Claudio Vergari

Isabelle Courtois

Eric Ebermeyer

Houssam Bouloussa

Raphaël Vialle

Wafa Skalli

Experimental validation of a patient-specific model of orthotic action in adolescent idiopathic scoliosis

Keywords: Finite element model, Spine deformity, Brace, Pediatrics

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Introduction

Adolescent idiopathic scoliosis (AIS) is a three-dimensional deviation of the spine from its physiological curvature [START_REF] Dubousset | Three-dimensional Analysis of the Scoliotic Deformity[END_REF]. Progression of the curve is often accompanied by vertebral wedging, ribcage deformity and a loss of spinal sagittal curvature ("flat back") that can induce respiratory or cardiovascular impairment [START_REF] Asher | Adolescent idiopathic scoliosis: natural history and long term treatment effects[END_REF] and more in general a decrease in quality of life. Corrective surgery is very invasive, with a loss of spinal motion and a significant risk of complications. Orthotic treatment aims at slowing down curve progression, especially during growth spurt, with a less invasive approach.

While the potential effectiveness of bracing has recently been demonstrated in AIS [START_REF] Weinstein | Effects of Bracing in Adolescents with Idiopathic Scoliosis[END_REF][START_REF] Lou | How quantity and quality of brace wear affect the brace treatment outcomes for AIS[END_REF], the planning and fabrication of the brace is still empirical and based on the experience of the clinicians and orthotists. This is partly due to the complex three-dimensional geometry of the scoliotic spine and of its biomechanical behavior; prediction of brace action from qualitative observation is difficult, sometimes resulting in in-brace spinal shapes similar or worse than the out-of-brace spine [START_REF] Courvoisier | 3D analysis of brace treatment in idiopathic scoliosis[END_REF].

The potential of biomechanical finite element models (FEMs) as a tool in orthopedics has been proven in several applications, such as surgical planning, implant design, etc. Several FEMs of the trunk have been reported in the literature [START_REF] Jalalian | Computational Biomechanical Modeling of Scoliotic Spine: Challenges and Opportunities[END_REF][START_REF] Wang | The Use of Finite Element Models to Assist Understanding and Treatment For Scoliosis: A Review Paper[END_REF]. Recent improvement in spinal imaging and feature detection [START_REF] Aubert | In Press) 3D Reconstruction of rib cage geometry from biplanar radiographs using a statistical parametric model approach[END_REF][START_REF] Humbert | 3D reconstruction of the spine from biplanar X-rays using parametric models based on transversal and longitudinal inferences[END_REF] allowed the development of subject-specific trunk models, while at the same time work has been done to introduce FEMs in brace design [START_REF] Cobetto | Braces Optimized With Computer-Assisted Design and Simulations Are Lighter, More Comfortable, and More Efficient Than Plaster-Cast Braces for the Treatment of Adolescent Idiopathic Scoliosis[END_REF][START_REF] Gignac | Optimization method for 3D bracing correction of scoliosis using a finite element model[END_REF][START_REF] Desbiens-Blais | New brace design combining CAD/CAM and biomechanical simulation for the treatment of adolescent idiopathic scoliosis[END_REF]. These models, however, retain a qualitative character because their experimental validation is often lacking or incomplete [START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF].

Our group recently presented a geometrical and clinically relevant framework for the evaluation of FEM for brace action [START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF]. The hypothesis of the present work was that a thorough validation of a personalized FEM of brace action would highlight potential means of improvement by quantifying of the model's reliability and weaknesses.

Methods

Subjects

Forty-two patients diagnosed with progressive AIS were included both retrospectively and prospectively in this multicentric study: 38 girls and 4 boys between 7 and 17 years old, 26.2° ± 14.4° Cobb angle. All were prescribed a treatment by either cast or brace; progressive AIS was diagnosed by the prescribing clinician. Stereoradiographs were acquired (EOS system, EOS imaging, Paris, France) with the patient in free standing position [START_REF] Steffen | 3D postural balance with regard to gravity line: an evaluation in the transversal plane on 93 patients and 23 asymptomatic volunteers[END_REF] at treatment decision (out of brace, T0) and in-brace (T1, Fig. 1). T1 acquisition was performed between 0 (i.e. same day) and 7 months after T0. The study was approved by the ethical committee (CPP 6001 Ile de France V).

Subject specific model

3D reconstruction of the pelvis [START_REF] Mitton | 3D reconstruction of the pelvis from bi-planar radiography[END_REF], spine [START_REF] Humbert | 3D reconstruction of the spine from biplanar X-rays using parametric models based on transversal and longitudinal inferences[END_REF] and ribcage [START_REF] Aubert | In Press) 3D Reconstruction of rib cage geometry from biplanar radiographs using a statistical parametric model approach[END_REF] was performed by an experienced user using validated methods. The pelvis was reconstructed in the T0 geometry and rigidly translated in the T1 geometry in order to define the same robust subject frame of reference in both configuration. The geometry of each vertebra (Fig. 2) was calculated by averaging the T0 and T1 vertebral geometries.

