Min-Young Yun

Pavel Simacek

Christophe Binetruy

Suresh Advani

Random field generation of stochastically varying through the thickness permeability of a plain woven fabric

Keywords: modeling, statistics, voids, vacuum infusion, Moran's I

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Random field generation of stochastically varying through the thickness permeability of a plain woven fabric

Min-Young Yun, Pavel Simacek, Christophe Binetruy, Suresh

Introduction

VARTM is a type of Liquid Composite Molding (LCM) process in which resin is pulled into a closed mold by a vacuum and distributed into a fibrous material. In the VARTM process, a dry fibrous media, usually made of carbon or fiberglass, is placed between a vacuum bag and a rigid tool surface. Resin is introduced into the fabric from one end to the other end with vacuum due to a maximum total pressure difference of around 1 atm. between the two ends. DM, which is a highly permeable fabric, is placed on top of the layers of the fabric to reduce the total filling time [1]. A schematic of the process is shown in Figure 1.The resin flow through the porous network of fabric is usually described by Darcy's law as shown below [START_REF] Whitaker | Flow in porous media I: A theoretical derivation of Darcy's law[END_REF].

= -• ∇

(1)

= (2)
In Equation 1, is the volume averaged resin velocity, is resin viscosity, ∇ is the pressure gradient across the resin domain, and K is the anisotropic permeability tensor, which is positive definite and symmetric. The permeability tensor, K, shown in Equation 2 is a measure of how easily resin moves through the fibrous reinforcement. There are only six independent components of the symmetric permeability tensor in three dimensions (x,y, and z). K xx , K yy and K zz are the permeability values in the chosen x, y and z co-ordinate directions respectively where the skew terms K xy , K xz and K yz provide information about the angles between the principle direction of the fabric and the chosen direction of the coordinate system. These values are zero if the coordinate directions coincide with the principal directions of the fabric.

Most composite parts are long and wide but only a few millimeters in thickness. In previous studies [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF]- [START_REF] Zhang | Efficient stochastic simulation approach for RTM process with random fibrous permeability[END_REF], it was found that variability in permeability exists in both the in-plane and through the thickness directions. There are many reasons for this variability such as handling, placement, and variations in fabric and VARTM manufacturing process [START_REF] Vernet | Experimental determination of the permeability of engineering textiles: Benchmark II[END_REF]. Nesting of layers during layup [START_REF] Hoes | Study of nesting induced scatter of permeability values in layered reinforcement fabrics[END_REF]- [START_REF] Zeng | Numerical prediction of in-plane permeability for multilayer woven fabrics with manufacture-induced deformation[END_REF], and shearing of fabrics [START_REF] Yang | Influence of fabric shear and flow direction on void formation during resin transfer molding[END_REF]- [START_REF] Aranda | Influence of shear on the permeability tensor and compaction behaviour of a non-crimp fabric[END_REF] are found to cause local variability in fabric permeability. Other variations in fabrics such as fiber misalignment and fiber angle distribution were found and studied by Yurgartis et al [START_REF] Yurgartis | Measurement of small angle fiber misalignments in continuous fiber composites[END_REF]. Deformation induced during the manufacturing process in the In-plane permeability of woven fabric was studied using numerical prediction and shown that the variability in permeability causes random resin flow variations through the fabric during the impregnation process [START_REF] Zeng | Numerical prediction of in-plane permeability for multilayer woven fabrics with manufacture-induced deformation[END_REF]. Markicevic et al [START_REF] Markicevic | Stochastic modeling of preform heterogeneity to address dry spots formation in the VARTM Process[END_REF] were the first ones to numerically study the random resin flow in through the thickness direction when distribution media (DM) is used in a VARTM process. The research by Yun et al. showed the effect of variability in through the thickness permeability (K pin ) due to the pinhole regions formed at the junction of two tows in a plain woven fabric [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF]. An example of the fabric with pinholes is shown in Figure 2. These pinholes vary in size throughout the fabric, hence their K pin values which is the K zz value at that location will be different as well. It is also notable that there are areas with pinholes (pinhole areas) and areas without pinholes (no pinhole areas), which are demonstrated through an image analysis in Figure 2b. This variation causes the resin to race preferentially through different pathways with varying K pin in through the thickness direction, and this variation leads to uneven resin flow causing formation of air pockets due to the merging of the flow fronts which result in voids. The air pockets result in a void within the composite part reducing its strength dramatically [START_REF] Fernlund | Experimental and numerical study of the effect of cure cycle, tool surface, geometry, and lay-up on the dimensional fidelity of autoclave-processed composite parts[END_REF], [START_REF] Liu | Effects of cure cycles on void content and mechanical properties of composite laminates[END_REF]. It was also found by experimental and numerical studies that more voids were formed when DM with higher permeability was used, because the higher permeability DM increases randomness in the resin flow in through the thickness direction [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF]. Although the effect of K pin on resin flow and void formation was well studied using experimental and numerical work in the research by Yun et al., statistical analysis of the heterogeneous K pin field was not carried out. To obtain random fields of K pin for use in numerical simulations, a number of images of a large sample must be taken. Obtaining all of the K pin values for large composite parts such as a wind turbine blade can be time consuming and may not be feasible. Thus, the statistical study of the random K pin field is important for understanding the degree of heterogeneity and so to generate the random K pin field using statistical variations in a fabric.The statistically generated random K pin field can then be incorporated into a numerical flow simulation which predicts the resin flow and void formation in the presence of this heterogeneity. The novelty of this study is that the pinhole field is statistically analyzed and the statistical properties found from this analysis are used to generate K pin random fields. These K pin random fields are then used to perform numerical simulations to study the effect of heterogeneity on the resin flow and compared with the previously reported experimental results.

Methodology

Generating the K pin random field requires several steps including image acquisition, image analysis, and statistical analysis. An algorithm illustrating the methodology used in this study to generate the K pin random field is presented in Figure 3. First, multiple images of a fabric of interest are captured and filtered using a MATLAB image analysis tool. Then, K pin are calculated using the cross-sectional area of pinholes from the image analysis [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF]. Next, the mean, standard deviation, and spatial correlation (semi-variogram) of K pin are calculated. To understand the spatial correlation of pinhole areas and no pinhole areas, a cluster analysis is carried out using Moran's I index. Moran's I is a widely used statistical measure of spatial autocorrelation [START_REF] Zhang | Use of local Moran's I and GIS to identify pollution hotspots of Pb in urban soils of Galway[END_REF].

Once Moran's I index of the K pin samples is obtained, random fields of this index are generated, which supply the locations of the pinholes. The probability density function (PDF) of the K pin field fits a gamma distribution, but it is difficult to directly generate gamma random numbers.

Thus, the transformation between gamma and normal random numbers is used in this study. In this transformation, the covariance function of the K pin gamma distribution is converted to the covariance function of a normal distribution. The result from the cluster analysis, along with the converted covariance function, is utilized to generate normal random numbers by Karhunen-Loève (KL) expansion. Finally, normal random numbers are transformed to gamma distribution numbers, which are used to generate the K pin field to be used as input in the numerical flow simulation.

Material and K pin statistical properties

Plain woven E-glass fabric was used as a sample in this study so one could compare it to previously obtained results. An image of the fabric is shown in Figure 2. The image on the top (Figure 2a) is an unedited picture and the image on the bottom (Figure 2b) is the image from Figure 2a filtered to show only the pinholes. As can be seen in Figure 2b, the pinholes vary in size throughout the fabric. The optimum number of pixels for a 5cm x 6cm image was found to be 1605 x1905 pixels. This optimum number of pixels was determined by taking images with various ranges of pixels to find the smallest number of pixels with which the size of K pin does not change. K pin is calculated using the measured cross-sectional area of each pinhole which is obtained from the image analysis. The detailed equation and method are presented in [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF]. An exampleof the random field obtained using this methodology is presented in Figure 4, in which color signifies permeability, and Figure 5, in which white signifies pinhole area and black signifies no pinhole area.

As can be seen in Figure 5, there are areas with pinholes and areas without pinholes. Regions in K pin field with no pinhole area are present because at the intersection of some tightly woven tows no pinhole was detected. For these no pinhole areas, a permeability of K zz,mic (micro scale fiber tow through the thickness permeability, 8.2*10 -14 m 2 ) is assigned, and this value is calculated from an analytic result of resin flow across a fiber tow [START_REF] Bruschke | Flow of generalized Newtonian fluids across a periodic array of cylinders[END_REF].

