Ismail Altinbasak

Roxana Jijie

Alexandre Barras

Bianka Golba

Rana Sanyal

Julie Bouckaert

Djamel Drider

Rostyslav Bilyy

Tetiana Dumych

Solomiya Paryzhak

Volodymyr Vovk

Rabah Boukherroub

Amitav Sanyal

Sabine Szunerits

Reduced Graphene-Oxide-Embedded Polymeric Nanofiber Mats: An "On-Demand" Photothermally Triggered Antibiotic Release Platform

Keywords: electrospinning, nanofibers, reduced graphene oxide, antibiotic release, photothermal effect 48

The steady increase in antimicrobial resistance in different pathogens requires the development of alternative treatment strategies next to the oral delivery of antibiotics. A photothermally activated platform based on reduced graphene oxide (rGO)-embedded polymeric nanofiber mats for on-demand release of antibiotics upon irradiation in the near-infrared is fabricated. Cross-linked hydrophilic nanofibers, obtained by electrospinning a mixture of poly(acrylic acid) (PAA) and rGO, show excellent stability in aqueous media. Importantly, these PAA@ rGO nanofiber mats exhibit controlled photothermal heating upon irradiation at 980 nm. Nanofiber mats are efficiently loaded with antibiotics through simple immersion into corresponding antibiotics solutions. Whereas passive diffusion based release at room temperature is extremely low, photothermal activation results in increased release within few minutes, with release rates tunable through power density of the applied irradiation. The large difference over passive and active release, as well as the controlled turn-on of release allows regulation of the dosage of the antibiotics, as evidenced by the inhibition of planktonic bacteria growth. Treatment of superficial skin infections with the antibiotic-loaded nanofiber mats show efficient wound healing of the infected site. Facile fabrication and implementation of these photothermally active nanofiber mats makes this novel platform adaptable for on-demand delivery of various therapeutic agents.

■ INTRODUCTION

One of the challenges frequently encountered in traditional methods of drug delivery relates to poor control over proper dosage of therapeutic agent. [1][2][3] Maintaining the drug concentration within a particular therapeutic window and below toxic concentrations is challenging, and lack of efficient treatment can lead to severe side effects, along with the development of drug resistance in cells and pathogens. These problems have fostered the development of different approaches that enable the controlled release of a precisely defined amount of drug, but allow in addition the release of the therapeutic dose on demand, upon the application of an external trigger rather than by passively driven diffusion One attractive alternative as a wound-healing material and a 86 protective scaffold after surgical procedures favoring site-87 specific therapy by increasing the local antibiotic concentration 88 might be the use of antibacterial-loaded nanofiber mats. These 89 polymeric scaffolds are engineered via a polymer-processing 90 technique called electrospinning, which allows usage of a 91 variety of polymers with different chemical composition and 92 morphology. [START_REF] Kalaoglu-Altan | Reactive and 'Clickable' Electrospun Polymeric Nanofibers[END_REF][START_REF] Teo | A Review on Electrospinning Design and Nanofibre Assemblies[END_REF][START_REF] Agarwal | Use of Electrospinning Technique for Biomedical Applications[END_REF] This enables to select the most appropriate 93 material for the intended application and enables tailoring of drug release profiles. [START_REF] Qi | Controlled Release and Antibacterial Activity of Antibiotic-loaded Electrospun Halloysite/Poly(lactic-co-glycolic acid) Composite Nanofibers[END_REF] Hadjiargyrou and co-workers demonstrated the incorporation of hydrophilic antibiotics (mefoxin and cefoxitin) and their release in a sustained manner from poly(lactide-co-glycolide) nanofiber-based scaffolds obtained using electrospinning, without any compromise in their bioactivity and structure. [START_REF] Kim | Incorporation and Controlled Release of a Hydrophilic Antibiotic using Poly(lactide-co-glycolide)-based Electrospun Nanofibrous Scaffolds[END_REF] A passive diffusion release of about 70% of loaded cefoxitin was observed in the first hour, and the rest of the loaded antibiotic was released over 1 week.

Although the antibiotic that was released from these nanofibers was effective in inhibiting Staphylococcus aureus growth (>90%), burst release is an undesirable feature. To achieve an antibiotic release at the constant rate over a prolonged time period, stimuli-responsive nanofibers have been designed, mainly using pH-based triggers. [START_REF] Son | Antibacterial Nanofibrous Mats Composed of Eudragit for pH-Dependent Dissolution[END_REF][START_REF] Demirci | pH-Responsive Nanofibers with Controlled Drug Release Properties[END_REF] For example, ciprofloxacin-loaded pH-responsive electrospun nanofibers fabricated from a copolymer of vinyl benzoic acid and vinylbenzyltrimethylammonium chloride, as reported by Uyar and coworkers, undergo enhanced drug release at pH 5.8. Although external modulation of pH is nontrivial, modulation of temperature is unique, as it can be considered to be either internal stimuli as some infections are naturally at elevated temperature, or to be external through the application or generation of heat in the nanostructure. In the case of polymers, a temperature change can result in rapid swelling of its structures, leading to high volume alterations and thus inducing enhanced drug release. 7 Some photothermal active nanofibers formed through the incorporation of gold nanostructures, [START_REF] Cheng | Gold Nanorod-Embedded Electrospun Fibrous Membrane as a Photothermal Therapy Platform[END_REF][START_REF] Maity | Spatial Temperature Mapping Within Polymer Nanocomposites Undergoing Ultrafast Photothermal Heating via Gold Nanorods[END_REF][START_REF] Chen | Electrical and Mechanical Self-Healing Membrane using Gold Nanoparticles as Localized "Nano-Heaters[END_REF] carbon nanotubes, [START_REF] Zhang | Electrospun PLA/MWCNTs Composite Nanofibers for Combined Chemo-and Photothermal Therapy[END_REF][START_REF] Zhang | Porous Electrospun Fibers with Self-Sealing Functionality: An Enabling Strategy for Trapping Biomacromolecules[END_REF] carbon nanoparticles, [START_REF] Li | Enhanced Cell Uptake of Fluorescent Drug-loaded Nanoparticles via an Implantable Photothermal Fibrous Patch for More Effective Cancer Cell Killing[END_REF] or more recently Cu 2 S 39 have been described. We have shown lately the interest in reduced graphene-oxide (rGO)-loaded hydrogels for photothermal-initiated insulin release. [START_REF] Teodorescu | Photothermally Triggered On-Demand Insulin Release from Reduced Graphene Oxide Modified Hydrogels[END_REF] Interestingly, although reports of graphene oxide (GO) and rGO-containing nanofibers have emerged in recent years, [START_REF] Qi | A Highly Stretchable Nanofiber-Based Electronic Skin with Pressure-, Strain-, and Flexion-Sensitive Properties for Health and Motion Monitoring[END_REF][START_REF] Luo | Enhanced Proliferation and Osteogenic Differentiation of Mesenchymal Stem Cells on Graphene Oxide-Incorporated Electrospun Poly(lactic-co-glycolic acid) Nanofibrous Mats[END_REF][START_REF] Wang | Improving Antibacterial Activity and Biocompatibility of Bioinspired Electrospinning Silk Fibroin Nanofibers Modified by Graphene Oxide[END_REF][START_REF] Shao | Biomineralized Poly(L-lactic-co-glycolic acid)/Graphene Oxide/Tussah Silk Fibroin Nanofiber Scaffolds with Multiple Orthogonal Layers Enhance Osteoblastic Differentiation of Mesenchymal Stem Cells[END_REF] only one report used the photothermal properties of the resulting nanocomposite, [START_REF] Mauro | Enhanced Adhesion and In Situ Photothermal Ablation of Cancer Cells in Surface-Functionalized Electrospun Microfiber Scaffold with Graphene Oxide[END_REF] and showed photothermal eradication of captured cancer cells. The photothermally triggered release of antibiotics from rGO-containing nanofibers and its use for the treatment of infections has not been explored until now. Herein, we disclose rGO-containing poly(acrylic acid) (PAA) based nanofiber mats (PAA@rGO) for the loading of different antibiotics due to their swelling and noncovalent interaction with rGO, as well as demonstrate controlled and on-demand release promoted by near-infrared photothermal f1 heating (Figure 1). To allow facile diffusion of antibiotics under aqueous environment into nanostructures, we opted for the formation of rGO-loaded hydrophilic nanofibers by electrospinning PAA in the presence of cyclodextrin as a cross-linker. These nanofiber mats showed controlled photothermal heating ability, with the temperature reaching 67 ± 2 °C using a light source of 980 nm and 1 W cm -1 power density. The PAA@rGO nanomats showed high loading capability for ampicillin (AMP) and cefepime (CFP) with minimal passive antibiotic release. Ampicillin, part of the aminopenicillin family, was chosen for its favorable structure (aromatic ring together with the presence of amine and acid functional groups), enabling ampicillin to interact with rGO through electrostatic and π-stacking interactions (Figure 1). The same is true for cefepime (CFP), an antibiotic belonging Figure 2. Characterization rGO-loaded PAA nanofiber mats formed by electrospinning: (A) photograph of electrospun PAA@rGO; (B) Raman spectra of rGO (black), PAA (gray), and PAA@GO (red); (C) scanning electron microscopy (SEM) images of fabricated PAA@rGO nanofiber mats at different scales; and (D) stability of β-cyclodextrin cross-linked PAA@rGO nanofibers in water at 37 °C for 60 h. was obtained from Fisher BioReagents (BP1760-25). Graphene oxide (GO) in powder form was purchased from Graphenea (Spain).