A personalized finite element beam model (Fig. 1) was then generated as previously described [START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF][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], including the pelvis, sacrum, thoracic and lumbar vertebrae (Fig 2 ), posterior articulations, intervertebral discs, ligaments, and rib cage. Ribs mechanical properties were personalized according to the patient's Risser sign [START_REF] Pezowicz | The mechanical properties of human ribs in young adult[END_REF] while their cross-sectional areas were adapted to the vertebral level, according to an existing database of scoliotic adolescent rib morphology [18]. The model was implemented in ANSYS V11 (Ansys Inc., Canonsburg, PA).

Boundary conditions

Boundary conditions were implemented by displacing only those regions where the brace was acting, while letting the rest of the trunk respond to this mechanical loading. These anatomical regions were identified by observing the deformation of soft tissues and the radiopaque components of the brace [START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF]. Those pads pushing on the lumbar region or posteriorly on the spine where implemented by displacing the corresponding vertebra. Those pads acting on the rib cage were explicitly implemented as soft cylinders (Fig. 1; 485 nodes, 433 hexahedral elements, 0.01 MPa Young's modulus) pushing on the ribs through mechanical contact. Pelvis and T1 vertebra were displaced in the T1 geometry to reproduce patient's balance and posture. Displacements were measured as differences between the 3D reconstructions at T0 and T1 in the same pelvis-based frame.

Analysis and statistics

The 3D model yielded by the simulated inbrace geometry of the patient's trunk (TS) was used to calculate vertebral positions, their orientations and the following relevant clinical indices (Table 1): kyphosis, lordosis, Cobb angle, vertebral axial rotation at the apical level (VAR), torsion index and 3D rib hump. Root mean squared errors (RMSE) and maximal differences were calculated between these parameters in the T1 geometry and the simulated ones (TS). These values were then compared with a measurement uncertainty corresponding to the error (ε, Table 1) expected when comparing two 3D reconstructions (T0 and T1) with known uncertainties, i.e. 𝜖 = √2(2𝑅𝑀𝑆 𝑆𝐷 ) 2 , where 2RMSSD is the previously determined reproducibility of the 3D reconstruction [START_REF] Aubert | In Press) 3D Reconstruction of rib cage geometry from biplanar radiographs using a statistical parametric model approach[END_REF][START_REF] Humbert | 3D reconstruction of the spine from biplanar X-rays using parametric models based on transversal and longitudinal inferences[END_REF].

A "patient RMSE" was determined for each patient by calculating the RMS of the differences between all simulated and actual parameters, as well as an overall "brace action" which was determined as the RMS of the difference between the clinical indices in T0 and T1 reconstruction.

Pearson correlation coefficients was used to analyse correlations; significance was set at p < 0.05. Calculations were performed with Matlab 2014b (Mathworks, Natick, MA).

Results

Bracing had an overall positive effect on the patients' clinical indices in the coronal plane (Table 2), but it had little or negative effect in the transversal and sagittal planes. Cobb angle was decreased in 70 % of the patients (average correction: 10.4°), but it increased more than the measurement uncertainty in 2 patients (5.4° and 6.8°). Torsion and VAR decreased in 24 and 25 % of the patients, respectively, but it also increased in 10 and 14 %, respectively. Kyphosis and lordosis decreased in approximately half of the patients (Table 2).

A typical simulation lasted about 10 minutes on a desktop PC and presented no convergence issues. Overall simulation performance is reported in Table 1; kyphosis, lordosis and Cobb angles RMSEs were lower than the measurement uncertainty. Fig. 3 and Fig. 4 show the RMSE of Cobb angle and vertebral axial rotation at apical level for each patient. Full clinical data at T0, T1 and Ts are reported as supplementary material (Online Resource 1). Pooling all patients and clinical indices, 87 % of the indices had lower errors than the corresponding measurement uncertainty.

Errors on vertebral orientations were lower than the measurement uncertainty (Table 1). Average RMSEs in vertebral positions were higher than the measurement uncertainty in the postero-anterior and lateral directions, but slightly lower in the vertical direction. Overall RMSE in vertebral position was 1.9 mm; when pooled together, more than 59% of the 714 considered vertebrae (42 patients times 17 vertebrae) showed lower position errors than the measurement uncertainty.

No correlation was observed between the patient's simulation error and the patient's brace action (p > 0.05) nor the clinical parameters at T0 (p > 0.05). Table 3 reports measured and simulated brace action on the clinical indices for the 3 patients with the lowest simulation errors (patient RMSE ≤ 1.5º) and 4 patients with the highest ones (patient RMSE ≥ 4.4º).

