Maxime Jonard

Maggy Colas

Yann Leventoux

Tigran Mansuryan

Julie Cornette

Alessandro Tonello

Stefan Wabnitz

Mario Zitelli

Fabio Mangini

Mario Ferraro

Yifan Sun

Sébastien Février

Jean-René Duclère

Vincent Couderc

Claire Lefort

Towards a new understanding of optical poling efficiency in multimode fibers

) is unveiled by means of multiphoton microscopy. The shortest period (tens of micrometers) is due to the beating between the fundamental and the SH beams, and it is responsible for their quasiphase matching (QPM). Whereas the longest period (hundreds of micrometers) is associated with the periodic evolution, or self-imaging, of the power density of the MM beam along the GRIN MM fiber. The complex modal beating, leading to spatial self-cleaning of the fundamental beam, is thus printed inside the fiber core, and revealed by our measurements. We considered two fibers of similar composition and opto-geometric parameters, and we compared the evolution of the optical poling process with time. Despite the rather similar fiber characteristics, we observed a striking difference in the poling efficiency between the two fibers. Such observation led us to point out the importance of considering the complete fiber fabrication process (both the preform elaboration and the drawing steps) on the final structure and microstructure of optical fibers.

INTRODUCTION

Optical fibers are commonly composed by amorphous silica glass, and their centrosymmetric nature forbids the efficient generation of a SH by using a laser at fundamental frequency (FF). However, in 1986, Österberg described for the first time the nonlinear effect which is induced by the optical poling mechanism [START_REF] Osterberg | Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber[END_REF]. In the following year, he showed how the writing of a second-order susceptibility (χ (2) ) in the fiber core can lead to a QPM mechanism [START_REF] Osterberg | Experimental studies on efficient frequency doubling in glass optical fibers[END_REF]. After such a major breakthrough, Stolen, Djanov, and Balakirev, theoretically described the phenomenon of SH generation in optical fibers [START_REF] Stolen | Self-organized phase-matched harmonic generation in optical fibers[END_REF][START_REF] Dianov | Photoinduced generation of the second harmonic in centrosymmetric media[END_REF][START_REF] Balakirev | Efficiency of optical poling of isotropic media[END_REF]. In particular, they showed how the susceptibility χ (2) is not homogeneously distributed along the fiber, since it is associated with the coherent periodic beating between a fundamental and its second harmonic. More recently, several groups have demonstrated the impact on SH generation of the optical poling mechanism in Ge-doped MM fibers, and its connection with the spatial self-cleaning effect at the FF and SH wavelengths [START_REF] Grudinin | Nonlinear mode coupling in multimode optical fibers; excitation of femtosecond range stimulated-Raman-scattering solitons[END_REF][START_REF] Eftekhar | Instant and efficient second-harmonic generation and down-conversion in unprepared graded-index multimode fibers[END_REF][START_REF] Ceoldo | Second harmonic generation in multimode graded-index fibers: spatial beam cleaning and multiple harmonic sideband generation[END_REF][START_REF] Krupa | Multimode nonlinear fiber optics, a spatiotemporal avenue[END_REF]. The study and understanding of nonlinear effects in MM fibers has recently regained considerable interest. Indeed, MM fibers are a cheap, easily accessible and ideal platform for the observation of new nonlinear phenomena, such as multimode solitons, Raman effect, geometric parametric instabilities (GPI), spatial Kerr self-cleaning, and optical wave condensation [START_REF] Zhu | Observation of multimode solitons in few-mode fiber[END_REF][START_REF] Krupa | Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves[END_REF][START_REF] Krupa | Spatial beam self-cleaning in multimode fibres[END_REF][START_REF] Podivilov | Hydrodynamic 2D turbulence and spatial beam condensation in multimode optical fibers[END_REF][START_REF] Fusaro | Dramatic acceleration of wave condensation mediated by disorder in multimode fibers[END_REF][START_REF] Liu | Kerr self-cleaning of femtosecond-pulsed beams in graded-index multimode fiber[END_REF][START_REF] Wright | Self-organized instability in graded-index multimode fibres[END_REF]. Quasi-single-mode second harmonic generation in MM fibers can be also added to the list of these novel processes.