Characterizations and Photothermal Setup. Details of characterization techniques and instrumental details for photothermal setup employed in this study can be found in the Supplementary Information.

Fabrication of rGO-Loaded PAA Nanofiber (PAA@rGO). A GO precursor was chemically reduced to reduced graphene oxide (rGO) using hydrazine according to a procedure previously reported by us. [START_REF] Teodorescu | Photothermally Triggered On-Demand Insulin Release from Reduced Graphene Oxide Modified Hydrogels[END_REF][START_REF] Boulahneche | On Demand Electrochemical Release of Drugs From Porous Reduced Graphene Oxide Modified Flexible Electrodes[END_REF] Briefly, GO aqueous suspension (5 mL, 0.5 mg mL -1 ) was treated with hydrazine (0.50 mL, 32.1 mM) at 100 °C for 24 h. After this time, the reduced GO gradually precipitates. Filtration through a poly(vinylidene difluoride) membrane (0.45 μm pore size) is used to collect the product. Obtained residue is washed with copious amounts of water (5 × 20 mL) and methanol (5 × 20 mL). Finally, the product is dried in an oven for 18 h at 100 °C. Thereafter, to rGO aqueous suspension (1.2 mL, 2.5 mg mL -1 ) was added PAA (100 mg) and βcyclodextrin (20 mg) and the resulting mixture was stirred for 24 h at room temperature. This corresponds to rGO (2.4 wt %), PAA (81.4 wt %), and β-cyclodextrin (16.2 wt %). Clear polymer solution of PAA, β-cyclodextrin, and rGO was electrospun using a 1 mL syringe fitted with a 14-gauge blunt needle at the rate of 0.005 mL min -1 with 15 kW. The distance was kept at 15 cm during the electrospinning process. Resulting electrospun fibers were cross-linked under vacuum at 140 °C for 30 min.

Loading of Antibiotics onto Nanofibers. Antibiotics loading into the nanofibers was achieved by immersing the nanofiber mat (4 mg) into the aqueous solution of ampicillin (80-400 μg mL -1 ) or cefepime (80-400 μg mL -1 ) and shaking (150 rpm) at 4 °C for 72 h. The concentration of ampicillin and cefepime loaded into the nanofibers was determined from the absorption intensity of the AMP and cefepime remaining in the solution using high-performance liquid chromatogram (HPLC). Ampicillin and cefepime calibration curves were obtained using a series of antibiotic-containing solutions (1-100 μg mL -1 ) (Figure S2).

Photothermal-Triggered Antibiotics Release. Antibiotic release was assessed in phosphate-buffered saline (PBS) (1 mL, pH 7.4) through direct irradiation of the nanofibers using a continuous wave laser at 980 nm at varying power densities (1-2 W cm -2 ) for several minutes. The amount of antibiotics released was determined from HPLC results of the solution collected after irradiation using previously established calibrations curves (Figure S2). Control experiments were carried out in an environmentally controlled cabin at 37 °C, and the samples were gently shaken during incubation.

Wound Healing and Histology. Full details of the study can be found in the Supplementary Information. Briefly, 6-8-week-old male Balb/c mice were used for this study. The superficial skin damaged infection model was performed as described by us previously [START_REF] Li | Flexible Nanoholey Patches for Antibiotic-Free Treatments of Skin Infections[END_REF] with some modifications. After removing the fur, a plaster was applied to the mouse skin (1 cm 2 ) several times to remove the superficial epidermis. The skin damaged was visible and characterized by reddening and glistening but no regular bleeding. Then, 10 μL of S. aureus bacterial cells (4 × 10 7 cfu mL -1 ) were applied to the skin and allowed to dry for 10 min. Superficial skin infection established after 24 h and PAA-or cefepime-loaded PAA@rGO nanofiber mats were applied to the skin of the anesthetized mice. Untreated mice were used as control. The mat was irradiated for 10 min with a nearinfrared light-emitting diode (LED) array (6 × 6 mm 2 in size, 8 W, 2A, 940 nm), previously shown to be a safe condition for animals. [START_REF] Li | Flexible Nanoholey Patches for Antibiotic-Free Treatments of Skin Infections[END_REF] The temperature was monitored by an infrared camera (Thermovision A40). Mice were photographed and images were processed with ImageJ software to detect erythema, and its area before and after a 24 h treatment was evaluated. After 24 h, the mice were sacrificed and the skin was removed and subjected to histological analysis.

■ RESULTS AND DISCUSSIONS

Fabrication and Characterization of rGO-Containing Nanofibers. First, rGO-containing PAA nanofibers were obtained through electrospinning of an aqueous dispersion of 242 rGO (2.4 wt %), PAA (81.4 wt %), and β-cyclodextrin (16.2 wt 243 %) as a cross-linker (Figure 1). Upon electrospinning, a free 244 f2 standing mat of electrospun fibers is obtained (Figure 2A).

245

Raman spectra of PAA and PAA@rGO were recorded to 246 confirm the incorporation of rGO into the nanofibers (Figure 247 2B). Raman analysis revealed the presence of the expected 248 bands at ≈1350 cm -1 (D-band) and ≈1580 cm -1 (G-band) 249 due to the defects and disorders, and the graphitized structure 250 of rGO, respectively (Figure 2B). The I D /I G intensity ratio was 251 found to be 0.93 for rGO. The PAA fibers did show a Raman 252 band at 1728 cm -1 assigned to CO functional groups, 253 whereas the bands at 1235 and 1285 cm -1 are ascribed to 254 -CH 2bonds. [START_REF] Koening | Raman Spectra of Poly(ethylene glycols) in Solution[END_REF] In the case of PAA@rGO, the bands of rGO 255 are identifiable in the Raman spectrum. Additionally, Fourier 256 transform infrared (FTIR) and X-ray photoelectron spectros-257 copy (XPS) spectra of PAA@rGO were obtained, where the 258 FTIR analysis did not provide any information about rGO 259 incorporation due to its low amount, but the presence of 260 delocalized π-electrons was evident in the XPS spectra (C 1s 261 scan) (Figure S3).

262

To ensure long-term stability in the aqueous media of the 263 hydrophobic PAA@rGO nanofibers, the fibers were cross-264 linked to prevent their dissolution. As reported earlier, β-265 cyclodextrin, a molecule containing multiple hydroxyl groups 266 can be efficiently used to cross-link the PAA polymer upon 267 heat treatment under vacuum for 30 min. [START_REF] Li | Ultra-fine Polyelectrolyte Fibers From Electrospinning of Poly(acrylic acid)[END_REF] The morphology 268 of the resulting cross-linked PAA@rGO nanofibers was probed 269 using scanning electron microscopy (SEM). Figure 2C shows rapid increase in the surface temperature of PAA@rGO nanofibers, reaching saturation at approximately 51 ± 2 °C within 5 min in a wet environment. No melting of nanofibers occurred under the used conditions, thus preserving the structural integrity of the fibrous mats. Thus, with modulation of laser power density, these nanofiber mats exhibited controlled photothermal heating ability within a temperature range from 20 to 67 ± 2 °C.

Loading and Release of Antibiotics into Nanofibers. Integration of antibiotics into the cross-linked PAA@rGO nanofiber mats was achieved by simply immersing the nanofibers into the aqueous solution of ampicillin or cefepime in water at 4 °C for 72 h. Both antibiotics contain aromatic structures together with amino and carboxylic acid functional groups, thus promoting their interaction with rGO through π-π stacking and/or electrostatic interactions. The loading capacity of PAA@rGO nanofibers for AMP and cefepime was determined from the amount of the antibiotic in the solution before and after loading using HPLC. The loading capacity of PAA@rGO for ampicillin and cefepime is comparable as seen f4 in Figure 4A. Using the solution concentration of 400 μg mL -1 of the antibiotics resulted in the loading of about 85 ± 3 μg mL -1 (21%) and 89 ± 3 μg mL -1 (22%) for ampicillin and cefepime, respectively. Ampicillin has a pK a ≈ 4-5 (COOH) and pKa ≈ 9 (NH 2 ), making it zwitterionic at physiological pH. A fair amount of the amine groups are positively ionized at physiological pH and this promotes their interaction with the PAA@rGO nanofiber mats (pK a ≈ 4.5). 52 The quaternary ammonium group of the N-methylpyrrolidine groups in cefepime (Figure 1) makes the drug positively charged and results in interaction with the ionized carboxylic acid groups in PAA and negatively charged rGO that has a ζ-potential of -50 ± 2 mV. Due to their hydrophilic nature, it can be expected that the nanofibers swell in aqueous media and thus load the antibiotics efficiently. Remarkably, the passive release from the antibiotic-loaded PAA@rGO nanofibers, PAA@rGO-AMP, and PAA@rGO-CFP, was found to be negligible. For the first 5 h, the amount of antibiotic release was below the detection limit of the HPLC analysis. After 24 h incubation in PBS (0.1 M, pH 7.4) about 0.8 ± 0.1% was released via passive diffusion (Figure 4B).