, = 1 3 1 - 3 tan "# $ % 1 + 1 - ' √1 - + 2 + 1 * + , "# (3)
= 4. /,012 3 (4)
. /,012 = . / -4 5 6 1 -4 5 6

In Equations 3-5, r is the radius of a single glass fiber, L is a non-dimensional parameter, . /,012 is a volume fraction of a tow, . / is a measured volume fraction of 4 layers of fabric under vacuum, and 4 5 6 is fraction of pinhole areas. . /,012 is calculated to be 0.66 with . / of 0.45 and 4 5 6 of 0.16 and is found to be 0.91. Average fiber diameter was measured to be 9.2 .

The location of no pinhole areas in a random field is obtained from a spatial correlation study of two areas, no pinhole and pinhole areas, using Moran's I index, which is described in the next section. The PDFs of the random fields with and without K zz,mic (the no pinhole permeability) show a clear discrepancy, which is presented in Figure 6. The PDF without K zz,mic fits a gamma distribution (shown at the right in Figure 6) and this gamma distribution is used to generate the K pin values in a random field. The gamma distribution is fitted using maximum likelihood estimation (MLE). The gamma distribution fits reasonably the PDF of K pin except for the range of low K pin (0~5× 10 "#: ; ) which is acceptable because the K pin effect is more prominent at higher values. Basic statistical properties such as mean and standard deviation were calculated for the whole area analyzed (~ 2 m 2 ) and are provided in Error! Reference source not found..

K pin Area (m 2 ) 1.936 K pin Mean (m 2 ) 9×10 -9 K pin Standard deviation (m 2 )
9×10 -9 Spatial correlation of K pin is another critical statistical property which is obtained using a semivariogram function. Semi-variogram (<(h)) is a measure of the spatial correlation between two random values at a function of distance (h).

< ℎ = 1 2> ℎ ? pin B -pin B + ℎ C D E# (6)
In the semi-variogram given in Equation 6, z is the coordinate of the random variable, > ℎ is the total number of pairs of random variables at a lag distance ℎ, pin B is K pin value at the B location, and pin B + ℎ is K pin value at B + ℎ location.

A semi-variogram of (10 8 )×K pin is obtained and plotted in Figure 7. An exponential function is fitted to the experimentally obtained semi-variogram as shown in Figure 7. The exponential semi-variogram function is given in Equation 7. The exponential covariance function is presented in Equation 8.

< ℎ = F 1 -exp I-J 3ℎ K JL (7)
M ℎ = F exp -J 3ℎ K J (8)
In equations 7 and 8, F is the maximum variance of the spatial process of the sample data, in which the semi variance reaches 95% of the maximum variance, a is the maximum lag distance at which semi variance reaches the maximum value, and h is the spatial distance between two data points. Here h is 5 mm which is the width of a tow of the selected plain woven fabric. The semi-variogram exponential function and the corresponding covariance function are presented in Figure 7b.

The exponential fit in Figure 7(b) has a value of F of 0.73 and a value of 3h (15 mm) 95% of maximum variance value is reached at the distance of 3h (15 mm) and 99% is reached at 5h (25 mm). Semi-variance varies a little over the distance lag of 5h (25 mm) to 15 h (65 mm). This means that K pin values are spatially correlated within a distance of up to 15h (65 mm). As the tow shifts or curves, the size of nearby pinholes (K pin value) are affected and this influence is found to be within the distance range (15 tows or 15h (65 mm)).

K pin cluster analysis: Moran's I

As can be seen in Figure 5, the total random field consists of two parts: no pinhole areas and pinhole areas. The location of no pinhole areas must be identified so that K zz,mic can be assigned to these areas. The generated K pin is then assigned to the remaining area in a random field. The spatial correlation between these areas (no pinhole and pinhole areas), which is the degree of clustering, is investigated using Moran's I index. Moran's I index varies from -1 (negatively correlated) to 1 (positively correlated) depending on the spatial correlation of the random values in a sample. Moran's I is described in Equation 9.

N = O ∑ ∑ Q R RE6 RE# E6 E# ∑ ∑ Q R S -S̅ S R -S̅ RE6 RE# E6 E# ∑ S -S̅ E6 E# (9)
Where Q R is the binary weight matrix, S is K pin at location i, S R is K pin at location j, and S̅ is the global mean of K pin , n is the total number of K pin .

The effect of the square sample's width on Moran's I index was also studied, and this effect is shown in Figure 8. Moran's I index steadily increases up to a specimen width of 50 mm and levels off at 0.30 for specimen widths exceeding 100 mm. This indicates that the optimum fabric sample size for random field generation should be 100 mm x 100 mm over which no pinhole and pinhole areas are not spatially related. The unit size for generating a random field used is therefore 105 mm x 105 mm, which is also over the maximum distance required for the spatial correlation between K pin (max 65 mm). Figure 9 presents two examples of samples, each with an index of 0.30 and a size of 105 mm by 105 mm.

In Figure 9, black areas (no pinhole areas) have K zz,mic (8.2*10 -14 m 2 ) assigned, and white areas (pinhole areas) have K pin assigned. However, it remains to generate K pin . The determined unit size of 105 mm x 105 mm is the size of fabric of interest which needs to be sampled for random field generation. The unit fabric size of 105 mm x 105 mm (~.01 m 2 ) is over two orders of magnitude smaller than the sample size of 2 m 2 used in the previous study [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF] in which statistical analysis was not carried out and the random field for numerical simulation was obtained by sampling a larger size of fabric. The statistical study of spatial correlation of random values introduced here determines the necessary sample size to generate random fields, which greatly reduces the effort and time to collect data from unnecessarily large sizes of samples.

Transformation between gamma and normal random variables

The PDF of K pin fits a gamma distribution rather than a normal distribution as seen in Figure 6.

Transformation between gamma and normal random variables is required since it is difficult to generate gamma random variables directly. The gamma random numbers are obtained by transforming normal numbers after the normal numbers are generated using a Gaussian random generator such as KL expansion [START_REF] Liou | A covariance conversion approach of Gamma random field simulation[END_REF]. The following methodology presented by Liou et al. [START_REF] Liou | A covariance conversion approach of Gamma random field simulation[END_REF] was adopted for the transformation. First, the covariance function of the K pin gamma distribution is converted to that of a normal distribution. In Equation 10, x is a gamma random variable (X~G (U, V)) and f X (x) is the gamma random variable density, U is a shape parameter, and V is a scale parameter.

4 W S = V X Γ U S X"# Z "[ , U, V > 0 KO] 0 ≤ S ≤ +∞ (10)
For the (10 8 )× K pin fitted gamma distribution, U is 1.08 and V is 1.16.

The covariance function of two normal variables w 1 and w 2 (`a #a is related to the covariance function of two gamma variables x 1 and x 2 as shown in Equation 11. Using the Equation 11, the covariance function of normal variables is obtained.

Mb. S # , S ≈ I U # V # U V L de + f`a g a h + M`a g a h + i`a g a h j - U # V # U V (11)
k # = 1 9U # , k = 1 9U e = 1 -k # 1 -k + 3 1 -k # k # 1 -k + 3 1 -k # 1 -k k + 9 1 -k # k # 1 -k k f = 9 1 -k # k # :.n 1 -k k :.n + 9k # #.n 1 -k k :.n + 9 1 -k # k # :.n k #.n + 9k # #.n k #.n M = 18 1 -k # k # 1 -k k i = 6k # #.n k #.n
The conversion of covariance functions works well when U # , U > 0.5 U # , U = 1.08 and a coefficient of skewness (< # ) is less than 3. Using Equation 12, < # is calculated to be 1.9.

< # = U + 1 U + 1 U V -3 U V U V - U V r U V s = 2 √U (12)
Next, the covariance of normal numbers is used to generate normal random numbers (w) in the KL expansion process. Then the numbers (w) are transformed back to gamma random numbers (x) point by point using Equation 13.

S = t 2V ≈ U V u1 - 1 9U + v w I 1 9U Lx ( 13
)
These generated gamma random numbers (x, K pin ) through the transformation are assigned to the pinhole areas (white areas in Figure 9) in a random field of Moran's I index of 0.3.

