Léonie Rey

Théo Tacail

Frédéric Santos

Stéphane Rottier

Gwenaëlle Goude

Vincent Balter
email: vincent.balter@ens-lyon.fr

Disentangling diagenetic and biogenic trace elements and Sr radiogenic isotopes in fossil dental enamel using laser ablation analysis

Keywords: laser ablation, trace elements, strontium isotopes, Neolithic, diet, mobility, enamel, bone Highlights

Enamel elemental and 87 Sr/ 86 Sr ratios track fossil mammal diet and mobility histories High-resolution life histories reconstructions are possible using laser ablation ICPMS Diagenetic effects cannot be ad hoc eliminated using leaching protocols Diagenetic effects are post hoc eliminated using statistical protocols

Introduction

The analysis of trace elements and radiogenic strontium isotopes in fossil bone and teeth to reconstruct ancient diet and mobility is nowadays of routine use in bioarchaeology and paleoanthropology. Of particular interest for ancient mammal dietary habits is the analysis of fossil enamel strontium/calcium ratio (Sr/Ca) and barium/calcium ratio (Ba/Ca). Sr and Ba are discriminated against Ca in biochemical pathways, which include Ca as an essential element, resulting in the overall decrease of the Sr/Ca and Ba/Ca ratios up trophic chains and allowing the reconstruction of ancient dietary behaviors (e.g., [START_REF] Austin | Barium distributions in teeth reveal early-life dietary transitions in primates[END_REF][START_REF] Balter | Were Neandertalians essentially carnivores? Sr and Ba preliminary results of the mammalian palaeobiocoenosis of Saint-Césaire[END_REF][START_REF] Gilbert | An Investigation of Barium, Calcium and Strontium as Palaeodietary Indicators in the Southwestern Cape, South Africa[END_REF][START_REF] Joannes-Boyau | Elemental signatures of Australopithecus africanus teeth reveal seasonal dietary stress[END_REF][START_REF] Sponheimer | Enamel diagenesis at South African Australopith sites: Implications for paleoecological reconstruction with trace elements[END_REF]. The radiogenic 87 Sr isotope abundance is determined after normalization of the stable isotope variations to a reference 88 Sr/ 86 Sr value, therefore the 87 Sr/ 86 Sr ratio is immune to biological and any other process up the trophic chain. Consequently, the 87 Sr/ 86 Sr of an animal ultimately reflects that of the bedrock on which it feeds and is used for the reconstruction of ancient mobility (e.g., [START_REF] Sillen | 87Sr/86Sr ratios in modern and fossil food-webs of the Sterkfontein Valley: implications for early hominid habitat preference[END_REF][START_REF] Müller | Origin and Migration of the Alpine Iceman[END_REF][START_REF] Balter | Evidence for dietary change but not landscape use in South African early hominins[END_REF][START_REF] Sillen | Strontium Isotopic aspects of Paranthropus robustus teeth; Implications for habitat, residence, and growth[END_REF][START_REF] Lugli | Strontium and stable isotope evidence of human mobility strategies across the Last Glacial Maximum in southern Italy[END_REF].

Since the very beginnings of this archeometric discipline, diagenesis has been recognized to be a major limitation and two methods have been developed to overcome this problem. The first method is to leach ad hoc the bone or enamel sample with dilute acetic acid to remove secondary Ca-carbonates (e.g., [START_REF] Balter | Evidence of physico-chemical and isotopic modifications in archaeological bones during controlled acid etching[END_REF][START_REF] Hopkins | When Dental Enamel is Put to the Acid Test: Pretreatment Effects and Radiocarbon Dating[END_REF][START_REF] Nelson | Effects of diagenesis on strontium, carbon, nitrogen and oxygen concentration and isotopic composition of bone[END_REF].

However, Ca-carbonates are not the only potential secondary phase, oxy-hydroxides being also frequent diagenetic phases, which are not removed by acetic acid. In addition, bone or enamel can be recrystallized, an extreme case where any leaching technique is helpful. The second method consists to monitor the concentration of an element which is known to be of diagenetic origin and perform post hoc correlation tests with the elements (mainly Sr and Ba) supposed to be of biogenic origin. Uranium (U), thorium (Th) and Rare Earth Elements (REE) accumulate in fossil bones and teeth (Kohn et al 1999, Reynard andBalter, 2014), and are good indicators of the intensity of the diagenesis. The influence of oxy-hydroxides on the biogenic elements concentration can easily be assessed by measuring manganese (Mn) concentration (e.g., [START_REF] Reynard | Trace elements and their isotopes in bones and teeth: Diet, environments, diagenesis, and dating of archeological and paleontological samples[END_REF]. Regarding the 87 Sr/ 86 Sr ratio, the existence of a correlation between the concentrations and isotope compositions along a mixing hyperbola will attest of a diagenetic overprinting [START_REF] Budd | Differential diagenesis of strontium in archaeological human dental tissues[END_REF][START_REF] Martin | Strontium isotopes reveal long-term residence of thalattosuchians in the freshwater environment[END_REF].

Thanks to the development of laser ablation, it is now possible to analyze in situ the trace elements concentration [START_REF] Dolphin | Variation in elemental intensities among teeth and between pre-and postnatal regions of enamel[END_REF][START_REF] Humphrey | Unlocking evidence of early diet from tooth enamel[END_REF][START_REF] Kohn | Trace element concentrations in teeth -a modern Idaho baseline with implications for archeometry, forensics, and palaeontology[END_REF][START_REF] Müller | Enamel mineralization and compositional time-resolution in human teeth evaluated via histologically-defined LA-ICPMS profiles[END_REF] and the 87 Sr/ 86 Sr ratio (e.g., [START_REF] Balter | Analysis of coupled Sr/Ca and 87Sr/86Sr variations in enamel using laser-ablation tandem quadrupole-multicollector ICPMS[END_REF][START_REF] Lugli | In situ high spatial resolution 87Sr/86Sr ratio determination of two Middle Pleistocene (c.a. 580ka) Stephanorhinus hundsheimensis teeth by LA-MC-ICP-MS[END_REF][START_REF] Montgomery | Evidence for long-term averaging of strontium in bovine enamel using TIMS and LA-MC-ICP-MS strontium isotope intramolar profiles[END_REF]. This is of noteworthy interest for enamel because it is less sensible to diagenesis than bone thanks to its less porous structure, and because it grows incrementally, allowing the reconstruction of individual dietary and mobility histories [START_REF] Austin | Barium distributions in teeth reveal early-life dietary transitions in primates[END_REF][START_REF] Balter | Evidence for dietary change but not landscape use in South African early hominins[END_REF][START_REF] Joannes-Boyau | Elemental signatures of Australopithecus africanus teeth reveal seasonal dietary stress[END_REF]. However, there is a major limitation for the use of laser ablation of fossil tooth enamel, which is that the leaching step is not possible because it needs to be carried out on powdered samples. Biogenic and diagenetic trace elements must be monitored along with the 87 Sr/ 86 Sr ratio and post hoc correlation tests processed to determine the areas free of diagenesis. To the best of our knowledge, this has been done in three studies only [START_REF] Balter | Evidence for dietary change but not landscape use in South African early hominins[END_REF][START_REF] Simonetti | In-situ elemental and Sr isotope investigation of human tooth enamel by laser ablation-(MC)-ICP-MS: Successes and pitfalls[END_REF][START_REF] Willmes | Improvement of laser ablation in situ micro-analysis to identify diagenetic alteration and measure strontium isotope ratios in fossil human teeth[END_REF], but no trace elements and radiogenic Sr systematics in fossil tooth enamel has been done yet using laser ablation.

The present study combines a unique set of biogenic (Sr and Ba), diagenetic (Mn and U) trace elements, major elements (Mg and Ca) and 87 Sr/ 86 Sr ratio time series obtained by means of laser ablation ICPMS and MC-ICPMS on a large number of fossil tooth enamel samples (n = 62 and 32 for humans and animals, respectively) from a set of neighboring Neolithic sites in France. Bone samples of same specimen are also analyzed for comparison. In the archaeological context of Neolithic Revolution, which is one of the biggest socio-cultural transitions in human history, dietary behavior and mobility of human groups are central issues because people settled down building villages and hunter-gatherers became farmer-pastoralists. The use of laser ablation in such an archaeological and chrono-cultural context is a crucial methodological step that will pave the way for studies on longitudinal life histories.

Laser ablation measurements of trace elements concentrations and 87 Sr/ 86 Sr ratios produced in the present study a large number of data (> 400,000). Global trends between diagenetic and biogenic trace and major elements are first identified using inclusive data analysis. These trends are then validated at the scale of the laser ablation raster, and a protocol of data cleaning is developed to identify areas free of diagenesis and with reliable 87 Sr/ 86 Sr ratio.

Most of the rasters unfortunately exhibit diagenetic portions so that the full time series are not exploitable. Non-significantly altered Sr/Ca, Ba/Ca and 87 Sr/ 86 Sr average values are thus gathered for each tooth enamel and bone samples and are discussed, along with previously measured bone collagen δ 13 C andδ 15 N values.