Encouraged by the excellent stability of the PAA@rGO to retain the loaded antibiotics, we explored the photothermal properties of the PAA@rGO nanofiber mat to trigger the drug f5 release. Figure 5A shows the release profiles for ampicillin as Escherichia coli K12 (Table 1). Ampicillin shows no activity for 342 S. aureus and Staphylococcus epidermidis.

343

In the case of cefepime-loaded nanofiber mats, photothermal 344 activation of the fibers with 2 W cm -2 leads to a complete 345 release of the entrapped antibiotic (25 μg mL -1 ) in a time 346 frame of ≈25 min, with a release rate of 1.36 μg mL -1 min -1 347 for cefepime for the first 10 min. The release rate can be tuned 348 upon using a lower power density: using a laser power of 1 W 349 cm -2 , the release rate of cefepime decreased to 0.91 μg mL -1 350 min Figure 5. Photothermal-triggered antibiotics' release for PAA@rGO nanofibers: (A) release profile of ampicillin from a PAA@rGO nanofibers loaded with ampicillin (25 μg mL -1 ) when activated at 980 nm at 2 and 1 W cm -2 and (B) release profile of cefepime from PAA@rGO nanofibers loaded with cefepime (25 μg mL -1 ) when activated at 980 nm at 2 and 1 W cm -2 . Whereas ampicillin is only effective toward Gram-negative E. coli K12, cefepime is active for Gram-negative and Grampositive strains, with a higher MIC for S. epidermidis strain. S. epidermidis are known to be one of the most frequently encountered skin-colonizing bacteria and the predominant causes of nosocomial and community-associated skin infections. As expected, cefepime doses proved to be active against S. epidermidis. Cefepime released from cefepime-loaded nanofibers shows a release-dependent killing effect on S. epidermidis in accordance with the release profile determined in Figure 5B. Figure 6C shows the SEM images of S. epidermidis treated with photothermally released cefepime. Whereas the amount of cefepime is below the MIC value after 5 min and does not effect in any way the S. epidermidis growth, the pathogen is completely destroyed above the MIC value (corresponding to times >10 min). This indicates that the developed approach can be easily adapted for any desired antibiotic to eliminate a particular bacterial strain.

In addition to sustained antibiotic release, an important feature of any drug-release system is its reusability. Reloading of PAA@rGO with ampicillin or cefepime, as well as photothermally induced release could be attained with the f7 similar efficiency over several cycles (Figure 7). Apart from just the possibility of reuse, the multiple loadings and release of antibiotics also demonstrate that the extent of upload and release is highly reproducible for these nanofibrous mats.

Infectious Wound-Healing Studies Using rGO Nanofibers. There are different experimental models of skin infections that are caused by S. aureus. 53,54 In our research, the bacteria were directly applied on the previously damaged skin. The tape-stripping approach, one of the most common models for the generation of superficial skin infection in mice, 55 was used here, as it allows to establish superficial infections in the epidermis, as well as the upper layer of the dermis. We monitored the skin infection progress in three animal groups: those treated with skin application of cefepime- fiber mats without embedded rGO (Figure 8B). This is in 420 contrast to cefepime-loaded PAA@rGO mats, wherein the 421 photothermal treatment prevented the bacteria from spreading 422 (Figure 8A). Infected layers after 10 min illumination with a 423 LED array through the antibiotic-loaded PAA@rGO nanofiber 424 mats (PAA@rGO-CFP) show signs of resolution of inflam-425 mation (Figure 8A) and reduced blood vascularization and 426 bacterial infiltration (Figure 8B). No damage to skin was ) and the amount of photothermally released ampicillin after 10 min laser irradiation (1 W cm -1 ). (B) Loading of cefepime (25 μg mL -1 ) and release of cefepime when activated at 980 nm at 2 W cm -2 . F observed with LED illumination of the PAA@rGO nanofiber patch during the in vivo experiments, as the skin surface temperature was kept maximal at 52 °C. This is opposed to skin heating up to 67 °C when tissue damage could be observed in meat samples (Figure S4). Histological section of a representative skin specimen (harvested at day 2 postinfection) after Gram staining (Figure f9 9) showed that S. aureus was superficially localized in the epidermis and penetrated the dermis layers of untreated and PAA-CFP skin samples. In addition, the leukocytic infiltration was abundant in the deep layer of hypodermis, indicating abundant bacterial presence. However, the infected wound irradiated through the antibiotic-loaded PAA@rGO patch for 10 min indicated active wound healing without marks of inflammation and bacterial foci. Epidermis revealed signs of active regeneration. Thus, it could be concluded that the topical application of PAA@rGO-CFP mats for photothermal therapy exhibited the best wound-healing capability among those tested.

■ CONCLUSIONS

In summary, a novel nanofiber-based platform for "ondemand" release of antibiotics is fabricated using rGOcontaining polymeric nanofibers. The rGO-embedded hydrophilic nanofibers obtained using solution electrospinning are loaded with two different antibiotics, namely, ampicillin and cefepime. Although negligible release of antibiotic is observed under physiological conditions, exposure to NIR irradiation leads to release amounts sufficient to kill Gram-positive and Gram-negative bacteria alike. A clear correlation between the NIR-triggered antibiotic release and bactericidal activity is

Figure 1 .

 1 Figure1. Illustration of the fabrication of antibiotic-loaded PAA@rGO nanofibers: (1) electrospinning of rGO-loaded PAA nanofiber mats followed by (2) loading with different antibiotics and photothermal-triggered antibiotic release.

  153 to the class of cephalosporin commonly applied for the 154 treatment of bacterial conditions such as pneumonia, kidney, 155 urinal, as well as skin infections. This antibiotic works by 156 simply stopping the growth of bacteria. 46,47 Enhanced drug 157 release was achieved under irradiation of the antibiotic-loaded 158 PAA@rGO nanofiber mats with near-infrared light at 980 nm, 159 where the antibiotic release rate can be tuned upon using 160 different power densities. In vitro antibacterial assay demon-161 strates clearly that the released antibiotics did not lose their 162 biological activity to inhibit growth of pathogens. The 163 nanofiber platform could be reloaded with antibiotic and 164 release was achieved in a controlled fashion, thus demonstrat-165 ing recyclability of the platform. Furthermore, through in vivo 166 studies on S. aureus infected Balb/c mice, the antibiotic-loaded 167 PAA@rGO nanofiber mats demonstrated excellent wound-168 healing capability, making them viable candidates for clinical 169 applications. 170 ■ EXPERIMENTAL SECTION 171 Materials. Poly(acrylic acid) (PAA, M n = 450 000 g mol -1 ), 172 hydrazine, β-cyclodextrin, phosphate-buffered saline (PBS, pH 7.4) 173 and cefepime were purchased from Sigma-Aldrich. Ampicillin (AMP)

Figure 3 .

 3 Figure3. Photothermal properties of cross-linked PAA@rGO: (A) photothermal heating curves of PAA (gray) and PAA@rGO (red) nanofiber patches (4 mg) immersed in PBS (0.1 M, pH 7.4) and irradiated at 980 nm (1 W cm -2 ) for 10 min and (B) temperature profile of PAA@rGO nanofiber mats upon 10 min irradiation at varying power densities.

  332well as cefepime upon irradiating PAA@rGO nanofibers 333 loaded with ampicillin (25 μg mL -1 ) and cefepime (25 μg 334 mL -1 ) with NIR light. Using a laser power density of 2 W 335 cm -2 results in an almost complete release of ampicillin (24 μg 336 mL -1 ; ≈96% of loaded ampicillin) with a release rate of 3.2 μg 337 mL -1 min -1 , which can be lowered to 0.5 μg mL -1 min -1 using 338 a phototrigger of 1 W cm -2 . The released ampicillin 339 concentrations are much larger than the minimum inhibitory 340 concentration (MIC) value of ampicillin for Gram-negative 341 t1

  photothermal-triggered ampicillin release, their antibiotic

Figure 4 .

