Patrice Castignolles
email: p.castignolles@uws.edu.au

Marianne Gaborieau

Viscosimetric detection in size-exclusion chromatography (SEC/GPC): the Goldwasser method and beyond

Keywords: Goldwasser method, hydrodynamic volume, molecular weight, size-exclusion chromatography

HAL is

Introduction

Separation of polymers is particularly challenging. A polymeric sample contains at least hundreds of molecules differing by their molecular weight (and also possibly by their topology, copolymer composition, etc.). Size-exclusion chromatography (SEC, also known as GPC) is the most widely used method to separate and characterize polymers. [START_REF] Striegel | Modern Size Exclusion Chromatography[END_REF] SEC however does not separate according to molecular weight, but according to hydrodynamic volume. [START_REF] Grubisic | [END_REF][3][4] To determine molecular weights, the most common method is using a single detector (concentration-sensitive), a calibration curve and the Mark-Houwink-Sakurada relation to relate the hydrodynamic volume of the analyte to that of the standards. [5] This method is however misleading since the error on the determined molecular weight strongly depends on the molecular weight itself and artefacts can appear. [6] Furthermore, the Mark-Houwink-Sakurada relation is not valid for low molecular weights or high molecular weights or branched polymers [7]. Method development in SEC has been devoted mostly to detection in the last 30 years. One breakthrough was the development of reliable viscometers that can be used as online detectors for SEC. [8][9][10] Viscometers allow determining the product of the intrinsic viscosity and the concentration. They are used in the literature in conjunction with a concentration-sensitive detector, typically a differential refractive index detector. There are however a number of limitations. A general limitation is that the difference in sensitivity of the detectors can lead to some artefacts where the signal-to-noise is too weak on one of the detectors. [11] A specific limitation is that a number of important polymers have a refractive index close to the one of common eluents. Poly(N-vinyl pyrrolidone) is a polymer used in pharmacy and many other fields. [12] Its SEC is best performed in N,N-dimethyl acetamide (DMAc). [13] The use of tetrahydrofuran (THF) as eluent is precluded by poly(N-vinyl pyrrolidone)'s iso-refracticity in this eluent, even though THF would be advantageous in terms of prize and safety compared to DMAc. Polysaccharides are commonly analysed in aqueous eluents, but their solubility is then generally not repeatable, such as in the case of starch. [14][15] Polar organic solvents have thus been used for SEC separations especially dimethyl sulfoxide (DMSO) [16] and DMAc [17]. These solvents allow to obtain highly repeatable separations. [18] However, the signal-to-noise ratio is low since the difference in refractive index of polysaccharides and DMSO or DMAc is low. Polysaccharides do not absorb in UV in these polar organic solvents. Labelling is possible, [18][19] but this additional step is generally not used. Low signal-to-noise ratio as obtained with the refractive index detector are however not desirable, since it can lead to important artefacts in the determination of molecular weight by multiple-detection SEC. [11,20] Finally, industrial polymers are generally copolymers so that they can combine different properties. A gradient in composition is however often leading to changes in specific refractive index increment dn/dc across the chromatogram. The refractive index detection is thus generally tedious or misleading to use for statistical copolymers, [21] which are industrial ones but are also natural polymers such as galactomannans [22] or chitosan [23].

Goldwasser proposed to use the viscometer as a single detector. [24][START_REF] Goldwasser | Proceedings of the International GPC symposium Waters[END_REF] Using the universal calibration curve and the viscosity detector, he showed that the number-average molecular weight, Mn, can be determined. Mn is one of the most important quantities determined using SEC for example for macromolecular engineering (controlled and living polymerization) [6]. This method is applicable to isorefractive polymers or copolymers.

Alternative methods to determine Mn are also of high interest since Mn appears to be the quantity determined in SEC with the lowest accuracy. [START_REF] Berek | IUPAC congress/ general assembly[END_REF][START_REF] Bruessau | [END_REF] The Goldwasser method has however attracted little attention. It was successfully tested on model polymer blends [28], poly(tetramethylene glycol)s [29] and branched polystyrenes [30]. In the polyglycols case, the Goldwasser method however suffered from a lower precision and some bias toward high values of Mn compared to SEC with conventional calibration or end-group detection. The first aim of the present work is thus to test the limits of the Goldwasser method. Second, we will study the applicability of the method to the determination of hydrodynamic volume distributions. Determination of molecular weight distributions by SEC can be plagued by a very low accuracy in the case of statistically branched polymers such as polyacrylates. [7,31] We thus proposed to use hydrodynamic volume distributions to characterize branched glucans [32] or copolymers. [33] Considering the derivation of detector signals, [34] the Goldwasser method can also be used to determine the number hydrodynamic volume distribution. This feature can significantly increase the potential of Goldwasser method and is tested in this work.

Materials and methods

The SEC equipment and the materials (eluents, standards) have been previously described in details in reference [20] and also its supporting information. The system consists of a Triple Detector Array (TDA, Viscotek) fitted with Polymer Laboratories columns and operated at 1 mL•min -1 in THF. The recovery is quantitative and the validity of universal calibration has been tested with this system including for low molecular weights. The polystyrene standards ranging from 162 to 257,000 g•mol -1 (molecular weight at peak maximum, Mp) were obtained from PSS (Mainz, Germany), polystyrene standards ranging from 2,790 to 3,800,000 g•mol -1 (Mp) from Viscotek (Orsay, France). All these standards have been used to obtain the universal calibration curves presented in [20]. Some of these standards have been used to test the Goldwasser method, when their injection concentration was accurately known (see Supporting Information). The poly(methyl methacrylate) standards were obtained from Polymer Expert (Bordeaux, France). The injection loop has been carefully calibrated (volume 53.6 L).

We are going to re-derive Goldwasser's equations in a more general way, taking band broadening into account [28,35] including possible heterogeneity due to branching or copolymer composition and following the formalism we recently proposed. [34] One of the definitions of the Mn is: [START_REF] Flory | Principles of Polymer Chemistry[END_REF]

Mn = ( ) ( ) ( ) ( )             0 el h el 0 0 el 0 h el 0 0 d d d , ' , ' d d d , ' , ' t V M V M N V t G t V M V M W V t G h h h h (1)
where tel is the elution time, M is the molecular weight, G'(tel, M) is the band-broadening function due to axial dispersion, W'(M, Vh) is the weight distribution of molecular weights M and hydrodynamic volumes Vh, N'(M, Vh) is the number distribution of molecular weights M and hydrodynamic volumes Vh. When the apparent recovery is quantitative:

( ) ( ) el 0 h h h el 0 0 d d d , ' , ' t V M V M W V t G       = Cinj×Vinj ( 2
)
where Cinj is the injection concentration and Vinj is the injection volume.

Band-broadening leads to the determination of a number-average hydrodynamic volume at each elution time. [35] The definition of the number-average hydrodynamic volume is: [34] Vh,n

' (tel) = h 0 h 0 h 0 h h 0 d d ) , ( ' ) , ( ' d d ) , ( ' ) , ( ' V M V M N V t G V M V M N V V t G h el h el         (3)
Combining equations (1) to (3) yields:

Mn = ( ) el el n h h h h h el nj i inj t d t V V d M d V M N V V t G V C ) ( ) , ( ' , ' ' , 0 0 0        (4)
Using the definition of hydrodynamic volume in equation ( 5), [32] Mn can be expressed as equation ( 6):

Vh = A h N M V M 5 . 2 )] , ( ' [ (5)
where ['(M,Vh)] is the intrinsic viscosity of a chain with molecular weight M and hydrodynamic volume Vh, and NA is Avogadro's number.

Mn = ( ) el el ' n h, 0 h h h h el 0 0 A inj inj d ) ( d d ) , ( ' )] , ( ' [ , ' 5 . 2 1 t t V V M V M N M V M V t G N V C         (6)
According to equation (41) of reference [34], the viscometer signal Svisc is expressed as:

Svisc(tel) = ( )     0 h h h h el 0 d d ) , ( ' )] , ( ' [ , ' V M V M N M V M V t G  (7)
Equation ( 6) can thus be written as:

Mn =     0 el el ' n h, el visc inj inj A d ) ( ) ( 5 . 2 t t V t S V C N ( 8
)
This corresponds to the formula used by Harrison and Mourey [29], Yau [35] or Netopilik et al. [30] assuming no band-broadening:

Mn =     0 el h h sp inj inj A d ) ( 2.5 t V V V C N  (9)
It slightly differs from the original Goldwasser expression by the constant used (originating in a different definition of the hydrodynamic volume): [24][START_REF] Goldwasser | Proceedings of the International GPC symposium Waters[END_REF]

Mn =     0 el h h sp inj inj d ) ( 4 3 t V V V C    ( 10
)
where  is the Flory parameter. Note that band broadening due to axial dispersion is neglected for the practical calculations below, because taking it into account would require assuming or determining the equation describing G'(tel, Vh). Band broadening due to axial dispersion is equipment-dependent, thus it can hardly be guessed. Furthermore, the determination of an actual band broadening equation is tedious and outside the scope of the current work. [START_REF] Baumgarten | [END_REF][38] In our previous works, we have been using the same definition as Goldwasser [34] for the hydrodynamic volume but moved to another more universal one (equation 5). [32] On a practical point of view, we used in our calculation the universal calibration curve, which is fitted by a 3 rd order polynomial:

