solution is:

F(t) = F c 1 -2e - σ 0 Fc θ (t)-θ (t 2 ) N 1 + 2e - σ 0 Fc θ (t)+θ (t 1 )-2θ (t 2 ) N 1 -e - σ 0 Fc θ (t)+2θ (t 1 )-2θ (t 2 ) N 1 ( 10
)
Details on the computation of these solutions are shown in [START_REF] Ciarla | Additional material for the paper: Genesis of booster curves in electric power assistance steering systems[END_REF]. For the purposes of this paper, the computation of the analytic solution is limited to three consecutive sign changes of the speed, but the proposed method can be applied even for more general cases. To compute the analytic solution, the time instant when the sign change takes place must be known. The friction force is only a function of the displacement and the sign of the relative velocity. This implies that it will depend only from the sign of the velocity, but not from its magnitude.

B. Perception of the load torque

At stand still, the main force opposing to the driver's effort is the contact friction. In this situation, it is possible to assume that the assistance U acts to compensate, first of all, a part of the contribution of the load torque τ a in Eq. ( 3). Indeed at steady-state conditions:

τ a N 1 = τ v +U (11)
In order to design the assistance amplification, the hypothesis that the driver's perception of the load torque obeys to the Stevens' power law ( [START_REF] Newberry | Driver perception of steering feel[END_REF], [START_REF] Copelli | Physics of psychophysics: Stevens and weber-fechner laws are transfer functions of excitable media[END_REF], [START_REF] Bertollini | Applying driving simulation to quantify steering efforts preference as a function of vehicle speed[END_REF]) is done:

δ τ a N 1 n = τ v ( 12
)
where the term δ is the intensity magnitude of the friction torque and n describes the rate of growth of the sensation of the stimulus and depends on the sensory modality of the driver (e.g. perception of force or perception of position).

The value of δ is tuned to obtain a realistic value of the amplification torque, while to choose the value of n, it is mandatory to refer to the literature, concerning the control of the movement and to some experimental results.

During the steering movement, some authors ( [START_REF] Hoult | A neuromuscular model featuring coactivation for use in driver simulation[END_REF], [START_REF] Pick | A mathematical model of driver steering control including neuromuscular dynamics[END_REF]), show that drivers prefer exerting their control, basing on the transfer function between the friction contact load and the steering angle (position-oriented control), rather than the transfer function between the friction torque and the steering torque (torque-oriented control). This can be explained by the fact that the neuro-muscular system is better suited to control the steering angle than the exerted torque, thanks to the gamma (γ) motor neurons, that adapt the length of the spindles according to the hand wheel angle [START_REF] Pick | A mathematical model of driver steering control including neuromuscular dynamics[END_REF].

In [START_REF] Newberry | Driver perception of steering feel[END_REF], authors determine experimentally the value of n for both cases of torque-oriented and position-oriented control.

For each case, they produce 3 experiments. In particular, for what concerns the position-oriented control, during the first experiment they require to 12 subjects to make a numerical estimation of the perceived magnitude of sensation. During the second one, they require to the same subjects to adjust the stimulus to produce a sensory magnitude equivalent to given numbers. Finally, they employ both magnitude estimation and magnitude production to develop a scale of perception of steady-state steering wheel angle. The value of the rate n is determined by least square identification of the real data with Stevens' power law. They obtain an average value of n = 0.93, that is n < 1, meaning that the sensation of the angle grows at a slower rate than the angle. Note that results concerning the torque-oriented experiments indicate a rate of growth of the sensation n > 1 to explain how human perceive the torque sensation in an opposite way.

Considering what has been highlighted to this point, in this paper a position-oriented control is considered and simulations are provided for values of n ≤ 1.

C. Relation with the assistance torque

To obtain a relation between the assistance torque and the driver's torque in steady-state, Eq. ( 11) is substituted in Eq. ( 12), as follows:

δ (τ v +U) n = τ v (13)
By solving for U, it is possible to obtain:

U = n τ v δ -τ v (14)
When the dynamic terms of inertia and viscosity are included, the same closed-form solution for the assistance U is not reachable, but it follows:

J θ + B θ + δ τ a N 1 n = τ v (15)
Let consider Eq. ( 3), we can express the assistance torque U, as the following difference:

U = τ a N 1 -δ τ a N 1 n (16)
In this case, it is not possible to retrieve the corresponding value for the assistance torque in closed form, because it is necessary to solve Eq. ( 15) to obtain the corresponding values in Eq. ( 16). For this reason, it is necessary to introduce the optimization problem, shown in Section III.

To generalize the problem, the normalized form of the time is adopted:

t * = t T ( 17
)
where T is the final simulation time, considered to execute the movement. Differentiating this time, it is possible to get:

dt * = dt T (18)
In the new set of coordinates, the equations of the model becomes:

J T 2 d 2 θ dt * 2 + B T dθ dt * + δ τ a N 1 n = τ * v (19)
The only time-invariant term in Eq. ( 19) is the friction torque, while the total inertia and the total viscosity decrease as slower the driver executes the movement.

III. PROBLEM FORMULATION A. Position-oriented control of the movement

As discussed in Section I, many criteria used to explain the human movement are based on the minimization of a cost function. They can be divided in two main classes: dynamic and kinematic criteria. Dynamic optimization criteria aim to minimize quantities like the energy or the power ( [START_REF] Li | Control of smart exercise machines. i. problem formulation and nonadaptive control[END_REF], [START_REF] Li | Control of smart exercise machines. ii. self-optimizing control[END_REF]), the torque and the torque change [START_REF] Ohta | Optimal trajectory formation of constrained human arm reaching movements[END_REF] exerted during a movement. The most common kinematic criterion is based on the minimization of the jerk [START_REF] Hogan | On rhythmic and discrete movements: reflections, definitions and implications for motor control[END_REF]. This function is widely used in literature to describe human pointing, because authors assume that the major goal of motor coordination is the production of the smoothest possible movement of the hand. Concerning the driving task, some authors formulated a position-oriented control ( [START_REF] Hoult | A neuromuscular model featuring coactivation for use in driver simulation[END_REF], [START_REF] Pick | A mathematical model of driver steering control including neuromuscular dynamics[END_REF]), that is in accordance with the kinematic optimization criteria. For this reason to obtain the profile of the booster curves for the dynamic case, an optimization problem basing on the minimization of the jerk function will be formulated in the following paragraph.

B. Optimization problem

The considered movement consists into bringing the steering wheel from 0 rad to π/2 rad and returning it to its initial position. The problem is to find the optimal trajectory θ , that minimizes the cost index I:

I = T 0 d 3 θ dt 3 2 dt ( 20
)
under the constraint to have a driver's torque τ v = 0 at the beginning and at the end of the movement.

In the normalized form of the time, the optimization problem becomes

min θ * 1 0 d 3 θ * dt * 3 2 dt * (21)
with the boundary conditions on the trajectory

θ * (0) = 0 θ * (1) = 0 θ * (0.5) = π/2 θ * (0) = 0 θ * (1) = 0 θ * (0.5) = 0 θ * (0) = 0 θ * (1) = 0 (22)
and on the driver's torque

τ v (0) = 0 τ v (1) = 0 ( 23
)
The condition τ v (0) = 0 is guaranteed by the constraint to impose that the movement begins with speed and acceleration null and by the initial condition imposed on the friction torque F(0) = 0. In the same way, to guarantee the condition τ v (1) = 0, it is mandatory to impose that the load torque τ a must be null at the final time τ a (1) = 0, but this implies F(1) = 0.

As the optimization procedure will use the analytic solution of the Dahl's friction torque, the constraint F(1) = 0 can be imposed on the function in Eq. ( 10), obtained for t ∈ [t 2 , 1], as follows:

F(1) = F c 1 -2e - σ 0 Fc θ * (1)-θ * (t * 2 ) N 1 + 2e - σ 0 Fc θ * (1)+θ * (t * 1 )-2θ * (t * 2 ) N 1 + -e - σ 0 Fc θ * (1)+2θ * (t * 1 )-2θ * (t * 2 ) N 1 = 0 (24)
Using the boundary conditions imposed on the optimization problem, the values of θ * (1) and θ * (t * 1 ), respectively, zero and π/2 rad, can be substituted in Eq. ( 24), and the only unknown variable becomes the angle θ * (t * 2 ):

F(1) = F c 1 -2e σ 0 Fc θ * (t * 2 ) N 1 + 2e - σ 0 Fc π 2 -2θ * (t * 2 ) N 1 + -e - σ 0 Fc π-2θ * (t * 2 ) N 1 = 0 (25) Setting x = e σ 0 Fc θ * (t * 2 )
N 1 , Eq. ( 25) can be written as the following second order algebraical equation:

1 -2x + 2e - σ 0 Fc π 2 1 N 1 -e - σ 0 Fc π N 1 x 2 = 0 (26)
The value for the angle θ * (t * 2 ) is obtained from the negative solution of this equation (the positive one is not compatible with the other constraints of the problem). Using this value, it possible to impose a further constraint on the trajectory, that guarantees the condition F(1) = 0:

θ * (t * 2 ) = θ 2 (27)
Nevertheless, it is not possible to predict a priori the instant t * 2 , when the steering wheel path may assume this value. To overcome this problem, an external dichotomy loop is used for the estimation of this value.