Table 2

Effect of bracing on the patients' clinical parameters reported as number (and percentage) of patients which had each value significantly decreased (compared to measurement uncertainty), unchanged or significantly increased. Average correction is also reported. Table 3 Absolute differences between out-of-brace (T0) and in-brace (T1) clinical indices (i.e., brace action) and absolute differences between simulated (Ts) and out-of-brace clinical indices (i.e., simulated brace action) for the three patients presenting the lowest simulation errors (#16, #32 and #38) and four patients with the highest ones. In this work we presented the validation of an improvement on previously described FEM [START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF][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], which was preliminarily validated on a small cohort of 10 patients. In this instance, the boundary conditions were improved by including an explicit model of those brace pads acting on the ribcage. Work is under way to include skin and muscle layers in the model, which will allow investigating their complex interaction with the pads. Further improvements should include gravity, muscular action and neuromuscular control.

Clinical indices

To our knowledge, this is the first series on 42 patients both for extensive quantitative evaluation of the 3D brace effect and for model evaluation. Bracing had a positive effect on the patient's clinical indices in the frontal plane where Cobb angle improved in 74 % of the cohort (Table 2, Online Resource 1). This is slightly better than the 50% cohort improvement previously reported by Courvoisier et al. [START_REF] Courvoisier | 3D analysis of brace treatment in idiopathic scoliosis[END_REF]. The absolute Cobb angle correction observed in this study was similar to the one previously reported by Lebel et al. [START_REF] Lebel | Three dimensional analysis of brace biomechanical efficacy for patients with AIS[END_REF] (-10.4° against ~14°), but VAR correction was lower (-1.7° against -6.5°). Comparison with previous studies, in particular concerning absolute values of correction, is difficult because of differences in the initial cohort (age, curve topology), brace compliance [START_REF] Weinstein | Effects of Bracing in Adolescents with Idiopathic Scoliosis[END_REF], etc. Moreover, brace planning relies on the experience of the orthotist and of the clinician, which adds to the variability of the results on brace effect.

Lordosis and kyphosis decreased in about 50 % of the cohort (Table 2). Hypolordosis and hypokyphosis are known features of the scoliotic spine [START_REF] Malfair | Radiographic Evaluation of Scoliosis: Review[END_REF], and it is well reported that brace treatment tend to flatten the sagittal alignment [START_REF] Courvoisier | 3D analysis of brace treatment in idiopathic scoliosis[END_REF]. The horizontal plane (torsion and VAR) was unchanged or worsened in the majority of patients, consistently with previous studies [START_REF] Courvoisier | 3D analysis of brace treatment in idiopathic scoliosis[END_REF]. It has been shown that restoration of sagittal spinal alignment and horizontal plane improves the rate of success scoliosis surgery [START_REF] Schwab | Predicting Outcome and Complications in the Surgical Treatment of Adult Scoliosis[END_REF] and global patient posture, but these results suggest that current brace designs tend to have little impact on the three-dimensional character of the scoliotic spine. Personalized and robust modeling of the trunk could drastically improve brace design and effectiveness.

One limitation of this work is that several types of braces and scoliosis severities were pooled together. Analyzing the effectiveness of a specific type of bracing, however, was beyond the scope of this work. The heterogeneity of bracing and scoliosis types actually allowed the model to be tested in several different situations. The second limitation is that the in-brace radiography was needed to define the boundary conditions. However, collecting the in-brace radiography and comparing it to the simulation results represents a powerful means of validating the model.

Comparison with the previous model [START_REF] Vergari | Evaluation of a patient-specific finite element model to simulate conservative treatment in adolescent idiopathic scoliosis[END_REF] shows improvements of the simulation performance in vertebral positions and orientations, as well as in all clinical indices but T4/T12 Kyphosis, which remained almost unchanged (3.8° against 3.5° in the previous work, Table 1). It is possible that this parameter is more influenced by the vertebral thoracic pads than by the newly introduced ribcage pads, or that a limit has been reached for this parameter; a further improvement might require reducing the uncertainty of the 3D reconstruction.

Statistical analysis showed that simulation accuracy did not depend on the degree of correction induced by the brace nor on the degree of spine deformity. In other words, the model had the same reliability for different curves and brace-induced displacements.

For 80 % of the patients, RMSEs were within the limits of uncertainty. For the remaining 20 % of the patients, the case-by-case analysis shows potential ways of improving the model. For instance, patient #40 (Table 3) shows large differences in Cobb angle and vertebral axial rotation at the apex (VAR). In-depth analysis showed that the brace increased his VAR by 2°.

In the simulation, VAR increased, but it actually increased too much (7°). At the same time, torsion decreased in the simulation, as well as in the measured stereoradiography, but not enough (2°). This suggests that the scoliotic curve in the simulation rotated too much in the axial plane, and it rotated too much rigidly (hence, the small change in torsion). A different distribution of spinal function units stiffness along the spine, and in particular at the junctional levels, might have decreased the VAR variation in the simulation while allowing a more natural detorsion of the curve.

