Sheng Wan

Liyun Cao

Yi Zeng

Tong Guo

Mourad Oudich
email: mourad.oudich@univ-lorraine.fr

Badreddine Assouar
email: badreddine.assouar@univ-lorraine.fr

Low-frequency nonreciprocal flexural wave propagation via compact cascaded time-modulated resonators

Keywords: Nonreciprocal acoustics, Elastic metamaterials, Unidirectional wave propagation, Flexural waves

Nonreciprocal mechanical devices are of great interest for directional elastic wave manipulation. In this letter, we introduce a design of a compact low-frequency nonreciprocal metamaterial for flexural waves, whose dimension is less than 1/3 of the operating wavelength. This structure is made of two well-placed coil-cantilever-magnet resonators where the electromagnetic forces can be temporally modulated, which enables time varying of the effective stiffness of the resonators. A phase shift is introduced between the stiffness modulations of these two resonators which breaks the time-reversal symmetry and enables nonreciprocal wave propagation at the resonance frequency of the structure. A semi-analytical method based on harmonic waves decomposition is developed to describe the system, leading to results that match well with the numerical predictions from finite element method. We also experimentally demonstrate nonreciprocal flexural wave propagation with good agreement with the predictions made. Our system could inspire the design of compact nonreciprocal devices for flexural waves.

Breaking reciprocity in classical waves has been gaining increasing interest in the last decade, motivated by the need for unidirectional wave propagation and robust one-way waveguding 1- 5 . Nonreciprocal materials or devices, i.e., diodes, are highly desired for the manipulation of the energy carried by the wave. In acoustics, a popular approach to realize nonreciprocal wave propagation by breaking the time reversal symmetry is the realization of acoustic circulators 6- 8 which is inspired from optical ones 9,10 . The circulator is a three-port system with a central ring cavity endowed with a circulating fluid flow to introduce the acoustic bias 6 . Another mainstream approach is modulated phononic crystals and metamaterials 1 . This idea can be traced back to last mid-century in photonics and electrical circuits, where permittivity, permeability or the electrical impedance is harmonically modulated both in space and time to create unidirectional band gaps for waves [11][START_REF] Cassedy | Proc. IEEE[END_REF][START_REF] Cassedy | Proc. Inst. Electr. Eng[END_REF] . The spatiotemporal modulation can also break the time reversal symmetry, leading to asymmetrical frequency conversions in opposite propagating directions. In elastodynamics, the spatiotemporal modulation is performed over the intrinsic properties of the material, namely the effective stiffness, using exotic physical and technical approaches. For the achievement of nonreciprocity for elastic waves, the challenge was to come up with a realizable method that can enable dynamic modulation of the stiffness with speed comparable to the propagating wave velocity. Wang et al. [START_REF] Wang | [END_REF] were the first to experimentally perform such modulation using coupled magnet rings and coils where the coupling can be varied in time via dynamically changing the magnetic force from the coils which in turn leads to the time modulation of the effective stiffness. The system is equivalent to a series of masses and springs connected to the ground where the effective stiffness of the springs is modulated both in space and time. This magnet-coil based approach was proven to be very effective for modulating the effective stiffness in time at high speed which enables nonreciprocal wave dispersion. Chen et al. 15 designed a tunable elastic metamaterial made of periodic resonators distributed on a plate. Each resonator is constructed with a permanent magnet and a coil to control its effective stiffness, which led to a demonstration of unidirectional propagation of flexural waves. Another interesting yet different approach was proposed by Goldsberry et al. 16 who used nonlinear large deformations to spatiotemporally vary the effective stiffness and enable nonreciprocal wave propagation. Differently, Ruzzene et al [17][18][19] proposed an efficient and fast approach to demonstrate nonreciprocal reflection and transmission of flexural waves. In their case, the modulation of the effective stiffness is performed using piezoelectric patches connected to well elaborated and controlled electrical circuits. Besides, a mechanical approach was introduced by Attarzadeh et al. 20 . They used a series of local resonators where their effective stiffness was modulated by varying the second area moment of inertia of each resonator's arm through dynamically changing its angular orientation. However, these experimental works rely on using several periods of the phononic crystal or the metamaterial in order to introduce a waveform variation of the effective stiffness both in space and time. This makes the design cumbersome and hard to be considered for subwavelength applications where compact and integrated designs with high performance wave functionalities are desired. Furthermore, in these proposed designs, a programmable micro-controller unit (MCU) is needed to synchronize the temporal modulation which seriously complicates the system. Nevertheless, promising solutions for enabling nonreciprocity using compact devices were proposed in acoustics which are based on only two cascaded local resonators. These include slab resonators 21 , Helmholtz resonators 22 , air cavity resonators 23 , and thin membranes 24 . The compactness of those structures makes them to be of great usability for miniaturized acoustic devices.

In this research, we designed and fabricated a compact low-frequency nonreciprocal waveguide for flexural waves using only two time-modulated mechanical resonators. Inspired by the work of Chen et al 15 and Wang et al. [START_REF] Wang | [END_REF] , the resonators are physically realized by a coil-cantilevermagnet system with controllable effective stiffness via the application of an alternating current (AC). These resonators can be modeled as spring-mass equivalent system with time-dependent effective stiffness. By introducing a phase shift between the applied alternating current (AC) of these two resonators, their effective stiffness is harmonically modulated in time with a controllable phase shift which provokes a spatial bias, and leads to nonreciprocal flexural wave transmission. A simplified analytic approach based on plane wave decomposition is developed to analyze the flexural wave propagation in the system. The analytical results support the observed experiment ones around the adopted operating frequency. The dimension of the cascaded resonator structure is less than 1/3 of the operating wavelength. We begin by conducting a theoretical study where we model our system by the equivalent cascaded mass-spring resonator system shown in Fig. 1(b). The thickness of the beam waveguide denotes ℎ, and its width denotes 𝑑. Two mass-spring resonators are attached to the beam, whose mass is denoted 𝑚, and the time-varying spring stiffness is 𝜅. The distance between the centers of the two resonators is 𝑙. The damping is not considered in this theoretical study. Fig. 1(a) shows the physical realization of this system where the resonator is made of a flexible cantilever in which a permanent magnet is fixed to the base of cantilever, and a coil is fixed to the flexible part of cantilever (Fig. 1(d)). the two coil-cantilever-magnet resonators system. When no temporal modulation is applied, the coil-cantilever-magnet resonator behaves as a simple mass-spring resonator with constant mechanical properties. On the first resonance mode of the coil-cantilever-magnet structure, the displacement of the coil is only out-of-plane (see Supplementary information), the cantilever and the coil can be considered as the spring and the mass respectively. When the displacement of the coil is relatively small, the out-of-plane force on the coil has a linear relationship with the displacement, respecting the Hooke's law. The equivalent effective spring stiffness and mass can be evaluated via eigenfrequency study by numerical simulation using finite element method. We used the commercial software COMSOL Multiphysics 5.6 to perform such simulation (see Supplementary information). As for the temporal modulation, it is realized via the electromagnetic force between the coil and the magnet. When applying an AC to the coil, an attraction or repulsion force, depending on the current direction and magnetic pole orientation of magnet, appears between the magnet and the coil. This force has a linear correlation with the relative displacement between the magnet and the coil when the displacement amplitude is relatively small 15 (see Supplementary information). So, an additional stiffness, which could be positive or negative, is provided by the magnet-coil design and can be linearly superposed with the static stiffness of the coil-cantilever structure.

Consequently, we can dynamically change the total stiffness by varying the AC applied to the coil.