C. Static optimization problem

The problem to solve is a dynamic, non-linear, constrained optimization problem. To simplify the research of the optimal solution, it can be modified in a static, non-linear, constrained optimization problem. Let make the hypothesis that among the set of the feasible solutions, the optimal one has the following polynomial form:

θ * (t * ) = P ∑ k=0 a k t * k ( 28
)
where P is the order of the polynomial and a k is the single coefficient of the polynomial. The derivatives of Eq. ( 28) provide the analytical expressions for θ * (t * ) and θ * (t * ), that can be substituted in the Eq. ( 21) of the cost function, in the equations of the constraints ( 22), ( 23), [START_REF] Hoult | A neuromuscular model featuring coactivation for use in driver simulation[END_REF] and in the movement equation [START_REF] Canudas De Wit | Control design for an electro power steering system: Part 2 the control design[END_REF], to retrieve the required torque in Eq. ( 16). The optimization algorithm looks for the combinations of the polynomial a k with k = 0 . . . P, that minimize the cost function.

To impose the boundary conditions at the initial, intermediate and final time, it is sufficient to substitute the numerical values for the time in the polynomial equations. Remark that 9 boundary conditions are imposed; as consequence, the degree of the polynomial must be greater in order to allow to the optimization procedure to choose among different solutions.

IV. SIMULATION RESULTS

The solution of this problem is obtained applying a convex programming algorithm, implemented with the software Matlab 2011 R . The produced trajectories, shown in Fig. 2, result in a twelfth order polynomial in time for the profile of the steering wheel angle and its derivatives. The cost function determines the form of the movement trajectory. The details are determined by the boundary conditions. Given this information and the duration of the movement, the trajectory of the steering wheel is specified in its entirety. No other information is required. As expected from an optimization that minimizes the jerk, the optimal trajectories are smooths and regulars. Note that the angular trajectory passes through the angle θ 2 at the time t 2 = 0.8 s. This passage allows to obtain both the load and the driver's torques to be null at the final time. Three examples of amplification torque are proposed. They are obtained by tuning the intensity magnitude δ and the rate of growth of the sensation of the stimulus n. For each case, two simulations are provided. They correspond, respectively, to steady-state case in Eq. ( 14) and to the general formulation in Eq. ( 16). The final simulation time is T = 15 s, that provides a quasi-static case and a realistic booster curve. In Fig. 3, the coefficients are n = 1 and δ = 0.3; in Fig. 4, n = 0.9 and δ = 0.3, while in Fig. 5, n = 0.5 and δ = 1. The predicted profiles of the booster curves are strongly dependent from the value of n. For the case in Fig. 3, the profile is linear in the stationary case; the hysteresis phenomena due to the influence of the inertia and the viscosity is evident when the transient state is considered. For the cases n < 1, shown in Figs. 4 and5, at steady-state the curve has an exponential behaviour. This characteristic is more accentuated, as the coefficient n diminishes. The amplification is almost negligible for driver's torques in the interval -1 ≤ τ v ≤ +1 N m, while it grows for more important values. The hysteresis effect is present when the optimization in transient state is carried out, due to the influence of the inertial and viscosity torques. Nevertheless, it is possible to conclude that the commonly used amplification curves correspond to the profile obtained with n < 1. This means that the Stevens' coefficient for the rate of growth of the stimulus corresponds to the hypothesis of the positionoriented control of the movement.

V. CONCLUSIONS

The purpose of this paper is to provide some rationality the existing criteria used in EPAS systems. To this aim, the study of the main physical forces acting on the steering system is proposed. In particular, attention focused on a realistic model of the contact friction torque, because it represents the main torque that the assistance compensates. The analysis was carried out in steady-state and transient conditions to provide a mathematical relation between the provided assistance and the driver's exerted torque. In steadystate, a relation in closed form between the assistance torque and the driver's torque was founded. For the transient case, an optimization procedure is applied to reproduce the shape of the booster curves. The study showed that the profile of the booster curve can be linked to minimization criteria based on the steering wheel jerk, coupled with the Stevens' power law. Moreover, the analysis showed that the profile of the predicted booster curves is strictly influenced by the rate of growth of the sensation of the stimulus, coming from the contact friction torque, but the commonly used booster curves are closed to those obtained, making the hypothesis of the positionoriented control of the movement.

  Fig.1. Example of the booster curve, provided by the EPAS system, reported in[START_REF] De | Fun-to-drive by feedback[END_REF].

Fig. 2 .

 2 Fig. 2. Evolution of the angular and speed profile used to evaluate the analytic solution of the contact friction model.

Fig. 3 .Fig. 4 .

 34 Fig.3. Amplification torque obtained to compensate the friction torque with rate of the sensation stimulus n = 1 in steady-state case (dotted) and dynamical one (full line)

Fig. 5 .

 5 Fig.5. Amplification torque obtained to compensate the friction torque with rate of the sensation stimulus n = 0.5 in steady-state case (dotted) and dynamical one (full line)

VI. ACKNOWLEDGEMENTS

This work was partially funded by the project VOLHAND ANR-09-VTT-14.

This work was partially funded by the project VolHand ANR-09-VTT-14. Canudas-de-Wit and Franck Quaine are with the


Bénédicte Jacquemin
email: <benedicte.jacquemin@inserm.fr

Francine Kauffmann

Isabelle Pin

Nicole Le Moual

Jean Bousquet

Frédéric Gormand

Jocelyne Just

Rachel Nadif

Christophe Pison

Daniel Vervloet

Ric Gormand

Val Rie Siroux

B N Dicte Jacquemin

Air pollution and asthma control in the Epidemiological study on the Genetics and Environment of Asthma

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

Both pollutants were associated with each of the three main domains of control.

Conclusions

The results suggest that long-term exposure to PM and O is associated with uncontrolled asthma in adults, defined by symptoms,

Introduction

Asthma control reflects disease activity over a short period of time. Achieving and maintaining the control of asthma is a major goal in asthma management. 1, 2 Acute exposure to air pollution is associated with adverse respiratory effects in asthmatic adults including [ ] increased respiratory symptoms or hospitalizations, or reduced lung function. 3 5 Evidence showing the effects of chronic exposure to air [ -] pollution on asthma incidence in adults is growing. 6 8 However, studies on the effect of chronic exposure to air pollution on asthma [ -] control are scant. In two studies, air pollution exposure was associated with the occurrence of asthma-like symptoms in the last three months and with emergency department visits and/or hospitalizations in the last year. 9, 10 In the first survey of the French

[ ]
Epidemiological study on the Genetics and Environment of Asthma (EGEA), higher exposure to O was associated with more severe 3 asthma in adults 11 .

[ ] Following clinical guidelines, asthma control integrates several dimensions, reflecting both acute and chronic activity of the disease:

daytime and night-time symptoms, the need for rescue treatment, exacerbations in the past year and lung function.

Methods

Study design

EGEA is an asthma case-control and family study (including spouses and 1 degree relatives of the cases), conducted for the first time from all participants at both surveys. Ethical approval to carry out the study was obtained for both surveys from the relevant committees (Cochin Royal Hospital, Paris, for EGEA1; Necker Enfants Malades Hospital, Paris, for EGEA2).

Asthma control

We defined asthma control in this population as previously published

Statistical analysis

First, the association between asthma control and air pollutants was expressed by odds ratios (ORs, reported for one interquartile range (IQR) of the pollutant), derived from multinomial logistic regression. For each factor, the simultaneous assessment of the risk for uncontrolled asthma and for partly-controlled asthma was compared to controlled asthma. Concerning the pollutants for which the proportional odds assumption hypothesis was verified in our data (O and PM ), we used the ordinal logistic regression leading to the estimate of a single odds ratio (OR) that gives the risk to go from controlled to partly controlled asthma and from partly controlled to uncontrolled asthma. Generalized linear mixed models were also conducted in order to take into account the family structure and the city dependence of the population. The model integrates that there is a correlation between the subjects living in the same family (i.e. all members of the family sharing genetic background and/or lifestyle determinants) or between the subjects living in the same city (i.e. all participants living in the same city being exposed to the same background concentrations of air pollution). The effect of the family structure or city dependence are random while the other effects of the model are fixed.

All the associations are first reported crude and then followed by the multivariate analysis, for each pollutant separately. Variables taken into account in the multivariate analysis were those known to be associated with asthma control in EGEA 14 (on-line supplement)

[ ] and another European cohort (ECRHS) 12 . In order to address the independent effect of each pollutant on asthma control, a two-pollutant

[ ]
model was performed, including O and PM . Finally, analyses were also conducted on the three domains of asthma control (lung 3-sum 10 function, symptoms, exacerbations), (on-line supplement). The lack of data on activity limitation in our study did not allow including this domain in the asthma control classification. Analyses were performed with Stata 9.

Results

Of the 481 subjects included in the analysis, 44 , 29 and 26 had controlled, partly-controlled and uncontrolled asthma. Asthma % % % % was more often uncontrolled in women (p 0.04) and in older subjects (p 0.003). Subjects with uncontrolled asthma used more inhaled

= =
corticosteroids (ICS) (p 0.001),. (Table 1) The IQR (defined by the difference between the third and the first quartiles) was 13 (25 38)

=

Table 2 shows the results of the crude and adjusted associations between each of the air pollutants and asthma control. O and PM

3-sum 10

were positively associated with partly-controlled and uncontrolled asthma, with a clear gradient from controlled, partly-controlled and uncontrolled. For these two pollutants, the ORs assessed using the ordinal logistic regression were significant (ORs were In the two-pollutant model, asthma control estimates slightly decreased but remained statistically significant for both air pollutants.

Using the ordinal logistic regression, the crude and adjusted ORs for those two pollutants included simultaneously in a unique model were sex, age, current active and passive smoking exposure, use of ICS in the last 12 months, atopy, season of examination, BMI and age of asthma onset. The results from the sensitivity analysis only including subjects who had been living for at least two years in 2004 at their current address are also shown (thus is subjects who had not moved since 2002). All the estimates were above 1, and most of them were significant. No significant interaction was found but the p-value for interaction was borderline significant for sex and PM (p 0.06), 10 = suggesting that the association could be more significant in men.

