Huan Zhao

Baptiste Gault

Dirk Ponge

Dierk Raabe

Frédéric De Geuser

Parameter free quantitative analysis of atom probe data by correlation functions: application to the precipitation in Al-Zn-Mg-Cu

Atom probe tomography enables precise quantification of the composition of second phase particles from their early stages, leading to improved understanding of the thermodynamic and kinetic mechanisms of phase formation and quantify structure-property relationships. Here we demonstrate how approaches developed for small-angle scattering can be adapted to atom probe tomography. By exploiting nearest-neighbor distributions and radial distribution function, we introduce a parameter free methodology to efficiently extract information such as particle size, composition, volume fraction, number density and inter-particle distance. We demonstrate the strength of this approach in the analysis of a precipitation-hardened model Al-Zn-Mg-Cu highstrength lightweight alloy.

Al-Zn-Mg-(Cu) alloys of the 7XXX Al-alloys are precipitation-strengthened Al-alloys exhibiting high-strength and expected to play an important role for lightweight transportation. The precipitation sequence in the bulk of Al-Zn-Mg-Cu alloys has been studied and is well established [1][2][3]: solid solution → GP zones→ metastable η'→ stable η (MgZn2). Atom probe tomography (APT) provides three-dimensional (3D), nanoscale analytical mapping of materials, and is uniquely positioned to measure the local chemical composition and 3D morphology of individual precipitates. However, early designs of the instruments had an angular field-of-view limited to less than 10 degrees and thus only small particle numbers would typically be intercepted and analyzed [4], thereby limiting the possibility of deriving precisely important metallurgical measures e.g. precipitate size, particle spacing, composition, volume fraction, and number density. The significant increase in the field of view of the technique associated with modern microscope designs [5] often allow for hundreds or thousands of nanoparticles to be captured within a single dataset [6], which makes data extraction and processing tedious, and most often erroneous [7].

Over 50 years of theoretical developments in the small-angle scattering community have enabled the development of a complete formalism to fit experimental results with analytical functions to derive microstructural characteristics [8,9]. Here, we introduce a new methodology to process radial distribution function (RDF)-based model fitting from atom probe data to provide complete characterization of both the precipitates and the matrix, without the need for any input parameters. Parameter-selection by various users is a key hurdle in ensuring reliability and reproducibility of data analysis as [10][11][12][13]. Our methodology makes use of widely available integral metrics, the distribution of distance to the first nearest-neighbor (1NN) and speciesspecific RDF computed on the entire dataset, making use of all available information, and thereby improving statistics. We evidence the strength of this new approach through the analysis of the temporal evolution of the precipitates formed during aging of a model Al-Zn-Mg-Cu alloy.

An Al-Zn-Mg-Cu alloy was cast into a 200mm*190mm*40mm ingot in a vacuum induction furnace. The ingot was homogenized at 475 °C for 1.5 hours and water quenched followed by hot rolling at 450 °C to 3mm thickness and water quenched. Samples were then solution treated at 475 °C for an hour and quenched in water, immediately followed by an aging treatment at 120 o C for 30 minutes, 2 h and 24 h. An overaging step was performed on the 24h aged sample by further aging for 6 h at 180°C. A specimen was also analyzed immediately after quench. It will be further called 'as quenched' even though it has in fact undergone roughly 6h of natural ageing before APT analysis which may have already caused some degree of clustering. Table 1 summarizes the chemical composition measured by wet chemical analysis after homogenization. Specimens for APT measurement and analysis were prepared to investigate the precipitation in the bulk by using a two-stage electrochemical polishing protocol described in [START_REF] Miller | Atom Probe Microanalysis: Principles and Applications to Materials Problems[END_REF]. APT was performed in high-voltage pulsing mode with a pulse fraction of 20% at a repetition rate of 250 kHz and at a base temperature of 50K in a Cameca Local Electrode Atom Probe (LEAP) 5000XS.

The total voltage was increased to maintain an average detection rate of 1 evaporative event per 100 pulses. Datasets containing 50-150 million ions were acquired for each aging state. Data reconstruction and analysis were performed using the Integrated Visualization and Analysis calibrate the reconstructions parameters as described by Gault et al. [START_REF] Gault | [END_REF].

The aging response was followed by Vickers hardness measurements using a 0. From a typical dataset, two integral information can be obtained: the global composition and the matrix composition. The former is derived from counting the relative number of ions of each element within the mass spectrum. The latter can be derived from the distribution of isolated atoms for the determination of the matrix composition (DIAM) method [16]. DIAM is based on the probability for each solute species to have no neighbor (i.e. to be isolated) at a given distance r, in comparison to that obtained from a random distribution of solutes. Both can be directly derived from the first nearest-neighbor distribution.