Nonlinear MM fiber optics is at the basis of a series of wave mixing mechanisms, leading to the creation of new frequencies. We show here that SH generation can be controlled by managing the optical poling process in MM fibers. This scenario also raises new questions: how a periodically poled second-order nonlinearity can compete and coexist with third-order spatial and spectro-temporal processes, such as Kerr self-cleaning, GPI generation, and soliton dynamics? Thus, a complete understanding of the physical phenomena that occur during the optical poling is a key issue for controlling the process of new frequency generation via the mixing of  (2) and  (3) nonlinearities.

In this paper, we describe experiments based on the optical poling of two MM Ge-doped GRIN fibers. The two fibers, which are produced by two different manufacturers (Thorlabs and Alcatel), have the same core and cladding diameters (50/125 µm). The refractive index difference between the core and the cladding is also the same, and in both fibers it is realized by Ge dopants. Although the poling process followed the same protocol, the two fibers showed two radically different SH conversion efficiencies. More specifically, in the case of the 50/125 µm MM fiber provided by Thorlabs, no significant SH signal was observed at the fiber output. Whereas by using the Alcatel MM fiber, optical poling led to 1% SH conversion efficiency. Our research focuses on the origin of this difference between those two, nominally identical, germanium-doped fibers. We first performed a characterization of the second-order nonlinearity in the core of the optical fibers by means of longitudinal multiphoton microscopy, in particular for detecting the local SH generation. Thus, for the first time the χ (2) inscription resulting from poling processing combined with spatial self-imaging (SSI) was experimentally visualized [START_REF] Hansson | Nonlinear beam self-imaging and self-focusing dynamics in a GRIN multimode optical fiber: theory and experiments[END_REF]. We completed this study by analyzing the core and cladding properties of the two fibers by means of energy dispersive X-ray spectroscopy (EDS) and Raman spectroscopy. We demonstrated that the poling efficiency is directly dependent on the silica structures, and more precisely on the different size of SiO2 rings, which compose the glass after fiber drawing. We also measured the competition between the different frequency conversion processes such as GPI, SH, and third-harmonic generation (THG).

MATERIALS AND METHODS

Figure 1 illustrates the experimental setup used for our poling experiments. A Nd:YAG laser delivers 740 ps pulses with a central wavelength fixed at 1064 nm. The average power is 1.5 W, with a repetition rate of 27 kHz. Such a system delivers peak powers up to 75 kW for 56 µJ of energy per pulse. This input beam is coupled into the two-meter-long Gedoped MM-GRIN fibers. Two Ge-doped MM-GRIN fibers with 50 µm core diameters and provided by two different manufacturers (Thorlabs and Alcatel), have been used for carrying out the comparative analysis. The laser beam is coupled into the MM-GRIN fibers by using a convergent lens of 8 mm of focal length, moved by a three-axis mechanical mount. The average power of the laser source and the input polarization beam state are controlled by two half-wave plates (λ/2) and a polarizer cube. A CCD camera with two bandpass filters (1064 nm, 10 nm FWHM and 532 nm, 10 nm FWHM) allows to record the spatial beam profile at FF and SH. A power meter, jointly with optical filters are used to record the average output power. A type-II KTP crystal, cut for second harmonic generation at 1064 nm, is placed before the optical fiber to initiate the poling process. After initial feeding, the KTP is removed, and the poling is left to grow larger by using only the initial SH which is created in the first centimeters of the MM fiber.

Experimental characterization of optical poling along the fiber

The characterization of the writing effect associated with the poling process was carried out along the fiber by means of multiphoton microscopy. The inscription of a χ (2) susceptibility in the core of the fiber can be detected by measuring the second harmonic light, which is side-emitted when launching femtosecond pulses in a direction which is perpendicular to the fiber axis. This characterization method is often used in microscopy, in order to image biological samples containing non-centrosymmetric structures, such as collagen or myosin. We used a commercial Olympus multiphoton microscope (BX61WI) coupled with a tunable titanium-doped sapphire (Ti:Sa) femtosecond laser system (Chameleon Ultra II, Coherent Inc). The excitation wavelength was set at 810 nm, and the detection was performed by a photomultiplier tube (PMT) combined with a detection filter centered at 405 nm, with a spectral width of 10 nm and a dichroic mirror (650 nm). We used two microscope objectives: the first was a Nikon objective with a large field of view (MRH00101, 10X, 0.3), whereas the second was an Olympus objective (XLPLN25XWMP, 25×, NA 1.05, W). A 2D translation stage allowed us to explore the sample with the infrared laser, in order to create 2D images at different optical planes. Sequential acquisitions of 2D image stacks combined with axial scanning (the microscope objective was moved by steps of 1 μm), permitted us to reconstruct the 3D distribution of the  (2) nonlinearity.