Log([]M)=A + B × tel + C × tel 2 + D × tel 3 (11)
The Mns have thus been calculated independently from the slightly differing definitions of the hydrodynamic volume using the relation:

Mn =    0 el t × D + t × C + t × B + A el inj inj d 10 ) ( 3 el 2 el el t t S V C visc (12)
Goldwasser's derivation is related to the previous one from Hamielec, who explained why "conventional" viscometry leads to a local number average molecular weight at each elution volume or hydrodynamic volume: [5,34,39] Mn(Vh). Light scattering yields Mw(Vh). When the local dispersity, Mw(Vh)/ Mn(Vh), is significantly greater than one, then the accuracy of the determined molecular weight distribution is limited. [31] The hydrodynamic volume distributions can be used instead. Goldwasser's derivation allows determining the number hydrodynamic volume distribution with single-detector distribution. Combining equations ( 5) and (7):

Svisc(tel) = ( )     0 h h h h el 0 A d d ) , ( ' , ' 5 . 2 V M V M N V V t G N ( 13
)
Taking equation ( 3) into account yields:

Svisc(tel) = ( )      0 h h h el 0 el ' n h, A d d ) , ( ' , ' ) ( 5 . 2 V M V M N V t G t V N ( 14
)
and after a change in variable from Vh to tel:

Svisc(tel) = ( )      0 el el h h h h el 0 ' , d d d dlog ) , ( ' , ' ) ( 5 . 2 t M t V V V M N V t G t V N el n h A (15)
where el t V d dlog h is the derivative of the universal calibration curve. Assuming now no band broadening, V'h,n(tel) is reduced to Vh and G'(tel, Vh)=1:

Svisc(tel) =    0 h el h 2 h d ) , ( ' dlog 5 . 2 M V M N t d V V N A ( 16
)
The number-average hydrodynamic distribution is:

N(Vh) =   0 h d ) , ( ' M V M N (17)
Now combining equations 16 and 17:

N(Vh) = ( ) el h 2 h A el visc dlog V 5 . 2 t d V N t S  (18)
For calculations, the following formula has been used:

N(Vh) = ( ) (
)

) × 3D + × 2C + B ( ) × D + × C + × B + (A 2.
Calculations were performed using Excell and Origin software.

3 Results and discussion

Importance of the injection concentration

The value of the injection concentration is not given in the original Goldwasser works. [24][START_REF] Goldwasser | Proceedings of the International GPC symposium Waters[END_REF] In the case of high molecular weight, it is however important to ensure that no shear degradation takes place in the injector due to too high viscosity. [40] The method will gain additional interest if we can determine the hydrodynamic volume distributions. This implies to prevent overloading, ie to keep injection concentration low enough to avoid viscous fingering. [41][42] The maximal injection concentration has been estimated in this work following the empirical relation proposed by Moore. [42] The Goldwasser method has then been tested by determining Mn of polystyrene standards at half the maximal injection concentration and the maximal concentration. Polystyrene yields the most reliable standards for SEC. THF is one of the safest eluents to avoid interactions with the stationary phase (using a styrene-divinyl benzene column as used in this work). Standards of two different manufacturers were used. The molecular weights of these standards were confirmed to be as given by the manufacturer by extensive measurements of their molecular weights by triple detection, low-angle laser light scattering and the "conventional" viscometric method using refractive detection and the universal calibration curve, as detailed in supporting information of reference [20]. Figure 1 shows the Mn values as determined by the Goldwasser method against the reference values. Reliable Mn values are not obtained at half the maximum injection concentration (as calculated using Moore empirical relation). The Mn values are rather over-estimated as observed also by Harrison and Mourey, [29] although it is not the case anymore above 600,000 g/mol. From 600, 000 to 4,000,000 g/mol, the Mn values are indeed under-estimated. It is thus not possible to predict if the Goldwasser method will rather underestimate or overestimate the Mn values when unknown samples are measured. It is necessary to inject at the maximum concentration in this case. This importance of the signalto-noise ratio was already reported by Goldwasser: the precision of his determinations was ±10 % in SEC, while it was going down to ±2 % by removing the columns. The latter leads to higher signal-to-noise ratio, but prevents from determining any distribution such as the hydrodynamic volume distribution. In addition to baseline determination, [24][START_REF] Goldwasser | Proceedings of the International GPC symposium Waters[END_REF] the injection concentration is thus an important parameter to optimize in order to use the Goldwasser method without compromising the possibility to determine distributions. Signal-to-noise ratio is known to be an important parameter in multiple-detection SEC. [11,20] It also plays a role in the single-detector method that Goldwasser method is.

Note that Mn values determined using the Goldwasser method at maximal injection concentration are close to the diagonal when plotted against theoretical value, but a slight difference of slope can be visually observed on Figure 1. Mn is however the least reproducible and least accurate molecular weight quantity that can be determined using SEC. [START_REF] Berek | IUPAC congress/ general assembly[END_REF][START_REF] Bruessau | [END_REF] Accuracy of 15 % is the best that can be expected and the deviation observed on Figure 1 is thus not significant.

Number hydrodynamic volume distributions, N(Vh) by the Goldwasser method

Number hydrodynamic volume distributions, N(Vh), have been determined in this work using equation ( 19) derived above and relying on the use of a single-detector (and the knowledge of the universal calibration curve for the chromatographic system in use). The weight and then number hydrodynamic volume distributions were also determined using the more conventional double detection method relying on viscometry, refractive index detection and the universal calibration curve. In that case, we use equation (65) from reference [34] to calculate w(logVh). Equation ( 4) from reference [32] then allows to convert w(logVh) into W(Vh) or N(Vh). The local number-average molecular weight, Mn(Vh), is required to use equation ( 4). It is determined from the same double detection system (refractive index detection + viscometry + universal calibration curve) as demonstrated and tested in [20]. For the same reasons, single-detector (Goldwasser) method can lead only to the number distribution, N(Vh). This distribution requires the knowledge of Mn(Vh) to be converted to W(Vh) or N(Vh), which is not possible using the single-detector Goldwasser method.

The determination of the number hydrodynamic volume distribution is first tested on a mixture of four poly(methyl methacrylates) standards (Figure 2). The SEC hydrodynamic volume distribution, w(logVh) makes it possible to see the four components. It is not the case using the number distribution N(Vh). This highlights the fundamental differences between both types of distributions. The number distributions determined by double detection (refractometer-viscometer) or single-detection (viscometer) agree well with each other for the high molecular weights. A strong discrepancy is however observed for oligomers, but this corresponds to low signal region and no method is expected to be accurate in that region.

The Goldwasser method is then further tested with branched polyacrylates. Previous tests of the determination of Mn of branched polystyrenes by Netopilik et al. has been successful. [30] The method is now tested for the determination of the number hydrodynamic volume distribution. Long chain branching in polyacrylates can be observed following a controlled polymerization process (namely nitroxide-mediated polymerization [43]) at high conversion targeting high molecular weights. Local dispersity up to values of two [20] are observed and this poly(n-butyl acrylate) is thus a good example of cases when SEC cannot determine molecular weight distribution accurately because of long-chain branching. [31] The number distributions are compared on Figure 3 and appear to agree. The same comparison is done with another branched polyacrylates, poly(ethyl acrylate), which is a model for adhesives. [44] The general agreement is confirmed (Figure 4). This sample however illustrates very well the difference between the two methods on the lower size side. For hydrodynamic volume lower than 10 nm 3 , no number distribution is obtained by double detection. This is because Mn(Vh) cannot be measured with some accuracy in this range.

Mn(Vh) can be averaged from duplicate injections to reduce noise and then fitted using a polynomial. The number distributions obtained by double detection are thus expected to be generally more precise than the Goldwasser, as soon as the dn/dc is high enough. The Goldwasser method does not allow any meaningful averaging or fit of the data when hydrodynamic volume distributions are determined. The Goldwasser method is however functioning on a broader range of sizes since it is based on a single-detector. One limitation of multiple-detection SEC is the difference of sensitivity of the different detectors: this likely prevents determination of the hydrodynamic volume on the low hydronamic volume side in this work using double-detection SEC. The use of single detector allows thus to determine size distributions on a broader size range, which is particularly helpful for broadly-distributed samples.

Complexity of polymeric materials is steadily increasing with the number and difficulty of their applications such as for biomaterials or food. Progresses in separation of polymers are of the highest importance to deal with the complexity of the new materials.

Research in new separation methods such as field flow fractionation [45] or liquid adsorption chromatography [46] is gaining momentum. SEC has however more to offer than currently exploited. Viscometric detection has thus more potential than commonly considered. We revisited the Goldwasser method. It has been proposed to determine Mn, but it has known very few applications till now. Different reasons exist, among them the important role of band broadening [35] and the importance of optimal signal-to-noise. The application of the Goldwasser method to branched polymers has on the other hand a high potential to determine number hydrodynamic volume distributions. Their determination has been successfully tested for poly(methyl methacrylates) standards as well as branched polyacrylates. The Goldwasser methods rely on the validity of universal calibration, which needs to be checked for every new combination of stationary phase, eluents and analyte and is still the source of some controversy [30]. This is currently a limitation for important system such as starch in polar organic solvents, DMSO [16] or DMAc [17], where the validity of universal calibration is still to be convincingly demonstrated. [18] The determination of number-hydrodynamic volume by the Goldwassser method has also clearly potential for the characterization of copolymers.