For characterizing the precipitates present in the volume, we use radial distribution functions calculated with each solute of a specific species as the central atom. The calculation is then repeated for each species separately. The RDF 𝑛 𝑖-𝑗 (𝑟) is the number of atoms of species 𝑗 at a distance 𝑟 of an atom of species 𝑖. To speed up the calculation, the RDF is computed on a randomly-selected subset of atoms, which does not affect the results, since the RDF is normalized by the composition. Calculation of an RDF for one solute in a 40 million ions dataset was timed to take approx. 20 minutes, while it lasted only approx. 1 minute on a subsampled dataset (1 in 40 ions). Even though subsampling increases statistical noise for low counts and should be used with care, no significant effect was observed.

The 𝑛 𝑖-𝑗 (𝑟) enable to compute the average composition 𝐶 𝑖-𝑗 (𝑟) of element 𝑗 at a distance 𝑟 of an element 𝑖:

𝐶 𝑖-𝑗 (𝑟) = 𝑛 𝑖-𝑗 (𝑟) ∑ 𝑛 𝑖-𝑗 (𝑟) 𝑗 (1)
We call 𝐶 𝑖 the average composition of element 𝑖 . In an isotropic system, 𝐶 𝑖 ⋅ 𝐶 𝑖-𝑗 (𝑟) is the correlation (convolution) of the spatial composition of element 𝑖 and that of element 𝑗.

𝐶 𝑖 ⋅ 𝐶 𝑖-𝑗 (𝑟) =< 𝐶 𝑖 (𝑟 1 ⃗⃗⃗ ) ⋅ 𝐶 𝑗 (𝑟 2 ⃗⃗⃗ ) > with 𝑟 = |𝑟 2 ⃗⃗⃗ -𝑟 1 ⃗⃗⃗ | (2)
At large 𝑟 this convolution necessarily approaches 𝐶 𝑖 ⋅ 𝐶 𝑗 . We can subtract this final value and introduce the 𝑖 -𝑗 pair correlation function (PCF) 𝛾 𝑖-𝑗 (𝑟):

𝛾 𝑖-𝑗 (𝑟) = 𝐶 𝑖 ⋅ 𝐶 𝑖-𝑗 (𝑟) -𝐶 𝑖 ⋅ 𝐶 𝑗 (3)
Where 𝛾 𝑖-𝑗 (𝑟) = 0 when there is no correlation, which is always true for large 𝑟. It can be rewritten:

𝛾 𝑖-𝑗 (𝑟) =< (𝐶 𝑖 (𝑟 1 ⃗⃗⃗ ) -𝐶 𝑖 ) ⋅ (𝐶 𝑗 (𝑟 2 ⃗⃗⃗ ) -𝐶 𝑗 ) > with r = |𝑟 2 ⃗⃗⃗ -𝑟 1 ⃗⃗⃗ | (4)
or

𝛾 𝑖-𝑗 (𝑟) =< Δ𝐶 𝑖 (𝑟 1 ⃗⃗⃗ )Δ𝐶 𝑗 (𝑟 2 ⃗⃗⃗ ) > with 𝑟 = |𝑟 2 ⃗⃗⃗ -𝑟 1 ⃗⃗⃗ | (5)
to highlight that only the fluctuation of composition Δ𝐶 𝑖 , i.e. the difference with the average, is relevant to the PCF. This correlation function is analogous to that introduced by Debye and Bueche [17] and which the basis of the small-angle scattering formalism. We can further introduce a normalized correlation function 𝛾 𝑖-𝑗 0 (𝑟) by writing:

𝛾 𝑖-𝑗 (𝑟) = Δ𝐶 𝑖 Δ𝐶 𝑗 ⋅ 𝛾 𝑖-𝑗 0 (𝑟) (6)
where 𝛾 𝑖-𝑗 0 (0) = 1 and 𝛾 𝑖-𝑗 0 = 0 at large 𝑟. 𝛾 𝑖-𝑗 0 (𝑟) is only dependant on the geometry of the objects. In particular, for 𝑖 = 𝑗, we have the auto-correlation:

𝛾 𝑖-𝑖 (𝑟) = Δ𝐶 𝑖 2 ⋅ 𝛾 𝑖-𝑖 0 (𝑟) (7)
From its definition, the value of 𝛾 𝑖-𝑗 at the origin Δ𝐶 𝑖 2 is the mean squared composition fluctuation, which directly depends on the quantity and composition of the objects. Contrasting with 𝛾 𝑖-𝑖 0 (𝑟), Δ𝐶 𝑖 2 is exclusively composition-based, it is essentially immune to typical APT reconstruction artefacts such as local magnification or preferential field evaporation caused by the difference in the electric field necessary to induce field evaporation for different species or phases [18,19]. In small-angle scattering, the separation of the geometry-based normalized correlation function and the mean squared fluctuation enables the measurement of the size of objects irrespective of their quantity or of the scaling of the measurement. In APT, especially for very small objects, the composition is likely more accurate, while 𝛾 𝑖-𝑗 0 is likely more questionable.

We assume 2 phases of homogeneous composition in element 𝑖, i.e. precipitates composition 𝐶 𝑝 𝑖 in a matrix of composition 𝐶 𝑚 𝑖 . We further assume that both share the same atomic volume Ω.

