Julien Raitif

Jean-Marc Roussel

Maxime Olmos

Christophe Piscart

Manuel Plantegenest

Assessing spatial deposition of aquatic subsidies by insects emerging from agricultural streams

Keywords: winged stream insects, agroecosystems, emergence, resource pulse, dry mass

The role of winged aquatic insects that emerge from streams and subsidize terrestrial ecosystems has been demonstrated for natural forest landscapes, but almost no information is available for intensive agricultural landscapes. This study is the first to estimate aquatic subsidies provided by flying insects that emerge from streams and land on cropland. We investigated three major groups of aquatic insects  Trichoptera, Ephemeroptera and Chironomidae (Diptera)  that emerged from 12 third-order temperate, agricultural streams.

We simultaneously monitored their emergence using floating traps and their terrestrial dispersal using passive interception traps. We estimated that the annual aquatic emerging dry mass (DM) of these groups varied from 1.4-7.5 g m -2 yr -1 , depending on the stream. We used a Bayesian approach to estimate parameters of the terrestrial dispersal function of each group.

We combined emerging DM and the dispersal parameters to estimate how terrestrial deposition of aquatic insect DM varied with increasing distance from streams. The results highlighted that emerging DM and dispersal to land could be higher in intensive agricultural landscapes than that previously described in natural settings. We estimated that 12.5 kg ha -1 yr -1 of winged aquatic insect DM fell to the ground 0-10 m from stream edges, composed mainly of Ephemeroptera and Trichoptera. We also estimated that 2.2 kg DM ha -1 yr -1 fell 10-50 m from the stream, especially small-bodied species of Chironomidae, throughout the year, except for the coldest weeks of winter. By influencing aquatic insect communities that emerge from streams, intensive agricultural practices change the magnitude and spatial extent of aquatic subsidy deposition on land. Implications for terrestrial food webs and ecosystem services provided to agriculture are discussed.

Introduction

Connections between adjacent ecosystems have attracted ecologists' attention in recent decades due to their importance in maintaining biodiversity in terrestrial and aquatic landscapes. Energy and matter that cross ecosystem boundaries, referred to as allochthonous inputs or subsidies, ultimately fuel food webs in the receiving ecosystem and influence its functioning (Polis et al. 1997). This phenomenon has been intensively investigated between aquatic and terrestrial ecosystems, likely because interconnections between land and water are common across the planet. Polis et al. (1997) listed several processes involved in the transport of subsidies across land-water ecotones, including physical vectors such as wind and water flow, or biotic vectors such as movement of prey and consumers. Focusing on the flow of invertebrate prey between stream and forest ecosystems, [START_REF] Nakano | Reciprocal subsidies: Dynamic interdependence between terrestrial and aquatic food webs[END_REF] demonstrated how two adjacent ecosystems could benefit from the alternating seasonal contrast between in situ prey availability and allochthonous prey supply. The biomass of aquatic subsidies to land is generally lower than that of terrestrial subsidies to water, but their average contributions to receiving food webs can be equivalent (Bartels et al. 2012). For instance, several studies in the literature highlight the presence of aquatic prey in the diets of birds [START_REF] Nakano | Reciprocal subsidies: Dynamic interdependence between terrestrial and aquatic food webs[END_REF], lizards [START_REF] Sabo | River-watershed exchange : effects of riverine subsidies on riparian lizards and their terrestrial prey[END_REF], bats [START_REF] Hagen | A landscape perspective on bat foraging ecology along rivers: does channel confinement and insect availability influence the response of bats to aquatic resources in riverine landscapes?[END_REF] or spiders [START_REF] Hoekman | Reducing allochthonous resources in a subarctic grassland alters arthropod food webs via predator diet and density[END_REF]. Aquatic insect prey contain physiologically essential fatty acids and provide critical resources for both stream and riparian consumers [START_REF] Twining | Aquatic and terrestrial resources are not nutritionally reciprocal for consumers[END_REF]).

As adults, many winged aquatic insects disperse to riparian ecosystems to mate (e.g. for Chironomidae, Armitage et al. 1995), and a small percentage ultimately return to the water, especially females for oviposition [START_REF] Baxter | Macroinvertebrate Drift, Adult Insect Emergence and Oviposition[END_REF]. Previous studies have estimated that less than 5% of total emerging biomass ultimately returns to the stream [START_REF] Jackson | Secondary Production, Emergence, and Export of Aquatic Insects of a Sonoran Desert Stream[END_REF], suggesting that most of it enters terrestrial food webs. [START_REF] Dreyer | Quantifying aquatic insect deposition from lake to land[END_REF] estimated that up to 100 kg ha -1 yr -1 of dry mass (DM) of midges in subarctic lakes fell 0-50 m from the shoreline. Similarly, [START_REF] Walters | Holy flux: spatial and temporal variation in massive pulses of emerging insect biomass from western U.S. rivers[END_REF] found that stonefly emergence in the most productive western USA streams resulted in a mean annual export of 10 g of carbon per m of streambank to riparian ecosystems. In a review of the spatial dispersal of winged stream insects, [START_REF] Muehlbauer | How wide is a stream? Spatial extent of the potential "stream signature" in terrestrial food webs using meta-analysis[END_REF] showed that among the aquatic insects that emerge (i.e. Ephemeroptera, Plecoptera, Trichoptera and Diptera), some can disperse up to 50 m or more from streams. However, most recent studies of adult stream insects have been conducted in natural settings (i.e. forest streams), but rarely on streams highly impacted by human activity (but see [START_REF] Carlson | Strong land-use effects on the dispersal patterns of adult stream insects: implications for transfers of aquatic subsidies to terrestrial consumers[END_REF][START_REF] Raitif | Seasonal and spatial variations of stream insect emergence in an intensive agricultural landscape[END_REF].

Several factors can explain why dispersal of winged adult stream insects to land differs between agricultural landscapes and natural ecosystems [START_REF] Raitif | From stream to land: Ecosystem services provided by stream insects to agriculture[END_REF]. First, intensive agricultural streams can be highly productive, and their annual flow of emerging insects is among the highest recorded to date (reviewed in [START_REF] Raitif | Seasonal and spatial variations of stream insect emergence in an intensive agricultural landscape[END_REF]. Second, agricultural intensification profoundly changes aquatic insect communities. The decrease in larger and more sensitive aquatic insects (Ephemeroptera, Plecoptera and Trichoptera) in favor of smallbodied taxa (Diptera, especially Chironomidae) in agricultural streams [START_REF] Greenwood | Influence of hydrological regime and land cover on traits and potential export capacity of adult aquatic insects from river channels[END_REF]Stenroth et al. 2015) may change the distance to which emerging aquatic insect communities disperse. Third, once emerged, winged stream insects experience environmental conditions that may promote their dispersal toward agricultural land. Notably, the lack of riparian vegetation and exposure to higher wind speeds could lead to farther inland dispersal than that in forested landscapes [START_REF] Delettre | Dispersal of adult aquatic Chironomidae (Diptera) in agricultural landscapes[END_REF][START_REF] Carlson | Strong land-use effects on the dispersal patterns of adult stream insects: implications for transfers of aquatic subsidies to terrestrial consumers[END_REF].

In this study, we sought to provide the first estimates of the spatial deposition of aquatic subsidies through the dispersal of winged adult insects emerging from streams in intensive agricultural landscapes. We simultaneously monitored the flow of emerging aquatic insects using floating traps and their terrestrial dispersal using passive interception (i.e. "sticky") traps along 12 agricultural streams in western France. Because we expected different dispersal distances and seasonal contrast in the phenology of emergence, we considered three dominant groups (Ephemeroptera, Trichoptera and Chironomidae) separately to estimate annual budgets. Our objectives were to (i) assess the pattern of inland dispersal of adult stream insects and (ii) estimate how the biomass of aquatic flying insects on agricultural land decreases with increasing distance from the stream. We hypothesized that in intensive agricultural landscapes, both the amount and distance of aquatic insect deposition would be larger than those previously reported in natural landscapes. We also hypothesized that the taxonomic composition of the emerging communities would influence the extent of the terrestrial deposition of aquatic subsidies.

Materials & Methods

Site selection

The study was conducted in Brittany, France. The climate is temperate, with a mean annual temperature of 10.5-12.5°C and cumulative annual rainfall of ca. 700 mm. Intensive farming dominates the landscape, involving large amounts of fertilizers and pesticides and significant modification of the landscape. In 8 watersheds, we selected sites on 12 third-order perennial streams [START_REF] Strahler | Hypsometric (area-altitude) analysis of erosional topography[END_REF], with a mean width of 6 m, that flowed along crop fields (winter wheat or barley). A grass strip (5-12 m wide) in each field separated the stream from the crop field (Figure 1). In selected sites, streams are greatly polluted by agriculture practices. In a companion study, [START_REF] Raitif | From stream to land: Ecosystem services provided by stream insects to agriculture[END_REF] highlighted for all sites high concentrations of nitrates through the year (mean = 20.4 mg NO 3 -L -1 ± 6.6). Each watershed's water chemistry and landscape characteristics are described in Supplementary Material S1 and further detailed in [START_REF] Raitif | From stream to land: Ecosystem services provided by stream insects to agriculture[END_REF].