The study of the associations between air pollution and each one of the three asthma control domains showed that increased levels of O and PM were associated with a lower FEV1. However, the association reached the significance level only for PM (p 0.002)

3-sum 10 10

=

(table 3). For the exacerbations, the ORs for O and PM were above 1. Higher exposure to both O and PM were positively and 3-sum 10 3-sum 10 significantly associated with higher symptom frequency (p 0.013 and p 0.002).

= =

Discussion

Long-term exposure to O and PM is associated with decreased asthma control in adults. This study is innovative since it shows for 3 10 the first time that long-term exposure to air pollution is associated with uncontrolled asthma.

The associations observed in a large sample of well-characterized adults with current asthma were robust: 1) the associations concern the three domains of asthma control which were studied; 2) the associations were confirmed after adjustment on covariates including sex, age, BMI, smoking and ICS use; 3) the associations remained in a multilevel analysis taking into account the family and the city; 4) the associations were not modified after stratification on several covariates.

Due to the multidimensional approach of the control definition, the results increase the evidence of the combined acute and chronic respiratory effects of air pollution.

A major strength of EGEA is the detailed characterization of subjects with asthma using not only epidemiologically-defined criteria but also extensive clinical characterizations, in a country with homogeneous health care access. Phenotype misclassification is thus unlikely. 17 The detailed EGEA2 questionnaire and examination of the subjects allowed the assessment of asthma control on the basis of

[ ]
the 2006 2009 GINA guidelines. However, EGEA had no information on activity restrictions. The lack of activity data may result in the misclassification of some of the subjects as having controlled asthma , resulting most likely in a loss of power of the effects of air ' '

pollution. In the ECRHSII study, 1032 patients were classified as having current asthma and it was found that activity limitation had an

" "
impact on the asthma control level in 8.7 subjects (unpublished data). Thus, the lack of this dimension in the EGEA data is expected to % impair asthma control classification in a few subjects only. We are aware that the current updated GINA guidelines now include aspects related to future risk, an aspect of importance from a clinical perspective, but difficult to assess clinically and impossible to include in epidemiological studies.

Another strength of our analysis is the robustness and consistency of the findings. For both pollutants (PM and O ), all estimates of 10 3 the stratified analyses by sex, age, smoking, use of ICS, atopy, BMI, season of examination and age of asthma onset were above one and in the same order of magnitude. Furthermore, both pollutants were associated with each of the three domains of asthma control, although the estimates were more stable and significant when using the integrated measure of asthma control. This indicates that results are not driven by one domain.

In the bi-pollutant model, the effect of both pollutants (O and PM ) remains, suggesting that the effect of both pollutants are local conditions, resulting in large and most likely random misclassifications of exposure. This could explain why we do not find any association between NO and asthma control. subjects who had been living for at least two years in the same place as in 2004 were similar, indicating that this issue not to be of major relevance in our study.

Stressful living conditions may confound the observed associations if those correlate both with asthma control and air pollution on the spatial scale used in our analyses. We do not have indicators of stress available, thus, a formal assessment of this concern is not possible.

However, the multilevel analyses took into account city , thus, stressors associated with the city level would have been taken into account.

' '

The estimates were similar with and without control for city.

PM concentrations are quite low in the study. In France, before 2007, PM measurements were underestimated because the volatiles 10 10 particles (such as the ammonium nitrate) were not considered. From 2007 (after the development of our map), the certified air-quality monitoring agencies (AASQA) changed their measurement methods. The difference between the old and the new methods varied from 1.3 to 1.4 fold according to the characteristics of each region. Such scaling of the absolute levels does not affect our estimates of effects.

While there is an extensive literature about the acute effects of exposure to air pollution on different asthma control features, the long term effects of exposure to air pollution on asthma control are unclear. Furthermore, most studies in asthma-air pollution were carried out in children. Hospitalizations or emergency visits for asthma were increased on days with higher air pollution concentrations. 5, 23 Fewer between O and asthma control only in the elderly, and between PM and asthma control only in women. 9 In their second study in 3 10 [ ] adults, O , PM and PM were significantly associated with symptoms but not with emergency department visits or hospitalizations. 9

3 10 2.5 [ ]
Our findings, in which asthma control features were combined with lung function and the use of reliever treatment, are in agreement with these studies.

In our study, the association of PM with asthma control seemed to be stronger in men. The existing literature about the difference of 10 the air pollution effects according to sex is quite inconsistent, even if more studies report greater effects in women. [START_REF] Clougherty | A growing role for gender analysis in air pollution epidemiology[END_REF] As underlined

[ ]
recently, more studies are needed on this aspect to clarify gender differences and assess the role of biological (i.e. men have larger airways allowing larger pollutants such as PM to penetrate deeper), socio-cultural, and exposure assessment factors (i.e. women tend to spend 10 more time at home) which may explain such differences. 26

[ ]
The association between O and PM and asthma control were not modified by smoking, the ICS use, atopy, BMI, age of asthma 3 10 onset and season; although we did observe some non-statistically significant differences in the point estimates for air pollution exposure between some of these groups. Larger studies may assess whether the apparently higher associations with pollution observed in some of these subgroups may be replicated, while we may conjecture about possible reasons for the observed but non-significant differences. In non-smokers exposed to ETS, stronger associations of pollution with asthma control tended to be shown compared to smokers or non-smokers not exposed to ETS. This could be explained by the fact that ETS and air pollution share similar mechanisms of lung damage. 26, 27 In subjects using ICS, there is also a tendency for higher effects of air pollution, possibly reflecting a subgroup with more

[ ]
severe asthma that could be more susceptible to air pollution effects. [START_REF] Sunyer | Effect of nitrogen dioxide and ozone on the risk of dying in patients with severe asthma[END_REF] In contrast to other findings, subjects with higher BMI are not pollution were for cardiovascular outcomes. Estimates were also somewhat stronger among non-atopic subjects, while few studies reported atopic subjects to possibly react stronger to air pollution due to interactions between aeroallergens and pollutants. 30 Estimates were also

[ ]
stronger in subjects with childhood asthma, this would suggest that air pollution affects more asthma control in subject who has been asthmatic for a long time. However, our study design is not tailored to address all these questions. The associations with O seemed to be 3 higher for subjects examined during summer rather than winter. Reporting is most accurately recalled for the conditions during the past few weeks and months, thus, participants during summer provide more accurate data for the spring and summer. Furthermore, the exposure metric is the summer condition (O ), therefore this finding is expected.

3-sum

The use of a composite asthma control classification is novel in air pollution research. Whereas air pollution was measured over one year, asthma control was assessed based on acute or subacute asthma events. In this study, the long-term expression is used as opposed to

" " day-to-day variations in the air pollutants concentrations. The models used to assess air pollution exposure were developed for the year 2004 which is a reasonable estimate of the longer-term average air quality given that the variation of annual means of background air pollutants is rather limited. An interesting question is whether asthma control reflects a summary of the acute effect of air pollution on formally disentangle the chronic from the acute effects of air pollution requires different study designs and estimates of daily levels of air pollution that were not available in our population. Results support an effect of long term exposure to air pollution on asthma control in adulthood in subjects with pre-existing asthma. It remains possible however, that as suggested for occupational asthmogens, environmental insults may also induce directly a more severe form of disease. 33 Increasing evidence suggest that environmental exposures play a role

[ ]
at the various steps of the disease process. However, whether long term exposure to air pollution is at the same time a cause for the development of the underlying chronic asthma pathology is subject to investigations and cannot be addressed with the data used in this analysis.

In summary, our results indicate that both ambient O and PM concentrations jeopardize asthma control in adults. The results are 3 10 robust. The clinically relevant concept of asthma control with its integrated assessment of acute and chronic dimensions of the disease

" "
offers novel ways to quantify and monitor the public health relevance of air pollution among adults with asthma.

What this papers adds

Acute exposure to air pollution is associated with adverse respiratory effects in adults with What is already known on this subject: asthma such as the increase in emergency visits, exacerbations, medication intake, symptoms, etc. However, the effect of long-term exposure to air pollution on asthma control, assessed by combining several domains of control reflecting both acute and chronic respiratory conditions, has never been studied.

Our results suggest a robust association between long-term exposure to O and PM and uncontrolled What does this study add:

  adjusted on sex, age, BMI, education, smoking and use of inhaled corticosteroids. The association between air pollution and the three domains of asthma control (symptoms, exacerbations and lung function) was assessed. Odds Ratios (ORs) are reported per Inter Quartile Range (IQR). Results Median concentrations ( g.m ) were 32(IQR 25 38) for NO (n 465), 46(41 52) for O and 21(18 21) for PM (n 481). In total, 44 , controlled, partly-controlled and uncontrolled asthma. The ordinal ORs for O and PM with asthma control were were not modified by sex, smoking status, use of inhaled corticosteroids, atopy, season of examination or BMI.

st between 1991 and 1995 on 2047 subjects from 5

 5 French cities. This analysis is based on the cross-sectional data of the follow-up study (EGEA2) conducted between 2003 and 2007 on 1571 adults. 15, 16, 17 (Figure 1, on-line supplement) Written consent was obtained [ ]

3 - 2 3

 32 for NO 11 (41 52) g.m for O , 13 (60 73) g.m for O and 3 (18 21) g.m for PM . Annual and summer O correlated (Pearson coefficient r 0.72). NO was strongly negatively correlated with O (r 0.76) and = -an =moderately correlated with PM (r 0.45). O and PM were not correlated (r 0.08), O and PM were weakly correlated (r 0.26).