While this is never strictly true, the difference in atomic volumes between phases is usually small compared to the possible apparent density differences due to e.g. local magnifications [18]. In these conditions, we can write the precipitates volume fraction as:

𝑓 𝑣 = 𝐶 𝑖 -𝐶 𝑚 𝑖 𝐶 𝑝 𝑖 -𝐶 𝑚 𝑖 ( 8
)
which should be true for any 𝑖.

Within these assumptions we can calculate the average of the product of the composition fluctuations:

Δ𝐶 𝑖 Δ𝐶 𝑗 = 𝑓 𝑣 (1 -𝑓 𝑣 )(𝐶 𝑝 𝑖 -𝐶 𝑚 𝑖 )(𝐶 𝑝 𝑗 -𝐶 𝑚 𝑗 ) (9)
In particular, for 𝑖 = 𝑗 Δ𝐶 𝑖 2 = 𝑓 𝑣 (1 -𝑓 𝑣 )(𝐶 𝑝 𝑖 -𝐶 𝑚 𝑖 ) 2 (10) or

Δ𝐶 𝑖 2 = (𝐶 𝑝 𝑖 -𝐶 𝑖 )(𝐶 𝑖 -𝐶 𝑚 𝑖 ) (11)
The value of the pair correlation function at 𝑟 = 0, in combination with the matrix composition obtained from DIAM, provides a mean to derive both the volume fraction and the precipitates composition, irrespective of the particles shape and without being affected by local magnification.

The normalized correction function 𝛾 0 (𝑟) can be calculated analytically for simple shapes. For a sphere of radius 𝑅, i.e. of homogeneous density and with a sharp interface with the matrix, it is

given by [START_REF] Guinier | Small-Angle Scattering of X-Rays[END_REF][START_REF] Philippe | [END_REF]:

𝛾 0 𝑠𝑝ℎ𝑒𝑟𝑒 (𝑟, 𝑅) = { 1 - 3𝑟 4𝑅 + 𝑟 3 16𝑅 3 (𝑟 ≤ 2𝑅) 0 (𝑟 > 2𝑅) ( 12
)
For a size distribution of spheres (e.g. normal, log-normal,…) this can be readily integrated numerically. We have fitted all the experimental 𝛾 𝑖-𝑗 (𝑟) for all aging conditions independently, but with the same size for all 𝑖 -𝑗 pairs. We use a lognormal distribution of spheres with a 20% dispersity. We also add a contribution of an excluded volume [22], which is a small correction to the PCF depending on the size and volume fraction which gives a negative contribution originating from the impossibility of having two precipitates on top of each other. This contribution essentially helps to reproduce the fact that some curves go through a negative minimum before reaching zero for larger 𝑟. In any case, the validity of the fitting model for 𝛾 0 (𝑟) should be assessed in regard with the distortions due to local magnifications as well as with the validity of the chosen shape and size dispersion. Nevertheless, it provides a robust effective average size measured through all existing objects in the volume.

The results are a complete set of Δ𝐶 𝑖 2 and 𝑅 for all times and 𝑖. The next step is to compute the 𝐶 𝑝 𝑖 from eq. ( 11) and 𝐶 𝑝 𝐴𝑙 = 1 -𝐶 𝑝 𝑍𝑛 -𝐶 𝑝 𝑀𝑔 -𝐶 𝑝 𝐶𝑢 . From these 𝐶 𝑝 we can derive the volume fractions 𝑓 𝑣 from eq. ( 10) which gives us a set of volume fractions calculated for each solute element. Since we assume that there is a single type of object, we will reduce the uncertainty by fixing the volume fraction as the average of that computed from eq. ( 10) with Zn and Mg (the low content of Cu both on average and in the precipitates, makes the calculations noisy for this element). The mean diameter of the precipitates is obtained from the fit, but as mentioned above, is affected by possible local magnification artefacts. The number density is derived from the ratio of the volume fraction to the average volume.

This combined DIAM and RDF-based protocol was applied to characterize the matrix composition and the precipitates evolution over the course of the aging process. Figure 2 (a-b) report the evolution of matrix composition as well as the composition measured in the entire dataset, as well as the precipitates composition over the course of the aging process. Figure 3 (ad) show the volume fraction of precipitates, their average radius, the number density, and the distance between precipitates roughly estimated as 𝑛 𝑣 -3 . Since the solute content of the precipitates evolves with ageing, we chose to represent only the contribution of solutes to the volume fraction to better visualize the advancement of the reaction.

While Cu low composition may be more sensitive to noise and ranging issues, Zn and Mg global dataset composition should be essentially independent of aging time and equal to the nominal composition. While this is observed initially, the global composition in Zn, and to some extent in Mg, eventually drops to a lower value in the peak aged state, and more importantly so after over aging. This could only be attributed to a loss of solutes to grain boundaries or to often-reported instrumental issues related to the preferential field evaporation of specific solutes [23].