To theoretically characterize the wave propagation in this system, we have considered the mass-spring model with variable effective stiffness of the springs. The out-of-plane displacement fields of the incident, reflected, and transmitted waves are denoted as 𝑤 ! , 𝑤 " , and 𝑤 # (Fig. 1(a) and (b)). In the one-dimensional theoretical model, the plate model is adopted, and the dimensions of the resonator are not considered. We first start with a system with only one resonator located at 𝑥 = 0. The temporal modulation on the spring stiffness of the form 𝜅(𝑡) = 𝜅 $ + 𝜅 % cos(𝛺𝑡 + 𝜙) is considered where 𝛺 is the modulation frequency, 𝜙 is the initial phase, 𝜅 $ is the static spring stiffness associated with the flexible cantilever, and 𝜅 % is the additional modulation stiffness added by the magnet and coil interaction. The spring stiffness can be decomposed in the generalized Floquet form,

𝜅(𝑡) = 6 𝜅 & 𝑒 '(#)* ! + &,-+ (1)
where 𝜅 ±+ equals to 0.5𝜅 % . At low frequency, the generalized Floquet form of flexural wave displacement in a thin plate can be expressed as the sum of harmonic propagation and evanescent modes 15 , 𝑤 = 6 :𝐴 / 𝑒 -'01 + 𝐵 / 𝑒 '01 + 𝑎 / 𝑒 -01 + 𝑏 / 𝑒 01 ?𝑒 '(3)/4)# 6 /,-6

(2

)
where 𝑘 is the wave number, and 𝜔 is the operational angular frequency. The displacement of the mass in the resonator is,

𝑤 % (𝑡) = 6 𝑤 / % 𝑒 '(3)/4)# 6 /,-6 (3)
The conditions of continuity on the displacement 𝑤, slope 𝜑, moment balance 𝑀, and beam shear force balance 𝑉, apply in the waveguide 25

at 𝑥 = 0, G 𝑤 ) -𝑤 -= 0 𝜑 ) -𝜑 -= 0 𝑀 ) -𝑀 -= 0 𝑉 ) -𝑉 -= 𝐹 (4)
The positive and negative signs mean right and left of the position 𝑥 = 0 of the beam. And the slope, the moment and shear force are,

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 𝜑 = 𝜕𝑤 𝜕𝑥 𝑀 = 𝐸𝐼 𝜕 7 𝑤 𝜕𝑥 7 𝑉 = -𝐸𝐼 𝜕 8 𝑤 𝜕𝑥 8 (5)
where 𝐼 = ℎ 8 12(1 -𝜐 7 ) ⁄ is the section moment of inertia, and 𝐸 and 𝜐 are the Young's modulus and Poisson's ratio of the waveguide, respectively.

At 𝑥 = 0, 𝐹(0) = (𝑤 ) (0) -𝑤 % )𝜅(𝑡), and an extra equation of the force balance on the mass exists,

𝑚 𝜕 7 𝑤 % 𝜕𝑡 7 = 𝐹(0) (6)
The dispersion relation is known as 𝑘 = (𝐸𝐼 𝜌ℎ𝜔 7 ⁄ ) -" # , where 𝜌 is the density of the waveguide. We insert Eqs (1) to (3) into Eqs (4) to (6); and by considering a finite number 𝑁 of plane waves and by eliminating 𝒘 %,6 , we are able to obtain the transfer matrix 𝑴 of

dimension 4(2𝑁 + 1), Y 𝑨 ),6 𝑩 ),6 𝒂 ),6 𝒃 ),6 ^= 𝑴 Y 𝑨 -,6 𝑩 -,6 𝒂 -,6 𝒃 -,6 ^(7)
where 𝑨 ),6 , 𝑩 ),6 , 𝒂 ),6 , 𝒃 ),6 , 𝑨 -,6 , 𝑩 -,6 , 𝒂 -,6 and 𝒃 -,6 are of the form 𝑿 :,6 = ⟨𝑋 -6 : , … , 𝑋 $ : , … , 𝑋 )6 : ⟩ ; where X can be either 𝑨, 𝑩, 𝒂 or 𝒃 and 𝑠 takes either the sign "-" or "+", and 𝒘 %,6 = ⟨𝑤 -6 % , … , 𝑤 $ % , … , 𝑤 )6 % ⟩ ; . This transfer matrix 𝑴 can be converted to the

scattering matrix 𝑺 Y 𝑨 ),6 𝒂 ),6 𝑩 -,6 𝒃 -,6 ^= 𝑺 Y 𝑨 -,6 𝒂 -,6 𝑩 ),6 𝒃 ),6 ^(8)
The incident, reflected and transmitted wavefields are 𝑤 ! = ∑ :𝐴 < -𝑒 -'01 ?𝑒 '(3)/4)# 6 /,-6

, 𝑤 " = ∑ :𝐵 < -𝑒 '01 + 𝑏 < -𝑒 01 ?𝑒 '(3)/4)# 6 /,-6

, and 𝑤 # = ∑ :𝐴 < ) 𝑒 -'01 + 𝑎 < ) 𝑒 -01 ?𝑒 '(3)/4)# 6 /,-6

, respectively. With a given 𝑤 ! , 𝑤 " and 𝑤 # can be calculated. If the points of the measurement are far enough from the two resonators system (one wavelength away), the evanescent terms in the 𝑤 " and 𝑤 # can be ignored. (with an effective current of 0.46 A ). The necessary current to reach a required 𝜅 % was estimated via finite element simulation, and the real current needed in the experiment was higher than the simulation results due to the fabrication imperfections of coils (see

Supplementary information).

The magnet is rigidly bonded to the base of the cantilever, which is glued on the beam (Fig. 1(d)), and the measurement was performed via laser vibrometer. The coil is glued on the skeleton of the cantilever, which enables the out-of-plane movement. The mass of the coil is 2.5 g, the frequency of the first resonance mode is about 115 Hz, and the distance between the centers of the two resonators is 70 mm. The spring stiffness 𝜅 $ under 20°C is approximately 1600 N/m (See Supplementary information for the details of evaluations of the effective stiffness 𝜅 $ and the effective mass 𝑚). We optimized the effect of nonreciprocity upon the modulation frequency 𝛺, the modulation strength 𝜅 % , and the distance between the two resonators 𝑙 using genetic algorithm. The magnet and the coil should be strictly coaxial and concentric. If not, the AC itself could become an excitation source at the AC frequency 𝛺. In this situation, high noise at the harmonics of the AC frequency would be generated.

In the experimental setup, the power consumption leads to a rapid heating of the resonators which may at some points makes the PLA lose its original rigidity and effects the resonance mechanism and the measurements. To reduce the heating effect, we adopted a low effective current 0.46 A and shortened the power-on time of the coils. With this current, the modulation strength 𝜅 % we can reach is approximately 200 N/m. The Fast Fourier Transform (FFT) resolution of the laser vibrometer was set to 1 Hz, and the measurements were performed on one point on the beam so that each measurement can be done in 1 s. Then, the power-on time was controlled by activating and disactivating the output of the modulation source generator.

The modulation amplifier was always on to prevent power-on sonic boom. The excitation source was also always on to reduce the influence of the astable state. The precise output phase setting is available on our modulation generator, so the phase shift was realized by applying different initial phases on the outputs of different channels. Further, to inverse the direction of propagation, it is sufficient to inverse the phase shift of the two output channels. The frequency of AC, i.e. the modulation frequency 𝛺, is 20 Hz. The phase shift between the two ACs is 90°

or -90°. At each frequency, we performed 5 measurements in each propagation direction. To better understand the mechanism of nonreciprocity in our structure, we have analyzed the mechanical energy of the transmitted and reflected waves, as well as in the resonators using numerical approaches for the case with time modulated effective stiffness. To conduct the transmission simulation using finite element simulation, the reflections of flexural waves at the boundaries of the beam are suppressed using the damping layer method 26 . An example evaluation of the reflection and transmission coefficients for an incident harmonic wave at 126 Hz is shown in Fig. S3 in the Supplementary information. Frequency conversion is depicted with the appearance of high order waves at frequencies 126 Hz + 𝑛𝛺 where 𝑛 = ±2, ±1.