Figures

Figure 1 :

 1 Figure 1: Number-average molecular weight, Mn, determined by single-detector viscometry (Goldwasser method) against reference Mn for a range of polystyrene standards. Red circles show injections done at the maximal injection concentration and black triangles show injections done half the maximal injection concentration. The diagonal is shown as a black line as a guide to the eyes.

Figure 2 :

 2 Figure 2: Hydrodynamic volume distributions of poly(methyl methacrylate) determined by single detection viscometry (full black line) and double detection (dashed or dotted red line). SEC hydrodynamic volume distributions, w(logVh) is indicated as dotted red line obtained by double detection. Number distributions are indicated as full black line and dashed red line.

Figure 3 :

 3 Figure 3: Hydrodynamic volume distributions of poly(n-butyl acrylate) determined by single detection viscometry (full black line) and double detection (dashed or dotted red line). Weight hydrodynamic volume distributions, W(Vh) is indicated as dotted red line obtained by double detection. Number distributions are indicated as full black line and dashed red line.

Figure 4 :

 4 Figure 4: Hydrodynamic volume distributions of poly(ethyl acrylate) determined by single detection viscometry (full black line) and double detection (dashed or dotted red line). Weight hydrodynamic volume distributions, W(Vh) is indicated as dotted red line obtained by double detection. Number distributions are indicated as full black line and dashed red line.

Acknowledgments PC thanks Prof. Bernadette Charleux (Lyon) and Laboratoire de Chimie des Polymeres (Paris) for use of the SEC equipment.


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Professeur des Universités-Praticien Hospitalier, Faculté de médecine Clermont Auvergne Chef de service de physiologie, CHU de Clermont-Ferrand.

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J'ai beaucoup appris a vos cotés durant 6 mois, je vous remercie de cela, la transmission de votre savoir en physiologie est un véritable atout pour nous.

Madame le Docteur Daniela Muti

Praticien Hospitalier, Faculté de médecine de Clermont Auvergne.

Service de pneumologie, CHU de Clermont-Ferrand.

Merci de m'avoir fait l'honneur de participer à mon jury de thèse.

Merci pour ta présence le long de ces quatre ans, ton écoute et ton aide tant au niveau professionnel que personnel , ta disponibilité également. Je t'en remercie sincèrement.

Merci a toutes les personnes qui ont contribué à la réalisation de cette thèse Remerciements personnels A Mizou, merci pour tout, de m'avoir soutenue tout ce temps , d'avoir été la quelque soient les circonstances , tu as fait ce qu'on est devenues.

A Papa, pour m'avoir encouragée , avoir cru en moi et fait de moi une personne un peu plus forte, tes conseils sont toujours les bienvenus.

A Papuche, Moh et les monsters munch, grâce a qui on a évité la médecine du travail aux Antilles Guyane sur un malentendu … ! merci d'être toujours la pour moi, de me faire rigoler autant ,et de m'aider a envisager mon avenir plus sereinement.

A Zed, tu es la pour moi depuis tant d'années, merci de ton aide et de ton soutien, on a partagé des galères et des moments géniaux, le plus dur est derrière maintenant.

A Thomas, depuis que tu es entré dans ma vie tu m'apporte tant de bonheur tous les jours, je sais ton soutient inconditionnel, on fera en sorte que la vie soit assez longue, je serais toujours la pour toi.

A tout le reste de ma famille ,Mamie, Youma, Pascal, malgré l'éloignement les choses restent identiques.

A A la coloc , ce fut une petite partie de mon internat, j'en garde de très bons souvenirs, merci a vous tous pour ces moments partagés A Stéphane et Chen , pour l'aide à la traduction A l'équipe de pneumologie, infirmières et chefs, merci de votre aide et de vos enseignements durant ces quatre ans.

SOMMAIRE

Table des matières

Introduction and objectives:

Seasonal asthma may be associated with pollen exposure, but the pollens responsible for these exacerbations are not well known. The association between ambient pollen and asthma reflected in emergency department (ED) visits and hospitalizations, although studied intensively, has shown inconsistent results [1][2]. This would be explained by differences between population, climate, and measurement of pollen.

We can talk about maple [3], charm [5], oak pollen and grasses, with in the Darrow's study a 3% increase in emergency department visits [1]. Another study shows that birch and oak pollen peaks were associated with antiallergic treatment sales and ED visits for asthma attacks [2].

Similarly, relationship between pollen peaks and allergic rhinitis, rhinosinusitis, conjunctivitis has been highlighted in the literature reviews, with a close link connecting these peaks to the consumption of antiallergic treatment (oral and local), including a study on Clermont Ferrand with grass pollen, ash, hazel and birch [4].

However, it is interesting to note that ED visits for asthma are in the case of severe exacerbation and do not represent the majority of asthma attacks [6].

Many cases of exacerbation are not identified in the emergency, even if we know that short-acting β2-agonists (SABA) are widely used by patients experiencing increased respiratory symptoms, which translates into increased sales. Respiratory drug sales have been successfully used in ecological studies to illustrate the relationship between asthma and outdoor air pollution like high levels of nitrous dioxide and carbon monoxide [7] [5]. That's why we will take this into account as a confounding factor.

In the central France region, which includes the Greater Clermont Ferrand area, the pollens mainly found are those of birch (March April), oak (April May), and ash (March). Conversely, pollen of charm are generally found in northeastern France, and pollens from March to May, such as the plane tree pollen known to be allergenic mainly affects the Mediterranean region.

This study is intended to test the relationship between exposure to outdoor pollen in the general population of a continental climate middle-sized town in the center of France, and SABA sales, over a 5-year period, taking into account the various confounding factors such as the days of the week, the pollution and the weather.

Methods

Study zone and health data :

Records of all SABA treatments prescribed for people living in the demographically stable Clermont-Ferrand area ,were provided during the study period (2010-12; 2014-15) by the French public health insurance database, which covers approximately 80% of the French urban population (and about 69 percent of the general population of this department) [4].

The Clermont-Ferrand aera including the city of Clermont-Ferrand and 17 communes located at a maximum distance of 13 km around Clermont-Ferrand, bringing together a population of 285,000

inhabitants.

Owing to missing data for technical reasons, 2013 was omitted. The health outcome was defined as the number of "cases" per day, whereby a case is defined as the reimbursement of a SABA treatment.

For each year of the study period, all individuals receiving at least one reimbursement on a prescription containing a SABA were identified in the health insurance database from their anonymous registration number (this did not concern inhaled corticosteroids of fixed combinations considered as background treatments). SABA sales for children <6 years were excluded because of the uncertainty of asthma diagnosis [8].

This study was entirely anonymous and so approval from the French Ethics Committee was not required.

Pollen data :

Clermont Ferrand is located in central France, it has a temperate climate with warm summers, usually from June to the beginning of September.

Pollen concentrations were collected through the participation of the RNSA (national network of aerobiologique surveillance).

Its purpose is to study the content of air loaded with biological particles and which may have an impact on the allergic risk of the population.

A pollen sensor (volumetric sensors of HIRST type) was installed on the roof of Clermont-Ferrand University Hospital (30m high) to collect data for 5 years. This sensor sucks a regular air flow similar to that of human breathing (10L / min), an adhesive tape collects the different pollen and spores while a mechanical clock allows to separate the band per daily slice for 7 days. For each sample, pollens were identified and counted by the RNSA.

The exposure shall be measured with the daily concentration number of grains per cubic meter of air for each pollen.

This allowed to precisely obtain the concentration of 15 different taxa: Ambrosia, Armoise, Alder, Birch, Charm, Oak, Cypress, Ash, Hazelnut tree, Olive tree, Plantain, Plane tree, Poaceae, Willow,

Urticaceae.

The study focused on these pollens because they have a high allergenic potential (at least 3). This score is established by the RNSA which measures the ability of the differents pollen to cause allergic reaction. It goes from 0 to 5 (very strong).

We know that pollens which trigger allergic reactions, need to diffuse in large quantity, have small size or have an important allergenicity [9].

However, cypress, olive, willow and armoise have not been retained in the analyzes either because of their small quantity in the air or because they are not considered allergenic in this region.

So eleven pollens were kept in the analysis (table 1) as were two outdoor molds, Alternaria and

Cladosporium, sporulating at the same period as the pollens, as potentially confounding factors.

Air pollution and meteorological data

Meteorological data including humidity, temperature, precipitation, wind speed and thunderstorm days were obtained via the National Institute of Meteorology (Météo France) while the ozone, nitrogen dioxide and PM10 particles were transmitted by the national air quality monitoring body (ATMO Auvergne).

This was analyzed by taking into account the number of days off. Data on influenza epidemics were obtained from a national network for transmissible disease surveillance.

Statistical analysis:

Data were analyzed by overdispersed Poisson regression with generalized additive models (GAMs) [START_REF] Hastie | Generalized additive models[END_REF], which are often used in air pollution studies.