Random number generation: KL expansion

The transformed covariance function of normal random numbers was used in the normal random generator, KL expansion, to generate gaussian normal random variables (w(x,y)) in Equation 14.

v S, y = v S + ? zV k y 4 S C E# (14)
In Equation 14, V and 4 S are the eigenvalues and eigenfunctions of the covariance function, k y is a normal random variable with mean of 0 and variance of 1, v S is the mean of normal random variables which is 0, and > is the finite number of terms which is 33 determined by studying the estimated decay of eigenvalues. The sum of 33 eigenvalues reaches 92% of the sum of total eigenvalues

Numerical simulation

Numerical flow simulation with the generated random field in a porous network where one can assign K pin values to through thickness permeability allows to study the effect of heterogeneity on the resin flow. LIMS is a finite element/control volume flow simulation software which was developed at the University of Delaware [START_REF] Šimáček | Desirable features in mold filling simulations for liquid composite molding processes[END_REF]. The woven fabric with pinholes was modeled into 3D mesh with 1D elements representing the pin hole values for the simulation [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF]. The mesh is shown in Figure 10.

Four layers of fully nested fabrics (0.12 m by 0.53 m) and pinholes are simulated using 3D elements (representing the woven fabric) and 1D elements (representing the pinholes). The thickness of each layer of fabric is 0.7 mm under vacuum (fully nested). One layer of DM (0.11 m by 0.48 m) with thickness of 1 mm is simulated using 2D elements. The permeability tensor of the woven fabric was obtained experimentally using the methodology presented in [START_REF] Yun | Characterization of 3D fabric permeability with skew terms[END_REF]. The bulk permeability is presented in Table 2.

Table 2 Permeability of the plain woven fabric[3]

; ; ; ; ; ; 8.8× 10 "## 9.1× 10 "## 1.36× 10 "# 9.89× 10 "#{ 1.58× 10 "#n 1.00× 10 "#n The K pin , generated using the methodology described earlier, was assigned to the 1D elements.

Three values of DM permeability (K DM of 1.45 × 10 ":| ; , 8.5 × 10 ":} ; , and 4 × 10 ":} ; ) were used to study the effect of K DM on void formation. Other experimental conditions such as fabric volume fraction, pressure, and viscosity are presented in Table 3.

Table 3 Experimental condition for numerical simulation study[3]

Fabric volume fraction 0.45 Pressure (Pa) 1× 10 n Viscosity (Pa.s) 0.1 Monte Carlo simulations were conducted for each type of DM. The number of iterations for each DM type is determined using a method presented in [START_REF] Driels | Determining the number of iterations for Monte Carlo simulations of weapon effectiveness[END_REF],

O = 100B • €S̅ (15)
In Equation 15, B is a confidence coefficient, • is sample standard variation, € is a percentage error of the mean, and S̅ is the mean. For 95% confidence level and 5% error, B is 1.96, • and S̅ are presented in Table 5, and € is 5. Using this, the number of runs n is calculated to be 134 for K DM of 1.45× 10 ":| , 232 for K DM of 8.5× 10 ":} , and 543 runs for K DM of 4× 10 ":} . Mean of void fraction as a function of run number is presented in Figure 11. It shows that 440 runs are sufficient for the case of K DM of 4× 10 ":} because the mean of void fraction levels off at by 440 runs. The random K pin field is generated for each simulation run. The void fraction was calculated as the area of the void divided by the mold area. The simulation result (void fraction) from this study was compared to the void fraction found in the experimental work and the simulation work with an experimentally determined K pin field presented in [START_REF] Yun | Stochastic modeling of through the thickness permeability variation in a fabric and its effect on void formation during Vacuum Assisted Resin Transfer Molding[END_REF].

Results and discussion

K pin random field

The properties of (10 8 ) K pin random field generated using the methodology described earlier are presented in Table 4. The parameters of the probability density function of the gamma distribution, U and V, fits the values of the observed K pin fields within 5% error. The parameter of semi-variogram, F , also matches the experimentally observed value within 5%. The normalized histogram of void fractions obtained from the simulation runs for each type of DM is presented in Figure 12. In Figure 12, the experimental result is given in (a), simulation result using experimentally determined K pin fields is presented in (b), and the simulation result using generated K pin fields is presented in (c). The void percentages for all three case studies are presented in Table 5. The results with generated random field qualitatively match the other two results. It shows the trend of void fraction increasing with higher K DM . The experimental and both of the simulation results also agree qualitatively in which the void fraction is within about 20% except for experimental study with K DM of 1.45× 10 ":| where one single experiment with 8.45% of void fraction significantly affects the mean void fraction. This shows that it is possible to generate the behavior of flow in a fibrous porous media through statistical analysis of the fabric pinholes by characterizing a small sample of the fabric.

Conclusion

In this paper, the methodology to generate gamma random field is presented. The K pin random field with a gamma distribution was successfully created based on the statistical analysis using the methodology. The spatial correlation between pinhole and no pinhole areas was studied using

Figure 2 Figure 3 Figure 4 Figure 5 KFigure 6 Figure 7 (Figure 8

 2345678 Figure 2 Image of E-glass fabric(120 mm by 60 mm) (a) and filtered image using image analysis (b)

Figure 9

 9 Figure 9 Two examples of a unit size of matrix with Moran's I of 0.3. White area represents pinhole areas and black area represents no pinhole areas.

Figure 10

 10 Figure 10 Woven fabric layer modeled as 3D elements pinholes as 1D elements in the flow simulation[3].

Figure 11 2 Figure 12

 11212 Figure 11 Mean of void fractions as a function of run number in Monte-Carlo simulations. K DM varying from (a) 4×10 -9 m 2 , (b) 8.5×10 -09 m 2 , and (c) 1.45×10 -8 m 2

Table 1 Mean and standard deviation of calculated K pin from Image Analysis

 1

Table 4 Parameters of generated density function and the semi-variogram model (From observed (10 8 ) K pin field

 4

	Simulation Experiment	U 1.04~1.14 1.08	, • = '. ƒ", … = '. ' †, ‡ ˆ= ƒ. ‰Š) V 1.08~1.19 0.70~0.76 F 1.16 0.73
	Error 3.2. Numerical simulation	±4.5%	±4.8%	±4.3%
	3.2.1

. K pin random field

Table 5 Void percentage obtained from (a) experimental and (b-c) simulation runs. ((b) Simulation 1 : simulation with experimentally determined K pin , (c)Simulation 2: simulation with generated K pin field)

 5

	K DM (m 2 )	(a)Experimental study Void (%)	(b)Simulation 1 Void (%)	(c)Simulation 2 Void (%)
		Range	Mean	Standard	Range	Mean	Standard	Range	Mean	Standard
		(%)	(%)	deviation	(%)	(%)	deviation	(%)	(%)	deviation

in a VARTM process. It should prove useful for numerical simulations of a manufacturing process of large composite parts.

Acknowledgement

The authors thankfully acknowledge Masoud Bodaghi for his input and discussions.


Ivan Mikšík

Marine Morvan

Jaroslav Brůžek

Peptide analysis of tooth enamel -A sex estimation tool for archaeological, anthropological, or forensic research

Keywords: archeology, sex determination, tooth enamel

Proteomics has become an attractive method to study human and animal material, biological profile, and origin as an alternative to DNA analysis. It is limited by DNA amplification in ancient samples and its contamination, high cost, and limited preservation of nuclear DNA. Currently, three approaches are available to estimate sex-osteology, genomics, or proteomics, but little is known about the relative reliability of these methods in applied settings. Proteomics provides a new, seemingly simple, and relatively non-expensive way of sex estimation without the risk of contamination. Proteins can be preserved in hard teeth tissue (enamel) for tens of thousands of years. It uses two sexually distinct forms of the protein amelogenin in tooth enamel detectable by liquid chromatography-mass spectrometry; the protein amelogenin Y isoform is present in enamel dental tissue only in males, while amelogenin isoform X can be found in both sexes. From the point of view of archaeological, anthropological, and forensic research and applications, the reduced destruction of the methods used is essential, as well as the minimum requirements for sample size.