2 A

 2 limitation of our exposure assignment relates to the use of a model based on measurements taken in 2004 (yearly average) while asthma control data were collected between 2003 2007. However, spatial contrasts of median-range pollutants relevant in our analyses--are unlikely to vary much from one year to another although the absolute concentrations may differ across years. 22 Results among [ ]

  associations between acute exposure to traffic-related air pollution and lung function in asthmatics. 24[ ]To our knowledge, only two studies aimed to address the long term effect of air pollution on some measures of asthma control. In a population based study, living close to high traffic density roads was associated with poorer asthma control, assessed by more than one respiratory symptom per week or at least emergency department visit or hospitalization in the last year. 10 They found an association [ ]

  air pollution in our data. 29 However, most studies showing greater susceptibility of overweight subjects to air [ ]

  it relates to the chronic development and worsening of the disease. As shown in general populations, a single measure of lung function may be affected independently by the level of pollution on the day of the exam and the long-term exposure. 31, 32 To[ ]

3 10 asthma

 310 , defined according to international clinical guidelines and combining three different domains (lung function, symptoms and exacerbations), in a large number of well-characterized current asthmatics from the Epidemiological study on Genetics and Environment of Asthma.

Figure 1 Figure 2

 12 Figure 1Flow chart of the EGEA population included in this analysis

10 3 exacerbations and lung function. Abstract Word count: 250 Key words: air pollution, asthma, asthma control MESH

Keywords Adult ; Air Pollutants ; adverse effects ; analysis ; Asthma ; epidemiology ; etiology ; genetics ; Case-Control Studies ; Cross-Sectional Studies ; Environmental Exposure ; adverse effects ; analysis ; Environmental Monitoring ; Follow-Up Studies ; France ; epidemiology ; Hospitalization ; statistics & numerical data ; Humans ; Logistic Models ; Lung ; physiopathology ; Nitrous Acid ; adverse effects ; analysis ; Ozone ; adverse effects ; analysis ; Residence Characteristics ; Respiratory Tract Diseases ; complications ; epidemiology ; genetics ; Seasons ; Severity of Illness Index

Table 1

 1 Description of health covariates and pollutants, for the total population and then defined by the level of control

	ALL	Controlled	Partly controlled	Uncontrolled

Table 2

 2 Association between an interquartile range of each air pollutant and asthma control. Each line represents a separate single-pollutant model. Odds ratios obtained from multinomial logistic regression comparing controlled versus partly-controlled asthma and uncontrolled versus controlled asthma † Odds ratios obtained from ordinal logistic regression ‡ Odds ratio obtained from generalized linear models taking into account family dependence (level 2) and the ordinal model § Odds ratio obtained from generalized linear models taking into account family dependence (level 2) and city (level 3) and the ordinal model NA not applicable, the ordinal model was not conducted for NO and O due to the characteristics of the estimates derived from the multinomial logistic regression that do not suggest a gradual effect[START_REF]Expert panel report 3: guidelines for the diagnosis and management of asthma[END_REF] 3-an from partly-controlled to uncontrolled asthma || Adjusted for sex, age, body mass index, educational level, smoking and use of inhaled corticosteriods in the last year estimates make reference to estimates with a p<0.05 bold

									Ordinal (taking into		Ordinal (taking into
			Partly controlled		Uncontrolled		Ordinal		account family		account family and
									dependence)		city dependence)
		n OR *	95 CI %	OR *	95 CI %	OR †	95 CI %	OR ‡	95 CI %	OR §	95 CI %
	Crude
	NO 2	465 0.79	(0.59 1.07) -	0.88	(0.64 1.19) -	NA		NA		NA
	O 3-an	481 1.45	(1.07 -1.97)	1.35	(0.98 1.86) -	NA		NA		NA
	O 3-sum	481 1.60	(1.08 -2.36)	2.16	(1.41 -3.30)	1.78	(1.31 -2.41)	1.73	(1.29 -2.31)	1.73	(1.29 -2.31)
	PM 10	481 1.18	(0.95 1.46) -	1.50	(1.19 -1.89)	1.34	(1.13 -1.59)	1.35	(1.13 -1.61)	1.26	(1.04 -1.53)
	Adjusted ||
	NO 2	454 0.84	(0.62 1.15) -	0.99	(0.71 1.40) -	NA		NA		NA
	O 3-an	470 1.33	(0.96 1.84) -	1.19	(0.83 1.70) -	NA		NA		NA
	O 3-sum	470 1.53	(1.01 -2.33)	2.14	(1.34 -3.43)	1.69	(1.22 -2.34)	1.69	(1.21 -2.36)	1.69	(1.22 -2.34)
	PM 10	470 1.16	(0.92 1.46) -	1.60	(1.24 -2.08)	1.36	(1.13 -1.64)	1.40	(1.14 -1.71)	1.33	(1.06

-1.67) *

[START_REF] Cazzoletti | Asthma control in Europe: a real-world evaluation based on an international population-based study[END_REF]

3-sum

[START_REF] Cazzoletti | Asthma control in Europe: a real-world evaluation based on an international population-based study[END_REF]

[START_REF] Cazzoletti | Asthma control in Europe: a real-world evaluation based on an international population-based study[END_REF]

[START_REF] Cazzoletti | Asthma control in Europe: a real-world evaluation based on an international population-based study[END_REF]

[START_REF] Cazzoletti | Asthma control in Europe: a real-world evaluation based on an international population-based study[END_REF]

[START_REF] Cazzoletti | Asthma control in Europe: a real-world evaluation based on an international population-based study[END_REF]

[START_REF] Cazzoletti | Asthma control in Europe: a real-world evaluation based on an international population-based study[END_REF]

Acknowledgements:

The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an Exclusive licence: exclusive licence (or non exclusive for government employees) on a worldwide basis to the BMJ Publishing Group Ltd to permit this article (if accepted) to be published in JECH and any other BMJPGL products and sublicences such use and exploit all subsidiary rights, as set out in our licence (

). http://jech.bmj.com/site/about/licence.pdf

Footnotes:

: None to declare.

Competing Interest

Air pollutants in g.m


PhD Lidwien A M Smit
email: l.a.smit@uu.nl

MD Emmanuelle Bouzigon

MD Jean Bousquet

PhD Nicole Le Moual

PhD Rachel Nadif

MD Isabelle Pin

PhD Mark Lathrop

MD Florence Demenais

MD Francine Kauffmann

PhD Valérie Siroux

Mold allergen sensitization in adult asthma according to integrin β3 polymorphisms and Toll

Keywords: Alternaria, Aspergillus, allergy, asthma, Cladosporium, epidemiology, epistasis, genetics, innate immunity Abbreviations CI: Confidence interval EGEA: Epidemiological study on the Genetics and Environment of Asthma FDR: False discovery rate GEE: Generalized estimating equations ICS: Inhaled corticosteroids ITGB3: Integrin 3 LD: Linkage disequilibrium OR: Odds ratio SNP: Single nucleotide polymorphism SPT: Skin prick test TLR2: Toll-like receptor 2

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

INTRODUCTION

Allergic sensitization to molds such as Alternaria and Cladosporium is a risk factor for asthma, asthma severity, and allergic rhinitis. (1)[START_REF] Randriamanantany | Alternaria sensitization and allergic rhinitis with or without asthma in the French Six Cities Study[END_REF][START_REF] Halonen | Alternaria as a major allergen for asthma in children raised in a desert environment[END_REF] The prevalence of mold sensitization depends strongly on geographic and climatic conditions, [START_REF] Halonen | Alternaria as a major allergen for asthma in children raised in a desert environment[END_REF][START_REF] Bousquet | Geographical variation in the prevalence of positive skin tests to environmental aeroallergens in the European Community Respiratory Health Survey I[END_REF] and exposure to indoor mold allergens has been associated with mold allergy and asthma symptoms in children and adults. [START_REF] Brunekreef | Home dampness and respiratory morbidity in children[END_REF][START_REF] Zock | Housing characteristics, reported mold exposure, and asthma in the European Community Respiratory Health Survey[END_REF][START_REF] Verhoeff | Damp housing and childhood respiratory symptoms: the role of sensitization to dust mites and molds[END_REF][START_REF] Salo | Exposure to Alternaria alternata in US homes is associated with asthma symptoms[END_REF] Besides the influence of the environment, heritable factors were shown to contribute to mold sensitization as well. Concordance for skin prick testing to a mixture of Alternaria allergens was significantly greater among identical twins than for non-identical twins, [START_REF] Karihaloo | Evidence for the genetic control of immunoglobulin E reactivity to the allergens of Alternaria alternata[END_REF] and maternal sensitization to Alternaria alternata significantly increased the risk of matched sensitization in their children. [START_REF] Misiak | Specific allergic sensitization in parents and their 18-year-old offspring in the Suburban Detroit Childhood Allergy Study[END_REF] Only a small number of candidate gene studies investigated the role of specific genetic variants in mold sensitization. [START_REF] Leung | RANTES G-401A polymorphism is associated with allergen sensitization and FEV1 in Chinese children[END_REF][START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF][START_REF] Donfack | Variation in conserved noncoding sequences on chromosome 5q and susceptibility to asthma and atopy[END_REF][START_REF] Carvalho | Polymorphisms in tolllike receptor genes and susceptibility to pulmonary aspergillosis[END_REF] Weiss et al. [START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF] found that single nucleotide polymorphisms (SNPs) in the integrin 3 gene (ITGB3), which is located on chromosome 17q21.32, were associated with asthma and sensitization to mold allergens in Hutterites, a founder population, and in three outbred replication populations, whereas other allergens showed no association. A candidate gene study and a study that used genome-wide genotyping to assess the reproducibility of previously published asthma genes also found associations between ITGB3 SNPs and asthma, but these studies did not investigate mold sensitization as an outcome. [START_REF] Rogers | Assessing the reproducibility of asthma candidate gene associations, using genome-wide data[END_REF][START_REF] Thompson | Integrin beta 3 genotype influences asthma and allergy phenotypes in the first 6 years of life[END_REF] ITGB3 encodes the beta chain of the receptor for a wide array of ligands including vitronectin and fibrinogen. Integrin 3 and its ligands play a key role in cell adhesion, cell proliferation and differentiation, platelet activation, and various other biological processes. [START_REF] Hynes | Integrins: bidirectional, allosteric signaling machines[END_REF] Vitronectin may participate in the remodelling process during lung development or response to injury by downregulating the expression of -smooth muscle actin and reducing the contractile ability of human lung fibroblasts. [START_REF] Scaffidi | Regulation of human lung fibroblast phenotype and function by vitronectin and vitronectin integrins[END_REF] Integrin 3 forms a complex with Toll-like receptor 2 (TLR2), and vitronectin and integrin 3 are required for the response of monocytes to bacterial lipopeptide and other TLR2 agonists such as fungal glucan. [START_REF] Gerold | A Toll-like receptor 2-integrin beta3 complex senses bacterial lipopeptides via vitronectin[END_REF] We therefore hypothesized that variants in genes encoding the TLR2-ITGB3 complex may play a role in susceptibility to asthma and mold sensitization. The present study is the first epidemiological study to address a gene-gene interaction between ITGB3 and TLR2. In adults from the French Epidemiological study on the Genetics and Environment of Asthma (EGEA), the TLR2/+596 (rs3804099) C a l l e l e w a s a s s o c i a t e d w i t h a s t h ma in both case-control and family-based analyses. [START_REF] Smit | CD14 and toll-like receptor gene polymorphisms, country living, and asthma in adults[END_REF] We aimed to study whether TLR2/+596 genotype modified associations between ITGB3 SNPs and asthma and sensitization to mold allergens. In addition, we aimed to confirm associations between ITGB3 SNPs and asthma and mold sensitization.

