Jesus Nuñez
email: jesus.nunez@ird.fr

F Duponchelle

M Cotrina-Doria

J.-F Renno

C Chavez-Veintimilla

C Rebaza

S Deza

C Garcia-Davila

F Chu-Koo

S Tello

J N Uñez-Rodr Iguez

C Garc Ia-D Avila

E Baras

Jes Us N Uñez-Rodr Iguez

Movement patterns and home range of wild

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Movement patterns and home range of wild and re-stocked Arapaima gigas (Schinz, 1822) monitored by radio-telemetry in Lake Imiria, Peru Introduction Arapaima gigas (paiche or pirarucu) is an air-breathing, giant fish of the Amazon basin and the largest freshwater fish with scales in the neotropics [START_REF] Henn | The range of size in the vertebrates[END_REF] at over 3.5 m and 250 kg. Although a single species, A. gigas, was recognized within the Arapaima genus, the number of species has recently increased with re-descriptions and new descriptions (Stewart, 2013a,b). As the taxonomic status of the Peruvian populations is under review (D. J. Stewart, unpubl. data), we will use A. gigas in the text that follows. In spite of the tremendous economic and cultural importance of this species, behavioural studies of A. gigas in its natural habitat are scarce. Studies on the distribution and migration indicate that its population density is strongly dependent on the morphological and hydrological characteristics of the area, such as flooding duration, surface area of the water body, water depth and connectivity [START_REF] Queiroz | Natural history and conservation of Arapaima gigas, Arapaima gigas, at the Amazonian V arzea: Red giants in muddy waters[END_REF][START_REF] Coutinho | Population dynamics modeling of Arapaima gigas[END_REF][START_REF] Arantes | Environmental influences on the distribution of arapaima in Amazon floodplains[END_REF]. Similarly, studies on the reproduction and growth [START_REF] Queiroz | Natural history and conservation of Arapaima gigas, Arapaima gigas, at the Amazonian V arzea: Red giants in muddy waters[END_REF][START_REF] Godinho | Gonadal morphology and reproductive traits of the Amazonian fish Arapaima gigas (Schinz, 1822)[END_REF]Castello, 2008b;[START_REF] Arantes | Population density, growth and reproduction of arapaima in an Amazonian river-floodplain[END_REF], and on the population dynamics of this species (Castello, 2008a;[START_REF] Castello | Modeling population dynamics and conservation of arapaima in the Amazon[END_REF] have been carried out in Brazil, but most of this information comes from a single area no larger than 1000 km 2 , the Mamirau a Reserve (Amazonas State, Brazil), which represents less than 1% of the total distribution of the species [START_REF] Castello | Assessing CITES non-detriment findings procedures for Arapaima in Brazil[END_REF]. As A. gigas has been overexploited for decades [START_REF] Castello | Understanding fishing-induced extinctions in the Amazon[END_REF], it is now seriously depleted over most of its range and is listed in CITES Appendix II and the IUCN Red List of Threatened Species as an endangered species. In Peru and Brazil, A. gigas was introduced into lakes or ponds for aquaculture purposes in many areas to face the decline of wild populations and it was hoped that it would adapt to pond culture and benefit the local people. A few decades ago, Lake Imiria was densely populated by A. gigas (according to local people), but by the 2000s was so scarce that its capture was prohibited in hopes of recovery in subsequent years. The population had not recovered by 2008, thus a pilot restocking program [START_REF] Lorenzen | Responsible approach to marine stock enhancement: an update[END_REF] tested for the possible recovery and enhancement [START_REF] Cowx | Stocking strategies[END_REF] of the A. gigas population in this natural area.

The interest of working in a relatively small area such as Lake Imiria (~38 km 2 ) was the possibility of quite easily capturing a few individuals of the remaining wild population to compare their behaviour with A. gigas cage-raised over a 4year period and then released into the lake. The purpose of this comparison was to determine if the behaviour of released cage-raised fish was similar to that of wild individuals and to assess how they would survive and adapt to their new environment. Such a comparison could prove insightful, as previous studies of salmon reported different behaviours between wild and cultured populations [START_REF] Jonsson | A review of ecological and behavioural interactions between cultured and wild Atlantic salmon[END_REF][START_REF] Jonsson | Cultured Atlantic salmon in nature: a review of their ecology and interaction with wild fish[END_REF]. Additionally we planned to determine, when possible, the gender of tagged individuals using the method based on plasma vitelogenin detection [START_REF] Chu-Koo | Gender determination in the Paiche or Arapaima gigas (Arapaima gigas) using plasma vitellogenin, 17b-estradiol, and 11-ketotestosterone levels[END_REF] to posteriorly analyze if male and female behaviours were similar and if mating pairs were formed during the period of study. Another advantage was that Lake Imiria represented a relatively small natural area with little connectivity to the surrounding river system, allowing a better monitoring of released animals and limiting their possibility of escape.

This study represents the first time that individual behavioural movements and localization of A. gigas males and females, home range and total travelled distances for restocked cage-reared individuals and wild individuals still present in Lake Imiria were monitored. We also tested survival rates and adaptation capabilities to the wild environment of re-stocked fish in comparison to wild individuals.

Materials and methods

Study site

Lake Imiria is one of the largest lacustrine environments in the Ucayali region (Fig. 1). In contrast to many other oxbow lakes in the Amazon basin, this water body is not an isolated river meander, but a small inundated basin resulting from local tectonic activity that progressively created a depression filled by rain falling into its watershed [START_REF] Garc Ia | The aquatic environment types of the peruvian Amazonia[END_REF]. The lake has a maximum depth of about 6-10 m with low water transparency, especially during the rainy season. Numerous small islands composed of dense herbaceous and floating vegetation (notably the water hyacinth) accumulate mainly in the north-west bank of the lake, where a narrow canal communicates with the Tamaya River, but with very low flow and water depth during the dry season, making the entrance or exit difficult for large fishes. Such characteristics relatively isolate Lake Imiria from the main rivers in the area (Tamaya and Ucayali). The lake has an average water surface of 38 km² and a pronounced dendritic shape (Fig. 1), with a perimeter of about 200 km composed mainly of herbaceous ridges with variable amounts of floating vegetation and tropical forests. Fourteen villages are spread out along the ridges representing a total of 3000-4000 inhabitants. In 2010 a regional conservation area (1370 km 2 ) was established to promote biodiversity protection and conservation of the lake and its surroundings ( Area de Conservaci on Regional Imiria). In 2002 the Instituto de Investigaciones de la Amazonia Peruana (IIAP) implemented a project of A. gigas captive breeding in the Iquitos -Nauta area, where local fish farmers were given a few juveniles depending on the pond surface available in their farms. A few years later, aquaculture production had increased significantly, reaching around 100 000 A. gigas fingerlings in 2010 [START_REF] Chu-Koo | Reproductive success and fry production of the paiche or Arapaima gigas, Arapaima gigas (Schinz), in the region of Iquitos, Per u[END_REF][START_REF] Chu-Koo | Estado actual del cultivo de paiche o Arapaima gigas en el Per u[END_REF]. Local exporters of ornamental tropical fish collected most of this production. At the same time, a small part of the produced fry was grown locally in small ponds, lakes or even in salmon-type cage culture systems. One of these cage-culture experiments was carried out in Lake Imiria (Ucayali Government project), resulting in fish as large as 10-12 kg body weight and 100-110 cm total length after approximately 1 year of rearing [START_REF] Chu-Koo | Estado actual del cultivo de paiche o Arapaima gigas en el Per u[END_REF]. Two years after the end of that experiment, 500 3year-old cage-produced A. gigas (120-145 cm; 18-30 kg) were selected for this restocking program in Lake Imiria.

Fig. 1. Localization of study area in the Peruvian Amazon, 50 km southeast of the city of Pucallpa. Map coordinates are expressed in UTM system, zone 18L Fish were followed by conventional radio telemetry, as described in many other species, including fish [START_REF] Baras | Fish telemetry in aquaculture: review and perspectives[END_REF][START_REF] Lucas | Migration and spatial behaviour[END_REF]. The choice of radio telemetry was driven by cost-benefit considerations of the technique when compared to acoustic telemetry and by its relative ease of implementation in a remote area. In such studies the most commonly used parameter is the home range, which describes the amount of area occupied by an individual during a determined period of time [START_REF] Dunn | Analysis of radio telemetry data in studies of home range[END_REF][START_REF] Crook | Is the home range concept compatible with the movements of two species of lowland river fish?[END_REF][START_REF] Økland | Patterns of movement and habitat use by tigerfish (Hydrocynus vittatus) in the Upper Zambezi River (Namibia)[END_REF][START_REF] Koehn | Movements of Murray cod (Maccullochella peelii peelii) in a large Australian lowland river[END_REF][START_REF] Nyboer | Movement and home range of introduced Nile perch (Lates niloticus) in Lake Nabugabo, Uganda: implications for ecological divergence and fisheries management[END_REF]. The home range calculations were made in earlier studies using the Minimum Convex Polygon (MCP) method, but have been replaced progressively by the Kernel Density Estimation (KDE) with the help of new computerized routines in combination with a Geographic information system (GIS) like HoRAE for Openjump, a free online package used in this study [START_REF] Steiniger | OpenJUMP HoRAEa free GIS and toolbox for home-range analysis[END_REF]. Although its reliability is sometimes questionable, the MCP parameter has nevertheless still been calculated in many recent studies for comparison purposes with previous works (B€ orger et al., 2006). Therefore, in this study, the MCP parameter will also be provided for comparison purposes.

Transmitters attachment

Wild A. gigas were captured directly in the lake by local fishermen using 100 m wide nets (3.5 m high, 40 mm mesh size); on the fishing boat a transmitter attachment was performed immediately after capture. Cage-raised specimens were sampled in the experimental floating cages located in the vicinity of Caimito village (Fig. 2). For practical reasons, not all fish could be tagged on the same day.