Characterization of the chemical composition of the core by electron microscopy

We use a chemical analysis electron microscope in order to obtain the features of the two fibers. Energy dispersive X-ray spectroscopy allows for determining the chemical composition of the samples. We carried out a profile analysis of the two fibers. In Figure 2, we may notice a parabolic evolution of the Germanium ions, leading to the parabolic refractive index profile of the MM fiber. Qualitatively the Germanium and Silicon content are the same between the two fibers, which is coherent with an identical nominal value of Δn of 0.015.

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EXPERIMENTAL RESULTS

Optical Poling of a 2-meters-long MM-GRIN fiber from Alcatel

In the case of the Alcatel fiber (drawn from a preform elaborated by the Modified Chemical Vapor Deposition (MCVD) process), optical poling successfully led to efficient SH generation: 10 mW of SH average power was obtained for 1 W of FF average power, reaching in these conditions a maximum SH conversion efficiency of 1%. Figure 3 shows the evolution over time of the average power of the SH, which is measured at the fiber output. A maximum of SH is obtained after minutes of laser exposure, before the saturation of the optical poling.

Characterization of the poling structure by multiphoton imaging

The quadratic nonlinearity inscription into the fiber core was revealed, thanks to a standard multiphoton microscope. The measurement was realized in the first 40 cm of the optical fiber, where the spatial self-cleaning effect of the FF MM beam was not yet obtained. The complex  (2) structures, which result from the poling process in the presence of MM beam propagation, are clearly visible in Figure 4a. The spatial self-imaging showing the periodic replication of the transverse spatial distribution of a beam is experimentally illustrated here for the first time in our knowledge. We can still observe the presence of a short-scale beating period, which creates a local  (2) leading to SH generation peaks, approximately spaced

A B

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by 20 µm. Because of the parabolic refractive index profile of the fiber, beam self-imaging occurs in the MM fiber, which leads to a modulation of the amplitude of the second-order nonlinearity with a periodicity close to 0.55 mm. The same measurements have also been carried out at distances further down the fiber, where spatial self-cleaning takes place. Here the poling profile is significantly more uniform: a more regular distribution of  (2) results, owing to the dominant contribution of the fundamental mode (see Figure 4b). Consequently, the transverse near-field profiles of both the output fundamental and SH beam exhibit a bell shape (see insets in the figure 4).

Figure 4. Experimental characterization of the χ (2) nonlinearity written into the Alcatel optical fiber by using multiphoton microscope. a, image of the  (2) nonlinearity distribution in the first 40 cm of the fiber, i.e., before the Kerr self-cleaning process takes place; b image of the  (2) nonlinearity distribution in the fiber after the occurrence of spatial self-cleaning. Insets: images of the output beam near-fields for FF and SH beams.

The second-order nonlinear conversion is obtained thanks to a mechanism of QPM between FF and SH, which is introduced by the periodic inscription of the χ (2) . The transverse distribution of the second-order nonlinearity is also modulated by the self-imaging process [START_REF] Mangini | Experimental observation of self-imaging in SMF-28 optical fibers[END_REF]: the experimental period of ξexperimental = 550 µm is consistent with the theoretical period of ξtheoretical = 545 µm [START_REF] Hansson | Nonlinear beam self-imaging and self-focusing dynamics in a GRIN multimode optical fiber: theory and experiments[END_REF]. Thus, for the first time, the presence of poling could be directly visualized inside the MM fiber core, which highlights the role of charge displacements under the effect of the optical field beating. The results of Figure 4 experimentally confirm the complex distribution of χ (2) , and also provide an experimental proof of the spatial MM evolution of the FF beam towards a spatially clean profile.

Please verify that (1) all pages are present, (2) all figures are correct, (3) all fonts and special characters are correct, and (4) all text and figures fit within the red margin lines shown on this review document. Complete formatting information is available at http://SPIE.org/manuscripts Return to the Manage Active Submissions page at http://spie.org/submissions/tasks.aspx and approve or disapprove this submission. Your manuscript will not be published without this approval. Please contact authorhelp@spie.org with any questions or concerns. Besides SH generation, as shown in Figure 5, we also observed other processes that lead to conversion of the FF into other wavelengths. In figure 5C, the fundamental beam is framed by two lateral lines, representing the Stokes and the anti-Stokes lines of Raman conversion. Generation of GPI is also visible close to 735 nm, which represents the anti-Stokes line of the first-order conversion. Finally, the wavelength at 355 nm represents the third-harmonic generation of the FF pump beam.