The results show a number density in the range of 10 25 m -3 of solute-rich clusters approx. 1 nm in size form in the as-quenched state. This might be caused by the natural aging during sample preparation. The precipitates composition in the three solutes plateaus after 30 min to approx. 75 at % Al, 13 at % Zn, 10 at% Mg and 2 at % Cu. Over the first 2 hours at 120°C aging, nearly η' phase and thus can be considered as GP zones. It should also be noted that within the precipitates, Cu remains in low composition and almost unchanged at 120°C aging, while exhibiting a strong increase in the overaging step. This likely originates from the low diffusivity of Cu, together with the solubility in the precipitates [24]. Since its content was stable from the beginning, however, it means that the very early clusters/GP zones are comparatively richer in Cu, which may indicate that Cu plays a significant role in GP zone nucleation. Significant coarsening is evidenced in the overaged state as revealed by the increase of precipitates radius, volume fraction and inter-precipitates distance. Only then does the composition of the precipitates reach a content compatible with η'. Our approach provides all the meaningful metallurgical information, similarly to what would usually be performed in small-angle scattering studies [25,26], except that here the composition of the objects can be directly determined. This information is necessary to develop mean-field models to explain the mechanical behavior of materials [27] but is rarely available directly from APT. The methodology we introduce here is parameter-free, versatile and can be applied to numerous systems, provided that the assumptions from the model are not invalidated. In cases where a large number of objects are imaged within the dataset, our alternative approach ensures the highest possible statistical significance of the results, as well as reproducibility of the results.

  5 kg load. The values reported in Figure 1 are the average of 10 individual measurements. The hardness of the supersaturated solid solution state is 120±3 HV0.5. The hardness then progressively increases up to 24 hours, with a peak hardness of 185±5 HV0.5. The overaging step resulted in significant coarsening and a decrease in hardness down to 171±3 HV0.5. Representative datasets across the aging process are shown inset in Figure 1. Iso-surfaces encompassing regions in the reconstruction containing over 10at% Zn highlights the formation and coarsening of Zn-Mg-rich precipitates.

Figure 1 :

 1 Figure 1: Evolution of the hardness as a function of aging time. Inset are atom maps to show the effect of nanostructures on the hardness. Al atoms are shown in grey and Zn atoms in dark cyan. The precipitates are visualized with 10 at% Zn iso-composition surface. Only part of the atoms maps are shown in order to obtain the same scale for clarity. The atom maps are to scale.

Figure 2 :

 2 Figure 2: (a) evolution of the composition measured in the entire datasets (discs, the solid line is a guide to the eye) and the matrix composition (diamonds, the dashed line is a guide to the eye) for the different solutes as a function of aging time. (b) evolution of the precipitates composition (discs, the dashed line is a guide to the eye) for the different solutes as a function of aging time.

Figure 3 :

 3 Figure 3: Evolution during the aging process of (a), the volume fraction of precipitates; (b), the precipitate radius; (c), volume density of precipitates; (d), average distance between precipitates.

Table 1 .

 1 Bulk chemical composition of a model Al-Zn-Mg-Cu alloy (in at%)

	Alloy	Zn	Mg	Cu	Zr	Fe	Si	Al
	(at %)	2.69	2.87	0.95	0.05	0.01	<0.01	balance

Acknowledgements H. Zhao would like to acknowledge the Chinese Scholarship Council for the PhD scholarship granted to support this work. U. Tezins and A. Sturm are acknowledged for their support in the use of the atom probe and PFIB facility at MPIE.


Romain Charmet

Astrid Van_Hylckama_Vlieg

Marine Germain

Ronan Roussel

Michel Marre

Stéphanie Debette

Philippe Amouyel

Jean-François Deleuze

Samy

Frits R Hadjadj

Rosendaal

Pierre-Emmanuel Morange

David-Alexandre Trégouët

Trégouët David-Alexandre

Association of impaired renal function with venous thrombosis: a genetic risk score approach

Keywords: genetics, estimated glomerular filtration rate, renal function, venous thrombosis, genetic risk score, association study Abbrevations : CKD: Chronic Kidney Disease eGFR: estimated Glomerular Filtration Rate GRS: Genetic Risk Score GWAS: Genome Wide Association Study SNP: Single Nucleotide Polymorphisms VT: Venous Thrombosis

Objective

The association between impaired kidney function and venous thrombosis has been previously reported but supportive data are still sparse. We here wish to strengthen this association by investigating, by use of a genetic risk score approach, whether single nucleotide polymorphisms (SNPs) known to decrease the estimated glomerular filtration rate (eGFR), a surrogate marker for renal dysfunction, are associated with increased risk of venous thrombosis.

Approach and Results

Fifty-one polymorphisms selected from the literature to robustly associate with eGFR were first tested for association with venous thrombosis in a French case-control collection of 1,953 patients and 2,338 healthy individuals. This led to the identification of a genetic risk score based on 9 polymorphisms that strongly associated with increased risk (Odds Ratio (OR) = 1.09 [1.06 -1.15], p = 1.44 10 -7 ). This genetic score association replicated (OR = 1.18 [1.11 -1.26], p = 8.86 10 -8 ) in an independent sample of 1,289 patients and 1,049 healthy controls part of the Dutch MEGA study. We then categorized the genetic score distribution observed in the combined samples into quintiles. Compared with the lowest quintile, the OR for increased risk of disease associated with the second, third, fourth and fifth quintiles were 1. 13 [0.94 -1.16], 1.47 [1.22 -1.77], 1.52 [1.26 -1.82] and 1.70 [1.41 -2.05], respectively. Conclusions Using a genetic risk score analysis, our study provides new elements supporting the association between impaired renal function and the risk of venous thrombosis.