Using non-parametric smoothing functions, GAMs allow flexible control of the effect of trend and seasonal components and of confounding factors (such as pollutants and meteorological factors)

whose relationship with SABA is not linear.

They can also identify the shape (linear or otherwise) of the curve for every pollen-SABA relationship.

The construction of the model began with the introduction of the long-term trend and seasonal variations, using a cubic smoothing spline of the day of the study. Dummy variables of holidays, days of the week and influenza occurrence were then introduced. Quantitative meteorological, pollution and mold variables were introduced as penalized cubic splines with different lags tested.

Minimization of the Akaike criterion identifies the most appropriate lag for each variable.

In each final model, a 3 day lag was retained for greatest temperature and wind speed. Nitrogen dioxide and humidity were introduced without lag, precipitation with a 0-1 day lag (i.e mean of 2 days), ozone with a 1 day lag and particulate matter and mold with a 0-3 day lag.

Finally, the pollen was introduced in the form of penalized cubic spline, with lags of up to seven days. Lags (single day or mean of several days) were retained after graph inspection. The effect of pollens on SABA sales in the short term is expressed as a relative risk (RR and 95%CI) for an increase of the interquartile range of grains (statistical program: SM). Results are given for the whole population and by age strata.

Results

Pollen distribution

Analysis of the pollen distribution per cubic meter shows that the most abundant pollen are those of ash birch and oak (70 grains/m3), with peak levels higher than 1000 grains/m3, whereas plane and charm averaged only 10 grains/m3 with peak levels around 100 and 200 grains/m3 respectively. (table 1)

The median of mean daily ozone concentration during the study period was 86µg/m3, the median maximum temperature was 22.4°C, relative humidity was 42%, PM10 was 17 µg/m3.

Correlations

The correlation between pollens was low (less than 0.55), the most important concern birch and oak pollen (0.51), birch and plane tree (0.54), cypress and hazelnut tree (0.54).

Charm and ash are not correlated with other pollens. (table 2)

SABA sales

The daily SABA sales (mean, SD) rose from 46.5 (23.6) in 2010 to 59.0 (30) in 2015. The annual number of people supplied with SABA on at least one occasion increased from 8553 to 9742.

(table 3)

Association between SABA sales and pollen concentrations

Mono pollen analysis: (table 4)

Within the entire population, the relative risk of SABA sales associated with an interquartile increase in pollen concentration increased significantly for ash (+7,9%), birch (+13%), charm (+3,2%), plane tree (+15,1%) and oak ( +1,4%).

The result was close to the significance for ambrosia. We did not find any significance for grasses.

Modeling by age class : (table 5)

When the influence of age was considered, the increased concentration of pollen from ash, birch, charm, oak and plane tree significantly increases the relative risk of SABA sales among 15-64 year olds, whereas oak is only significant between 15 and 44 years old.

There were significant positive associations with grasses 1.05 [1.01-1.09] and hazelnut tree pollen 1.08 [1.001-1.17] in 6-14 year-old children and with ambrosia 1.13 [1.01-1.26] in young adults.

After 65, we no longer find any significant link between the 11 taxa and the risk of SABA sales.

Discussion

Our study confirms the relationship between SABA sales and exposure to birch, ash and oak pollen, and shows a link between plane tree pollen and charm despite their low concentration.

This takes into account various confounding factors such as pollution and weather. Indeed, some studies have shown that pollution and weather can affect the number of pollen grains, that can be reduced when temperatures decrease [11]but also with humidity and rain [12], while there is not necessarily a correlation with wind.

These weather variations also have an impact on the population and we notice an increase in the number of respiratory allergy symptoms with exposure to air pollution [13], and an increase in the number of people suffering from rhinoconjunctivitis symptoms when temperatures increase (it can be explained by the concomitant increase of concentration in pollens) [14].

We note a first result in our study showing that SABA sales increase over time. This is consistent with other studies that point out that with climate change, there has been an increase in the duration of pollination and of pollen concentrations since the 1980s. In parallel, the percentage of sensitized people has also increased as the number of patients with asthma (+ 38% in 10 years in Italy) [START_REF] Marco | Trends in the prevalence of asthma and allergic rhinitis in Italy between 1991 and 2010[END_REF].

Our study has demonstrated that the most important pollen concentration is that of oak and birch. This differs from other studies carried out in southern Europe where the predominant pollens are those of plane tree, grass [START_REF] Alcázar | Airborne plane-tree (Platanus hispanica) pollen distribution in the city of Córdoba, South-western Spain, and possible implications on pollen allergy[END_REF][START_REF] Pérez-Badia | Pollen spectrum and risk of pollen allergy in central Spain[END_REF], olive tree and oak [START_REF] Belmonte | Characteristics of the aeropollen dynamics at several localities in Spain[END_REF].

For comparison, birch pollen awareness is higher in central/northern Europe than in the south [START_REF] Bousquet | Geographical variation in the prevalence of positive skin tests to environmental aeroallergens in the European Community Respiratory Health Survey I: Prevalence of positive skin tests to environmental aeroallergens[END_REF].

For a start, the Betulaceae family can be divided into two categories [START_REF]Plantes et botanique -famille des Betulaceae[END_REF]:

-betuloïdées, including the genera of alder and birch -coryloidea, including hazelnut and hornbeam Some people consider carpineae as a category in its own right.

Birch is the main pollen producing tree in northern Europe, the most common species is betula verrucosa. The average levels in our study is around 75 grains per m3 with a maximum of 1080 grains. However, these peaks may be up to 16000 grain / m3 [START_REF] Yli-Panula | Analysis of Airborne Betula Pollen in Finland; a 31-Year Perspective[END_REF].

Percentage of birch sensitization varies considerably in studies, ranging for example from 5% (the Netherlands) to 54% (Zurich) [START_REF] Amato | Allergenic pollen and pollen allergy in Europe[END_REF].

Among the most important allergenic proteins of birch pollen, we find Betv1 with a high prevalence of sensitization in allergic patients in all age groups (like in an Austrian study where 16% of adolescents showed a sensitization to betv1) [START_REF] Ghunaim | Sensitization to different pollens and allergic disease in 4-year-old Swedish children[END_REF][START_REF] Biedermann | Birch pollen allergy in Europe[END_REF].

It should be noted that this major betv1 allergen crosses with other trees in the same family and that it is rare to have mono sensitization to birch [START_REF] Lavaud | Allergie au pollen de bouleau[END_REF].

A previous study of our staff showed a significant link between the increase in the concentration of birch pollen and the symptoms of allergic rhinitis, for a pollen grain count equivalent to 45 grains / m3 [START_REF] Caillaud | Airborne pollen levels and drug consumption for seasonal allergic rhinoconjunctivitis: a 10-year study in France[END_REF].

In addition to allergic rhinitis symptoms, studies in North America and Europe have reported a link between ED visits and hospital admission for asthma caused by birch pollen .

However our study is the first to demonstrate an association between saba sales and birch pollen in the general population.

Because charm and birch bloom simultaneously, it is not possible to distinguish the allergy symptoms specifically induced by the pollen of charm.

Unlike birch, the number of grains of pollen of charm in our study is low (inferior to 1% of the total pollen concentration) with average levels of 12 grains /m3 and maximum of 190 grains/m3.

However here, the correlation between birch and charm was not significant, suggesting that betula and charm have distinct allergenic effects even though some studies find different results not highlighted in our study.

In Cuinica's study, allergens present in birch and charm corresponds to proteins whose weight is between 58 and 17KDA, and there would be existence of common reactive bands in immunoblot, which would suggest precisely that there may be common allergenic proteins [START_REF] Cuinica | Effect of air pollutant NO2 on Betula pendula, Ostrya carpinifolia and Carpinus betulus pollen fertility and human allergenicity[END_REF].

Regarding sensitization to charm, a study in Switzerland of 207 ambulatory patients with seasonal allergic rhinitis showed that 12.5% of patients sensitized to betulaceae pollen were monosensitized to the charm and half of these patients had asthma [START_REF] Gumowski | The importance of hornbeam (Carpinus sp.) pollen hypersensitivity in spring allergies[END_REF].

Only two studies in Croatia and Belgium showed a significant association between the levels of charm pollen and hospitalization for asthma with a low level of charm pollen compared to birch .

Ash is widespread in northern and central Europe, Great Britain and North America.

In Central Europe, ash pollen concentrations can reach levels similar to those of birch with peaks of pollen levels up to 2000 grains / m3 [START_REF] Kosisky | Pollen aeroallergens in the Washington, DC, metropolitan area: a 10-year volumetric survey[END_REF] , and both trees co-pollinate in march.

In outpatients, sensitization to a global ash extract was 11,6% in Strasbourg and 25,7% in Paris [START_REF] Metz-Favre | Actualité dans l'allergie au pollen de frêne[END_REF]. This sensitization is often found in the context of polysensitization (food trees) and patients monosensitized to ash pollen are rare (less than 10%) [START_REF] Metz-Favre | Actualité dans l'allergie au pollen de frêne[END_REF].

Recent studies have demonstrated a relationship between ash pollen and ecological events.