All fish were measured for total length (Tables 1 and2). External radio transmitters (75 9 17 mm diameter, 35 g in air, external whip antenna, Advanced Telemetry Systems, Isanti, MN) were attached with a side saddle harness, below the anterior part of the dorsal fin while the fish laid in lateral recumbence on a soft and humid foam carpet, with its head covered by a damp cloth to reduce holding stress. Local anaesthesia was performed with intra-muscular injections of a 1% lidoca€ ıne sterile solution of 1 ml on each side of the fish. Two assistants held the fish in place during transmitter attachment. Prior to surgery, two holes had been drilled in the epoxy resin coating of the transmitter, and a plastic protected braided wire of stainless steel (2.5 mm in diameter) had been passed through the holes. At time of surgery two large hollow needles were inserted through the dorsal musculature, in between the pterygiophores of the dorsal fin, after removal of two scales at each entry and exit point, then the two ends of the attachment wires were passed through the fish body. After needle removal, the attachment wire was further passed through a pierced plastic attachment plate, to minimize the risks of 'tunnelling' into the fish muscles in the mid-or long term. Finally, the wires were tightened with an aluminium connecting sleeve onto the plastic plate. At the Fig. 2. General view, central part of Lake Imiria where wild fish (W1-W7) were captured, tagged and released (red dots), and restocked fish (R1-R17) were released (blue squares). A total of 8 wild and 17 restocked pirarucus Arapaima gigas were monitored until transmitter batteries collapsed (after ca. 18 months). Map coordinates are expressed in the UTM system, zone 18L same time a blood sample was obtained from the caudal vein and placed in a 1.5 ml heparinized Eppendorf-type tube. All tagging and blood sampling procedures lasted approx. 1.30 min. The blood sample was then centrifuged for 3 min at 10 000 g and supernatant plasma was collected and stored frozen until posterior use for sex determination according to the methodology developed for A. gigas [START_REF] Chu-Koo | Gender determination in the Paiche or Arapaima gigas (Arapaima gigas) using plasma vitellogenin, 17b-estradiol, and 11-ketotestosterone levels[END_REF].

Radio tracking

Tracking began on 5 August 2009 and lasted circa 18 months until the transmitter batteries died. Wild fish were released at the same location where they were caught; restocked fish (from cage-bred stock) were released in five different locations in Lake Imiria (Fig. 2). We started active tracking approx. 1 week following release, to allow recovery from potential stress accompanying fish capture, handling and tagging. Fish were successively relocated approx. every 15 days during the battery life period using a 3-element Yagi antenna and a Lotek Biotracker receiver (Lotek Wireless Inc., Newmarket, Ontario, Canada) using the homing method, i.e. the operator followed the shoreline at the vicinity of the last recorded fish position until finding the signal of its specific frequency. The operator then moved towards the direction of the strongest signal until its strength changed suddenly, as the fish moved rapidly because of immediate boat proximity and recorded the GPS position of the boat. Fish bearings were recorded with a GPS Garmin unit (Garmin International, Inc., Olathe, KS) with an overall accuracy of AE8 m. This procedure was repeated for each frequency until all tagged fish were located.

Fish movement analysis

All fish locations were plotted with the open source Geographic Information System (Quantum GIS, QGIS 2.0, <http://www2.qgis.org/en/site/index.html>) to visualize fish movements over the entire period of survey. Home range area (HR) and total travelled distance were determined with the package HoRaE integrated in Openjump v. 1.6.3 (Jump Open source Mapping Platform, <http://www.openjump. org/>) known as MOVEAN extension [START_REF] Steiniger | OpenJUMP HoRAEa free GIS and toolbox for home-range analysis[END_REF]. Home ranges [START_REF] Dunn | Analysis of radio telemetry data in studies of home range[END_REF][START_REF] Horne | Selecting the best home range model: an information-theoretic approach[END_REF] were calculated using two methods: the MCP 0.95 , a line connecting the outermost points for each fish, as well as the KDE at 95 and 50% that produces concentric lines (isopleths) corresponding to a fixed percentage of presence (typically 50 and 95% for comparison purposes) during the tracking period as previously described for other species [START_REF] Silverman | Density estimation for statistics and data analysis[END_REF][START_REF] Worton | Kernel methods for estimating the utilization distribution in home-range studies[END_REF][START_REF] Lowe | Movement patterns, home range, and habitat utilization of adult kelp bass Paralabrax clathratus in a temperate no-take marine reserve[END_REF][START_REF] Vokoun | Kernel density estimates of linear home ranges for stream fishes: advantages and data requirements[END_REF][START_REF] Horne | Selecting the best home range model: an information-theoretic approach[END_REF][START_REF] Topping | Site fidelity and seasonal movement patterns of adult California sheephead Semicossyphus pulcher (Labridae): an acoustic monitoring study[END_REF]. The 95% isopleth corresponds to the largest area used by a fish over the study period where 95% of the locations are found, while the 50% isopleth represents the core range area of an individual [START_REF] Worton | Kernel methods for estimating the utilization distribution in home-range studies[END_REF] and corresponds to the area where 50% of the locations are found; only aquatic areas were considered (Fig. 3). The total distance travelled by a fish is calculated as the sum of the linear distances between each pair of consecutive fixes, except when the line between two particular fixes crossed the shoreline. In this particular case, it was assumed that the minimal distance between the two locations was around the shoreline.

Statistics

Comparisons of means for travelled distance, mean MCP and KDE areas and between male and female and group origin were performed after Levene's test of homogeneity of variances, using t-test at alpha = 0.05 by two independent readers.

Results

Tracking

Radio-tagged A. gigas ranged from 117 to 153 cm total length (mean AE SD = 145.8 AE 12.7) for wild individuals and from 124 to 143 cm (132.9 AE 5.3) for restocked ones. Overall 'survival' of tagged fish averaged 83% after approx. 18 months of tracking, as five out of 29 fish disappeared (two wild and three restocked). It is uncertain whether these missing fish were captured by poachers, died of other causes, emigrated outside of the lake, or if the absence of detection resulted from transmitter malfunctions. A total of 946 detections were obtained, 316 from wild fish and 630 from restocked ones. On average, the time between two consecutive fixes of a particular fish was 13.7 AE 1.5 days. The mean detection number per individual fish was 37.05 AE 8.5 for wild fish and 39.5 AE 6.8 for restocked fish. There was no significant correlation between the number of relocations for a single fish, which ranged from 28 to 52, and the corresponding home range (KDE 50% : r 2 = 0.003, P = 0.905 for a linear correlation), indicating that a lower number of fixes for some A. gigas does not influence the size of home range calculations.

Preferential localization

The distance from the centre of KDE 50% to the shoreline (Fig. 4), as calculated for all individuals on the KDE 0.50 projected envelopes, was low and similar for wild and restocked fish (31 AE 17 and 39 AE 20 m, respectively; P = 0.709) indicating a marked preference for the vicinity of the shoreline. No significant differences were observed between male and female preferences.

Travelled distance

Apparent travelled distances were calculated for each individual over the entire survey period. Maximal and minimal travelled distances were 30.83 and 1.33 km for wild fish (Table 1) and 17.34 and 2.87 km for restocked fish (Table 2). In both groups there was high individual variability; no statistical differences were found in terms of travelled distance between wild and restocked fish (P = 0.856), nor between male and female groups for restocked fish (P = 0.758). No statistical test was computed for wild fish since there was only a single female in this group. Nevertheless, it is worth noting that a single wild female had covered a total distance about thrice as long as that covered by a male that travelled the longest distance and about thirty times more than the male that had travelled the shortest distance (Table 1).

Regarding restocked fish, only one fish stayed in the southern part of the lake, with the maximum distance between release point and centre of KDE 50 around 2 km for Home range Substantial home range variability was observed for wild A. gigas: from 0.4 to about 70 ha while relying on MCP 95 , from 0.4 to about 350 ha while relying on KDE 0.95 and from 0.1 to about 31 ha when relying on KDE50% (Fig. 5). Restocked fish showed similar variability: from 1.2 to approx. 400 ha, 0.9 to about 225 ha, and 0.6 to about 23 ha for MCP 0.95 , KDE 0.95 and KDE 0.50 , respectively (Fig. 6).

Neither male-female restocked fish mean HR comparisons (MCP 0.95 , KDE 0.95 and KDE 0.50 ) nor wild male vs restocked male HR means revealed any significant differences. No statistical test was computed for wild females since there was only a single female in this group. Nevertheless the sole wild female that could be tagged occupied a much broader range (based on KDE 50 and KDE 95 ) than all wild males. Its HR revealed an overlapping of approx. 50% of the total area with the HR of a wild male, which could indicate the formation of a mating pair.

Discussion

Although the low number of tagged individuals (only one wild female) and the relatively small size and age ranges available for this study, our findings in Lake Imiria give interesting indications of young adult A. gigas behaviour in such an environment. Nevertheless, additional studies with A. gigas showing wider age and size ranges and new tracking technologies will be needed to further understand their behaviour in the wild.

Preferential localization

One of the first results indicates in Lake Imiria that wild or restocked A. gigas are highly sedentary. In a previous work on wild tagged fish in the lower Amazon (close to Santarem) in Brazil [START_REF] Crossa | Investigaci on participativa. Una experiencia promisora para el subsidio de programas de manejo del Arapaima gigas (Arapaima gigas) en el bajo amazonas[END_REF], a strong sedentary behaviour was also reported for this species. Additionally, those authors reported a limited migratory behaviour that could be explained by trophic migrations: A. gigas would follow their prey in river systems for a while, but would return after a few months to their initial living zone.

Our findings also indicate a strong preference for locations near the shoreline, where floating vegetation appeared to be a constant parameter in the locations selected by A. gigas. Possible explanations could be the suitability of these environments for resting, hiding from fishermen and also for foraging on their piscine prey, which abound in these vegetated shoreline ecotones [START_REF] Frankiewicz | The role of the shoreline ecotonal zone in spawning success and early life history of dominant fish species in the lowland Sulejow Reservoir[END_REF][START_REF] Petry | Relationships between fish assemblages, macrophytes and environmental gradients in the Amazon River floodplain[END_REF]. Such preferences were also observed in other large tropical predatory fishes in both rivers (Økland et al.,Fig. 5. Home ranges (KDE 50 ) of wild pirarucus, Arapaima gigas. Largest ranges partially overlapping and correspond to male 264 and female 334. Insert = an area where calculated home ranges of three males partially overlap. Map coordinates expressed in UTM system (Universal Transverse Mercator projection) zone 18L, where coordinates are expressed directly in meters 2005) and lakes [START_REF] Nyboer | Movement and home range of introduced Nile perch (Lates niloticus) in Lake Nabugabo, Uganda: implications for ecological divergence and fisheries management[END_REF]. The importance of floating vegetation for the distribution of A. gigas in Lake Imiria is particularly interesting because abundance has been found to be unrelated to macrophyte cover in the Mamirau a Reserve in Brazil [START_REF] Arantes | Environmental influences on the distribution of arapaima in Amazon floodplains[END_REF] despite the positive correlation observed between macrophyte cover and the abundance of other predatory fishes [START_REF] Petry | Relationships between fish assemblages, macrophytes and environmental gradients in the Amazon River floodplain[END_REF]. When comparing A. gigas abundance between lakes [START_REF] Arantes | Environmental influences on the distribution of arapaima in Amazon floodplains[END_REF], it appeared that macrophyte cover was less important than surface, depth and volume. Nevertheless it can become an important factor within a given lake, as in the present study.

