Claudio Vergari

Mathilde Gaume

Sylvain Persohn

Lotfi Miladi

Wafa Skalli

From In Vitro Evaluation of a Finite Element Model of the Spine to In Silico Comparison of Spine Instrumentations

Keywords: neuromuscular scoliosis, bipolar technique, minimally invasive fusionless surgery, numerical model

Growth-preserving spinal surgery suffer from high complications rate. A recent bipolar instrumentation using two anchoring points (thoracic and pelvic) showed lower rates, but its biomechanical behaviour has not been characterised yet. The aim of this work was to combine in vitro and in vivo data to improve and validate a finite element model (FEM) of the spine, and to apply it to compare bipolar and classical all-screws implants.

Spinal segments were tested in vitro to measure range of motion (ROM). Thoracic segments were also tested with bipolar instrumentation to measure ROM and rod strain using a strain gage.

A subject-specific FEM of the spine, pelvis and ribcage of an in vivo asymptomatic subject was built. Spinal segments were extracted from it to reproduce the in-vitro mechanical tests. Experimental and simulated ROM and rod strain were compared. Then, the full trunk FEM was used to compare bipolar and all-screws instrumentations.

The FEM fell within 1° of the experimental corridors, and both in silico and in vitro instrumentation rods showed 0.01% maximal axial strain. Bipolar and all-screws constructs had similar maximal Von Mises stresses. This work represents a first step towards subject-specific simulation to evaluate spinal constructs for neuromuscular scoliosis in children.

Introduction

Neuromuscular spinal deformity (NMSD) is due to abnormal muscle tone and muscle imbalance which often starts in the first years of life. Progression of the deformity can lead to loss of sitting ability and respiratory insufficiency [START_REF] Mayer | Scoliosis and the Impact in Neuromuscular Disease[END_REF]. Therefore, those cases that progress without response to non-operative treatment (physiotherapy or bracing) must undergo early spinal surgery to stop the progression. Such an early fusion, however, can lead to cessation of trunk growth and of lung development, and this complex surgery presents a relatively high rate of complications: the meta-analysis by [START_REF] Sharma | Prevalence of complications in neuromuscular scoliosis surgery: a literature meta-analysis from the past 15 years[END_REF] reports 13% prevalence of mechanical complications such as implant breakage, loosening or cut-out of implant.

Growth-preserving surgical techniques have been developed to treat NMSD [START_REF] Spine ; Sarwahi | Minimally Invasive Scoliosis Surgery: A Novel Technique in Patients with Neuromuscular Scoliosis[END_REF]; while they present the advantage of not stopping trunk growth, they can result in complication rates of 40-70% [START_REF] Akbarnia | Dual Growing Rod Technique for the Treatment of Progressive Early-Onset Scoliosis: A Multicenter Study[END_REF][START_REF] Bess | Complications of Growing-Rod Treatment for Early-Onset Scoliosis: Analysis of One Hundred and Forty Patients[END_REF]) including more than 20% which are due to implant failure or rod breakage [START_REF] Thakar | Systematic review of the complications associated with magnetically controlled growing rods for the treatment of early onset scoliosis[END_REF]. Screw pull-out and implant migration are often due to the general poor health status of neuromuscular patients (malnutrition, osteopenia, etc.), while rod breakage may also occur in dynamic and heavy patients due to the long spinal constructs that are necessary to stabilize the whole spine.

Recently, a minimally-invasive fusionless surgical approach was developed [START_REF] Gaume | Minimally Invasive Surgery for Neuromuscular Scoliosis: Results and Complications at a Minimal Follow-up of 5 Years[END_REF][START_REF] Miladi | Minimally Invasive Surgery for Neuromuscular Scoliosis: Results and Complications in a Series of One Hundred Patients[END_REF] as both an early surgical treatment that preserves growth and a definitive treatment avoiding arthrodesis at skeletal maturity. This technique is proposed as an alternative to arthrodesis which provides a high rate of complications in neuromuscular scoliosis [START_REF] Rumalla | Spinal fusion for pediatric neuromuscular scoliosis: national trends, complications, and in-hospital outcomes[END_REF]. This method uses two fixation points for the construct: a pelvic anchoring with iliosacral screws and a proximal thoracic anchoring with supralaminar and pedicle hook claws. This differs from classical arthrodesis which employ pedicle screws at most (or all) vertebral levels to anchor the implant [START_REF] Modi | Treatment of neuromuscular scoliosis with posterior-only pedicle screw fixation[END_REF]. Rod lengthening during growth can be achieved using the previous distal incision, thus respecting the minimal invasive philosophy of the technique.

While this method resulted in a mechanical complication rate similar to the lower end of fusion surgeries (30 % at 5 years follow-up (Gaume et al., n.d.)), the biomechanical behaviour of such "bipolar" construct, and its differences relative to an all-screws approach, has not been studied yet. Particularly, as rod breakage may be a clinical issue in the growing spine, whether an allscrew approach can limit mechanical stress in the rods is an open question. While iliosacral screws are known to be mechanically reliable [START_REF] Miladi | Iliosacral Screw Fixation for Pelvic Obliquity in Neuromuscular Scoliosis: A Long-Term Follow-Up Study[END_REF][START_REF] Shabtai | Sacral Alar Iliac (SAI) Screws Fail 75% Less Frequently Than Iliac Screws in Neuromuscular Scoliosis[END_REF], the effect of only anchoring the instrumentation proximally with thoracic hooks in bipolar instrumentation is not known.

Numerical modelling has been widely used to simulate spine biomechanics, but model evaluation using in-vivo data is often challenging [START_REF] Lafon | In vivo distribution of spinal intervertebral stiffness based on clinical flexibility tests[END_REF][START_REF] Lafon | Intraoperative thraee-dimensional correction during rod rotation technique[END_REF]. Furthermore, when considering numerical simulation of spinal instrumentation, implant or screw stresses are very important to evaluate risk of breakage, but such values are difficult to measure in vitro or in vivo to validate the model. However, implant strain can be measured experimentally, and these values are directly related to the stress.

A finite element model (FEM) of the scoliotic trunk has been previously described in the literature and it has been applied to simulate surgical approaches in severe scoliosis [START_REF] Lafon | Intraoperative thraee-dimensional correction during rod rotation technique[END_REF]. The aim of this work was to combine in vitro and in vivo data to improve and validate

Methods

General approach

A subject-specific FEM of the trunk of an asymptomatic subject was built, including spine, pelvis and ribcage. Models of the thoracic and lumbar spinal segments were extracted from this full model. Previous biomechanical tests were used to validate these segmental models in terms of range of motion (ROM) in three directions [START_REF] Gaume | Biomechanical cadaver study of proximal fixation in a minimally invasive bipolar construct[END_REF]. Cadaver tests on the thoracic sections also included testing of a bipolar instrumentation, and the comparison of instrumentation strain with the numerical results validated the FE model with regards to instrumentation. Finally, the full FEM of the subject, including pelvis and ribcage, was used to predict and compare instrumentation stress in two conditions: bipolar and all-screws instrumentations. Figure 1 shows the process, which is detailed hereafter.