Material

The bone and tooth enamel samples come from seven Neolithic sites within a radius of 10 km along the Yonne valley, in the South-East of the Paris basin, at the Northern edge of the Morvan massif, France (Fig. 1). The sites with the corresponding material are presented in Table 1. They are dated to different and overlapping periods covering the 5th millennium BC and they refer to different and mixed cultural spheres (Table 1). Further archaeological details are available in [START_REF] Rey | A multiisotope analysis of Neolithic human groups in the Yonne valley, Northern France: insights into dietary patterns and social structure[END_REF]. The bioavailable Sr local range is determined on the grounds of the geological variability from plants and soil samples given by the iRhum database regionally (within a 15 km radius around the sites, including layers q3, q2, c1, c2 and j3; Fig. 1), and is found to vary from 0.7075 to 0.7145 [START_REF] Willmes | The IRHUM (Isotopic Reconstruction of Human Migration) database -bioavailable strontium isotope ratios for geochemical fingerprinting in France[END_REF]. For humans, all the teeth are second molar (M2) except for 2 individuals for whom the teeth are first molar (M1). This corresponds to a life history between approximately 2.5 and 8.5 years ± 0.5 for M2 and between approximately 0.5 and 3.5 years ± 0.5 for M1 [START_REF] Alqahtani | Brief communication: The London atlas of human tooth development and eruption[END_REF]. When it was possible, bone from the same individual was also analyzed to assess dietary and mobility changes between childhood and adulthood because bone records a signal corresponding to the individuals' last years of life [START_REF] Hedges | Collagen turnover in the adult femoral mid-shaft: modeled from anthropogenic radiocarbon tracer measurements[END_REF][START_REF] Szulc | Biochemical Measurements of Bone Turnover in Children and Adolescents[END_REF] and to assess potential differential diagenetic sensitivity relative to enamel.

All observations (anatomical variations, pathologies, stress indicators, wear, maturation stage) and external metrics were recorded and teeth pictured. In addition, calculus samples, impressions of the crown and µCT-scans were computed whenever possible for further complementary studies [START_REF] Luyer | Internal Tooth Structure and Burial Practices: Insights into the Neolithic Necropolis of Gurgy (France, 5100-4000 cal. BC)[END_REF][START_REF] Rey | Tracking male vs. female Neolithic behaviors: a new multi-element and multi-isotoperatio analysis to reconstruct diet and mobility in northern France[END_REF]. The teeth were cut in two pieces with a diamond saw, along the longitudinal bucco-lingual axis, passing through the top of the mesial cusps and perpendicular to the collar (crown root junction, or crj). The mesial part was embedded, with a bone fragment from the same individual whenever possible. Bone fragments were taken from long bone cortical fragments (the bone type is indicated in table S1).

The fragments were surface cleaned with a sandblaster with aluminium oxides, washed by compressed air, embedded with tooth enamel in epoxy resin and finally polished manually (granulometry P4000) to obtain a smooth surface.

Method

Laser ablation

In tooth enamel, rasters were processed along the enamel dentine junction (edj) to cross the Retzius' striae and the transverse striations. For humans and pigs, the profiles were drawn from the apex (« ocl ») to the crj (« col »). The rasters for concentration and isotopic composition were as close as possible. In bone, one or two small rasters were processed to obtain sufficient data to average. Samples were run according to a fixed sequence procedure according to [START_REF] Tacail | Spatial distribution of trace element Ca-normalized ratios in primary and permanent human tooth enamel[END_REF]. Each sequence was composed of 3 to 6 samples and was bracketed by a sintered international standard SRM1400 "bone ash" [START_REF] Tacail | Precise analysis of calcium stable isotope variations in biological apatites using laser ablation MC-ICPMS[END_REF] at the beginning and the end of the sequence to correct for instrumental biases. Blank was measured during 5 seconds (laser off) before each measurement. The laser ablation device was connected to a quadrupole-ICPMS (Q-ICPMS, X series, ThermoFisher) for the measurement of element concentrations and to a multicollector-ICPMS (MC-ICPMS, Nu500 HR, Nu Instruments) for the measurements of Sr isotopes. The spot size for the acquisition of trace elements and Sr isotopes was respectively 50 and 150 µm, with a frequency of 10 and 20 Hz and a speed of 10 µm/s for both. Operating conditions are summarized in Table 2.

Data processing

The laser ablation technique generates a considerable amount of data that must be treated and reduced before being interpreted accurately. Each sequence (two standards bracketing 2-3 samples) corresponds to a single block of measurements, either on the Q-ICPMS and MC-ICPMS. These raw data sequences were semi-automatically processed with Spyder Python 2.7 software to obtain corrected profiles for each sample. The procedure notably detects and isolates samples and standards measurements using blanks (5 s) that are added between each sample or standard. The procedure for element concentration is fully described in [START_REF] Tacail | Spatial distribution of trace element Ca-normalized ratios in primary and permanent human tooth enamel[END_REF]. For Sr isotopes, the measurements were corrected using the classical 85 Rb and 83 Kr corrections and the 87 Sr/ 86 Sr ratio of the samples was subsequently normalized by the bracketing SRM1400 standards with a factor depending on their position relative to the standards. Because ICPMS and MC-ICPMS have dramatically different data integration time, we use relative position expressed as percent of the raster length to match trace elements concentration and Sr isotope composition at a given location. Elemental ratios are expressed relative to Ca*1000 otherwise specified. Statistical analyses were performed using the FactoMineR and PerformanceAnalytics packages of the R software.

Results and discussion

Quality control of the measurements

As previously mentioned, we used a sintered international standard SRM1400 "bone ash" [START_REF] Tacail | Precise analysis of calcium stable isotope variations in biological apatites using laser ablation MC-ICPMS[END_REF] at the beginning and the end of the sequence to correct samples for instrumental biases. A total of 98 and 140 measurements of the SRM1400 standard has been processed for Sr isotopes and trace elements, respectively. Ablation of the SRM1400 standard, certified to contain 250ppm of Sr, produces here a signal for 88 Sr of ≈0.9 V on the MC-ICPMS and of ≈140,000 cps on the Q-ICPMS. The average value of the 87 Sr /86 Sr ratio is 0.71310 ± 0.00218 (2SD, n = 98) very close to the TIMS value of 0.71308 ± 0.00005 (2SD, n =25; [START_REF] Brazier | R( 87 Sr/ 86 Sr) and δ 88/86 SrSRM987 values of mineral, vegetal and animal reference materials[END_REF]. The average value of the Sr/Ca, Ba/Ca and Mg/Ca ratios are 0.653 ± 0.038, 0.630 ± 0.049 and 17.93 ± 0.73, respectively, which are always very close to certified values (0.652 ± 0.018, 0.629 ± 0.026 17.91 ± 0.35, for Sr/Ca, Ba/Ca and Mg/Ca, respectively; [START_REF] Balter | Determination of Sr and Ba partitioning coefficients between apatite and water from 5°C to 60°C: a new thermometer for aquatic environments[END_REF].

Bulk radiogenic Sr isotope compositions

The standard deviation of standard and sample corrected 87 Sr/ 86 Sr ratios are plotted as a function of the 88 Sr voltage in Fig. 2A and show an increase of the variability as the 88 Sr voltage decreases, a pattern that has been recognized by [START_REF] Horstwood | Determination of Sr isotopes in calcium phosphates using laser ablation inductively coupled plasma mass spectrometry and their application to archaeological tooth enamel[END_REF]. Comparing the discrepancy between laser ablation and solution 87 Sr/ 86 Sr measurements, [START_REF] Simonetti | In-situ elemental and Sr isotope investigation of human tooth enamel by laser ablation-(MC)-ICP-MS: Successes and pitfalls[END_REF] and [START_REF] Copeland | Strontium isotope ratios (87Sr/86Sr) of tooth enamel: a comparison of solution and laser ablation multicollector inductively coupled plasma mass spectrometry methods[END_REF] have also observed that the accuracy of the laser ablation measurements decreases with Sr total voltage. The decreasing 88 Sr voltage is also accompanied by an increase of the corrected 87 Sr/ 86 Sr ratios mean values (Fig. 2B). [START_REF] Horstwood | Determination of Sr isotopes in calcium phosphates using laser ablation inductively coupled plasma mass spectrometry and their application to archaeological tooth enamel[END_REF] and [START_REF] Simonetti | In-situ elemental and Sr isotope investigation of human tooth enamel by laser ablation-(MC)-ICP-MS: Successes and pitfalls[END_REF] argued that the increase of the 87 Sr/ 86 Sr ratio is due to a 40 Ca-31 P- 16 O polyatomic interference at mass 87. However, using Sr/Rb-free concentrated Ca/P solutions, [START_REF] Müller | Accuracy of laser-ablation (LA)-MC-ICPMS Sr isotope analysis of (bio) apatite-a problem reassessed[END_REF] recently demonstrated that the 40 Ca-31 P-16 O polyatomic interference does not occur at the required intensities to explain the observed increase of the 87 Sr/ 86 Sr ratio. [START_REF] Horstwood | Determination of Sr isotopes in calcium phosphates using laser ablation inductively coupled plasma mass spectrometry and their application to archaeological tooth enamel[END_REF] proposed that the complete elimination of this interference should be achieved using rigorous calibration to known reference materials, which is actually not the case given the present results. The increase of the variability of the 87 Sr/ 86 Sr ratio is likely due to degraded counting statistics for too low voltage. The concomitant increase of the average value of the 87 Sr/ 86 Sr ratio with decreasing Sr voltage remains unexplained, but must be ultimately linked, at least indirectly, to degraded counting statistics and thus, could not be corrected anyway. We have selected a threshold value at 0.4 V for 88 Sr below which the value of the 87 Sr/ 86 Sr ratio is considered inaccurate and thus eliminated for further discussion. This value holds for a Nu Plasma HR MC-ICPMS and should be different for a Neptune instrument. We also note that there is an apparent increase of the variability of the 87 Sr/ 86 Sr ratio for 88 Sr voltage ≥ 1V (Fig. 2A), but which does not seem to be followed by an increase, or a decrease, of the average value (Fig. 2B). The analysis of the 87 Sr/ 86 Sr ratio in bone and tooth enamel by laser ablation should be adapted for each sample, by varying the diameter of the spot size and/or the sampling rate of the laser to obtain enough signal that should ideally lie between 0.6 V to 0.9 V for 88 Sr.