Because of these multiple frequency conversions, it is clear that the poling process competes with several other nonlinear effects, each of them depleting the initial pump, and limiting the writing of a second-order nonlinearity.

Optical Poling of a 2-meters-long MM-GRIN fiber from Thorlabs

We performed a second set of experiments under the same experimental conditions as in subsections 3.1 and 3.2. We used the 50/125 Ge-doped MM-GRIN fiber from Thorlabs (drawn from a preform elaborated by the Outside Vapor Deposition (OVD) process). The same poling protocol was implemented in all of the experiments. In this case, the average SH power measured at the output of the 2-meters long MM-GRIN fiber was very low when compared with the previous results obtained with the Alcatel fiber. The average SH power was at best 0.1 mW, indicating a failure of the poling process. As expected, the multiphoton microscope images did not reveal any significant second-order nonlinearity.

Analysis of the local structure of optical fibers by Raman spectroscopy

In order to elucidate the reason for such a significant difference in the poling process efficiency, we carried out a complementary investigation for each fiber. Specifically, we characterized the local structure (short and medium range orders) of the fiber core by means of Raman spectroscopy. Figure 6 illustrates the Raman spectra that were recorded for the two fibers. One can appreciate a clear difference in the spectrum at three distinct wave numbers: below 400 cm -1 , which is representative of the largest tetrahedron rings, at 489 cm -1 , which is representative of the 4 tetrahedron rings, and at 606 cm -1 , which is representative of the 3 tetrahedron rings [START_REF] Martinet | Radial distribution of the fictive temperature in pure silica optical fibers by micro-Raman spectroscopy[END_REF]. Thus, despite the same Ge doping and opto-geometric parameters, these vibrational spectroscopy data testify to a slight difference in the local structure of these two fibers, which might be at the origin of the different poling efficiencies [START_REF] Lancry | Fictive temperature in silica-based glasses and its application to optical fiber manufacturing[END_REF]. More specifically, it is reasonable to connect all that to the different overall processes undergone for the production of the two MM GRIN fibers, i.e. different methods employed for the fabrication of the preform (MCVD vs OVD) and different fiber drawing conditions [START_REF] Geissberger | Raman studies of vitreous SiO2versus fictive temperature[END_REF][START_REF] Tomozawa | Optical Fiber Reliability and Testing[END_REF].

CONCLUSION

The optical poling technique has recently regained interest for the generation of new spectral frequencies by using MM fibers. In the present work, we have revealed that a drastic difference in the poling efficiency may exist between two nominally identical fibers. These MM fibers are provided by two different fiber suppliers (Thorlabs and Alcatel), but otherwise exhibit the same chemical composition and similar opto-geometric parameters. In particular, it was only possible to observe a clear generation of SH, during the time of exposure of the poling process, when using the Alcatel fiber. The imprinted second-order nonlinearity has been experimentally visualized by using a multiphoton microscope, which permits to reveal its complex distribution along the fiber, as a result of MM propagation along the initial fiber section. When repeating the same characterization at the fiber end, we obtained a much more uniform distribution. Here, the poling process was mainly driven by the presence of a Kerr self-cleaning process for both the FF and the SH. Such regularity in the local writing process may, in turn, provide a clear proof of the presence of the spatial self-cleaning process which is obtained along GRIN optical fibers. The experimental analysis carried out through EDS and spontaneous Raman scattering spectra measurements has guided our reasoning towards the impact of the internal structure and microstructure of the material, for explaining the observed drastic difference in poling efficiency between the two MM fibers. All this will be commented in details in a forthcoming full article.

Figure 1 .

 1 Figure 1. Experimental setup for all-optical poling of MM GRIN fibers.

Figure 2 .

 2 Figure 2. Molecular profile of chemical elements within the diameter of the two fibers. A. Chemical distribution of the 50/125 fiber from Thorlabs B. Chemical distribution of the 50/125 fiber from Alcatel.

Figure 3 .

 3 Figure 3. Optical poling of a 50/125 Alcatel MM-GRIN fiber. The red line is a guide for the eyes, to evidence the SH signal saturation.

Figure. 5 .