Model

The FEM of a thoracolumbar spine, ribcage and pelvis was generated based on previously described work [START_REF] Descrimes | Introduction des facettes articulaires dans une modélisation par éléments finis de la colonne vertébrale et du thorax scoliotique : aspects mécaniques[END_REF][START_REF] Lafage | 3D finite element simulation of Cotrel-Accepted Manuscript[END_REF][START_REF] Lafon | Intraoperative thraee-dimensional correction during rod rotation technique[END_REF][START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF]. Model's subject-specific geometry was obtained from standing biplanar radiography and CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.

3D reconstruction (

Figure 3A) of one asymptomatic female subject (40 years old) who underwent low dose biplanar X-Rays acquisitions, after ethical committee approval (CPP Ile de France VI 6036), and was retrospectively included in the study. The spine model consisted in the vertebral bodies, posterior arches, spinous processes, articular facets and intervertebral discs and ligaments. Bony structures were modelled by linear elastic behaviour (Poisson's ratio: 0.3, Elastic modulus: 1 GPa for the vertebral body, 3.5 GPa for spinous and transverse processes, and 5 GPa for other vertebral structures), while ligaments were multi-linear elastic [START_REF] Chazal | Biomechanical properties of spinal ligaments and a histological study of the supraspinal ligament in traction[END_REF] and articular facets were non-friction contacts. Mechanical properties were previously detailed [START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF], while the behaviour of intervertebral discs was approximated with a 3 rd degree polynomial describing its moment (M) vs rotation (∆Θ) relation in the form:

𝑀 = 𝑘 0 . ∆𝜃. (1 + ( ∆𝜃 𝜃 𝑐 ) 2 )
(Equation 1)

Here k0 represents the initial segment stiffness and Θc is a stiffening parameter. These parameters were calculated by regression to fit the experimental moment vs rotation curves of thoracic and lumbar samples. When this mechanical property was implemented in the model, k0 was utilized to calculate an equivalent elastic modulus (E) as follows: 2)

𝐸 = 𝑘 0 𝐿 𝐼 ⁄ (Equation
where I is the intervertebral second moment of area corresponding to the loading direction and L is the disc height. This allowed to adapt the mechanical behaviour relative to the subjectspecific geometry.

Since only thoracic and lumbar segments were tested (see below), experimental data was not available for all discs; therefore, mechanical properties of the T6-L1 segment in the FEM was extrapolated from the available data CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.

Segmental model evaluation

In order to evaluate crucial parts of the model, a thoracic (T1-T6, Figure 2C-D) and lumbar spinal segments (L2-L5) were extracted from this trunk model.

in vitro experiments

Existing in vitro experiments on five lumbar spinal segments (L1 to S1, 3 men, age range: 62-77 years) and six thoracic segments (C6 to T7, 6 men, age range: 43-63 years) were considered.

The mechanical testing protocol was previously described by [START_REF] Gaume | Biomechanical cadaver study of proximal fixation in a minimally invasive bipolar construct[END_REF], and is briefly described here. Upper (L1 or C6) and lower vertebrae (S1 or T7) were embedded in rigid blocks. The lower block was fixed while the upper block was attached to a custom testing rig equipped with a ± 10Nm load cell. Samples were loaded in flexion-extension (FE), lateral bending (LB) and torsion (TO) by applying pure moment: thoracic segments were loaded between ± 5 Nm in steps of 1 Nm while lumbar segments were loaded between ± 8 Nm in steps of 1.6 Nm.

Thoracic segments were then instrumented with a bipolar instrumentation and the segments were submitted to the same loading. Instrumentation spanned the whole segment from T1 to T7, and it was fixed with supralaminar and pedicle hooks fixed on two adjacent vertebrae (T1-T2 and T4-T5). Cross links were present at T3 and T6. The lower ends of the rods were embedded in the fixing block of the T7 vertebra. A strain gage was installed on the posterior face of the rod to measure its axial strain at the last loading step in FE. For motion measurement, the loading rig was installed within a biplanar radiographic device (EOS Imaging, Paris, France). Five steel beads of 2 mm diameter were inserted in each vertebra (Figure 2A-B. Biplanar radiographs were acquired at each loading step, and the beads were tracked in 3D to calculate intervertebral rotations in the three loading directions (Muth-seng et al., 2019). Furthermore, geometry of all vertebrae was reconstructed with previous validated methods CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. [START_REF] Humbert | 3D reconstruction of the spine from biplanar X-rays using parametric models based on transversal and longitudinal inferences[END_REF]. Second moment of area of each intervertebral disc was estimated by averaging the second moments of area of the adjacent vertebral endplates.

In vitro model evaluation.

The segmental spine models were used to reproduce the in-vitro tests boundary conditions. The vertebrae which were embedded in rigid blocks (C7, T6, L1, S1) were not considered, to avoid border effects. A virtual spinal instrumentation was also generated for the thoracic segment, including thoracic hooks (T1-T2 and T4-T5), to reproduce the instrumented in-vitro experimentation. Elastic modulus of instrumentation was 110 GPa [START_REF] Niinomi | Mechanical properties of biomedical titanium alloys[END_REF]. ROM of the intact thoracic and lumbar segments, as well as instrumented thoracic segment [START_REF] Lafon | Intraoperative thraee-dimensional correction during rod rotation technique[END_REF], were compared to the experimental corridors. Longitudinal strain of the rod in FE of the thoracic segment was compared to the strain which was measured experimentally.

In-silico application

For the same in vivo subject above, the full trunk model was built, including spine, ribcage and pelvis (

Figure 3). The virtual spinal instrumentation was extended from T1 to the pelvis, with the addition of ilio-sacral screws and a transverse element at L2 level. The instrumented trunk model was blocked at the pelvis, and rotations at the T1 vertebra were computed according to the hybrid method described by [START_REF] Panjabi | Hybrid multidirectional test method to evaluate spinal adjacent-level effects[END_REF], i.e., pure moments of ± 5 Nm were applied to the model, and the resulting rotations at the T1 vertebra were measured. These rotations (2.3° in flexion, 1.6° in right bending and 7.7° in torsion) were then imposed as boundary conditions in both instrumented configurations.

The model was then modified by adding pedicle screws at all vertebral levels between T6 and L5, and the simulations were repeated with the same boundary conditions. Maximal stress was

Results

Intervertebral segment behaviour

Table 1 reports the values of k0 and Θc approximating each intervertebral disc behaviour in the three loading directions. Loading curves were well approximated by the polynomial in Equation 1, with an R² > 0.9 in all loading conditions. Figure 4 shows the experimental corridor of thoracic (intact and instrumented) and intact lumbar spinal segments ROM, represented by the average ± 2*SD of all curves. Ranges varied between samples. simulated curves were outside of the two standard deviations experimental corridor by less than 1°.

Maximum axial strain obtained in the simulated rod at maximal FE loading was 0.010%, which is similar to the value measured by strain gauge in the thoracic rods (0.013 %).

Comparison of instrumentations

Supplementary Content 2-4 show comparison of the simulated behaviour of the two instrumentations under FE, LB and TO loadings, respectively. Maximal Von Mises stresses for the bipolar fixation were obtained in the upper thoracic region in LB (43.9 MPa), and in the lower lumbar region for the other two loadings (37.8 MPa in FE and 75.0 MPa in TO, Table 2). All-screws fixation yielded maximal stresses in the upper thoracic region for all loadings (34.8, 50.3 and 94.8 for FE, LB and TO respectively). Both instrumentations showed maximal stresses in torsion. Stress values was similar between the two fixations; the largest difference was obtained in torsion, where all-screws construct maximal stress was higher than the bipolar one by 20 MPa (26 %).