Travelled distance

Our results also suggest that travelled distance are not influenced by fish gender, at least for restocked fish. Although the only wild female tagged showed a larger travelled distance than all tagged wild males, general conclusions cannot be drawn for wild specimens from this single observation. Longer movements or migrations of A. gigas are hypothesized as linked to trophic or spawning migrations [START_REF] Lucas | Migration and spatial behaviour[END_REF][START_REF] Crossa | Investigaci on participativa. Una experiencia promisora para el subsidio de programas de manejo del Arapaima gigas (Arapaima gigas) en el bajo amazonas[END_REF]Castello, 2008a) rather than to movements inside the home-range or shifts between successive home ranges [START_REF] Leigh | Movement and mortality of Murray cod, Maccullochella peelii, during overbank flows in the lower River Murray, Australia[END_REF]. It must also be emphasized that reported travelled distances most likely under-estimated the actual distances travelled by the fish, owing to the 2-week interval between successive fixes [START_REF] Baras | Selection of optimal positioning intervals in fish tracking: an experimental study on Barbus barbus[END_REF][START_REF] Rowcliffe | Bias in estimating animal travel distance: the effect of sampling frequency[END_REF]. Nevertheless in this study, reported values remain comparable between all tracked fish since the time intervals between two consecutive fixes was quite similar for all fish. The very small travelled distances observed in some individuals seem to be related to the characteristics (relative isolation) of Lake Imiria. A previous study in a river network in the lower Amazon near Santarem, Brazil [START_REF] Crossa | Investigaci on participativa. Una experiencia promisora para el subsidio de programas de manejo del Arapaima gigas (Arapaima gigas) en el bajo amazonas[END_REF], showed that most tagged wild A. gigas travelled relatively small distances, but that a few travelled around 80 km and returned to their initial area only after a few months. Another molecular study in Brazil on wild A. gigas populations sampled along the amazon axis has also emphasized the relatively sedentary behaviour of this species, which exhibits low (but significant) to high gene flow between populations separated by distances of less than 100 km and 25 km, respectively [START_REF] Araripe | Dispersal capacity and genetic structure of Arapaima gigas on different geographic scales using microsatellite markers[END_REF]. These results confirm the sedentary behaviour of the species and suggest that high river connectivity might foster larger movements in some individuals.

In Lake Imiria, the detailed observation of cumulated apparent travelled distance as a function of elapsed time after tagging revealed a more contrasting situation among all fish: i) some travelled long distances during the first 60 days following tagging, then short movements within their KDE 50 HR; ii) other fish displayed relatively moderate but continuous movements throughout the survey, and iii) a group showed seemingly random variations of cumulated travelled distances during the entire survey period (results not shown). Contrasting movements have also been observed in other large freshwater predatory fish. The Murray cod, Maccullochella peelii travelled distances varying from 2 km to more than 50 km over an 8-month period [START_REF] Leigh | Movement and mortality of Murray cod, Maccullochella peelii, during overbank flows in the lower River Murray, Australia[END_REF], with a clear relationship between travelled distance and fish size [START_REF] Koehn | Movements of Murray cod (Maccullochella peelii peelii) in a large Australian lowland river[END_REF]. The same was observed in the tucunar e, Cichla temensis, where the largest males also showed the highest propensity to travel over long distances [START_REF] Hoeinghaus | Movement of Cichla species (Cichlidae) in a Venezuelan floodplain river[END_REF]. By contrast, many other tracking studies found no relationship between fish size and travelled distance, and sometimes with higher between-individual variability than here (e.g. 0.5-105 km) during a sixmonth survey of Hydrocynus vittatus (Økland et al., 2005).

Home range

There was no home range gender difference in restocked A. gigas (comparison was not possible between genders in wild fish, since we had only one wild female) or between wild and restocked males, suggesting that restocked and wild fish had similar patterns of space utilization. High HR variability with no correlation between home range and fish size, has also been reported in other large tropical predatory species such as Lates calcarifer [START_REF] Heupel | Short-term movement of barramundi in a seasonally closed freshwater habitat[END_REF][START_REF] Nyboer | Movement and home range of introduced Nile perch (Lates niloticus) in Lake Nabugabo, Uganda: implications for ecological divergence and fisheries management[END_REF], Lates niloticus [START_REF] Nyboer | Movement and home range of introduced Nile perch (Lates niloticus) in Lake Nabugabo, Uganda: implications for ecological divergence and fisheries management[END_REF] or H. vittatus (Økland et al., 2005). In Lake Imiria, even when the water level dropped during the dry season, A. gigas could find suitable habitats year round, which probably favoured their strong sedentarity, as attested by the very small home ranges observed for the majority of tagged fish. Nevertheless, as for total travelled distance, it must be pointed out that the mean observed home ranges are undoubtedly underestimated because of the significant delay between two successive positions (15-day sampling interval) as previously reported in other studies [START_REF] Crook | Is the home range concept compatible with the movements of two species of lowland river fish?[END_REF][START_REF] Rowcliffe | Bias in estimating animal travel distance: the effect of sampling frequency[END_REF]. Yet this underestimation is likely to be lower than for travelled distance [START_REF] Baras | Selection of optimal positioning intervals in fish tracking: an experimental study on Barbus barbus[END_REF]. Monitoring the home range through the use of automatic receivers (acoustic telemetry) could be a new and useful tool to obtain more accurate information in future studies.

The results presented here are the first in A. gigas, comparing the movements and home ranges between wild and restocked fish in a natural environment.

The sedendarity of the species and Lake Imiria characteristics certainly contributed to the good survival of restocked fish by limiting the movement of introduced A. gigas to other surrounding areas. These results attest the relevance of restocking this valuable species in other similar environments where wild populations have been decimated. It must be emphasized, however, contrary to previously thought [START_REF] Hrbek | Population genetic analysis of Arapaima gigas, one of the largest freshwater fishes of the Amazon basin: implications for its conservation[END_REF], that A. gigas is not formed of a single Amazon basin population. Several natural populations showing substantial degrees of genetic differentiation have been found in the Brazilian Amazon [START_REF] Araripe | Dispersal capacity and genetic structure of Arapaima gigas on different geographic scales using microsatellite markers[END_REF] and in the Peruvian Amazon [START_REF] Garcia-Davila | Avances en el estudio de la variabilidad genetica de cinco poblaciones naturales de paiche, Arapaima gigas, en la Amazonia peruana[END_REF]. In order to preserve local genetic resources, further restocking programs should systematically be accompanied by genetic analyses, evaluating the compatibility between the natural genetic variability of A. gigas in the area to be restocked and that of the fish used for restocking. In other words, adults or juveniles produced in captivity for restocking programs must be genetically as close as possible to the individuals still present in the area intended for restocking.

In addition to population genetics considerations, studies are also needed to further evaluate the reproductive success and interactions between wild and restocked fish.

Fig

  Fig. 3. Example of Track length calculation (yellow line), 95% Minimum Convex Polygon (MCP 95% ) and Kernel Density Estimation (KDE 50% , KDE 95% ) for one pirarucu, Arapaima gigas, after an 18-month period. Tracks correspond to restocked female #104, fixed 38 times from 7/08/2009 to 28/ 01/2011 (average time between each fix 14.1 days)

Fig. 6 .

 6 Fig. 6. Home ranges (KDE 50 ) of restocked pirarucu, Arapaima gigas. Insert = area where calculated home ranges of two females partially overlap. Map coordinates expressed in UTM system, zone 18L

Table 2

 2 Travelled distance (km), Maximum Convex Polygon at 95% (MCP 95 ), Kernel Density Estimation (KDE 50 and KDE 95 ) of cageraised restocked pirarucu, Arapaima gigas. F (female) or M (male) in the fish code indicates fish gender, C (Cage-raised)

		Total	Travelled
		length	distance	MCP 95	KDE 95	KDE 50
	Fish code	(cm)	(km)	(ha)	(ha)	(ha)
	C 185 F	134	30 825	24.2	9.1	2.2
	C 315 F	133	4857	12.8	3.8	2.8
	C 394 F	128	2872	44.2	18.0	1.6
	C 404 F	143	16 486	189.2	76.8	12.0
	C 104 F	134	5570	8.4	7.6	1.7
	Mean	134.4	12.1	55.8	23.1	4.1
	Std dev.	5.4	11.7	75.9	30.5	4.4
	C 096 M	135	3967	84.2	7.0	2.5
	C 286 M	133	9349	115.2	41.6	10.7
	C 304 M	127	2654	2.1	2.7	0.6
	C 375 M	137	9868	55.7	67.6	15.0
	C 214 M	141	2293	1.2	0.9	0.7
	C 084 M	131	7759	4.6	14.3	4.3
	C 364 M	134	17 342	400.5	225.6	22.8
	C 023 M	127	10 142	7.2	19.9	2.5
	C 355 M	124	6040	29.0	2.4	0.9
	Mean	132.1	7.7	77.8	42.4	6.7
	Std dev.	5.4	4.7	127.7	72.1	7.8

J. N uñez-Rodr ıguez et al.

Movement patterns and home range of wild and re-stocked A. gigas

Acknowledgements

This work was funded by the Ucayali regional Government (Gobierno Regional del Ucayali) and carried out as part of the scientific collaborations between the Instituto de Investigaciones de la Amazon ıa Peruana (IIAP) and the Institut de Recherche pour le D eveloppement (IRD), both part of the research network known as Red de Investigaci on sobre la Ictiofauna Amaz onica (RIIA) (http://www.riiaamazonia.org). The authors wish to thank all of the technical team and field assistants from the indigenous Shipibo-Conibo people of the Caimito community who helped us during this study.