 5 Figure. 5. Spectral analysis of all of the wavelength conversion phenomena observed during the poling process in the Alcatel MM GRIN optical fiber. A and B show the average power of SH (top) and GPI (bottom) versus the poling time. C illustrates the evolution of all of the wavelengths which are observed at the fiber output, vs. the poling time.

Figure 6 .

 6 Figure 6. Raman spectra collected at the central part of the core for the two MM fibers. ABP and TBP respectively stands for Alcatel and Thorlabs Before Poling.

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ACKNOWLEDGEMENTS

We acknowledge the financial support of the following grants: Agence Nationale de la Recherche (ANR-10-LABX-0074-01, ANR-18-CE080016-01); Horizon 2020 EU programme via the European Research Council Advanced Research Grant (740355); Ministero dell'Istruzione, dell'Universit`a e della Ricerca (R18SPB8227); As well, this work was supported by institutional grants from the LabEX SigmaLim (ANR-10-LABX-0074-01) and benefited of some fundings via both the TRAFIC project (ANR-18-CE08-0016-01) and the F2MH project (AAP NA 2019-1R1M01).


Alexandre Saadi

Alice Rogier

Anita Burgun

Rosy Tsopra

Design of an ontology-based triage system for painful patients

Keywords: Clinical Decision Support System, Chronic pain, Ontology

Objective: Waiting time for a consultation for chronic pain is a widespread health problem. This paper present the design of an ontology use to assess patients referred to a consultation for chronic pain.

Methods: We designed OntoDol, an ontology of pain domain for patient triage based on priority degrees. Terms were extracted from clinical practice guidelines and mapped to SNOMED-CT concepts through the Python module Owlready2. Selected SNOMED-CT concepts, relationships, and the TIME ontology, were implemented in the ontology using Protégé. Decision rules were implemented with SWRL. We evaluated OntoDol on 5 virtual cases.

Results: OntoDol contains 762 classes, 92 object properties and 18 SWRL rules to assign patients to 4 categories of priority. OntoDol was able to assert every case and classify them in the right category of priority.

Conclusion: Further works will extend OntoDol to other diseases and assess OntoDol with real world data from the hospital.

Introduction

Chronic pain is reported by 30% of people in occidental countries and 7% of them suffer from neuropathic pain [START_REF] Bouhassira | Prevalence of chronic pain with neuropathic characteristics in the general population[END_REF]. The increase in demand for access to specialized pain management services continues, and waiting time for an appointment with a specialist is a problem in many countries [START_REF] Gilron | Economics of chronic pain: How can science guide health policy?[END_REF]. Therefore methods to prioritize patients with the greatest need becomes of increasing importance. Contrasting with other domains where algorithms may be learnt from data bases (e.g., image classification), patient triage relies on explicit gudelines-based criteria established by medical associations. The International Association for the Study of Pain (IASP) published guidelines about the waiting time for some disease and painful situations. In France, the Health Authorities published guidelines about the pathway that patients should follow before being referred to a Pain Clinic. Patients must go through a pre-defined list of exams, including biological tests and specialized consultation (e.g., consulting a rheumatologist for chronic low back pain). Only when all these tests have been performed, the general practitioner may ask for an advice by the pain physician. Patient is referred with a letter. The pain physician has to make a decision about the rank of priorities of the referral according to the queue and a list of criteria. Many determinants that influence the risk of chronic pain have been identified, regarding for example the risk of transition from acute to chronic pain after surgical procedures [START_REF] Glare | Transition from acute to chronic pain after surgery[END_REF]. The aim of the project was to develop and implement a triage system for referrals to a pain clinic. It would create a standardized automated process based on evidence and guidelines thus ensuring equity for patients; improve access to the pain clinic leading to prompt assessment based on patient needs; and overall improve the referral system to increase referrer satisfaction and the quality of patient care. In order to ensure explainability and adherence to guidelines, the first step consisted in building a knowledge base of expert rules based on a domain ontology. The ontology provides formal definitions of concepts and their relationships using the Web Ontology Language (OWL 2) [START_REF]OWL 2 Web Ontology Language Document Overview (Second Edition)[END_REF], as well as inference capabilities to classify patients. In this paper, we present the design of our ontology, called OntoDol, as well as the results obtained on virtual patients' cases of complex regional pain syndrome.