In studies in Brussels [START_REF] Guilbert | Short-Term Effect of Pollen and Spore Exposure on Allergy Morbidity in the Brussels-Capital Region[END_REF], Canada [START_REF] Dales | Tree Pollen and Hospitalization for Asthma in Urban Canada[END_REF] and New York [2], ash pollen concentration was associated with increased consumption of antiallergic drugs, and in North America it was associated with emergency room visits or hospitalizations for asthma [2].

By revealing a relationship between ash pollen and SABA sales, our study confirms the allergenic potential of ash pollen.

Oak is widely distributed in the United States and in the northern hemisphere. Pollination occurs in late april and early may, pollen peaks can reach 1000 to 3000 grains/m3 and in Turkey, 44.6% of patients with asthma or allergic rhinitis had positive skin prick [START_REF] Gorczynski | Pollen aero allergens and the climate in mediterranean region and allergen sensitivity in allergic rhinoconjunctivitis and allergic asthma patients[END_REF].

A study in Mexico on 628 patients with blinded skin prick found a 23% sensitization to oak, which was more important in agricultural areas. Most of these subjects were suffering from allergic rhinitis (82.2%) and seasonal allergic rhinitis was significantly associated with tree pollen sensitization [START_REF] Larenas-Linnemann | Allergen sensitization linked to climate and age, not to intermittent-persistent rhinitis in a cross-sectional cohort study in the (sub)tropics[END_REF].

In a Korean study [START_REF] Lee | Variability of Offending Allergens of Allergic Rhinitis According to Age: Optimization of Skin Prick Test Allergens[END_REF], oak pollen sensitization was more commonly found in younger age groups ( < 6 years old ) and in the 40-49 age groups, although our study shows an increasing of SABA sales for oak pollen in the 15/44 years age group.

Several studies carried out in North America have also revealed correlations between oak pollen concentrations and increased visits to the ED for asthma and hospitalization [3]. For example oak pollen was associated with 21,200 (95% confidence interval, 10,000-35,200) asthma ED visits in the Northeast, Southeast and Midwest U.S. In 2010 [START_REF] Anenberg | Impacts of oak pollen on allergic asthma in the United States and potential influence of future climate change: Climate Impacts on Oak Pollen and Health[END_REF].

In some studies, this link was more important in the younger population [1][2].

However,our study is the first to report an link between SABA sales and oak pollen.

Before being recognized as having an allergenic potential, plane tree was not considered to be an allergy provider [START_REF] Belmonte | Characteristics of the aeropollen dynamics at several localities in Spain[END_REF].

Consequently, the plane tree has been used as an ornamental tree and in these urban areas, plane tree pollen is detected at high concentrations during the spring bloom season -up to 62% of total Córdoba pollen with daily peaks reaching more than 2500 grains / m3 [START_REF] Alcázar | Airborne plane-tree (Platanus hispanica) pollen distribution in the city of Córdoba, South-western Spain, and possible implications on pollen allergy[END_REF]. This distribution varies according to cities and quantities of ornamental trees. For example, in Porto [START_REF] Abreu | Allergenic pollen in the city of Porto (Portugal)[END_REF], a 2005 study of plane tree pollen showed a rate of 7.3% of the total rate of air pollens.

In contrast, in the whole of France, plane tree is the ninth most abundant pollen taxon and accounts for about 5,6% of all pollen suspended in the air in the south of France [START_REF] Bousquet | Allergy in the Mediterranean area. I. Pollen counts and pollinosis of Montpellier[END_REF].

In Cordoba in 1996, there was a sensitization rate of 17% plane tree [START_REF] Alcázar | Airborne plane-tree (Platanus hispanica) pollen distribution in the city of Córdoba, South-western Spain, and possible implications on pollen allergy[END_REF].

At the beginning of the 90s, the prevalence of plane tree sensitization in Madrid was shown to be very high (56%) [START_REF] Subiza | Seasonal asthma caused by airborne Platanus pollen[END_REF]. In these patients, there were associations between exposure to pollen and pollinosis.

Despite low pollen concentration, several studies find significant connections with the consumption of anti allergic treatment [START_REF] Caillaud | Airborne pollen levels and drug consumption for seasonal allergic rhinoconjunctivitis: a 10-year study in France[END_REF] and hospitalization for asthma [2][3] , even if some of them report rather the absence of an obvious link.

But for other authors, there were no clear patterns of association between the number of hospital admissions for asthma and concentration of plane pollen [START_REF] Osborne | Pollen exposure and hospitalization due to asthma exacerbations: daily time series in a European city[END_REF].

These discordant results can be explained by the distance between plane trees and pollen traps, proximity and direction of the wind playing a key role in the capture of the pollen. According to Bricchi [11], pollen of plane trees decreases rapidly at a distance greater than 400 m from the source (25% of the pollen remains in a perimeter of 400m, after 800m, the concentration decreases significantly).

But most studies converge towards a significant allergenic potential as we can see by the rise in SABA sales in our study.

In our study, a significant effect was observed for Hazelnut tree pollen, ambrosia and grasses in some age classes.

Hazelnut tree pollinates before birch in France, at the beginning of the year (mid-January to mid-March) [START_REF] Mcinnes | Mapping allergenic pollen vegetation in UK to study environmental exposure and human health[END_REF], and relationship has been established between grasses and emergency consultations in Spain [START_REF] Tobias | Short term effects of airborne pollen concentrations on asthma epidemic[END_REF][START_REF] Tobias | Non-linear short-term effects of airborne pollen levels with allergenic capacity on asthma emergency room admissions in Madrid, Spain[END_REF] and between grass pollen, hazelnut tree pollen and consumption of anti allergic treatment in Central France [START_REF] Caillaud | Airborne pollen levels and drug consumption for seasonal allergic rhinoconjunctivitis: a 10-year study in France[END_REF].

In the city of New Orleans, a study has shown a link between Ambrosia pollen and asthma admissions rate [START_REF] Salvaggio | New Orleans asthma *1V. Relationship between Charity Hospital asthma admission rates, semiquantitative pollen and fungal spore counts, and total particulate aerometric sampling data[END_REF], while in Canada, correlation was shown with Hazelnut tree [START_REF] Dales | Tree Pollen and Hospitalization for Asthma in Urban Canada[END_REF].

In our study we don't find a link between pollen and SABA sales for people after 65, an age when COPD diagnostic is much more common than asthma in case of obstructive pathology (prevalence of asthma after 65 : 6-10% [START_REF] Burr | Asthma in the elderly: an epidemiological survey[END_REF][START_REF] Gillman | Asthma in the elderly[END_REF], prevalence of COPD approximately 14-15% after 65 [START_REF] Orvoen-Frija | La bronchopneumopathie chronique obstructive (BPCO) du sujet âgé en huit questions/réponses[END_REF][START_REF] Khelafi | Épidémiologie de la bronchopneumopathie chronique obstructive dans la wilaya d'Alger[END_REF]) especially because of tobacco exposure.

And in the analysis by age class, the relative risk of saba sales is significant for people with the 15-65 age group. It is consistent with the Peternel 's study [START_REF] Peternel | Airborne ragweed (Ambrosia artemisiifolia L.) pollen content in the city of Zagreb and implications on pollen allergy[END_REF] where they found a higher sensitization to pollen for the 30-50 age group and results were dropping after 50.

So the lack of association found between pollen exposure and SABA sales in subjects over 65 years supports the argument of SABA sales being mainly for asthmatic and not COPD patients, even if we cannot draw any definite conclusion because we know that SABA are used in case of exacerbation of these two diseases.

The main strength of this work is a very large dataset, representative of one region with subjects of all ages over 5 years. Our study opens a window on regional trends with large age ranges. All individuals studied in the Clermont Ferrand area lived within 15 km of the pollen trap, and we know that the trap is representative of pollens found several kilometers around [START_REF] Katelaris | Spatial variability in the pollen count in Sydney, Australia: can one sampling site accurately reflect the pollen count for a region?[END_REF] corresponding to pollen spread distances [START_REF] Erbas | Outdoor pollen is a trigger of child and adolescent asthma emergency department presentations: A systematic review and meta-analysis[END_REF] which can go up to a hundred kilometers [START_REF] Sofiev | Towards numerical forecasting of long-range air transport of birch pollen: theoretical considerations and a feasibility study[END_REF]. So this spore trap is useful for performing continuous daily series.

The relationship between drug sales and pollen has been examined on the individual taxa and not large families.

Another strength is the adaptation of our model to take into account outdoor air pollution , influenza epidemics and mold because we know that pollen viability depends on the environment and that future climate changes will probably increase pollen-related allergic diseases as we can see in the Anenberg's study, with an increasing of hospitalizations for asthma attack in relation to oak pollen, leading to a higher cost for the health system [START_REF] Anenberg | Impacts of oak pollen on allergic asthma in the United States and potential influence of future climate change: Climate Impacts on Oak Pollen and Health[END_REF].

However there are a number of limitations. Our local study is not representative of the French population. Our population was urban and the observed trends can not be extrapolated to rural areas. The pollen effect depends on climatic conditions and its effects will vary from one climatic region to another.

On top of that, there is the problem of cross-reactions where we can first have sensitizations with one pollen, then the symptoms when pollinating another.

For example, we find charm and birch pollinating at the same time out of birch is considered highly allergenic so it becomes difficult to determine the role of charm.