Highlights

 We identified a genetic risk score based on 9 eGFR-associated SNPs that impact on the risk of VT.  Individuals with a score higher than 11 are associated with a 1.42 increased risk of disease  Biological mechanisms underlying this association need to be further investigated

Introduction

Venous thrombosis (VT), that encompasses both deep vein thrombosis and pulmonary embolism, is the second most common cardiovascular disease and the third in terms of mortality. Its incidence is estimated to be ~200 per 100 000 person-years in Europe [START_REF] Heit | The epidemiology of venous thromboembolism[END_REF] and its recurrence rate within 10 years is close to 30%. The disease also represents a significant spending in health care 2 , it is for example associated with a total annual cost ranging from €1.5 to 13.2€ billion for the EU. [START_REF] Kröger | Prevalence and economic burden of pulmonary embolism in Germany[END_REF] The nature of the complex pathophysiological mechanisms that lead to VT is not fully characterized. Disturbances of the coagulation and fibrinolysis cascade leading to hypercoagulable states are clearly the most important contributor to VT etiology. Obesity-related mechanisms, inflammation [START_REF] Lwaleed | Inflammation, Endothelial Dysfunction, and Thromboembolism[END_REF] , platelets [START_REF] Montoro-García | The Role of Platelets in Venous Thromboembolism[END_REF] and complement cascade [START_REF] Foley | Examining coagulation-complement crosstalk: complement activation and thrombosis[END_REF] are additional biological systems that contribute to the development of the disease. However, despite these results of intensive research efforts, there are so far limited prognosis tools that help clinicians to predict which individuals are at risk for a VT event. More investigations are thus needed to better disentangle the etiological architecture underlying VT. A meta-analysis of 5 community-based cohorts has shown that decreased estimated glomerular filtration rate (eGFR) was associated with increased VT risk [START_REF] Mahmoodi | Association of mild to moderate chronic kidney disease with venous thromboembolism: pooled analysis of five prospective general population cohorts[END_REF] . It was further hypothesized that this association was partially mediated by elevated levels of coagulation Factor VIII and von Willebrand factor. [START_REF] Ocak | Role of hemostatic factors on the risk of venous thrombosis in people with impaired kidney function[END_REF] Inflammation and coagulation biomarkers are associated with decreasing kidney function in ambulatory adults without established cardiovascular disease or chronic kidney disease. Investigations in the ARIC study [START_REF] Bash | Inflammation, hemostasis, and the risk of kidney function decline in the Atherosclerosis Risk in Communities (ARIC) Study[END_REF] demonstrated that increased levels of factor VIIIc, fibrinogen, and von Willebrand Factor were significantly associated with increased risk of incident chronic kidney disease, of which decreased eGFR is a surrogate marker, in European Americans. The pathophysiology underlying the association of hemostatic factors to kidney function decline is unclear, although triggers of hemostatic activation, including vascular injury, endothelial dysfunction, and inflammation, have been proposed as potential mechanisms. To provide additional support to this hypothesis, we here propose the first genetic risk score approach addressing where genetic polymorphisms that have been robustly associated with eGFR, a marker for renal function, associate with VT risk. Main outlines of the workflow are summarized in Figure 1. In a first step, we sought the literature for single nucleotide polymorphisms (SNPs) robustly associated with eGFR. These SNPs were then tested for association with VT risk in 1,953 VT patients and 2,338 healthy individuals from a French case control study (MARTHA/EOVT). [START_REF] Germain | Genetics of venous thrombosis: insights from a new genome wide association study[END_REF] We derived a genetic risk score (GRS) based on the VT-associated SNPs and tested it for replication in an independent sample of 1,289 VT patients and 1,049 controls from a Dutch case control study (MEGA study). [START_REF] Blom | Malignancies, prothrombotic mutations, and the risk of venous thrombosis[END_REF] We finally confirmed the association of the derived GRS with eGFR in a third independent study.