Methods

OntoDol is intented to be used by physicians when they manage a new referral into a pain consultation center. Therefore, OntoDol requires concepts associated with pain findings and characteristics, painful diseases and comorbidities (present or past), drugs (substances and products), procedures either for pain treatment or causing pain, anatomic descriptors, functionnal activities, biologic or imaging data, risk factor of chronic pain, demographics data and social context information. The following principles guided the design of OntoDol: reuse of existing ontologies as much as possible, coverage driven by the content of the international guidelines related to chronic pain, alignment with reference ontologies like SNOMED CT® (Systemized Nomenclature of Medicine -Clinical Termes) to make the clinical decision system interoperable with EHR systems, use of the capabilities of descriprion logics to classify patient cases, and addition of rules if needed.

Reuse of existing ontologies

We explored the National Center for Biomedical Ontology (NCBO) Bioportal and OBO Foundry repositories to search for existing resources. We found that 'Pain' was a class present in 71 ontologies, and 'Neuropathic pain' in 31 ontologies. None of the corresponding ontologies provided a complete coverage for patient triage for a first consultation in a pain clinic.

We decided to use SNOMED CT® as reference ontology since it is the most comprehensive international clinical terminology. The 2021-01-31 release contains more than 350 000 concepts. and is broadly used to document patients' signs, symptoms, and diagnoses in EHRs.

We also imported the TIME ontology to model temporal aspects such as duration of symptoms, the date of onset of a disease, or demographic data like date of birth and age.

Identification of key clinical entities

Two clinical practice guidelines (CPGs) related to chronic pain were explored, namely, the CPGs from IASP [START_REF]IASP_Wait_Times[END_REF], which are based on CPGs from Canada, the United Kingdom, Finland, Norway, and Australia, and the CPGs established in France by the French Health Agency , "Haute Autorité de Santé' and the French Society for the Study and Treatment of Pain (SFETD). Moreover articles published on PubMed, were reviewed by a clinicial specialist in chronic pain. Based on these resources, a set of key clinical terms that are central to the domain of chronic pain management were identified to populate the core OntoDol ontology. Starting from this seed ontology, we used a broad medical ontology, namely SNOMED-CT to extend its coverage, provide mapping to standard concepts, and enrich the seed ontology with further concepts and relations.

Design of OntoDol

We used Python module Owlready 2 to create our ontology from the key clinical concepts and SNOMED-CT [START_REF] Lamy | Owlready: Ontology-oriented programming in Python with automatic classification and high level constructs for biomedical ontologies[END_REF]. Owlready 2 uses the release 2020AB-full of the Unified Medical Language System (UMLS) to import Metahthesaurus terms. Every term is mapped to SNOMED CT® Terminology. The PyMedTermino module from Owlready 2 mapped a list of terms with SNOMED CT® identifiers. Axioms were generated using object properties of interest. When some terms were not mapped within SNOMED CT®, experts had to map them manually to the closest concept, using the SNOMED CT® browser. Experts were asked to choose the smallest level of granularity with a significant clinical definition. We developed a bottom-up method to extract the parents in SNOMED-CT® and integrate them in OntoDol. When the level of granularity of the mapped concept was too coarse, we used a top-down a to collect the descendants. Thus Owlready 2 created an automatic hierarchy with an is_a relationship between classes.

Object properties, i.e., relations between classes are defined in the SNOMED CT® as attributes of the Concept Model Object Attribute top class. Starting from the list of concepts obtained from the SNOMED CT®, we selected a set of object properties of interest. Then, a Python script using Owlready was used to retrieve all axioms using all defined classes and object properties. When relations between concepts were missing, new object properties were created, e.g. the relation between a disease and its phase. Data properties are relations between an individual and a primitive data type. In OntoDol, they are used to describe time and duration data using TIME i.e. 'Date of symptom onset' and 'Time since symptom onset' and value of pain assessment i.e. 'has Value (EVA) xsd:int [0-10]'

Create SWRL rules

We implemented the clinical reasoning extracted from CPGs in the form of SWRL rules. According to IASP guidelines, there are four categories of priority: 'Immediately', 'Most urgent', 'Urgent or Semi-urgent' and 'Routine or regular'. Using SNOMED CT® concepts, we defined four categories of priority: 'Immediate', 'High', 'Delayed' and 'Normal'. The objective was to support the classification of all patients in one of those categories.

Most of OntoDol classes are defined classes. SWRL rules and built-in rules were added to support deductive reasoning, i.e. 'antecedent'  (implies) 'consequent', assumptions where antecedent and consequent are conjunctions of atoms.