Estimating the amount of aquatic insect deposition on land 2.2.1 Sampling period

The study was conducted from spring 2016 to winter 2017 (Table 1). Adult aquatic insects were trapped during 7-day periods. We targeted the main months of aquatic insect emergence in temperate latitudes (i.e. in spring and, to a lesser degree, in summer and early autumn).

Due to the risk of equipment damage, aquatic emergence and dispersal were assessed at only one site in winter (December 2017). We observed no emergence or dispersal then, which confirmed the results of [START_REF] Corbet | Temporal Patterns of Emergence in Aquatic Insects[END_REF], who observed negligible aquatic insect activity during the coldest period of the year (i.e. end of autumn to the end of winter). We collected 111 emergence samples, totaling 777 days of trapping (10% of the samples were damaged by extreme weather events or suspected vandalism). At the same time, 590 sticky traps were collected (3% of the samples were lost for the same reasons).

Emergence

At each site, we measured aquatic emergence by setting up two floating emergence tents (basal area = 1 m², Figure 1). Each tent was secured to the shoreline with ropes. One tent was set in a pool habitat of the river and the other in a riffle to consider the influence of aquatic habitat on aquatic insects. A plastic container was installed outside the peak of the tent to collect adult flying insects. It was filled with propylene glycol (ca. 20%) and water to preserve the insects. After collection, aquatic insects were kept in 70% alcohol. In the laboratory, a stereomicroscope was used to sort and count insects from three taxonomic groups:

Ephemeroptera, Trichoptera and Chironomidae. Other aquatic insects, especially Plecoptera and Megaloptera, usually emerge by crawling on land [START_REF] Hynes | Biology of Plecoptera[END_REF][START_REF] Elliott | British freshwater Megaloptera and Neuroptera: a key with ecological notes[END_REF].

Consequently, their emergence cannot be accurately assessed using floating emergence traps, and they were excluded from the analysis. Insects were dried at 60°C for at least 24 h and weighed to the nearest 0.2 mg (for more details on methods, see [START_REF] Raitif | Seasonal and spatial variations of stream insect emergence in an intensive agricultural landscape[END_REF].

We calculated mean emerging insect DM, expressed in g DM m -2 d -1 , at each site for each sampling date using data from the two emergence traps. Mean daily values obtained for each campaign were extrapolated forward and backward to adjacent days to fill temporal gaps between campaigns. Daily emergence was then summed to estimate cumulative annual emerging DM (g DM m -2 yr -1 ) at each site and for each taxonomic group (Ephemeroptera, Trichoptera and Chironomidae).

Dispersal to land

Sticky traps (Figure 1) were used to monitor terrestrial dispersal of winged stream insects.

They are simple to use in the field and are reported not to attract flying insects [START_REF] Smith | Building a better sticky trap: description of an easy-to-use trap and pole mount for quantifying the abundance of adult aquatic insects[END_REF]. Each trap was made from a sheet of transparent film (29.7×42 cm) to which we applied a non-drying, odorless and colorless adhesive (Tangle-trap TM ). The coated transparent sheets were attached to a transparent plastic panel and installed vertically on a pole 1 m above the ground. Each site contained two lines of five sticky traps: the first trap was located on the riverbank 1 m from the stream. The remaining traps were randomly and individually installed within four distances  2-7, 8-15, 16-30 and 31-50 m  to capture the dispersal gradient from the stream edge to the crops (Figure 1). We chose a maximum distance of 50 m from the edge since most adult aquatic insects, except for Chironomidae, usually disperse less than 50 m from their emergence site [START_REF] Muehlbauer | How wide is a stream? Spatial extent of the potential "stream signature" in terrestrial food webs using meta-analysis[END_REF]. We also wanted to avoid the potential influence of other aquatic ecosystems (permanent or temporary). For instance, ditches around crop fields provide habitats for aquatic insects [START_REF] Delettre | Dispersal of adult aquatic Chironomidae (Diptera) in agricultural landscapes[END_REF]. When collected, each sticky trap was detached, wrapped in plastic film and frozen at -20°C until the insects on it were counted in the laboratory. They were then sorted into three groups: Ephemeroptera, Trichoptera and Chironomidae. Like with the emergence traps, other aquatic insects were not considered due to their low contribution to the total abundance captured.

Data processing

We assumed that data collected using the sticky traps were dispersal decay-function observations. Data consisted of the abundance of each taxonomic group (Ephemeroptera, Trichoptera and Chironomidae) for each site and sampling date at multiple distances from the stream. For all insect groups, count data showed overdispersion and, for Ephemeroptera and

Trichoptera, an excess of zero values (40% and 55%, respectively). We used a negative binomial distribution to accommodate overdispersion in the observed abundance of Chironomidae and a zero-inflated negative binomial distribution to accommodate the high frequency of zeros observed in abundances of Ephemeroptera and Trichoptera. When fewer than 100 individuals of a given taxonomic group had been captured during a given sampling campaign (all sites combined), the data for that group were discarded. Similarly, for a given site and campaign, when fewer than 6 individuals had been captured (all traps combined), the entire sample from this site was discarded. Consequently, we used dispersal data from sampling campaigns 1-5 for Chironomidae, 1-2 for Ephemeroptera and 2-4 for Trichoptera.

Few Chironomidae were caught during the 6 th campaign (late fall) on the sticky traps, but an abnormal dispersion pattern was observed: more individuals were caught as distance to stream increased. [START_REF] Raitif | From stream to land: Ecosystem services provided by stream insects to agriculture[END_REF] previously highlighted that emergence of stream insects, including Chironomidae, was almost inexistent at this time of year. We assumed that this dispersal was due to terrestrial sources of emergence [START_REF] Delettre | Terrestrial Chironomidae: contribution of local emergence to global aerial flow in a heterogeneous environment[END_REF], such as ephemeral puddle of waters or ditches nearby our study streams, and discarded the associated data from the analysis.

Models

Plotting the raw dispersal data revealed two distinct patterns: an exponential decrease in abundance with increasing distance [START_REF] Parent | Dispersal of adult aquatic insects in catchments of differing land use: Dispersal of adult aquatic insects[END_REF]) for Ephemeroptera and Trichoptera, but a different pattern for Chironomidae, previously described by [START_REF] Dreyer | Quantifying aquatic insect deposition from lake to land[END_REF], with an initial plateau or moderate decrease near the stream edge, followed by an exponential decrease.

Accordingly, a classic exponential decay model was fitted to Ephemeroptera and Trichoptera data (Eq. 1), while an alternative model inspired by [START_REF] Dreyer | Quantifying aquatic insect deposition from lake to land[END_REF] was fitted to Chironomidae data (Eq. 2) for each site (s) and date (t):

𝐴𝑏𝑢𝑛𝑑𝑎𝑛𝑐𝑒 𝑠,𝑡 = 𝑏 • 𝑒 -𝑎•𝑋 (Eq. 1) 𝐴𝑏𝑢𝑛𝑑𝑎𝑛𝑐𝑒 𝑠,𝑡 = 𝑏 𝑠,𝑡 • 𝑒 -𝑎 𝑠,𝑡 •𝑋 + 𝑑 • 𝑋 • 𝑒 -𝑐 𝑠,𝑡 •𝑋 (Eq. 2)
For both models, b is the abundance of insects at the stream edge (i.e. X = 0) and a is the slope of exponential decrease in abundance with increasing distance from the stream. For the alternative model (Eq. 2), parameters c and d determine the slope and the shape of the potential plateau with increasing distance from the stream. Several models were fitted to the data to assess whether the dispersal function depended on the site, the date or both (Table 2).

Parameter inference

No information was available to generate informative priors for parameters. We assessed the sensitivity of the models to different sets of weakl informative priors and hyperpriors distributions and values (Supp.Mat S5 for further details). Posterior estimates of total aquatic insect dry mass were not sensitive to the prior distributions and values tested and we therefore retained configuration V3 (Supp.Mat S5, table S5.1), commonly used in hierarchical models [START_REF] Gelman | Bayesian data analysis[END_REF], in the subsequent analysis.

Posterior distributions of parameters were estimated using Monte Carlo Markov Chain methods in the Rjags package of R software (www.Rproject.org). We ran three chains independently, with 600 000 iterations each. For each chain, the first 100 000 iterations were discarded. Posterior distributions were obtained by keeping 1 out of every 50 iterations, which yielded 10 000 iterations per chain.