In patient #28 (Table 3), VAR decreased by 18°, while in the simulation VAR decreased by 20°. Torsion decreased by 13° while it only decreased by 1° in the simulation. Once again, this patient's spine seems too stiff in rotation; a decrease in his functional units mechanical properties (discs, vertebrae, articular contacts) might improve the simulation. Cobb angle, however, present a small difference of 1.3°. This case underlines the importance of not basing the validation on the frontal plane only; such approach would have missed the simulation's actual performance on the horizontal plane.

Mechanical properties of the ribs were personalized with subject age, while their geometry was accurate because of recent developments in 3D reconstruction [START_REF] Aubert | In Press) 3D Reconstruction of rib cage geometry from biplanar radiographs using a statistical parametric model approach[END_REF]. This have probably played a role in the model performance, given how the ribs transmits loads to the spine. Although the intervertebral disc mechanical properties were not personalized, the simulations gave satisfactory results for the majority of the patients, thus highlighting the importance of the geometry in the behavior of this complex structure. However, it is likely that more severe curves (pre-surgery) would present stiffer spines, thus needing a specific personalization of the functional units' mechanical properties. Methods for obtaining disc properties in-vivo are being investigated [START_REF] Vergari | In Press) Lumbar annulus fibrosus biomechanical characterization in healthy children by ultrasound shear wave elastography[END_REF][START_REF] Lafon | In vivo distribution of spinal intervertebral stiffness based on clinical flexibility tests[END_REF][START_REF] Little | The effect of soft tissue properties on spinal flexibility in scoliosis: biomechanical simulation of fulcrum bending[END_REF], which will allow introducing personalized disc properties.

As hypothesized, a through validation of the model on a relatively large number of subjects allowed highlighting the model's limitations and potential means of improvement. Future work will aim at determining which mechanical properties are key to lower simulation errors, but also at developing non-invasive techniques to personalize mechanical properties thus improving the model towards the prediction of brace action. However, as of this day, it will be possible to modify the boundary conditions of the model to explore alternative and more effective brace action.

Fig. 1

 1 Fig.1Example of stereo-radiographies at decision of treatment (T0) and in-brace (T1); personalized finite element model buildt from 3D reconstruction at decision of treatment (T0) and after simulation of brace action (TS). The cylindrical structure on the rib cage are the brace's thoracic pads; intercostal membrane was hidden for clarity.

Fig. 2

 2 Fig. 2 Top, lateral and oblique view of a 3D model of a L1 vertebra: 3D volume reconstruction from stereoradiography and beam model of the vertebra. The vertebral body is composed of a single beam with two beams linking it to the posterior arch, spinous process and vertebral articulations. The latter, are modelled with shell elements (not represented for clarity) held in place by an array of structural beams. The endings of the lateral and spinous processes provide insertion points for ligaments.

Fig. 3

 3 Fig. 3 Root mean square error (RMSE) of Cobb angle between in-brace and simulated geometries for all patients: the dashed line represents the measurement uncertainty.

  |T1-Ts| |T1-T0| |T1-Ts| |T1-T0| |T1-Ts| |T1-T0| |T1-Ts| |T1-T0| |T1-Ts| |T1-T0| |T1-Ts| |T1-T0| |T1-Ts| T1/T12 Kyphosis (°)

Fig. 4

 4 Fig. 4 Root mean square error (RMSE) of vertebral axial rotation at apical level (VAR) between in-brace and simulated geometries for all patients: the dashed line represents the measurement uncertainty.

Table 1 .

 1 Measurement uncertainty, root mean square error (RMSE) between in-brace (T1) and simulated geometries (TS), and number of values out of 42 patients lower than the measurement uncertainty. (VAR: vertebral axial rotation at the apex).

			Maximal
		Measurement	difference	RMSE between Ts	# values <
		uncertainty	Ts -T1	and T1	uncertainty
	Clinical indices
	T1/T12 Kyphosis (°)	7.8	6.7	2.5	100 %
	T4/T12 Kyphosis (°)	5.4	8.4	3.8	83 %
	L1/L5 Lordosis (°)	6.5	9.0	4.0	93 %
	Cobb angle (°)	4.4	87	4.1	79 %
	VAR (°)	4.8	9.3	3.9	79 %
	Torsion (°)	5.7	12.7	4.7	86 %
	3D Rib Hump (°)	7.1	12.9	4.4	90 %
	Vertebral orientation
	Frontal rotation (°)	3.4	4.8	2.6	90 %
	Lateral rotation (°)	3.3	4.5	2.7	81 %
	Axial rotation (°)	5.5	14.1	5.0	86 %
	Vertebral position
	Postero-anterior (mm)	1.7	5.9	2.3	50 %
	Lateral (mm)	1.6	4.4	2.1	45 %
	Vertical (mm)	1.1	2.3	0.9

  Accepted Manuscript. European Spine Journal. The original publication is available at www.springerlink.com. DOI: http://dx.doi.org/10.1007/s00586-016-4511-7