 4 Figure 4. (A) Loading capacity of PAA@rGO nanofiber mats (4 mg) with ampicillin and cefepime upon incubation for 24 h into PBS (0.1 M, pH 7.4) under shaking at different drug concentration. (B) Passive release from antibiotic-loaded cross-linked PAA@rGO nanofibers when immersed in 0.1 M PBS (pH 7.4) for 24 h at 37 °C.

antibiotic MIC 50 /

 50 μg mL -1 ( E. coliK12) MIC 50 /μg mL -1 (S. aureusATCC 25923) MIC 50 /μg mL -1 (

  406 loaded either PAA (PAA-CFP) or PAA@rGO (PAA@rGO-407 CFP) nanofiber mats and untreated mice (controls). The 408 treatment in all groups started 24 h following the infection 409 f8 induction. Figure 8 displays images of the noninfected-and 410 infected-wound groups untreated and treated with antibiotic-411 loaded nanofiber mats 48 h after infection initiation. The 412 dressing (white arrows) was applied tightly to the wound area. 413 The untreated areas and those treated with cefepime-loaded 414 PAA nanofiber mats (PAA-CFP) and light activated for 10 min 415 to release the antibiotics revealed inflammation and areas with 416 abundant edema, erythema, and bacterial infiltration/pus. 417 Blood vascularization and bacterial infiltration are in addition 418 detected in the untreated groups and cefepime-loaded PAA 419

Figure 6 .

 6 Figure6. (A) Planktonic growth of E. coli K12 (1 × 10 8 cfu mL -1 ) (A) without ampicillin (black, t = 0) and when treated with ampicillin released photothermally from PAA@rGO nanofiber mats at different time intervals corresponding to Figure5A. (B) Planktonic growth of S. epidermis without cefepime (black, t = 0) and when treated with cefepime released photothermally from PAA@rGO nanofiber mats at different time intervals corresponding to Figure5B. (C) SEM images of S. epidermidis treated with cefepime photothermally released from PAA@rGO nanofiber mats for 5 and 30 min.

Figure 7 .

 7 Figure 7. (A) Loading of ampicillin (85 μg mL -1) and the amount of photothermally released ampicillin after 10 min laser irradiation (1 W cm -1 ). (B) Loading of cefepime (25 μg mL -1 ) and release of cefepime when activated at 980 nm at 2 W cm -2 .

  457 observed. It can be anticipated that the facile fabrication and 458 modular nature of the construct reported here provides a 459 platform that can be adapted for on-demand delivery of various 460 drugs for combating different diseases. Although only two 461 specific antibiotics were chosen in this study, the platform is 462 amenable to loading of other antibiotics, either solo or in 463 combination to combat a plethora of bacterial infections. 464 ■ ASSOCIATED CONTENT 465 * S Supporting Information 466 The Supporting Information is available free of charge on the 467 ACS Publications website at DOI: 10.1021/acsami.8b14784. 468 SEM images of fabricated PAA nanofiber mats at 469 different scales, HPLC plot, and calibration curves of 470 antibiotic release studies, FTIR and XPS of PAA@rGO 471 and images of skin samples treated with NIR irradiation 472 mail: amitav.sanyal@boun.edu.tr. Tel: +902123597613 476 (A.S.). 477 *E-mail: sabine.szunerits@univ-lille.fr. Tel: +33 (0)3 62 53 17 478 25 (S.S.). 479 ORCID 480 Rana Sanyal: 0000-0003-4803-5811 481 Julie Bouckaert: 0000-0001-8112-1442 482 Rostyslav Bilyy: 0000-0002-2344-1349 483 Rabah Boukherroub: 0000-0002-9795-9888

Figure 8 .

 8 Figure 8. (A) Photographs of wound scars 24 h after treatment (980 nm, 1 W cm -2 ) for 10 min with cefepime-loaded nanofibers mats (PAA-CFP; PAA@rGO-CFP). Negative controlintact skin; positive controlinfected untreated skin. Insert at top left demonstrates the setup for animal treatment. (B) Photographs of intact mouse skin and three representative skin samples after 48 h of infection under different treatment conditions.

Figure 9 .

 9 Figure 9. Histological examination of skin wound healing 48 h after the infection. Sections of skin tissues with Gram staining. Intact mouse skin; untreated skin (after infection); and photothermally treated infected skin part of the wound (PAA-CFP and PAA@rGO-CFP).

  -1 . Importantly, no burst release was observed in any of

	these examples and the maximal amount released is about	351
	twice of the MIC value for cefepime for S. epidermidis and	352
	several times larger than the MIC value for cefepime for E. coli	353
	K12 and S. aureus ATCC 25923 (Table 1).	354
	Antibacterial Activity under Passive and Active	355
	Release. Although ampicillin has sufficient stability in the	356
	dry state, it is only short lived in a solution. Following	357

Table 1 .

 1 Minimum Inhibitory Concentrations of Ampicillin and Cefepime for Different Bacteria Strains

ACS Appl. Mater. Interfaces XXXX, XXX, XXX-XXX


domain: math shs

text:
Cathleen Heil
email: cathleen.heil@leuphana.de

Double perspective taking processes of primary children adoption and application of a psychological instrument

Keywords: Egocentric transformations, geometric thinking, perspective taking, spatial abilities

 PTSOT is a test instrument for adults that investigates double perspective taking processes. Both perspective taking processes can be defined by certain egocentric transformations. An adoption of this test for primary children reveals that they are able to understand the test and verbalize easily their thinking processes. 8 items were solved by 254 fourth graders. Results show a variety of typical difficulties that can be interpreted in detail using the egocentric transformations framework. The theoretical framework and the straightforward way of item construction allow us to systematically generate items for various applications in psychology and mathematics education.

Theoretical background

Spatial abilities have widely been debated within mathematics education, with a multitude of meanings and definitions [START_REF] Mulligan | Looking within and beyond the geometry curriculum: Connecting spatial reasoning to mathematics learning[END_REF]. Discussions within WG4 in CERME highlight implicitly the implication of those abilities on all four geometrical competencies to support geometrical thinking that were proposed by Manschietto et al. (2013).

Psychometric studies on individual differences have shown that the construct of spatial ability is multidimensional and consists of several spatial ability factors (e.g,, [START_REF] Mcgee | Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences[END_REF][START_REF] Linn | Emergence and characterization of sex differences in spatial ability: A meta-analysis[END_REF]. Although the exact factor structure of spatial abilities remains a subject of intensive debate, some of these factors were studied in detail, both for adults and children. One of these factors, spatial orientation, also denoted as perspective taking in the literature, was proposed to measure the ability to imagine the appearance of a set of objects from different orientations (perspectives) of the observer [START_REF] Mcgee | Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences[END_REF].

In the experimental cognitive literature, spatial abilities have been conceptualized as the ability to engage different mental transformations that require the subject to update an encoded visual stimuli with respect to three different frames of reference: the intrinsic reference frame of objects, which encodes relations among objects, the egocentric frame of reference, which encodes object locations with respect to one's body, and the environmental frame of reference [START_REF] Huttenlocher | Mental rotation and the perspective problem[END_REF][START_REF] Zacks | Mental spatial transformations of objects and perspective[END_REF]. Perspective taking ability has been defined as the ability to perform a set of egocentric transformations on objects, in which the relationship between the environmental coordinate frame and those of the objects remain fixed, while each of their relationships with the observer's egocentric reference frame are updated. Although the conceptualization of perspective taking within the theoretical framework of mental transformations is logically equivalent to the qualitative description of the factor spatial orientation, it adds value for the deconstruction of complex perspective taking into separable, analyzable transformation processes.

Perspective taking abilities have been studied extensively in the developmental psychology literature (see [START_REF] Newcombe | The development of spatial perspective taking[END_REF], for a full review). It has been highlighted that children demonstrate first perspective taking abilities even in infancy, show first achievements on more advanced tasks at around 4 or 5 years and improve performance considerably between the age of 6 and 8 [START_REF] Frick | Picturing perspectives: Development of perspective-taking abilities in 4-to 8-year-olds[END_REF]. Complex perspective taking tasks that involve typically conflicting frames of references such as [START_REF] Piaget | The child's conception of space[END_REF] Three Mountains Task are not fully mastered until the end of primary school. Although the involvement of conflicting frames of reference in perspective taking tasks, e.g. the involvement of a to-be-imagined frame of reference that conflicts with the child's direct relation to the visual stimulus, has received criticism (see [START_REF] Huttenlocher | Mental rotation and the perspective problem[END_REF], for a detailed discussion), it is valuable from a spatial cognition point of view. Tasks with conflicting frames of reference are of high interest, because they demand for the ability to represent, maintain and coordinate multiple frames of references within one coherent spatial framework. This ability is meaningful and predictive for a whole range of everyday life spatial abilities, such as misaligned map reading [START_REF] Lobben | Tasks, strategies, and cognitive processes associated with navigational map reading: A review perspective[END_REF], environmental learning and wayfinding [START_REF] Allen | Spatial abilities, cognitive maps, and wayfinding[END_REF][START_REF] Hegarty | Spatial abilities at different scales: Individual differences in aptitude-test performance and spatial-layout learning[END_REF]. A deeper understanding of perspective taking processes involving conflicting frames of references allows us therefore to discuss spatial abilities of primary children in a much broader context. This is consistent with the mathematics curriculum but also curricula of applied sciences and geography.