Validation and model selection

To assess convergence, we used the Gelman-Rubin diagnostic [START_REF] Brooks | General Methods for Monitoring Convergence of Iterative Simulations[END_REF] in the R coda package. In addition, to check the ability of the model to replicate a posteriori data similar to those observed, we calculated Bayesian p-values from chi-square discrepancies tests [START_REF] Gelman | Bayesian data analysis[END_REF]. In this study, the prediction/observations couple were the abundance of individuals within each taxonomic group at various distances from stream.

Bayesian p-value should be close to 0.50 for good model, but in practice, p-value between 0.1 and 0.9 are accepted [START_REF] Royle | GLMs and Bayesian Analysis[END_REF]) and lack of fit is pinpoint when p-value ranged between 0.05 and 0.95 [START_REF] Conn | A guide to Bayesian model checking for ecologists[END_REF].

Alternative hierarchical models were compared using the Watanabe-Akaike information criterion (WAIC) [START_REF] Watanabe | A Widely Applicable Bayesian Information Criterion[END_REF]). The best model was the one with the lowest WAIC, and we considered that a model performed better than another when its WAIC was at least 5 points lower.

Calculating the deposition of dry mass on land

We estimated annual terrestrial deposition of aquatic insects with increasing distance from the stream edge by combining the decay function with the estimated annual DM of emerging insects at each site. We assumed that (i) aquatic insects dispersing from the stream and collected on a sticky trap would have fallen on the ground close to it, and (ii) the abundance of insects on a sticky is a good indicator of terrestrial deposition. For each taxonomic group, we used the dispersal model with the lowest WAIC and predicted the number of captures from 0-150 m from each stream using the Bayesian posterior distribution of parameters of the selected model. We then estimated the relative deposition rate with increasing distance from the stream by calculating the fitted area under the curve (AUC) divided by the total AUC (from 0-150 m). We then calculated the deposition rate for seven ranges of distance: 0-1, 1-5, 5-10, 10-20, 20-50, 50-100 and 100-150 m. We used the R pracma package [START_REF] Brochers | pracma: Practical Numerical Math Functions[END_REF] to calculate AUC using the trapezoidal rule.

Finally, we multiplied these deposition rates by total annual emerging DM to estimate the annual DM of aquatic insect deposition with increasing distance from a 6 m-wide stream for each site. The resulting deposition rates were combined for each distance from 0-100 m from the stream to obtain an average profile of the annual terrestrial deposition of DM of aquatic insects emerging from a third-order stream in an intensive agricultural landscape (in kg DM ha -1 yr -1 ).

Results

Aquatic insect emergence

In total, more than 64 000 insects were captured in emergence traps during the study, of which 91% were Chironomidae, 6% were Trichoptera and 3% were Ephemeroptera. As expected, due to their emergence behavior, Plecoptera were rarely captured (< 0.1%) and thus excluded from further analysis. Chironomidae emerged throughout the year, except in winter.

Trichoptera and Ephemeroptera emergence peaked in spring and then decreased in summer (see Supplementary Material S2 for detailed results for all campaigns). Trichoptera contributed the most to annual emerging DM, followed by Chironomidae and Ephemeroptera (2.1, 1.1 and 0.7 g DM m -2 yr 1 , respectively). Estimates of annual emerging DM ranged from 1.4-7.4 g DM m -2 yr -1 among sites, with a mean of 3.8 g DM m -2 yr -1 (Figure 2).

Dispersal of adult aquatic insects

Captures

We captured 416 783 insects on sticky traps during the study. More than 90% of them were terrestrial (Diptera, Hymenoptera, Coleoptera) and were thus discarded. Aquatic insects accounted for ca. 8% of total captures (32 406 insects), and 7% were Chironomidae, 0.1%

were Ephemeroptera and 0.2% were Trichoptera. Megaloptera were also captured (704 specimens) on sticky traps, but Plecoptera were extremely rare (< 0.01%). Because their emerging DM could not be estimated using the floating emergence traps, Plecoptera and Megaloptera were excluded from further analysis. Chironomidae dispersal was detected during all campaigns and peaked in April (campaign 1), accounting for nearly 50% of total captures (Figure 3). Ephemeroptera dispersed mainly in May (campaign 2) and April (67% and 19% of Ephemeroptera captures, respectively). Trichoptera captures peaked in May (campaign 2, 42% of captures) but remained abundant in June and early July (campaigns 3 and 4), accounting for 20% and 23% of captures, respectively. Total annual captures varied greatly among sites, ranging from 706-5125 for Chironomidae, 23-131 for Ephemeroptera and 19-298 for Trichoptera (Figure 3, Supplementary Material S3).

Dispersal functions

For Ephemeroptera and Trichoptera, the best model was an exponential decay model with parameters depending on Site only (Table 2). Mean P values for Trichoptera (0.29) and Ephemeroptera (0.37) confirmed that models fitted the data accurately (SuppMat S4). Plotting P values as a function of distance from the stream revealed that some of the best models fit poorly for distances greater than 20 m (ca. 7.5% and 6.5% of P values were less than 0.05 for Trichoptera and Ephemeroptera, Supplementary Material S4). The alternative model (Eq. 2)

best explained the dispersal of Chironomidae, with parameters depending on both Site and Date (Table 2, Supplementary Material S4). The mean P value of 0.50 (± 0.20) confirmed that the model fit the observed data accurately.

The abundance of Ephemeroptera decreased to 50% at a mean distance of 8 m from the edge (range: 3-25 m among sites) (Figure 4). It decreased to 10% at 35 m (10-78 m) and 1% at 86 m (27-130 m). For Trichoptera, the mean distances corresponding to 50%, 10% and 1% of abundance were 5 m (2-36 m among sites), 22 m (5-36 m) and 51 m (10-71 m), respectively (Figure 4). For Chironomidae, the mean distances corresponding to 50%, 10% and 1% of abundance were 25 m (6-34 m), 66 m (49-71 m) and 114 m (98-117 m), respectively (Figure 4).

Annual deposition of winged aquatic insect dry mass on land

Approximately 52% of the total aquatic DM fell 0-10 m from the stream, 40% from 10-50 m and 8% from 50-100 m (Figure 5). On average, 2.3 kg DM ha -1 yr -1 of Ephemeroptera, Trichoptera and Chironomidae fell to the ground on a 100 meters wide strip of land, ranging from 0.9-4.4 kg DM ha -1 yr -1 . The amount of total aquatic dry mass deposited varied greatly among the ranges of distance from the stream, with a mean of 12.5 kg DM ha -1 yr -1 from 0 to 10 m (range: 4.4-24.9 kg DM ha -1 yr -1 among streams). Similarly, 2.19 and 0.32 kg DM ha -1 yr -1 (range: 0.82-4.20 and 0.12-0.62 kg DM ha -1 yr -1 ) of aquatic insect DM was estimated to fall from 10-50 m and 50-100 m, respectively. Deposition of DM from 100-150 m was negligible (< 0.05 kg DM ha -1 yr -1 ).

Discussion

While dispersal of aquatic insects has been assessed for several decades (e.g. [START_REF] Williams | The Recolonization Mechanisms of Stream Benthos[END_REF][START_REF] Hershey | Stable Isotopes Resolve the Drift Paradox for Baetis Mayflies in an Arctic River[END_REF], inland dispersal and terrestrial deposition of winged aquatic insects emerging from streams are not well known. Because most studies of dispersal of adult aquatic insects (reviewed by [START_REF] Muehlbauer | How wide is a stream? Spatial extent of the potential "stream signature" in terrestrial food webs using meta-analysis[END_REF] were conducted in forested areas, information from intensive agricultural contexts is rare. In a companion study [START_REF] Raitif | Seasonal and spatial variations of stream insect emergence in an intensive agricultural landscape[END_REF], we showed that insect biomass emerging from streams in intensive agricultural landscapes was greater than most of those reported for more pristine systems. For Chironomidae, we highlighted the propensity of agricultural streams to produce and deliver large amounts of aquatic subsidies to surrounding terrestrial ecosystems [START_REF] Raitif | Seasonal and spatial variations of stream insect emergence in an intensive agricultural landscape[END_REF].

Notably, increasing agricultural pressure in a watershed, water pollution due to nitrate leaching after fertilizer application, alteration of stream banks and a decrease in riparian vegetation strongly promote the emergence of small aquatic dipterans such as Chironomidae.

Stenroth et al. ( 2015) confirmed that the proportion of agricultural land in the landscape positively correlates with the emergence of small aquatic insects, especially Chironomidae.

Conversely, [START_REF] Raitif | Seasonal and spatial variations of stream insect emergence in an intensive agricultural landscape[END_REF] highlighted that biomass of Ephemeroptera and Trichoptera emerging from water significantly decreased in streams strongly impacted by agriculture.