			Value	Value	Average
		Value increased	unchanged	decreased	correction (°)
	T1/T12 Kyphosis	4 (10 %)	18 (43 %)	20 (48 %)	-4,8
	T4/T12 Kyphosis	5 (12 %)	14 (33 %)	23 (55 %)	-4,2
	L1/L5 Lordosis	2 (5 %)	15 (36 %)	25 (60 %)	-5,9
	Cobb angle	2 (5 %)	9 (21 %)	31 (74 %)	-10,4
	VAR	6 (14 %)	25 (60 %)	11 (26 %)	-1,7
	Torsion	4 (10 %)	28 (67 %)	10 (24 %)	-1,3
	3D Rib Hump	1 (2 %)	28 (67 %)	13 (31 %)	-2,7

Acknowledgements

The authors are grateful to the ParisTech BiomecAM chair program on subject-specific musculoskeletal modelling (with the support of ParisTech and Yves Cotrel Foundations, Société Générale, Proteor and Covea) and to the "Investissements d'Avenir" program for funding the CORSIN Project, in collaboration between Proteor and our institution. We would also like to thank Ms Sonia Simoes for her technical help.

Conflict of interest statement

No conflict of interest to disclose.


Clara Lagomarsini

Giulia Lombardi

Claire Jean-Mistral

Alain Sylvestre

come     Alternatives to external polarization source for dielectric elastomer generators: electrets versus piezoelectric materials

Alternatives to external polarization source for dielectric elastomers generators: electrets versus piezoelectric materials

Among the different technologies for kinetic energy harvesting, dielectric elastomers generators (DEGs) may represent a promising solution for supplying power to wearable low power consumption sensors and devices. These electrostatic generators provide a low-cost and lightweight solution to harvest high electrical energy densities from the mechanical deformation of an elastomeric membrane. The main disadvantage of these structures is the need of an external high voltage supply to perform the energetic cycle. In order to overcome this limitation and have a completely autonomous energy scavenger, our research group has been working since 2012, on coupling dielectric elastomers with electret materials (i.e. insulator materials that can hold a permanent electric charge over a long period of time). In the present work, a new hybrid solution for wearable energy harvesters based on DEG will be presented. This new autonomous device is based on the combination of a DEG with a piezoelectric material, which is used as new polarization source for the DEG energetic cycle. The working principle and the first results obtained on this new prototype are presented and a comparison between the two polarization solutions (electret and piezoelectric materials) is discussed.

State of the art

Classical DEGs: Working principle Clara Lagomarsini [START_REF] Lagomarsini | New approach to improve the energy density of hybrid electret-dielectric elastomer generators[END_REF] , Giulia Lombardi (2) , Claire Jean-Mistral (3) , Alain Sylvestre [START_REF] Lagomarsini | New approach to improve the energy density of hybrid electret-dielectric elastomer generators[END_REF] (1) Univ.

••

  ELECTRET materials (electric charges reservoirs) as DEG polarization source[1] Comparison between ELECTRET and PIEZOELECTRIC materials as polarization sources for autonomous DEG devices New AUTONOMOUS hybrid device based on a trapezoidal structure • POLARIZATION SOURCE for the DEG energetic cycle represented by a PIEZOELECTRIC BUZZER which is located in the lower part of the structure = V DEG MIN * λ 2 STRETCHED STATE C DEG MAX = C DEG MIN * λ 2 An uni-axial deformation λ equal to 50% was imposed to the device with a mechanical test bench • The deformation frequency was set to 1 Hz, corresponding to the step frequency while walking ENERGY STORED on a CAPACITOR (1 nF) : Comparison between the piezoelectric buzzer alone and the hybrid PZT+DEG device final air gap value between the DEG and the electret material and on the surface potential of the electret Depends on the deformation force acting on the piezoelectric element and on the number of buzzers used (stack configurations) axial stretch) ENERGIES BOOSTED VOLTAGE (V max )

  Grenoble Alpes, CNRS, Grenoble INP, G2Elab, Grenoble, France; (2) Dept. Of Electrical, Electronic And Information Engineering, University Of Bologna, Italy; (3) Univ. Lyon, INSA Lyon, CNRS UMR 5259, LaMCoS, Villeurbanne, France

Acknowledgments

Participation to this conference was partially supported by Région Rhône-Alpes (France) among the program "Communautés de Recherche Académique (ARC)" through grant No. 04, year 2014


Narsimhulu Pittala

Franck Thétiot

Catherine Charles

Smail Triki

Kamel Boukheddaden

Guillaume Chastanet

Mathieu Marchivie

Unprecedented trinuclear FeII triazole-based complex exhibiting a concerted and complete sharp spin transition above room temperature