Figure 5 shows stress distributions; in both configurations, maximal stresses were concentrated near the fixations for all loadings. However, high stress was also present along the rods in torsion, while rod stress in FE and LB was lower.

Discussion

Numerical models are the obvious means to compare different spinal instrumentations, but these models require prior validation against experimental data if their results are to be trusted. In this work, a subject-specific FEM of the intact and instrumented spine was evaluated against experimental data in terms of range of motion and rod axial strain, and then it was used to compare a bipolar and all-screws implants. In particular, it was not clear if only two anchoring points (distal and proximal), linked by long rods, could offer sufficient stability and resistance compared to more classical approaches which benefit from anchoring points at all vertebral levels. Indeed, growth-preserving surgery for NMSD could substantially benefit patients, but they still present very high complication rates. The novel bipolar instrumentation with minimally-invasive surgery described by [START_REF] Miladi | Minimally Invasive Surgery for Neuromuscular Scoliosis: Results and Complications in a Series of One Hundred Patients[END_REF] showed promising clinical results, but its mechanical behaviour has not been analysed yet. 12 CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. Instrumentation was only tested in vitro on the thoracic spine, and the tested segment was relatively short (C7-T7) compared to the in vivo instrumentation, which would span the whole spine. This choices were made because the biomechanical behaviour and stability of thoracic hook fixation is much less studied than the distal fixation by iliosacral screws [START_REF] Casaroli | What do we know about the biomechanics of the sacroiliac joint and of sacropelvic fixation? A literature review[END_REF]. The comparison of experimental and simulated axial rod strains is an important aspect of this works. Indeed, while stress is informative when comparing instrumentations, it is usually not feasible to validate the values obtained in a model. Strain, on the other hand, can be measured directly and it is directly related to stress, especially in linear elastic materials such as titanium.

The main limitation of this study is that different spinal specimens were used to characterize thoracic and lumbar discs, rather than full spines. Furthermore, the instrumented spine segment was shorter than the in vivo instrumentation. This is due to the difficulty of obtaining human cadaveric full spines without disc degeneration, osteophytes and other pathologies potentially affecting intervertebral mobility. Moreover, since the two tested segments did not represent the whole spinal column, mechanical properties of the T6-L1 segment in the FEM was extrapolated from the available data. Finally, gender of the subjects was not accounted for [START_REF] Lang-Tapia | Differences on Spinal Curvature in Standing Position by Gender, Age and Weight Status Using a Noninvasive Method[END_REF]. Nevertheless, the ROM of the upper thoracic region (T1-T7) was characterized in this work, a segment that is often neglected in the literature which mostly focused on the thoracic spine below T3 [START_REF] Balabaud | Biomechanical Evaluation of a Bipedicular Spinal Fixation System: A Comparative Stiffness Test[END_REF][START_REF] Kuklo | Biomechanical Contribution of Transverse Connectors to Segmental Stability Following Long Segment Instrumentation With Thoracic Pedicle Screws[END_REF] or on shorter segments [START_REF] Kingma | Coupled motions in human and porcine thoracic and lumbar spines[END_REF][START_REF] Wilke | In vitro analysis of the segmental flexibility of the thoracic spine[END_REF].

Another limitation is the use of cadaveric specimens of elderly subjects, when the instrumentation is mainly used in prepubertal or adolescent subjects. Not only the two differ in geometry and overall size, but also in mechanical properties, especially for the soft tissues. While this is a common limitation found in the literature, in this study the mechanical properties which were estimated from the mobility curves were normalized with the specimens' geometrical properties, and therefore they could be at least partially adapted to any subject's geometry. Moreover, in the present case of direct comparison between two instrumentation CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material. Finally, the trunk FEM was passive, as it did not include neuromuscular components, and it represented an adult's geometry. While implementing muscular action and control would lead to more realistic results, and instrumentation loadings, this is a common challenge in the existing literature, which still has to be overcome.

Simulations show that stresses were concentrated near the anchoring sites in both configurations (Figure 5). Comparisons with the literature are sparse because only few studies focused on the stress in long, growing rods in situ. For instance, Agarwal et al. found a maximal stress of 56 MPa applying 1 Nm moment in flexion [START_REF] Agarwal | Towards a validated patient-specific computational modeling framework to identify failure regions in traditional growing rods in patients with early onset scoliosis[END_REF], which is higher than the present results probably because those authors used a pre-stressed model with a follower load; in their case, the application of the flexion moment did not have any effect on implant stress. [START_REF] Ribesse | Fracture mechanisms in Ti and Co-Cr growing rods and impact on clinical practice[END_REF] found maximal stresses near the distal anchoring site, at the thoracolumbar junction, while stresses were higher in the proximal anchoring site in the present work. However, shorter constructs were analysed in that work.

Results suggest that bipolar configuration shows similar stresses than all-screws configuration (Table 1, Figure 5). The bipolar technique overall demonstrated slightly higher stresses in FE CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.

and LB, and lower stresses in TO than the all-screws configuration. Maximal Von Mises stress in flexion and lateral bending was 9% higher in bipolar than in all-screws, but the latter showed 26 % higher stress in torsion. It is not surprising that torsion loading yields higher stresses: the narrow rectangle formed by the thoracic and lumbar transverse elements and the two longitudinal rods does not offer high resistance to this loading. Nevertheless, both configurations were well below the yield strength of titanium medical grade alloys (about 850 MPa, [START_REF] Niinomi | Mechanical properties of biomedical titanium alloys[END_REF]. Although the two constructs provide a similar order of magnitude of strains [START_REF] Miladi | Minimally Invasive Surgery for Neuromuscular Scoliosis: Results and Complications in a Series of One Hundred Patients[END_REF], the in vitro and in silico approaches in the present work were limited to simple loading cases. Further in-vivo studies are necessary to go towards more realistic in-vivo loadings.

In conclusion, in this work a subject-specific FEM of the spine was evaluated in terms of ROM and implant strain against in vitro experiments: the model fell within the experimental curves in most conditions, and showed the same rod strain as the experimental measurement. Then, the model was completed with the subject's rib cage and pelvis and applied to compare bipolar and all-screws configuration. Results show that the two constructs were biomechanically similar, with similar locations and levels of maximal stress. Further work could aim at reproducing in silico the specific muscular activity patterns of NMSD patients. These patients present specific trunk deformities that can be reproduced with the subject-specific model described in this work, which represent a first step towards the simulation of proximo-distal spinal construct behaviour for NMSD patients.

Declaration of interest statement

The in vitro study was funded by EUROS company and the in vivo modelling by the BiomecAM chair program on subject-specific musculoskeletal modelling (with the financial support of ParisTech and Yves Cotrel Foundations, Société Générale, Proteor and Covea). The sponsors of this study were not involved in the design, collection, analysis of data or writing the report.

CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.

Figure 1 .

 1 Figure 1. Schematic view of the methodological approach.

Figure 2 .

 2 Figure 2. Frontal (A) and lateral (B) radiographies of a C7-T7 intact thoracic sample. Metal beads which were used to track vertebral motion are visible in the vertebral bodies and spinous processes. (C) Frontal view of the 3D reconstruction of T1-T7 vertebrae (volume models) and beam finite element model: bones are represented as black lines and ligaments in red. (D) and (E) show radiographs of an instrumented sample.