METHODS

Population

The present analysis uses data from the 12-year follow-up of the EGEA survey. The design and protocol of EGEA, a family study and a case-control study of asthma, have been reported in detail elsewhere. [START_REF] Kauffmann | Epidemiological study of the genetics and environment of asthma, bronchial hyperresponsiveness, and atopy: phenotype issues[END_REF][START_REF] Kauffmann | EGEA (Epidemiological study on the Genetics and Environment of Asthma, bronchial hyperresponsiveness and atopy)--design issues. EGEA Co-operative group[END_REF] Briefly, 2047 subjects were enrolled at baseline (1991-1995): 388 asthma patients (aged 7 to 70 years) from six chest clinics in five French cities, their 1244 first degree relatives, and 415 population-based controls. At follow-up (2003-2007), 92.2% of the alive cohort returned a self-completed questionnaire, and 77.1% completed a detailed questionnaire. [START_REF] Siroux | Phenotypic determinants of uncontrolled asthma[END_REF] At the follow-up survey, all subjects were adults. For the present cross-sectional analysis, we used 1243 subjects (62.8% of the alive cohort) with complete data on asthma, mold sensitization, and genotyping (Figure E1 in the online supplement shows a flowchart). The 1243 subjects with complete data were slightly older, had more often studied at university level, and reported rhinitis more often than the 300 subjects who were excluded due to missing genotype or phenotype (mold sensitization) data (Supplementary Table E1). All participants gave written informed consent.

Health outcomes and exposure variables

Inclusion criteria used to define asthma in probands were based on self-reported answers to the four questions "Have you ever had attacks of breathlessness at rest with wheezing?", "Have you ever had asthma attacks?", "Was this diagnosis confirmed by a physician?", and "Have you had an asthma attack in the last 12 months?", or a positive response to at least two questions and a positive review of their medical record. [START_REF] Kauffmann | Epidemiological study of the genetics and environment of asthma, bronchial hyperresponsiveness, and atopy: phenotype issues[END_REF] Asthma in relatives of probands was defined as a positive answer to at least one of the first two questions. [START_REF] Kauffmann | Epidemiological study of the genetics and environment of asthma, bronchial hyperresponsiveness, and atopy: phenotype issues[END_REF] Atopy was defined by the presence of a positive skin prick test (SPT) (mean wheal diameter 3 mm) to at least one of 11 aeroallergens (Aspergillus, C l a d o s p o r i u m h e r b a r u m , Alternaria t e n u i s ( = a l t e r n a t a ) , cat, Dermatophagoides pteronyssinus, Blattella germanica, olive, birch, Parietaria judaica, timothy grass, and ragweed pollen) using extracts made by Stallergènes (Antony, France). Mold sensitization was defined as a positive SPT to at least one of the 3 mold allergens. Mold species tested in EGEA were the same as in the study by Weiss et al. [START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF] Environmental exposure to molds was assessed by questionnaire using items from the European Community Respiratory Health Survey. [START_REF] Zock | Housing characteristics, reported mold exposure, and asthma in the European Community Respiratory Health Survey[END_REF] A small lake near Montpellier was assumed to be a source of molds, [START_REF] Kauffmann | The protective role of country living on skin prick tests, immunoglobulin E and asthma in adults from the epidemiological study on the genetics and environment of asthma, bronchial hyper-responsiveness and atopy[END_REF] we therefore investigated recruitment in Montpellier as an environmental determinant of mold sensitization.

Genotyping

Fourteen SNPs in ITGB3 (located at chromosome 17q21.32) with a minor allele frequency >5% were selected using a tagging approach. All SNPs were in Hardy-Weinberg equilibrium (P>0.01). Online Figure E2 shows linkage disequilibrium (LD) between SNPs. Genotyping was performed using Taqman Probes (Applied Biosystems, Foster City, CA) on an ABI7900HT Sequence Detection System at the Centre National de Génotypage (CNG, Evry, France).

Data analysis

Analyses using mold sensitization as an outcome were conducted i n s u b j e c t s w i t h a n d w i t h o u t a s t h m a separately, because mold sensitization is strongly associated with asthma, and subjects were recruited through patients with asthma. Determinants of mold sensitization were first explored by using univariate analyses (Chisquare test or t-test). All further analyses were done by generalized estimating equations (GEE model) to account for dependence among subjects sharing the same household. Odds ratios (ORs) and 95% confidence intervals (CIs) were adjusted for age and sex, unless stated otherwise. In the lack of evidence for a recessive or dominant genetic model, the effect of ITGB3 SNPs on health outcomes was tested under an additive genetic model with the minor allele as risk allele. [START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF][START_REF] Rogers | Assessing the reproducibility of asthma candidate gene associations, using genome-wide data[END_REF][START_REF] Thompson | Integrin beta 3 genotype influences asthma and allergy phenotypes in the first 6 years of life[END_REF] To test whether association between ITGB3 SNPs and health outcomes were modified by TLR2/+596 (rs3804099) genotype (TT or CC+CT) we introduced a multiplicative gene-gene interaction term in the GEE model and used a generalized score test which follows a chi-square distribution with 1 degree of freedom. False Discovery Rate (FDR) adjusted P-values were calculated to take multiple comparisons (n=14 SNPs) into account. [START_REF] Benjamini | Controlling the false discovery rate: a practical and powerful approach to multiple testing[END_REF]

RESULTS

Association of mold sensitization and asthma

The present study comprised 524 subjects with asthma and 719 subjects without asthma. Mold sensitization was significantly more prevalent among subjects with asthma (n=115, 22.0%) than in subjects without asthma (n=61, 8.5%), with an adjusted OR (95%CI) of 2.80 (2.03-3.87). Exclusive mold sensitization was rare: only 13 (2.5%) subjects with asthma and 16 (2.2%) subjects without asthma were sensitized to mold without being sensitized to any of the other common allergens. Alternaria, Cladosporium, and Aspergillus sensitization were present in 71 (13.5%), 39 (7.4%), and 29 (5.5%) subjects with asthma and 27 (3.8%), 25 (3.5%), and 22 (3.1%) subjects without asthma, respectively. Atopy (sensitization to any of the 11 allergens tested) was found in 414 (79.0%) subjects with asthma, and in 277 (38.5%) subjects without asthma. Subjects with asthma who were sensitized to mold had more often used corticosteroids in the past year, and tended to have a lower age at the onset of asthma than those who were not sensitized to mold (52.6% vs. 40.1% and 13.1 y vs. 16.1 y, respectively; Table 1).

Determinants of mold sensitization

Table 1 shows determinants of mold sensitization in subjects with and without asthma (univariate analysis). Subjects with asthma who were sensitized to mold were younger, and more likely to be recruited in Montpellier than in the other centers. Among subjects without asthma, those sensitized to mold allergen were more often female, and recruited in Montpellier than those who were not sensitized to mold. Smoking habits and the presence of molds or water damage in the home were not associated with mold sensitization. Multiple regression models that included age, sex, and recruitment in Montpellier showed similar results as the univariate analyses. Recruitment in Montpellier was more strongly associated with sensitization to Alternaria alternata than to other mold allergens (OR 7.99 (3.24-19.66) and OR 4.18 (1.81-9.69), respectively).