Bulk trace elements compositions

The dataset has been explored using principal component analysis (PCA). PCA consists at reducing the dimensionality of dataset while preserving most of the information. The basic representation provides eigenvectors of the covariance matrix in two dimensions, the principal components (PCs) which are the new variables. Co-variation of the eigenvectors yields information about correlation of the variables. PCA are particularly useful for large dataset, such as in the present study which considers six independent variables (Mg, Ca, Mn, Sr, Ba and U) representing ~350,000 and 40,000 measurements for enamel and bone, respectively. We have first performed PCA on the whole dataset (Fig. 3A and3B). For enamel, the first two PCs account for 31.7% and 21.6%, respectively, of the total variation in the dataset, so the twodimensional scatterplot given by Fig. 3A represents 53.3% of the variance of the original eleven-dimensional space. All eigenvectors except Mg/Ca are positive along PC1, indicating that they are all positively correlated and negatively correlated to Mg/Ca. Along PC2, eigenvectors of biogenic (Mg, Ca, Sr, Ba and related Ca-ratios) and diagenetic (Mn, U and Caratios) variables are clustered indicating that the set of data contains clear biogenic and diagenetic components that intrinsically positively correlated. The direction of the Mg/Ca eigenvector is opposed to that of U/Ca demonstrating that these ratios are strongly anticorrelated. The direction of the Sr/Ca and Ba/Ca eigenvectors is approximately perpendicular to those of Mn/Ca and U/Ca ones, indicating that the biogenic and diagenetic variables are not correlated. To resume, the information carried by the PCA on enamel suggests that the Sr/Ca and Ba/Ca ratios are not correlated with those of Mn/Ca and U/Ca and that the Mg/Ca ratio negatively correlated to the U/Ca and of Mn/Ca ratios. These conclusions apparently hold for bone, except that the Mg/Ca ratio is positively correlated to those of Sr/Ca and Ba/Ca (Fig. 3B).

However, inspection of the variance for a given location provides more complex results for enamel (Fig. 3C) and bone (Fig. 3D). Abbreviations of the archaeological sites are given in Table 1. For enamel, the Sr/Ca and Ba/Ca ratios are free of diagenesis at GLN and BMT, while low and high Mg/Ca ratio, respectively, is associated to high Mn/Ca and U/Ca ratios. At NZ, Mon, CHI-ED and CHI-Pat, the enamel Ba/Ca ratio has a diagenetic component because the Ba/Ca, Mn/Ca and U/Ca eigenvectors have closely related directions. In these sites, the enamel Sr/Ca ratio seems to be free of diagenetic influence. For bone, the Sr/Ca and Ba/Ca ratios have most often a diagenetic component, except at Mon, as illustrated by the common direction of the biogenic and diagenetic eigenvectors.

Cleaning data from diagenesis and too low Sr content PCA indicates that diagenesis occurs on a site-by-site systematics and that the chemical composition of bone and enamel is differently affected by diagenesis. Analysis of the effects of diagenesis at the individual scale reveals even more complicated patterns. An example is provided for the GLN-210 individual (Fig. 4A and4B). Two diagenetic zones can be identified.

In the diagenetic Zone 1, the increase of the Mn/Ca and U/Ca ratios is accompanied by a concomitant increase of the Ba/Ca ratio and of the Ca concentration, and a decrease of the Mg/Ca ratio (Fig. 4A). A simultaneous increase of the Sr/Ca ratio is less evident and is not associated to variations of the 87 Sr/ 86 Sr ratio anyway. The most likely explanation is that a Carich, probably calcite, secondary phase precipitated in a crack of the enamel, as recognized earlier by [START_REF] Grün | High resolution analysis of uranium and thorium concentration as well as U-series isotope distributions in a Neanderthal tooth from Payre (Ardeche, France) using laser ablation ICP-MS[END_REF] to be a classic process. This secondary calcite was U-and Ba-rich, but Mg-poor, and has a comparable Sr concentration and isotopic composition than enamel.

The crack was also filled with Mn-rich oxy-hydroxides. In the diagenetic Zone 2, a small increase of the U/Ca ratio, but not of the Mn/Ca one, is associated to an increase of the Ba/Ca ratio and a decrease of the Mg/Ca ratio, without any change in the Sr/Ca ratio, Sr concentration nor isotopic composition (Fig. 4A). Here, U diffusion only cannot explain the observed diagenetic pattern because it would not take the associated Ba-enrichment and Mg-depletion into account. The observed diagenetic pattern is more likely explained by the presence of a secondary U-enriched phase, which must have been also Ba-enriched. The diagenetic effect on the Mg/Ca ratio is discussed in a subsequent section. The trace elements data were thus cleaned according to the following conditions: increase of the 43 Ca concentration or U/Ca or Mn/Ca ratios correlated to an increase of the Sr/Ca or Ba/Ca ratios or a decrease of the Mg/Ca ratio. pattern for the tooth enamel and bone samples analyzed here. Magnesium, as carbonate groups, represents defects in the hydroxyapatite (HAP) lattice, which decrease crystallinity and increase solubility (e.g., [START_REF] Laurencin | Magnesium incorporation into hydroxyapatite[END_REF][START_REF] Legeros | Magnesium and Carbonate in Enamel and Synthetic Apatites[END_REF]. [START_REF] Laurencin | Magnesium incorporation into hydroxyapatite[END_REF] also suggested, using Density Functional Theory calculations that a local clustering of Mg within the HAP lattice is likely to occur. A picture of Mg diagenesis in fossil HAP can be emphasized, which posits that Mg clusters, which are poorly crystallized, are likely to preferentially dissolve and react with the diagenetic fluids. The pending question, which requires further experiments, is whether the leaching of Mg is associated with an isotopic fractionation. If the leaching is quantitative, fossil bone and enamel would be Mg-depleted, but without Mg isotopic fractionation, allowing the analysis of accurate δ 26 Mg values for paleontological studies.

Clean radiogenic Sr isotope and trace elements compositions

After cleaning the data, most of the samples exhibited truncated radiogenic Sr and trace elements profiles, so we calculated average and standard deviation for all parameters, which are given in Table S1. Cleaning the data has resulted in the identification of significant correlations among all averaged variables (Fig. 6A). These relationships are first discussed in bone and then in enamel.

Bone

Generally, bone 87 Sr/ 86 Sr ratios have local values (Fig. 6B), and the 87 Sr/ 86 Sr ratio is correlated with the Sr/Ca ratio (Fig. 6A), which would suggest that diagenesis is still overprinting the 87 Sr/ 86 Sr ratio [START_REF] Budd | Differential diagenesis of strontium in archaeological human dental tissues[END_REF]. However, a close examination of the scatterplot between the 87 Sr/ 86 Sr and Sr/Ca ratios (Fig. 6C) shows that the human (GLN_221B), with the highest 87 Sr/ 86 Sr value and the lowest Sr/Ca ratio contributes to the observed correlation as an outlier.

The observed correlation is also due to the higher Sr/Ca ratios of the BMT assemblage, which is composed of livestock remains only, which are known to be enriched relative humans thanks to the Ca biopurification process [START_REF] Burton | Correlation of bone Ba/Ca and Sr/Ca due to biological purification of calcium[END_REF][START_REF] Balter | Allometric constraints on Sr/Ca and Ba/Ca partitioning in terrestrial mammalian trophic chains[END_REF][START_REF] Peek | Ontogenetic variations in Sr/Ca and Ba/Ca ratios of dental bioapatites from Bos taurus and Odocoileus virginianus[END_REF].

However, there is no human remains at BMT so that the Ca biopurification process cannot be validated for this site. At GLN, where human and faunal remains are associated, the Ca biopurification process between human and livestock exists but does not exhibit a typical bone Sr/Ca trophic Sr-enrichment of half a log unit (Fig. 6D, [START_REF] Balter | Allometric constraints on Sr/Ca and Ba/Ca partitioning in terrestrial mammalian trophic chains[END_REF], being closer to ~ 0.1.

While humans have clearly lower bone Ba/Ca than livestock at GLN (Fig. 6D, Wilcoxson, P value*** = 0.0004), the typical bone Ba/Ca trophic Ba-enrichment of one log unit is not preserved (it is rather close to ~0.5 at GLN, Fig. 6D). The bone biogenic Ba/Ca values seem however to be well-maintained as illustrated by the very good correlation with collagen δ 15 N values, where human and livestock samples exhibit a species-and location-specific distribution (Fig. 6E). A distribution of the bone Ba/Ca and collagen δ 13 C values according to species and location is also observed (Fig. 6F).