  Figure3).The model was implemented in ANSYS V15 (Ansys Inc., Canonsburg, PA, USA).

Figure 3 .

 3 Figure 3. (A) Biplanar radiographies of a 40-years old healthy woman and (B) 3D reconstruction of her pelvis and spine, with the model of T1-S1 all-screws constructs. Rods are represented in red, crosslinks in blue, claw hooks in black and screws in green. Model of bipolar construct is similar, including iliosacral screws but without pedicle screws (in green). (C) Subject-specific finite element model.

Figure 5 .

 5 Figure 5. Von mises stress of the bipolar (first row) and all-screws instrumentations (second row) in flexion/extension, lateral bending and torsion, with a top view and lateral view in each loading. Stresses are concentrated near the anchoring points rather than along the rods. Color are different in each loading, showing that torsion presented the higher stresses.

  Figure3), these limitations should have marginal effects on the results. Indeed, the claim of the present work is not the validation of the recent bipolar implant for use in adolescents, for which clinical validations already exist at 5-years follow-up, but to compare two instrumentation configurations. Besides, using an adult geometry in the simulation is closer to the experimental conditions, thus closer to the range of validation of the numerical model.The results of the simulations reproducing the in vitro experiments are encouraging; the spinal geometry used to test the model was collected from in vivo data and was independent from the in vitro tests, and the results still fell within the experimental corridors of 2SD (Figure4), which corroborates the model's reliability. In other words, the validation procedure is closer to a potential in vivo application than comparing simulation and experiments performed on the same specimens. Moreover, simulated rod strain corresponded to the measured one, providing a further degree of confidence in the model's results.

Table 1 :

 1 Constants for polynomial approximation of disc properties (" indicates the same value as the cell above)

	Segment	Lateral bending	Flexion/Extension	Torsion
		k0 (Nm/rad)	Θc (rad)	k0 (Nm/rad)	Θc (rad)	k0 (Nm/rad)	Θc (rad)
	T1-L1	24.9	0.037	1.40 * 24.9	0.037	24.9	0.037
	L1-L2	"	"	0.3 * 24.9	0.037	24.9	"
	L2-L3	"	"	"	0.037	1.1 * 24.9	"
	L3-L4	"	"	"	1.5 * 0.037	1.2 * 24.9	"
	L4-L5	"	"	"	2.0 * 0.037	1.3 * 24.9	"
	L5-S1	"	"	"	2.5 * 0.037	1.4 * 24.9	"

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Table 2 .

 2 Comparison of maximum Von Mises stresses of the implant in the two configurations (bipolar and allscrews) and in different regions under three directions of imposed rotations. Plus signs at superscript indicate maximal values per loading and configuration.

			Bipolar			All-screws
		Flexion	Lateral bending	Torsion	Flexion	Lateral bending	Torsion
	Upper thoracic (MPa)	22.4	43.9 +	67.5	34.8 +	40.3 +	94.8 +
	Mid-shaft (MPa)	32.8	31.0	69.1	17.1	29.1	86.3
	Lower lumbar (MPa)	37.8 +	31.4	75.0 +	27.2	28.9	80.8

  Accepted Manuscript. Published in Journal of the Mechanical Behavior of Biomedical Materials.

DOI : https://doi.org/10.1016/j.jmbbm.2021.104797 11 CC-BY-NC-ND license. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not use the material for commercial purposes. If you remix, transform, or build upon the material, you may not distribute the modified material.

9

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Model evaluation

Supplementary Content 1 shows an example of lateral inflexion in vitro and in silico test. Simulations based on in-vivo patient geometry (Figure 4, black curves) fell within the experimental range of 2SD for all intact configurations, and for all instrumented loadings except at maximal loading in LB and at initial negative loading in TO (Figure 4); in these cases,

Supplementary Content legends

Supplementary Content 1: The animation shows an example of lateral inflexion in vitro and in silico test. Frontal and lateral radiographies are shown at each loading step. Metal beads which were used to track vertebral motion are visible in the vertebral bodies and spinous processes. Frontal and posterior views of T1-T7 vertebra 3D reconstruction (volume models) and beam finite element model are also shown: bones are represented as black lines, intervertebral discs in cyan and ligaments in red. Supplementary Content 2: Flexion/extension loading of the spinal implant (T1-S1) in bipolar (A) and all-screws (B) configuration, in top, lateral and front views. Color scale represents Von Mises stresses (MPa). Spine, ribcage and pelvis were hidden for clarity. Supplementary Content 3: Lateral inflexion loading of the spinal implant (T1-S1) in bipolar (A) and all-screws (B) configuration, in top, lateral and front views. Color scale represents Von Mises stresses (MPa). Spine, ribcage and pelvis were hidden for clarity. Supplementary Content 4: Torsion loading of the spinal implant (T1-S1) in bipolar (A) and allscrews (B) configuration, in top, lateral and front views. Color scale represents Von Mises stresses (MPa). Spine, ribcage and pelvis were hidden for clarity.


Keywords:

This research explores the contribution of Niklas Luhmann's radical systemic sociology to External Fraud Risk Management. To do this, we use two Luhmannian distinctionsbetween risk and danger, and between confidence and trust -to verify their (in)validity based on two empirical studies on

Healthcare Insurance Companies (HIC) to reduce the risk of external fraud. This study concludes that the Luhmannian framework is relevant for external fraud management issues.

décidée -pour vérifier leur (in)validité à partir de deux travaux empiriques de réduction du risque de fraude dans le cadre des mutuelles santé (HIC). Cette étude conclut à la pertinence du cadre luhmannien en tant que clé de lecture de la gestion du risque de fraude externe.

Introduction

Fraud is a never-ending, ongoing activity that might need radical thinking to be reduced. Therefore, the aim of this article is to apply Niklas Luhmann's systemic sociology to fraud in order to obtain another comprehension of the involved mechanisms that can lead to the development of refined tools to lessen external fraud.

Fraud, a white-collar crime, substantially costs society. Though this seems to be a perilous exercise, some studies tried to assess the total cost of fraud [START_REF] Button | Measuring the cost of fraud: an opportunity for the new competitive advantage[END_REF][START_REF] Gee | The Financial Cost of Fraud 2017: Center for counter fraud studies of the University of Portsmouth[END_REF] and the 2017 th report measured a cumulative loss of $4.39 trillion for 2016… Some studies dealing with fraud are related to the sociology of risk and promote a new way of thinking about risk management (Meric et al., 2009;Pesqueux, 2011), especially after the financial crisis of 2007[START_REF] Beck | La société du risque. Sur la voie d'une autre modernité[END_REF][START_REF] Mikes | From counting risk to making risk count: Boundary-work in risk management[END_REF]Power, 2007;2009). Some essential sociological works have already provided a conceptual framework for this risk control issue [START_REF] Beck | La société du risque. Sur la voie d'une autre modernité[END_REF][START_REF] Perrow | Complex organizations: a critical essay[END_REF]. However, as Luhmann (213a, stated, all previous works have to be reexamined for the underlying methods considered fraud to be exogenous, whereas sociology must structurally include fraud schemes. From our standpoint, this is of major interest, fraud has always existed and will never be stopped entirely (Gandhi, 2015) therefore, it might well be constitutive of our social system. In the first part of this work, we present Luhmann's theoretical framework. Then, we evaluate an approach termed "RaAS" (Responsibility of actors, Autonomy, Sanction) devoted to fraud reduction. We conclude by discussing the contributions of Luhmann's sociological framework to the field and we identify avenues to reduce fraud occurrences; mainly by improving the sense, considering the danger and enhancing confidence, with the parings of risk/danger and trust/confidence being two major Luhmannian distinctions.