Association of ITGB3 SNPs, mold sensitization, asthma and atopy

The ITGB3 rs2056131 A allele was associated with a lower prevalence of mold sensitization in subjects with asthma, with a frequency of 26% in mold sensitized subjects and 37% in subjects not sensitized to mold (OR 0.60 (0.43-0.83); Table 2). The P-value (0.001) was still statistically significant after correction for multiple testing. The same direction of association was shown for subjects without asthma, but the association was not significant (P=0.16). Among subjects with asthma, similar associations with ITGB3 rs2056131 were found for each of the mold allergens: Cladosporium OR 0.49 (0.27-0.89), Aspergillus OR 0.47 (0.25-0.86), and Alternaria OR 0.70 (0.49-1.01). Excluding subjects from Montpellier, or adjusting for recruitment in Montpellier did not change results (OR 0.56 (0.39-0.81) and OR 0.57 (0.41-0.81), respectively). Correction for other potential confounders (educational level, use of corticosteroids, and smoking habits) did also not change results (OR 0.58 (0.37-0.90)). Analysis restricted to 414 atopic subjects also resulted in a similar OR (0.62 (0.45-0.86)). ITGB3 SNPs were not associated with asthma or atopy (P>0.05; Supplementary Table E2 andE3).

Gene-gene interaction between ITGB3 and TLR2

TLR2/+596 CC+CT was associated with asthma at the follow-up survey (OR 1.75 (1.36-2.26); P<0.0001), confirming the earlier reported association among adults at baseline. [START_REF] Smit | CD14 and toll-like receptor gene polymorphisms, country living, and asthma in adults[END_REF] TLR2/+596 CC+CT was not associated with mold sensitization in subjects with asthma (OR 1.13 (0.70-1.83) or subjects without asthma (OR 1.25 (0.70-2.24)). Among subjects with asthma, the associations between ITGB3 SNPs and mold sensitization analyzed according to TLR2/+596 genotype showed statistically significant associations between 11 ITGB3 SNPs and mold sensitization in TLR2/+596TT subjects (P=0.03 to 0.002), whereas much weaker or no associations were found in carriers of the TLR2/+596 C allele (P=0.60 to 0.04). Gene-gene interaction was statistically significant for 10 ITGB3 SNPs (P interaction=0.05 to 0.001), and remained significant for 7 SNPs after adjusting for multiple comparisons (Table 3). Excluding subjects from Montpellier or adjusting for recruitment did not change these findings. The LD pattern (online Figure E2) shows that the SNPs involved in the interaction belong to different haplotype blocks. When a forward stepwise regression was applied in TLR2/+596TT subjects, two ITGB3 SNPs that were not in LD (r 2 =0.00) entered the model with P<0.05, suggesting that they were both independently associated with mold sensitization (rs15908 (V381V) and rs11079772 (3'UTR)). Both gene-gene interaction terms were statistically significant in a multiple regression model (rs15908 x TLR2/+596, p=0.02; rs11079772 x TLR2/+596, p=0.006; Figure 1). Among subjects without asthma, association between ITGB3 SNPs and mold sensitization was not modified by TLR2/+596 (P interaction>0.05; Supplementary Table E4). Furthermore, TLR2/+596 did also not modify associations between ITGB3 SNPs and asthma (P interaction>0.05; Supplementary Table E5) or atopy (P interaction>0.05; data not shown).

DISCUSSION

In the present study, we found significant associations between ITGB3 SNPs and mold sensitization among adults with asthma, which were confined to carriers of the TLR2/+596TT genotype. Our findings suggest a gene-gene interaction between ITGB3 a n d TLR2/+596 in mold allergen sensitization. These results are consistent with the biological interaction between integrin 3 and TLR2 that was recently demonstrated, suggesting an important role of the integrin 3-TLR2 complex in the innate immune response to fungal agents. [START_REF] Gerold | A Toll-like receptor 2-integrin beta3 complex senses bacterial lipopeptides via vitronectin[END_REF] Testing associations of multiple ITGB3 SNPs and three phenotypes may have resulted in chance findings, which is a limitation of our study. However, our finding of epistasis between ITGB3 and TLR2 was still significant for seven ITGB3 SNPs after correction for multiple testing. Another limitation is that skin tests were performed with mold extracts which were not fully standardized and some subjects with mold allergy may have been missed. The allergen extracts were however of similar quality as those tested by Weiss et al. [START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF] T h e biochemistry of mold allergens is still poorly understood, and the concordance between skin prick test (SPT) and specific serum IgE results for individual molds is much lower than for non-fungal allergens. [START_REF] O'driscoll | Comparison of skin prick tests with specific serum immunoglobulin E in the diagnosis of fungal sensitization in patients with severe asthma[END_REF] Interestingly, TLR2/+596 T/C did not modify associations between ITGB3 SNPs and asthma or atopy, suggesting that the gene-gene interaction between TLR2 and ITGB3 may be specific for the response to molds. Weiss et al. also found associations between ITGB3 SNPs and allergic sensitization to molds, but not to other common allergens. [START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF] It is not clear whether our results concern one or more specific mold species, or rather mold allergens in general. We found similar risk estimates for the association between ITGB3 rs2056131 and each of the three molds studied, but there was insufficient statistical power to study the interaction between TLR2 and ITGB3 for allergic sensitization to each of the three individual mold species. Multiple regression analysis showed that at least two ITGB3 SNPs, rs15908 (V381V) and rs11079772, were independently involved in the interaction with TLR2. Rs2015729, a noncoding ITGB3 SNP in high LD with rs15908, was previously associated with decreased ITGB3 expression levels, which may provide a potential mechanism by which noncoding ITGB3 variants have a functional effect. [START_REF] Weiss | ITGB3 shows genetic and expression interaction with SLC6A4[END_REF] Another functional ITGB3 SNP (rs5918, Leu33Pro) has been associated with various effects, including enhanced thrombin formation, [START_REF] Undas | Pl(A2) polymorphism of beta(3) integrins is associated with enhanced thrombin generation and impaired antithrombotic action of aspirin at the site of microvascular injury[END_REF] coronary heart disease, [START_REF] Rossouw | Inflammatory, lipid, thrombotic, and genetic markers of coronary heart disease risk in the women's health initiative trials of hormone therapy[END_REF] and cancer susceptibility. [START_REF] Bojesen | Integrin beta3 Leu33Pro homozygosity and risk of cancer[END_REF] ITGB3 Leu33Pro was not genotyped in the present study, but it was in LD (r 2 =0.76) with rs10514919, a SNP that showed a significant interaction with TLR2 (P=0.05). Besides main effects of ITGB3 variants on various clinical outcomes, three studies have presented evidence for epistasis between ITGB3 and the serotonin transporter gene SLC6A4 in autism susceptibility [START_REF] Weiss | ITGB3 shows genetic and expression interaction with SLC6A4[END_REF][START_REF] Coutinho | Evidence for epistasis between SLC6A4 and ITGB3 in autism etiology and in the determination of platelet serotonin levels[END_REF][START_REF] Ma | Association and gene-gene interaction of SLC6A4 and ITGB3 in autism[END_REF] and in serotonin levels. [START_REF] Coutinho | Evidence for epistasis between SLC6A4 and ITGB3 in autism etiology and in the determination of platelet serotonin levels[END_REF] Altogether, these findings suggest that multiple functional ITGB3 SNPs may have different pleiotropic effects, possibly in interaction with other genes. We can only speculate on the mechanism by which the effect of ITGB3 SNPs on mold sensitization is modified by TLR2/+596. A recent study has shown that peripheral blood leukocytes of TLR2/+596 TT subjects produce significantly less cytokines in response to bacterial lipoprotein stimulation than those of TLR2/+596 CT and CC subjects. [START_REF] Chen | Identification of haplotype tag SNPs within the entire TLR2 gene and their clinical relevance in patients with major trauma[END_REF] Moreover, TLR2/+596 TT was the only TLR2 variant associated with a lower sepsis morbidity rate. [START_REF] Chen | Identification of haplotype tag SNPs within the entire TLR2 gene and their clinical relevance in patients with major trauma[END_REF] The TLR2/+596 C allele was associated with asthma in both case-control and family-based analyses among EGEA adults, which is consistent with a functional role of TLR2/+596. [START_REF] Smit | CD14 and toll-like receptor gene polymorphisms, country living, and asthma in adults[END_REF] However, the exact functional significance of TLR2/+596 is so far unknown. A possible explanation could be a different expression of TLR2 on the surface of innate immune cells among subjects carrying the TT genotype compared with subjects carrying the C allele. In subjects with certain functional ITGB3 SNPs, a modified TLR2 expression may potentially result in a decreased function of the ITGB3-TLR2 complex. Finally, it can be hypothesized that this altered function could lead to a less effective response to fungal agents resulting in an increased risk of mold sensitization. We did not replicate associations between ITGB3 variants and asthma. [START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF][START_REF] Rogers | Assessing the reproducibility of asthma candidate gene associations, using genome-wide data[END_REF] In a recent study that used genomewide genotyping to assess reproducibility of SNPs in 39 previously reported asthma genes, only 10 SNPs in 6 genes were significantly associated with childhood asthma, including one SNP in ITGB3, which was not included in the present study. [START_REF] Rogers | Assessing the reproducibility of asthma candidate gene associations, using genome-wide data[END_REF] Our study had sufficient statistical power (80%) to detect a relative risk (RR) between 1.32 and 1.40 for the association between ITGB3 SNPs and asthma, and a RR between 1.66 and 1.82 for the association between ITGB3 SNPs and mold sensitization in asthmatics, depending on disease allele frequency (varying between 0.19 and 0.40), and using the conservative Bonferroni correction for multiple comparisons. These RR seem reasonable and suggest that the lack of association cannot be attributed to a lack of power in our study. Replicating asthma susceptibility genes is a major challenge, and failure to replicate may be caused by heterogeneity between studies. Replicating interactions appears even more complicated. [START_REF] Ober | Gene-environment interactions in human disease: nuisance or opportunity?[END_REF][START_REF] Ege | Gene-environment interaction for childhood asthma and exposure to farming in Central Europe[END_REF] Findings of our epidemiological study were analogous to a previously reported biological interaction between integrin 3 and TLR2. [START_REF] Gerold | A Toll-like receptor 2-integrin beta3 complex senses bacterial lipopeptides via vitronectin[END_REF] In addition, we have attempted to replicate our findings in the population of adult Hutterites. [START_REF] Weiss | Variation in ITGB3 is associated with asthma and sensitization to mold allergen in four populations[END_REF] However, in that population only 93 subjects carried TLR2/+596 TT, and only 42 subjects were sensitized to mold (Dr. C. Ober, personal communication). Thus, there was no sufficient power to study interactions in this population. Moreover, Hutterites in general have a mild form of asthma, with corticosteroid use being quite rare. Other populations that were considered had not assessed sensitization to (the same) mold allergens. Variation between studies in asthma definition, age at onset, ethnicity, and other characteristics of the study population may reduce reproducibility. Furthermore, the influence of environmental exposures may also obscure genetic associations. For example, consistent associations between CD14/-260 and asthma or allergic sensitization were observed only after taking environmental endotoxin levels into account. [START_REF] Simpson | The role of lipopolysaccharide in the development of atopy in humans[END_REF] The present study would have benefited from measured fungal allergen and/or glucan levels in settled house dust. Due to the lack of objectively assessed environmental exposure, we cannot exclude the possibility that gene-environment interactions play an additional role in association of ITGB3 and asthma or mold sensitization. In the present study we found an expected higher prevalence of mold sensitization in subjects recruited in Montpellier, where environmental exposure to mold was elevated. [START_REF] Kauffmann | The protective role of country living on skin prick tests, immunoglobulin E and asthma in adults from the epidemiological study on the genetics and environment of asthma, bronchial hyper-responsiveness and atopy[END_REF] However, excluding subjects from Montpellier, or adjusting for recruitment did not affect the results. In US homes, Alternaria antigen concentrations were higher in homes where either residents or field workers observed signs of mold or dampness, [START_REF] Salo | Dustborne Alternaria alternata antigens in US homes: results from the National Survey of Lead and Allergens in Housing[END_REF] and exposure to Alternaria was associated with asthma symptoms. [START_REF] Salo | Exposure to Alternaria alternata in US homes is associated with asthma symptoms[END_REF] We also investigated water damage and visible mold in the home as selfreported mold exposures, but these were not associated with mold sensitization. We did not study severity of asthma as another phenotype, although mold sensitization is known to be associated with a more severe asthma phenotype. (1) In adult asthma patients from EGEA who did not use inhaled corticosteroids (ICS), mold sensitization was significantly associated with an increased risk for uncontrolled asthma (OR, 95% CI of 3.15, 1.02-9.78), but not for partly controlled asthma. [START_REF] Siroux | Phenotypic determinants of uncontrolled asthma[END_REF] However, mold sensitization was not associated with an increased risk for uncontrolled asthma in ICS users. [START_REF] Siroux | Phenotypic determinants of uncontrolled asthma[END_REF] The number of subjects did not allow further stratification for ICS use, or stratification for multiple levels of asthma control or asthma severity, and therefore we decided not to study associations between uncontrolled asthma or asthma severity and ITGB3 genotype in the present study. In conclusion, our epidemiological study suggests that genetic variants in ITGB3 and TLR2 interact to increase susceptibility to mold sensitization among subjects with asthma. Following an experimental study that demonstrated the essential role of integrin 3 in TLR2 signaling, [START_REF] Gerold | A Toll-like receptor 2-integrin beta3 complex senses bacterial lipopeptides via vitronectin[END_REF] our population study was the first to show this specific gene-gene interaction, which may influence the demonstrated biological interactions. Future studies need to replicate these findings, and functional experiments are needed to assess the mechanism by which ITGB3 and TLR2 SNPs influence susceptibility to mold sensitization.