A qualitative re-analysis of typical markers of perspective taking ability such as the [START_REF] Guilford | The Guilford-Zimmerman aptitude survey[END_REF] Spatial Orientation Test for adults turned out not to be construct valid as being solved mostly by mental rotation strategies [START_REF] Barratt | An analysis of verbal reports of solving spatial problems as an aid in defining spatial factors[END_REF]. [START_REF] Kozhevnikov | A dissociation between object manipulation spatial ability and spatial orientation ability[END_REF] proposed a novel, psychometric paper and pencil perspective taking/spatial orientation test (PTSOT) for adults in order to overcome the drawbacks of the Guilford-Zimmermann task. The test instrument consists of 12 items that display an arrow of seven 2D-objects. On each item, the participant is asked to imagine being at the position of one object (anchor point), facing another object (defining the imagined perspective within the array) and is asked to indicate the direction to a third object (target). Item formulation stimulates therefore complex perspective taking processes with conflicting frames of references. The answer is noted on an "arrow circle" (see example item in Figure 1, left side, item adopted for better readability). Participants are neither allowed to rotate physically the object array nor the "arrow circle".

The PTSOT has been shown to be construct valid by the authors themselves, involving mostly selfreported perspective taking processes in adults (Kozehevnikov & Hegarty, 2001). Due to its accepted validity the test has been used to underline perspective taking abilities to be predictive for environmental layout learning in real world and virtual contexts [START_REF] Hegarty | A dissociation between mental rotation and perspective-taking spatial abilities[END_REF].

The present study aimed to address the development of an instrument that stimulates complex perspective taking processes with conflicting frames of reference. One goal of the study was an adoption of the original PTSOT for primary children. A second goal was to describe the instrument with respect to test characteristics and typical error patterns that are caused by problems or failure in a set of mental transformations that are necessary to solve the items. Finally, an overall goal was to conclude potential applications of the instrument within the field of psychology and mathematics education.

Adoption and item construction Design of an adopted instrument

The adoption process was conducted throughout a qualitative study with 25 fourth graders in a bachelor thesis project. We adopted the PTSOT with respect to 12 design parameters that are listed in Figure 1. We will elaborate in detail on the literature background in a following publication. The adopted instrument consists of a 3D, small scale array of six farm animals that are placed on a green sheet of paper (the "meadow"). The child is sitting in front of the fixed array of objects, taking an oblique view on the whole scene. Just in front of the child there is a fixed, circular disk with 12 numbered sections and a mobile arrow on it. Animals can be stuck on the disk using glue dots.

Verbal item formulation is standardized as following:

Tutor: "Imagine that you are animal A (sticks animal A in the middle on the arrow of the disk) on the meadow and are facing animal B (places animal B on on the semicircle attached to the disk). In which direction do you have to turn in order to see animal C?"

The child turns the arrow of the answering disk at the section which corresponds to the right direction and the tutor notes the answer. During the solution process, the child is allowed to gesture but not to turn the array, the answering disk or itself.

Item construction & framework for item analysis

We constructed eight initial items with the help of two parameters that describe two perspective taking processes within one item. In Figure 2 you can see that each item is defined by a set of four subsequent mental transformations of the egocentric frame of reference, whichpairwisedefine one perspective taking process within the item.

Exploratory Studies

We studied the range of strategies that children use to solve different items in a qualitative interview study with 16 fourth graders in the context of a second bachelor thesis. Interviews served as an aid for the interpretation of results of the exploratory study as well as verification of the goal of the instrument.

In a main study, we performed the eight items of our adopted test instrument with 254 fourth graders (mean age was 9.17 years; 116 boys and 138 girls) out of 11 classes in Lüneburg; forming a heterogeneous sample in terms of scholar achievement and social background. The test was administered in a separate room in a 1:1 situation with the experimenter. We documented children's solutions, but we did not film the children.

Results and discussion

Test theoretical considerations

In a first approach, Item Response Theory (IRT) analysis, we scaled the data using a Rasch-model 1 in Conquest. The characteristics prove that data fit well with dichotomous data from the exploratory study with a MNSQ within 0.95 and 1.07 for all items. EAP reliability is poor, 0.456, yet might be influenced by the small number of items. Discrimination values show poor discrimination (0.24 and 0.33) for two items and acceptable (0.42-0.56) discrimination for the other items. Item difficulties are between -0.52 and 2.8 (0 being medium difficulty), yet showing a tendency towards a selection of very difficult items. We conclude that from a test theoretical point of view, our selection of eight items is still far away from been applied as a psychometric measure of perspective taking. However, a first analysis pointed out a set of items with good characteristic values.

Quantitative results

1 Rasch-models are one specific class of measurement models in IRT in which latent trait estimates depend on both persons' responses and the properties of the item (difficulty, discrimination).

Thematic Working Group 04

Proceedings of CERME10

In a second analysis, we interpreted the number of answers per section in the answering disk within the mental transformation framework that was presented in Figure 2.

(Item 6) "Imagine that you are the cow and you are facing the dog. In which direction do you have to turn in order to see the chicken?"

Item 6 is characterized by α=250°, thus demanding the child to rotate its egocentric frame of reference by more than 90° to the right while indicating the direction of the chicken (β=33°), thus asking for a clear left/right decision at this point of view. IRT analysis showed that the item is difficult (1.06) and has an acceptable discrimination value (0.55).

We performed the analysis of item solutions within our mental transformation framework. Errors were classified into "problems" (task is basically understood but there are a few inaccuracies within one transformation), "failure" (one transformation is not performed at all, but the item is solved within the general item structures) and "neglect" (the goal of the item is changed due to a misunderstanding/heavy problem with one of the two perspective taking processes) in order to stress the amount of difficulty that a child showed during the solution of an item.

A detailed analysis in Figure 3 demonstrates the depth in which item solutions might be interpreted with the mental transformation framework. Figure 3 shows typical error patterns, such as  neglect of the first perspective taking process, thus solving the item from a fixed egocentric viewing direction  failure at the last transformation T4, thus having left-right problems  failure at T2, the item is thus solved by taking the initial, fixed heading of the first animal (cow) and the child fails to shift the viewing direction from α0 to α  problems with estimation of the angle β in T3

 neglect of the first perspective taking process and projection of the egocentric viewing direction on the first animal (cow), thus pointing towards the relative position of the dog (Item 8) "Imagine that you are the chicken and you are facing the horse.

In which direction do you have to turn in order to see the cow?"

Item 8 is characterized by α=170°, thus demanding the child to transform its egocentric frame of reference by almost 180° while indicating the direction of the cow (β=68°), thus asking for clear left/right decision at this point of view. IRT analysis showed that the item is very difficult (2.48) and has an acceptable discrimination value (0.53). The high difficulty of this item results from the need to take almost an opposite perspective while indicating to the front right.

For the analysis we expected therefore a large percentage of children to fail at the last transformation T4 (thus producing right-left-errors) as well as a high number of children to neglect the first perspective taking process, thus solving the item from an egocentric viewpoint. Figure 4 demonstrates that the last item shows a whole range of typical difficulties.

However, although the solution rate is for this item was low, many children managed to perform most of the transition processes correctly. Almost 77% of the children succeeded on performing at least T1, 47% succeeded in doing at least T1 and T2 correctly, 30% managed T1, T2 and T3 and almost 10% managed to do all the transformations correctly. Figure 4 shows that problems with the first perspective taking process may occur due to egocentric behavior, the failure to perform T2 or due to the projection of the egocentric viewing direction on the chicken. We explain errors in the first perspective taking process by difficulties that are inherent to children at this age (see [START_REF] Huttenlocher | Mental rotation and the perspective problem[END_REF] but also by problems in understanding the item formulation and the item structure itself. The latter might be improved by doing multiple examples with the children (we explained the item structure with only one example).

Applications of the instrument in different contexts

We analyzed performance on our adopted version of the perspective taking test at two different levels in order to underpin the argumentation on possible applications of the instrument.