-Theoretical Framework: Luhmann's Sociology and Fraud Risk Management

Research on fraud -a white-collar crime -and control has started long ago with [START_REF] Sutherland | White-Collar Criminality[END_REF] and [START_REF] Cressey | The Criminal Violation of Financial Trust[END_REF] in an attempt to develop a theory of criminal behavior on bridging two bodies of knowledge: crime and business. This theory eventually ends up considering that fraudsters knew no other solution to their non-sharable problems than to violate trust, justifying this violation by rationalization (Cressey, 1950, p. 742). Cressey identified three elements creating favorable conditions for committing fraud: pressure, motivation and rationalization; in the white-collar crime literature, this is referred to as Cressey's "fraud triangle". This scheme became famous and is regularly updated by new research [START_REF] Kassem | The new fraud triangle model[END_REF][START_REF] Mackevicius | Transformational research of the fraud triangle[END_REF]Ouaniche, 2015). Nevertheless, Cressey (1950, p. 739) reckoned that "trust violation is caused by the existence of institutions whose functioning depends upon varying degrees of trust" and pointed the economic system of our modern society. This is specified years later by Sutherland et al. (1992, p. 13775ff) for whom criminal behavior is an effect of the economic, political and social order. In this work we are not saying that a Luhmannian perspective is the only one to account for fraud, but that a change of perspective may be of some interest to help cope with it.

Before going into details, we need to explain -even in a flash -Luhmann's framework and his conception of organizations.

Luhmann's Framework

In Luhmann's sociology, the social world is made of functionally differentiated autopoietic social systems (political, economic, legal…). Autopoiesis refers to self-contained unities whose only reference is to themselves. Luhmann posits that social systems are autonomous, self-referring and self-constructing operationally closed but cognitively opened systems. They are closed as they only rely to their proper rules but opened as they need to interact with their environment (composed of the rest of the world) in order to perform operations of communications with a binary coding. If systems were only connecting their own operations to their own operations in isolation, they could not evolve and adapt to their environment, hence they structurally integrate parts of their environment that are essential for their autopoiesis (Luhmann 2012, p. 109). Not only is this compatible with the operational closure of the system but operational closure is also a condition for structural coupling as, without such couplings, the autopoiesis will come to a standstill and the system will die -as it cannot adapt to its changing environment. Coupling systems are connected to highly complex environmental conditions in a simplified way that can be handled with the either-or schema of the binary code, sufficient to its autopoiesis (Luhmann 2013b, p. 108). Each system is coupled with its environment that can be more or less irritating. In case of irritation, the system changes its behavior to adapt to the world and to keep going.

Systems are composed of subsystems themselves composed of subsystems… and organizations are subsystems of a special kind. As any other systems, the only operations permitted by organizations are communications (that permit further communications), but for organizations, communications take the form of decisions (Luhmann, 2005, p. 187s) that permit decisions in a recursive manner so that they can adapt through this sense-making process. Thus, decisions in economic organizations build recursively a sense for further decisions and then for the organization itself.

Luhmann wrote little about fraud but he dedicated an entire book to risk (2005). Thus, we extracted what we thought relevant in regard to fraud and made a distinction regarding this notion. This was a rather subjective task, as there is not a shared acceptance of what fraud is. In some countries -notably in the USA -fraud has diverse definitions depending on which State it occurs. This has been well known for decades (see for example Cressey, 1950, p. 740;1986, p. 208), and the fact that fraud has persisted suggests that society underestimate its cost or, worse, accordingly to decision theory, that it believes that it can take no action to efficiently fight it. Even if there is no current acceptance of the notion of fraud, some main traits are being acknowledged.

Fraud is an immoral action, an antisocial behavior that betrays confidence (Blanqué, 2003, p. 61;[START_REF] Cressey | The Criminal Violation of Financial Trust[END_REF][START_REF] Stichweh | Towards a General Theory of Function System Crises[END_REF]Stichweh, , p. 1362Stichweh, -1363)). Other research dealing with fraud defines this risk as a consequence of an internal control weakness in client acceptance decision [START_REF] Caplan | Internal Controls and the Detection of Management Fraud[END_REF][START_REF] Johnstone | Risk Management in Client Acceptance Decisions[END_REF]. [START_REF] Derrig | Insurance Fraud[END_REF] defines insurance fraud as a consequence of moral hazard and asymmetric information in the claim process of insurance companies. Some research specifies other types of fraud such as documentary, on financial statements, on transactions, by manipulation, via fictitious acts or operations not carried out… [START_REF] Derrig | Insurance Fraud[END_REF]Hammerlsey and al., 2010). Such frauds are observable in the case of insurance fraud [START_REF] Viaene | Insurance Fraud: Issues and Challenges. The Geneva Papers on Risk and Insurance[END_REF]. For others [START_REF] Dionne | Does Insurance Fraud in Automobile Theft Insurance Fluctuate with the Business Cycle[END_REF] fraud is a function of the economic cycle. According to [START_REF] Murphy | Psychological Pathways to Fraud: Understanding and Preventing Fraud in Organizations[END_REF], fraud risk management is also a question of how to build specific typologies in the organization.

Fraud is a well-defined concept in management and accounting. The AFCE (2018) as well as other professional organizations have their own definition and typology. It includes corruption (conflicts of interest, Bribery, Illegal Gratuities), asset misappropriation (Cash Fraud, Sales and Receivable Fraud, Billing and Payroll schemes), and financial statement fraud (Fictitious Revenues, Improper Asset Valuations, Timing Differences). Each of these categories has many complex schemes and depends on numerous factors (Organization size, Countries, Legislation, Behavioral Conducts, Internal Control degrees of Maturity). Consistent with these definitions, the Agency for the Prevention of Insurance Fraud defines fraud as "An intentional act, carried out by a legal or natural person, in order to unduly obtain a profit from the insurance contract" (ALFA, 2020)1 . Thus, fraudulent operations can be considered as any process that consists in making believe in the reality of an operation by concealing its material elements such as supporting documents of the operation or the advisability of an operation (no claim for reimbursement, unjustified health benefit…)

Unfortunately, there is no definition for fraud accepted by all parties despite some commonalties synthesized in the two keywords "intent" and "deception" which soon fail to help to characterize fraud as, for example, abuses respect both terms. In this respect, we interviewed more than 30 people (mostly risk controllers) in a HIC (forthcoming study) asking them to define fraud and we collected a lot of hesitant definitions or at best, of how it should be defined, but no statement of what fraud is.