Introduction

The estimation of sex is fundamental to many archaeological, anthropological, and forensic research. This determination has three possible approaches: osteology, genomics, or proteomics [START_REF] Buonasera | A comparison of proteomic, genomic, and osteological methods of archaeological sex estimation[END_REF]. The first two approaches are traditional methods, but the proteomic one is a relatively new method with the increasing attention of scientists. Recently the use of proteomic methods in paleontology (so-called "Paleoproteomics") is rapidly growing, and it is expected that these methods can be helpful for many general applications and connect molecular biology, paleontology, archaeology, paleoecology, and history. Warinner et al. said about Paleoproteomics: ''Growing from a handful of studies in the 1990s on individual highly abundant ancient proteins, paleoproteomics today is an expanding field with diverse applications ranging from the taxonomic identification of highly fragmented bones and shells and the phylogenetic resolution of extinct species to the exploration of past cuisines from dental calculus and pottery food crusts and the characterization of past diseases." [START_REF] Warinner | Paleoproteomics Paleoproteomics[END_REF]. From this point of view, the most frequently analyzed protein is collagen type I, which is a stable and rigid protein, as was demonstrated in a well-known study in 2007 by determining collagen type I at 68-million-year-old bones of Tyrannosaurus rex [START_REF] Schweitzer | Analyses of soft tissue from Tyrannosaurus rex suggest the presence of protein[END_REF][START_REF] Asara | Protein sequences from Mastodon and Tyrannosaurus rex revealed by mass spectrometry[END_REF]. However, at the last years, the ability to detect and identification of proteins in ancient (but not only) tissue was significantly increased and allows to use of protein not only for identification in tissue but also for various problems such as interaction with food, interaction animal-human, environmental exchanges but also (from the view of this review) estimation of sex. Also, the significance of proteomic research has increased in archaeology [START_REF] Hendy | Ancient protein analysis in archaeology[END_REF]. It is important to note the differences in using the terms sex/gender. The terms sex and gender are often interchanged in conversation, documentation, and scientific literature, although they are not synonymous, and confusion in their usage is increasing. The biological concept of sex fundamentally differs from the social concept of gender, and the two terms are not interchangeable [START_REF] Garofalo | The confusion between biological sex and gender and potential implications of misinterpretations[END_REF]. In this article, we will stick strictly to using the term sex only.

Osteological (morphological) estimation of sex

The existence of sexual dimorphism, that is, of differences in bone variables between males and females, is an inevitable prerequisite for any anthropological sex estimation method. According to the approach, the methods are divided into visual, which evaluates the development of characters according to categories, metric methods, which use the dimensions of bones and their size; and geometric-morphometric methods, which explore the interplay and differences between shape and sizes from a metric perspective [START_REF] Klales | Sex estimation of the human skeleton[END_REF]. Both genetic factors and the action of sex hormones influence the sexual dimorphism of the skeleton. Its final state is modified by external environmental factors (e.g., [START_REF] Dunsworth | Expanding the evolutionary explanations for sex differences in the human skeleton[END_REF]). Before the development of secondary sexual characteristics, however, there was limited sexual dimorphism in skeletal features, rendering sexing methods unreliable it is not recommended to use them [START_REF] Scheuer | Skeletal development and ageing[END_REF].

The full development of sexual dimorphism exists only in adulthood. In adults, the accuracy of the methods is different in every population and age group and depends on which bone is used. The dimensions of the skeleton show considerable variability. For these reasons, the methods must contain more variables that are not correlated with each other. In forensic anthropology and bioarchaeology, most methods for sex estimation rely on statistical models and tools generated through osteometric data collected from identified populations [START_REF] Obertová | Statistics and probability in forensic anthropology[END_REF]. The most common method of sex estimation is discriminant function analysis (DFA). A discrimination score greater than the cut-off point between the sexes corresponding to a probability of 0.5 indicates a male and a score less than the cut-off point indicates a female. The accuracy of the methods is not absolute, and we always find a certain number of misclassified individuals who match the error. The skull and pelvis are still the preferred skeletal elements for sex estimation, with an accuracy that varies from 80% to 95% [START_REF] Brůžek | Methodology and reliability of sex determination from the skeleton[END_REF].

An overview of all possible anthropological methods for determining sex according to the skeleton is given in recent publications (e.g., [START_REF] Krishan | A review of sex estimation techniques during examination of skeletal remains in forensic anthropology casework[END_REF][START_REF] Klales | Current State of Sex Estimation in Forensic Anthropology[END_REF][START_REF] Kotěrová | Current trends in methods for estimating age and sex from adult human skeleton[END_REF]).

A common misunderstanding of DFA results is that the overall accuracy of sex classification can be applied to every individual in the sample. Every bone measurement and discriminant score shows an overlap between female and male distributions. The overlapping area represents the "zone of uncertainty", where the skeletal variables of females and males are similar and cannot reliably be distinguished from one another [START_REF] Galeta | Sex estimation using continuous variables: problems and principles of sex classification in the zone of uncertainty[END_REF]. This "zone of uncertainty" varies depending on the size difference between the population where the method was proposed and the population in which we want to use it. We call this the population specificity of morphological methods, and ignoring it causes a dramatic decrease in accuracy and an increase in misclassification [START_REF] Kotěrová | Disregarding population specificity: its influence on the sex assessment methods from the tibia[END_REF]. Exceptions are methods that use pelvic bone dimensions, which describe sexual dimorphism as a whole. Such methods have general validity and can be applied to all anatomically modern people with a high success rate and an error risk of less than 5% [START_REF] Brůžek | Validation and reliability of the sex estimation of the human os coxae using freely available DSP2 software for bioarchaeology and forensic anthropology[END_REF]. Unfortunately, in archaeological discoveries, the pelvis is often very damaged or completely missing [START_REF] Waldron | The relative survival of the human skeleton: implications for palaeopathology[END_REF]. For these reasons, the approach of primary and secondary sex diagnosis was proposed [START_REF] Murail | A new approach to sexual diagnosis in past populations. Practical adjustments from Van Vark's procedure[END_REF]. Primary sex diagnosis applies reliable methods in individuals with pelvic bone. In the sample obtained in this way, classification methods specific to the given population are proposed, which use extra-pelvic dimensions of the skeleton. These methods are applied to individuals with a missing pelvis [START_REF] Santos | rdss: an R package to facilitate the use of Murail et al.'s (1999) approach of sex estimation in past populations[END_REF]. Sex estimation in the "zone of uncertainty", that is, the overlapping region between sexes, should be avoided to reduce misclassification. Sex should be assigned only to those individuals with a posterior probability of being female or male higher than 0.95. Although such an approach limits the practical applicability of DFAs, because some portion of the individuals remains unclassified, it allows a high classification accuracy to be maintained at the individual level [START_REF] Galeta | Sex estimation using continuous variables: problems and principles of sex classification in the zone of uncertainty[END_REF].

Another way to estimate the sex of a skeleton is to use visual methods and assess the degree of trait development using categories. These are highly subjective, and the variability of sexual dimorphism within and between populations is considerable. Only methods with a reference set from multiple populations and designed software for sex estimation can provide usable results [START_REF] Klales | Examining the reliability of morphological traits for sex estimation implications for the Walker (2008) Klales et al. (2012) methods[END_REF][START_REF] Klales | MorphoPASSE: morphological pelvis and skull sex estimation program[END_REF][START_REF] Santos | A method of sexing the human os coxae based on logistic regressions and Bruzek's nonmetric traits[END_REF].

Genetic estimation of sex

For a long time, hundreds of years, scientists searched for a system of sex-determining pathways. Aristotle (in 335 BCE) proposed that heat/cold could determine sex. This environmental theory was popular until about 1900 -when sex chromosomes were discovered. However, Aristotle was partly right when in some reptiles, the temperature of the nest can determine the sex of the embryo [START_REF] Hake | Genetic mechanisms of sex determination[END_REF]. The discovery of chromosomal sex determination is credited to Nettie M. Stevens in 1905 with the finding that in most animals' sex is determined chromosomally, with males producing two types of gametes (carrying a Y or X chromosome) and thus being heterogametic, while females produce only one type and they are therefore homogametic [START_REF] Ramos | Decoding sex: Elucidating sex determination and how high-quality genome assemblies are untangling the evolutionary dynamics of sex chromosomes[END_REF]. Despite the great variety of sex determination mechanisms in some lineages, there is a surprising consistency. Amongst eutherian mammals, birds and some insects rely on heteromorphic sex chromosomes, which differ from each other in size, morphology, and gene content, to determine the sex of the individual [START_REF] Mank | Sex-specific morphs: the genetics and evolution of intra-sexual variation[END_REF].