Diagnostics

We demonstrated that item construction is straight forward using the construction parameters α and β. Our instrument allows therefore purposeful item construction in order to investigate individual differences and developmental issues in complex double perspective taking abilities. Children verbalized easily their thinking processes in our qualitative study, using gesture for showing viewing directions and the direction of the third animal. A combination of item solution and explaining aloud the solution process might help to diagnose the transformation processes that are still problematic for each child.

During construction and evaluation process, we identified two problems with our instrument that should be considered during item formulation: First, we measured angles from head to head of each animal. As the animals are quite large, the correct estimation of the angle β might depend on whether the child focuses on the head or the tail of each animal. Second, as the rabbit was placed at the center of the animal array, children had problems with taking the viewing direction of the rabbit. Instead, they projected their egocentric viewing direction onto the rabbit and answered items as giving relative positions of animal C to the rabbit.

Learning environment

Our adopted instrument consists of easily purchasable, inexpensive material. Again, our study showed that children are able to verbalize their spatial thinking processes with ease, using a whole range of gestures. Our instrument might be used for teaching of complex perspective taking processes (children solve pre-formulated items by the teacher), in communicative settings (children formulate items on their own), in discussions that address the transformation processes explicitly ("Can you explain me why this item is so complicated?"), or in creative settings (formulation of own items within constraints, e.g. difficulty, or re-configuration of all animals on the meadow).

Psychological test instrument

The original PTSOT has gained much attention concerning psychometric measurement of perspective taking ability because it is construct valid and reveals the predictive nature of perspective taking abilities for environmental learning. Another wishful application of our adopted version of the PTSOT is therefore in psychometrical measurement of children's perspective taking abilities. IRT analysis revealed a poor reliability and pointed out some inappropriate items with low discrimination values. In a further study, an exploratory analysis on a larger set of items of intentionally different difficulties is planned. IRT analysis might then reveal good items for a psychometric test of spatial ability in children. An IRT analysis of the test instrument might then be linked to our analysis technique based on egocentric transformations in order to develop a typology of complex perspective taking in children.

Figure 1 :

 1 Figure 1: Comparison between the PTSOT and the adopted instrument with respect to 12 design parameters. One item of the PTSOT is shown on the left, the whole adopted instrument is shown from a quasi-bird perspective on the right side, showing the object field and the solution answering disk

Figure 2 :

 2 Figure 2: Item analysis for an arbitrary item showing the two mental viewing directions (dashed lines), the original viewing direction of animal A (black line), the egocentric viewing direction of the observer as well as the item construction parameters α and β

Figure 3 :

 3 Figure 3: Analysis of solutions for item 6.

Figure 4 :

 4 Figure 4: Detailed analysis of item 8, revealing problems in the T4 transformation process. Answer patterns that are not interpretable within our framework might be explained by counting in the field of animals or arbitrarily guessing the answer.

Proceedings of CERME10


domain: math shs shs.edu

text:
Keith Jones

Michela Maschietto

Joris Mithalal-Le Doze

Introduction to the papers of TWG04: Geometry education

Keywords: Geometry education, instruments, proof and argumentation, spatial skills, visualization

Introduction

Around 25 researchers of various geographical origins (from across Europe and also from North America, the Middle East, East Asia) participated in Working Group 4 on Geometry Education. Some 20 contributions (15 papers and 5 posters) informed five discussion sessions and two further sessions dedicated to debates and the preparation of a final report that was presented at the end of the conference. Each discussion session was structured around a selection of contributions, each of which was briefly introduced and followed a reaction from a pre-arranged reactor to inform the collective discussion.

The name of this group was previously Geometrical Thinking, and this was modified for this CERME to emphasize the focus on the teaching and learning of geometry. During the previous CERME, four competencies were used to describe geometrical thinking: reasoning, figural, operational and figural. The group took these dimensions as a background that was very helpful to understand each other and to compare our approaches to the issue of what is at stake in the teaching and learning of geometry.

This choice was all the more crucial given that many approaches and issues were discussed during the group sessions. Three main issues were addressed during the working group:

• The role of material activity in the construction of mathematical concepts, including using instruments, manipulation, investigation, modelling…

• Visualization and spatial skills;

• Language, proof and argumentation.

In comparison to the previous CERME, this time psychological points of view, among others, were represented. This raised new questions, often with very different theoretical and methodological backgrounds. As rich as the discussions were, mutual understanding was a great issue. Consequently, we did not focus, during the discussions, especially on one single topic at a given school level. In each of the three issues aforementioned, we tried to identify the interest of various theoretical or methodological approaches, of different cultural or institutional contexts, and the ruptures or continuity during the education process.

It is important to note that almost all the papers addressed 'classical' issues in this WG: this means teaching geometry to young children, the impact of specific contexts, geometrical activities in preservice teacher training, moving from practical to theoretical geometry, using Digital Geometry Environments, and so on. Nevertheless, the main part of the discussions were about confronting, sometimes in passionate ways, the theoretical and methodological approaches (for instance, didactical engineering was a 'classical' element for this WG) of the phenomena being studied. We try here to give an overview of these debates.

Topics of rich debate in the group

Role of manipulation and thoughtful experiment

This very broad topic has been a great field of study and experiment during the previous CERMEs. The discussed papers concerned students at all level, from kindergarten to university and included the use of instruments for investigation, manipulation and modeling. As these subtopics were strongly linked in the papers, we decided not to split the topic.

The use of two kinds of instruments was evident. One kind of instrument was in the form of 'material manipulatives' used as ways to enhance the didactical potentialities of the manipulation by pupils: such manipulatives include the protractor, paper-pin, mathematical machine, 2D and 3D shapes, miniature, compasses, and so on. The other kind of instrument the participants studied comprised various technological tools, including DGEs, videos, IWB, tutorial system, touch-screen tablet. Some papers described the use of only one kind of instruments, while other ones proposed educational environments in which the two kinds of tools were used by students and teachers within complementary and synergistic approaches.

Those papers had different approaches and theoretical backgrounds. For instance, there was discussions about papers that aimed at fostering the use of tools to mediate mathematical meanings (e.g. geometric reflection, Pythagorean theorem), with explicit reference to the theory of semiotic mediation. In papers that used DGEs or manipulation (of shapes, 3D models, geometric miniatures) to pass from the global spatial perception (iconic visualization) to an analytic visualization and to identify proprieties (non-iconic visualization), the main references were to the instrumental approach, the works of Duval and Van Hiele's levels.

Some of the papers examined how the use of tools give opportunities for new experiments that can be useful in teaching. These tools included images used as a way to stimulate dialogic talk amongst student, or technological tools used to change the way of teaching. In this last case, the double approach (didactic and ergonomic) was used.

Two papers focused on teacher education (pre-service and in-service) and reported on the use of DGE to improve generalization and geometrical construction (with their justifications within Euclidean geometry). Here it seems that DGEs are no longer 'new' and specific in the classes but nevertheless remain somewhat complicated within teachers' education.

The group noted, as detailed later, that there is a true need for improving the 'networking' between the didactical approach and the psychological approach concerning the use of tools.

Visualization and spatial skills

Some 8 contributions mentioned visualization or spatial skills as a keyword. This topic has been raised over the three previous CERMEs and continues to be an important and autonomous subject in our discussions. We chose to use the word skills rather than abilities, capacity or capability, as it can be that these latter terms induce pejorative interpretations, seeing it as something innate that cannot be changed or trained. The research questions were multiple and intertwined: What are the children spatial skills? How can we evaluate or train it? What is the role of spatial skills in the teaching and learning of mathematics? Visualization: what are we talking about? How to train visualization in geometry? What for? What are the links with language issues? We first had to clarify the relations between visualization and spatial skills: are these referring to the same thing?

In terms of spatial skills, these are related to a psychological point of view. They are linked to the perception, representation, (mental) manipulation of objects, orientation (following a path...), spatial knowledge, location in space. Spatial skills have many facets, and from a psychological point of view visualization is one of these (but it is not very precisely defined in the literature). Spatial skills are very important in mathematics education and has various meanings: sometimes it is not specific to geometry (STEM education), and sometimes it is linked to spatial problems and spatial knowledge (Berthelot & Salin). We pointed some mutual understanding issues between the two fields: for instance, micro/macro space (Berthelot & Salin) are similar to small/large scale (Montello).

What we called visualization is more specific to geometry, and involves combination of perception, interpretation and reasoning. It links perception to reasoning, and helps back and forth between practical and theoretical matters in geometry, so that it depends on spatial skills, mathematical constraints and language. Then, the precise meaning of visualization depends on the topics: visualization is not the same when drawing plane projections of 3D models or when trying to prove a result. From a didactical perspective it has a double naturepsychological and mathematicaland, in this case, spatial skills are a part of visualization. We will keep this acceptation in this text.