Chironomidae are frequently associated with farther terrestrial dispersal [START_REF] Muehlbauer | How wide is a stream? Spatial extent of the potential "stream signature" in terrestrial food webs using meta-analysis[END_REF], in particular due to their ability to be carried away by the wind because of their low individual mass [START_REF] Delettre | Dispersal of adult aquatic Chironomidae (Diptera) in agricultural landscapes[END_REF]. Consequently, by promoting shifts in assemblages of stream insect species, intensive agricultural practices could greatly alter the magnitude and spatial extent of aquatic subsidies delivered to land.

To our knowledge, the present study is the first to model inland dispersal of winged insects emerging from streams in an intensive agricultural context. Our results suggest that aquatic insects dispersed much farther than expected, based on previous observations of forest streams [START_REF] Muehlbauer | How wide is a stream? Spatial extent of the potential "stream signature" in terrestrial food webs using meta-analysis[END_REF]. Half of the emerging Trichoptera and Ephemeroptera dispersed farther than 5 and 8 m from the stream edge, respectively. This distance was observed to be only 1 m along forest streams [START_REF] Muehlbauer | How wide is a stream? Spatial extent of the potential "stream signature" in terrestrial food webs using meta-analysis[END_REF]. Similarly, half of the Chironomidae dispersed farther than 25 m from our agricultural streams, which is nearly twice the distance observed by [START_REF] Muehlbauer | How wide is a stream? Spatial extent of the potential "stream signature" in terrestrial food webs using meta-analysis[END_REF] along forest streams. Thus, according to Muehlbauer et al.'s definition, the "biological width" of a stream, as opposed to its hydrogeomorphic width, is broader in agricultural contexts than in forest contexts. The recent study of [START_REF] Carlson | Strong land-use effects on the dispersal patterns of adult stream insects: implications for transfers of aquatic subsidies to terrestrial consumers[END_REF] observed shorter dispersal distances of emerging insects from agricultural streams in Sweden than those we observed. Agriculture was less prominent in their study landscape, with a higher percentage of forest (49% ± 10%) than in our study (8% ± 9%), and much wider strips of riparian vegetation (26 ± 23 m). [START_REF] Delettre | Dispersal of adult aquatic Chironomidae (Diptera) in agricultural landscapes[END_REF] showed that riparian vegetation could act as a natural barrier that strongly restricts inland dispersal of Chironomidae that emerge from streams. Because adult Chironomidae [START_REF] Frouz | Spatial distribution of different life stages of one Dipteran community along hedgerow and field margin[END_REF] and other taxa (e.g. Trichoptera, [START_REF] Petersen | Emergence and lateral dispersal of adult Plecoptera and Trichoptera from Broadstone Stream[END_REF]) can take shelter in riparian habitats, agricultural intensification and alteration of riparian vegetation may modify inland dispersal of winged aquatic insects by increasing landscape permeability to aerial movement.

We observed between-site variations in dispersal distances for all groups of aquatic insects, suggesting that local environmental parameters influence dispersal. Riparian vegetation density was visually assessed by measuring channel openness [START_REF] Raitif | Seasonal and spatial variations of stream insect emergence in an intensive agricultural landscape[END_REF], which varied among stream channels (Supplementary Material S1). We calculated correlations between this proxy of riparian density/structure and dispersal results estimated for each taxonomic group, but none of them were strong or significant (results not shown). Accurately assessing the influence of riparian vegetation on aquatic insect dispersal will require more detailed studies that examine the density, structure and diversity (i.e. species composition) of riparian vegetation over space and time (i.e. seasons). Regional or local weather conditions may also have an influence. For instance, most Chironomidae are passive dispersers that are frequently blown away from streams by the wind. Conversely, [START_REF] Sabo | A network theory for resource exchange between rivers and their watersheds[END_REF] showed that their dispersal could be restricted by wind blowing along the stream channel. A similar reduction in Chironomidae dispersal was observed along steeper banks [START_REF] Carlson | Strong land-use effects on the dispersal patterns of adult stream insects: implications for transfers of aquatic subsidies to terrestrial consumers[END_REF]. Finally, species composition of the adult Chironomidae community is likely to change throughout the year, mainly due to changes in water temperature. Among Chironomidae, the Orthocladiinae subfamily can emerge in spring and autumn, while the Chironominae and Tanyponinae subfamilies can emerge in summer [START_REF] Eggermont | The chironomid-temperature relationship: expression in nature and palaeoenvironmental implications[END_REF]. Changes in the community can thus result in changes in dispersal distances, which would be amplified by differences in mean body and wing sizes among subfamilies [START_REF] Delettre | Chironomid wing length, dispersal ability and habitat predictability[END_REF].

The mean estimated annual deposition of aquatic insects was 12.5 kg DM ha -1 yr -1 from 0-10 m from the stream, reaching 24.9 kg DM ha -1 yr -1 along the most productive stream. A large amount of aquatic insect biomass fell 10-50 m from the streams (mean: 2.2 kg DM ha -1 yr -1 , range: 0.8-4.2), in crop fields in the sites of this study. In addition, we observed many Megaloptera (Sialis lutaria) on the sticky traps located near the streams, but none on emergence traps. Consequently, we could not calculate their resulting terrestrial deposition. It is thus likely that we underestimated the terrestrial deposition of aquatic insect DM. These results highlight how streams can subsidize agroecosystems greatly through aerial dispersal and inland deposition of winged adult aquatic insects.

Insect communities that emerge from temperate streams provide a variety of subsidies to agroecosystems. Large-bodied taxa (e.g. Trichoptera, Ephemeroptera and Megaloptera) provide great amount of aquatic-derived biomass to a narrow strip of land along streams within a short period of time (spring and early summer). The spatial distribution and temporal availability of resources influence ecosystem functioning greatly [START_REF] Polis | Food Web Complexity and Community Dynamics[END_REF], especially through resource pulses, which have been described for many ecosystems [START_REF] Noy-Meir | Desert Ecosystems: Environment and Producers[END_REF], Connell 1978[START_REF] Nakano | Reciprocal subsidies: Dynamic interdependence between terrestrial and aquatic food webs[END_REF]. A short period of substantial emergence of insects has been shown to fuel the community of soil decomposers [START_REF] Lovett | Carbon and nitrogen mineralization from decomposing gypsy moth frass[END_REF] [START_REF] Riechert | Spiders as Biological Control Agents[END_REF]birds, Maas et al. 2013). Our results suggest that these aquatic subsidies could drive the spillover of several terrestrial predators from areas near streams to crops at different times of year. This effect has been shown to be significant in sustaining ecosystem services, such as biocontrol, in terrestrial agricultural landscapes [START_REF] Tscharntke | The landscape context of trophic interactions: insect spillover across the crop-noncrop interface[END_REF].

Conclusion

Based on a unique dataset, our results indicate that aquatic insect deposition on land could provide abundant, diverse and high-quality resources to terrestrial predators over a broad temporal and spatial scale. In an agriculture landscape in which streams run along crop fields, this deposition of aquatic DM could complement several ecosystem services, such as soil fertilization with labile organic matter that stimulates microbial soil activity, or biological control by supplying alternative prey to sustain natural enemy populations. From an agroecological perspective, a complex and abundant insect community is necessary in agricultural landscapes. The involvement of aquatic subsidies in providing ecosystem services to agriculture is a new topic of research that requires further study.

Figure 1 .

 1 Figure 1. Photographs of (a) sticky traps set up from the streambank to a cereal field and across the grass strip, (b) sticky traps lined up perpendicular to the stream and (c) an emergence tent set up in the stream.

Figure 2 .

 2 Figure 2. Estimate of annual emerging dry mass (in g m -2) of aquatic insects at each site. The estimate for the Ormal site is missing because one sampling session (in autumn) could not be performed due to farm operations.

Figure 3 .

 3 Figure 3. Log-transformed abundance of insects of three taxonomic groups captured on sticky traps at each site (sum of all dates and distances from the stream)

  Figure 1

  or the activity of a diverse macroarthropod community (e.g.Carabidae and Staphylinidae, Yang 2006). Moreover, stream-derived subsidies in agricultural landscapes contain abundant small-bodied dipteran taxa (especially Chironomidae) that disperse far from streams nearly all year round (except in the middle of winter), which diversifies the prey available to terrestrial consumers. Recently,[START_REF] Twining | Aquatic and terrestrial resources are not nutritionally reciprocal for consumers[END_REF] demonstrated that aquatic insects supply terrestrial ecosystems with essential amino and fatty acids. By entering terrestrial food webs in early spring and late autumn, when terrestrial secondary production is low, with a diverse prey community of high nutritional quality, aquatic subsidies may function as a resource pulse and sustain multiple communities of terrestrial predators near streams[START_REF] Larsen | Resource subsidies between stream and terrestrial ecosystems under global change[END_REF]. Finally, several terrestrial predators that feed on aquatic insects help to regulate crop pests at different times of the year (e.g. spiders, Riechert and Lockley

Table 1 .