Table 1 .

 1 Asthma characteristics and determinants of mold sensitization in 524 adults with asthma and 719 adults without asthma.

			Subjects with asthma			Subjects without asthma
		Data				Data
		available for n	Mold SPT-	Mold SPT+	P	available for n	Mold SPT-	Mold SPT+	P
		subjects				subjects
	N	524	409	115		719	658	61
	Sex, n (%) men	524	212 (51.8)	65 (56.5)	0.37	719	312 (47.4)	20 (32.8)	0.03
	Age (y), mean ± sd	524	39.9 ± 16.8	36.3 ± 16.5	0.04	719	46.5 ± 16.3	43.4 ± 16.2	0.16
	Status at inclusion	524			0.06	719			0.57
	Probands, n (%)		188 (46.0)	68 (59.1)			0 (0)	0 (0)
	Relatives, n (%)		182 (44.5)	39 (33.9)			383 (58.2)	39 (63.9)
	Spouses, n (%)		4 (1.0)	2 (1.7)			67 (10.2)	4 (6.6)
	Controls, n (%)		35 (8.6)	6 (5.2)			208 (31.6)	18 (29.5)
	Recruited in Montpellier, n (%)	524	19 (4.7)	18 (15.7)	<0.0001	719	33 (5.0)	10 (16.4)	0.0003
	Smoking habits	519			0.70	711			0.45
	Never, n (%)		204 (50.4)	58 (50.9)			339 (52.1)	32 (52.5)
	Former, n (%)		106 (26.2)	26 (22.8)			166 (25.5)	19 (31.2)
	Current, n (%)		95 (23.5)	30 (26.3)			146 (22.4)	10 (16.4)
	Education at university level, n (%)	518	197 (48.8)	63 (55.3)	0.22	710	304 (46.7)	39 (66.1)	0.004
	Living in a rural commune before 16y, n (%)	511	156 (39.0)	39 (35.1)	0.46	696	238 (37.3)	15 (26.3)	0.10
	Water damage last year, n (%)	429	38 (11.3)	12 (12.9)	0.67	590	59 (11.0)	9 (17.7)	0.15
	Mold in any surface inside the home last year, n (%)	457	72 (20.1)	17 (17.4)	0.55	619	100 (17.6)	9 (17.3)	0.95
	Asthma onset (y), mean ± sd	492	16.1 ± 15.7	13.1 ± 14.2	0.07	--	--	--	--
	FEV1 % predicted, mean ± sd	523	92.5 ± 17.4	91.5 ± 18.8	0.60	--	--	--	--
	Inhaled corticosteroids in the past 12 months, n (%)	520	163 (40.1)	60 (52.6)	0.02	--	--	--	--
	Active asthma * , n (%)	522	275 (67.6)	87 (75.6)	0.10
	* Active asthma: asthma attack or asthma treatment in the past 12 months
	--Data only shown for subjects with asthma

Table 2 .

 2 Association of ITGB3 SNPs with mold sensitization under an additive model in 524 adults with asthma and 719 adults without asthma. FDR-corrected P<0.05; † Major/Minor allele; MAF, minor allele frequency.

	Subjects with asthma	Subjects without asthma

*

Table 3 .

 3 Association of ITGB3 SNPs with mold sensitization under an additive model in adults with asthma, according to TLR2/+596 genotype.

				Carriers of			Carriers of
				TLR2/+596 TT (n=126)	TLR2/+596 CT or CC (n=362)
			Minor allele in	Minor allele in		Minor allele in	Minor allele in
	ITGB3 SNP	Alleles †	mold SPT-	mold SPT+	OR (95% CI)	mold SPT-	mold SPT+	OR (95% CI)	P interaction
			subjects, n (%)	subjects, n (%)		subjects, n (%)	subjects, n (%)
	rs2317385	G/A	37 (19)	11 (21)	1.19 (0.58-2.43)	101 (18)	34 (21)	1.24 (0.79-1.97)	0.91
	rs2056131	G/A	82 (41)	10 (19)	0.36 (0.18-0.72)	202 (36)	46 (29)	0.70 (0.47-1.03)	0.09
	rs4525555	C/T	54 (27)	23 (44)	1.94 (1.04-3.63)	185 (33)	47 (30)	0.89 (0.61-1.30)	0.04
	rs3892084	G/A	32 (16)	10 (19)	1.17 (0.54-2.55)	111 (20)	31 (19)	1.01 (0.65-1.55)	0.75
	rs10514919	G/T	44 (22)	19 (37)	1.89 (1.05-3.40)	145 (26)	36 (23)	0.83 (0.52-1.33)	0.05
	rs8074094	T/C	47 (24)	21 (40)	2.08 (1.16-3.73)	158 (28)	40 (25)	0.85 (0.55-1.32)	0.02*
	rs3851806	G/C	33 (17)	11 (21)	1.29 (0.63-2.62)	105 (19)	30 (19)	0.99 (0.63-1.56)	0.55
	rs2015729	G/A	66 (33)	30 (58)	2.79 (1.46-5.33)	231 (41)	61 (38)	0.91 (0.63-1.31)	0.003*
	rs2292699	C/T	62 (31)	28 (54)	2.43 (1.28-4.62)	218 (39)	57 (36)	0.90 (0.62-1.31)	0.009*
	rs15908	A/C	62 (31)	26 (54)	2.42 (1.24-4.70)	219 (39)	57 (36)	0.89 (0.61-1.29)	0.01*
	rs2292863	C/G	53 (27)	22 (42)	1.85 (1.03-3.33)	175 (31)	44 (28)	0.83 (0.54-1.27)	0.04
	rs3809863	C/T	103 (52)	15 (29)	0.37 (0.18-0.77)	252 (45)	86 (54)	1.38 (0.96-1.99)	0.001*
	rs11650072	C/T	61 (31)	27 (52)	2.38 (1.29-4.38)	201 (36)	42 (27)	0.65 (0.43-0.99)	0.001*
	rs11079772	A/C	53 (27)	22 (42)	1.89 (1.06-3.34)	174 (31)	39 (24)	0.72 (0.47-1.11)	0.01*

* FDR-corrected P<0.05. † Major/Minor allele

Acknowledgements

We thank Dr. Carole Ober and Dr. Emma Thompson for their helpful comments.