Molecular biology and genetics can use aDNA at the individual level to identify the biological sex of a skeleton, make phenotypic inferences from an individual's genotype, and identify specific pathogens within an infected individual [START_REF] Raff | Ancient DNA and bioarchaeology. A companion to anthropological genetics[END_REF]. Molecular biology techniques are increasingly used to identify the sex of skeletal remains when traditional anthropometric analyses do not successfully identify the sex of remains that are incomplete, fragmented, and/or refer to immature individuals [START_REF] Stone | Sex determination of ancient human skeletons using DNA[END_REF][START_REF] Afonso | Sex selection in late Iberian infant burials: Integrating evidence from morphological and genetic data[END_REF][START_REF] Poma | A qPCR-duplex assay for sex determination in ancient DNA[END_REF]. As Raff [START_REF] Raff | Ancient DNA and bioarchaeology. A companion to anthropological genetics[END_REF] reports, aDNA research cannot be done in regular molecular biology laboratories. While nextgeneration methods have made it much easier to distinguish contamination from endogenous DNA based on DNA damage patterns, preventing contamination during the extraction process is still extremely difficult (e.g., [START_REF] Willerslev | Ancient DNA[END_REF][START_REF] Yang | Contamination controls when preparing archaeological remains for ancient DNA analysis[END_REF]). Contamination is such a pervasive problem that the work requires specialised facilities and workers trained in aDNA protocols. Sample decontamination is essential before beginning extraction. They will include one or more of the following steps: drilling or removing surface material, soaking or rinsing in bleach, and UV irradiation to cross-link surface DNA and extraction [START_REF] Kaestle | Ancient DNA in anthropology: Methods, applications, and ethics[END_REF]. Laboratories investigating aDNA must be positively pressurised, with HEPA-filtered air, polymerase chain reaction (PCR) enclosures, separation from post-PCR or modern DNA laboratories, and strict access protocols. They should be staffed by researchers trained in the specialised laboratories and methods necessary for ancient biomolecules [START_REF] Raff | Ancient DNA and bioarchaeology. A companion to anthropological genetics[END_REF].

From the analytical point of view, we can also mention sex estimation by capillary gel electrophoresis with amelogenin locus as a marker from 1998 [START_REF] Komuro | Gender determination from dental pulp by using capillary gel electrophoresis of amelogenin locus[END_REF]. The analysis of ten male and ten female samples and double peaks verified the male sample, while one peak verified the female sample. As a result, two peaks were obtained-the first peak was for the X and the second for the Y locus.

The most common method of genetic sex estimation relies on differences in the amelogenin gene (e.g., [START_REF] Faerman | Sex identification of archaeological human remains based on amplification of the X and Y amelogenin alleles[END_REF][START_REF] Gibbon | Novel methods of molecular sex identification from skeletal tissue using the amelogenin gene[END_REF]). Using cloning techniques, the amelogenin gene was localized to the sex chromosomes. With the advent of PCR, researchers developed robust and relatively simple amplification techniques for determining the presence of X and Y chromosome versions of this gene. This technique exploited the fact that insertion/deletion polymorphisms between the X and Y chromosomes lead to differently sized amplicons, which can easily be visualised by size separation using gel electrophoresis. These methods were used in the first commercially available kits [START_REF] Thomas | Sex determination using DNA and its impact on biological anthropology. Sex estimation of the human skeleton: history, methods, and emerging techniques[END_REF]. However, the amelogenin-based method can be problematic due to allelic dropout. It means that if only the copy present on the X chromosome is retained and not the copy on the Y chromosome, the individual will be falsely identified as female rather than male. Another problem is modern contamination from a male source, which could mislabel an ancient individual as male [START_REF] Raff | Ancient DNA and bioarchaeology. A companion to anthropological genetics[END_REF]. However, more recent profiling kits include assays for a separate insertion/deletion polymorphism and a short tandem repeat locus found only on the Y chromosome. Additionally, analysis of other short tandem repeats, other insertions, deletions, or single nucleotide polymorphisms on the X or Y chromosome can also be used to determine sex [START_REF] Thomas | Sex determination using DNA and its impact on biological anthropology. Sex estimation of the human skeleton: history, methods, and emerging techniques[END_REF][START_REF] Butler | Genetic markers for sex identification in forensic DNA analysis[END_REF][START_REF] Hagelberg | Ancient DNA: the first three decades[END_REF][START_REF] Dash | Alternatives to amelogenin markers for sex determination in humans and their forensic relevance[END_REF].

To overcome the before mentioned shortcomings, high-throughput shotgun sequencing has been proposed, which represents a more accurate method of sex assignment, as it simultaneously avoids the problem of allelic dropout by testing many more discriminating loci and allows the detection of contaminating fragments by assessing DNA damage patterns [START_REF] Skoglund | Origins and genetic legacy of neolithic farmers and hunter-gatherers in Europe[END_REF]. Skoglund et al. [START_REF] Skoglund | Accurate sex identification of ancient human remains using DNA shotgun sequencing[END_REF] evaluated the feasibility of this approach for applications in population-scale aDNA investigations. They found that approximately 100 000 reads are required for accurate sex estimation so that indexed genomes of up to 13 individuals could be pooled and simultaneously sequenced at low coverage at an estimated cost of < $300 per sample. While considerably more expensive than a simple amelogenin size-based analysis, it does have the advantage of being more accurate. It is likely that as shotgun sequencing costs continue to decrease, this approach will become much more routinely applied to archaeological populations [START_REF] Raff | Ancient DNA and bioarchaeology. A companion to anthropological genetics[END_REF]. However, this degree of preservation may be problematic for many archaeological remains, as Mittnik et al. [START_REF] Mittnik | A Molecular approach to the sexing of the triple burial at the upper paleolithic site of Dolní Věstonice[END_REF] noted. To reduce the required number of mapped human sequences, Mittnik and colleagues proposed an alternative method of sex estimation using high-throughput shotgun sequenced DNA. This method relies on the proportion of reads mapped to the human X chromosome compared to the proportion of reads mapped to each autosomal chromosome. By downsampling reads from the same high-quality ancient DNA data sets used in Skoglund et al. [START_REF] Skoglund | Origins and genetic legacy of neolithic farmers and hunter-gatherers in Europe[END_REF], the proposed method could give confident assignments with as few as 1000 human genomes reads [START_REF] Buonasera | A comparison of proteomic, genomic, and osteological methods of archaeological sex estimation[END_REF].

However, both Skoglund's and Mittnik's approaches [START_REF] Skoglund | Accurate sex identification of ancient human remains using DNA shotgun sequencing[END_REF][START_REF] Mittnik | A Molecular approach to the sexing of the triple burial at the upper paleolithic site of Dolní Věstonice[END_REF] are limited and admit some risk of error when the confidence interval is within certain parameters [START_REF] Loreille | Biological sexing of a 4000-year-old Egyptian Mummy head to assess the potential of nuclear DNA recovery from the most damaged and limited forensic specimens[END_REF]. To determine the genetic sex is compared the ratio for the number of Y-chromosomal 1240k positions with available data relative to the 1240k position on the X-chromosome. Individuals with a ratio greater than 0.35 were considered genetic males and individuals with a ratio less than 0.03 were considered genetic females [START_REF] Fowler | A high-resolution picture of kinship practices in an Early Neolithic tomb[END_REF]. The current rapid development of genomics will certainly enable even more sophisticated methods of genetic sex estimation. Current research is yielding very encouraging results in the field of archeology that were previously unavailable (i.e., [START_REF] Sjögren | Kinship and social organization in Copper Age Europe. A cross-disciplinary analysis of archaeology, DNA, isotopes, and anthropology from two Bell Beaker cemeteries[END_REF][START_REF] Villalba-Mouco | Genomic transformation and social organization during the Copper Age-Bronze Age transition in southern Iberia[END_REF][START_REF] Reitsema | The diverse genetic origins of aClassical period Greek army[END_REF]).