 1 Sampling campaigns of aquatic insect emergence and dispersal

	Campaign Emergence	Dispersal
	1	-	April 25 to May 4 (2016)
	2	May 17 to 26 (2016)	May 17 to 26
	3	June 6 to 15	June 6 to 15
	4	June 27 to July 6	June 27 to July 6
	5	September 12 to 21	September 12 to 21
	6	November 28 to December 5	November 28 to December 5
	7	February 27 to March 9 (2017)	-

Table 2 .

 2 Results of model evaluation. Ephemeroptera and Trichoptera models were exponential decay models with increasing distance from the stream. The Chironomidae model was an alternate exponential model. Bold text indicates the results of the best models (i.e. lowest Watanabe-Akaike information criterion or WAIC).

	Taxon	Hierarchy	WAIC
		level
	Ephemeroptera None	761
		Site	728
		Date	752
		Site & Date 740
	Trichoptera	None	913
		Site	886
		Date	905
		Site & Date 892
	Chironomidae None	5072
		Site	4949
		Date	4784
		Site & Date 4373

Acknowledgments

We thank those who contributed to the fieldwork, especially the farmers who allowed us to enter their properties to sample insects, and Océane Agator for her exhaustive work in the laboratory on invertebrate samples. This study received financial support from the EcoServ Metaprogram of the French National Institute for Agricultural Research (INRA) to JM Roussel and from the French Ministry for Research (Ph.D. grant, 2015-2018) to J Raitif.

Credit authorship contribution statement JMR, MP, JR conceived the study. JR conducted fieldwork and laboratory analysis. JR analysed data with contributions from MO and MP. JR wrote the manuscript with input and revision of all contributing authors.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Highlights  We show that aquatic insects dispersed farther in agricultural than forest streams  12.5 kg ha -1 yr -1 of winged aquatic insect drymass fell at 0-10 m from stream  Ephemeroptera and Trichoptera are dominant at the stream vicinity  50% of emerging Chironomidae dispersed farther than 25 m inland  Such aquatic insect deposition on land could influence the terrestrial food web


Roland Dreyfus

Quentin Boehler

Bradley J Nelson

A Simulation Framework for Magnetic Continuum Robots

Keywords: Surgical Robotics: Steerable Catheters/Needles, Simulation and Animation, Modeling, Control, and Learning for Soft Robots

Remote magnetic navigation is a technology used to robotically steer magnetic medical instruments, such as magnetic catheters and guidewires, for minimally invasive surgery. The ability to model and simulate the behavior of these magnetic instruments in complex anatomies is important for their clinical use in many ways. Simulation frameworks can improve their design, characterization, and automatic control capabilities, as well as provide training simulators for physicians. In this work we introduce a new simulation framework that accounts for both magnetic actuation and interactions forces with meshed collision models. The simulations are validated experimentally in planar rigid models using a pre-clinical electromagnetic navigation system. We also demonstrate the use of our framework to build training simulators for two endovascular navigation tasks including the exploration of the aortic arch and the internal carotid artery.

I. INTRODUCTION

R EMOTE magnetic navigation (RMN) is a technology in which magnetic fields are used to wirelessly navigate devices containing magnetic material [START_REF] Abbott | Magnetic Methods in Robotics[END_REF]. Magnetic continuum robots (m-CRs) actuated by RMN, such as magnetic catheters and guidewires, are of increasing interest for several minimally invasive surgeries including cardiac ablations [START_REF] Bradfield | Catheter ablation utilizing remote magnetic navigation: a review of applications and outcomes[END_REF] and neurovascular interventions [START_REF] Dabus | Neuroendovascular magnetic navigation: clinical experience in ten patients[END_REF]. An m-CR is composed of permanent magnets [START_REF] Edelmann | Magnetic control of continuum devices[END_REF] or magnetic particles [START_REF] Kim | Telerobotic neurovascular interventions with magnetic manipulation[END_REF], [START_REF] Zhang | Design and characteristics of 3d magnetically steerable guidewire system for minimally invasive surgery[END_REF] embedded along a flexible body in which deflection is induced by the torques produced on the magnets by externally generated magnetic fields. These magnetic fields can be generated with an electromagnetic navigation system (eMNS) [START_REF] Charreyron | Modeling electromagnetic navigation systems[END_REF]. This distal actuation allows an m-CR to generate tip forces while having a soft body, making it safe for interactions with human tissue.

The ability to model and simulate the behavior of minimally invasive flexible tools in complex anatomies is central for their clinical use [START_REF] Hoda | Navigation of guidewires and catheters in the body during intervention procedures: a review of computer-based models[END_REF]. Simulators are useful tools for characterizing and evaluating new instruments and for aiding in their design process [START_REF] Rahman | Simulation based patient-specific optimal catheter selection for right coronary angiography[END_REF]. When pre-or intraoperative anatomical data are available, simulators can also be used for the automatic control of the instrument [START_REF] Zhang | Motion control of cable-driven continuum catheter robot through contacts[END_REF], and for planning the procedure [START_REF] Hong | 3d path planning for flexible needle steering in neurosurgery[END_REF].

Manuscript received: February, 24, 2022; Revised May, 13, 2022; Accepted June, 13, 2022. This paper was recommended for publication by Editor Pietro Valdastri upon evaluation of the Associate Editor and Reviewers' comments. This work was supported by the Swiss National Science Foundation through grant number 200020B 185039, the ITC-InnoHK funding, and the ERC Advanced Grant 743217 Soft Micro Robotics (SOMBOT).

1 Multi-Scale Robotics Lab, ETH Zurich dreyfusr@ethz.ch Digital Object Identifier (DOI): see top of this page. The training of physicians can also be significantly improved by the use of realistic endovascular simulators [START_REF] See | Evidence for endovascular simulation training: A systematic review[END_REF].

The modeling and simulation of m-CRs received sustained research attention over the past fifteen years. Because of the different steering paradigms between magnetic and nonmagnetic instruments, the simulator must incorporate additional physical laws to deal with the behavior of soft and hard magnetic materials. Models are based on constant curvature [START_REF] Tunay | Modeling magnetic catheters in external fields[END_REF] and pseudo-rigid body modeling [START_REF] Venkiteswaran | A magnetically-steerable stenting catheter for minimally invasive cardiovascular interventions[END_REF], Cosserat rod theory [START_REF] Edelmann | Magnetic control of continuum devices[END_REF], and Euler-Bernoulli beam theory [START_REF] Le | Accurate modeling and positioning of a magnetically controlled catheter tip[END_REF]. Numerical tools have also been used to analyse singularities and unstable behaviors of m-CRs [START_REF] Peyron | Kinematic analysis of magnetic continuum robots using continuation method and bifurcation analysis[END_REF]. More recently, several efforts proposed the use of finite elements models [START_REF] Zhao | Mechanics of hard-magnetic soft materials[END_REF]- [START_REF] Zhou | Ferromagnetic soft catheter robots for minimally invasive bioprinting[END_REF], which includes the consideration of tip contact force in the context of cardiac catheters [START_REF] Wang | Magnetic soft continuum robots with contact forces[END_REF]. However, these investigations are limited by the absence or simplicity of the collision environment in which the magnetic instruments are simulated. The introduction of the Simulation Open Framework Architecture (SOFA) [START_REF] Faure | SOFA: A Multi-Model Framework for Interactive Physical Simulation[END_REF] and its BeamAdapter plugin [START_REF] Duriez | New approaches to catheter navigation for interventional radiology simulation[END_REF] constitutes a promising option to simulate m-CRs and their interaction forces with complex and soft anatomies. This framework has already been successfully used for the automatic control of guidewires in neurovascular applications [START_REF] Karstensen | Autonomous guidewire navigation in a two dimensional vascular phantom[END_REF], [START_REF] Behr | Deep reinforcement learning for the navigation of neurovascular catheters[END_REF], the design of patient-specific catheters in coronary angiography [START_REF] Rahman | Simulation based patient-specific optimal catheter selection for right coronary angiography[END_REF], and the development of training simulators for endovascular procedures [START_REF] Guo | A novel VR-based simulator for the interventional surgical catheter and guidewire cooperation[END_REF], [START_REF] Wei | FEM-based guide wire simulation and interaction for a minimally invasive vascular surgery training system[END_REF]. Though, these efforts are limited to applications using conventional, non-magnetically guided instruments.

In this work, we introduce a SOFA-based simulator that includes magnetic interactions to simulate the behavior of m-CRs in a variety of environments. We couple this simulator to a Robot Operating System (ROS) environment [START_REF] Quigley | ROS: an open-source Robot Operating System[END_REF] to include magnetic models of an eMNS that generates nonhomogeneous external magnetic fields [START_REF] Charreyron | Modeling electromagnetic navigation systems[END_REF]. We provide an experimental validation of our approach in planar rigid environments and show navigation tasks performed in simulated 3d anatomies.