To summarize the results on bone, the overall picture argues for a diagenetic overprinting of Sr, but not Ba, despite the cleaning of the supposed diagenetic data. It is likely that part of the bone Sr burden supposedly cleaned from diagenesis is in fact overprinted by diagenesis in a pervasive way that could not be detectable by local disturbances as identified here with laser ablation in enamel. These results stress the importance of the leaching protocols for eliminating diagenetic compounds in fossil bone and conclude that bone is not a suitable material for laser ablation.

Enamel

The variability of the enamel 87 Sr/ 86 Sr ratios (Fig. 6G) is higher than in bone (Fig. 6B). Enamel 87 Sr/ 86 Sr ratios are not correlated to Sr/Ca ratios (Fig. 6H) and Sr and Ba are more depleted in enamel (Fig. 6I) than in bone (Fig. 6D). These first observations are in agreement with a lack of significant diagenetic effects on the original Sr and Ba contents [START_REF] Budd | Differential diagenesis of strontium in archaeological human dental tissues[END_REF][START_REF] Peek | Ontogenetic variations in Sr/Ca and Ba/Ca ratios of dental bioapatites from Bos taurus and Odocoileus virginianus[END_REF]. In addition, while the Sr/Ca ratio exhibits a slight Sr-enrichment from human to livestock (~ 0.3 log unit), the Ba/Ca ratio has here the expected log unit (>1). These results are in agreement with previous studies [START_REF] Sponheimer | Enamel diagenesis at South African Australopith sites: Implications for paleoecological reconstruction with trace elements[END_REF][START_REF] Tacail | Calcium isotopic patterns in enamel reflect different nursing behaviors among South African early hominins[END_REF], confirm that the Sr/Ca ratio in enamel is a poor proxy of trophic level and validate that cleaned enamel has not been significantly altered by diagenesis. Noteworthy is the intermediate trophic position of pigs between bovids and humans (Fig. 6I). To summarize the results on enamel, the overall picture to argues for an absence of diagenetic overprinting of the 87 Sr/ 86 Sr, Sr/Ca and Ba/Ca ratios, suggesting that the cleaning of the supposed diagenetic data has been efficient.

The context of the Neolithic revolution

Considering the geochemical differences highlighted for human and livestock among locations (Fig. 6E, 6F, 6I), it is likely that the Neolithic society was organized into small communities, managing their resources independently and locally, although probably exchanging people and goods with outside. For instance, the clear distinct bone Ba/Ca signatures between the livestock at BMT and GLN is a strong argument for specific livestock management, as it has already been proposed on the grounds of stable isotopes for these sites [START_REF] Rey | A multiisotope analysis of Neolithic human groups in the Yonne valley, Northern France: insights into dietary patterns and social structure[END_REF] or for other Neolithic sites [START_REF] Oelze | Early Neolithic diet and animal husbandry: stable isotope evidence from three Linearbandkeramik (LBK) sites in Central Germany[END_REF][START_REF] Goude | A Multidisciplinary Approach to Neolithic Life Reconstruction[END_REF]. Pending questions regarding livestock management are whether it was free-ranging and to what extent the livestock was allowed to range (e.g., [START_REF] Bickle | Moving on: the contribution of isotope studies to the early Neolithic of Central Europe[END_REF]. Here, livestock have local enamel 87 Sr/ 86 Sr ratios while humans have generally higher enamel 87 Sr/ 86 Sr ratios (Fig. 6F). This seems to indicate that humans, during the formation of the M2 tooth, i.e., approximately between 2.5 and 8.5 ± 0.5 years old, included a non-local diet with high 87 Sr/ 86 Sr value, and were more mobile than the livestock. However, a close examination of the data reveals a more thorough pattern that cannot rule out the existence of micro-regional differences in the bioavailable Sr isotopic baseline. Indeed, some of human Sr isotope values come from MON and CHI-Pat for which there is no associated fauna. The human mobility, as recorded by the enamel 87 Sr/ 86 Sr ratio, is more likely due to practises unrelated to livestock herding.

One obvious 87 Sr/ 86 Sr outlier can be identified, i.e., Mon_99-520 (0.7196 ± 0.0018, ± 2SD, Fig. 6H), who is a female (Table S1). Differences in bone collagen for the δ 13 C and δ 15 N values are observed between males and females (Fig. 6J, MANOVA, p-value** = 0.0031, [START_REF] Rey | A multiisotope analysis of Neolithic human groups in the Yonne valley, Northern France: insights into dietary patterns and social structure[END_REF], suggesting dietary sex-related differences [START_REF] Goude | Carbon and nitrogen isotopic variability in bone collagen during the Neolithic period: Influence of environmental factors and diet[END_REF][START_REF] Nehlich | The application of sulphur isotope analyses in archaeological research: A review[END_REF].

We thus performed histograms on enamel 87 Sr/ 86 Sr ratios according to sex (Fig. 6K). The distribution of the 87 Sr/ 86 Sr ratio is not statistically different between sexes (Student t test, pvalue = 0.61), but that of males seems to have higher 87 Sr/ 86 Sr values than of females in enamel (Fig. 6G). Interestingly, the distribution of the 87 Sr/ 86 Sr values for indeterminate is bimodal, suggesting that the sex difference of the 87 Sr/ 86 Sr is real. Despite the small number of samples having provided exploitable results (8 males and 4 females) and that sex differences should be considered in a site-by-site approach, this indicates a differential sex-related mobility pattern.

The case of Mon 99-520 is interesting, because it suggests that this girl has grown in a very distinct area with a very high 87 Sr/ 86 Sr value, probably in the neighboring granitic Morvan area.

Inclusion of foreign females in Neolithic group is a still debated question (e.g., [START_REF] Bentley | Community differentiation and kinship among Europe's first farmers[END_REF][START_REF] Goude | A Multidisciplinary Approach to Neolithic Life Reconstruction[END_REF][START_REF] Goude | New insights on Neolithic food and mobility patterns in Mediterranean coastal populations[END_REF]Rey et al.2021), that could be further assessed by 87 Sr/ 86 Sr variation in enamel using laser ablation.

Concluding remarks

The laser ablation technique is capable to generate simple profiles of trace elements concentrations and radiogenic Sr isotope compositions in tooth enamel, but not in bone. In enamel, spatial variation not only allows the reconstruction of life traits histories such as diet and mobility, but also the identification of areas where diagenesis has left clues of modifications of the original signatures. Once identified, these areas can be withdrawn from the results. The identification of diagenetic areas in bone is more difficult, probably because the diffusion is higher than in enamel and hence contrasts with normal areas more attenuated. One disadvantage of laser ablation technique is that the sample cannot be cleaned from extraneous components using wet chemistry because the sample needs to be powdered. However, none of this prevents the possibility to soak the chip of fossil bone and tooth enamel in dilute acetic acid to remove surficial calcitic contaminants before laser ablation measurements. The efficiency of such a strategy could be evaluated by performing laser ablation profiles before and after the leaching pretreatment in further studies. Finally, to the best of our knowledge, the Laboratoire de Géologie de Lyon is the only lab that uses solid, homogeneous, matrix-matched, concentrationmatched, and certified standard to correct for any interference of the 87 Sr/ 86 Sr ratios in Caphosphate samples analyzed by laser ablation. These standards can be shared on demand.

Figure captions

Figure 1 :

 1 Figure 1: Localization of the sites and regional geological map. Information is from

Figure 2 :

 2 Figure 2: Quality control of Sr radiogenic isotopes. A) Scatterplot of the standard deviation of the 87 Sr/ 86 Sr ratio a function of the 88 Sr voltage showing an increase of the variance with decreasing voltage. B) Scatterplot of the standard deviation of the 87 Sr/ 86 Sr ratio a function of the 88 Sr voltage showing an increase of the 87 Sr/ 86 Sr ratio with decreasing voltage.

Figure 3 :

 3 Figure 3: Principal component analysis (PCA) of raw results. A) PCA of all enamel results.

Figure 4 :

 4 Figure 4: Effect of cleaning the diagenetic overptinting. A) Chemical characterization of the

Figure 5 :

 5 Figure 5: Magnesium is leached during diagenesis. A) Scatterplot of the Mg/Ca ratio as a

Figure 6 :

 6 Figure 6: Paleoecological and paleobiological significance of clean data. A) Correlation

Table caption Table 1 :

 caption1 Summary of archaeological sites location and samples provenance.Mg, 43 Ca, 55 Mn, 88 Sr, 138 Ba, 238 U