The risk/danger distinction: a call to think in "duration"

Risks under discussion are risks that can be evaluated in alternatives. Evaluations have then the double disadvantage of having only short-term perspectives and considering only risks that have influence on the project. All other risky aspects are forgotten, and to avoid this Luhmann (1991, p. 87;2005, p. 33ff) suggests a new distinction, between risk and danger. Luhmann (2005, p. 33ff) substitutes the risk/security distinction with the risk/danger distinction. Because seeking absolute security is illusory, security is not opposable to risk. However, it is critical to distinguish what Luhmann termed "risk", which represents a choice among many possibilities and a vehicle for opportunities, from what he termed "danger", which is an often-remote consequence of a constellation of "risks". "Dangers" are not retrospectively attributable (both because of the passage of time and the large number of risks originating the danger) and are supported by third parties, although they are usually not involved in the decisions. Luhmann and Beck (2008) join on this topic by stating that while older organizations' primary concerns were "dangers," "modern society has until recently preferred to mark risk, being concerned with optimizing the exploitation of opportunity" (Luhmann 2005, p. 25). Luhmann (2005, p. 41ff) argues that we are held hostage by a wrong conception of time because "the unity of time is not the unity of a movement," and the present is not the preferred time for distinctions between past and future to be made. Luhmann observes a society in motion, rich in its memory of past elements that lead to actual and simultaneous events.

For Luhmann, modern society is located in a spatialized time that conceals movement and provides an anchor that secures and enforces a reference point. By insisting on the distinction between risk and danger, Luhmann thinks of time as a "danger" and as a phenomenon that can be grasped over time through movements induced by numerous previous decisions. For example, a carmaker can bear the risk of deciding to make powerful cars based on the opportunity to obtain higher profits. This decision is a (business) risk because these cars might be too expensive to be sold, but it is also a danger because, getting increasingly powerful and polluting, they are detrimental to the environment; thus, such a decision could lead to poorer quality of life.

At that time, both observers -the carmaker as first-order observer and the air health agency controller as second-order'sare right in making their selection as the future cannot be inferred from the past. This is what Luhmann meant when he wrote that the symmetry breaking makes risk conceivable: the risk to make the distinction… Here, we would like to emphasize the question of fraud regarding Luhmann's framework in light of the distinction risk/danger.

The Question of Fraud

In a systemic perspective, solely communication can communicate, and the selection of the value of the code is unpredictable. Correlated to this improbability of value selection is, said Luhmann (2012, p. 245) the probability of "sabotage". And once sabotage occurs, it stands in the memory of the system and is available for further communications (Luhmann, 2013b, p. 36-37). Internal fraud and external fraud are often distinguished as both schemes and prosecution are different. An internal fraud is a fraud made by an employee of the company while an external one comes from the outside of the company, be it made by a natural or legal person. While it is up to the organization so settle internal frauds, external ones originate outside of the organization and healthcare insurance fraud involves insurance companies, healthcare providers, policyholders and subscribers. In any case, as for the carmaker example, a selection between the two sides of the risk/danger distinction has to be made. As a second-order observer marking the 'risk' side of the distinction, we can notice that the risk linked to fraud is twofold. First, the fraudster takes the risk of being caught (weighed against the potential gain), but the fraud also impinges on the organization both as the victim and as a responsible party, weighted against the gain that represents fewer financial resources dedicated to fighting fraud. As a secondorder observer marking the 'danger' side of the distinction, we can fear that confidence in the system erodes, and, that after a certain threshold, a disaster takes place as consequence of a myriad of non-retrospectively attributable actions (Luhmann, 2005, p. 26). As far as fraud is concerned, the danger lies in the betrayal of confidence. If this were the case, its autopoiesis could not be pursued because its structure -its code or programs selecting code values -would appear suspicious to its environment. The very point here is to remind that every system makes a copy of its environment through coupling. When a system communicates a way expected (and notably with a "standard" level of fraud), their copies in other subsystems duplicate properly the functioning of the system, couplings are accurate. On the contrary, when a system communicates quite differently of what it was used to, all other systems it is coupled with need to reassess their coupling. Structural couplings become loose. While this is the normal course of evolution (Luhmann, 2012, p. 253) if the system dramatically changes, couplings may not renew and, with no coupling the autopoiesis will come to a standstill and the system will die.

Trust and Confidence

Luhmann (1988) considers this distinction between risk and danger with the help of two kinds of faith, "confidence" and "trust." This distinction is made based on the possibility of a choice. If there is no choice, "confidence" is at stake, just like one leaves their house every morning with no weapon to protect themselves. However, if the situation has alternatives, then "trust" is at stake. Having faith in systems (in a Luhmannian sense) pertains to "confidence," and conversely, while systems are sensemakers, their autopoiesis can only occur in the case of "confidence". Like for any distinction between forms, the frontier between each side is blurred, and relationships exist between the two. They can support each other because confidence encourages trust, and it is easier to make choices in stable environments. Trust, when internalized in a system's expectations, produces confidence. However, when one is defective, it can also serve to lessen the other and this is why it is said that sabotage carries sabotage (Luhmann 2013b, p. 40). Lost confidence triggers the necessity of making the choice of whether to trust the system or not, and eventually leads it to die. Being aware of danger instead of being focused on risk is a way to build confidence, since strengthened confidence results in the ability to better distinguish between risk and danger.

The distinction between risk and danger is also difficult for another reason, termed "bounded willpower" by [START_REF] Jolls | A Behavioral Approach to Law and Economics[END_REF]Jolls et al. ( , p. 1480)), which is "most relevant when decisions have consequences over time; our example is criminal behavior […], where the benefits are generally immediate and the costs deferred." Because the costs are deferred, sometimes far into the future, danger dissolves and does not penetrate the systems' expectations. According to Luhmann (2012, p. 245) only the law can help and the legal system should encourage this distinction and give strength and resonance to the "danger" side of the form to the detriment of the "risk" one.

In this section we have explained why fraud is both ineluctable and an important topic to be addressed in a systemic perspective. Systems are self-(re)forming thanks to their binary coding and adapting thanks to their couplings. They rely on a recursive stream of communications which operates as a memory. When a "sabotage" occurs, it stays in the memory of the system and is available for further communications, and when many sabotages occur, the system becomes less efficient, its aim is questioned and its autopoiesis is threatened. Luhmann proposes two helpful distinctions to help us understand what is at stake: trust/confidence and risk/danger. These distinctions can be bound together, with trust and danger with confidence as both risk and danger face a situation of choice while confidence and danger do not. To overcome this problem, the distinction between risk and danger should be clearly made by systems and this can be done by two means: 1) strengthening the legal response and 2) taking micro-level actions to articulate co-enhancement of trust and confidence.

-A fraud Risk Management approach based on actors' responsibility, autonomy and sanctions. The case of health insurance organizations

In this section, we evaluate how Luhmann's sociology proves helpful to understand an approach designed to lessen external fraud occurrences experienced by insurance companies. This work makes the statement that fraud is multifaceted and flourishes in different contexts, thus requiring strong relationships between stakeholders. The context concerns organizations that must provide benefits to policyholders on a declaratory basis. In a Luhmannian perspective, it is a question of second-order observations concerning relationships between multiple stakeholders of different systems impacting the whole insurance industry. This can be shown in the example of fraud with respect to the price of glasses, in which opticians optimized insurance reimbursements by altering the amounts dedicated to eyeglass frames and to lenses. The policyholder, as first-order observer, knows that this is an optimization favoring himself detrimental to the HIC. In turn, HICs (first-order) facing lower revenues raise their premium to offset this effect. Eventually, the customer became the losing one.