Spatial skills are very important for early geometry, as most of the tasks are related to the perception of the space: role in the learning of geometric characteristics of the shapes (Douaire & Emprin), need for the coordination of small/large scale, micro/macro space, local/holistic perception (Vendeira, Papadaki, Klaren)… A psychological point of view is crucial to make more clear general cognitive difficulties of the tasks, and a didactical one links it to the teaching of mathematics.

Visualization is more a mathematics education issue, so it is related both to spatial skills and to mathematical knowledge. In a general way, the question is "How to get enough information using a drawing to solve a given problem?". It is declined, with very different aims, in every context: as an obstacle (prototypical shapes or too obvious results), using DGS, differences with Autistic Syndrom Disorder students, identification of geometrical properties or characteristics on a drawing… It is a great issue for early geometry, but it is often neglected when students get older, and we suggest this should be studied.

Language, proof and argumentation

The former topics are linked to proof and argumentation by langage. Argumentation and formal proof are linguistic activities about abstract objects, but they involve working on material objects (and then manipulation and visualization). Many works pointed this out. For instance Fujita's dialogic process involves both visualization and social interaction, Klaren's work on ASD students suggests that not seeing a square as a rectangle could be lined to the dutch word for rectangle, and we worked on Duval's dimensional deconstruction which is a discursive process and visualization at the same time.

Some five contributions addressed proof and argumentation, not necessarily about proof itself but about ways of motivating proofs or argumentation. One topic for discussion was the influence of prototypical images on the reasoning process. Another topic was how teachers can have different concept images of a geometric figure (such as a rhombus) and different conceptions of a valid geometric construction of the shape. A third topic for discussion was the design of tasks that can provoke surprise, uncertainty or cognitive conflict, and tasks that can provoke the reconsideration of conjectures or proofs. This last consideration was strongly linked to the visualization issues, as for instance using non-euclidean geometry was seen as a way to give less visual information and to provoke the use of mathematical proof.

A particular focus for discussion was the digital environment QED Tutrix which is being designed to provide hints to the student user, while taking into account a judgment of the student's cognitive state based on the way they are using the system.

Perspectives and conclusion

As might be discerned from the introduction, and as can be found in the papers that follow, there are a number of topics that continue to be of great interest to this topic working group. These include the role of instruments, manipulation, representations, proof and argumentation, and initial geometrical knowledge, in geometry education. We also note that the variety of the teaching and learning contexts increased: young children, secondary school, pre and in-service teachers training, but also university, specific education (ASD students), clinical studies… The synthesis of this numerous points of view required intense and rich debates. At this CERME, in the continuity to the former ones, a number of topics became more important. These include visualization and spatial skills which had already been discussed in the last CERMEs, and language in doing geometry, whose role has increased during this session.

In conclusion, the working group continues to feature great diversity: in cultural backgrounds (curricula, school culture, teaching culture, research culture …), research questions, theoretical backgrounds and methodology. This continues to present some challenges in people understanding each other, sometimes linked to language and sometimes to what can be implicit meanings due to different research backgrounds.

A very visible benefit of the great diversity is that it invariably leads to very fruitful discussions and to attempts (and success) to clarify participants' points of view. In taking forward the work of the group, there is an increasingly important need for combining the frameworks, both theoretical and methodological.

Proceedings of CERME10


Thomas Martinelli
email: tmartinelli@chu-grenoble.fr

Jean-Luc Bosson

Luc Bressollette

Franck Pelissier

Eric Boidard

Jocelyne Troccaz

Philippe Cinquin

Robot-based tele-echography: Clinical evaluation of the TER system in abdominal aortic exploration

Keywords: Ultrasound, Abdominal cavity, remote operations, aorta

Objective: The TER system is a robot-based tele-echographic system allowing remote ultrasound (US) examination. The specialist moves a mock-up of the US probe at the master site and the robot reproduces the movements of the real probe, which sends back US images and force feedback. This tool could be used to perform US examinations in small health centers or from isolated sites. The objective of this study was to prove, in real conditions, the feasibility and the reliability of TER in detecting abdominal aortic and iliac aneurysms. Methods: Fifty-eight patients were included in two centers in Brest and Grenoble, France. The remote examination was compared to the gold standard, the bedside examination, on measuring diameters of the aorta and iliac arteries, detecting and describing aneurysms, detecting atheromatosis, duration, and acceptability. Results: All aneurysms (eight) were detected by both techniques as intramural thrombosis and extension to the iliac arteries. The interobserver correlation coefficient was 0.982 (p<0.0001) for aortic diameters. The rate of concordance between two operators in evaluating the atheromatosis was 84%±11 CI 95% . Conclusion: The TER system is a reliable, acceptable, and effective robot-based system to perform remote abdominal aortic US examination.

Introduction

Ultrasound (US) imaging is a key imaging modality because of its convenience and noninvasiveness, but it requires a specialist with the patient to perform the examination. This could be problematic for small healthcare centers or isolated locations. Tele-echography and robot-based echography could be a solution to provide US imaging capability to these locations. A pure telemedicine project such as the EU-TeleInViVo project still requires a specialist to move the probe, although an expert can provide an opinion remotely. Another type of project automates an echographic examination using a robot [START_REF] Pierrot | Hippocrate: a safe robot arm for medical applications with force feedback[END_REF][START_REF] Salcudean | Robot-assisted diagnostic ultrasounddesign and feasibility experiments[END_REF][START_REF] Abolmaesumi | Image guided control of a robot for medical ultrasound[END_REF]. Finally, a third category of robotbased systems enables the remote examination of patients by an expert who is not onsite [START_REF] Arbeille | Echographic examination in isolated sites controlled from an expert center using a 2-D echograph guided by a teleoperated robotic arm[END_REF][START_REF] Arbeille | The robot and the satellite for tele-operating echographic examination in Earth isolated sites, or onboard ISS[END_REF][START_REF] Arbeille | Fetal tele-echography using a robotic arm and a satellite link[END_REF][START_REF] Masuda | Three dimensional motion mechanism of ultrasound probe and its application for tele-echography system[END_REF]. The system presented herein comes within this third category; it includes force-feedback like the system used by Arbeille et al. This study aims to show that the TER system was clinically effective in real conditions of use.

Material and methods 1. Study population From March 2004 to March 2005, 58 patients were included by two centers separated by 1000km. Any patient with an abdominal aortic aneurysm and/or atherosclerosis could be included. Neither the method used for diagnosis (CT-scan, US, clinical examination, etc.), nor the operator who carried out the examination, were used as criteria for inclusion. In order to be in more realistic conditions, no exclusion was made based on age or morphological type. Pregnant women were excluded. All patients signed the agreement after being clearly informed of the aim and the modalities of the protocol, in conformity with the bioethics law. The protocol received the agreement of our national Health Committee. Patients were informed and signed an informed consent form.

The Robot-Based Tele-Echography

The goal of this study was to evaluate the master-slave robotized system called TER on clinical points to demonstrate the feasibility, reproducibility, and sensitivity of a remote US examination. We focused on the detection of aortic abdominal aneurysm (AAA) and iliac aneurysms. This system has already been described in the literature [START_REF] Vilchis | TER: a system for robotic tele-echography[END_REF][START_REF] Vilchis | Experiments with the TER tele-echography robot[END_REF][START_REF] Vilchis | A new robot architecture for tele-echography[END_REF]. It is a two-part system with a master site and a slave site. In this study, an experimental network was used.

The master site

The master site is the location of the physician during the examination. It is composed of a computer connected to a virtual US probe. This virtual probe is placed on a haptic control system to control the real probe. This haptic control integrates a PHANToM device (from SensAble Device Inc.), which has 6 degrees of freedom (dof) and renders 3D-force information. Position and orientation tracking of the virtual probe is performed within a workspace of 16 cm×13 cm×13 cm and with maximum a force of 6.4N. Information on the movement of the virtual probe is sent to the slave site to move the real probe. The physician watches the continuous ultrasound-image flow sent by the slave site. He can talk to the slave site and hear it (Figure 1). A webcam is also connected. Different data are visible on the screen of the master site (Figure 2): the ultrasound image, real-time force feedback information, and a virtual geometric model of the patient, views of the operator at the master site and of the examination room (sent by webcams) and information on the network status (transfer rates, connection status, etc.).

The slave site

The slave site is composed of the robot and the ultrasound device (Figure 3).

The robot

The slave robot is a parallel, uncoupled robot based on two independent structures dedicated to gross and fine positioning movements. Flexible cables are used to position and orient the US probe. The cables are connected to electrical motors. The translation movements on the surface of the body are controlled by four identical electrical motors connected by straps to a metal ring supporting the second parallel structure, as can be seen in Figure 4. The second parallel structure enables 3D orientation and translation along the Z axis of the US probe. Both subsystems can be controlled simultaneously.

The robot is controlled by a computer, which sends and receives data to and from the master site. A webcam and a microphone are also connected. Images from the ultrasound system are received by the computer and sent to the master site.