The lack of knowledge about pollen sensitization in the general population should be recognized.

Because of similarities between the symptoms of exacerbations of asthma and COPD, SABAs are prescribed for both disorders as discussed previously, for the future it would be interesting to carry out a prospective study by differentiating asthmatic or COPD patient and to note their consumption not only the SABA sales.

In conclusion, using an entire urban population in central France over a 5-year period, our study is the first to support the well documented relationship between SABA sales, and birch, ash and oak pollen exposure while also showing relationships with plane tree and charm pollens despite their low pollen counts. Increased SABA sales were also associated with Grasses, hazelnut tree and ambrosia in some age classes. Further studies in other geographical areas with different climatic conditions are needed to complement these results. Seasonal asthma may be associated with pollen exposure [1], but the pollens responsible for these exacerbations are not well known. The association between ambient pollen and asthma reflected in emergency department (ED) visits and hospitalizations, although studied intensively, has shown inconsistent results [2][3][4]. In contrast to these infrequent events, short-acting β2-agonists are widely used by patients experiencing increased respiratory symptoms, which translates into increased sales. Respiratory drug sales have been successfully used in ecological studies to illustrate the relationship between asthma and outdoor air pollution [5]. This study is intended to test the relationship between exposure to outdoor pollen in the general population of a continental climate middle-sized town in the center of France, and SABA sales, over a 5year period.

Tables

Records of all SABA treatments prescribed for people living in the demographically stable Clermont-Ferrand area (approximately 285,000 inhabitants) were provided during the study period (2010-12; 2014-15) by the French public health insurance database, which covers approximately 80% of the French urban population [6). Owing to missing data for technical reasons, 2013 was omitted. The health outcome was defined as the number of "cases" per day, whereby a case is defined as the reimbursement of a SABA treatment. For each year of the study period, all individuals receiving at least one reimbursement were identified in the health insurance database from their anonymous registration number. SABA sales for children <6 years were excluded because of the uncertainty of asthma diagnosis [1]. This study was entirely anonymous and so approval from the French Ethics Committee was not required. Air pollution (PM10, O3, NO2), meteorological data and pollen samples (Hirst trap), collected from mid-February to early October, were provided as described previouly [6]. Eleven pollens were identified (Table 1) as were two outdoor molds, Alternaria and

Cladosporium, sporulating at the same period as the pollens, as potentially confounding factors. Data on influenza epidemics were obtained from a national network for transmissible disease surveillance. Age and sex were also available from the database.

Data were analyzed by overdispersed Poisson regression with generalized additive models (GAMs) [7].

Using non-parametric smoothing functions, GAMs allow flexible control of the effect of trend and seasonal components and of confounding factors whose relationship with asthma is not linear. They can also identify the shape (linear or otherwise) of the curve for every pollen-asthma relationship. The construction of the model began with the introduction of the long-term trend and seasonal variations, using a cubic smoothing spline of the day of the study. Dummy variables of holidays, days of the week and influenza occurrence were then introduced. Quantitative meteorological, pollution and mold variables were introduced as penalized cubic splines with different lags tested. Minimization of the Akaike criterion identifies the most appropriate lag for each variable. Finally, the pollen was introduced in the form of penalized cubic spline, with lags of up to seven days. Lags (single day or mean of several days) were retained after graph inspection. The effect of pollens on asthma in the short term is expressed as a relative risk (RR and 95%CI) for an increase of the interquartile range of grains (statistical program: SM).

Betula, Fraxinus and Quercus averaged around 70 grains/m 3 , with peak levels higher than 1000 grains/m 3 , whereas Platanus and Carpinus averaged only 10 grains/m 3 with peak levels around 100 and 200 grains/m 3 respectively. The correlation between pollens was low (less than 0.55). The daily SABA sales (mean, SD) rose from 46.5 (23.6) in 2010 to 59.0 [START_REF] Kosisky | Pollen aeroallergens in the Washington, DC, metropolitan area: a 10-year volumetric survey[END_REF] in 2015. The annual number of people supplied with SABA on at least one occasion increased from 8553 to 9742. Within the entire population, the relative risk of SABA sales associated with an interquartile increase in pollen concentration increased significantly for Fraxinus, Betula, Carpinus, Platanus and Quercus (Table 1). When the influence of age was considered, there were significant positive associations with Poaceae 1.05 [1.01-1.09] and Corylus 1.08 [1.001-1.17] in 614 year-old children and with Ambrosia 1.13 [1.01-1.26] in young adults. Betula is the main pollen-allergen producing tree in Northern Europe. ED visits or hospitalizations for asthma induced by Betula pollen have been demonstrated [3,4,8]. In contrast to Betula (peak levels: 1080 grains/m 3 ), Carpinus counts in our study are low, with peaks of 190 grains/m 3 . Only two ecological studies have shown a significant association between Carpinus pollen levels and asthma hospitalizations with low mean Carpinus levels [4,9]. Fraxinus is widespread in Northern Europe and America. In Europe, high Fraxinus pollen levels can reach similar peak levels to Betula, and both trees copollinate in March-April. Only two recent studies have demonstrated a relationship between Fraxinus pollens and asthma ED visits or hospitalizations in North America [3,8].

Three studies performed in North America, with peaks exceeding 20,000 grains/m 3 , reported associations between Quercus pollen and asthma ED visits or hospitalizations [2,3,8]. Our study is the first to report an association between SABA sales and Quercus pollens despite lower peaks (1011 grains/m 3 ). Associations between exposure to Platanus pollen concentrations (peaks > 2000 grains/m 3 ) and asthma were reported in outpatients in Madrid [10]. In contrast, despite low Platanus pollen counts (peak < 60 grains/m 3 ), significant associations have been reported with hospitalizations for asthma in NYC [3] and with SABA sales in our study.

Significant effect modification by age was observed for Poaceae, Corylus and Ambrosia. Our study is in accordance with a meta-analysis showing a significant relationship between Poaceae pollen and ED presentation only in children and adolescents [11], with a Spanish study relating Corylus pollen to ED visits [12] and with a Hungarian study on the relationship between Ambrosia pollen and asthma [13].

The main strength of the present work lies in the study of an extremely large regionally representative dataset comprising subjects of all ages ≥ 6 years, living within 15 km of the spore trap. The relationship between drug sales and pollens was examined on the basis of individual taxa. We used appropriate statistical tools to look at the shape of the curve for every pollen spore studied, adjusting for influenza epidemics,

  DE LA COMMISSION DE LA RECHERCHE VICE PRESI-DENTE DE LA COMMISSION DE LA : HENRARD Pierre FORMATION ET DE LA VIE UNIVERSITAIRE : PEYRARD Françoise DIRECTEUR GENERAL DES SERVICES : et Traitement de l'Image Mle GOUMY Carole Cytologie et Histologie, Cytogénétique REMERCIEMENTS A MON PRESIDENT DE THESE Monsieur le Professeur Denis Caillaud Professeur des Universités-Praticien Hospitalier, Faculté de médecine Clermont Auvergne Chef de service de pneumologie, CHU de Clermont-Ferrand.

Annexe 1 : Letter published in the European Respiratory journal

  Introduction and objectives: .......................................................................................................................... Air pollution and meteorological data ....................................................................................................... Statistical analysis: ...................................................................................................................................... Results ............................................................................................................................................................. ............................................................. ................................................................ Bibliography ....................................................................................................................................................

	Discussion ........................................................................................................................................................
	Conclusion : .....................................................................................................................................................
	Tables ..............................................................................................................................................................

Methods .......................................................................................................................................................... Study zone and health data : ...................................................................................................................... Pollen data : ................................................................................................................................................ Pollen distribution ...................................................................................................................................... Correlations ................................................................................................................................................. SABA sales ................................................................................................................................................... Association between SABA sales and pollen concentrations ................................................................... Mono pollen analysis: ............................................................................................................................. Modeling by age class : .............................................................

SERMENT D'HIPPOCRATE .

  ..............................................................................................................................

Table 1 :

 1 Outdoor pollen concentration per cubic metre of air,Clermont-Ferrand, 2010[START_REF] Marco | Trends in the prevalence of asthma and allergic rhinitis in Italy between 1991 and 2010[END_REF], 2014-2015.