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Unprecedented trinuclear Fe II triazole-based complex exhibiting a concerted and complete sharp spin transition above room temperature. Narsimhulu Among the molecular switchable materials, the spin crossover (SCO) complexes are particularly of interest, notably because of their potential applications in the development of new generations of electronic devices such as memories, molecular sensors and displays. 1 When the spin pairing energy is close to the splitting energy, 1,2 a SCO transition between the high-spin (HS, S = 2, 5 T 2g ) and low-spin (LS, S = 0, 1 A 1g ) states can be induced by different external solicitations such as temperature, pressure, magnetic field and/or light irradiation. 2,3 To date, Fe(II) metal complexes involving [ standard monoanions), display wide thermal hysteresis loops around room temperature. 4 However, the current and longstanding challenge to obtain single crystals of such coordination polymers makes difficult to access structural data at the molecular and inter-molecular scales; the latter are essential to understand and fine tune their SCO properties by acting on their cooperativity. Alternatively, new trinuclear triazole-based complexes, involving similar triple triazole bridges, are currently extensively studied (Table S1, ESI †).

5-8

These polynuclear systems could assist the tunable modeling and design of the SCO characteristics of the 1D chain polymers. However, in all these complexes, only the central Fe(II) ion undergoes a SCO transition, while the two terminal ones, commonly coordinated to two or three water molecules (or other oxygenated species), stringently remain in the HS state.

5-

8 Thus, those trinuclear complexes can be viewed as mononuclear SCO complexes in which the single active center experiences similar environment to the one described for the 1D chain polymers. Besides deepening the minutiae of the local environment of the Fe(II) active center, the investigations of larger SCO molecular discrete complexes, such as "true" trinuclear systems with three active SCO Fe(II) centers, could be crucial to elucidate the origin of the striking cooperativity observed in the 1D systems. Distinctly, the chemical control of cooperative hysteretic SCO polynuclear or oligomeric architectures is also of particular interest for the integration of discrete or isolated units into molecular devices. 1,9 In this context, we have extended this polynuclear approach to atypical combinations of new functionalized triazole ligands (Scheme 1a), and cyanocarbanions (Scheme 1b) which can act as co-ligands through their N-donor nitrile groups. The present work reports the synthesis and full structural and magnetic characterizations of the first example of triazole-based SCO Fe II trinuclear complex [Fe 3 (bntrz) 6 (tcnset) 6 ] (1) exhibiting a complete and one-step spin transition above room temperature.

Single crystals of 1 have been synthesized using diffusion technique in fine glass tube (3.0 mm diameter) by layering methanolic solution of the bntrz ligand onto aqueous solution containing K(tcnset) and Fe(BF 4 ) 2 .6H 2 O salts (see Experimental section and Figs S1-S7, ESI †). [10][11] Compound 1 has been structurally characterized at 360 K (HS state, colorless crystal), 250 K (LS state, pink crystal), and around the transition region (280-345 K) (Tables S2-S3). The magnetic susceptibility (χ m ) for 1 was measured over the 2-300 K temperature (T) range on a set of single crystals sample. The thermal variation of the χ m T product is displayed in Fig. 1. At 380 K, the χ m T value (9.48

cm 3 •K•mol -1
) is consistent with three isolated HS (S = 2) hexacoordinated Fe(II) ions. Upon cooling, the χ m T product decreases gradually down to a temperature value of ca. 320 K.

Below this temperature, it sharply decreases to a minimum value of ca. 0.0 cm

3 •K•mol -1
, which is reached around ca. 250 K, indicating the presence of a sharp and complete HS to LS SCO first-order phase transition at 318 K. Upon warming and cooling at a scan rate of 0.7 K/min in settle mode, no thermal hysteresis effects were detected. Irradiation at 10 K did not reveal LIESST effects. The DSC study for 1, performed in the temperature range 290-340 K with a temperature scan rate of 2 K/mn, shows exo-and endo-thermic transitions with maxima at 317.5 and 318.7 K, respectively (Inset Fig. 1). The small difference between DSC peak positions is most likely due to a kinetic effect. This phase transition occurs with an enthalpy and entropy changes of ΔH = 54.1 kJ.mol , respectively. These values are in the range of those reported in the literature for similar SCO compounds. Based on the magnetic observations, the crystal structure of 1 has been determined at 360 K and 250 K (see Table S2, ESI †). Selected Fe-N bond lengths and N-Fe-N bond angles at 360 K and 250 K are gathered in Table S3. Average Fe-N distances and distortion parameters for both metal centers (Fe1 and Fe2) are listed in Table 1 for the two spin states. The structure of 1 is built from two crystallographically inequivalent Fe(II) ions (Fe1 and Fe2), located respectively on (1/3 2/3 1/6) and ( 1 is bound on both sides to two other Fe(II) centers (Fe2) through three µ 2 -bridging bntrz ligands (Fig. 2). The central metal ion (Fe1) is surrounded by six nitrogen atoms from six equivalent µ 2 -bntrz ligands, while each external Fe2 ion adopts FeN 3 N 3 octahedral environments arising from three equivalent bridging bntrz ligands and three unidentate (tcnset) -anions (Fig. 2). 1). 13 The average values of the Fe-N distances at 360 K (d Fe1-N = 2.175(2) Å and 〈d Fe2-N 〉 = 2.158(3) Å) and 250 K (d Fe1-N = 1.979( 2) and 〈d Fe2-N 〉 = 1.940(2) Å) are in agreement with the presence of full HS and LS states, respectively. This observation is consistent with the presence of a complete [HS-HS-HS]↔[LS-LS-LS] SCO transition, as initially revealed by the magnetic data (see Fig. 1).