However, it cannot be neglected that the and extraction process is invasive and generally involves the destruction of a small (<0.5 g) amount of bone or tissue. The material for extraction should not be used for osteological research, such as non-pathological ribs. Recently, a petrous bone from the inner ear has been an excellent source of well-preserved, high-quality aDNA and should therefore represent an optimal extraction target [START_REF] Rasmussen | Ancient human genome sequence of an extinct Palaeo-Eskimo[END_REF][START_REF] Pinhasi | Optimal ancient DNA Yields from the inner ear part of the human petrous bone[END_REF]. However, even petrous bone is an essential element in anthropology that should not be sacrificed to obtain high-quality aDNA [START_REF] Trinkaus | The labyrinth of human variation[END_REF]. In addition, petrous also has several applications for scientific analysis beyond sex estimation from ancient DNA. There is a risk of potential bias in using the pars petrosa for ancient DNA analysis [START_REF] Charlton | The problem with petrous? A consideration of the potential biases in the utilization of pars petrosa for ancient DNA analysis[END_REF]. Ethical guidelines for petrous bone sampling need to be expanded further, as the demands for destructive sampling will only increase as the number of researchers and laboratories conducting aDNA research increases.

However, the genomic method looks like a standard and required method for the estimation of sex; there is also a developed proteomic method (see next section). One could ask the question: why? One of the answers is that genetic material is not so resistant to degradation, but what about the precision of sex estimation? An interesting comparison of the three methods (osteological, genomic, and proteomic) was made on 55 individuals between 2440 and 100 cal BP [START_REF] Buonasera | A comparison of proteomic, genomic, and osteological methods of archaeological sex estimation[END_REF]. Agreement between all methods was excellent when DNA shotgun sequencing was about 100 000 total sequences. However, more than half samples were below this threshold, and the conflict of sex estimation increased. On the opposite proteomic signal was not decreasing so significantly. It was concluded that proteomic data could complement osteological and genomic results/data.

Proteomics estimation of sex

Nowadays, proteomic methods enable us to determine minor differences in protein composition (qualitative and quantitative) enabled by many influences such as diet, aging, breeding, and sex [START_REF] Miller | Encore -Sex dependency of the proteome[END_REF]. Of course, the gender approach is a popular modern society theme, as visualized by the European Commission: "Gendered Innovations. How Gender Analysis Contribute to Research", and thirty years of research have revealed that sex and gender biases are socially harmful and costly [START_REF]Gendered innovations: how gender analysis contributes to research: report of the expert group 'Innovation through gender[END_REF].

For archaeological, anthropological, or forensic research, it is necessary to consider tissues resistant to degradation caused by long-term effects, aggressive decomposition phenomena in the soil, and external physical and chemical damage. For these purposes, the ideal tissue is teeth enamel. Enamel is one of the most calcified tissues in mammalian organisms and can protect teeth for tens of thousands of years [START_REF] Ziganshin | Optimization of method for human sex determination using peptidome analysis of teeth Enamel from teeth of different biological generation, Archeological Age, and degrees of taphonomic preservation[END_REF]. A nanocomposite bioceramic shields teeth against multiple chemical and physical (mechanical) efforts to disturb them. Protein amelogenins regulate crystallite formation during enamel development; however, they are specifically degraded during teeth maturation [START_REF] Jágr | Proteomics of human teeth and saliva[END_REF]. Amelogenin genes, in humans, are located on X and Y chromosomes (AMELX and AMELY, respectively). Proteins encoded by these genes have a different amino acid sequence (see Figure 1). The result of the presence of these two genes on the X and Y chromosomes is the sex-dependent presence of different proteins: AMELX for females and AMELX and AMELY for males [START_REF] Salido | The human enamel protein gene amelogenin is expressed from both the X and the Y chromosomes[END_REF]. During enamel maturation, proteins are degraded (proteolytic procedure), so mature tooth enamel is rich in various peptide fragments of constituted proteins [START_REF] Ziganshin | Optimization of method for human sex determination using peptidome analysis of teeth Enamel from teeth of different biological generation, Archeological Age, and degrees of taphonomic preservation[END_REF]. We have to remind that amelogenin is a relatively small molecule highly concentrated in the extracellular matrix [START_REF] Gil-Bona | Tooth Enamel and Its Dynamic Protein Matrix[END_REF]. Because amelogenin is a major enamel protein, these peptides mainly originated from amelogenin. For this reason, free peptides from sex-dependent amelogenins (AMELX and AMELY) are a good choice for estimating sex. If we are looking for a universal sex determination pathway for all mammals, we have to pay attention: AMELX gene on the X chromosome X and AMELY on the Y chromosome are presented not in all mammalian families; it is presented in Hominidae, Suidae, and Bovidae, but rodent species have only one AMELX [START_REF] Gil-Bona | Tooth Enamel and Its Dynamic Protein Matrix[END_REF]. We must also mention that the tissue used (teeth enamel) is difficult to cross-contaminate. In 1991 Fincham et al. [START_REF] Fincham | Human developing enamel proteins exhibit a sex-linked dimorphism[END_REF] remark that a diagnosis of differences in human enamel proteins can permit the distinction of specimens according to the sex of the individual. Porto et al. [START_REF] Porto | Recovery and identification of mature enamel proteins in ancient teeth[END_REF][START_REF] Porto | New techniques for the recovery of small amounts of mature enamel proteins[END_REF] discover/describe enamel proteins looking for sex-depending peptides. They used whole-crown etching, enzymatic (trypsin) treatment, and analysis by MALDI-TOF/TOF. They found the aminoterminal amelogenin peptides in the ancient sample (Mummy-ad 800-1100). They also found a peptide (WYQSIRPPYP) specific for the amelogenin X-isoform but no peptide specific for Y isoform. However, the authors did not specify the sex of the samples [START_REF] Porto | Recovery and identification of mature enamel proteins in ancient teeth[END_REF]. Although the MALDI-TOF/TOF method is suitable for protein and peptide analysis, nanoLC-MS/MS is a method of choice due to its higher sensitivity for peptide detection and identification. [START_REF] Yi | Advances in microscale separations towards nanoproteomics applications[END_REF].

Another attempt to analyze human teeth enamel was made by Castiblanco et al. [START_REF] Castiblanco | Identification of proteins from human permanent erupted enamel[END_REF] in 2015. They investigated the protein composition of healthy contemporary pulverized teeth without the digestion of an enzyme (trypsin). After extraction and cleaning on C18 StageTips, they analyzed peptides/proteins on nLC/MS-MS using QExactive MS (Thermo Fisher Scientific). Seven proteins were identified when four were specific for enamel (AMELX/AMELY, enamelin, and ameloblastin). Although eight teeth were used, the sex was not mentioned, and the method was not used for its detection.

Stewart et al. [START_REF] Stewart | The identification of peptides by nanoLCMS/MS from human surface tooth enamel following a simple acid etch extraction[END_REF] first published specific etching of single teeth to identify sex-sensitive amelogenins from enamel in 2016. This procedure (and with some slight modification) is now commonly used for peptide extraction from enamel (for the scheme, see Figure 2). The method consists of two parts [START_REF] Stewart | Sex determination of human remains from peptides in tooth enamel[END_REF]: etching and extraction. First teeth are mechanically treated (by dental burr) to clean them from all macroscopic impurities. Cleaning continued by water washing. Next, procedures were continued in the cap of a separate microcentrifuge tube (leaving a convex meniscus protruding above the lip when the tooth was lowering into the cap). The tooth's crown was washed with 3% H2O2 for 5 min, twice washed with H2O, and etched with 10% (v/v) HCl for 2 min. All these solutions were discarded. A second 2-min etch was used for analysis. The next stage was extraction. C18 resin-loaded ZipTip (Millipore, MA, USA) was used for extraction. ZipTip was previously conditioned three times with 100% ACN and then three times with 0.1% (vol/vol) formic acid (each draw discarded). The peptides were bound to the ZipTip (by up and down pipetting by 10 times. The ZipTip was washed six times with 0.1% (vol/vol) formic acid (each wash discarded). Bounded peptides were eluted by 4-μl of 60% ACN/0.1% formic acid. This fraction was lyophilized and dissolved in 12 μl of 2% formic acid in water and analyzed by reversedphase nanoLC/MS (with gradient similarly generally used for peptide separation, when used solvents were water and ACN with 0.1% TFA). The mass spectrometer was a hybrid linear ion trap orbitrap (Orbitrap XL, Thermo Scientific). They selected peptides AMELY-(58-64; SM(ox)IRPPY ([M + 2H]2+, m/z 440.2233) peptide and AMELX-(44-52; SIRPPYPSY ([M + 2H]2+, m/z 540.2796) (Figure 3).