Zahira Nakhli

Fafa Ben Hatira

Martine Pithioux

Patrick Chabrand

Khemais Saanouni

FEMORAL FRACTURE LOAD AND DAMAGE LOCALISATION PATTERN PREDICTION BASED ON A QUASI-BRITTLE LAW: LINEAR AND NON-LINEAR FE MESHING

Keywords:

Finite element analysis is one of the most used tool for studying femoral neck fracture. Nerveless, consensus concerning either the choice of material characteristics, damage law and /or geometric models (linear on nonlinear) still remains unreached.

In this work, we propose a numerical quasi-brittle damage model to describe the behavior of the proximal femur associated with two methods to evaluate the Young modulus. 8 proximal femur finite elements models were constructed from CT scan data (4 donors, 3 men; 1 woman). The results obtained from the numerical computations showed a good agreement between the numerical curves (loaddisplacement) and the experimental ones. The computed fracture loads were very close to the experimental ones (R 2 =0.825, Relative error =6.49%). The damage patterns were similar to those observed during the failure during sideway fall experimental simulation. Finally, a comparative study based on 32 simulations, using a linear and nonlinear mesh has led to the conclusion that the results are improved when a nonlinear mesh is used. In summary, the numerical quasi-brittle model presented in this work showed its efficiency to find the experimental values during the simulation of the side fall.

Introduction

The osteoporosis disease, which is defined as a decrease in bone strength, can be estimated by bone mineral density (BMD) measuring [START_REF] Briot | Actualisation 2012 des recommandations françaises du traitement médicamenteux de l´ostéoporose post-ménopausique[END_REF]. This pathology causes fractures in different bone structure and is classified as the most important ones affecting the femoral neck [START_REF] Tellache | Etude expérimentale de la rupture osteoporotique du col femoral[END_REF][START_REF] Tellache | Femoral neck fracture prediction by anisotropic yield criteria[END_REF][START_REF] Curtis | The impact of fragility fracture and approaches to osteoporosis risk assessment worldwide[END_REF]. It usually occurs without apparent symptoms until the provocation of the fracture. Fracture prevention if this pathology based on diagnosis can delay surgical procedures. Finite element (FE) modeling can be a reliable tool to better screen up the different factors related to bone fractures and give surgeons more reliable criteria on fracture risk factor. Indeed, numerical modeling based on Finite element method has appeared in the 1950s and helped engineering to deal with different problems of structural mechanics. Some specific models were developed in mechanical to predict human proximal femur fracture and to assess the pressure distribution under physiologic loading in bone structures.

Most of proposed models were focusing on the prediction of the ultimate force at fracture as well as the fracture pattern by using different mechanical approaches. These studies were based on linear and non-linear isotropic and /or anistropic FE models [START_REF] Bettamer | Using visual image measurements to validate a novel finite element model of crack propagation and fracture patterns of proximal femur[END_REF][START_REF] Viceconti | Are spontaneous fractures possible? An example of clinical application for personalised, multiscale neuro-musculo-skeletal modelling[END_REF][START_REF] Haider | Femoral fracture load and fracture pattern is accurately predicted using a gradient-enhanced quasi-brittle finite element model[END_REF][START_REF] Marco | Numerical Modelling of Femur Fracture and Experimental Validation Using Bone Simulant[END_REF][START_REF] Enns-Bray | Mapping anisotropy of the proximal femur for enhanced image based finite element analysis[END_REF][START_REF] Bettamer | Prediction of proximal femoral fracture by using Quasi-brittle damage with anisotropic behaviour model[END_REF][START_REF] Lekadir | Statistical estimation of femur micro-architecture using optimal shape and density predictors[END_REF][START_REF] Zagane | Numerical simulation of the femur fracture under static loading[END_REF][START_REF] Vargaa | Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup[END_REF][START_REF] Nawathe | Theoretical effects of fully ductile versus fully brittle behaviors of bone tissue on the strength of the human proximal femur and vertebral body[END_REF] The various works mentioned above have tried to give a unique answer to the solution of modeling the behavior of bone structures and more precisely in the context of this work to the problem of fracture of these structures. No consensus has yet been reached, but each scientific work carried out can help to move towards a construction of an efficient prediction. Most of the last studies were carried out with nonlinear FE modeling for a better efficiency of the proximal femur fracture. In order to propose a new efficient numerical tool, inexpensive (from computing side of view) and of course close to experimental, a method for estimating the proximal femur fracture based on a non linear FE model is presented in this study. The Continuum Damage Mechanics CDM framework is chosen to develop the isotropic quasibrittle fracture law with two elasticity properties (homogenous and non homogenous). The model is implemented into a user routine VUMAT in the finite element software (Abaqus) and applied in linear and non linear meshing model. The Finite element simulations were carried out using the explicit dynamic algorithm. Numerical computations for four osteoporotic femurs (right and left, height specimens) were compared with success to experimental fracture data (values and curves) with linear and non linear meshing.

Méthode

CT Scan

Eight femurs (right and left) coming from four donors (3men, 1 women), were scanned individually with high resolution by using alight speed VCT scanner from GE Medical Systems available in Medical imagery service of La Timone University hospital, (Marseille). The resolution system used provides a three-dimensional map of the bone mineral density through the studied bone structures. [START_REF] Enns-Bray | Mapping anisotropy of the proximal femur for enhanced image based finite element analysis[END_REF][START_REF] Schmidt | Finite element analysis of stem dimensions in a revision total knee arthroplasty using visible human computed tomography data[END_REF][START_REF] Abdulkadir | Finite Element Model Construction[END_REF] The different steps taken to apply the protocol required to create the finite element model from CT data are described in Figure 1.

The first step was the reconstruction of the 3D geometry of each femur from the Xrayscanner images based on the generation of the voxel element using the research software Mimics 17.0. Densities described by grey value level were assigned to each voxel element [START_REF] Dieter | A comparaison of enhanced continuum FE with micro FE models of human vertebral bodies[END_REF].

The second step was the femur volume 3D mesh generating with tetrahedral elements by the research software 3Matic 9.0.0.231. In order to assign the material parameters, the volume mesh was finally imported a second time in Mimics (step 4). Thereby, a 3D model specific to each patient respecting his anatomy and possessing material properties related to the quality of his bone was created and imported to the Abaqus/CAE software (step 5). More details of this protocol can be found a previous article [START_REF] Nakhli | DEPENDENCE DE LA MODELISATION PAR ELEMENTS FINIS DU FEMUR HUMAIN DE LA RECONSTRUCTION TRIDIMENSIONNELLE[END_REF].

Experimental Mechanical Compression test

To reproduce a simulation of a sideways fall on the greater trochanter, each proximal femur was loaded to failure in the INSTRON 5566 machine. Specimens were fixed in resin (Epoxy Axon F23) at 15.12° internal rotation. The femoral shaft was oriented at 10° adduction in the apparatus (Figure 2 left). For this Specimen in Figure 2 Right, the neck forms an angle with the shaft in about 125.08° degrees, which is called diaphysealangle, in this case it is a Normal diaphysealangle (between 120° and 137°). The load was applied to the greater trochanter through a pad, which simulated a soft tissue cover, and the femoral head was molded with resin to ensure force distribution over a greater surface area [START_REF] Corroller | Combination of texture analysis and bone mineral density improves the prediction of fracture load in human femurs[END_REF]. The figure 2 shows the mechanical test conditions of thesideway fall simulation. The results of the different conducted experiences are reported in Table 1. It gives the details of the obtained ultimate failure load and the bone mineral density (BMD) for all femurs, which are composed of three osteoporotic femurs and one healthy. The mean value of the BMD was found to be 0.7017 g/cm2. From experimental data, eight load-displacement curves are plotted in Figure 3. The obtained curves for right and left femurs taken from the same donor showed different tendency with Neck Surf different fracture load magnitude. Exception is however reported for the curves of Specimen 2 where similarity is noticed for the left and the right femurs.

Quasi Brittle LAW

The model is based on an isotropic behavior law coupled to a quasi-brittle damage law in order to describe the progressive initiation and propagation of cracks within human proximal femur under quasi-static load.

In this work, the damage behavior law describing a quasi-brittle behavior is proposed using an isotropic Continuum Damage Mechanics (CDM) based on Marigo [START_REF] Marigo | Formulation of a damage law for an elastic material[END_REF] modeling of the damage for brittle and quasi-brittle material.

• Constitutive framework: A quasi brittle damage model

The approach of irreversible thermodynamics with internal variables(Chaboche1988;Germain1973;Krajcinovic1989;;Kachanov1986; Lemaitre1987, Saanouni et al. 1996, Saanouni 2012) is chosen to present a coupled damage elastic model to describe the initiation and the accumulation of the damage in bone structure, more precisely the femur.

The new energy based model is described throughout state variables (external and internal).Thestate variables describing the constitutive equations are represented by theexternal and the observable state variables, namely the elastic strain tensor 𝜀 𝑒 andand the Cauchy stress tensor𝜎. For the sake of simplicity, damage is supposed isotropic described by a couple of scalar internal variables (D,Y) where Y is the damage force associated to the damage variable D.

The effective variables ε ̃eand σ ̃ including the damage effect, which are defined in the framework of the elastic strain equivalence assumption, are presented hereafter. The expression of the stored elastic energy density is given by: (1 -D)ε e : A: ε e + ψ ⏞ (D) [START_REF] Bettamer | Using visual image measurements to validate a novel finite element model of crack propagation and fracture patterns of proximal femur[END_REF] According to the Marigo hypothesis:ψ ⏞ (D) = 0 dire ce que c'est ψ ⏞

Where A is thesymmetric fourth-rank tensor of elastic properties of the virgin (not affected by damage) material, which in the isotropic case can be written in terms of the well-known Lame's constantsand according to:

A 1 1 2 1 =   +   = 𝐸 (1 -2) ;  = 𝐸 (1 + )(1 -2)
Where 1 is the second-rank identity (Krönecker) tensor while 1 is a fourth-rank unit tensor.