The most intriguing and atypical feature of the present SCO compound 1 concerns the occurrence of a one-step transition despite the existence of two chemically different metal centers in the trimer (Fe2-Fe1-Fe2), as revealed by the crystallographic data in the two spin states. Thus, in order to undoubtedly confirm the absence of a two-step (or multi-step) transition, and to further understand the evolution of each Fe(II) environment (Fe1 and Fe2) during the transition, the crystal structure of 1 has been solved every 5 K around the transition region, i.e. between 280 K and 345 K (see CCDC numbers 1500728-1500740, ESI †). Thus, it must be noted that these additional structural investigations have not revealed any change of symmetry on the whole temperature range, while they have shown that the thermal evolution of the average Fe-N distances (〈d Fe-N 〉) matches excellently the magnetic data (see Fig. 1). Moreover, the respective thermal behavior of Fe-N distances for the two Fe II centers almost perfectly overlap the thermal magnetic behavior (see Fig. 3). This appraisal suggests that both iron centers (Fe1 and Fe2) of the trinuclear complex, although displaying different crystallographic environments, undergo the spin transition in a concerted way, which is consistent with the one-step transition scenario from [LS-LS-LS] to [HS-HS-HS] states. The careful examination of the shortest inter-molecular contacts (πstacking, hydrogen bonding and van der Waals contacts) in 1 reveals that the trinuclear moieties are linked together by six hydrogen bonds involving the triazole ring and the CN branches from the cyanocarbanions of adjacent trinuclear complexes. Such inter-trinuclear contacts lead to a supramolecular chain oriented along the c axis (Fig. 4). The corresponding chains are connected to each other through van der Waals contacts involving the S-Et groups of the cyanocarbanions and by weak interactions involving the π system of benzyl moieties (centroid-centroid distances = 4.26 Å at 250K; Fig. S8). During the LS to HS transition, the intratrinuclear Fe1-Fe2 distances increase from 3.657( 1 This antagonistic co-evolution of the intra-and inter-trinuclear distances implies that the anisotropic change of the SCO is accompanied by a structural rearrangement involving both the cyanocarbanions and the side chains of the triazoles, as evidenced by the very weak modifications of the H-bonds between 250 K and 360 K. Thus, this rearrangement keeps the inter-trimer interactions very similar in both spin states. This observation further confirms the strong links connecting the trinuclear units along the c direction, which prevents the absorption of the total intratrinuclear Fe1-Fe2 deformation. As a result, the metal centers (Fe1 and Fe2) of the trimers slightly move away from each other (along the c axis) upon LS to HS conversion. In the other directions (a and b), the evolution of the inter-chain distances during the LS to HS transition follows a more expected behavior, with an increase from 14.664(1) Å at 250 K to 15.043(1) Å at 360 K; the same applies to the molecular volume and the thermal expansion, which is the signature of weaker interactions within the ab plane. These thermal structural evolutions clearly indicate the existence of a strong 1D character of the crystal along the [001] direction which dominates the system's behavior. This one-dimensional structural feature constitutes a unique specimen within the trinuclear SCO systems available in the literature.

5-8

We have prepared and fully characterized a new trinuclear [Fe 3 (bntrz) 6 (tcnset) 6 ] (1) neutral complex that exhibits a complete and sharp one-step spin transition above room temperature (T 1/2 = 318 K), and defined to our best knowledge as the first SCO trinuclear complex exhibiting such a complete spin transition. The one-step nature of the magnetic transition has been notably confirmed by DSC measurements and detailed structural studies around the transition region that clearly demonstrated that the thermal evolutions for the three Fe II environments are similar and fit adequately the one-step transition from [LS-LS-LS] to [HS-HS-HS] states. This unprecedented behavior has been mainly assigned to the presence of a rigid elastic interaction between the central metal ion and its neighbours within the trimer. Yet the inter-trimer interaction along the supramolecular chain is also significant, as proven by the observed smallest variation of the corresponding lattice parameter c (Δa/a upon the transition is 4 times greater than Δc/c); the latter involves not only Fe2•••Fe2 distance change (from 7.419(1) Å at250 K to 7.094(1) Å at 360 K) but also that of Fe1-Fe2 sites (from 3.657(1) Å at 250 K to 3.865(1) Å at 360 K). Besides, although the two Fe(II) centers display different environments and related ligand fields within the trimer, their transition takes place concomitantly due to the strong ferro-elastic coupling linking the two iron centers. Indeed, the LS-HS-LS or HS-LS-HS configurations in the present case are very high in energy, due to the excess of elastic stress which cannot be accommodated within the trimer, which then excludes the occurrence of a two-step transition. Referring to the cooperative character of the transition, it is mostly due to the interactions within the chains (strong intra-and weak inter-trimers coupling), thus explaining the absence of a thermal hysteresis at the transition. The rigid nature of the trimer and its rather high transition temperature support the argument that the transition of either the central or the external metal ions drives the whole cluster, which basically behaves as a strongly correlated entity. In summary, this study opens the way to a rich family of discrete SCO polynuclear complexes by tuning the rigidity of the anions, and the present derivative constitutes an excellent model system for theoretical investigations using elastic models 14 in order to disentangle the contributions of intra-and inter-molecular elastic interactions and to clarify how from their competing character at the microscopic level emerges the two-or one-step transitions at the macroscopic scale.