II. SIMULATION FRAMEWORK

An overview of the simulation framework 1 is depicted in Fig. 1. The interface is realized with RViz and is composed of the models of the eMNS, the anatomical environment, and the m-CR.

A. Electromagnetic navigation system

The eMNS is modeled as a set of magnetic multipoles using the approach described in [START_REF] Petruska | Model-Based Calibration for Magnetic Manipulation[END_REF] where the currents i ∈ R nc in the n c coils composing the system are linearly mapped to the magnetic field b(p) ∈ R 3 at any position p within the calibrated volume of the system using an actuation matrix

A(p) ∈ R 3×nc so that b(p) = A(p) i (1)
The matrix A(p) sums the contribution of each electromagnet to the magnetic field as

b(p) = A 1 (p) • • • A j (p) • • • A nc (p)         i 1 . . . i j . . . i nc         (2)
A j (p) is the contribution of the j-th current i j to the magnetic field at p based on a magnetic multipole expansion presented in [START_REF] Petruska | Model-Based Calibration for Magnetic Manipulation[END_REF].

B. Magnetic continuum robot

The mechanical behavior of the m-CR is modelled with the open source SOFA simulation framework [START_REF] Faure | SOFA: A Multi-Model Framework for Interactive Physical Simulation[END_REF] combined with the BeamAdapter plugin [START_REF] Duriez | New approaches to catheter navigation for interventional radiology simulation[END_REF]. The framework uses a 1-dimensional FEM of the continuum robot based on Kirchhoff rod theory, where the robot is discretized into beam elements composed of n nodes. Contacts are solved with Lagrange multipliers upon collision detection.

C. Coupling the models

An m-CR is steered by remotely applying torques on the embedded magnets with the external magnetic field generated by the eMNS. The magnets are characterized by the magnetic moment m i at the i-th node of the discretized m-CR with i ∈ {1 . . . n}. The external magnetic field b(p i ) induces an external torque t i on the magnet that tends to reduce the offset angle between m i and b(p i ). The torque exerted on the node i is given by the relationship

t i = m i × b(p i ) (3)
as also depicted in the close-up Fig. 1. At every time step, the position p i of each magnet is extracted from the SOFA simulation and fed into the magnetic model ( 1), providing the magnetic field b(p i ). The external torque is then computed using (3) and applied on the corresponding node in the simulator.

D. User interface

ROS is used for multi-threading and to interface the simulation modules. The built-in visualization plugin RViz and a dedicated graphical user interface serves as a visual interface to the user. For all manual steering, a Sony PS4 DualShock Wireless-Controller is used. It allows the user to control the insertion and retraction of the m-CR, and the magnetic field.

III. EXPERIMENTAL VALIDATION

Our simulator is evaluated experimentally to validate the behaviour of the simulated robots compared to the real ones. In the experiment, we navigate the m-CR in different environments and record the magnetic field and advancer inputs provided by the user. The simulated m-CR is then calibrated based on a calibration sequence and navigated in open-loop in the simulated environments, using the recorded user inputs from the experiment. The m-CR behavior is compared qualitatively by comparing the overall behaviour and quantitatively by estimating the error in tip position and orientation. An overview of the experimental setup is shown in Fig. 3, and a block diagram of the system control during experiments and simulations in Fig. 4.

A. Electromagnetic navigation system

We use a system composed of n c = 3 parallel coils arranged on a triangular base (see Fig. 3). The input currents that result

B. Magnetic continuum robot

An m-CR composed of two segments with different rigidity and embedding three magnets is used for this experimental validation (see Fig. 2). The m-CR has an outer diameter (OD) of 1.5 mm (4.5 Fr). Insertion and retraction is performed by applying an axial force f adv on the proximal end. It is realized by coupling the m-CR to a remote controlled advancer unit, where the user controls the insertion speed v.

C. Environments

The instrument is navigated in planar, 4 mm high, rigid environments made from polyoxymethylene (POM) and poly(methyl methacrylate) (PMMA). The environments allow for simple experimental work and robust visual tracking of the m-CR tip. The m-CR can both move freely and collide with obstacles to adopt complex shapes (see Fig 5). The first environment has no obstacles and is used for calibration, the second environment is designed to resemble vasculature, and in the third environment, obstacles are freely arranged to provoke non-trivial situations. Each environment is centered around p 0 .

D. Visual tracking

Image feedback is provided with a Canon EOS 6D camera with a resolution of 1920 × 1080 pixels and is operated at 25 fps. The tip of the m-CR is equipped with a green and blue color marker. An image processing pipeline is used to extract the 2d tip position p tip,exp and orientation q tip,exp with respect to the environment. The video frames are converted into HSV color space to segment the color markers providing information on the markers positions, orientation, and distance from one another. To add robustness and avoid false detections, all detected markers that are too close or too far apart are discarded. All image processing steps are performed using OpenCV [START_REF] Bradski | The opencv library[END_REF].

E. Simulation

The m-CR model is composed of 7 nodes on the distal section and a node density of 1.15 cm -1 on the proximal section. The visual model is based on a 1d regular grid with 4.0 mm spacing. The simulation uses a time step of 20 ms and a coefficient of friction of 0.01. The 3d magnetic field of the eMNS is modelled using the method described in section II-A. The simulations were performed on an Intel i5-4590 3.30 Hz computer processing unit (CPU) with 7.7 GB of random access memory (RAM).

F. Magnetic continuum robot calibration

A calibration sequence is performed in the obstacle-free environment to tune the simulation parameters. The calibration sequence is depicted in Fig. 5 under Calibration. Parameter tuning is performed by first fixing the remanence of the magnets and m-CR geometry, followed by sweeping the Young's moduli of the proximal stiff segment and the distal flexible segment by hand. Once the m-CR model is calibrated, the same parameters are used in the collision environments. The parameters that define the mechanical properties of the m-CR resulting from the parameter tuning are summarized in Table I under Validation.

G. Comparing experiment and simulation

After calibrating the simulated m-CR, the recordings of the experimental user inputs are used to actuate the simulated m-CR in open-loop in the simulated environments. The tip pose (p tip,sim and q tip,sim ) is extracted from the simulation and compared to the tracked pose from the experiments by calculating the errors between the two (see Fig. 5). The simulation runs at 18 Hz and the recorded data has a sampling rate of 25 Hz. To synchronize data points, the data are resampled during postprocessing. The error in position is calculated by taking the Euclidean distance between points in the experiment and in the simulation at a given time. The angle error corresponds to the angle between the experimental and simulated tip pointing vectors. The position and orientation errors are evaluated during the entire navigation time T tot . The average position error e p and orientation error e q taken across all error points of an entire navigation range from 5.1 to 6.8 mm and from 3.8 to 7.2 degrees. The errors at critical waypoints such as bifurcations and target end-points are presented in Table II.

IV. APPLICATIONS

Our framework is used to build simulators for two realistic scenarios in endovascular interventions performed by neuroradiologists. The first scenario is the navigation in the aortic arch (AA), which is the gateway to the brain vessels in minimally invasive neurosurgery. The second is the exploration of the internal carotid artery (ICA), an intracranial vessel where aneurysms are commonly found [START_REF] Zada | Internal carotid artery aneurysms occurring at the origin of fetal variant posterior cerebral arteries: surgical and endovascular experience[END_REF].

We demonstrate simulated navigation tasks using twomagnet m-CR. The robots are composed of a magnet at the tip of a flexible distal section of Young's modulus E dist , and a stiffer proximal section of Young's modulus E prox (see Table I). The second magnet is placed at the junction between the two sections.

For each task, we record a first navigation performed by the user. These inputs are then replayed with different lengths of the distal flexible section in order to illustrate the influence of design parameters on the behavior of the robot (see Table I).

A. Aortic arch navigation

The results are illustrated in Fig. 6a. We use a type I AA model composed of the aorta and three supra-aortic vessels: the left subclavian artery (LSA), the left common carotid artery (LCC), and the brachiocephalic artery (BCA). This simulates a realistic task in which a catheter is placed in the AA or the supra-aortic vessels to perform roadmap and diagnostic angiographies by injecting a contrast agent through the catheter. We simulate a magnetic angiography catheter with a short, medium, and long distal section (see Table I). Magnets are 4 mm long with a remanence of 1.45 T, and with the same diameters as the robot. The catheter model is composed of 6 nodes on the distal section, and a node density of 0.6 cm -1 on the proximal section (variable inserted length). A visual model based on a 1d regular grid with 2.5 mm spacing is interpolated on the resulting nodes poses of the behavioral model. The simulation is run with a time step of 20 ms and a coefficient of friction of 0.02.

The figure illustrates navigation into the aorta and passing the tip into the BCA. The simulation captures different conformations of the flexible tip, when the catheter is shaped by the magnetic field and pushed further into the aorta. This includes the presence of inflexion points in the shape of the distal section as the latter becomes longer and collides with the aorta wall (see t = 15 s for the long tip).