According to the theory of Marigo, the global energy depends only on the two state variables namely the elastic strain tensor and the damage.

The state laws𝝈and Y,are classically derived from the state potential are obtained from the freeenergy by: σ = ρ ∂ψ ∂ε e = (1 -D)A: ε e (6.1)

A = ρ ∂ 2 ψ ∂ 2 ε e > 0 (6.2) σ = (1 -D) ( 1  1 + 2 1 ) : ε e (6.3) 𝑌 = -𝜌 𝑑𝜓 𝑑𝐷 = 1 2 𝜀 𝑒 : 𝐴: 𝜀 𝑒 (7)
The damage criterion(or damage yield function) is described by Y:

f(Y, D) = Y - 1 2 Y 0 -mD 1 s = 0 (8)
where 𝑌 0 ,s and m are material parameters. The parameters s and m are related to the damage "hardening" of the material. It is here to be noticed that the damage yield function Eq.( 8) can describe the initiation of micro-cracks starting from undamaged state (D=0).

In the present model, the dissipation potential 𝝋 is reduced to the yield function f according to the associative theory:

φ = f = Y - 1 2 Y o -mD 1 s = 0(9)
The damage evolution equation derived from the dissipation potential is:

φ̇= 0 ⇔ ∂φ ∂Y Y
̇+ ∂φ ∂D D ̇= 0 [START_REF] Bettamer | Prediction of proximal femoral fracture by using Quasi-brittle damage with anisotropic behaviour model[END_REF] For this approach, the coupling between damage and elasticity is completed with the following damage evolution law.

𝐷 ̇=

𝑠 𝑚 𝑌 Ḋ1-𝑠 𝑠 (11)
With: ee Y : :

=    & & (12)
According to Eq. ( 6.3), when damage increases by Eq. ( 11), then the stress tensor decreases due to the decrease of the Lame's constants (i.e. the Young's Modulus).

Solving the non linear problem described by Eqs ( 6)-( 12) in order to determine the unknowns of the problem is performed through an approximation of these variables in total time interval

𝐼 𝑡 = [t 0 , t f ] = ⋃ [t n , t n+1 = t n + ∆t] Nt n=0
,t being the increment between two successive time steps. This approximation is done for every integration point related to every finite element.

Thus knowing the initial variables at tn, the discretized problem is solved giving the final solution at the final time tn+1.The discretization leads to the following expressions of the problem variables at tn+1=tn+t, the end of the step time:

f n+1 = Y n+1 - 1 2 Y 0 -mD n+1 1 s = 0 (16)
From this last equation, the "admissible" value of the damage variable is deduced as:

𝐷 𝑛+1 = 〈 𝑌 𝑛+1 - 1 2 𝑌 0 𝑚 〉 𝑠 (17)
In this isotropic damage model, some remarks can be made:

• If the scalar variable describing damage is zero (D=0.0), then the material state is described by the classical isotropic elastic model.

If the fracture condition of the critical value (D=1.0) is reached, then the material point is declared as fully damaged and the following value is assigned to D in that point D=0.999.

The proposed Algorithm

As mentioned earlier, one of the goals of this work is to propose a reliable quasi brittle damage model of proximal Femur fracture based on the finite element model ( FEM).The proposed algorithm followed to implement the model is summarizedin figure 4.

The first stepconsists of the global modeldefinition: geometry, load conditions and initial bone density distribution. The Second Step is concerned with the determination of Young's modulus, Poisson's ratio and the density. These material properties are obtained by two methods. The first one, the homogeneous material distribution calculate through the research software Mimics 17.0, based on the Hounsfield Units 'HU' or Units Gray values on the scanned images. The second one, the heterogeneous material distribution, assigns to each element a distinct mechanical property. The third step is related to the calculation of the displacement, by solving the linear variational equation of the displacement field. During step 4, the evaluation of the strain, the stress and the damage at each discrete location is performed and it is based on the finite element method. Thereafter, an update of the stress (step 5) and damage (step 6) values are applied. The model being implemented into the Abaqus/Standard code using the subroutine UMAT, a check for convergence is executed. The final result is obtained when the convergence criterion is satisfied; otherwise, the iterative process continues from Step 2.An illustration of the algorithm used is described in Figure4. In the present work and for the sake of comparison, bone was modeled as an isotropic material with two mechanical properties (Young modulus E (MPa)) estimated through two different methods. These techniques were used in previous works. Indeed, most of these studies, adopted a non homogenous elastic modulus related the density. As examples of these works we can recallmorgan E.F et al. [START_REF] Morgan | Trabecularbonemodulus-density relationships depend on anatomic site[END_REF], Keyak J.H. [START_REF] Keyak | Improved prediction of proximal femoral fracture load using nonlinear finite element models[END_REF], Ariza O. [START_REF] Ariza | Comparison of explicit finite element and mechanical simulation of the proximal femur during dynamic drop-tower testing[END_REF], Pithioux et al. [START_REF] Pithioux | Improved Femoral Neck fracture predictions using anisotropic failure criteria models[END_REF] and Haider et al. [START_REF] Haider | Femoral fracture load and fracture pattern is accurately predicted using a gradient-enhanced quasi-brittle finite element model[END_REF]. However, some researchers adopted the method based on the assumption that the elastic modulus is homogenous and a function of volume fraction (BV/TV) . These studies can found in the references (Hambli R. et al. [START_REF] Hambli | Finite element prediction of proximal femur fracture pattern based on orthotropic behaviour law coupled to quasi-brittle damage[END_REF] and Varga P. et al. [START_REF] Vargaa | Nonlinear quasi-static finite element simulations predict in vitro strength of human proximal femora assessed in a dynamic sideways fall setup[END_REF]). We will recall here after these two methods of E determination.

Method 1 : Non homogenous Young Modulus

The first method using the following expression gives a varying Young modulus (E) related to the bone apparent density ρ such as defined by Kaneko et al. [START_REF] Kaneko | Mechanical properties, density and quantitative CT scan data of trabecular bone with and without metastases[END_REF],

E1= 2000 ρ 1.89 (1) ρ: apparent density (g/cm 3 )

This method is based on a phenomenological law and allows to assign to each element a distinct mechanical property using a direct correlation between apparent density and Young Modulus.

In the end, a heterogeneous material distribution was obtained.

Method 2 : Homogenous Young Modulus

For method 2, homogenization techniques were considered, allowing to obtain a homogeneous material distribution. The following relationship is proposed by Hernandez et al. [START_REF] Hernandez | The influence of bone volume fraction and ash fraction on bone strength and modulus[END_REF]:

E 2 = 84370 ( 𝐵𝑉 𝑇𝑉 ) 2.58 (2)
BV/TV:bone volume/total volume fraction;

Thirty-two numerical computations based on eight Femurs reconstructions are validated through a comparison of the experimental crack localization and of the estimated failure loads.

The material properties E and ρ are summarized in Table 2. Poisson ratio is set at 0.3 based on the work of [START_REF] Jundt | Modèles d´endommagement et de rupture des matériaux biologiques[END_REF][START_REF] Currey | The effect of porosity and mineral content on theYoung's modulus elasticity of compact bone[END_REF][START_REF] Carter | The compressive behavior of bones as a two-phase porous structure[END_REF].

Simulations

• Boundary and Loading conditions

The numerical validation is conducted with the boundary condition and load case representing the experimental conditions (Figure 5). The load was applied on femoral Greater trochanter reproducing the sideway fall case, whereas the femoral head and the lower surface were constrained. During the conducted computations, the stiffness of elements degrades gradually as damage increase, and the crack is modeled as the region of elements whose stiffness has been reduced to near zero.

Results

The general purpose of this work is to compare the prediction of the damage localization as well as of the ultimate fracture load for different specimens tested experimentally for two meshing model, linear mesh with linear tetrahedral elements (C3D4), and nonlinearmesh with quadratic tetrahedral elements (C3D10) (six degrees of freedom per node which are the three displacements and the three rotations). The ultimate strength load value obtained experimentally was applied for the two methods which are based on two different approaches to estimate the Young modulus as previously presented. The analysis details the fracture load and the localized damaged zones dependency on the young modulus estimation as well as the linearity or not of the meshing. Special attention will now be paid to one of the specimens presented in the previous overall results. The final goal is to better underlined the quantitative and qualitative results obtained for the eight specimens. The specimen chosen is the one named SP3R. It is a representative sample of all the studied specimens. We begin by a comparison between the experimental and numerical behavior curves (with linear and non linear meshing) obtained during the simulation of the sideways fall. This comparison which is illustrated in Figure [START_REF] Marco | Numerical Modelling of Femur Fracture and Experimental Validation Using Bone Simulant[END_REF] shows a good simulation between experimental and numerical results. Besides, the nonlinear case shows the best agreement with experimental curve, as well as a sharp drop in force during failure. Figure 9 shows a validation between the numerical for both cases of meshing /linear and nonlinear) and experimental results of the fracture pattern, and clearly demonstrate that the fracture line is located in the neck region Also, Figures9a and 9b show that regardless of the choice of type of meshing (linear or nonlinear), we obtain fracture localizations similar to the ones obtained experimentally (Figure 9c).

In conclusion, this validation of load fracture and localization proves the performance of the adopted numerical method, which is formulated in the CDM framework. It also clearly demonstrated that the result is affected by the choice of the type of mesh (linear or nonlinear) whereas the damage pattern does not depend on this parameter.

Discussion

The aim of the present study was to implement a comparative study based on 32 simulations, using a linear and nonlinear mesh to show that the results are improved when a nonlinear mesh is used. As a first remark, we can say that the predicted force-displacement curve shows the same trend as the one observed experimentally. Regarding the relative error, the average error is about 6.49% with a very good fracture pattern predictions for all specimens, compared to previous works presetend by Haider I.T and al [START_REF] Haider | Femoral fracture load and fracture pattern is accurately predicted using a gradient-enhanced quasi-brittle finite element model[END_REF]. The average percentage errors of predicted fracture load was about 9.6% and peak error of only 14%. However, they have recalled that the average errors found in previous studies was less than the previously published studies which are from 10% to 20% [START_REF] Haider | Femoral fracture load and fracture pattern is accurately predicted using a gradient-enhanced quasi-brittle finite element model[END_REF].