	Code site Laser (Excite 193 nm, Photon Machine) Name site Cultural attribution LA pulse [ns] He MFC1 [L.min -1 ]	< 4 0.8	14 C date	Spatial organization	Number of humans buried	Animal remains	Enamel samples	Bone samples	Stable isotopes**
	NZ He MFC2 [L.min -1 ] Gurgy "Le Nouzeau" Laser Output [%] Rep Rate [Hz]	Cerny (+ local)	5300-4700 cal BC 100 0.4 10	enclosure with scattered remains + 2 associated burials	2 + scattered remains	yes	humans animals	2 humans 2 animals	CNS
	GLN Spot Size [µm] Gurgy "Les Noisats" Scan speed [µm]	50/150 local component ? 5200-3800 cal BC 10	big and dense cemetery	128	yes	34 animals humans	12 animals humans 6	CNS
	Mon ICPMS (X Series, ThermoFisher) Monéteau "Macherin" Chassean (+Cerny +local) CHI-ED RF-power [W] 1350 5200-3500 cal BC ? Chichery "l'Etang David" * local component ? 5100-4100 cal BC Ar gas flow Sample [L.min -1 ] 1	cemetery divided in separated groups cemetery partially destroyed	62 20	no no	13 humans 1 human 1 humans 2 humans	CNS CN
	CHI-Pat Coolant [L.min -1 ] Chichery "Sur les Pâtureaux" Auxiliary [L.min -1 ]	Cerny	13 0.8	4700-4350 cal BC	funerary site with aligments of burials + 1 isolated burial	15	no	humans 3 humans	CNS
	BMT Analyzed isotopes Beaumont "Le Crôt aux Moines" *	Chassean 24		4800-4000 cal BC	enclosure with scattered remains + other structures	scattered remains	yes	humans 18 animals	animals 12	CNS
	Bon	Bonnard "Le Poirier" *	Chassean		4500-4000 cal BC	2 burials of several inhumations	6	no	1 human	none	CN
	*ancient excavation, **Rey et al., 2017; Rey et al., 2019

MC-ICPMS (Nu Plasma HR, Nu Instruments)

	RF-power [W]	1400
	Cones	Ni
	Gas flow
	He Sample [L.min -1 ]	1
	Ar Coolant [L.min -1 ]	13
	Ar Auxiliary [L.min -1 ]	0.7
		H4( 88 Sr),
	Cup configuration	H2( 87 Sr+ 87 Rb),
		Ax( 86 Sr+ 86 Kr),
		L2( 85 Rb),
		L3( 84 Sr+ 84 Kr), L4( 83 Kr)

Acknowledgement

The authors are very grateful to J.-B. Mallye and P. Magniez who provided anthropological material and related information for this study, G. Devilder for his assistance with the CAD and S. Ciliberto and V. Queste for the financial contribution of the Fonds Recherches of the Ecole Normale Supérieure de Lyon to the laser ablation device. This work was supported by the Institut Danone France/Fondation pour la Recherche Médicale 2015 partnership.

The efficiency of the removing of the data suspected to be representative of a diagenetic process was globally followed using correlation matrix in which the lower half is filled with bivariate scatterplots (Fig. 4A and4B). Highlighted are areas exhibiting diagenetic patterns (Fig. 4A) which are absent after the cleaning procedure (Fig. 4B). The procedure was done manually and checked iteratively. The cleaning procedure removed 24% of the original data. We observed that diagenesis occurs very often in the crj area, where the enamel is the thinnest. Regarding the accuracy of the 87 Sr/ 86 Sr ratio, all data with a 88 Sr voltage below 0.4 V were removed (Fig. 4A and4B). This procedure removed 76% of the original data. Reduced data are given in Table S1.

The case of Mg diagenesis

Magnesium is a bioessential element and as such, its concentration in the body is metabolically regulated to lie between the deficiency and toxicity thresholds. The concentration of Mg thus cannot be of any interest for tracing the consumption of Mg-enriched or Mgdepleted food items for paleodiet reconstructions [START_REF] Klepingera | Magnesium ingestion and bone magnesium concentration in paleodietary reconstruction: cautionary evidence from an animal model[END_REF][START_REF] Reynard | Trace elements and their isotopes in bones and teeth: Diet, environments, diagenesis, and dating of archeological and paleontological samples[END_REF]. However, the Mg stable isotope composition (δ 26 Mg) of bone and tooth enamel is now recognized to vary according to the position of the animal in the trophic chain [START_REF] Martin | Natural variation of magnesium isotopes in mammal bones and teeth from two South African trophic chains[END_REF][START_REF] Martin | Magnesium stable isotope ecology using mammal tooth enamel[END_REF]. It is therefore necessary to know how Mg behaves during diagenetic processes before using the Mg isotope compositions to paleontological applications. [START_REF] Lambert | Bone diagenesis and dietary analysis[END_REF] measured the Mg concentration in a set of excavated bones and found higher values than in a reference set of modern bones. However, no information is available on the initial Mg concentration of the excavated bones. To the best of our knowledge, the results of the present study could the first robust evidence of Mg diagenesis in enamel. The example of the GLN-210 individual provided in Fig. 4 suggests that the Mg/Ca decreases when U/Ca increases, i.e., that Mg is leached out of enamel and bone during diagenesis. The Fig. 5 shows that this is a general


Nicolas Reneaud
email: nicolas@tedorthopedics.com

Pauline Gerus

Olivier Guérin

Maurine Garda

Elodie Piche

Frédéric Chorin

Raphael Zory

Affiliations

6MWT on a new self-paced treadmill system compared with overground

Highlights

-Participants walked a greater distance on treadmill compared with overground 6MWTs -A low-cost LIDAR sensor was a reliable tool to self-pace a treadmill -Similar gait parameters were found between the treadmill and overground 6MWTs -The use of a LIDAR sensor was demonstrated for self-pacing a 6MWT on a treadmill

Background

The growing number of ageing adults is associated with an increase in the incidence of chronic conditions that may affect functional capacity. Functional tests are now widely used by clinicians and other health professionals to measure exercise capacity. The results are an indicator of a patient's condition and mobility-related function. Analysis of spatiotemporal gait parameters (gait speed, distance, step time, step length, cadence) is becoming crucial in predicting fall risk or to quantify mobility in older adults, particularly after a stroke or to monitor the progression of Parkinson's diseases [START_REF] Bayat | Speed and temporal-distance adaptations during treadmill and overground walking following stroke[END_REF][START_REF] Nakakubo | Association of walk ratio during normal gait speed and fall in community-dwelling elderly people[END_REF][START_REF] Donath | Validity and reliability of a portable gait analysis system for measuring spatiotemporal gait characteristics: Comparison to an instrumented treadmill[END_REF]. Exercise performance is, therefore, an important clinical feature to evaluate functional capacity.

The guidelines approved by the American Thoracic Society (ATS) in 2002 definitively recognized the 6-minute walk test (6MWT) as a useful tool and it has been used by clinicians and researchers to estimate gait performance and fatigue affecting functional mobility [START_REF] Elazzazi | Measurement of distance walked and physiologic responses to a 6-minute walk test on level ground and on a treadmill: A comparative study[END_REF][START_REF]ATS Statement : Guidelines for the Six-Minute Walk Test[END_REF].

The 6MWT is performed in a long, straight and undisturbed 33-metre hallway. The 6MWT is a submaximal exercise test used to assess aerobic capacity and endurance. The distance covered in a time of six minutes is used as the outcome by which to compare changes in performance capacity. The patient has to walk as far as possible during the six minutes and is allowed to self-pace and rest as needed. The distance covered during the six minutes reflects the functional exercise level for daily physical activities because most of them are performed at a submaximal level of exertion [START_REF] Elazzazi | Measurement of distance walked and physiologic responses to a 6-minute walk test on level ground and on a treadmill: A comparative study[END_REF][START_REF]ATS Statement : Guidelines for the Six-Minute Walk Test[END_REF][START_REF] Szczurek | THE 6-MINUTES WALK TEST ON THE TREADMILL CONTROLLED BY A PATIENT'S WALK[END_REF]. However, in laboratories that have restricted space less than 33 m long, the patient will need to perform many U-turns, which will affect the total distance covered during a 6-minute walk because the patient will need to slow down for each U-turn. This underestimation will affects the clinical outcome compared to standard outcome metrics defined by the ATS [START_REF] Ng | Walkway length, but not turning direction, determines the six-minute walk test distance in individuals with stroke[END_REF]. Therefore, for a 6MWT, the walkway length is of great importance.

To better assess mobility-related functions from gait deviations, a portable optometric system can be coupled to the gait test to obtain additional data like walking speed, stride time, stride length, etc. [START_REF] Donath | Validity and reliability of a portable gait analysis system for measuring spatiotemporal gait characteristics: Comparison to an instrumented treadmill[END_REF]. Likewise, in-ground force plates provide more consistent measures of forces, moments and centres of pressure to obtain spatiotemporal and dynamic data, although force plates are limited in the number of strides they are able to capture. These additional results

give more indicators for patient condition than just the distance walked [START_REF] Plotnik | Self-selected gait speed -Over ground versus self-paced treadmill walking, a solution for a paradox[END_REF][START_REF] Riley | A kinematic and kinetic comparison of overground and treadmill walking in healthy subjects[END_REF][START_REF] Papegaaij | CLINICAL GAIT ANALYSIS: TREADMILL-BASED VS OVERGROUND[END_REF].