The mechanical energy in the flexural wave on the plate can be calculated 27 ,

𝐸 = = 𝜔𝐸𝐼𝑘 8 |𝑋 y | 7 , (9)
where |𝑋 y | is the amplitude of the flexural wave. The mechanical energy in the resonator can also be calculated using the formula,

𝐸 0 = 1 2 𝑚(𝜔|𝑤 % |) 7 (10)
𝐸 & = z 1 2 [𝑘 $ + 𝑘 % cos(𝛺𝑡)]|𝑤 % | 7 𝑑𝑡 ; $ $ (11)
where 𝐸 0 is the kinetic energy of the mass, 𝐸 & is the potential energy of the spring, and 𝑇 > = 2𝜋 𝛺 ⁄ is the cycle of the temporal modulation. Fig. 4 exhibits the stacked area charts of the mechanical energy of the system in both propagation directions for incident harmonic waves with frequencies between 117 and 135 Hz. The chart represents the calculated energy for the transmission (green) and reflection (pink) waves in the plate, the energy stored in the resonators (yellow), and the sum of the energies carried by the high order waves at frequencies 𝜔 + 𝑛𝛺 where 𝑛 = ±2, ±1 for the transmitted (orange) and reflected waves (blue), as well as in the resonators (purple), all normalized by incident wave energy. Considerable frequency conversions appear in this time-modulated system, which is the principal incentive for the nonreciprocity in our structure. We observe that the low transmitted energy (green) of the fundamental mode (0th order) in the negative direction is attributed to frequency conversion in the transmitted (orange) and reflected waves (blue). Another observation is that the total energy in our structure surpasses the input energy from incident wave due to the input energy from active time modulation. In conclusion, we have introduced in this work a compact time-modulated mechanical biresonators system to achieve nonreciprocal flexural wave transmission at low frequency. The resonators were designed with a vibrating cantilever with magnetically coupled coils and magnets. The temporal modulation of the effective stiffness of each resonator was realized by an AC applied to the coil which couples to the fixed magnets via the varying magnetic field.

The dimension of this device is less than 1/3 wavelength. A physical realization of such a system based on coil-cantilever-magnet resonators has been experimentally conducted. The obtained measurements have evidenced high nonreciprocal flexural waves propagation with results that agree well with our simplified analytical predictions. Our concept provides a promising perspective on the design of compact nonreciprocal metamaterials that can integrate flexural waveguiding systems for smart wave control in phononic communication devices.

Supplementary material

See supplementary material for all the details regarding the manuscript. Negative direction

FIG. 1 .

 1 FIG. 1. (a) Realization of a coil-cantilever-magnet bi-resonator system with temporally modulated effective stiffness through an applied AC in the coil. (b) Schematic of the equivalent model for the cascaded mass-spring resonator system. AC is the alternating current, 𝑚 is mass of the resonator, 𝜅 is its stiffness, 𝐼 is the real-time current, 𝑤 ! is the incident wave, 𝑤 " is reflected wave, and 𝑤 # is transmitted wave. (c) Fabricated on-beam coil-cantilever-magnet resonator in our experimental setup. (d) Schematic design of the coil-cantilever-magnet resonator system.

Fig. 1 (

 1 c) shows the fabricated sample with 𝑤 𝑖 𝑤 𝑟 𝑤 𝑡

FIG. 2 .

 2 FIG. 2.Experimental platform for flexural wave transmission. AMP: amplifier.

Figure 2

 2 Figure2shows the experimental setup of the system. We first have constructed a beam waveguide by 3D printing using PLA material and the beam width and thickness are 𝑑 = 20 mm and ℎ = 3 mm, respectively. Damping adhesives were sticked on the two extreme boundaries of the beam to eliminate the flexural wave reflections at low frequency, and ensure weak reflection above 120 Hz. The whole length of the beam is over 3 m, and the usable length of this beam is approximately 0.8 m , about 3 wavelengths at 126 Hz . A large circular piezoelectric patch with a radius of 15 mm was used as an excitation source, which prevents the appearance of torsional modes on the beam. An additional amplifier was connected to the piezoelectric patch to perform a strong excitation while reducing the influence of the

FIG. 3 .Fig. 3 (

 33 FIG. 3. (a) Results of the transmission measurements from 121Hz to 130Hz with error bars, normalized by the results of the bare beam (without resonators). The positive direction means the initial phase of current of the coil close to the piezoelectric excitation is 90°, while that close to the laser measurement point is 0°. The negative direction means the former is -90°, while the latter is 0°. (b) Analytical transmission coefficient 𝐴 $ ) in the frequency

FIG. 4 .

 4 FIG. 4. Stacked area chart of global mechanical energy distribution for positive (a) and negative (b) directions calculated using FE simulation at various incident frequencies. FC:frequency conversion. Here we represent the mechanical energy for the transmitted (green) and reflected (pink) fundamental modes (0th order) in the plate, the energy stored in the resonators (yellow), and the sum of the energies carried by the high order waves at frequencies 𝜔 + 𝑛𝛺 where 𝑛 = ±2; ±1 for the transmitted (orange) and reflected waves (blue), as well as in the resonators (purple), all normalized by incident wave energy.

Acknowledgements

This work is supported by the Air Force Office of Scientific Research under award number FA9550-18-1-7021, and by la Région Grand Est.

Data availability

The data that support the findings of this study are available within the article and its supplementary material.

Author declarations

Conflict of interest

The authors have no conflicts to disclose.


MD Marie-Noëlle Méaux
email: mn.meaux@gmail.com

Candide -2-*

Agnès Alioli 2-*

Linglart

Sandrine Lemoine

Emmanuelle Vignot

Aurélia Bertholet-Thomas

Olivier Peyruchaud

Sacha Flammier

Irma Machuca-Gayet

Justine Bacchetta

X-linked hypophosphatemia, not only a skeletal disease but also a chronic inflammatory state

Keywords: hypophosphatemia, Obesity, Inflammation, Osteoclastogenesis, vitamin

Introduction: X-linked hypophosphatemia (XLH) is a rare genetic disease caused by a primary excess of FGF23. FGF23 has been associated with inflammation and impaired osteoclastogenesis, but these pathways have not been investigated in XLH. The aim was to evaluate whether XLH patients display peculiar inflammatory profile and increased osteoclastic activity.

Methods: We performed a prospective multicenter cross-sectional study analyzing transcript expression of 8 inflammatory markers (Il6, Il8, Il1β, CXCL1, CCL2, CXCR3, Il1R, Il6R) by RT-qPCR on PBMCs purified from total blood samples extracted from patients and healthy controls. The effect of native /active Vitamin D on osteoclast formation was also assessed in vitro from XLH patients' PBMCs.

Results: In total, 28 XLH patients (17 children, among them 6 undergoing standard of care SOC and 11 burosumab therapy) and 19 controls were enrolled. Expression of most inflammatory markers was significantly increased in PBMCs from XLH patients as compared to controls. No differences were observed between burosumab and SOC sub-groups. Osteoclast formation was significantly impaired in XLH patients. XLH mature osteoclasts displayed higher levels of inflammatory markers, however being lower in cells derived from the burosumab sub-group (as opposed to SOC).

Conclusion:

We describe for the first time a peculiar inflammatory profile in XLH. Since XLH patients have a propensity to develop arterial hypertension, obesity and enthesopathies, and since inflammation can worsen these clinical outcomes, we hypothesize that inflammation may play a critical role in these extra-skeletal complications of XLH.

Introduction

X-linked hypophosphatemia (XLH) is an orphan genetic disease most associated with an inactivating mutation in the PHEX gene encoding the phosphate-regulating neutral endopeptidase. It induces chronic hypophosphatemia, due to increased circulating levels of FGF23 [START_REF] Beck-Nielsen | FGF23 and its role in X-linked hypophosphatemia-related morbidity[END_REF]. Classical clinical symptoms associate growth retardation, legs bowing, dental illness and rickets, but other clinical abnormalities have been recently described [START_REF] Beck-Nielsen | FGF23 and its role in X-linked hypophosphatemia-related morbidity[END_REF][START_REF] Bacchetta | Physiology of FGF23 and overview of genetic diseases associated with renal phosphate wasting[END_REF][START_REF] Rothenbuhler | Diagnosis, treatment-monitoring and follow-up of children and adolescents with X-linked hypophosphatemia (XLH)[END_REF]; notably a propensity to overweight/obesity (4 -8), and to a likely higher cardiovascular risk [START_REF] Bloudeau | X-linked hypophosphatemia, obesity and arterial hypertension: data from the XLH21 study[END_REF][START_REF] Nakamura | Hypertension is a characteristic complication of X-linked hypophosphatemia[END_REF][START_REF] Nehgme | Cardiovascular Abnormalities in Patients with X-Linked Hypophosphatemia[END_REF][START_REF] Alon | Hypertension in hypophosphatemic rickets-role of secondary hyperparathyroidism[END_REF][START_REF] Hernández-Frías | Risk of cardiovascular involvement in pediatric patients with X-linked hypophosphatemia[END_REF]. Indeed, patients with XLH display higher BMI and systolic blood pressure (BP) than general populations [START_REF] Bloudeau | X-linked hypophosphatemia, obesity and arterial hypertension: data from the XLH21 study[END_REF][START_REF] Nakamura | Hypertension is a characteristic complication of X-linked hypophosphatemia[END_REF][START_REF] Nehgme | Cardiovascular Abnormalities in Patients with X-Linked Hypophosphatemia[END_REF][START_REF] Alon | Hypertension in hypophosphatemic rickets-role of secondary hyperparathyroidism[END_REF][START_REF] Hernández-Frías | Risk of cardiovascular involvement in pediatric patients with X-linked hypophosphatemia[END_REF]. Conventional treatment (or standard of care, SOC) consists in replacement therapy: phosphate supplementation and active vitamin D analogs treatments [START_REF] Haffner | Clinical practice recommendations for the diagnosis and management of X-linked hypophosphataemia[END_REF].