B. Internal Carotid Artery exploration

The results are illustrated in Fig. 6b. We use a model of the ICA comprising a giant intracranial aneurysm and simulate a magnetic guidewire with a short, medium, and long distal section (see Table I). Magnets are 1 mm long with a remanence of 1.45 T and with the same diameters as the robot. The guidewire model is composed of 10 nodes on the distal section and a node density of 1.5 cm -1 on the proximal section. The visual model is based on a 1d regular grid with 0.3 mm spacing. The simulation uses a time step of 5 ms and a coefficient of friction of 0.3.

The different tools show different placement within the tortuous anatomy of the ICA depending on the tool design, which affect their contact on the vessel wall and the resulting friction forces. The short and long tip configuration show unfavourable behaviour such as kinking (Figure 6b Short tip) and buckling (Figure 6b Long Tip), which can be expected when instruments are excessively pushed while the distal tip is prevented from advancing [START_REF] Beppu | Localized kinking during deployment of a flow redirection lumen device (fred) could be due to excessive pushing[END_REF]. The aneurysm can ultimately be reached with the medium tip after 4 min of navigation (see right of Fig. 6b). In this configuration, the simulation clearly shows the accumulated elastic energy in the proximal section of the tool due to the friction of the distal part inserted into the ICA. This behavior is well-known by neuroradiologists. It leads to unstable elastic behavior that constitute one of the main challenges of the procedure.

V. DISCUSSION

The simulated m-CR showed similar behaviour to its physical counterpart used in our experiments. The average errors in position and angle in the different environments range from 5.1 to 6.8 mm and from 3.8 to 7.2 degrees, respectively. The errors can be attributed to experimental inaccuracies, timing sensitivity of the error measurement, and by the fact that the parameters were tuned by hand. Furthermore, errors can be caused by the general limitations of simulations where physical properties such as friction and material homogeneity are idealized and numerical inaccuracies can accumulate.

The results from the experimental section confirm that the simulated m-CRs behave similarly to real m-CRs, even in situations with collisions and multiple contact points.

In the present work, we did not consider soft tissue deformations due to the general high flexibility of m-CRs. However, when stiff non-magnetic instruments are passed through highly tortuous vessels, the vessels can undergo large non-linear deformations. Furthermore, in the presence of high magnetic field gradients, m-CRs with particularly high magnetic volumes and very high flexibility can be moved by magnetic forces. To further bridge the reality gap, we will enhance the simulator by adding deformable anatomy modelling, include a model for magnetic forces based on the equations shown in [START_REF] Kummer | Octomag: An electromagnetic system for 5-dof wireless micromanipulation[END_REF], and implement a stereo tracking system to perform model-matching in 3d anatomical environments.

We demonstrate that the simulator can be used to analyze the behaviour of m-CRs in simulated anatomical environments I). The magnetic field controlled by the user at the center of the eMNS is depicted by the yellow arrow.

and to perform parameter optimization, which has application in the design process of new m-CRs. Once parameter tuning is automatized, parameter optimization performed in simulation promises to be faster and less expensive than fabricating and testing real m-CRs. Moreover, the contact forces between an m-CR and the vessel wall can be extracted from the simulation, which is an indicator for the invasiveness of the chosen m-CR design. This information is challenging to obtain by conventional means and is usually revealed only late in the m-CR development process.

As computer assistance and automation finds its adoption in robotic assisted surgery, our simulator has the potential to accelerate the development and evaluation of m-CR specific control strategies and human-machine interfaces. Further potential lays in operator training. New adopters can become accustomed to RMN systems more easily by practicing on the simulator. For experienced users, the simulator can be used to practice on particularly challenging anatomies. This can even be patient specific; neuroradiologists can prepare for an intervention by practicing on a patient model based on segmented vessels from preoperative images.

VI. CONCLUSION

In this work, we presented a simulation platform for m-CRs by coupling the SOFA framework with an eMNS field model, and we validated it experimentally. We demonstrated that the simulation can be used to design and analyze m-CRs and has the potential to be used as a training simulator for physicians.

Fig. 1 .

 1 Fig. 1. Overview of the simulation framework in RViz. The magnetic fields generated by the electromagnetic navigation system are represented by the yellow arrows on a discretized 2d grid. The magnetic continuum robot is inserted from its proximal side by an advancer. A magnet of dipole moment m embedded along the flexible body of the robot experiences a torque t = m×b when submitted to a magnetic field b.

  1 https://github.com/ethz-msrl/mCR simulator (release v1.0.0)

Fig. 3 .

 3 Fig. 2. m-CR used in the experimental validation. The m-CR has a rigid proximal and flexible distal section with three permanent ring magnets. The tip holds a green and blue color marker for optical tracking of the tip position and orientation.

Fig. 4 .

 4 Fig. 4. Block diagram of the experiment and the simulation. The simulated mCR is actuated with the same user inputs as the real mCR.

Fig. 5 .

 5 Fig.5. Experimental validation of the m-CR simulator in planar environments. The simulated m-CR is first calibrated using a calibration sequence and then navigated in environments with obstacles and collisions.

Fig. 6 .

 6 Fig. 6. Applications of the simulator framework to endovascular navigation tasks. a) Navigation in the aortic arch, and b) exploration of the internal carotid artery toward a giant intracranial aneurysm. The simulation is repeated with three different instrument designs of various distal length (see TableI). The magnetic field controlled by the user at the center of the eMNS is depicted by the yellow arrow.

TABLE I PARAMETERS

 I OF THE SIMULATED M-CR.

	Task	Design Distal	OD	ID	E dist	Eprox
			length	[mm]	[mm]	[MPa]	[MPa]
			[mm]
	Valida-	-	110	1.0	0.8	40	600
	tion
		Short	14
	AA	Medium 34	1.33	0.8	21	170
		Long	54
		Short	10
	ICA	Medium 30	0.7	0	500	20000
		Long	40

TABLE II POSITION

 II AND ORIENTATION ERROR BETWEEN THE REAL AND SIMULATED M-CR.

		1	end-point	5.7	9.2	19.5
	Calibration	2	end-point	12.8	1.9	6.1	20.7	6.8	7.0
		3	end-point	20.7	2.0	3.6
		4	bifurcation	14.9	0.6	3.1
	Vasculature	5 6	bifurcation end-point	30.0 37.1	4.9 1.1	1.9 1.3	48.6	4.8	3.8
		7	end-point	48.6	5.0	3.0
		8	end-point	10.0	2.4	0.2
	Free-form	9 10	end-point bifurcation	24.7 32.8	2.6 1.5	0.9 7.4	46.0	5.1	7.2
		11	end-point	46.1	3.6	2.7

Environment Way-point number Way-point type T [s]

ep

(t = T ) [mm] eq(t = T ) [ • ] Ttot [s] ep [mm] eq [ • ]

ACKNOWLEDGMENT

The authors would like to thank Christian Duriez from the DEFROST team and Hugo Talbot from the SOFA Consortium for providing support with the SOFA framework.


Ivan Magrin-Chagnolleau
email: ivan.magrin-chagnolleau@cnrs.fr

A Phenomenological Approach to Color Theory and Aesthe6cs

Keywords: Phenomenology of Color, A Prac2ce-based Theory of Color, Color and Aesthe2cs, Color and Emo2ons, Color as a Lived Experience

This paper proposes to invesHgate color theory and aestheHcs from a phenomenological point of view, that is, from the point of view of the lived experience. Two angles of study are suggested: one is from the point of view of the arHst creaHng a piece, the other is from the point of view of the audience receiving the work. In each case, it is possible to interrogate the lived experience in order to find some cues about the aestheHc components that contribute to this lived experience, in parHcular as they relate to color. A tool, the explicitaHon interview, is proposed as a mean to conduct such invesHgaHon.

Introduc6on

For many years, I have approached color and aestheHcs from a pracHcal point of view. Being both a scholar and a pracHHoner, I consider my research in the framework of the creaHon research paradigm (Magrin-Chagnolleau, 2022a), also called for instance the pracHce-based research paradigm [START_REF] Candy | PracHce-Based Research in the CreaHve Arts[END_REF]. My pracHce as an arHst being at the foundaHon of my research on color and aestheHcs, it was natural for me to look into phenomenology [START_REF] Husserl | Idées directrices pour une phénoménologie[END_REF][START_REF] Husserl | L'idée de la phénoménologie[END_REF], and to approach color and aestheHcs from a phenomenological point of view, that is, from the point of view of the lived experience. This was also for me a way to put the creaHve process at the centre of my research. In other words, I am interested in the creaHve process as it is experienced by the person who is involved in this process. And I am parHcularly interested, in this creaHve process, in the moments when we make decisions that impact the aestheHc of the work at hand, and in parHcular decisions, conscious or unconscious, that involve color.