To overcome these limitations a modified 6MWT, administered on instrumented treadmills (TMs), can be an efficient, space-saving alternative to performing the 6MWT [START_REF] Elazzazi | Measurement of distance walked and physiologic responses to a 6-minute walk test on level ground and on a treadmill: A comparative study[END_REF]. These TMs can be monitored with an optoelectronic camera network and electromyography to obtain a complete set of gait parameters with no restrictions on the duration of the experiment or the number of gait cycles measured [START_REF] Plotnik | Self-selected gait speed -Over ground versus self-paced treadmill walking, a solution for a paradox[END_REF]. This enables a more reliable measurement of gait parameters such as gait variability, which requires at least 50 consecutive cycles to be measured reliably [START_REF] König | Is gait variability reliable? An assessment of spatio-temporal parameters of gait variability during continuous overground walking[END_REF]. However, several studies have reported that walking performance is altered in TM walking compared with overground (OG) walking. Studies have reported shorter stride and increased cadence or higher stance time on a treadmill [START_REF] Warabi | Treadmill walking and overground walking of human subjects compared by recording sole-floor reaction force[END_REF][START_REF] Watt | A three-dimensional kinematic and kinetic comparison of overground and treadmill walking in healthy elderly subjects[END_REF]. The most common reasons for these differences are the fixed walking speed of the TM, the optical flow, proprioceptive inputs and the treadmill paradox [START_REF] Plotnik | Self-selected gait speed -Over ground versus self-paced treadmill walking, a solution for a paradox[END_REF][START_REF] Yang | Dynamic gait stability of treadmill versus overground walking in young adults[END_REF]. Indeed, patients tend to choose a lower walking speed on the fixed treadmill speed in comparison to overground walking [START_REF] Ray | Walking speed changes in response to novel user-driven treadmill control[END_REF].

To increase the similarity between TM and OG walking, having a self-selected walking speed rather than an imposed walking speed on the treadmill could be a solution. Different methods may be used to compute the self-selected speed. The most common method is to take the speed from a 10-meter walking test on the ground and then implement it on the treadmill [START_REF] Plotnik | Self-selected gait speed -Over ground versus self-paced treadmill walking, a solution for a paradox[END_REF][START_REF] Hollman | A comparison of variability in spatiotemporal gait parameters between treadmill and overground walking conditions[END_REF]. Then, the operator determines the preferred walking speed by asking participants if they wants to speed up or slow down [START_REF] Bayat | Speed and temporal-distance adaptations during treadmill and overground walking following stroke[END_REF][START_REF] Elazzazi | Measurement of distance walked and physiologic responses to a 6-minute walk test on level ground and on a treadmill: A comparative study[END_REF]. However, this manual selection process is time-consuming and exhausting for participants who are not familiar with the treadmill [START_REF] Song | Using force data to self-pace an instrumented treadmill and measure self-selected walking speed[END_REF]. An alternative is to use an interactive TM system with self-pacing controllers. These consist of two parts, the first estimates the participant's speed and position and the second controls the treadmill speed. The system keeps the subject within the desired area of the treadmill belt while allowing the participant to freely accelerate or decelerate [START_REF] Sloot | Self-paced versus fixed speed treadmill walking[END_REF][START_REF] Kim | Commercial Motion Sensor Based Low-Cost and Convenient Interactive Treadmill[END_REF][START_REF] Souman | CyberWalk: Enabling unconstrained omnidirectional walking through virtual environments[END_REF]. Several approaches to estimate speed and position exist but the most commonly used method is based on reflective markers and an optical motion capture system using a commercially available virtual reality apparatus (GRAIL, Motek Medical BV, The Netherlands) [START_REF] Song | Using force data to self-pace an instrumented treadmill and measure self-selected walking speed[END_REF][START_REF] Sloot | Self-paced versus fixed speed treadmill walking[END_REF][START_REF] Liu | Reproducibility and Validity of the 6-Minute Walk Test Using the Gait Real-Time Analysis Interactive Lab in Patients with COPD and Healthy Elderly[END_REF]. Other approaches have been proposed using an ultrasonic sensor [START_REF] Minetti | A feedbackcontrolled treadmill (treadmill-on-demand) and the spontaneous speed of walking and running in humans[END_REF], a harness with force sensors [START_REF] Von Zitzewitz | Treadmill Speed Adaptation[END_REF], force plates on an instrumented treadmill [START_REF] Song | Using force data to self-pace an instrumented treadmill and measure self-selected walking speed[END_REF] or marker-free infrared sensors [START_REF] Kim | Commercial Motion Sensor Based Low-Cost and Convenient Interactive Treadmill[END_REF]. Most of these approaches are costly (GRAIL, instrumented TM) or not ecological, with the patient wearing accessories (a harness for the force sensor or passive reflectors on the chest for the ultrasonic sensor), that cause inconvenience and contribute to an unnatural feeling while walking.

Cost and inconvenience are major limitations for clinicians to administer a self-paced (SP) TM 6MWT. The LIDAR sensor partly overcomes these limitations. It is a cost-effective, noncontact sensor that measures position in the same way as an ultrasonic sensor but without requiring a passive chest reflector and with more accurate detection of the patient's position than sonar systems because it does not suffer from absorption by clothing. The device projects a frequency-modulated light beam onto a target. The distance from the target is calculated using the time taken for the beam to travel to and from the target by measuring the phase difference between transmission and reception.

The first aim of this study was to investigate if a 6MWT on an SP TM produced similar results compared with an OG 6MWT among healthy participants. We hypothesised that users would demonstrate similar gait parameters during an OG 6MWT and an SP TM 6MWT with a low-cost LIDAR sensor for self-pacing control. The second aim was to assess the withinand between-day reliability of the SP TM sessions. We hypothesised that gait parameters would be reliable within SP TM sessions and between sessions on different days.

Methods

Subjects

Twelve healthy young adults (8 women, 4 men; age: 23.5 ± 3.4 years; height: 173.2 cm ± 10 cm ; weight : 68.2 kg ± 11.4 kg) volunteered to participate in the study after providing informed written consent and GDPR consent. One participant enrolled in the first session only. They were free of any known neurological, musculoskeletal, or other systemic disorders that would affect gait or functional mobility. The study was approved by the local ethics committee and conduced in accordance with the declaration of Helsinki.

Protocol

Each participant first performed one OG 6MWT then one SP TM 6MWT on the same day. A second SP TM 6MWT on a different day was conducted to assess the reliability of the TM between days. All tests were performed in barefoot conditions to avoid footwear effects on spatiotemporal parameters and to enable future data processing of the SP TM 6MWT data with inverse dynamics [START_REF] Franklin | Barefoot vs common footwear: A systematic review of the kinematic, kinetic and muscle activity differences during walking[END_REF]. A seated rest was provided between the OG and SP TM 6MWTs for at least 30 minutes [START_REF] Liu | Use of the Six-Minute Walk Test Poststroke: Is There a Practice Effect?[END_REF]. Standardised instructions were provided before each trial with a reminder every 2 minutes: "walk as far as possible in 6 minutes without running or jogging" [START_REF]ATS Statement : Guidelines for the Six-Minute Walk Test[END_REF]. A warmup of two minutes with a five-minute rest was imposed for the OG 6MWT. The test was performed in accordance with the 2002 guideline of the ATS, using a 20 m corridor [START_REF]ATS Statement : Guidelines for the Six-Minute Walk Test[END_REF][START_REF] Stellmann | Ecological validity of walking capacity tests in multiple sclerosis[END_REF]. Regarding the SP TM 6MWT, all participants completed a familiarisation session of at least 5 minutes on the TM with a five-minute rest prior to the test. This session included an explanation of the system and the use of the treadmill's SP function. During the familiarisation session, participants were encouraged to interact with the system until they felt confident to try fast speed walking for one minute. Participants were not allowed to hold the handrails during the evaluation unless there was a loss of balance.

Materials

A 10 m long OptoGAIT portable optometric system (Microgate, Bolzono, Italy) was placed in the middle of the course to measure spatial and temporal gait parameters. Participants walked through the OptoGAIT on each pass of the 20 m course and made a U-turn at each end marker [START_REF] Stellmann | Ecological validity of walking capacity tests in multiple sclerosis[END_REF] [Figure 1]. SP TM 6MWT sessions were conducted on a Bertec dual-belt instrumented TM (Bertec Corp., Columbus, OH, USA) sampled at 1000 Hz with a network of 8 Optitrack Prime 13 optoelectronic cameras (NaturalPoint, Inc. Oregon, USA) sampled at 100 Hz.

The feedback-controlled speed was assessed with a purpose-built controller made of a Garmin LIDAR (Garmin Ltd, Lenexa, Kansas, USA) and an Arduino Uno REV3 microcontroller board (Arduino SRL, Torino, Italy) [Figure 2]. The position of the subject was filtered with a first-order discrete-time low-pass filter with I for input and O for output [Equation 1] [START_REF] Von Zitzewitz | Treadmill Speed Adaptation[END_REF] with a sampling at 20 Hz to reduce trunk oscillations. Then, a Matlab algorithm aimed to keep users in the centre of the treadmill via a speed correction [START_REF] Souman | CyberWalk: Enabling unconstrained omnidirectional walking through virtual environments[END_REF], sent directly to the TM system with incremental position and speed defined as x and respectively [Equation 2]. was used to eliminate a potential systematic bias due to the position of the LEDs in the OptoGAIT system, 3 mm above the ground [START_REF] Healy | Agreement between the Spatiotemporal Gait Parameters of Healthy Adults from the OptoGait System and a Traditional Three-Dimensional Motion Capture System[END_REF]. The distance of the OG 6MWT was computed with the standard method from the number of turns and the remaining distance covered (the number of metres in the final partial lap) using the markers on the floor as distance guides. In order to compare SP TM and OG distances calculated by similar methods, another OG 6MWT distance was estimated by multiplying the average walking speed measured by the OptoGAIT system during the test by 6 minutes (average-speed-based estimation method).