In general, we found statistically moderate correlations between the experimentally and computationally results using a homogeneous young modulus (method2) and using nonlinear meshing(R²=0.825). However, no correlation was found between experimental and FE model for the heterogeneous young modulus distribution using the linear meshing and for two meshing model of the heterogeneous method. Regarding the localization issue, we found that in general, the experimental bone failure locations agreed with the locations of the FE for the method 2.

Referring to the Garden Classification [START_REF] Frandsen | Garden´s Classification of femoral Neck Fractures[END_REF], different fracture can be observed experimentally and the numerically, depending on the femoral geometry, the material properties and the boundary conditions. In this work, the fracture patterns correspond to a Transervical neck fracture with stage II (Complete fracture with minimal or no displacement from anatomically normal position) of the Garden classification. To the best of the author's knowledge, this is the first time a comparison of linear and nonlinear meshing was established for the prediction of femoral fracture. Although we find the results encouraging, one limitation of this study is related to the mesh sensitivity, which should adopt an effective technique to better predict fracture load, fracture pattern, and fracture initiation independently of mesh density. Overall, the FE model precision was demonstrated by comparing the simulation results to the experimental results for each specimens.

Conclusion

The purpose of this work was to develop and validate a simple FE model based on continuum damage mechanics in order to simulate the complete force-displacement curve of femur failure. Femoral fracture load was predicted using a quasi brittle-damage FE model for four studied cases, combining homogeneous and heterogeneous material distribution with a linear and nonlinear mesh. The obtained results show a strong linear relationship between FE predicted and experimentally measured fracture load (R 2 = 0.825) in the case combining homogenous material distribution with non linear mesh. Furthermore, all eight cadaveric specimens present a similar failure locations between the experimental and the FE simulation, when the method 2 is adopting.

The presented FE model shows strong correlations between experimental and numerical values however is spurious mesh sensitivity. The size of the damaged region corresponds to the size of the mesh used to solve the problem. As the mesh is refined, the size of the damaged region Despite limitations of our study, cited above, the relatively low average error in the fourth case suggests that this FE methodology may be useful in helping the surgeon choose a patientspecific treatment, and allowing them to make the right decision before the surgery by evaluating the risk factor from the fracture pattern.

Figure 1 .

 1 Figure 1. The protocol established to create a 3D FE Model from computed tomography data using the element-by-element material properties using the Hounsfield unit of CT data.

Figure 2 -

 2 Figure 2-The mechanical compression test conditions (left) :CT scans before fracture (Right) : Normal diaphysealangle125.08°, Femur was fixed in resin (Epoxy Axon F23) at 15.12° internal rotation

Figure 3 -

 3 Figure 3 -Experimental load vs. displacement for the eight specimens

Figure 4 -

 4 Figure 4-Schematic representation of the Bone Damage algorithm proposed.

Figure 5 -

 5 Figure 5 -The mechanical compression test conditions (Left) and BCs applied to the FE model(Right)

Figure 7 -

 7 Figure 7 -Predicted fracture pattern from different view and quasi-brittle damage distribution.

Figure 8 -

 8 Figure 8 -Predicted and experimental force-displacement curves of the present FE model Sp 3R for the Method 2, Linear and nonlinear mesh

Figure 9 -

 9 Figure 9-Qualitative evaluation of the FE based fracture pattern prediction, for linear mesh (a) and nonlinear mesh (b) by comparing with experimental compression-test photos (c) showing the anterior View for Specimen 3 Right and Left adopting method 2.

Table 1 :

 1 Failure values for the eight proximal Femur

	Specimen	femur	BMD(g/cm2)	Load (N)
	Sp1L	Osteoporotic	0.651
				1524.42
	Sp1R	Osteoporotic	0.722
				2318.69
	Sp2L	Osteoporotic	0.615
				973.00
	Sp2R	Osteoporotic	0.508
				743.00
	Sp3 L	Osteoporotic	0.714
				1477.17
		Osteoporotic	0.701
	SP3R			1293.23
	Sp4L	healthy	0.842
				1493.98
	Sp4R	healthy	0.861
				1113.92
	Mean value		0.7017

Table 2 .

 2 Material Properties for height specimens

	Femur	Strength	Density	Young	Young	Poisson
		Load (N)		Modulus (Mpa)	Modulus(Mpa)	ratio
				Method 1	Method 2
	Sp1 G	1524.42	0.28 -2.45 121 -14475
	D	2318.69	0.25 -2.46 103 -14552
	Sp2 G	973	0.47 -2.44 384-14293
	D	743	0.35 -2.42 199 -13991	3777	0.3

Acknowledgements

The contribution of Saint Marguerite hospital radiology team specially P. Champsaur, T. Lecorroller, and D. Guenou is gratefully acknowledged.

The 32 correlations between the experimental and FE computed fracture loads for the four studied cases are exposed in Figure 6. In summary and as it appears in Figure 6 (D), the numerical computations based on the use of an homogeneous material distribution with a nonlinear mesh, present a good agreement with the experimental data (fracture load magnitude) with the best correlation ( R²= 0.825). For the other cases (Figure 6 In Table 3 the relative errors between the experimental and the computed fracture loads are reported. The best results is obtained for the case where we use Young modulus E related to the microarchitecture parameter (method 2) for the non-Linear mesh. The fracture load error average was found to be 6.49 %. The propagations of the cracks and the distribution of the quasi-brittle damage of the eight femurs are plotted in Figure7

The results of the numerical computations gave two different crack localizations based on the choice of the elastic property. Indeed, the FE simulations performed with the method 2,showed a femoral neck (transcervical) fracture, the crack is initiated locally at the superior surface of femoral neck. Then the crack continues to grow, resulting a separation of the proximal femur. However, in this case the damage surface corresponded to the fracture surface observed in the experience, differently from the first method, where fracture occurred in the Greater trochanter. The same observations are obtained for the two femurs (right and the left) for the all studied femurs. The crack localizations for the two models linear and nonlinear are quasi similar, except that in the nonlinear modeling case, the entire femur is affected by the damage as shown in Figure 7 for the SP4 R and SP4 L. These observations are very interesting since as it has been related in previous studies, nonlinear meshing can be computationally expensive (cpu).


Loïc Bertrand
email: loic.bertrand@synchrotron-soleil.fr

Claire Gervais

Admir Masic

Luc Robbiola

Harold E Edgerton

Paleo-inspired systems: Durability, Sustainability and Remarkable Properties

Keywords: Ancient Materials, Archaeology, Durability, Paleontology, Redox Chemistry

Lead-in

The process of mimicking properties of specific interest (such as mechanical, optical, and structural) observed in ancient and historical systems is designated here as paleo-inspiration. For instance, recovery in archaeology or paleontology identifies materials that are a posteriori extremely resilient to alteration. All the more encouraging is that many ancient materials were synthesized in soft chemical ways, often using low-energy resources and sometimes rudimentary manufacturing equipment. In this Minireview, ancient systems are presented as a source of inspiration for innovative material design in the Anthropocene.

Introduction

From archaeological remains to fossils, historical and ancient materials provide a fundamental window on our past, gathering materiality and function in an integrative manner. [1] These materials are essential to elucidate the origin and evolution of life forms on Earth, [START_REF] Benton | Vertebrate palaeontology[END_REF] are tangible testimonies of past Human activities, [START_REF] Renfrew | Archaeology: Theories, Methods, and Practice[END_REF] and allow assessing anthropic impacts on Earth climate and environment. [START_REF] Dincauze | Environmental archaeology: principles and practice[END_REF] Less discussed is their potential of inspiration for the design of novel chemical and material systems or devices. Ancient materials have often undergone a high-level of sequential selection and filtering over time, leading to highly-efficient properties, such as in the metallic luster finishes in ancient ceramics. [START_REF] Sciau | [END_REF] They can be considered as a subcategory of materials produced under extreme conditions, where extreme values are attained in time instead of pressure or temperature. The time component is a fundamental characteristic of their elaboration, evolution and understanding. [6,7] Long-term preservation in natural contexts provides examples of physicochemical resilience -stability over time in a dynamic environment -to environmental conditions up to billions of years. We therefore argue that the added value of their history endow ancient materials with chemical specificities that are of great interest to conceive novel synthetic paleo-inspired systems incorporating functionalities, such as tailored optical response or environmental resilience. In many cases, however, precise knowledge on the raw materials, recipes, and conditions to produce ancient artefacts has been at least partly lost. Some knowledge can be retro-engineered from direct in-depth material studies. The whole process involves the steps of understanding the composition of the collected material with interesting functionalities, designing synthesis routes to reproduce corresponding functionalities, and comparing the properties of the newly produced material to expected performances. This process contributes to a description and fundamental understanding of long-term kinetic and thermodynamic behavior laws of material systems. This review therefore discusses the exceptional potential of identifying properties of interest from direct harvesting in ancient materials. We present a selection of examples from the literature and our works that illustrate the diversity of these properties and show how paleo-inspiration could further be developed to design resilient materials, systems with remarkable properties and novel chemical processes with low environmental impact.

Durably Environment-Resilient Materials

With increasing environmental challenges, durability is a key parameter for the material design. Rising levels of anthropogenic CO 2 encourage the development of more sustainable materials. An observation of archaeological and paleontological remains allows identifying a posteriori a range of unexpected preservation cases that have either resisted or been transformed to a new material able to survive the filtering effect produced by changing environmental conditions over a long period of time.

Roman concrete is an exemplary case of long-lasting, resilient and sustainable ancient inorganic material.