Material & Methods

Studied populations

Informed consent was obtained from all participants in accordance with the Declaration of Helsinki, and the study met all institutional ethics requirements. Discovery VT case-control samples The discovery cohort was composed of 1,953 VT patients and 2,338 healthy individuals from two French VTE case-control studies, MARTHA and EOVT that have been extensively described before. [START_REF] Germain | Genetics of venous thrombosis: insights from a new genome wide association study[END_REF][START_REF] Germain | Meta-analysis of 65,734 individuals identifies TSPAN15 and SLC44A2 as two susceptibility loci for venous thromboembolism[END_REF] Patients were individuals with documented personal VTE history and lacking strong genetic risk factors (Antithrombin, Protein C or Protein S deficiencies, FV Leiden homozygosity, FII G20210A homozygosity). Controls were apparently healthy individuals free of any chronic conditions and of a personal VT history. Replication VT case-control samples The replication stage was based on the same data from the Multiple Environmental and Genetic Assessment of risk factor for venous thrombosis (MEGA) study [START_REF] Blom | Malignancies, prothrombotic mutations, and the risk of venous thrombosis[END_REF] as those that were used in a recent meta-analysis of Genome-Wide Association Study (GWAS) data for VT [START_REF] Germain | Meta-analysis of 65,734 individuals identifies TSPAN15 and SLC44A2 as two susceptibility loci for venous thromboembolism[END_REF] . 1,289 Dutch VT patients with no prior event of VT and no cancer were compared with 1,049 controls genetically matched for geographical ancestry. [START_REF] Germain | Meta-analysis of 65,734 individuals identifies TSPAN15 and SLC44A2 as two susceptibility loci for venous thromboembolism[END_REF] Additional validation cohorts The Genesis/Genediab study group was composed of 1,370 individuals with Type 1 diabetes from the French population. [START_REF] Hadjadj | Death, end-stage renal disease and renal function decline in patients with diabetic nephropathy in French cohorts of type 1 and type 2 diabetes[END_REF] A.

Clinical characteristics of this population are provided in Supplementary Table

Genotyping

All individuals used in the work have previously been typed for genome-wide genotype SNPs using dedicated DNA microarrays and imputed with 1000 Genomes reference. Genotyping, quality controls and imputation analyses of the genotype data have been previously described in [START_REF] Germain | Meta-analysis of 65,734 individuals identifies TSPAN15 and SLC44A2 as two susceptibility loci for venous thromboembolism[END_REF] for the MARTHA, EOVT and MEGA studies and in [START_REF] Germain | SORBS1 gene, a new candidate for diabetic nephropathy: results from a multi-stage genome-wide association study in patients with type 1 diabetes[END_REF] for Genesis/Genediab.

SNP selection

Sixty-nine SNPs were identified to robustly associate with eGFR in different GWAS studies. [START_REF] Pattaro | Genetic associations at 53 loci highlight cell types and biological pathways relevant for kidney function[END_REF][START_REF] Okada | Meta-analysis identifies multiple loci associated with kidney function-related traits in east Asian populations[END_REF][START_REF] Pattaro | Genome-wide association and functional follow-up reveals new loci for kidney function[END_REF][START_REF] Köttgen | New loci associated with kidney function and chronic kidney disease[END_REF] These were selected as they have demonstrated genome-wide significance (p < 5 10 -8 ) association with eGFR and replicated in independent studies. From this list of candidate SNPs, we discarded SNPs from any pair of SNPs in linkage disequilibrium and excluded SNPs with bad imputation quality (r 2 <0.3) in both French GWAS cohorts. This resulted in 51 candidate SNPs (Supplementary Table B).

Statistical methods

Derivation of the Genetic Risk Score (GRS) Each of the 51 selected candidate SNPs was tested for association with VT in the French case-control samples using logistic regression analysis where the expected number of alleles (often referred to as imputed dose) at each SNP was used as a covariate in a model adjusting for age, sex and principal components derived from genotype data. Of note all SNPs had imputation quality r 2 > 0.30. From these analyses, we selected only SNPs for which the risk-allele was the one that was reported in the literature to associate with eGFR decrease, as compatible with the hypothesized relationship between renal dysfunction and VT risk. Only SNPs (Supplementary Table B) satisfying this condition were kept for the subsequent GRS analysis. In order to identify the most parsimonious and information SNP combination with respect to VT, an Akaike Information Criterion (AIC) [START_REF] Akaike | A new look at the statistical model identification[END_REF] strategy was adopted using a backward logistic regression procedure, while adjusting for sex, principal components and French sub-study group. SNPs selected by this AIC procedure were then entered into a GRS defined, for each individual, as the sum of the imputed risk-allele dose at each selected SNP. We confirmed that selected SNPs were also well imputed in the replication MEGA study. Association of the GRS with VT risk Association of the derived GRS with VT was then tested using logistic regression analysis using the same covariates as for the AIC strategy, both in the discovery (MARTHA/EOVT) and replication (MEGA) studies. Results observed in the discovery and replication studies were then pooled using fixed effect model (as implemented in the rmeta R package).

Association analysis with eGFR

The association of the proposed GRS was investigated in relation to eGFR in the Genesis/Genediab study where eGFR was estimated using plasma creatinin and the CKD-EPI equation. [START_REF] Levey | A new equation to estimate glomerular filtration rate[END_REF] Association was tested using linear regression analyses adjusted for age, sex and principal components derived from genotype data.