	Pollen	Number of days	Mean (SD)	Minimum	Q1	Median	Q3	Maximum
	Ambrosia	155	6 (8)	1,12	1,12	3,39	5,65	40,68
	Armoise	240	4 (4)	0,97	1,12	2,26	4,52	42,93
	Alder	200	29 (52)	0,97	1,94	6,78	29,72	316,39
	Birch	262	75 (145)	0,97	3,39	21,47	87,01	1079,15
	Charm	123	12 (25)	0,97	1,12	3,39	11,3	186,44
	Oak	346	67 (126)	0,97	3,39	10,42	62,15	1011,35
	Cypress	726	27 (66)	0,97	2,25	5,4	22,6	761,62
	Ash	282	76 (195)	0,97	2,25	9,03	47,45	1371,58
	Hazelnut tree	194	37 (66)	0,97	3,88	12,43	45,2	663,3
	Olive tree	31	2 (2)	0,97	0,97	1,94	3,39	7,9
	Plantain	671	6 (5)	0,97	2,25	4,51	7,9	32,98
	Plane tree	138	12 (17)	0,97	1,12	4,51	15,81	94,91
	Poaceae	730	44 (81)	0,97	2,26	9,03	47,46	604,55
	Willow	237	6 (6)	0,97	1,13	3,88	7,76	45,2
	Urticaceae	662	51 (60)	0,97	7,9	28,25	76,84	310,75

Table 2 :

 2 Correlations between pollens Clermont-Ferrand, 2010-2012, 2014-2015In bold : correlation greater than 0,40

	Corrélations Ambroisia Armoise	Alder	Birch	Charm Oak	Cypress	Ash	Hazelnut	Olive	Plantain	Plane	Poaceae	Willow
	Armoise	0,06	1
	Alder	-0,05	-0,07	1
	Birch	-0,05	-0,08	-0,04	1
	Charm	-0,04	-0,05	-0,02	0,26	1
	Oak	-0,06	-0,09	-0,06	0,51	-0,02	1
	Cypress	-0,07	-0,10	0,49	0,16	0,03	0,15	1
	Ash	-0,04	-0,06	-0,03	0,32	0,22	0,04	0,15	1
	Hazelnut	-0,05	-0,07	0,50	-0,05	-0,03	-0,06	0,54	-0,02	1
	Olive	-0,01	-0,05	-0,03	-0,02	-0,02	0,04	-0,02	-0,02	-0,03	1
	Plantain	0,13	0,23	-0,16	-0,03	-0,10	0,12	-0,11	-0,10	-0,15	0,13	1
	Plane	-0,05	-0,07	-0,04	0,52	0,11	0,30	0,07	0,19	-0,04	-0,02	-0,08	1
	Poaceae	-0,09	-0,08	-0,09	-0,09	-0,06	-0,07	-0,10	-0,08	-0,09	0,31	0,41	-0,09	1
	Willow	-0,08	-0,12	0,02	0,38	0,22	0,26	0,24	0,40	0,03	-0,03	-0,12	0,32	-0,10	1
	Urticaceae	0,15	0,39	-0,13	-0,14	-0,09	-0,15	-0,17	-0,11	-0,12	0,07	0,51	-0,12	0,38	-0,18

Table 4 :

 4 Relative risk (RR) and 95% confidence interval of SABA sales for an interquartile increase in pollen concentration,Clermont-Ferrand, 2010[START_REF] Marco | Trends in the prevalence of asthma and allergic rhinitis in Italy between 1991 and 2010[END_REF], 2014-2015.

	Pollen	Lag (days)	Interquartile RR	Confidence interval 95%
	Ambroisia	3	5	1,051	[0,993 ; 1,112]
	Alder	0-7	15	1,003	[0,957 ; 1,051]
	Birch	0-5	60	1,130	[1,063 ; 1,202]
	Charm	2-5	7	1,032	[1,019 ; 1,046]
	Oak	1	59	1,014	[1,003 ; 1,025]
	Ash	4	45	1,079	[1,037 ; 1,122]
	Hazelnut	2-3	40	1,004	[0,939 ; 1,073]
	Plantain	0-7	5	0,971	[0,908 ; 1,037]
	Plane tree	0-1	12	1,151	[1,076 ; 1,231]
	Poaceae	0-7	43	0,982	[0,935 ; 1,031]
	Urticaceae	1-2	66	1,023	[0,963 ; 1,086]

Table 5 :

 5 Relative risk of SABA sales and 95% confidence interval, by age , associated with a variation equal to an interquartile range of pollen distribution ,Clermont-Ferrand, 2010[START_REF] Marco | Trends in the prevalence of asthma and allergic rhinitis in Italy between 1991 and 2010[END_REF], 2014-2015.

	Significant resultas ( p<0,05) in bold
					6-14 years		15-44 years		45-64 years		≥ 65 years
	Pollen Lag (days) Interquar-	RR	Confidence interval	RR	Confidence interval	RR	Confidence interval	RR	Confidence interval
			tile		95%		95%		95%		95%
	Ambroisia	3	5	1,000	[ 0,999 ; 1,001 ]	1,130	[ 1,011 ; 1,264 ]	1,000	[ 0,999 ; 1,001 ]	0,966	[ 0,917 ; 1,017 ]
	Alder	0-7	15	1,000	[ 0,9996 ; 1,0004 ]	1,016	[ 0,991 ; 1,041 ]	0,912	[ 0,823 ; 1,012 ]	1,000	[ 0,9996 ; 1,0004 ]
	Birch	0-5	60	1,168	[ 0,974 ; 1,401 ]	1,153	[ 1,068 ; 1,244 ]	1,110	[ 1,04 ; 1,186 ]	1,006	[ 0,992 ; 1,020 ]
	Charm	2-5	7	1,069	[ 0,882 ; 1,295 ]	1,047	[ 1,031 ; 1,064 ]	1,043	[ 1,009 ; 1,078 ]	1,000	[ 0,9999 ; 1,0001 ]
	Oak	1	59	1,015	[ 0,863 ; 1,194 ]	1,022	[ 1,008 ; 1,037 ]	1,001	[ 0,996 ; 1,005 ]	1,010	[ 0,998 ; 1,022 ]
	Ash	4	45	1,013	[ 0,985 ; 1,042 ]	1,069	[ 1,022 ; 1,117 ]	1,088	[ 1,027 ; 1,152 ]	1,013	[ 0,983 ; 1,044 ]
	Hazelnut	2-3	40	1,084	[ 1,001 ; 1,175 ]	1,012	[ 0,989 ; 1,036 ]	0,894	[ 0,813 ; 0,984 ]	1,055	[ 0,958 ; 1,161 ]
	Plantain	0-7	5	0,996	[ 0,862 ; 1,150 ]	0,942	[ 0,861 ; 1,030 ]	0,962	[ 0,877 ; 1,056 ]	0,944	[ 0,862 ; 1,034 ]
	Plane tree	0-1	12	1,114	[ 0,949 ; 1,308 ]	1,174	[ 1,073 ; 1,284 ]	1,132	[ 1,043 ; 1,229 ]	1,015	[ 0,975 ; 1,057 ]
	Poaceae	0-7	43	1,048	[ 1,007 ; 1,091 ]	0,951	[ 0,882 ; 1,026 ]	1,000	[ 0,9998 ; 1,0002 ]	1,000	[ 0,999 ; 1,001 ]
	Urticaceae	1-2	66	1,000	[ 0,999 ; 1,001 ]	1,035	[ 0,954 ; 1,122 ]	1,029	[ 0,943 ; 1,123 ]	0,992	[ 0,974 ; 1,011 ]

(Conseil national de l'ordre des médecins)

SERMENT D'HIPPOCRATE

Au moment d'être admis(e) à exercer la médecine, je promets et je jure d'être fidèle aux lois de l'honneur et de la probité.

Mon premier souci sera de rétablir, de préserver ou de promouvoir la santé dans tous ses éléments, physiques et mentaux, individuels et sociaux.

Je respecterai toutes les personnes, leur autonomie et leur volonté, sans aucune discrimination selon leur état ou leurs convictions. J'interviendrai pour les protéger si elles sont affaiblies, vulnérables ou menacées dans leur intégrité ou leur dignité. Même sous la contrainte, je ne ferai pas usage de mes connaissances contre les lois de l'humanité. J'informerai les patients des décisions envisagées, de leurs raisons et de leurs conséquences.

Je ne tromperai jamais leur confiance et n'exploiterai pas le pouvoir hérité des circonstances pour forcer les consciences.

Je donnerai mes soins à l'indigent et à quiconque me les demandera. Je ne me laisserai pas influencer par la soif du gain ou la recherche de la gloire.

Admis(e) dans l'intimité des personnes, je tairai les secrets qui me seront confiés. Reçu(e) à l'intérieur des maisons, je respecterai les secrets des foyers et ma conduite ne servira pas à corrompre les moeurs. Je ferai tout pour soulager les souffrances. Je ne prolongerai pas abusivement les agonies. Je ne provoquerai jamais la mort délibérément.

Je préserverai l'indépendance nécessaire à l'accomplissement de ma mission. Je n'entreprendrai rien qui dépasse mes compétences. Je les entretiendrai et les perfectionnerai pour assurer au mieux les services qui me seront demandés. J'apporterai mon aide à mes confrères ainsi qu'à leurs familles dans l'adversité.

Que les hommes et mes confrères m'accordent leur estime si je suis fidèle à mes promesses ; que je sois déshonoré(e) et méprisé(e) si j'y manque.

Nom, Prénom

Signature

Funding: Acknowledgement of partial funding by Astra-Zeneca, Boehringer Ingelheim, ALK-Abello. The researchers are totally independent of the funder.

Conclusion :

Pour conclure, notre étude menée pendant 5ans dans l'agglomération de Clermont-Ferrand est la première à mettre en évidence le rôle des pollens de Bouleau, Chêne, Frêne dans l'augmentation du risque relatif de ventes de bronchodilatateurs de courte durée d'action (SABA), et montre également une relation avec les pollens de Charme et de Platane malgré leur faible concentration dans l'air ( inférieure à 1% du total des pollens).