In the history of concrete material, it represents a technological breakthrough. Ancient Roman structures have withstood millennia of seismic events and environmental pressure, while modern concrete structures constructed with ordinary Portland cement have a predicted lifetime of about 100 years. [8] Addition of 'pozzolana' (volcanic ash) provides binding mortar with 5-8 times greater compressive strength than the pure lime mortar previously used in Ancient Greece. Roman concrete could also set in aqueous environments. Despite advances made on the understanding of their resilience, [9,10] the exact recipe and physicochemical process leading to their environmental stability is still not well defined and represents an active research area in the cement industry (Figure 1A-C). The Iron pillar in New Delhi, about 6 tons and over 7 m in height, is another remarkable case of century-old durability. [11] Its longevity is attributed to its composition, a phosphorus-rich wrought iron with low carbon content. [12] The passive protective surface remained unaffected by the important material heterogeneity linked to the forging process, including slag inclusions. [13] An archetypal example of paleo-inspiration --from observation to synthesis of novel compounds -comes from Maya blue (MB), one of the oldest synthetic pigments. Seen in Central American wall paintings and sculptures from the 8th to the 15th c., MB exhibits remarkable durability and resilience to harsh environments (Figure 1D). MB results from boiling a clay (palygorskite, sepiolite) in the presence of an organic dye (indigo). Its chemical resilience has been attributed to the hydrogen-bonded organic-inorganic complex formed by indigo molecules in the channels of the clay structure. [14] Substitution of the indigo dye led to the design of a range of paleo-inspired hybrid pigments of different hues (Figure 1E-F). [15][16][17] The clay framework itself could be substituted by zeolites. [18] Multifunctional MB-based materials could be synthesized such as superhydrophobic MB and functionalized "organoclays". [19][20][21] In the three previous cases, the final goal is to reproduce the ancient materials or at least to transfer their environmental resilience into modern materials. Their study can lead to the design of innovative paleoinspired materials. Ancient artefacts can also be used as "analogues" to assess the long-term evolution of grow through the relict volcanic scoria and its interfacial zone, forming obstacles to microcrack propagation within the cementitious binding matrix [10] (C). D-F: mural containing Maya Blue paint (D), the methyl red@palygorskite pigment [15] (E), and optimized model structures for methyl red@palygorskite [16] (F). G-I: as-cast bronze zoomorphic ornament (Late Iron Age, ca. 300 BCE, La Fosse-Cotheret, France), detail of the central part corresponding to an animal head with a small muzzle and prominent eyes (G), synthetic as-cast Cu-Sn bronze (Sn 22.0 wt%), SEM-BS image of the δ phase (in white) within the (α+δ) eutectoid, surrounding the primary solidified α copper solid solution (in black, full image width: 190 µm; H), and representation of the octuple unit cell crystal structure of a γ Cu-Zn brass (416 atoms) on which is based the δ Cu-Sn structure (412 atoms, fcc lattice parameter a=1.798 nm; I). [99] J-L: copper-based slab fragment covered by a mineralized cellulosic textile, Nausharo, Pakistan, IV mill. BCE, musée du Quai Branly (J), FEG-SEM image of "artificially fossilized" zirconia paper [86] (K), and fabrication of hierarchical porous PVA from "artificial fossilization" of cellulose [100] (L). modern materials in a range of environments. For example, buried archaeological iron and glass are used to evaluate solutions for the long-term containment of used nuclear fuel. [22,23] Several organic molecules constitutive of plant or animal remains have shown remarkable resilience to long-term chemical degradation. Polymeric materials involved in the exo-and endoskeleton, tegument, appendages of animals and the structural parts of plants (based on chitin, cellulose, keratins, fibroins, collagen, sporopollenin) are particularly prone to exceptional preservation. [24][25][26] Beyond their intrinsic molecular and folding properties, these molecules are involved in supramolecular architectures that contribute to their longterm resilience. [27] DNA can remain amplifiable, although under a chemically altered form, after millennia, particularly in cold or humid micro-environments, or within specific compact bones. [START_REF] Pääbo | Proc. Ntl Acad. Sci[END_REF][START_REF] Donoghue | [END_REF][30][31] A range of other organic compounds or functional moieties where sufficiently well preserved to be used as markers of past biochemical activities, e.g. heme compounds, [START_REF] Greenwalt | Proc. Ntl Acad. Sci[END_REF][START_REF] Schweitzer | Proc. Ntl Acad. Sci[END_REF] quinones, [START_REF] Glass | Proc. Ntl Acad. Sci[END_REF] and several proteins. [START_REF] Kaup | [END_REF]36] Weak points in bioorganic molecules such as the amino acid side chains that are prone to long-term racemization or hydrolysis have been identified, [24] an essential milestone in the study of ancient proteomes. [37] Exceptional preservation of supposedly less stable molecules was also reported. Fatty acids, terpenic resins, or carbohydrates were identified in a variety of contexts from food-containing vessels to hydrophobic coatings in archaeological potsherds, adhesives, or ancient art objects. [25,38] Frequent fine-scale association with mineral phases suggests a general mechanism assuring long-term conservation of organic-inorganic complexes. Beside their invaluable help to understand the history of life on Earth and past cultural practices, these examples suggest routes to design organic or organometallic materials with exceptional resilience to the effect of time and to harsh environments. For instance, the protection of nucleic acids within ancient fossils was recently mimicked by encapsulating DNA into amorphous silica spheres, leading to nucleic acids withstanding high temperatures and aggressive oxic environments. [39] 3 Man-made materials with remarkable properties Past societies have developed skills and technologies to produce systems that address specific needs, while taking into account available raw materials, local conditions and knowledge. Invention and trial-and-error have led to cultural innovation processes and products optimized towards specific functions, and therefore materials with remarkable properties.

An extreme human chemical creativity has been exerted in producing pigments and dyes for colors where only rare stable compounds exist in nature. The search for alternatives to the expensive blue pigments lapis lazuli, indigo and azurite is particularly illustrative, and led to very early and innovative development of chemical syntheses: Egyptian, [40][41][42][START_REF] Riederer | Artists' pigments. A handbook of their history and characteristics[END_REF] Han [START_REF] Berke | [END_REF]45] and Maya blues, cobalt minerals and glasses (cobalt and cerulean blue, smalt), turquoise ivory, [46] and more recently the ferrocyanide Prussian Blue, phtalocyanins, up to the contemporary International Klein Blue. A particular level of "perfection" was attained in term of optical properties through inspiring early chemical syntheses that are of significant interest for current material chemistry. [41,[START_REF] Berke | [END_REF]46,47] A similarly appealing example is early Islamic lusters, that are universally renowned for their golden shine obtained from an optimization of surface plasmon resonance effects from copper and silver nanoparticles nucleated at the glaze surface. [48] Verger et al. studied the ZnAl 2 -x Cr x O 4 phases employed to color ceramics since the middle of the 19th century by the Sèvres manufacture. These pink to green spinel compounds were optimized for their optical response, as well as for their physicochemical stability during cooling in the melt glaze. [49,50] Improved refractory materials and assessment of the impact of high chromium loading in nuclear glass wastes could benefit from a better understanding of such dissolution / crystallization behavior of these chromium compounds. [50] The chemistry of chromium is indeed not the only case of a potentially highly toxic compounds documented by ancient uses. Archaeology demonstrates advanced chemistry based on heavy elements such as lead over more than four millennia. A range of Pb-based materials were found in ancient Egyptian burials, as paint and cosmetic formulations. In addition to well-known natural minerals such as black lead sulphide (from crushed galena PbS, still used today in traditional make-up), other chemical compounds, e.g. laurionite PbCl(OH) and phosgenite Pb 2 Cl 2 CO 3 , were identified. [51,52] Another typical case is the widespread use of arsenic instead of tin as alloying element in early bronzes (up to 5%wt). Arsenical bronzes have been widely used since the late Chalcolithic in the Middle East [START_REF] Mckerrell | Proc. Prehist. Soc[END_REF][START_REF] De Ryck | [END_REF] as well as in ancient Americas. [55] Beyond the undeniable toxicity and health impact of these compounds, this reveals an in-depth knowledge in the specific processing of these toxic materials. Paleo-inspired chemistry could therefore bring innovative concepts towards both a targeted use and processing of toxic substances.

Intriguingly, a range of phases normally identified as thermodynamically metastable or unstable are identified in abundance in ancient systems. A typical example is the δ phase of tin bronze (Figure 1G-I), one of the earliest alloys produced, widely used over five millennia. According to the Cu-Sn equilibrium phase diagram, the temperature existence domain of this phase, hard and brittle, is very limited (621-863 K). [START_REF] Hanson | Chill-cast tin bronzes[END_REF][START_REF] Saunders | [END_REF][58][59] Although identified as metastable at room temperature in low or high-tin bronzes, as-cast or annealed ancient artefacts prove this intermetallic cubic phase to withstand millennia. [START_REF] Chase | Ancient and historic metals: conservation and scientific research[END_REF][START_REF] Srinivasan | [END_REF] This discrepancy between full equilibrium and metallurgical steady state still remains to be understood. [59,62] A number of other metastable inorganic compounds were unexpectedly identified in ancient systems, such as the ferrous hydroxychloride β-Fe 2 (OH) 3 Cl in corroded archaeological iron artefacts, [63] plumbonacrite Pb 10 (CO 3 ) 6 O(OH) 6 in paints, [64] laurionite PbCl(OH) in cosmetics from Ancient Egypt, [51] or pseudobrookite Fe 2 TiO 5 --identified as the main source of the yellow color in Roman marbled sigillata slips. [65] In contrast to synthetized references obtained at a higher temperature, archaeological pseudobrookite is characterized by the presence of magnesium and aluminium atoms within the crystal structure, [START_REF] Sciau | [END_REF] which could account for their greater chemical stability and high reflective index. This formulation could thus inspire new pigment formulations. The particularly interesting metastable phase ε-Fe 2 O 3 was identified in the lustrous black glaze of ancient Jian Chinese potteries from the Song dynasty (960-1279 CE). [66] ε-Fe 2 O 3 is a rare ferric oxide polymorph, intermediate between hematite α-Fe 2 O 3 and maghemite γ-Fe 2 O 3 , which crystal structure has only been described in the late 90s. [67] At the glaze surface of Jian ceramics, surface crystals of ε-Fe 2 O 3 form a 2D dendritic network micrometric in size, [67] which is remarkable as only submicrometric ε-Fe 2 O 3 crystals could be synthesized so far in a laboratory environment. [67,68] Large ε-Fe 2 O 3 crystals show promise for fundamental solide state physics studies and for applications in new recording media and telecommunication owing to their magnetic properties. [68,69] A paleoinspired synthesis of ε-Fe 2 O 3 could be proposed based on processing a high iron containing glass at elevated temperature in a reducing atmosphere. [66] 4 Materials produced with scarce resources Archaeology as ethnology provide numerous examples of ingenious adaptation to specific environments and constraints, including in the context of limited energy resources. In an essay, Molles & Flonneau described the creativity deployed to circumvent the oil shortage during WWII. [START_REF] Molles | La fin du pétrole: histoire de la pénurie sous l'Occupation [The end of oil: history of the shortage under the Occupation[END_REF] Similarly, ancient technologies may inspire sustainable modern practices, as well as system-level solutions locally adapted to problems.