Even if we are not able to provide an exhaustive inventory of all sets of expectations of all stakeholders, we can still raise some commonalities.

• Managing fraud is a regulatory requirement -Solvency IIand a financial necessity; • Healthcare professionals are accountable for medical expenditures through justification for their (para)medical acts; • The autonomy of healthcare professionals makes fraud easier;

• The lack of deterrents has sectorial impacts; • Fraud can be perpetrated by policyholders or/and healthcare professionals, since they become each other's accomplice; • HIC are often "blind payers" as they pay benefits before they can make any verification, if possible…; • As shown by the eyeglasses' fraud, fraudulent operations cause damage to insurance companies and raise policy prices. Thus, policyholders pay for the fraud.

Based on an action research study of more than 3 years in a HIC as an internal controller -researcher as a reflexive practitioner [START_REF] Schön | The Reflexive Practitioner. How Professionals think in Action[END_REF] we detected different kinds of fraud. In the case study, external frauds correspond to frauds perpetrated by a third party. It has been frequently faced by the organization-48 times in 3 years -134 payments of benefits for a total amount exceeding 500,000 euros. These external frauds comprise:

• The creation of false documents in order to have benefits related to healthcare that has never been realized (fraudsters are opticians, dentists, physiotherapists). These documents are fake orders, invoices or delivery notes; • The creation of faked papers of membership by individuals or fictitious companies to be reimbursed for actual care expenses while reimbursements have already been done by other HICs; • Unjustified cares. Dental care was performed but was not medically justified for the patient. The dentist is paid for actions that should not have taken place. • The creation of false health reports for a group insurance contract. The company that defrauds the insurer modified the figures for disability or care expenses to be reimbursed in a misleading manner.

In our case study, internal fraud (that can be defined as any case of fraud occurring within the organization by an employee, manager or subcontractor acting on behalf of the company) was considered to be infrequent and most difficult to detect. In fact, in 3 years, the insurer observed only 3 cases of internal fraud. The investigation in our case study focuses on the following internal frauds:

• The creation by a commercial of a "ghost" policyholder in order to receive unjustified sales commission; • The sale of a product by a salesperson to a policyholder without the latter being notified or having given his consent. The insured people is then the victim of an identity theft; • The payment on his own account by a health claim indemnifier, using the bank details of one of his relatives or directly his own. This scheme involves the use of unjustified computer access.

Prior to the detection of these cases, the investigated organization considered fraud to be unlikely. Controls focused on operational errors or quality improvement. Trust in the system was considered natural, according to one of the managers of the organization. Thus, thinking about activities via the risk of fraud was not considered desirable because it implied considering that the payment system might be dysfunctional. Our work has made possible to better highlight cases of risk but has also led to the disclosure of flaws in the HIC reimbursement system.

While external fraud is also a matter of first-order observations (internal control), it is mostly an affair of secondorder observations, as the coupling of systems between each other are at stake. Moreover, there are three types of healthcare insurance companies: mutual companies, which are regulated (in France) by the Mutual Insurance Code; private companies, which are regulated by the French Insurance Code; and provident institutions, which are regulated by the French Social Security Code. Thus, we have to distinguish the three subsystems, each of which is coupled with a different legal and political subsystem. In particular, Article L111-1 of the Social Security Code states that "the organization of social security is to be based on the principle of national solidarity." Article L111-1 of the Mutual Insurance Code states that "mutuals are nonprofit legal persons governed by private law […] that can engage in, notably thanks to premiums paid by their members, and in their best interest […], any action of solidarity and mutual assistance (our translation)." The Insurance Code states that their affiliates are recorded in the commercial register. Despite these differences, the method of accessing healthcare is the same: the patient gets (para)medical attention, and all or part of the amount due is paid by the insurance company on a declarative basis. According to the CEO of the HIC in which the case study was conducted: "From the fraudster's perspective, operationally speaking, there is no difference with regard to the type of insurance company". There is also no difference in public opinion, and because of its low level of trust "Insurance is 'fair game' for fraud". The Technical Risk Executive of the company said: "We have no control over fraud. This risk can arise from members as well as from health professionals. If you don't strengthen the controls, you're facing that risk. If you strengthen them too much, the risk is a commercial one or even reputational because the company may stand for an entity that is reluctant to pay its policyholders". A lawyer acting for the company pursued: "Legislation protects fraudsters because companies are asked to prove any fraud within a very constraining framework". This statement is completed by the manager of the company: "The requirements for protecting private data often leads to fraud without being able to ask for a health certificate to confirm that it is a fraudulent transaction. For example, for dental fraud, you would need the dental X-rays, but only a dentist consultant can ask for and analyze them and very few accept to undertake analyses going against their confreres".

An audio recording of a transaction in a call center cannot be kept for more than 15 days, and by the time one realizes that a fraud has occurred, the 15-day timespan is usually over. Such delays rarely permit accurate investigations.

Considering these points, an anti-fraud approach is being used in this environment: the RaAS approach. It revolves around three points: Responsibility of actors, their Autonomy and the Sanctions they face. Responsibility stands for the capacity (and incentives) of actors to take their environment into account, especially relationship between all stakeholders. Autonomy relies on room for maneuver that actors have in potentially threatening affairs like billing, reimbursement… Sanction refers to the capacity of the organization to react to fraud events and impose sanctions.

Systemic Evaluation of the RaAS Approach

For Schnebel (2000, p. 86) responsibility is key for Luhmann's framework as it empowers "the personal responsibility needed to create transparent organizational structures as well as to overcome the restrictions given by institutions, organizations and the economic system." In addition, taking into consideration the consequences of our actions (marking the distinction risk/danger in favor of the latter) is a way to access what Luhmann (1991, p. 87) calls "an ethics of responsibility".

While responsibility can hardly develop with no autonomy -not being autonomous is doing what we are told to do -we cannot be deemed responsible for having done what we are told to2 . This is a paradox at first sight: the more the autonomy, the more risk of fraud. The paradox is easily ruled out since the couple responsibility/autonomy apply for different observers. Indeed, RaAS' responsibility applies to second-order observers while RaAS' autonomy refers to the system (the organization) itself. Nevertheless, even if no paradox exists, we hardly find any contribution of Luhmann's framework to this point.

As an operationalized approach, RaAS' sanctions refer to intra-organizational punishment. As anticipated, in compliance with micro-level actions, the strengthening of the (not legal but) legalistic response can be located at the level of the organization.

When confronting external fraud, more than one system is involved. This intuition was asserted very early by the pioneers of "white-collar" crimes, notably Sutherland et al. (1992, p. 13775ff) and Cressey (1950, p. 739), for whom criminal behavior is an effect of the economic, political and social order. Many systems are involved in case of external fraud. Since the minds are coupled with all social systems, an efficient way to impact their structure of expectations is through irritations by the minds of systems (unavoidably) coupled with the minds. As for internal fraud, this can be done in reference to ethical contingency.

In some respects, the RaAS' approach also relies on ethics of contingency, this is what presupposes the responsibility dimension. This suggests that fraud occurrences may diminish. We are not sure that the dimension of autonomy (and its reduction) could help reduce fraud, not at least as far as such a systemic framework is concerned, as diminishing systems autonomy is also impoverishing them.