Authors [START_REF] Stewart | The identification of peptides by nanoLCMS/MS from human surface tooth enamel following a simple acid etch extraction[END_REF] also compared the influence of trypsin digestion on protein/peptide identification. However, trypsin increased the variety of peptides, but no significant differences were observed in "sex" proteins (enamel specific proteins) when trypsin-treated and untreated samples were compared.

The same approach was used for sex estimation of the Late Antique (probably 4th-6th century) 'Lovers of Modena' [START_REF] Lugli | Enamel peptides reveal the sex of the Late Antique 'Lovers of Modena[END_REF]. The authors extracted peptides (after etching of teeth) by HyperSep SpinTips (Thermo Scientific) with C18 phase, and the analytical system was UHPLC-HRMS (Q Exactive MS from Thermo Scientific). Besides SM(ox)IRPPY (m/z 440.2233) peptide, they used at least two other peptides-SMIRPPY (m/z 432.2258) and M(ox)IRPPY (m/z 396.7073). All these peptides agreed in the distinction of specimens according to the sex, i.e. in the determination of AMELY. Surprisingly the 'Lovers of Modena' were males. The same method was successfully used to research sex-related morbidity and mortality for 30 nonadults from the Early Medieval Italian site from the 7 th century AD [START_REF] Lugli | Sex-related morbidity and mortality in non-adult individuals from the Early Medieval site of Valdaro (Italy): the contribution of dental enamel peptide analysis[END_REF]. The authors concluded that this method is used for archaeological (and forensic) research. This method was also successfully used for sex estimation from deciduous and permanent teeth from non-adults (incl. perinatal subjects) from archaeological sites in England (1st-2nd centuries AD, and 18th-19th centuries) [START_REF] Gowland | Sex estimation of teeth at different developmental stages using dimorphic enamel peptide analysis[END_REF].

Again the same method [START_REF] Lugli | Enamel peptides reveal the sex of the Late Antique 'Lovers of Modena[END_REF][START_REF] Lugli | Sex-related morbidity and mortality in non-adult individuals from the Early Medieval site of Valdaro (Italy): the contribution of dental enamel peptide analysis[END_REF] was used for the sex estimation of the horsemen of the Early Middle age (7th century AD) [START_REF] Gasparini | Biological sex VS. Archaeological Gender: Enamel peptide analysis of the horsemen of the Early Middle age necropolises of Campochiaro (Molise, Italy)[END_REF]. Determination of sex by proteomic (enamel) method was in agreement with osteological and archaeological determination when in many cases, only proteomic analysis was the only acceptable method for sex estimation. Authors also used confident identification of AMELY by triple-peptide approach (m/z 396.7073 for M(ox)IRPPY, m/z 432.2258 for SMIRPY, and m/z 440.2233 for SM(ox)IRPPY).

The above-described etching techniques were studied for optimization using three treatment procedures by 1.5M HCl: 3-sequential 4-min, 4 min only, and 10 min incubations [START_REF] Ziganshin | Optimization of method for human sex determination using peptidome analysis of teeth Enamel from teeth of different biological generation, Archeological Age, and degrees of taphonomic preservation[END_REF]. Samples were desalted on SDB-RPS StageTips before analysis on nLC-MS/MS (using Q Exactive Plus Mass spectrometer) system. From the point of view of sex estimation, AMELX, and AMELY peptides authors recommend 10-min etching. The method was validated on a set of 23 archaeological teeth in comparison to two different methods of sex estimation: morphological and archaeological (based burial rite) methods. All three methods agreed except in one case (when the archaeological method was opposite to morphological and protein methods) [START_REF] Ziganshin | Optimization of method for human sex determination using peptidome analysis of teeth Enamel from teeth of different biological generation, Archeological Age, and degrees of taphonomic preservation[END_REF]. Besides morphological methods, sex determination by this method was also described for sex estimation of prepubertal individuals from Roman Italy (1st-4th c. CE) and Late Roman Gaul (4th-5th c. CE) era [START_REF] Avery | Pubertal timing as an indicator of early life stress in Roman Italy and Roman Gaul[END_REF].

Osteological, proteomic, and isotopic analyses were used to evaluate a 9000-year-old human burial from the Andean highland site. These analyses indicate that this early hunter was a young adult female. This challenge the man-the-hunter hypothesis [START_REF] Haas | Female hunters of the early Americas[END_REF]. For proteomic analysis, a small piece of enamel (20 mg) was cut from teeth, powdered, and demineralized by 1.2 M HCl. After reduction and alkylation, samples were treated with trypsin. The next step was extraction on SepPak C18. Peptides were analyzed by nLC-MS/MS (Thermo ScientificQ-Extractive Plus Orbitrap mass spectrometer). Multiple peptide detection was used for AMELX (and AMELY) identification [START_REF] Haas | Female hunters of the early Americas[END_REF].

Two fast methods (1-3 min) were also developed for sex estimation without the separation step [START_REF] Casas-Ferreira | Fast methods based on mass spectrometry for peptide identification. Application to sex determination of human remains in tooth enamel[END_REF]. Both methods are based on the FIA (flow injection analysis) using high-resolution mass spectrometry (Q Exactive Orbitrap MS from Thermo Scientific) or tandem MS (Xevo TQ-S from Waters, Milford). Analyzed peptides were again SM(ox)IRPPY and SIRPPYPSY when specific transition ions were selected. Sample preparation is the same as above. The advantages of these methods are rapid analysis (three, respectively 1 min per sample) and the possibility to use low-resolution mass spectrometers (MS/MS), i.e. relatively low-cost instruments, for sex estimation.

There are also described other amelogenin peptides as diagnostic peptides using a nanoLC system coupled to a Q Exactive orbitrap mass spectrometer [START_REF] Rebay-Salisbury | Child murder in the Early Bronze Age: proteomic sex identification of a cold case from Schleinbach, Austria[END_REF][START_REF] Rebay-Salisbury | Gendered burial practices of early Bronze Age children align with peptide-based sex identification: a case study from Franzhausen I, Austria[END_REF]. The sample preparation was, in principle, the same as in the method by Stewart et al. [START_REF] Stewart | Sex determination of human remains from peptides in tooth enamel[END_REF], but the AMELY peptide was SM(ox)IRPPYS (m/z 486.7393), and AMELX peptide was YEVLTPLKWYQSIRPPYP (m/z 750.7368) (Figure 4). This method was successfully applied for the estimation of the sex of a child (5-6-year-old boy) murdered in the Early Bronze Age from Schleinbach, Austria (c. 1950-1850 BCE) [START_REF] Rebay-Salisbury | Child murder in the Early Bronze Age: proteomic sex identification of a cold case from Schleinbach, Austria[END_REF] as well as for successful sex classification of 70 (from 75) children under 12 years at death buried at the Early Bronze Age cemeteries in Franzhausen I, Austria (c. 2050-1680 BCE). The coincidence between archaeological and peptide-based results was very high (62 of 63 individuals, 98.4%) when one was of the female sex, based on body position and orientation [START_REF] Rebay-Salisbury | Gendered burial practices of early Bronze Age children align with peptide-based sex identification: a case study from Franzhausen I, Austria[END_REF]. Another approach for analysis of archaeological samples was described for Iron Age individuals (ca. 2000-1000 years B.P.) from the tropical environment (northwest Thailand) [START_REF] Wasinger | Analysis of the preserved amino acid bias in peptide profiles of Iron Age teeth from a tropical environment enable sexing of individuals using amelogenin MRM[END_REF]. It was possible to identify 212 proteins. Analyses were done at nLC-MS/MS system (OrbitrapVelos, Thermo Electron, Bremen, Germany) using the multiple reaction monitoring methods were used for the identification of two AMELX peptides (TALVLTPLK and WYQSIRPPYPSY(G)), and one AMELY peptide (IALVLTPLK). Regarding sample preparation, the tooth enamel/dentin was crushed, treated with 0.5MHCl, reduced, alkylated, and cleaved by trypsin.