Information on the screen of the slave site is similar to what is rendered at the master site.

The US system

Two different systems were used on each site: a TITAN (Sonosite Inc., Bothell, WA) with a 3-to 5-MHz probe was used on one site, an HDI 5000 (Philips, Eindhoven, Netherlands) with a 3-to 5-MHz probe was used on the other site.

The network

The TER system used a VTHD network during experiments. This is a very high-speed experimental communication network created and supported by France Telecom with data rates of 1 Gb/s between the two sites.

Description of examinations

A single-blind protocol was used. A physician included a patient and the second physician redid the US exam with no information on the patient. The second operator used the same US system with the same probe but with the remote TER system instead of the normal examination procedure. There was no operator present during the remote exam. A second person was present during the TER exam, at the slave site, to help set up the patient, install the robot, and use the US system (taking measures, freezing the image acquisition, adjusting image parameters). Although this person had to be familiar with the usage of the US and the TER system, he or she could not comment or give medical advice during the examination. Depending on the day, this person was a nurse, a resident, or a physician, present to monitor the patient during the procedure. The exploration of the abdominal aorta and common iliac arteries was chosen because it provided the opportunity to explore a diffuse disease with multiple aspects (atheromatosis) and a focal disease (abdominal aortic aneurysm). Thus, qualitative and quantitative data could be evaluated.

For each examination (at the bedside and remotely), the following information was noted in the protocol register:

• Evaluation of the atheromatosis. Three stages can be noted: none, segmentary, and diffuse.

• Presence of an AAA and, if present, the maximum anteroposterior diameter and the presence or absence of intramural thrombosis. • Anteroposterior diameter of each primitive iliac artery.

• Evaluation of the examination with three score values ranging from 0 to 100.

The first two were for the operator and concerned the feasibility and the global quality of the exam. The third one was the evaluation of patient acceptance of the procedure.

At the end of the study, the right renal diameter was also recorded.

The classical method of examination (at the bedside) was used as the reference during this study.

Images of all measures were stored. Data are represented by median and range and/or percentage. The reproducibility of quantitative data was assessed by calculating interobserver correlation coefficients and relative errors. The reproducibility of the qualitative data was assessed by calculating κ (kappa). We used the Stata 9 software from Stata Corp. for statistics.

Results

1 1.

Aneurysms

Eight patients presented an abdominal aortic aneurysm (AAA) among the 54 who had a complete examination, for a 15% prevalence of AAA. The average anteroposterior diameter was 6.5 cm [3-17] CI 95% and the median was 5.4 cm. All aneurysms were diagnosed by both methods, as were the six cases of intramural thrombosis and the four extensions to the iliac arteries.

Evaluation of the atheromatosis

The conventional examinations found 14 patients without atheromatosis, 11 with segmentary lesions, and 28 with diffuse atheromatosis. The κ was 84% ±11 CI 95% . The mismatches were four diffuse forms graded as segmentary, two segmentary graded as normal, and one segmentary graded as diffuse.

4. Diameters a. Aorta The interobserver correlation coefficient was 0.982 (p<0.0001). The difference in measurements was less than 4 mm in 52 cases (96.3%), between 4 and 10 mm in one case (1.9%) and above 10 mm in one case (1.9%).

The median of the relative errors was 0 (Figure 5). The maximum and minimum relative errors were 34.5% and -26.1%. Of the measurement errors, 50% were less than 5% and 80% were less than 15%.

b. Common iliac arteries

The interobserver correlation coefficient was 0.760 (p<0.0001). The median relative error was -0.044. The maximum and minimum relative errors were 27.5% and -64.1%.

Examination duration and global satisfaction

The medium duration increased from 12 min ± 7 with the classical US exam to 17 min ± 8 with the remote examination on T-test for repeated measures (p<0.001).

The evaluation of the global quality of the examination was 75.6 ± 15 (SD) (p<0.01) for the remote examination and 87 ± 12.5 (SD) (p<0.01) for the classical examination. The patients evaluated the acceptability at 84 ± 18 with 90 for the median. Two patients gave a score less than 50.

Discussion

We collected clinical data on a new modality in radiology. We selected a pathology that allowed us to explore three types of echography data (qualitative, quantitative, semiquantitative).

We achieved the remote vascular exploration in nearly every case and we were able to explore every objective for each patient. The failures occurred at the beginning of the study and were mainly caused by the immaturity of this prototype system. The exploration was limited to the main vascular structures of the abdomen and pelvis but TER performed well in exploring an ideally placed structure such as the aorta and a more lateral structure such the common iliac artery. An examination of the entire abdominal cavity seems to be more difficult. In fact, the robot control is more delicate on the lateral sides of the abdomen. Consequently, the exploration of kidneys, spleen, and liver could be more difficult because the probe must be placed on the patient's sides or on the thoracic wall. Another study is needed to evaluate this point.

Every abdominal aortic aneurysm was diagnosed. The remote measurements were reliable. The greatest discrepancy between the remote and classical examinations occurred for the patient with the largest aneurysm (17 cm in anteroposterior diameter). The interobserver variability was good in comparison to data from the literature [START_REF] Singh | Intra-and interobserver variability in ultrasound measurements of abdominal aortic diameter. The Tromso Study[END_REF][START_REF] Wilmink | Quality of the measurement of the infrarenal aortic diameter by ultrasound[END_REF]. However, the reproducibility of the measurements was better for the aorta than for the iliac arteries but the absolute value for this difference was low.

In evaluating atheromatosis, the remote exam remained sensitive. We never had a difference greater than one level. We assume that some of the errors stemmed from the definition of levels. A fourth level between the 2 nd and 3 rd would have been useful.

The remote examination was slightly longer, but the duration of both types of procedure increased equally in a difficult examination situation. The practice of using the TER system seems to play an important role in the feeling of achievement of the examination. This is also a major point in the practitioner's overall satisfaction. In fact, this satisfaction decreases significantly with the remote exam, although nothing objectively proves that the remote examination is less effective than the bedside procedure.

The patients reported a very high satisfaction level. The two patients who gave a low score had an examination with a technical problem (among the four failed procedures).

The TER system can explore a large area but it may be harder to use over convex surfaces. The telemedicine systems using pure video transfers such as TeleInVivo are less appropriate for US exploration than TER because an expert is needed to carry out the exam; moreover, specifying probe motion remotely to the operator by oral orders may be difficult and nonintuitive. Another approach to robot-based tele-echography is illustrated in the Otelo system [START_REF] Arbeille | Echographic examination in isolated sites controlled from an expert center using a 2-D echograph guided by a teleoperated robotic arm[END_REF][START_REF] Arbeille | The robot and the satellite for tele-operating echographic examination in Earth isolated sites, or onboard ISS[END_REF][START_REF] Arbeille | Fetal tele-echography using a robotic arm and a satellite link[END_REF], which can explore only a small zone at a time and requires someone to move the system frequently to another zone, although this is done easily whatever the location. Having to reposition the system by hand may be an obstacle for easy clinical use. Today the TER system remains the only procedure that has been clinically evaluated using appropriate methodology. The other studies [START_REF] Arbeille | Echographic examination in isolated sites controlled from an expert center using a 2-D echograph guided by a teleoperated robotic arm[END_REF][START_REF] Arbeille | The robot and the satellite for tele-operating echographic examination in Earth isolated sites, or onboard ISS[END_REF][START_REF] Arbeille | Fetal tele-echography using a robotic arm and a satellite link[END_REF] were designed to evaluate the feasibility of the exams but not their sensitivity and specificity in detecting a disease in real patients, whatever their weight or age or echogenicity. They compared the ability of the robotized examination to visualize organs well but never tested real efficacy. Our system showed good results on qualitative variables (atheromatosis, aneurysms, and intramural thrombosis) and quantitative (diameters) data.

Conclusion

We have demonstrated that a remote examination with the TER system is possible as an everyday examination to detect, measure, and describe an abdominal aortic aneurysm or iliac aneurysm. It is a safe, sensitive, and reliable exploration. Compared to the bedside examination, it is as sensitive and the measurements are reliable. It is the first tele-echography system that has proved its reliability in real conditions. Another study has begun to determine whether these results can be extended to the exploration of the entire abdominal cavity in an emergency unit.

Legends : Figure 1: The master site Figure 2: Screen of the master site Figure 3: The slave site Figure 4: The probe and the support Figure 5: Relative errors of the aorta diameters

Table 1 :

 1 Risk factors

	Risk Factor	Nb of
		patients
	Hypertension	14 (26%)
	Dyslipemia	9 (17%)
	Smoker (old or active)	30 (52%)
	Coronary failure	9 (17%)
	Supra-aortic trunk atheromatosis	8 (15%)
	Claudication (stage II)	13 (21%)