Phenomenology is a paradigm that put the lived experience at the centre. But how can we access the lived experience with an approach that is objecHve enough and can be reproducible? This is where the explicitaHon interview, developed by Pierre Vermersch, comes into play [START_REF] Vermersch | L'entre2en d'explicita2on[END_REF]. This interview technique allows to access the lived experience of a subject as it really happened, as opposed to how the subject thinks it happened. Developed iniHally in the framework of experimental psychology, and parHcularly in the context of pedagogy, this interview technique has been used by people who were interested in phenomenology, and more parHcularly in a pracHcal approach to phenomenology [START_REF] Bitbol | Neurophenomenology and the Micro-phenomenological Interview[END_REF]. I have been using this interview technique for the past few years in order to learn about the creaHve process, about the decisions that impacted the aestheHc dimensions of a creaHve project, and in parHcular decisions that had to do with color.

Why is color such an important component of aestheHcs? Following the theories of embodied cogniHon [START_REF] Varela | The Embodied Mind[END_REF], I believe this has to do with the fact that color relate to our daily experiences. Colors are everywhere. And because they are, we have a rich web of associaHons with them. That means that colors have an important impact on us, in parHcular emoHonally. And that means that arHsts manipulate colors, consciously or not, in order to create something in the viewer, at an emoHonal level, but also in more subtly ways. There is a reason why we speak for instance of warm colors and cold colors, in terms of what experience those colors create for the viewer.

I have already wri]en, in the past, about my experience with color as a pracHHoner (in Film, Theatre, Photography), included for AIC [START_REF] Magrin-Chagnolleau | The Use of Color in Theater and Film[END_REF][START_REF] Magrin-Chagnolleau | Handling Color in Photography and Film: From Photo Retouching to Color Grading[END_REF], 2022b). Each Hme, I have wri]en from the point of view of a pracHHoner developing a theoreHcal reflecHon based on his pracHce. Here, I would like to go one step further and address the phenomenological dimension of pracHcing art-making, aestheHcs decision-making, and color choices. The ambiHous goal of this research would be to develop a theory of color based on pracHce, that is, based on the lived experience, in other words, a phenomenological approach to color theory and aestheHcs. More modestly, in this paper, we will discuss the bases of such an approach to color theory, as well as its feasibility.

A Prac6cal Approach to Phenomenology

What is phenomenology? A phenomenological approach is an approach that deals with the lived experience of a phenomenon. Phenomenology puts experience in the center. Phenomenology tries to get rid of any theory or preconcepHon one can have about a phenomenon, and tries to approach a phenomenon from the point of view of the lived experience, relying only on the lived experience itself to extract any knowledge about the phenomenon [START_REF] Husserl | Idées directrices pour une phénoménologie[END_REF][START_REF] Husserl | L'idée de la phénoménologie[END_REF][START_REF] Heidegger | Être et Temps[END_REF][START_REF] Merleau-Ponty | Phénoménologie de la percep2on[END_REF].

What does it mean to have a phenomenological approach of color? It means invesHgaHng color as a lived experience, that is, trying to extract knowledge about color as a phenomenon from the experience we have of color. It refers to mostly two broad categories of experiences we can have of color as a phenomenon. One is on the side of recepHon: how do I experience receiving color? For instance: how do I experience viewing a painHng? How do I experience viewing a photograph? How do I experience viewing a film? How do I experience viewing an orange? a tree? etc.

The other is on the side of the creaHve process: how do I experience making choices about color as I create something? For instance: how do I experience choosing and using a color in a parHcular area of a painHng? how do I experience choosing the color of a piece of cloth for an actor? how do I experience grading color for a parHcular shot in a film? etc.

Phenomenology can be approached from a theoreHcal point of view, in which case we deals mostly with the idea of phenomenology. This is someHmes what has been said of Husserl, the founder of phenomenology. But phenomenology can also be approached from a pracHcal point of view. How can I interrogate the lived experience? How can I extract knowledge from the lived experience? How can I use the lived experience to learn something concrete about a phenomenon and the way we experience it?

There is a way to do it through the use of the explicitaHon interview [START_REF] Vermersch | L'entre2en d'explicita2on[END_REF]. The explicitaHon interview was created by Pierre Vermersch in the framework of experimental psychology. The interview was developed in order to be able to interrogate a subject on a past experience and have access to what the subject had precisely done during this past experience, as opposed to what they thought they had done. This is parHcularly useful in the framework of training, when someone makes a mistake during a process, without being able to pinpoint the moment of that mistake. Through conducHng an explicitaHon interview, it is very easy to find the moment when the person deviates from the learned procedure.

The explicitaHon interview was then used in the framework of research, in parHcular as a tool to approach phenomenology from a pracHcal point of view [START_REF] Depraz | À l'épreuve de l'expérience[END_REF][START_REF] Vermersch | Explicita2on et phénoménologie[END_REF]. What is unique about this interview technique is the fact that it can have access to some pre-reflected knowledge, that is, knowledge that is stored in someone's mind and can be accessed through the interview, but that the subject themselves were not aware about. For instance, when led by a skilled interviewer, this technique gives access to mental operaHons conducted by the subject while living the experience, such as informaHon taking or decision making.

There is also a version of the explicitaHon interview called auto-explicitaHon [START_REF] Vermersch | Bases de l'auto-explicitaHon (1)[END_REF][START_REF] Vermersch | IntrospecHon et auto-explicitaHon: Bases de l'auto-explicitaHon (2)[END_REF], which consists in administering the explicitaHon interview to oneself, using in that case parHcular techniques to be able to be in turn the interviewer and the interviewee. Now, there is one drawback to the explicitaHon interview. It takes between 45 and 90 minutes to conduct an explicitaHon interview, and during such an interview, one can only interrogate a very brief moment of the past experience of the subject. In order to be pracHcal, you usually need to already have a good understanding of the task at hand, and of the parHcular moment of the task that you want to finely interrogate. SomeHmes, you acquire that understanding by first doing some interviews without really knowing what you are aher, and then you will conduct some interviews more specifically on a moment that you are interested in.

Rela6ng Phenomenology, Aesthe6cs, and Color

Now that we have defined phenomenology and how to approach it from a pracHcal point of view, let us have a further look at how we can apply it to aestheHcs, and more parHcularly to color. What does it mean to approach aestheHcs from a phenomenological point of view? Let us go back to the way aestheHcs can be seen from the point of view of the lived experience. Here again, there are two angles.

The first one is the angle of the arHst. As an arHst, when creaHng a piece, I go to a series of decisions, some conscious, some unconscious. Each decision contributes to making me go through a creaHve process that culminates in the producHon of the piece. Most of these decisions impact the aestheHc of the final piece. As the arHst, this creaHve process, that is, the succession of all these decisions and acHons, are experienced by me. This builds my lived experience of this creaHve process. By interrogaHng this process, these decisions, these acHons, someone can have access to this process, to this lived experience, and relate all these decisions and acHons to the aestheHc of the final piece. This is what I mean by a phenomenological approach of aestheHcs. Rather than relying on a pre-conceived theory about aestheHcs, it is possible to have access to the lived experience of the arHst and correlate some of the decisions made and acHons taken to the resulHng piece and its aestheHc.

The same can be said about colors. Some of these decisions and these acHons directly deal with color. Therefore, if there is a possibility to have a phenomenological approach to aestheHcs, then there is a possibility to have a phenomenological approach to color.

The second angle concerns the way a piece is received by an audience. The audience, when receiving the piece, goes through a lived experience that can also be interrogated. And this interrogaHon can lead to understanding how the person interviewed experienced the piece and its aestheHc. This is a way to understand, from a phenomenological point of view, how the aestheHc of a piece impacts the lived experience of an audience. And again, part of the lived experience of an audience is impacted by colors, and this can also be interrogated.

I would like to point here that color is an important component of aestheHcs, mostly because of the parHcular relaHonship between color and emoHons. There is a reason why we speak of warm or cold colors. This refers to the lived experience that we go through when being exposed to such colors. Color is also a component that is easily manipulated by arHsts in order, precisely, to create such lived experiences in an audience.

Conclusion

In this paper, I have tried to describe what a phenomenological approach of color theory and aestheHcs could look like, and how we could develop it through the use of the explicitaHon interview. It speaks of the possibility of interrogaHng the lived experience of an arHst creaHng a piece or of an audience receiving it. In both cases, through this interrogaHon, we can access some elements that relate to the aestheHc of the piece, in parHcular as it relates to color. By doing that, we can establish some ground rules concerning aestheHcs and colors that are free from any preconceived ideas and theories about aestheHcs and colors, but rely directly on the lived experience, therefore allowing to establish a phenomenological approach to color theory and aestheHcs.

The future of this work will consist in tesHng the possibility of developing a phenomenological approach to color theory and aestheHcs by conducHng some explicitaHon interviews with arHsts creaHng pieces and audience members receiving them, as well as using auto-explicitaHon.