To compare the two modalities, the 6MWT was split into three 1-minute intervals, T1

(initial):0 -1 min; T2 (middle): 2 min 30 s -3 min 30 s; T3 (end): 5 min -6 min. These intervals were chosen to better compare the different strategical periods of adaptation and tolerance involved in performing a 6MWT [START_REF] Hadouiri | Evaluation of Prolonged Walking in Persons with Multiple Sclerosis: Reliability of the Spatio-Temporal Walking Variables during the 6-Minute Walk Test[END_REF].

Statistical Analysis

The assumption of normality was checked with the Shapiro-Wilk test. Given the very definition of the p-value, it cannot provide evidence in favour of an equivalence. However, an alternative to the traditional H0 significance testing approach is possible by treating H0 and H1

differently with the two one-sided test (TOST) [START_REF] Leppink | A Pragmatic Approach to Statistical Testing and Estimation ( PASTE )[END_REF]. For the primary outcome, the equivalence between OG and SP TM Day 1 distance was checked by TOST. The equivalence interval was fixed at ±45m (~7% of the mean distance) and alpha levelat 5% for a clinical difference [START_REF] Resnik | Reliability of Outcome Measures for People With Lower-Limb Amputations: Distinguishing True Change From Statistical Error[END_REF][START_REF] Schrover | Minimal clinically important difference for the 6-min walk test: Literature review and application to Morquio A syndrome[END_REF].The Bland-Altman method was used to assess agreement between the two modalities, to compare the OG distance defined by the standard method and the OG distance estimated from the average speed, without U-turns and therefore more similar to the SP TM distance.

For the secondary outcome, to assess the validity of gait parameters of the SP TM 6MWT compared to the OG 6MWT, Bland-Altman plots were used to test the agreement of cadence, step length, stance phase, double support, and gait speed. Then, cadence, stance phase, double support and step length were analysed using a mixed-model multivariate analysis of variance (MANOVA) with one factor (OG compared to SP TM). The assumption of partial correlation between variables was checked with Pearson's partial correlation of the MANOVA variables.

Box's M Test was significant with p-value = 0.066 > 0.001 indicating that potential distortion of the alpha level is not significant. Pillai's trace was chosen due to the small population of fewer than 30 participants.

The reliability of the feedback-controlled speed algorithm for the SP TM 6MWT was assessed through within-day and between-day reliability. The within-day reliability was determined by the intraclass correlation (ICC) type (2,1) between participants and gait cycles based on the first 20 strides of each of the three 1-minute periods in the day 1 SP TM 6MWT [START_REF] König | Is gait variability reliable? An assessment of spatio-temporal parameters of gait variability during continuous overground walking[END_REF]. ICC values were considered poor (<0.50), moderate (0.50 -0.75), good (0.75 -0.90), or excellent (>0.90) [START_REF] Cuesta-Vargas | The use of inertial sensors system for human motion analysis[END_REF]. To examine the test-retest reliability of the gait parameters obtained from the SP TM 6MWT between days, 20 strides of each of the three 1-minute periods were combined between the day 1 and day 2 sessions to construct each trial. Reliability was determined by the ICC type (3,1) [START_REF] Koo | A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research[END_REF].

Results

10

A comparison between the SP TM and OG modalities for the 6MWT is shown in [Figure 3] with two computed distances for OG: the standard method and the average-speed-based estimation. In the OG condition, participants walked 664.8 m ± 48.9 m with the standard method using floor markers and 721. Bland-Altman plots showed a significant difference in the distance between the adaptive treadmill and the OG 6MWT with the distance calculated by the usual method but not with the average-speed based estimation [Figure 3]. The cadence, step time, step length, stance phase, double support and gait speed were similar between both systems with no significant difference shown on the Bland-Altman plots [Figure 4].

There was no significant main effect between SP TM and OG walking (p-value = 0.847) using Pillai's test for cadence, step length, stance phase and double support.

The ICC values for gait parameters showed good to excellent reliability for the SP TM algorithm during the three parts of the 6MWT on the adaptive TM [Table 1]. For test-retest reliability, ICC values between both 6MWT sessions on the adaptive TM showed moderate to excellent between-day reliability [Table 2].

Discussion

The main purpose of this study was to examine if the results of a 6MWT on an SP TM were similar to an OG 6MWT. Our results showed a significant difference for the distance between modalities with a 9% greater distance on the SP TM 6MWT compared to the OG 6MWT.

However, neither the spatiotemporal parameters nor the average-speed-based distance estimation demonstrated a significant difference to their counterparts between 6MWT modalities. Moreover, the SP TM algorithm showed high reliability of the spatiotemporal parameters within and between days.

Our findings support that SP TMs are a reliable tool to evaluate gait speed with no significant difference in gait speed between the two modalities at points T1, T2 and T3 during a 6MWT after a 5-minute accommodation period. Plotnik et al. and Song et al. found similar results in their studies, with no significant difference in gait speed between SP TM and OG after an adaptation period [START_REF] Plotnik | Self-selected gait speed -Over ground versus self-paced treadmill walking, a solution for a paradox[END_REF][START_REF] Song | Using force data to self-pace an instrumented treadmill and measure self-selected walking speed[END_REF]. This accommodation time is an essential step in TM gait tests due to the treadmill paradox. Paradoxically, any chosen fixed gait speed on a TM, including a manually self-selected walking speed, does not reflect OG walking accurately and therefore underestimates distance. Through an analysis of speed convergence, Plotnik et al. suggested a longer speed-adaptation period for SP TM than for OG, with at least 2 m needed to reach selfselected gait speed for OG, compared with 30 m or more for SP TM walking [START_REF] Plotnik | Self-selected gait speed -Over ground versus self-paced treadmill walking, a solution for a paradox[END_REF]. Additional studies confirm the effect of the familiarisation period, suggesting a small learning effect.

Sloot et al. found a small difference between the two modalities, with a 3 min accommodation period and recommend, like the Zeni et al. study, at least 5 min to become accustomed to SP walking to avoid the TM paradox [START_REF] Sloot | Self-paced versus fixed speed treadmill walking[END_REF][START_REF] Zeni | Gait parameters and stride-to-stride variability during familiarization to walking on a split-belt treadmill[END_REF]. These findings bring to light the importance of feedback-controlled, self-paced walking speed on a treadmill after an accommodation period to limit the TM paradox, which will underestimate walking speed.

In contrast to the gait speed comparison, the mixed results of the distance comparison led to a better understanding of the impact of U-turns on the 6MWT. Indeed, the OG distance with the standard method underestimated the distance by 72.7 m when compared with the distance predicted using the average walking speed taken in the middle of the hallway. This difference could be clinically meaningful for measuring a patient's condition [START_REF] Resnik | Reliability of Outcome Measures for People With Lower-Limb Amputations: Distinguishing True Change From Statistical Error[END_REF]. The distance estimated from the average walking speed showed no significant difference with SP TM 6MWT. This significant difference observed with the standard method may be due to the Uturns required during the OG 6MWT. In the present study, the distance with the usual method was underestimated because the use of a 20 m hallway introduced a large number of turns.

Elazzazi et al. found no significant difference between the OG, using the usual calculation method to obtain the distance, and the SP TM conditions. They attributed this result to the use of a 33 m hallway. The authors suggested that increasing the walkway length to reduce the number of turns would possibly increase the distance covered by participants during the 6MWT. Unfortunately, gait speeds were not recorded during the OG 6MWT so it was not possible to compare possible effects of the U-turns on the distance. The authors highlighted the problem of the lack of standardisation of hallway length, which may lead to underestimated distances for OG compared with SP TM 6MWTs [START_REF] Elazzazi | Measurement of distance walked and physiologic responses to a 6-minute walk test on level ground and on a treadmill: A comparative study[END_REF]. The effect of different walkway length for a 6MWT was studied by Shamay S. Ng et al. with 10 m, 20 m, and 30 m.

Their findings support the significant effect of the walkway length on the distance covered in the 6MWT in patients with stroke and among the elderly [START_REF] Ng | Walkway length, but not turning direction, determines the six-minute walk test distance in individuals with stroke[END_REF][START_REF] Ng | Effect of walkway length and turning direction on the distance covered in the 6-minute walk test among adults over 50 years of age: a cross-sectional study[END_REF]. This effect highlights the importance for clinicians to use the norm value of the 6MWT with much more care, depending on walkway length. It is possible that new norm values may be needed to effectively compare OG distances with those on SP TM, because distances estimated from the average speed walking back and forth several times may be different from walking in a straight line. This difference, of slowing down and turning, may allow participants to walk at a higher speed in the walkway [START_REF] Van Den Akker-Scheek | Recovery of Gait After Short-Stay Total Hip Arthroplasty[END_REF]. Finally, the difference in distance between the SP TM and the OG 6MWT distances means that the reader should be cautious in applying the previously established norms.