In 2018, a novel biotherapy has been approved, i.e., burosumab, an anti-FGF23 recombinant antibody. Clinical trials have reported favorable outcomes on clinical and paraclinical features: higher height and physical ability, lower pain, higher phosphorus levels, and better radiographic score [START_REF] Haffner | Clinical practice recommendations for the diagnosis and management of X-linked hypophosphataemia[END_REF][START_REF] Carpenter | Burosumab Therapy in Children with X-Linked Hypophosphatemia[END_REF][START_REF] Imel | Burosumab versus conventional therapy in children with X-linked hypophosphataemia: a randomised, active-controlled, open-label, phase 3 trial[END_REF].

We recently showed in the prospective multicenter cross-sectional XLH21 study that XLH patients receiving burosumab displayed lower BP and higher Klotho levels than XLH patients under SOC, with all the limitations of an open-label study [START_REF] Bloudeau | X-linked hypophosphatemia, obesity and arterial hypertension: data from the XLH21 study[END_REF]. Despite their potential relevance for long-term outcomes as highlighted by the 2019 European guidelines promoting prevention of overweight and cardiovascular risk in XLH patients [START_REF] Haffner | Clinical practice recommendations for the diagnosis and management of X-linked hypophosphataemia[END_REF], the mechanisms underlying obesity and cardio-vascular risk in XLH remains to be defined. FGF23 has been first described in the early 2000's. The main action of this osteocytic hormone is to control phosphate metabolism, mainly by inhibiting its reabsorption in the kidney proximal tubule. Other effects on phosphate/calcium metabolism have been described, notably inhibition of both PTH and 1,25(OH)2D3 [START_REF] Bacchetta | Physiology of FGF23 and overview of genetic diseases associated with renal phosphate wasting[END_REF][START_REF] Goltzman | Physiology of the Calcium-Parathyroid Hormone-Vitamin D Axis[END_REF]. Even though it is probably of less relevance in daily practice, FGF23 also stimulates calcium reabsorption in the distal tubule [START_REF] Vervloet | Renal and extrarenal effects of fibroblast growth factor 23[END_REF]. Besides its effects on phosphate/calcium metabolism, FGF23 is a systemic hormone involved in multiple other pathways (in bones, heart, brain, liver, lung), with global deleterious effects (decreased neuronal network, decreased immune defense, increased blood pressure and inflammation, decreased osteoblastogenesis and mineralization, etc) [START_REF] Bacchetta | Physiology of FGF23 and overview of genetic diseases associated with renal phosphate wasting[END_REF][START_REF] Vervloet | Renal and extrarenal effects of fibroblast growth factor 23[END_REF]. The knowledge of multiple effects of FGF23 mainly comes from experimental, animal and human data on chronic kidney disease (CKD), a frequent disease with secondary FGF23 excess [START_REF] Gutiérrez | Fibroblast Growth Factor 23 and Mortality among Patients Undergoing Hemodialysis[END_REF][START_REF] Simic | Glycerol-3-phosphate is an FGF23 regulator derived from the injured kidney[END_REF][START_REF] Cannata-Andía | Chronic Kidney Disease-Mineral and Bone Disorders: Pathogenesis and Management[END_REF]. Indeed, FGF23 induces hypertrophy of cardiomyocytes and further risk of left ventricular hypertrophy (LVH) in patients [START_REF] Ali | Fibroblast Growth Factor-23 in Obese, Normotensive Adolescents Is Associated with Adverse Cardiac Structure[END_REF][START_REF] Faul | FGF23 induces left ventricular hypertrophy[END_REF](23). It also stimulates sodium reabsorption in the distal tubule [START_REF] Andrukhova | FGF 23 regulates renal sodium handling and blood pressure[END_REF], and stimulates the renin/angiotensin system indirectly through the inhibition of 1,25(OH)2D3. These three points explain an increased blood pressure induced by FGF23 [START_REF] Bacchetta | Physiology of FGF23 and overview of genetic diseases associated with renal phosphate wasting[END_REF][START_REF] Vervloet | Renal and extrarenal effects of fibroblast growth factor 23[END_REF][START_REF] Zając | Urine fibroblast growth factor 23 levels in hypertensive children and adolescents[END_REF][START_REF] Freundlich | Fibroblast growth factor 23-Klotho and hypertension: experimental and clinical mechanisms[END_REF][START_REF] Chonchol | Low Vitamin D and High Fibroblast Growth Factor 23 Serum Levels Associate with Infectious and Cardiac Deaths in the HEMO Study[END_REF].

FGF23 and inflammation are closely intertwined: inflammatory cytokines (such as IL6, IL1β, IL8, TNFα) enhance production of FGF23 [START_REF] Mendoza | Fibroblast Growth Factor 23 and Inflammation in CKD[END_REF][START_REF] Czaya | FGF23 and inflammation-a vicious coalition in CKD[END_REF], that in turn, increases inflammation by stimulating the production of inflammatory cytokines by hepatocytes [START_REF] Singh | Fibroblast growth factor 23 directly targets hepatocytes to promote inflammation in chronic kidney disease[END_REF], bronchial epithelial cells [START_REF] Krick | Fibroblast growth factor 23 and Klotho contribute to airway inflammation[END_REF] and macrophages [START_REF] Han | Counter-regulatory paracrine actions of FGF-23 and 1,25(OH) 2 D in macrophages. Ellmeier W[END_REF]. Among them, C-Reactive Protein (CRP), IL1β, TNFα and IL6 are induced by FGF23 (30 -32). Last, FGF23 inhibits in vitro osteoclastogenesis [START_REF] Allard | Biphasic Effects of Vitamin D and FGF23 on Human Osteoclast Biology[END_REF].

Osteoclastogenesis is linked to inflammation, promoted by IL1β, IL6, IL8 [START_REF] Amarasekara | Regulation of Osteoclast Differentiation by Cytokine Networks[END_REF] and inflammation has been proved to increase bone resorption (35).

These extra-skeletal effects of FGF23 in inflammation have never been studied in XLH, but affected patients display higher blood pressure and higher BMI than their healthy peers. Since both obesity and arterial hypertension have been associated in other populations to inflammation [START_REF] Hall | Obesity, kidney dysfunction, and inflammation: interactions in hypertension[END_REF], the aim of our study was to evaluate inflammation and osteoclastogenesis (as osteoclastogenesis, inflammation and bone resorption are linked) in XLH peripheral blood mononuclear cells (PBMCs) directly isolated from total blood of patients (37 -39). Our working hypothesis was that PBMCs from XLH patients would display a peculiar inflammatory phenotype as compared to PBMCs obtained from healthy controls, and that this profile may be different depending on the sub-group of treatment, i.e., SOC versus burosumab.

We also hypothesized that osteoclastogenesis may be impaired in PBMCs extracted from XLH patients, with a different response to 25OHD in culture according to treatment. This last hypothesis was based on the clinical observation that XLH patients receiving burosumab require more native vitamin D supplementation than their peers receiving SOC and have better skeletal growth, suggesting that higher 25OHD consumption is associated with better bone formation under burosumab [START_REF] Bacchetta | Xlinked hypophosphatemia and burosumab: Practical clinical points from the French experience[END_REF].