Another protein/peptide extraction was used by Froment et al. [START_REF] Froment | Analysis of 5000 year-old human teeth using optimized large-scale and targeted proteomics approaches for detection of sex-specific peptides[END_REF] to analyze 5000-year-old human teeth. In principle, they powdered whole teeth demineralized in EDTA, and proteins were denatured, lysed, washed, and alkylated. Finally, proteins were treated with trypsin. For analysis of peptides, nanoLC coupled to Orbitrap Fusion MS (Thermo Scientific) was used when using the targeted MS approach and parallel reaction monitoring (PRM). They demonstrated that the PRM method maximizes the sensitivity and reproducibility of "sex" peptides. The selected "sex" peptides were TALVLTPLK (m/z 478.3130) for AMELX and IALVLTPLK (m/z 474.3325) for AMELY (Figure 5). A similar method for sample preparation, that is, demineralized (by 1.2 M HCl) milled teeth were alkylated and treated by trypsin, was used to analyze teeth aged up to 7300 years [START_REF] Parker | Sex estimation using sexually dimorphic amelogenin protein fragments in human enamel[END_REF]. ZipTip C18 tips cleaned samples/peptides. These peptides were analyzed by nLC-MS/MS using Q Exactive Plus Orbitrap MS (Thermo Scientific). The authors used bioinformatic methods for the identification of AMELX and AMELY proteins. To elute false negative samples, that is, samples with low male signal, authors used a probability curve of female sex as a function of the logarithm of AMELX using logistic regression.

False female assignments were discussed in this context [START_REF] Parker | Sex estimation using sexually dimorphic amelogenin protein fragments in human enamel[END_REF][START_REF] Štamfelj | Sex estimation based on the analysis of enamel peptides: false assignments due to AMELY deletion[END_REF][START_REF] Parker | AMELY deletion is not detected in systematically sampled reference populations: a reply to Štamfelj[END_REF]. It is some probability that the method using AMELX and AMELY could produce inaccurate results due to the presence of low frequency of AMELY deletion variants in some populations [START_REF] Štamfelj | Sex estimation based on the analysis of enamel peptides: false assignments due to AMELY deletion[END_REF]. However, after analysis of many genomic projects, it was concluded that the probability of false sex estimation is low, and AMELY deletion should not affect the routine estimation of the biomolecular sex [START_REF] Parker | AMELY deletion is not detected in systematically sampled reference populations: a reply to Štamfelj[END_REF].

The oldest dental proteome was probably studied in the Early and Middle Pleistocene hominin (Homo antecessor) and Homo erectus tooth [START_REF] Welker | The dental proteome of Homo antecessor[END_REF]. For protein/peptide extraction, authors used three methods: 1) demineralization by HCl without alkylation and enzymatic digestion, 2) pellet after demineralization was reduced, alkylated, and digested by LysC and trypsin, and 3) demineralization by TFA without alkylation and enzymatic digestion. The first and third extraction gave more extensive peptide recovery than the second one. Peptides were analyzed by nLC-MS/MS using Q-Exactive HF or HF-X mass spectrometer (Thermo Fisher Scientific). It was described that an average peptide length decreased with the age of the enamel sample. Enamel-specific proteins were identified as enamelin, ameloblastin, MMP20, and amelogenins (both AMELX and AMELY). At the teeth of Homo antecessor, AMELY-specific peptide sequences (such as SM(ox)IRPPY) were found, and so it was concluded that he was male [START_REF] Welker | The dental proteome of Homo antecessor[END_REF]. We must mention that Homo antecessor is an extinct archaic human species recorded in Spain that lived between 1.2 and 0.8 million years ago during the early Pleistocene.

In the end, we have to mention that acid etching of teeth is, mainly in comparison to genetic methods, a limited destructive method, but still is (limited) destructive and not quantitative (the signal cannot be normalized).

Concluding remarks

Sexual diagnosis is often crucial to archaeological, anthropological, and forensic research. Proteomic methods are relatively young, rapidly growing, and have applications in many scientific areas. Nowadays, there are used three methods of sex estimation: osteology, genetics, and proteomics. In the sex estimation method, use protein amelogenin in X-and Y-form (AMELX and AMELY). It was established as a method that overcomes osteological and genomic methods as a more precious, sensitive, and relatively simple and rapid method. The crucial advantage is that this method uses teeth enamel. The enamel is one of the most calcified tissues in the mammalian organism. For this reason, it is relatively resistant to degradation caused by long-term effects, aggressive decomposition phenomena in the soil, and external physical and chemical damage. It was proven that proteins (peptides) in the enamel could be protected for tens or hundreds of thousands of years.

So it can be concluded that the proteomic method for sex estimation using isoforms of amelogenin be successfully used in archaeological, anthropological, and forensic research and overcome other previously used methods.

Figure 1 .

 1 Figure 1. Structure of Amelogenins and their comparison. Data are from UniProtKB reviewed (Swiss-Prot): Q99217 Amelogenin, X isoform, Q99217-3 Amelogenin, X isoform, Rare isoform 3; Q99218 Amelogenin, Y isoform. Differences in amino acid sequence between X and Y amelogenins are indicated by white characters highlighted in black.

Figure 2 .

 2 Figure 2. Workflow of the sample preparation (etching method) for amelogenin analysis.

Figure 3 .

 3 Figure 3. A base peak chromatogram (300-1600 m/z) with two marked peptides of amelogenin: AMELY-[58-64] and AMELX-[44-52]. The reconstructed ion chromatograms (to 4 ppm) for each are shown in

Figure 4 .

 4 Figure 4. Left: MS/MS fragment spectrum of peptide SM(ox)IRPPYS (m/z 486.7393) (AMELY) and corresponding mass errors in ppm; Right: MS/MS fragment spectrum of peptide YEVLTPLKWYQSIRPPYP (m/z 750.7368).(AMELX) and corresponding mass errors in ppm. Reprinted [73] with permission. Copyright 2020 Springer Nature.

Figure 5 .

 5 Figure 5. MS/MS spectra of specific peptides: (A) AMELX peptide, TALVLTPLK (precursor m/z 478.3130). (B) AMELY peptide, IALVLTPLK (precursor m/z 484.3325). (C) AMELX peptide, WYqSIRPPYP (precursor m/z 654.3259), and (D) AMELY peptide, WYqSmIRPPY (precursor m/z 679.3165). The series of y-and bions are highlighted in blue and red, respectively. q: deamidated glutamine residue; m: oxidized methionine residue. Reprinted [76] with permission. Copyright 2019 Elsevier B.V.

Data availability statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Conflict of interest statement

The authors declare no conflict of interest.


Fabienne Laura Lepage

Management of the disease by osteoporotic patients :

Preliminary results of a qualitative approach.

Laura Lepage

Contact : laura.lepage@univ-lorraine.fr

Poster presented at the 35 th Annual Conference of the European Health Psychology Society

Management of the disease by osteoporotic patients : Preliminary results of a qualitative approach

Laura Lepage (PhD student, 3rd year) & Fabienne Lemétayer (thesis director) Université de Lorraine -APEMAC ❖ Osteoporosis is a chronic bone disease that is asymptomatic until the first fracture.

❖ Its asymptomatic nature can make disease management and compliance with medication difficult.

❖ Patients may decide to continue or stop treatment or refuse it outright. This decision represents a choice that goes against the usual management.

❖ Independently of the choice to continue or stop treatment, certain resources and strategies that can promote osteoporotic patients conscientization and reappropriation of their disease. ❖ Overall, osteoporotic patients implement health-promoting behaviours by following hygienic and dietary measures (e.g. reduction of smoking).

Method Context

Results

❖

❖ Regardless of the type of treatment, patients use coping strategies. Patients undergoing oral treatment used more coping strategies focused on emotions (positive reinterpretation). Injection patients use coping strategies focused on problem (planning).

❖ Positive reinterpretation would counteract harmful thoughts related to oral treatment (e.g. expectations about effects). Planning would reinforce treatment compliance by organising medical appointments to go for the injection. Gossec, L., & Nataf, H. (2012). Le patient, copilote de la gestion de sa maladie: pourquoi, comment?. La Lettre du rhumatologue, (382), 4-7.

Meziat, K., Sahraoui, I. E., & Mouhoubi, R. ( 2015). Les stratégies de coping chez les femmes atteintes de polyarthrite rhumatoïde: étude de huit ( 8) cas (Doctoral dissertation, Université de Bejaia).

References Discussion

Coping strategies

Problem solving

Active coping (10 references)

▪▪▪Figure 1 :

 1 Figure 1 : Health behaviours of osteoporotic patients under oral treatment and patients under injection treatment.

Figure 2 :

 2 Figure 2 : Personal resources and coping strategies of osteoporotic patients on oral therapy and patients on injection therapy in managing their disease.