Results

From the 51 independent SNPs reported to robustly associate with eGFR in GWAS studies, only 27 presented with an eGFR decreasing allele that was also associated with an increased risk of VT (Supplementary Table B). The AIC based strategy applied to these 27 SNPs further selected a subset of 9 SNPs (Table 1) as the most parsimonious and informative group of SNPs to discriminate between patients and controls in the French populations. The minimal p-value of association of these 9 SNPs with VT in the French study was p = 0.011 for the DDX1 rs807601 and the highest p-value was p = 0.255 for the SLC34A1 rs6420094 (Table 1). A GRS variable was then derived from these 9 SNPs for each individual as the expected number of alleles associated with decreased eGFR levels carried by this individual. The distribution of the GRS in the French populations was shown in Supplementary Figure 1A. The GRS was significantly higher in VT patients than in controls (10.4 ± 0.04 vs 10.1 ± 0.047, p = 1.03 10 -7 ). One unit increase of the GRS was associated with an increased risk for VT of 1.09 [1.06 -1.15] (p = 1.44 10 -7 ). In an independent collection of 1,289 Dutch patients and 1,049 controls, the proposed GRS exhibited a distribution similar to that observed in the French population (Supplementary Figure 1B). One unit increase of the GRS was found associated with an increase in VT risk of 1.18 [1.11 -1.26] (p = 8.86 10 -8 ). The GRS association did not differ between the two studies (p = 0.06) and the combined Odds Ratio (OR) for VT associated with one unit increase of the GRS was 1.12 [1.09 -1.16] (p = 3.77 10 -

13

). When individual data from French and Dutch populations were combined together, the corresponding OR was 1.10 [1.06-1.14]. Figure 2 displayed the association of the GRS with VTE according to the quintiles of its distribution. In the French samples, the association was not completely linear as individuals in the 3 rd , 4 th and 5 th GRS quintiles were at similar risk of VT, OR = 1.39 [1.12 -1.73], 1.32 [1.06 -1.64] and 1.54 [1.24 -1.92] respectively, compared to individuals in the lowest quintile. This association was not completely linear in the Dutch population either. When the GRS distribution observed in the Dutch population was divided according to the same GRS quintiles as those used in the French studies, individuals in the 4 th and 5 th highest quintiles were at increased odds of 2.20 [1.54 -3.14] and 2.23 [1.56 -3.19], respectively, compared with individuals in the lowest quintiles. In the combined population, compared with lowest quintile, the OR for increased risk of VT associated with the second, third, fourth and fifth quintiles were 1.13 [0.94 -1.36], 1.47 [1.22 -1.77]), 1.52 [1.26 -1.82] and 1.70 [1.41 -.05], respectively. Based on these observations and the GRS quintiles distribution, these results can be translated into a 1.42 [1.25 -1.61] increased risk of VTE associated with a GRS greater than 11 in the combined studied populations. Corresponding ORs were 1.31 [1.13 -1.51] and 1.78 [1.39 -2.27] in the French and Dutch samples, respectively. Note that one of the SNPs, rs6088580, included in the definition of the GRS, is in moderate linkage disequilibrium (r 2 = 0.15; D'=1) with the rs867186 known to associate with VT risk. [START_REF] Dennis | The endothelial protein C receptor (PROCR) Ser219Gly variant and risk of common thrombotic disorders: a HuGE review and meta-analysis of evidence from observational studies[END_REF] Nevertheless, the GRS still remained significantly associated with VT risk in the discovery (OR = 1.10 for one unit increase, p = 6.24 10 -7 ) and replication case-control studies (OR = 1.17, p = 1.20 10 -6 ) after adjustment for the rs867186. The resulting meta-analyzed OR was 1.12 [1.08 -1.15]. In addition, when the rs6088580 was discarded from the GRS definition, the restricted GRS was still associated with VT in the French (OR = 1.10 for one unit increase, p = 7.08 10 -7 ) and the Dutch (OR = 1.18, p = 5.48 10 -7 ) populations. The metaanalyzed OR for VT associated with such restricted GRS was 1.13 [1.09 -1.16].

SNPs defining the GRS had been previously reported to individually associate with eGFR but their joint effect have never been assessed. Therefore, we investigated the impact on eGFR levels of the proposed GRS in a collection of 1,325 patients with Type 1 diabetes. In this study, the distribution of the GRS was similar to those observed in the discovery and replication VT studies (Supplementary Figure 1C). In this study, only one of the 9 assessed SNPs, the STC1 rs3758086, showed nominal association with eGFR (p = 0.035), all other SNPs having association p-value>0.05 (Supplementary Table C). Nevertheless, one unit increase of the GRS was associated with a decrease of -1.19 [-1.92 --0.39] (p = 3.54 10 -3 ) in eGFR levels (Supplementary Table C).