We used SWRL rules to:

-Define priority rules, -Define diseases as an association of findings, -Calculate time duration between dates (date of onset of symptom, current date, date of an event like a surgery…)

Evaluation of the ontology

We conducted a two-stage evaluation of OntoDol. First, we evaluated its intrinsic properties, then we performed a user evaluation. Our ontology should respect some properties:

 Clarity : all terms are given an understandable rdfs:label based on SNOMED CT® terminology.

 Accuracy and reliability: OntoDol is based on guidelines published worldwide.

 Completeness of content coverage: OntoDol covers key elements of the domain, allowing a closed-world assumption.

 Consistency checking: Pellet was used for consistency checking

The ability of the OntoDol to classify parients was tested on a set of 5 virtual cases of complex regional pain syndrome (CPRS). This disease is characterized by a neuropathic pain on a limb and can be associated with a disability for walking.

Considering the previous clinical guidelines, the proirity depends on the clinical findings (disease or finding), duration of the pain, pain intensity, and associated disabilities.

Results

OntoDol ontology

We used the open source editor Protégé developed by Stanford in its version 5.5.0. We chose Pellet as the reasoner, as it supports Semantic Web Rule Language (SWRL) and SPARQL queries [START_REF] Dentler | Comparison of reasoners for large ontologies in the OWL 2 EL profile[END_REF]. OntoDol ontology is encoded in OWL 2 file format using Protégé 5.5.0. Metrics are listed in Table 1.

Owlready imported understandable rdfs: label, rdfs:Prefered US Terms and rdfs: Synonym US Terms. We provided textual rdfs:definition.

Top hierarchy of OntoDol is shown on Figure 1, it reuses the hierarchy of SNOMED CT® so it could be interoperable with EHR data. TIME, as a recommandation of W3C, infered temporal concept from SNOMED CT® as time:instant or time:duration.

SWRL rules 18

Asserted properties come from Owlready 2. Eighteen SWRL rules were implemented. An example of axioms in SWRL used for triage is shown in Table 3.

Testing with a focus on clinical case

We ran Pellet reasoner in OntoDol to classify five virtual patient referred for a consultation for an acute phase of CPRS of the right foot, with different evolution phases and different levels of pain.

OntoDol was able to classify the 5 patients in the correct categories 'immediate priority', 'high priority', 'delayed priority' or 'normal priority', according to the recommandation of IASP (Table 2), Ontodol was able to:

 Infer that the association of findings reported by the virtual patient was a CPRS (Figure 2);  Determine the acute or chronic phase of CPRS depending on the duration, less or more than 3 months since the onset of symptoms, using TIME data properties;

 Provide an assessment of the level of pain according the 0 to 10 visual analogic pain scale as a mild, moderate or severe pain;

 Determine the priority of the consultation for pain (Figure 3 & Figure 4); A painful severe condition with the risk of deterioration or chronicity, such as the acute phase of complex regional pain syndrome (CRPS) [...] 'Consultation for pain (procedure)'(?c), 'has Focus'(?c, ?f), 'Complex regional pain syndrome (disorder)'(?f), 'has Phase'(?f, ?ph), 'Acute phase (qualifier value)'(?ph), 'has Priority'(?c, ?p), 'Priorities (qualifier value)'(?p)  'Consultation for pain (procedure)'(?c), 'has Focus'(?c, ?f), 'Complex regional pain syndrome (disorder)'(?f), 'has Priority'(?c, ?p), 'High priority (qualifier value)'(?p)

Discussion

We developed OntoDol ontology as a basis for a clinical decision support system and we presented it with a focus on a set of five cases of CPRS with different assessments of pain intensity, clinical courses, and disability due to the pain.

OntaDol was able to assign all the virtual clinical cases to the correct category of priority for a consultation in a pain center.

The solution adopted in OntoDol provides a high-level ethical framework that can be used to guide decision-making in the domain of chronic pain. Whereas data-driven AI algorithms may be questionable for patient triage, the algorithm implemented in OntoDol is a knowledge-based one, thus it is :

 Transparent, i.e. the decisions and their justifications are explicit;

 Consistent, i.e. all cases in the same category are classified in the same way;

 Accountable, i.e. the decisions rely on the guidelines established by the domain experts.

Although further external evaluation is required before using OntoDol for automated triage, the preliminary results are encouraging. The originality of this work is that we directly use parts of SNOMED CT® making it interoperable with EHR. The pain domain has not been covered entirely in OntoDol yet. We need to add more clinical findings related to pain, body structures related to those clinical findings and scales use in assessment of pain, mood or disability. A new version of the SNOMED CT® is published every six months.