-Discussion and conclusion

The following table represents how fraud-related key concepts can be understood in a Luhmannian framework.

-Fraud and Luhmann's framework

Environment

Everything that is not the system itself

The organization sees its environment globally and only reacts to its irritations. It has to extend to relevant parts.

HIC are highly exposed to external fraud because they pay benefits on a declarative basis with very few possibilities to assess the validity of the claim. This framework is relevant for the distinction between risk and danger to be promoted in Risk Management. Risk is immediate and is primarily carried by decision makers, while the effects of danger last over a significantly longer period and concerns a large group of people. Systems must clearly make this distinction to characterize danger when it exists. Another conclusion is that internal fraud can be fought on the micro level by encouraging "trust". When this trust is internalized, it can change into "confidence". If external fraud can also be confronted by developing such mechanisms, the political and legal systems and their coupling with organizations must also be considered. This framework helps considering fraud in a peculiar way: it is encouraged by systems as they impose their own meaning, which, because of its amorality -a system reproduces itself according to its own rule with no notion of intrinsic morality -conveys an unfamiliar sense. People are involved in systems they cannot escape (for example, they cannot live outside the economic, political or legal systems) that are conveying a sense they might not accept and are engaging in strategies of circumvention (de Vaujany, 2006) sometimes involving fraud. Here is one reason why fraud is consubstantial with social systems: meanings cannot be clear and adopted by everyone in all systems, therefore strategies of circumvention will always exist. This is precisely also a way to fight fraud efficiently, by giving sense to the operation people do within the system they are in, by helping them mark the "danger" side of the distinction risk/danger. When confronted with danger, society defends itself, and Luhmann (2005, p. 102) hypothesizes that forms of social solidarity emerge from danger. This suggests that an efficient way to fight fraud is to illustrate the danger it represents. A conclusion of significant importance is then that the distinction between risk and danger must be reinforced (Luhmann, 2005, p. 114) so that systems can better address fraud issues. Because systems are operationally closed and functionally autonomous, it is their local responsibility through the structural effects of differentiation in which control can occur, since systems cannot control their subsystems (Luhmann, 2012, p. 17). In other words, the selfobservation capacities of systems must be enhanced (Luhmann 1995, p. 36).

Risk

The main interest of this work is not in its retrospective justification of a Luhmannian framework, for we believe that this sort of justification could have been performed with many other sociological frameworks. The true value of this research lies in the mobilization of a sociological framework that seems to be relevant to understand the internal control stake that implies fraud risk.

https://www.alfa.asso.fr/fraude-a-lassurance/

While this can be disputable, even during the Holocaust, great criminals felt no guilt for having obeyed. See for example the "banality of evil" raised by Hannah Arendt.


A Quéméner

F Dessauge

M H Perruchot

N Le Floc'h

I Louveau

Housing hygiene conditions impact adult stem cell populations in adipose and muscle tissues of pigs

In pigs, the lean mass/fat mass ratio determines production efficiency and is strongly influenced by the number and size of cells in the tissues. During growth, the increase in the number of cells results from the recruitment of different populations of multipotent adult stem cells residing in the tissues. We hypothesized that the impact of a hygiene challenge on the proportions of adult stem cells in adipose tissue and skeletal muscle may differ between pigs with different residual feed intake (RFI), a measure of feed efficiency. At the age of 11 weeks, Large White pigs from two lines divergently selected for low and high RFI were placed in two contrasting housing hygiene conditions (good vs poor). After six weeks of challenge, pigs were slaughtered (n = 6/group). Samples of subcutaneous adipose tissue and longissimus muscle were removed, and cells from the stromal vascular fraction (SVF), which includes adult stem cells, were isolated for each tissue. Adipose and muscle cell populations from the SVF were phenotyped by flow cytometry using antibodies that targeted different cell-surface markers (CD45 to identify hematopoietic cells; CD34, CD38, CD56 and CD140a to identify cells with adipogenic and/or myogenic potential). Adipose tissue and muscle shared some common cell populations with differences in their proportions. For example, CD45-CD56+ cells were abundant in both tissues, with an average proportion of 74% in muscle and 40% in adipose tissue. Among the cell populations identified in adipose tissue, the proportion of CD45-CD56-CD34-cells were higher (P < 0.05) in pigs housed in poor hygiene than in good hygiene conditions whatever the RFI line. In skeletal muscle, preliminary analyses indicate there was an increase (P < 0.05) in the proportion of CD45+ cells in pigs of both RFI lines housed in poor hygiene conditions compared with those housed in good conditions. Other cell populations are poorly affected by hygiene of housing. This study shows that hygiene of housing conditions has an impact on some populations of adult stem cells in adipose and muscle tissue, without any difference between the two pig lines. The animal experimentation was funded by the EU FP7 PROHEALTH project (no. 613574).

Dear Dr Louveau, Thank you for submitting your abstract, we have received your contribution for EAAP Annual Meeting 2021, Davos, Switzerland in good order.

Abstract no.: 35966

Abstract title: Housing hygiene conditions impact adult stem cell populations in adipose and muscle tissues of pigs Author: Quéméner, A., Dessauge, F., Perruchot, M.H., Le Floc'h, N., Louveau, I.

Preferred presentation: Theatre Preferred session: 71: Nutrient competition between production and animal health -crosstalk between nutrition, immunity, and microbiota win-win strategies between growth and maintenance functions (including health and welfare)

Abstract text:

In pigs, the lean mass/fat mass ratio determines production efficiency and is strongly influenced by the number and size of cells in the tissues. During growth, the increase in the number of cells results from the recruitment of different populations of multipotent adult stem cells residing in the tissues. We hypothesized that the impact of a hygiene challenge on the proportions of adult stem cells in adipose tissue and skeletal muscle may differ between pigs with different residual feed intake (RFI), a measure of feed efficiency. At the age of 11 weeks, Large White pigs from two lines divergently selected for low and high RFI were placed in two contrasting housing hygiene conditions (good vs poor). After six weeks of challenge, pigs were slaughtered (n = 6/group). Samples of subcutaneous adipose tissue and longissimus muscle were removed, and cells from the stromal vascular fraction (SVF), which includes adult stem cells, were isolated for each tissue. Adipose and muscle cell populations from the SVF were phenotyped by flow cytometry using antibodies that targeted different cell-surface markers (CD45 to identify hematopoietic cells; CD34, CD38, CD56 and CD140a to identify cells with adipogenic and/or myogenic potential). Adipose tissue and muscle shared some common cell populations with differences in their proportions. For example, CD45-CD56+ cells were abundant in both tissues, with an average proportion of 74% in muscle and 40% in adipose tissue. Among the cell populations identified in adipose tissue, the proportion of CD45-CD56-CD34-cells were higher (P < 0.05) in pigs housed in poor hygiene than in good hygiene conditions whatever the RFI line. In skeletal muscle, preliminary analyses indicate there was an increase (P < 0.05) in the proportion of CD45+ cells in pigs of both RFI lines housed in poor hygiene conditions compared with those housed in good conditions. Other cell populations are poorly affected by hygiene of housing. This study shows that hygiene of housing conditions has an impact on some populations of adult stem cells in adipose and muscle tissue, without any difference between the two pig lines. The animal experimentation was funded by the EU FP7 PROHEALTH project (no. 613574).