Materials and methods

Study population

We performed a prospective multicenter cross-sectional study including children/teenagers (above 2 years of age) and adults affected with XLH, hereafter designed as 'XLH patients', followed in two reference centers for rare diseases of calcium and phosphate metabolism (Lyon and Bicêtre Paris Saclay). XLH diagnosis was suspected on clinical symptoms or familial history, and all patients had genetically confirmed diagnosis. The severity of patients was determined independently of the current study during a multi-disciplinary clinical meeting which aim was to define which adult patients may benefit from burosumab in view of the extension of approval in adults in France. Of note, all patients were evaluated while receiving SOC, and 4 patients were found to have a clinical indication to burosumab; these 4 patients have been classified here as the "most severe" XLH adult patients. They had more altered quality of life (evaluated by the Short Form (36) Health Survey questionnaire), suffered more enthesopathies and had higher PTH values. Patients were excluded if they were on oral corticosteroids during the last 3 months, on immunosuppressive therapies, pregnant, or during lactation. Demographic and clinical data were collected such as age, height, blood pressure (BP, systolic SBP and diastolic DBP). Percentiles for height, weight, BMI (according to age and gender) and BP (according to age, gender, and height) were calculated thanks to the Baylor College of Medicine. Biochemical parameters were recorded in adults and children such as calcium, phosphate (expressed as SDS for age in children [START_REF] Ardeshirpour | Evaluation of bone and mineral disorders[END_REF][START_REF] Bacchetta | Assessment of mineral and bone biomarkers highlights a high frequency of hypercalciuria in asymptomatic healthy teenagers[END_REF], and absolute value in adults), creatinine (allowing the calculation of the estimated Glomerular Filtration Rate (eGFR) by All patients undergoing SOC and all patients receiving burosumab receive native vitamin D supplementation, as proposed in the 2019 European guidelines on XLH [START_REF] Haffner | Clinical practice recommendations for the diagnosis and management of X-linked hypophosphataemia[END_REF] and in the French consensus expert on burosumab in XLH [START_REF] Bacchetta | Xlinked hypophosphatemia and burosumab: Practical clinical points from the French experience[END_REF], and adjusted according to 25OHD measurement levels.

Children controls were out-clinics screened in Lyon hospital and matched on age and gender as much as possible. Exclusion criteria were: CKD or other pro-inflammatory diseases or recent infection, diseases with known abnormal FGF23 levels [START_REF] Grau | Interactions between FGF23 and Genotype in Autosomal Dominant Polycystic Kidney Disease[END_REF][START_REF] Bertholet-Thomas | Teenagers and young adults with nephropathic cystinosis display significant bone disease and cortical impairment[END_REF], oral corticosteroids during the last 3 months, and undergoing immunosuppressive therapies. Demographic, clinical and biochemical data were collected for pediatric controls and expressed as percentiles for children, as detailed above. Adult healthy controls were members of the staff of the clinical and/or lab units; they were matched on age and gender as much as possible; only age, height and weight were collected.

Peripheral Blood Mononuclear Cells obtention

Blood sample volumes ranged from 15 to 30 mL, according to French law on maximal allowed volumes per sample for clinical research depending on body weight. PBMCs were isolated by density gradient centrifugation using Lymphocyte Separating Medium (Ficoll, Eurobio ®), as previously described [START_REF] Bernardor | Peripheral Blood Mononuclear Cells (PBMCs) to Dissect the Underlying Mechanisms of Bone Disease in Chronic Kidney Disease and Rare Renal Diseases[END_REF][START_REF] Claramunt-Taberner | Bone disease in nephropathic cystinosis is related to cystinosin-induced osteoclastic dysfunction[END_REF][START_REF] Quinaux | Response to Cysteamine in Osteoclasts Obtained from Patients with Nephropathic Cystinosis: A Genotype/Phenotype Correlation[END_REF].

Reverse transcription and real-time quantitative PCR (RT-qPCR)

RNA from PBMCs was extracted using trizol reagent (Invitrogen) followed by purification with Macherey-Nagel® purification kit, according to the manufacturer's instructions. Alternatively, RNA from Osteoclasts were isolated by RNA purification Norgen® kit. After reverse transcriptase step (iScript cDNA synthesis kit Biorad) quantitative PCR was performed using Itaq® enzyme, specific exon spanning primers in duplicate. Expression of 8 genes involved in inflammation and chemotaxis (IL1β, IL6, IL8, CXCL1, CCL2 -also named MCP1-, IL1R, IL6R, CXCR3) were quantified and normalized to hGAPDH values, then expressed as relative expression using the 2^(-ΔCq) method. Those genes are related to FGF23 (IL1β, IL6) and the most commonly studied inflammatory markers. Primers are presented in Supplementary Table 1. In case of large heterogeneity of results, normalization on one reference sample was performed.

Osteoclasts differentiation and treatment

PBMCs were seeded on 96-well plates or on 6-well plates at 37°C in α-Minimum Essential Medium (α-MEM, Life technologies®) supplemented with L-Glutamine (2 mM, Gibco®) and penicillin/ streptomycin (50 µg/mL streptomycin, Gibco®), enriched with 10% FBS (Sigma-Aldrich®). They were differentiated into osteoclasts using M-CSF at 20 ng/mL (PeproTech®) and RANK-L at 40 ng/mL (PeproTech ®), as previously described [START_REF] Allard | Biphasic Effects of Vitamin D and FGF23 on Human Osteoclast Biology[END_REF][START_REF] Bernardor | Inhibition of Osteoclast Differentiation by 1. 25-D and the Calcimimetic KP2326 Reveals 1. 25-D Resistance in Advanced CKD[END_REF]. 25OHD (100 nmol/L, Enzo Life Science®) and 1,25(OH)2D3 (5 nmol/L, Enzo Life Science®), were used from day 0 in comparison to vehicle-treated cells (pure ethanol). Medium, cytokines and vitamins were changed every 2 or 3 days.

At the end of the differentiation process, cells were fixed with 4% Paraformaldehyde (PFA). Inflammation expression at the end of the osteoclast differentiation process was also evaluated by RT-qPCR, as previously described.

Statistical analyses

Statistical analyses were performed using Graphpad Prism 8 software. Mann-Whitney non parametric tests were used. Kruskal-Wallis non parametric tests were used for multiple comparisons, followed by Dunn's non parametric test. A p value below 0.05 was considered significant. Values were expressed as median (min-max).

Ethical considerations

The HYPOCLAST study (NCT04184661) was approved by an ethical comity (Comité de Protection des Personnes Sud Est I, 2019-A02914-53, session 12/12/2019). In accordance with French law classifying the study as a Jardé type 3 study, all parents and patients were informed and oral consent was obtained.

Results

Patients

In total, 11 XLH adults (all SOC) and 17 XLH children (SOC, n=6 and burosumab, n=11), and 19 controls (9 adults) were included. In the sub-group of patients receiving burosumab, the median time between the last injection and sampling was 11 [START_REF] Zhukouskaya | SAT-259 Natural History of Anthropometric Parametres of Obesity in Children Affected by X-Linked Hypophosphatemia: Longitudinal Obserbational Study[END_REF][START_REF] Bosy-Westphal | Diagnosis of obesity based on body composition-associated health risks-Time for a change in paradigm[END_REF][START_REF] Bloudeau | X-linked hypophosphatemia, obesity and arterial hypertension: data from the XLH21 study[END_REF][START_REF] Nakamura | Hypertension is a characteristic complication of X-linked hypophosphatemia[END_REF][START_REF] Nehgme | Cardiovascular Abnormalities in Patients with X-Linked Hypophosphatemia[END_REF][START_REF] Alon | Hypertension in hypophosphatemic rickets-role of secondary hyperparathyroidism[END_REF][START_REF] Hernández-Frías | Risk of cardiovascular involvement in pediatric patients with X-linked hypophosphatemia[END_REF][START_REF] Haffner | Clinical practice recommendations for the diagnosis and management of X-linked hypophosphataemia[END_REF][START_REF] Carpenter | Burosumab Therapy in Children with X-Linked Hypophosphatemia[END_REF][START_REF] Imel | Burosumab versus conventional therapy in children with X-linked hypophosphataemia: a randomised, active-controlled, open-label, phase 3 trial[END_REF] days. Tables 1 and2 summarize clinical and biochemical data in adults and children, respectively. As expected, XLH patients are shorter than controls, and the BMI of XLH children receiving SOC is higher than controls. XLH children display higher SBP than controls. The four most severe adults suffered from multiple enthesopathies (heel, hips, vertebral column) whilst only one patient from the less severe subgroup displayed enthesopathy of the heel. Biochemical parameters of phosphate/calcium metabolism are altered in XLH. As expected, XLH patients have a hypophosphatemia with normal-high calcemia and normal-high PTH. Patients under burosumab have higher phosphatemia and better ALP control than SOC. 1,25(OH)2D3 is high under burosumab. No differences are observed between patients and controls for renin/aldosterone levels (n=8 controls, n=16 patients), nor between SOC and burosumab subgroups. Notably, children receiving SOC display significantly lower renal sodium excretion than children under burosumab.