  -based trinuclear complex as the first related example to date that displays a complete one-step first-order [HS-HS-HS]↔[LS-LS-LS] spin transition at 318 K. The strong ferroelastic interactions, between the three metal centers, have been identified as the source of the concerted spin transition in this trinuclear complex.

  FeN 6 ] octahedron coordination spheres have been the most studied SCO compounds. Among the few examples exhibiting remarkable SCO behavior, the systems based on the 1,2,4triazole ligands still remain among the most promising materials for future applications in electronic devices since some of them, particularly the coordination 1D-polymers of general formula [Fe((NH 2 -trz) 3 ](X) 2 and [Fe(Htrz) 2 (trz)](X) (NH 2trz = 4-amino-1,2,4-triazole, Htrz = 4-H-1,2,4-triazole, X -=

Scheme 1

 1 Scheme 1 Examples of 1,2,4-triazole (a) and cyanocarbanions (b) ligands.

12 Fig. 1

 121 Fig. 1 Thermal evolutions of the χmT product (•), and the average Fe-N distances ( ) around the transition region for 1. Inset: DSC study for 1 showing the exo-and endo-thermic transitions.

  two Fe(II) environments are defined by N1 ([Fe1(N1)6]) and by N2 and N4 ([Fe2(N2)3(N4)3]) nitrogen atoms.

  /3 2/3 z) special positions, and one bntrz molecule and one (tcnset) -anion, both located on general positions. The molecular structure of 1 consists of a neutral trinuclear complex of formula [Fe 3 (bntrz) 6 (tcnset) 6 ] which can be viewed as a [Fe2(bntrz) 3 Fe1(bntrz) 3 Fe2] linear and centrosymmetric fragment in which the central metal ion (Fe1)

Fig. 2

 2 Fig. 2 View of the centrosymmetric trinuclear complex in 1 at 360 K. (a): 2/3-y+x, 1/3+x, 1/3-z.; (b): 1-y, 1+x-y, z; (c): y-x, 1-x, z; (d): 2/3-x, 4/3-y, 1/3-z; (e): -1/3+y, 1/3-x+y, 1/3-z.

Fig. 3

 3 Fig. 3 Thermal evolutions of the average Fe-N distances of each Fe(II) center (Fe1 and Fe2) in the trinuclear units of 1 ([Fe2-Fe1-Fe2]), and of the χmT product in the 280-345 K range.

Fig. 4

 4 Fig. 4 View of 1 along the direction axis showing the hydrogen bond contacts between trinuclear units: C2…N5 = 3.329 (4) Å at 360 K; C2…N5 = 3.349(3) Å at 250 K. (a) = 2/3-x,4/3-y,1/3-z ; (b) 2/3-y+x,1/3+x,4/3-z ; (c) -1/3+y,1/3-x+y,4/3-z.

  7.419(1) Å (250 K) to 7.094(1) Å (360 K), as depicted in Figs. S9-S10. Nevertheless, it is noteworthy that the corresponding molecular separation along the c axis varies little upon the transition, as the distances between trinuclear centroids slightly increase from 14.734(2) Å (250 K) to 14.824(2) Å (360 K).

Table 1

 1 Average Fe-N distances (〈dFe-N〉) and distortion parameters

	T (K)	250		360
	*Fe II	Fe1	Fe2	Fe1	Fe2
	center
	Fe1-N1	1.979(2)		2.175(2)
	Fe2-N2		1.959(2)		2.170(2)
	Fe2-N4		1.940(2)		2.146(3)
	〈dFe-N〉 (Å)	1.979(2)	1.949(3)	2.175(2)	2.158(3)

Σ/Θ (°)

13

Acknowledgements

We thank the CNRS, the Universities of Brest (UBO), Versailles (Paris-Saclay) and Bordeaux, the "Agence Nationale de la Recherche" (ANR-12-BS07-0030-01) and the European community (FP7 project: PCIG-GA-2011-304193 NANOCOORD).

Notes and references