L'augmentation des ventes de SABA est également associée aux pollens de Noisetier, Poacées et Ambroisie dans certaines classes d'âge. pierre molds and outdoor air pollution. The lack of knowledge about pollen sensitization in our general population should be acknowledged as a limitation. Our population was entirely urban. Pollen effect will vary by climatic region [14]. The lack of association found between pollen exposure and SABA sales in subjects over 65 years supports the argument of SABA sales being mainly for asthmatic and not COPD patients.

In conclusion, using an entire urban population in central France over a 5-year period, our study is the first to support the well documented relationship between asthma exacerbations, as demonstrated by SABA sales, and Betula, Fraxinus and Quercus pollen exposure while also showing relationships with Platanus and Carpinus pollens despite their low pollen counts. Increased SABA sales were also associated with Poaceae, Corylus and Ambrosia in some age classes. Further studies in other geographical areas with different climatic conditions are needed to complement these results.

Conflicts of interest

The authors have no conflicts of interest to declare.

SERMENT D'HIPPOCRATE

En présence des Maîtres de cette FACULTE et de mes chers CONDISCIPLES, je promets et je jure d'être fidèle aux lois de l'Honneur et de la Probité dans l'exercice de la Médecine.

Je donnerai mes soins gratuits à l'indigent et je n'exigerai jamais un salaire au-dessus de mon travail. Admis dans l'intérieur des maisons, mes yeux ne verront pas ce qui s'y passe, ma langue taira les secrets qui me seront confiés et mon état ne servira pas à corrompre les moeurs ni à favoriser le crime.

Respectueux et reconnaissant envers mes MAÎTRES, je rendrai à leurs enfants l'instruction que j'ai reçue de leurs pères.

Que les HOMMES m'accordent leur estime si je suis fidèle à mes promesses. Que je sois couvert d'OPPROBRE et méprisé de mes confrères si j'y manque.

Nom, Prénom Signature


Alexandre Bouënard

Sylvie Gibet

Marcelo M Wanderley

Hybrid Motion Control combining Inverse Kinematics and Inverse Dynamics Controllers for Simulating Percussion Gestures

Keywords:

Virtual characters playing in a realistic way virtual musical instruments need to interact in real-time with the simulated sounding environment. Dynamic simulation is a promising approach to finely represent and modulate this interaction. Moreover, capturing human motion provides a database covering a large variety of gestures with different levels of expressivity. We propose in this paper a new data-driven hybrid control technique combining Inverse Kinematics (IK) and Inverse Dynamics (ID) controllers, and we define an application for consistently editing the motion to be simulated by virtual characters performing percussion gestures.

Introduction

Playing a musical instrument involves complex human behaviours. While performing, a skilled musician is able to precisely control his motion and to perceive both the reaction of the instrument to his actions and the resulting sound. Transposing these real-world experiences into virtual environments provides the possibility to explore novel solutions for designing virtual characters interacting with virtual musical instruments.

This paper proposes a physics-based framework in which a virtual character dynamically interacts with a physical simulated percussive instrument. It enables the simulation of the subtle physical interactions that occur as the stick makes contact with the drum membrane, while taking into account the characteristics of the preparatory gesture. Our approach combines human motion data and a hybrid control method composed of kinematics and physics-based controllers for generating compelling percussion gestures and producing convincing contact information.

Such physics framework makes possible the real-time manipulation and mapping of gesture features to sound synthesis parameters at the physics level, producing adaptative and realistic virtual percussion performances1 .

Related Work

Controlling adaptative and responsive virtual characters has been intensively investigated in computer animation research. Most of the contributions have addressed the control of articulated figures using robotics-inspired ID controllers. This has inspired many works for handling different types of motor tasks such as walking, running [START_REF] Hodgins | Animating Human Athletics[END_REF], composing these tasks [START_REF] Faloutsos | Composable Controllers for Physics-Based Character Animation[END_REF] and easying the hard process of tuning such controllers [START_REF] Allen | On the Beat!: Timing and Tension for Dynamic Characters[END_REF]. More related to our work are hybrid methods, based on the tracking of motion capture data performed by a fully dynamically controlled character. The specificity of our contribution lies in the integration and the collaboration of IK and ID controllers, rather than handling strategies for transtionning between kinematic and dynamic controllers [START_REF] Shapiro | Hybrid Control for Interactive Character Animation[END_REF][START_REF] Zordan | Dynamic Response for Motion Capture Animation[END_REF]. IK has also been used as a pre-process for modifying the original captured motion and simulating it on a different character anthropometry [START_REF] Zordan | Tracking and Modifying Upper-body Human Motion Data with Dynamic Simulation[END_REF]. We rather use IK as a basis of our hybrid control method for specifying the control of a dynamic character from end-effector trajectories. This hybrid collaboration is particularly consistent for the synthesis of percussive gestures, which is not taken into account in previous contributions [START_REF] Zordan | Tracking and Modifying Upper-body Human Motion Data with Dynamic Simulation[END_REF]Bouënard et al, 2008-a).

Data-driven Hybrid Motion Control

A motion capture database contains a set of various percussion performances including different drumstick grips, various beat impact locations and several musical playing variations. We propose two ways for achieving the motion control (Figure 1), either by tracking motion capture data in the Joint space (angular trajectories), or tracking end-effector trajectories in the 3D Cartesian space. Tracking motion capture data in the Joint space requires ID control, whereas tracking in the end-effector (Cartesian) space requires both IK and ID (hybrid) control.

In the latter case, end-effector targets (X T ) in the 3D Cartesian space are extracted from the motion capture database, and used as input for the IK algorithm to compute a kinematic posture Θ T (vector of joint angular targets). We chose the Damped Least Squares method [START_REF] Wampler | Manipulator Inverse Kinematic Solutions based on Vector Formulations and Damped Least Squares[END_REF] driven by equation (1), a robust adaptation of the pseudo-inverse regarding the singularity of the inverse kinematics problem. J + Θ is the pseudo-inverse of the Jacobian and X S represents the current end-effector position of the system to be controlled. Other IK techniques may be equally used, such as the Jacobian transpose or learning techniques [START_REF] Gibet | Expressive Gesture Animation based on Non-Parametric Learning of Sensory-Motor Models[END_REF].

Angular targets Θ T and current states (Θ S , ΘS ) are then used as inputs of the ID algorithm, as expressed in equation ( 2), for computing the torque (τ ) to be exerted on the articulated rigid bodies of the dynamical virtual character. This one is composed of rigid bodies articulated by springs parameterized by damping and stiffness coefficients (k d , k s ). This hybrid approach enables the manipulation of physically simulated motion capture data in the 3D Cartesian space (X T ) instead of the traditional angular space (Θ T ), which is more consistent and intuitive for controlling percussion gestures by using end-effector trajectories, for instance drumsticks extremities obtained from the motion capture database.

∆Θ T = -λ.J + Θ .(X S -X T ), Θ T = Θ S + ∆Θ T (1) τ = k s .(Θ S -Θ T ) -k d . ΘS (2)

Results

The results obtained by the two tracking modes are compared, keeping the same parameterization of the damped springs composing the virtual character. We ran the simulation on a set of percussion gestures (French grip, legato) recorded at a sample rate of 250 Hz for capturing the whole body of the performer as well as the drumsticks. The hybrid control scheme tracks one percussion gesture for synthesizing whole arm movements solely from the specification of drumstick tip trajectories.

Figure 2 presents the comparison between raw motion capture data and data generated by the IK process. It shows that data generated by the IK formulation are consistent with real ones, especially for the elbow flexion angle that is one of the most significant degree of freedom of the arm in percussion gestures, especially during preparatory phases (Bouënard et al, 2008-b).

We finally present the comparison of the two control modes (ID control only and hybrid control) in Figure 3. One interesting issue is the accuracy of the hybrid control mode compared to the simple ID control. This observation lies in the fact that the convergence of motion capture tracking is processed in the Joint space in the case of ID control, adding and amplifying multiple errors on the different joints and leading to a greater error than processing the convergence in the Cartesian space for the hybrid control. The main drawback of this improvement is however the additional computationnal cost of the IK algorithm which is processed at every simulation step. It provides nevertheless a more consistent and flexible motion edition technique for controlling a fully physics-based virtual character.

Conclusion

We proposed in this paper a physically-enabled environment in which a virtual character can be physically controlled and interact with the environment, in order to generate virtual percussion performances. More specifically, the presented hybrid control mode combining IK and ID controllers leads to a more intuitive yet effective way of editing the motion to be simulated only from drumstick extremity trajectories. Future work includes the extension and improvement of our hybrid control technique for editing and simulating percussion motion in the 3D Cartesian space.

Figure 1 :

 1 Figure 1: Physics-based motion capture tracking, either in the Joint Space from angular trajectories, or in the Cartesian Space from end-effector trajectories. The Hybrid Control involves the combination of IK and ID controllers.

Figure 2 :

 2 Figure 2: Comparison of elbow flexion angle trajectories: original motion capture data vs. data generated by the IK algorithm.

Figure 3 :

 3 Figure 3: Comparison of drumstick trajectories: original motion capture data vs. Joint space (ID) physics tracking vs. Cartesian space (IK + ID) physics tracking.

More details about sound synthesis schemes as well as our system architecture can be found in(Bouënard et al,

2009).