PBMCs from XLH patients display a peculiar inflammatory profile

We isolated PBMC from total blood samples for patients and controls, adults and children. We characterized their inflammatory profile by RT-qPCR on 8 inflammatory gene expression. We first compared gene transcript levels between adult and children. As illustrated in Figure 1, no differences were found between children and adults, except for hCCL2 in controls and hIL1R in patients, thus allowing us to pool data for further analyses. When comparing the expression of inflammatory genes between patients and controls, we find a statistical difference for most of them, including hIL6, hIL1β, hCCL2, hIL8, hCXCL1, hCXCR3 and hIL1R. There is no difference for hIL6R expression, but the pattern of expression seems different between adults and children. These results are presented in Figure 2 When excluding the clinically most severe adult patients, the statistical difference remained between XLH adults patients and healthy controls for hIL1β, hCCL2, hIL1R, and hCXCR3, thus reinforcing the hypothesis of a true inflammatory state in XLH. Unfortunately we were not able to measure circulating levels of inflammatory cytokines, and future studies in the field may evaluate this peculiar point.

The inflammatory profile observed in PBMCs from XLH patients is not modified by burosumab

We compared the inflammatory profile according to treatment. Only children were treated by burosumab, but as explained above, we kept pooling adults and children receiving SOC, and controls. As illustrated in Figure 3, the inflammatory profile observed in PBMCs from XLH patients receiving SOC or burosumab is similar. Median dose of burosumab treatment (n = 11) was 50 mg / 15 days (30 -90). No statistical correlation was found between burosumab dose and genic inflammatory markers, nor between inflammatory markers and delay since last injection of burosumab.

Osteoclastogenesis is impaired in XLH patients

Our blood samples were of low volume on a pediatric population, especially for the youngests.

In that setting, we obtained enough cells to differentiate PBMCs into osteoclasts (in presence of native vitamin D, active vitamin D or ethanol control) and assess osteoclastogenesis in 2 XLH children under SOC, 5 XLH children under burosumab, and 5 pediatric healthy controls.

Figure 4A illustrates the number of osteoclasts per well obtained for each of three groups under the three conditions: osteoclastogenesis is significantly impaired in PBMCs from XLH patients, especially in cells obtained from patients receiving SOC.

Burosumab restores osteoclastic response to native vitamin D

The differentiation process was made in presence of native or active vitamin D and compared to the control condition. As illustrated in Figure 4B and as expected from previous reports from our group, 1,25(OH)2D3 almost completely inhibits osteoclast formation, by more than 90%, in all conditions. In contrast, the effects of 25OHD are milder, impairing osteoclastogenesis by 50% in cells from healthy controls and patients receiving burosumab, while only 20% decrease was observed in cells from patients receiving SOC. Inhibition by 25OHD is statistically different between the SOC and control sub-groups, but not between the burosumab and control sub-groups. Thus, burosumab restores response of XLH osteoclast progenitors to 25OHD action. Photographs of representative individuals with the different culture conditions are shown in Figure 4C.

Attenuated inflammatory profile in osteoclasts derived from burosumab treated patients

When possible, inflammatory profiles were monitored in mature osteoclasts under control or 1,25(OH)2D3 condition. Due to low cell count, this was possible for 3 children under SOC, 6 children under burosumab and 5 pediatric controls. Osteoclasts obtained from XLH children tend to display higher transcript levels for hIL6, hCCL2, hCXCR3, hIL6R and hIL1R than controls, however without reaching statistical significance (Figure 5A). When comparing subgroups, differences between cells obtained from patients under SOC or burosumab are significant in osteoclasts. Indeed, hIL1β is more expressed in osteoclasts obtained from patients under SOC than from patients under burosumab, and a similar trend is observed for hIL8, hCXCL1, hCCL2, hIL1R (Figure 5B).

Active vitamin D decreases the osteoclastic inflammatory profile in cells obtained from healthy controls and XLH patients

Discussion

The main result of the present study is the finding for the first time that XLH patients display an inflammatory profile as compared to healthy controls, shown here in PBMCs and osteoclasts. Indeed, both pro-inflammatory chemokines (hCCL2, hCXCL1, hIL8), pro-inflammatory receptors (hCXCR3, hIL1R) and inflammatory cytokines (hIL6, hIL1β) are more expressed in PBMCs derived from XLH patients than in cells extracted from controls. As osteoclastogenesis is linked to inflammation [START_REF] Amarasekara | Regulation of Osteoclast Differentiation by Cytokine Networks[END_REF] and inflammation induces bone resorption (35) we also screened osteoclastogenesis. Osteoclastogenesis was significantly impaired in cells obtained from XLH patients as compared to controls, and osteoclasts derived from XLH patients also expressed more inflammatory markers. The addition of active vitamin D to culture during the osteoclastic differentiation decreased the expression of inflammatory markers, as expected [START_REF] Yin | Vitamin D and inflammatory diseases[END_REF].

Interestingly, no differences were observed in PBMCs between the two sub-groups of patients, namely SOC and burosumab, whilst the inflammatory profile at the end of the osteoclastic differentiation process was decreased in cells derived from patients receiving burosumab. Last, cells extracted from patients receiving burosumab were more prone to respond to native vitamin D during osteoclastogenesis. This cellular "imprinting" by patients related factors during osteoclastogenesis may be surprising, but has already been described in other pathogenic models, and notably pediatric chronic kidney disease [START_REF] Bernardor | Inhibition of Osteoclast Differentiation by 1. 25-D and the Calcimimetic KP2326 Reveals 1. 25-D Resistance in Advanced CKD[END_REF].

In this setting, blood sample numbers are low and of reduced volume especially for pediatric's one; proper to orphan diseases studies. Therefore, we decided to pool the results obtained for children and adults, after showing that the expression of the different genes of interest was similar between these two groups, with the exception of hCCL2 (controls) and hIL1R (patients).

However, when comparing only children or only adults, we found more significant results in adults and more trends in children. This could be explained by the fact that this study was performed in France in early 2021, when barrier actions and telework were the rule in adults whilst children were still going to school. As such children were therefore more prone to common viral infections of the pediatric age, likely explaining a more variable expression of inflammatory markers in children (observed both in controls and in XLH patients). In contrast, in adults, levels of inflammatory transcripts seem related to the clinical severity of the disease, since the four most severe patients displayed the highest levels of transcripts. These four patients were older, and were all eligible to a switch from SOC to burosumab therapy after a multi-disciplinary discussion of their medical files (that was independent and blind of these experimental results). Thus, inflammation in XLH is a chronic phenomenon that appears as early as the pediatric age, likely associated with clinical severity and impaired quality of life [START_REF] Freundlich | Fibroblast growth factor 23-Klotho and hypertension: experimental and clinical mechanisms[END_REF]. It can appear intriguing that only adult women were included, but in the Lyon adult unit, currently, only women are followed for XLH. Our transition program from pediatric to adult care is quite recent in Lyon, and we hypothesize that at the moment women are more concerned about the disease than men. Indeed, we have fathers of children followed in the pediatric unit who are affected with XLH, but who do not want to be followed.