An updating system is necessary to collect new terms or new relations.

Chronic pain has been defined as a global public health priority during the last decade [START_REF] Goldberg | Pain as a global public health priority[END_REF]. The high prevalence and incidence of chronic pain, its substantial and growing comorbidities, contrasting with the limited number of specialists in pain medicine provide ample justification for providing computerized aids to clinicians. Patient triage and priority setting have been identified as major concerns for all health systems. When specialized resources are limited, setting priorities is required, but choices must be explicit and based on shared recommendations. Some authors created ontologies of pain [START_REF] Smith | Towards an Ontology of Pain[END_REF], but the clinical application for referral management is limited. Some previous work designed webbased clinical decision support for patients with low back pain in primary healthcare in the Netherlands [START_REF] Nijeweme-D'hollosy | Design of a Web-based Clinical Decision Support System for Guiding Patients with Low Back Pain to the Best Next Step in Primary Healthcare[END_REF]. In other domains, similar solutions have been designed for triage, for exemple in emergency department [START_REF] Wunsch | A Semantic-Based Model for Triage Patients in Emergency Departments[END_REF] using concepts of a web semantic computing.

Further works will map OntoDol with ICD11 for diagnosis and LOINC for clinical, biological and scales concepts and ATC for drugs labels. The 10 th version of the ICD is currently used in most countries and the 11 th version is about to be released with a new classification regarding painful diseased [START_REF] Treede | Chronic pain as a symptom or a disease: the IASP Classification of Chronic Pain for the International Classification of Diseases (ICD-11)[END_REF]. In the future, OntoDol will be plugged to our clinical data warehouse to evaluate it on real cases extracted from the hospital information system and to compare the classification made by OntoDol against the classification by a pain specialist.

Conclusions

Using a semi-automatic method, we designed OntoDol, an ontology for chronic pain referral management, based on expert guidelines. Further work will add more classes, and more rules according to specific pathologies, defined indicators for risk of chronic pain and will have to evaluate validity compared to standard of care using real patient case from the clinical dataware house.

Figure 1 :

 1 Figure 1: Top hierarchy of OntoDol' using a part of SNOMED CT® top-hierarchy and TIME.

Figure 2 :

 2 Figure 2: Example with a fictional patient having 'Swelling of lower limb (finding) and a Pain in lower limb (finding) and a Walking disability (finding). Object property assertions make relations with qualifier value related to clinical course, an evaluation of pain using a visual analogic pain scale and date of symptom onset.

Figure 3 :Figure 4 :

 34 Figure 3: The fictitious patient is related to a consultation (procedure). OntoDol is able to infer that the consultation has a focus on painful disease,

Table 1 :

 1 OntoDol metrics

	Metrics	Values
	Number of classes	762
	Axioms	4368
	Object properties	92
	Data properties	30
	Individuals	62

Table 2 :

 2

	# Situation	IASP	OntoDol
		guidelines
	1 Acute CPRS and moderate	Urgent	High
	pain and walking disability		Priority
	2 Acute CPRS after surgery	Immediate	Immediate
	and severe pain and walking
	disability
	3 Chronic CPRS and mild	Routine	Normal
	pain and no disability
	4 CPRS > 6 months and	Semi-urgent Delayed
	severe pain and walking
	disability
	5 CPRS > 12 months and	Routine	Normal
	moderate pain and walking
	disability

Priorities inferred by OntoDol in a set of fictional training cases comparing to IASP guidelines. All the patients were accurately classed in the correct category.

Table 3 :

 3 An exemple of SWRL rules to classify an acute phase of CPRS according to the IASP recommmandation

	Priority	IASP Recommandation	SWRL Rule
	Most urgent:

Acknowledgements

Authors have no disclosure or disclamers to declare. Protégé 5.5.0 is available on http://protege.stanford.edu/ We thank J.B. Lamy for his help in Owlready 2. The Python package is available at: https://pypi.python.org/pypi/Owlready2 (stable version). UMLS was downloaded on: https://download.nlm.nih.gov/umls/kss/2020AB/umls-2020AB-full.zip

Address for correspondence

alexandre.saadi@aphp.fr Department of evaluation and treatment of pain European Georges Pompidou Hospital 20 rue Leblanc, 75015 Paris, France (+33)156093355