Regarding the spatiotemporal parameters, the study showed similar step length, cadence, gait speed, stance phase, and double support between the two modalities. For comparison, Cronin et al. measured comparable outcomes for gait speed, stance time, step time and stance phase, between TM and OG in barefoot conditions [START_REF] Cronin | Treadmill versus overground and barefoot versus shod comparisons of triceps surae fascicle behaviour in human walking and running[END_REF]. In running tests, García-Pérez et al. reported no significant difference in cadence at 3.33 m/s between TM and OG [START_REF] García-Pérez | Effect of overground vs treadmill running on plantar pressure: Influence of fatigue[END_REF]. Hollman et al.

similarly measured no differences for stride time, stride length, cadence, and stance phase between SP TM walking and OG walking [START_REF] Hollman | A comparison of variability in spatiotemporal gait parameters between treadmill and overground walking conditions[END_REF]. In contrast, some studies have highlighted differences in spatiotemporal parameters between SP TM and OG. In particular, Van Der Krogt et al. found similar gait speed but with shorter and wider strides on the TM, possibly due to the dual-belt treadmill. These results were in line with the findings of Schellenbach et al. in adult participants with, in addition, an increase in cadence and time in double support compared with OG walking. After a familiarisation period, these participants reached a stable pattern with small differences compared to overground walking but did not fully abandon a careful walking style. However, these differences between modalities, do not necessarily mean that TM walking is less suitable for clinical analysis [START_REF] Schellenbach | Adult age differences in familiarization to treadmill walking within virtual environments[END_REF][START_REF] Van Der Krogt | Overground versus self-paced treadmill walking in a virtual environment in children with cerebral palsy[END_REF]. These findings are in agreement with our results that no significant difference between SP TM and OG gait parameters is observed after a 5-minute accommodation period.

Our results suggest that the feedback-controlled speed algorithm for the SP TM 6MWT provides excellent reliability for step time and cadence and good reliability for gait speed, step length, stance phase and double support during the three parts of the 6MWT on the adaptive TM. Matsas et al. found similar results for the ICC of the stride time, step length and cadence after 6 min of treadmill walking, with ICC values higher than 0.94, 0.93 and 0.94, respectively, from six consecutive gait cycles [START_REF] Matsas | Knee joint kinematics from familiarised treadmill walking can be generalised to overground walking in young unimpaired subjects[END_REF]. For test-retest reliability, our data suggest 14 moderate to excellent between-day reliability, depending on the spatiotemporal parameter.

Analogous test-retest reliability was found for a comfortable speed with an ICC of 0.982 (0.956 -0.992) for stride time and 0.960 (0.904 -0.983) for stride length [START_REF] Donath | Validity and reliability of a portable gait analysis system for measuring spatiotemporal gait characteristics: Comparison to an instrumented treadmill[END_REF]. Choi et al.

confirm this hypothesis with a series of 6 trials on a 10 min gait test spread over 2 days with ICC> 0.90 for speed, stride time and stride length [START_REF] Choi | Reliability of the walking speed and gait dynamics variables while walking on a feedback-controlled treadmill[END_REF]. Another study found high betweenand within-day reliability for most of the spatiotemporal gait parameters, including stride frequency, stride length and stride time [START_REF] Faude | Reliability of gait parameters during treadmill walking in community-dwelling healthy seniors[END_REF]. However, stance phase and double support were less reliable on the treadmill compared to the other spatiotemporal gait parameters, in agreement with our results. Faude et al. found a similar result with a lower reliability for double support, with an ICC of 0.86, comparable to the 0.80-0.88 measured in our study [START_REF] Faude | Reliability of gait parameters during treadmill walking in community-dwelling healthy seniors[END_REF].

To conclude, the reliability of gait parameters on an SP TM allows clinicians to use the 6MWT to better analyse mobility-related function using gait deviation.

This study has some limitations which need to be considered. The test-retest reliability was based on only 2 sessions which was not very consistent with ICC interpretation [START_REF] Koo | A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research[END_REF][START_REF] Choi | Reliability of the walking speed and gait dynamics variables while walking on a feedback-controlled treadmill[END_REF]. Also, to get more consistent data in order to perform inverse dynamics on the 6MWT, participants were in a barefoot condition. This limits the generalisability, as the OG 6MWT is usually performed in a shod condition. Further, all participants included in the study were healthy young adults. This population is not representative of patients with fatigue and gait variability performing 6MWTs. This lack of variability is the main limitation of this study to fully highlight the capabilities of the SP algorithm. Only the stability of the system was assessed in the study, as participants experienced no fatigue during the three parts of the 6MWT. In addition, young people typically require less familiarisation time compared with the patient group. This parameter can be a serious limitation for patients with endurance issues. Another limitation is the possible learning effect, as the OG 6MWT was performed before the SP TM 6MWT. Further investigation of SP TM including individuals with gait limitation is needed to show the feasibility of the SP algorithm to reveal fatigue and gait variability. Related to this, another investigation with longer gait tests on healthy participants will show the potential use of an endurance test and will focus on natural low-frequency variability between OG and SP TM tests [START_REF] Hollman | A comparison of variability in spatiotemporal gait parameters between treadmill and overground walking conditions[END_REF]. Finally, the SP TM system used was based on different studies, but its performance is not representative of all SP TM, which will depend on the algorithm and the user-driven treadmill control.

Conclusion

In conclusion, the distance walked on an SP TM presents a significant difference compared with that measured in an OG 6MWT. This difference highlights that the norm values cannot be compared with measurements in this modality and establishes the necessity of new norm values for SP TM 6MWT. However, a comparison of spatiotemporal parameters highlighted no significant difference between modalities. These results indicate that, after a familiarisation period, SP TM walking does not notably affect gait parameters for clinical analysis.

Moreover, the SP TM 6MWT allows the use of optoelectronic camera networks, force platforms and other tools to perform more accurate gait analysis while observing walking speed, gait variability and endurance.

Tables

  Ground reaction force (GRF) data were low-pass filtered at 20 Hz. Strides with foot placement on both belts were excluded from the data analysis. The distance of the SP TM 6MWT was calculated from the integral of the walking speed over the 6 minutes. Gait parameters were calculated using the initial contact and toe off from the ground reaction force as well as the walking speed to derive step length, step time, stance phase, double support, cadence, and average walking speed.The first and last step of the OptoGAIT acquisitions in each direction were excluded to remove partial steps. Gait parameters were calculated taking the initial contact and the toe off from when the foot crossed the infrared beam light between the two bars. A filter of 2 LEDs

  3 m ± 56.2 m with the walking speed method. For the SP TM 6MWT, they covered 729.4 m ± 40.8 m in the first session and 727.4 m ± 49.9 m in the second session. A comparison between the SP TM day one and day two sessions showed significant equivalence with an average of -2.0 m difference (95% CI -27.8 -23.8, p-value< 0.05). Participants walked, on average, -64.6 m (95% CI 45.3 -83.9 m, p-value >0.05) between the OG 6MWT and the day 1 SP TM 6MWT, i.e., 9% less in the OG test with the standard distance method than the TM distance. The difference was 8.1 m (95% CI -17.1 -33.4 m, p-value < 0.05) with the average-speed-based estimation.

FiguresFiguresFigure 1 :

 1 Figures Figures Figure 1: OG 6MWT setup.

Figure 2 :

 2 Figure 2: Speed adaptation treadmill setup: Position x computed by the LIDAR sensor sends the trunk position to the computer and with a Matlab algorithm, sends a speed command to the treadmill to place the participant in the centre.

Figure 3 :Figure 4 :

 34 Figure 3: Bland-Altman plots of the difference in distance between the SP TM and OG 6MWTs with the standard method (a) and the average-speed-based estimation (b)

Table 1

 1 Intraclass reliability of the 6MWT on the adaptive treadmill for Step Length (SL), Step Time (ST), Cadence (Cad), Walking Speed (WS), Stance Phase (SPh) and Double Support (DS):

	Gait parameters:		ICC (CI 95%)
		T1	T2	T3
	SL	0.87 (0.76 -0.95)	0.96 (0.92 -0.99)	0.90 (0.83 -0.97)
	ST	0.96 (0.92 -0.99)	0.96 (0.92 -0.99)	0.97 (0.94 -0.99)
	Cad	0.97 (0.93 -0.99)	0.96 (0.92 -0.99)	0.97 (0.94 -0.99)
	WS	0.81 (0.68 -0.93)	0.95 (0.91 -0.98)	0.91 (0.83 -0.97)
	SPh	0.82 (0.68 -0.93)	0.85 (0.74 -0.94)	0.85 (0.73 -0.94)
	DS	0.80 (0.65 -0.92)	0.88 (0.79 -0.96)	0.88 (0.77 -0.95)

Table 2

 2 Test-retest reliability of the 6MWT on the adaptive treadmill for Step Length (SL), Step Time (ST), Cadence (Cad), Walking Speed (WS), Stance Phase (SPh) and Double Support (DS):

	Gait parameters:		ICC (CI 95%)
		T1	T2	T3
	SL	0.90 (0.84 -0.95)	0.97 (0.95 -0.99)	0.89 (0.83 -0.95)
	ST	0.95 (0.90 -0.97)	0.96 (0.94 -0.98)	0.87 (0.79 -0.93)
	Cad	0.96 (0.93 -0.98)	0.96 (0.93 -0.98)	0.89 (0.82 -0.94)
	WS	0.93 (0.89 -0.97)	0.98 (0.96 -0.99)	0.98 (0.96 -0.99)
	SPh	0.80 (0.68 -0.89)	0.87 (0.79 -0.93)	0.74 (0.61 -0.86)
	DS	0.80 (0.69 -0.90)	0.88 (0.81 -0.94)	0.86 (0.78 -0.93)

Conflict of interest statement

The authors have no professional relationship with companies of manufacturers who might benefit from the results of the study.