EGEA cooperative group

Coordination: F Kauffmann; F Demenais (genetics); I Pin (clinical aspects). Respiratory epidemiology: Inserm U 700, Paris M Korobaeff (Egea1), F Neukirch (Egea1); Inserm U 707, Paris: I Annesi-Maesano; Inserm CESP/U 1018, Villejuif: F Kauffmann, N Le Moual, R Nadif, MP Oryszczyn; Inserm U 823, Grenoble: V Siroux Genetics: Inserm U 393, Paris: J Feingold; Inserm U 946, Paris: E Bouzigon, F Demenais, MH Dizier; CNG, Evry: I Gut , M Lathrop. Clinical centers: Grenoble: I Pin, C Pison; Lyon: D Ecochard (Egea1), F Gormand, Y Pacheco; Marseille: D Charpin (Egea1), D Vervloet; Montpellier: J Bousquet; Paris Cochin: A Lockhart (Egea1), R Matran (now in Lille); Paris Necker: E Paty, P Scheinmann; Paris-Trousseau: A Grimfeld, J Just. Data and quality management: Inserm ex-U155 (Egea1), Paris: J Hochez; Inserm CESP/U 1018, Villejuif: N Le Moual, Inserm ex-U780, Villejuif: C Ravault; Inserm ex-U794, Evry: N Chateigner; Grenoble: J Ferran.

Supported by the French Ministry of Higher Education and Research, University Paris Diderot-Paris 7, grants from the French Agency for Environmental and Occupational Health Safety (grant AFSSET-APR-SE-2004), the French National Agency for Research (grants ANR 05-SEST-020-02/05-9-97 and ANR 06-CEBS), Merck Sharp & Dohme (MSD), Hospital program of clinical research (PHRC)-Paris, and by the Netherlands Organisation for Scientific Research (NWO) Van Gogh Programme for French-Dutch cooperation. Lidwien Smit was supported by a European Academy of Allergology and Clinical Immunology-Global Allergy and Asthma European Network (EAACI-GA 2 LEN) exchange fellowship award.


Valentina Ciarla

Violaine Cahouet

Carlos Canudas De Wit

Franck Quaine

Notes on the analytic solution for the Dahl's friction model

Notes on the analytic solution for the Dahl's friction model

V. Ciarla, V. Cahouet, C. Canudas de Wit and F. Quaine Abstract-This document provides the analytical solution of the friction model for different changes in the sign of the vehicle speed, as shown in the paper "Genesis of booster curves in Electric Power Assistance Steering Systems" by the same authors. It is not intended to be self contained; it is only an additional note.

I. APPENDIX

The load torque τ a is described by the Dahl's model and is given by the following differential equation:

dF dθ = σ 0 1 - F F c sgn θ (1)
Let make the hypothesis to have a positive speed signal during the time interval t ∈ [0,t 1 ]. At the time t = 0, we have the corresponding value for the angle θ (0) = θ 0 . This hypothesis implies that we have sgn θ = +1 in Eq. ( 1) for θ ∈ [θ 0 , θ ]. We make also the hypothesis to start from null initial conditions, this implies that we need to solve the following differential equation:

dF dθ = σ 0 1 - F F c (2)
with the following initial condition:

F(θ 0 ) = 0 (3)
We divide both terms of Eq. ( 2) by 1 -F F c and F c , in order to obtain a suited primitive:

-1 F c dF dθ 1 -F F c = - σ 0 F c (4)
To obtain the analytic solution of Eq. ( 4) for positive speeds, we integrate both terms during the interval (θ 0 , θ (t)):

θ (t) θ 0 -1 F c dF dθ 1 -F F c dθ = - σ 0 F c θ (t) θ 0 dθ (5)
The result of this integral is: valentina.ciarla@gipsa-lab.grenoble-inp.fr, carlos.canudas-de-wit@gipsa-lab.grenoble-inp.fr, franck.quaine@gipsa-lab.grenoble-inp.fr, violaine.cahouet@gipsa-lab.grenoble-inp.fr)

ln 1 - F(θ (t)) F c -ln 1 - F(θ 0 ) F c = - σ 0 F c (θ (t) -θ 0 ) (6)
By substituting the initial condition (3), it is easily to obtain the solution for positive speeds:

F(θ (t)) = F c 1 -e -σ 0 Fc (θ (t)-θ 0 ) (7)
At the time instant t = t 1 , the speed changes in sign and becomes negative (sgn θ = -1 in Eq. ( 1)) during the time

interval t ∈ [t 1 ,t 2 ].
To guarantee the continuity of the function, we require that the initial condition corresponds to the last values assumed from F(θ (t)) during the interval t ∈ [0,t 1 ],

i.e. F(θ (t - 1 )) = F(θ (t + 1 )). Under these hypothesis, the new Cauchy problem to solve is:

dF dθ = σ 0 1 + F F c (8) F(θ (t - 1 )) = F(θ (t + 1 )) (9)
To solve this problem, we proceed as for Eqs. ( 4) and ( 5), then we integrate between θ (t 1 ) and θ (t), as follows:

θ (t) θ (t 1 ) 1 F c dF dθ 1 + F F c dθ = θ (t) θ (t 1 ) σ 0 F c dθ (10)
The solution of this integral is:

ln 1 + F(θ (t)) F c -k 1 = σ 0 F c (θ (t) -θ (t 1 )) (11)
Where k 1 is a constant, depending from the initial conditions. By inverting this equation, we obtain:

F(θ (t)) = F c -1 + e σ 0 Fc (θ (t)-θ (t 1 )) • e k 1 (12)
To determine the constant k 1 , we introduce the initial condition F(θ (t - 1 )) = F(θ (t + 1 )):

F(θ (t - 1 )) = F c 1 -e -σ 0 Fc θ (t 1 ) (13) F(θ (t + 1 )) = F c -1 + e σ 0 Fc (θ (t 1 )-θ (t 1 )) • e k 1 ( 14
)
It follows:

F c 1 -e -σ 0 Fc θ (t 1 ) = F c -1 + e k 1 ( 15
)
By solving for k 1 , we obtain:

k 1 = ln 2 -e -σ 0 Fc θ (t 1 ) (16)
So the solution for negative speeds is:

F(θ (t)) = F c   -1 + e σ 0 Fc (θ (t)-θ (t 1 )) • e ln 2-e - σ 0 Fc θ (t 1 )   (17)
By rearranging all terms, this expression can be simplified as follows:

F(θ (t)) = F c -1 + 2e σ 0 Fc (θ (t)-θ (t 1 )) -e σ 0 Fc (θ (t)-2θ (t 1 )) (18)
If we make the hypothesis that the speed changes in sign and becomes positive during the time interval t ∈ [t 2 ,t f ], we can find the analytic solution F(θ ) for this last interval, by repeating the same steps as for the previous cases. In this case, the boundary condition is

F(θ (t - 2 )) = F(θ (t + 2
)), so we need to solve:

dF dθ = σ 0 1 - F F c (19) F(θ (t - 2 )) = F(θ (t + 2 )) (20)
We proceed as in the previous cases and we integrate the primitive between [θ 2 , θ (t)]:

θ (t) θ 2 -1 F c dF dθ 1 -F F c dθ = - σ 0 F c θ (t) θ 2 dθ (21)
We obtain the following analytic solution:

F(θ (t)) = F c 1 -e -σ 0 Fc (θ (t)-θ (t 2 )) • e k 2 (22)
We can determine the constant k 2 by introducing the boundary condition

F(θ (t - 2 )) = F(θ (t + 2 )): F(θ (t - 2 )) = F c -1 + 2e σ 0 Fc (θ (t 2 )-θ (t 1 )) -e σ 0 Fc (θ (t 2 )-2θ (t 1 )) (23) F(θ (t + 2 )) = F c 1 -e -σ 0 Fc (θ (t 2 )-θ (t 2 )) • e k 2 (24)
It follows:

F c 1 -e k 2 = F c -1 + 2e σ 0 Fc (θ (t 2 )-θ (t 1 )) -e σ 0
Fc (θ (t 2 )-2θ (t 1 ))

(25) From Eq. ( 25) we get the following expression for the constant k 2 :

k 2 = ln 2 -2e -σ 0 Fc (θ (t 2 )-θ (t 1 )) + e σ 0
Fc (θ (t 2 )-2θ (t 1 ))

(26)

If we substitute Eq. ( 26) in Eq. ( 22) and we simplify, we get the solution for the friction torque when the speed is positive and the initial condition is different from zero:

F(θ (t)) = F c 1 -2e -σ 0 Fc (θ (t)-θ (t 2 )) + 2e -σ 0 Fc (θ (t)+θ (t 1 )-2θ (t 2 )) -e -σ 0 Fc (θ (t)+2θ (t 1 )-2θ (t 2 ))

II. ACKNOWLEDGEMENTS This work was partially funded by the project VOLHAND ANR-09-VTT-14.