Archaeology reveals reuse and recycling strategies applied to a range of materials: glass, metals, construction materials, etc. [START_REF] Bray | [END_REF][START_REF] Schiffer | Formation processes of the archaeological record[END_REF] Past societies developed advanced life cycle management of materials that can be regarded as early "design-for-recycling". Ancient Roman builders used recycled construction materials (e.g. brick or terra cotta fragments) to enhance concrete, opus caementicium (from Latin opus -wall, caementa -aggregate). [START_REF] Malacrino | Constructing the ancient world: Architectural techniques of the Greeks and Romans[END_REF] This was significantly more economical than squared stone and provided opus caementicium with improved static capacity. The embodied energy of ancient Roman cement formula is significantly lower to that of ordinary Portland cement, and could lead to more environmentally-friendly construction materials. [10,[START_REF] Degryse | [END_REF] Steel, aluminum and cement, three major modern construction materials, account for 47% of industrial CO 2 emissions globally. [START_REF] Allwood | Sustainable Materials Without the Hot Air: Making Buildings, Vehicles and Products Efficiently and with Less New Material[END_REF] Opportunities across the life cycle of these materials exist to reduce the environmental footprint of buildings and infrastructure. The resulting production of new material and demolition waste can take inspiration from ancient techniques to reduce material impact over the entire product life cycle. Recycling generally reduces the environmental impact of construction materials. However, this process is still being rediscovered. For instance, modern attempts to recycle concrete aggregate led to a decrease in the durability and strength of the new material. [START_REF] Pellegrino | Sustainability Improvements in the Concrete Industry: Use of Recycled Materials for Structural Concrete Production[END_REF] Numerous other examples of soft physical and chemical manufacturing processes are provided by archaeological materials. In ancient worlds, many metallic artefacts were produced via a process involving annealing and hammering. This thermo-mechanical process had three functions: shaping, improving mechanical properties, as well as in some cases modifying surface aspects such as in Damascus steel. [START_REF] Reibold | [END_REF]78] In this way, ancient production techniques may inform new processing methods for modern materials such as regarding the transposition of the damasked approach to copper for providing rich surface patterns. [START_REF] Gupta | Copper Interconnect Technology[END_REF] An insightful case of soft chemical conversion is the corrosion of copper to cuprite identified in a very early lost-wax cast from the Chalcolithic site of Mehrgarh. [START_REF] Thoury | [END_REF] Preservation of a submicrometric eutectic structure is observed over centimeters, while about 39% of initial copper atoms left the original copper metallic structure during oxidation. [START_REF] Thoury | [END_REF] Long-term pseudomorphic conversion of organic compounds is also often observed. Fossilization is the chemical transformation of an original material in organic imprints or pseudomorph minerals that retains the morphology of the original material. Typical pseudomorph minerals are apatites, pyrite, clay minerals, calcite, and silica (see Briggs [81] and references therein). Exceptional preservation of soft tissues through authigenic mineralization, e.g. preservation of the morphology of muscle fibers, [82] can be observed up to a mineral grain size of a few tens of nanometers. [81] In archaeological sites, organic matter such as textile, leather, or other biological tissues sometimes "mineralize" in contact with iron or copper-based objects while preserving their microstructure at a scale that allows identifying the animal or the plant of origin, yarn manufacturing methods, or weaving techniques. [83] (Figure 1J). Study of ancient cosmetic treatments led to the identification of an interesting reaction product of archaeological wool with keratinous fibers. Nanoparticles of galena (PbS) form from cleavage of disulfide bridges in keratin, with a local ordering controlled by the organic matrix. [84] This offers an elegant synthesis route to the organically-templated nucleation, growth, and mesotexturation of PbS nanoparticles. [52] Similarly, Spadavecchia et al. observed the collagen-aided formation of Au nanoparticules in ancient gold-plated ivories. [85] Reproduction of fossilization and mineralization processes at increased speed would allow the templated production of mineral structures complex in shape at potentially nanometric scales, in a sort of "chimie douce" nano-investment casting. Several successful attempts were carried out in this direction. Huang et al. report the nanoreplication of cellulosic fibers in titania (TiO 2 ) by mimicking their permineralization after a functionalization of their surface comparable to that possibly involved in fossilization (Figure 1K-L). [86,87] Mizutani et al. synthesized porous titania, alumina, and zirconia ceramic woods using a similar approach of "artificial" or "synthetic" fossilization. [88] 5 Towards new paleo-inspired material design and processing?

In addition to the traditional strategy that consists in identifying new physicochemical behavior in pure materials and optimizing their use in new systems, this review suggests that harvesting physicochemical properties from paleontological or archaeological systems can provide remarkable solutions. Several key generic features of ancient materials have been or could be further exploited in modern ones. Many durable ancient materials consist in inorganic matrix incorporating organic molecules, e.g. exceptionally-preserved organics in fossil remains, alumina-supported lake pigments, or mineralized textiles. The chemistry of adjacent inorganic surfaces may play a lead role in stabilizing organic molecules. Even in primarily organic systems, long-term ageing appears to be driven by host-guest interactions. For instance, fading of Prussian Blue (used as dye in paintings, watercolors and photography) upon anoxia or intense illumination is significantly modified by the redox interaction with the medium in which it is dispersed. [89] Many ancient materials are impure and built upon a multiscale organization, which may contribute to impeding the emergence of general failure mechanisms thereby further increasing their resilience. Material heterogeneity creates multiple diverse chemical micro-environments (atmosphere, percolating fluids, pressure, temperature) that could allow investigating the link between local microstructure and reactivity. [90] This solid-state combinatorial probing of material properties agrees well with modern developments in high-throughput material sciences. [91,92] Retro-engineering can be considerably facilitated by access to written or oral ethnological evidence. [START_REF] Wisner | Anthropotechnologie : vers un monde industriel pluricentrique[END_REF] However, in many cases, synthesis has to be reinvented as knowledge has been lost. Lessons can be learned both from the study of aged materials and of ageing processes themselves. Modelling of ancient materials opens a promising way to characterize and predict new structures and properties but is still in its infancy. [START_REF] Bellot-Gurlet | Neff in Nanoscience and Cultural Heritage[END_REF] The fundamental interest of the paleo-inspired approach rests in the "bottom-up" process of selecting systems in the archaeological and paleontological record that already have demonstrated properties of interest (Figure 2). Ancient solutions have often been developed as a whole in integrated multifunctional systems Figure 2: The paleo-inspired chemistry approach. A thorough understanding of ancient systems (material and functional aspects) allows application of their transformation processes or of specific physicochemical properties to new materials and devices. Long-term alteration and ageing conducts from raw materials 1, to an elaborated system 2 (for anthropic systems), and to their current transformed state 3.

that synergistically connects materials, material interfaces, and functions. For instance, Maya Blue "combines the color of the organic pigment and the resistance of the inorganic host, [and is] a synergic material, with properties and performance well beyond those of a simple mixture of its components". [START_REF] Sanchez | [END_REF]96] Art materials may have been optimized jointly for a range of functionalities such as optical reflectance, rheology, chemical compatibility, and durability (see for instance Viguerie et al. [97] ). Historical process optimization and taphonomy filtering (literally by the "laws of death", which govern material behavior in archaeological and paleontological burial settings) regard the systems in a holistic manner. This goes along with the vision by P. Yang & J.-M.

Tarascon who emphasize on whole system optimization and interface design in materials science towards functional properties and applications, rather than "revolv[ing] around single material component". [1] As for bio-inspiration, paleo-inspiration provides an additional "point of view" [98] that adds up to the toolbox of the material scientist, built on the considerable body of knowledge that can be extracted from the history and behavior of ancient systems.

Summary and Outlook

Ancient and historical systems are promising sources of inspiration. Systems studied in archaeology, in paleontology, and in cultural heritage are observed a posteriori, after processes of natural and/or cultural selection. [7] Systems that have resisted this filtering exhibit enhanced resilience capacities. A better understanding of their intrinsic properties may both suggest new materials and new route of synthesis to existing ones. Contrarily to pure synthetic materials, ancient systems are often very heterogeneous in chemical composition and morphology. Even the purest ancient compounds generally contain a range of defects and trace elements that may be unequally distributed in the material and often play a lead role in their physicochemical behavior.

There is therefore a great interest to increase our level of knowledge on the detailed multi-scale properties of ancient systems, to develop strategies to model their behavior taking into account their complexity, and to mimic the effects of selection processes towards the generation of novel materials and devices

Figure 1 :

 1 Figure 1: Examples of paleo-inspiration. A-C: the Markets of Trajan constructed in the early 1st c. CE in Rome (credits: M. Vitti; A), mortar of the Great Hall of the Trajan's Markets, interfacial zone along scoria perimeter [10] (B), and authigenic fibrous and platey strätlingite Ca 2 Al 2 (SiO 2 )(OH) 10 • 2.5(H 2 O) crystals, that

Acknowledgments

We are particularly grateful to Jean-Paul Itié (Synchrotron SOLEIL) and Mathieu Thoury (IPANEMA) for discussions regarding this work. LB acknowledges support from Région Île-de-France / DIM Matériaux anciens et patrimoniaux, and the European Commission programs IPERION CH and E-RIHS PP (GA. 654028 and 739503). CG acknowledges the Swiss National Science Foundation for her professorship grant (n. 138986).

We thank Christophe Moulherat (musée du quai Branly -Jacques Chirac) for access to the mineralized textile from Nausharo, and Marta Bellato (IPANEMA) for the photograph of the textile. AM thanks Linda M. Seymour, Marc Walton, Heather Lechtman, Marco Nicola, Giacomo Chiari, John Ochsendorf, and Mastro Gilberto Quarneti for fruitful discussions. We are indebted to Jianguo Huang (Zhejiang University, Hangzhou), Roberto Giustetto (Univ. Torino), Marie D. Jackson (Univ. Utah), and Toyoki Kunitake for providing high-resolution images of their work.