One of the complications of XLH during adulthood that remains the most intriguing is the onset of enthesopathies, as described in the murine Hyp model [START_REF] Faraji-Bellée | Development of Enthesopathies and Joint Structural Damage in a Murine Model of X-Linked Hypophosphatemia[END_REF] and in patients, affecting up to 67% of adults [START_REF] Che | Impaired quality of life in adults with X-linked hypophosphatemia and skeletal symptoms[END_REF][START_REF] Herrou | Prevalence of Enthesopathies in Adults With X-linked Hypophosphatemia: Analysis of Risk Factors[END_REF]. The underlying pathophysiology of enthesopathy in XLH is not well understood, and this disabling symptom is neither prevented nor improved by SOC [START_REF] Beck-Nielsen | FGF23 and its role in X-linked hypophosphatemia-related morbidity[END_REF][START_REF] Connor | Conventional Therapy in Adults With X-Linked Hypophosphatemia: Effects on Enthesopathy and Dental Disease[END_REF]. Risk factors appear to be an older age and a severe dental disease [START_REF] Herrou | Prevalence of Enthesopathies in Adults With X-linked Hypophosphatemia: Analysis of Risk Factors[END_REF]. Other authors have reported associations between enthesopathies and PTH level, age and BMI [START_REF] Connor | Conventional Therapy in Adults With X-Linked Hypophosphatemia: Effects on Enthesopathy and Dental Disease[END_REF]. However, it is questionable whether chronic inflammation may also be a risk factor of enthesopathies, since enthesopathies are also frequent in chronic inflammatory diseases such as psoriasis arthritis [START_REF] Araujo | Enthesitis in psoriatic arthritis (Part 1): pathophysiology[END_REF]. To date, the results of the industry-sponsored trial in 134 XLH adults randomized 1/1 to burosumab or placebo showed that adults with XLH experience substantial pain, stiffness, fatigue and impairment in physical and ambulatory function. Patients receiving burosumab displayed a consistent reduction in the burden of disease associated with XLH, with statistically significant improvements from baseline in patient related outcomes and ambulatory function seen as early as week 24 and at week 96, achieving meaningful change from baseline in pain, stiffness and fatigue scores [START_REF] Briot | Burosumab treatment in adults with X-linked hypophosphataemia: 96-week patient-reported outcomes and ambulatory function from a randomised phase 3 trial and open-label extension[END_REF]. Still, the direct effects of burosumab, either for its ability to prevent the onset of enthesopathies in teenagers and young adults or for its ability to improve existing enthesopathies, remain to be proved.

Burosumab does not seem to modify the inflammatory profile in PBMCs, both in children and in adults. As such, we could imagine additional therapeutic strategies against inflammation to improve quality of life and pains in the most severe XLH patients. Our initial hypothesis was that since FGF23 has been shown to induce inflammation (29 -32), patients receiving burosumab may display an attenuated inflammatory profile. The absence of difference observed in PBMCs may be due in part to a lack of power, but an anti-inflammatory effect of vitamin D per se can also be hypothesized [START_REF] Yin | Vitamin D and inflammatory diseases[END_REF]. The fact that our initial hypothesis is supported by osteoclasts studies but not in PBMCs may also indicate an effect that would be seen locally in the target tissues and organs, and not in the systemic circulation. Also, the samples were collected just before the next dose of burosumab as part of the routine biological follow-up of patients [START_REF] Bacchetta | Xlinked hypophosphatemia and burosumab: Practical clinical points from the French experience[END_REF], and this may have attenuated the biological differences. Last, those results could also be due to another pathophysiological mechanism increasing inflammation in XLH, yet to be determined.

The rationale to look for difference between the SOC and burosumab sub-groups was the previous results we obtained in a XLH21 study: indeed, despite being more overweight or obese than their peers receiving SOC, teenagers with XLH receiving burosumab displayed lower blood pressure than children under SOC (yet greater than matched healthy peers) [START_REF] Bloudeau | X-linked hypophosphatemia, obesity and arterial hypertension: data from the XLH21 study[END_REF]. Here, we confirm that XLH children and teenagers display higher systolic blood pressure than healthy controls. As detailed in the introduction, many different mechanisms may explain this increased cardio-vascular risk in XLH (21 -27). We hypothesized that the renin/angiotensin system may be different between controls and XLH on the one hand, and between SOC and burosumab on the other hand. However, we were not able to find any difference in circulating renin or aldosterone levels between controls and XLH patients, and between SOC and burosumab subgroups. This may be explained by a lack of power but also because we assessed renin and aldosterone using the method we use in daily routine for the follow-up of salt-losing tubulopathies, namely without respecting at least one hour of bed-rest. In this setting of subtle pathophysiological mechanisms, this may have not been enough accurate, but our study was a "Jardé type 3" study by French law, allowing us to perform additional samples only during classical biological follow-up. In contrast, we were able for the first time to demonstrate the physiological relevance of tubular sodium handling by FGF23 ( 24): indeed, sodium excretion fraction (FENa) was significantly lower in the SOC sub-group as compared to patients receiving burosumab. This could lead to higher sodium reabsorption, and further increased blood pressure.

Last, using our non-invasive technique allowing us to study human osteoclasts in vitro by obtaining circulating PBMCs from patients and controls [START_REF] Allard | Biphasic Effects of Vitamin D and FGF23 on Human Osteoclast Biology[END_REF][START_REF] Claramunt-Taberner | Bone disease in nephropathic cystinosis is related to cystinosin-induced osteoclastic dysfunction[END_REF][START_REF] Quinaux | Response to Cysteamine in Osteoclasts Obtained from Patients with Nephropathic Cystinosis: A Genotype/Phenotype Correlation[END_REF][START_REF] Bernardor | Inhibition of Osteoclast Differentiation by 1. 25-D and the Calcimimetic KP2326 Reveals 1. 25-D Resistance in Advanced CKD[END_REF], we confirm our previous study showing an inhibitory effect of FGF23 on osteoclastogenesis [START_REF] Allard | Biphasic Effects of Vitamin D and FGF23 on Human Osteoclast Biology[END_REF]. Indeed, in XLH patients, osteoclastic formation is impaired, especially in cells derived from patients receiving SOC, who display high FGF23 levels. We confirm that 1,25(OH)2D3 also inhibits osteoclastogenesis in XLH, as shown previously in controls [START_REF] Allard | Biphasic Effects of Vitamin D and FGF23 on Human Osteoclast Biology[END_REF][START_REF] Bernardor | Inhibition of Osteoclast Differentiation by 1. 25-D and the Calcimimetic KP2326 Reveals 1. 25-D Resistance in Advanced CKD[END_REF]; as such, we believe that this experiment validates the current in vitro model. Interestingly, we found that 25OHD inhibits osteoclastogenesis in cells derived from pediatric controls by about 50% whilst it has no effect on osteoclast differentiation in cells derived from XLH under SOC subgroup.

Interestingly, the inhibition of 25OHD on osteoclastogenesis is restored in cells derived from patients under burosumab, with a similar inhibitory effect than the one observed in cells from healthy controls. In clinical practice, patients receiving burosumab need more 25OHD supplementation, based on the doses required to maintain target circulating levels [START_REF] Claramunt-Taberner | Bone disease in nephropathic cystinosis is related to cystinosin-induced osteoclastic dysfunction[END_REF]. Two hypotheses may be discussed to explain this increased 25OHD requirements, namely the increased 1,25(OH)2D3 levels because of the inhibition of FGF23 (thus requiring more substrate) and a local increased use of 25OHD, that may for example help patients receiving burosumab to restore normal osteoclastogenesis. As such, this improvement in vitamin D metabolism as a secondary effect of the anti-FGF23 therapy could partly explain the beneficial effects of burosumab on growth and skeletal deformities [START_REF] Carpenter | Burosumab Therapy in Children with X-Linked Hypophosphatemia[END_REF], especially since the adjunction of 1,25(OH)2D3 in vitro attenuates the global inflammation profile in all sub-groups.

In conclusion, we describe for the first time a peculiar inflammatory profile in XLH patients, independent of the underlying management in PBMCs but not in differentiated osteoclasts.

Since XLH patients have a propensity to develop arterial hypertension and obesity, and since inflammation can worsen these clinical outcomes, we hypothesize that inflammation may play a crucial role in these extra-skeletal complications of XLH. Results are presented as median (min -max). Mann-Whitney tests were performed for significance.

Figure legends

  Pierce et al. formula (according to sex and age) in children and adults under 25 years old, and the CKD-EPI formula in adults (43, 44)), PTH (Roche electroluminescence immunoassay in Lyon, normal local values 15-65 ng/L; Siemens chemiluminescent immunometric assay in Paris, normal local values 18.5-88.0 ng/L, expressed as x times the upper normal limit, xx-ULN), 25OHD and 1,25(OH)2D3, natriuresis. FGF23 was only measured in patients under SOC because of analytical interferences under burosumab (45). C-Terminal fraction was measured by ELISA tests (reference ranges: 25.0 -73.0 RU/mL). Total Alkaline Phosphatase (ALP), urinary electrolytes (calcium, phosphate allowing calculation of the tubular maximum phosphate reabsorption reported to glomerular filtration rate, TmP/GFR (46), renin and aldosterone (Chemiluminescence on YSIS from IDS) were also measured in children.