Discussion

Employing a two-phase discovery-validation strategy on individual genetic data of two independent studies, we identified a GRS derived from 9 SNPs that, collectively, strongly associated with the risk of VT. These 9 SNPs combined altogether define a GRS that associates with the risk of the disease, individuals with an elevated GRS greater than 11 being at 1.42 increased risk of VT, whereas individually these SNPs showed very modest associations with the disease. These SNPs map to loci (DDX1, CPS1, SKIL, SLC34A1, ZNF204P, STC1, FBXL20, SLC7A9, TP53INP2) that have not been clearly associated with VT in recent large scale association studies [START_REF] Germain | Meta-analysis of 65,734 individuals identifies TSPAN15 and SLC44A2 as two susceptibility loci for venous thromboembolism[END_REF][START_REF] Hinds | Genome-wide association analysis of self-reported events in 6135 individuals and 252 827 controls identifies 8 loci associated with thrombosis[END_REF] and whose associated biology is poorly documented with respect to VT. Nevertheless, it could be mentionned that genetic variations at the SLC34A1 locus have been found associated with Factor XII antigen levels. [START_REF] Williams | Ischemic stroke is associated with the ABO locus: the EuroCLOT study[END_REF] In addition, the CPS1 and STC1 genes both play role in the phosphate mechanisms of action and are involved in vascular angiogenesis. [START_REF] Zlot | Stanniocalcin 1 is an autocrine modulator of endothelial angiogenic responses to hepatocyte growth factor[END_REF][START_REF] Yoshiko | Stanniocalcin 1 as a pleiotropic factor in mammals[END_REF][START_REF] Summar | Relationship between carbamoylphosphate synthetase genotype and systemic vascular function[END_REF] These observations could be of particular relevance and open novel research avenues in light of recent works emphasizing the emerging role of the polyphosphate / factor XII pathway in thrombosis [START_REF] Nickel | The polyphosphate/factor XII pathway in cancer-associated thrombosis: novel perspectives for safe anticoagulation in patients with malignancies[END_REF] . Finally, rare mutations in SLC7A9 are known to cause cystinuria, which could link this gene to VT via some homocysteine associated mechanisms [START_REF] Ragone | Homocystine solubility and vascular disease[END_REF] .

The SNPs defining this GRS had been individually associated with eGFR in previous large meta-analysis of GWAS studies and we here showed that, while these SNPs were mildly associated with eGFR in a moderate sample size study, the derived GRS was much more significantly associated with eGFR. However, the GRS impact on eGFR variability was rather modest ,R 2 = 0.67%, a value that must be compared to the 3.22% of eGFR variability explained by the 53 SNPs found to significantly associate with eGFR in the recent GWAS studies. [START_REF] Pattaro | Genetic associations at 53 loci highlight cell types and biological pathways relevant for kidney function[END_REF] This observation indicates that the influence of the GRS on VTE risk could not be solely mediated by eGFR that is an imperfect surrogate marker of impaired renal function. The use of genetic score approach to evidence a causative association between impaired renal function and VT is appealing as the genetic risk score is fixed at birth for each individual and should thus be independent from confounders normally affecting eGFR such as age or body mass index. We did not observe any association between the proposed GRS and BMI, age or sex (data not shown). However, several limitations need to be acknowledged. The main one relates to the fact that we do not have eGFR measurements in the studied case-control samples preventing us from conducting mediation analysis to assess whether the impact of the GRS on VT risk vanishes after adjusting for eGFR. Similarly, proteinuria or cardiac biomarkers were not available in our samples to assess how the proposed GRS associates with CKD. While we obtained strong evidence that the GRS is associated with VT risk and eGFR, we have so far no evidence of inflammatory, vascular or hemostatic markers that could be influenced by this GRS. We investigated its association with several biological traits available in the MARTHA participants (including D-dimers, endogenous thrombin generation, plasma antigen or activity levels of fibrinogen, coagulation factors II, VIII, and XI, von Willebrand factor, antithrombin, protein C, protein S, activated partial thromboplastin time, haemoglobin, and white blood cell and platelet counts) but without any robust findings (data not shown). Unfortunately, factor XII antigen had not been measured and , according to the point discussed above, its association with the proposed GRS deserves further investigations. It is important to stress that the GRS was derived from SNPs that have been found robustly associated with eGFR in several studies but without any evidence they could be functional. They likely serve as markers for the underlying functional variants that need to be identified. One could speculate that once these functional variants are identified, the GRS they define would likely be a more accurate marker of the risk of VT. All these points deserve further investigations as well as further validation of the proposed GRS in large prospective cohorts for incidence, but also for recurrence of the disease.

Conclusion

This work provided additional elements supporting the association of impaired renal function with increased risk of venous thrombosis. However, the mechanisms underlying this association risk are far to be understood and require further deep investigations.

Acknowledgments

We are grateful to Elise GAND (Pole DUNE -CHU Poitiers) for data-management, Ahmed Amine KASMI (INSERM CIC1402, Poitiers) for clinical management and CRB BB 0033-00068 for biological handling and shipment of DNA to genomic platform Sources of funding R.C was supported by a PhD grant from the Region Ile de France (CORDDIM program). MARTHA genetics research program was supported by the GENMED Laboratory of Excellence on Medical Genomics (ANR-10-LABX-0013), the French Clinical Research Infrastructure Network on Venous Thrombo-Embolism (F-CRIN INNOVTE) and the ICAN Institute for Cardiometabolism and Nutrition (ANR-10-IAHU-05), three research programs managed by the National Research Agency (ANR) part of the French Investment for the Future initiative. The Juvenile Diabetes Research foundation (JDRF-I) funded the genotyping of the Genesis/Genediab population (Grant -Diabetic Nephropathy Initiative).

Disclosures None