  Osteoclast differentiation was evaluated by cell staining with tartrate-resistant acid phosphatase (TRAP) kit (ref 387A, Sigma-Aldrich®). Following image acquisition by scanning (with Epson Perfection V850 Pro) TRAP positive multinucleated cells (8 wells per condition) were counted with the ImageJ software.

Active 1 ,

 1 25(OH)2D3 treatment impact on cytokine and chemokine expression was analyzed on mature osteoclasts derived from PBMCs cultivated either in ethanol, either with 1,25(OH)2D3 at 5 pmol/L. Samples from 2 children under SOC, 3 children under burosumab and 2 pediatric controls were assessed. The expression of all but one (hIL1β) inflammatory marker are decreased with 1,25(OH)2D3. This inhibitory effect is present in cells obtained from XLH patients (whatever their subgroup) and healthy controls, and is significant for hIL6, hCXCL1 and hCCL2. These data confirm the anti-inflammatory effect of 1,25(OH)2D3 in vitro. These results are shown in Figure 5C.

Figure 1 :Figure 2 :

 12 Figure 1: Adults and children display similar transcript levels for the eight pro-inflammatory

Figure 3 :

 3 Figure 3: PBMCs from SOC and Burosumab treated XLH patients show the same inflammatory

Figure 4 :

 4 Figure 4: Active vitamin D fully impairs osteoclastogenesis in XLH patients

Figure 5 :

 5 Figure 5: The high increased expression of inflammatory markers in XLH mature osteoclasts is

  p<0.05*, p<0.005** n: number of person per group. XLH: X-Linked Hypophosphatemia. kg: kilograms. cm: centimeters. BMI: Body Mass Index. kg/cm 2 : kilogram per square centimeter. BP: Blood Pressure. mmHg: millimeter of Mercury. mmol/L: concentration in millimole per liter. PTH: parathormone. pg/mL: picogram per milliliter. 25OHD: 25-hydroxy-vitamin D, native vitamin D. nmol/L: nanomole per liter. 1,25(OH)2D3: 1,25-dihydroxy-vitamin D, active vitamin D. pmol/L: picomole per liter. FGF23: Fibroblast Growth Factor 23. RU/mL: relative units per milliliter. eGFR: estimated glomerular filtration rate. mL/min/1.73m 2 : milliliter per minute per body surface.

  Results are presented as median (min -max). Mann-Whitney tests were performed for significance. p<0.05*, p<0.005** n: number of person per group. XLH: X-Linked Hypophosphatemia. SOC: Standard Of Care. BMI: Body Mass Index. BP: Blood Pressure. mmol/L: concentration in millimole per liter. SDS: Standard Deviation Score. PTH: parathormone. xx-ULN: x time Uper Limit Normal. 25OHD: 25-hydroxyvitamin D, native vitamin D. nmol/L: nanomole per liter. 1,25(OH)2D3: 1,25-dihydroxy-vitamin D, active vitamin D. pmol/L: picomole per liter. ALP: Alkaline Phosphatases. IU/L: international unit per liter. FGF23: Fibroblast Growth Factor 23. RU/mL: relative units per milliliter. eGFR: estimated glomerular filtration rate. mL/min/1.73m 2 : milliliter per minute per body surface. TmP/GFR: maximal phosphate tubular reabsorption rate reported to glomerular filtration rate. FENa: sodium extraction fraction by kidneys

Figure 1 Figure 2 Figure 3 Figure 4

 1234 Figure 1

Figure 5

 5 Figure 5

Table 1 . Clinical and biochemical characteristics of the adult cohort

 1

		Controls	XLH patients	XLH most severe	XLH less severe
		n = 9	n = 11	patients **	patients
				n = 4	n = 7
	Age	30	24	42	20
	(years)	(20 -60)	(19 -55)	(37 -53)	(19 -55)
	Gender	100	100
	(female, %)
	Weight	63	54	63.5	54
	(kg)	(53 -72)	(47 -75)	(54 -75)	(47 -72)
	Height *	168	153	149.5	155
	(cm)	(157 -173)	(144 -165)	(144 -157)	(148 -165)
	BMI	23.0	22.5	28.3	21.2
	(kg/cm 2 )	(17.7 -25.6)	(19.1 -32.9)	(22.5 -30.4)	(19.1 -32.9)
	Systolic BP nb	NA	120	127	105
	(mmHg)		(89 -138)	(125 -138)	(89 -124)
	Diastolic BP	NA	72	82	69
	(mmHg)		(50 -89)	(80 -89)	(50 -82)
	Calcium	NA	2.39	2.46	2.37
	(mmol/L)		(2.18 -2.65)	(2.18 -2.56)	(2.29 -2.65)
	Phosphate	NA	0.64	0.49	0.70
	(mmol/L)		(0.39 -0.83)	(0.39 -0.65)	(0.54 -0.83)
	PTH	NA	74	89	67
	(pg/mL)		(39 -155)	(59 -144)	(39 -155)
	25OHD	NA	85	88	83
	(nmol/L)		(32 -115)	(83 -115)	(32 -107)

1,25(OH)2D3

		NA	67	67	69
	(pmol/L)		(48 -121)	(57 -77)	(48 -121)
	FGF23	NA	129	194	90
	(RU/mL)		(58 -354)	(158 -230)	(58 -354)
	eGFR	NA	120	120	130
	(mL/min/1.73 m²)		(73 -135)	(117 -131)	(73 -135)

Table 2 . Clinical and biochemical characteristics of the children cohort

 2

		Controls	XLH patients	XLH SOC	XLH burosumab
		n = 10	n = 17	n = 6	n = 11
	Age	12	11	10	13
	(years)	(4 -17)	(2 -16)	(2 -14)	(7 -16)
	Gender (Female/Male)	3 / 7	7 / 10	2 / 4	5 / 6
	Duration of treatment	NA	3.0	7.5	2.7
	(years)		(0.3 -11.8)	(0.3 -11.8)	(0.5 -3.7)
	Body Weight	65.1	32.4	27.0 *	43.2
	percentile	(9.7 -95.8)	(7.9 -83.1)	(7.9 -55.9)	(11.9 -83.1)
	Height	57.2	9.7 *	2.1 *	10.0 *
	percentile	(0.0 -95.0)	(0.2 -42.2)	(0.7 -33.7)	(0.2 -42.2)
	BMI	55.4	73.9 *	67.1	74.3
	percentile	(8.0 -93.1)	(20.7 -95.6)	(24.7 -94.2)	(20.7 -95.6)
	Systolic BP	50	83 *	90	78
	percentile	(16 -90)	(15 -98)	(18 -98)	(15 -98)
	Diastolic BP	33	67	64	68
	percentile	(15 -80)	(8 -97)	(37 -97)	(8 -83)
	Calcium	2.45	2.41	2.33	2.47
	(mmol/L)	(2.33 -2.68)	(2.16 -2.64)	(2.16 -2.48)	(2.3 -2.64)
	Phosphate
	(SDS)

The Hospices Civils de Lyon received a research grant from Kyowa Kirin for the HYPOCLAST study.

The

INSERM 1033 lab is supported by grants from -INSERM, Université Claude Bernard Lyon 1 (Univ Lyon, Olivier Peyruchaud, Irma Machuca-Gayet) -The cystinosis Research Foundation (Irma Machuca-Gayet,Justine Bacchetta) -The ANR grant BoneTax (Grant No ANR-20-CE14-00036-01)

The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results

Disclosures of interest

MNM, CA, SL, EV, ABT, OP, SF, IMG have nothing to declare. JB received travel fees and consultant/speaker fees from Kyowa Kirin, and is an investigator for clinical trials for Kyowa Kirin. AL is an investigator for clinical trials for Kyowa Kirin and her research team receives research grants from support Kyowa Kirin; she receives honoraria from Alexion and Kyowa Kirin.

Data availability

Some or all datasets generated during and/or analyzed during the current study are not publicly available but are available from the corresponding author on reasonable request.

nb: 2 adult patients were under anti-hypertensive therapy, one from the most severe sub-group 781 and one from the less severe sub-group.