Ines Ben Hamida
email: ines.ben.hamida@univ-poitiers.fr

Med Amine Laribi

Abdelfattah Mlika

Lotfi Romdhane

Saïd Zeghloul

Giuseppe Carbone

Multi-Objective Optimal Design of a Cable Driven Parallel Robot for Rehabilitation Tasks

Keywords: Cables driven parallel robots, dimensional synthesis, topological synthesis, performance criteria, optimization approaches Nomenclature CDPR Cable Driven Parallel

This paper addresses the topological and dimensional synthesis of cable-driven parallel robots. A combined methodology for type and size optimization is proposed and applied to a cable driven parallel robot, which is intended for upper-limb rehabilitation exercises. The proposed approach deals with a set of deterministic and non-deterministic parameters within a multi-objective genetic algorithm. The proposed study aims to select a suitable architecture having optimal dimensions by considering several optimality criteria such as minimizing the cable tensions and achieving the smallest footprint. An illustrative application of the proposed synthesis approach is developed for LAWEX, a cable driven parallel robot for upper limb rehabilitation. Four different topology solutions have been considered for LAWEX robot. It is also proposed to use an additional safety criterion to select a solution on the obtained Pareto front.

Introduction

A CDPR (cable driven parallel robot) is a parallel robot where the moving platform is suspended by flexible cables instead of classic rigid kinematic chains. This characteristic gives CDPRs valuable performances in terms of large workspace, high payload, high speed and acceleration as compared with classical parallel robots. CDPRs allow design solutions having a larger workspace when compared to parallel robots with rigid links having a comparable size. Accordingly, several researchers have been investigating this research topic. The first CDPRs have been intended for industrial applications. RoBoCrane [START_REF] James Albus | The NIST RoBoCrane[END_REF] is considered as the first cable driven parallel robot implemented in 1989 in the National Institute of Standards and Technology (NIST) of America. This 6-DOF robot has been used for several applications e.g. cutting, shaping, finishing, lifting and positioning, [START_REF] James Albus | The NIST RoBoCrane[END_REF]. Lately, several CDPRs have been proposed and developed in Japan, Italy, France and Germany. For example, Falcon-7, [START_REF] Tang | An Overview of the Development for Cable-Driven Parallel Manipulator[END_REF] is a 6-DOF Japanese Robot with ultra-high speed and small actuators. Driven by 7 cables, this fully constrained robot was used for applications that require high precision and stiffness. Cable robots are also used for construction tasks, given their large workspace and high stiffness as compared with classic parallel mechanisms. For example, Pinto et al. [START_REF] Pinto | A cable-driven robot for architectural constructions : a visual-guided approach for motion control and path-planning[END_REF] proposed SPIDERobot, a 4-DOF robot, for architectures projects. Paper [START_REF] Pinto | A cable-driven robot for architectural constructions : a visual-guided approach for motion control and path-planning[END_REF] presented an optimization of the robot's trajectory to avoid collisions using a new Vision-Guided Path Planning System. Likewise, cable robots have demonstrated their efficiency in medicals applications, such as haptic devices and rehabilitation robots. Haptic devices require an independent control system that allows the user not only to feed information but also to receive a feedback from the machine as a felt sensation. Many haptic devices have been proposed in the literature. For example, Billette and Gosselin [START_REF] Billette | Producing Rigid Contacts in Cable-Driven Haptic Interfaces Using Impact Generating Reels[END_REF] proposed a haptic interface using a 3-DOF cable driven parallel robot for a sword-fighting simulator. RIME is a telesurgical device with a cable driven 5-dof haptic master developed at university of Padua [START_REF] Boschetti | A haptic system for robotic assisted spine surgery[END_REF]. Experiments reported by Boschetti et al [START_REF] Boschetti | A haptic system for robotic assisted spine surgery[END_REF] evoke the advantage of the wire driven haptic master to drive naturally and simply the surgical tool. The simplicity of assembly and reconfiguration of CDPRs, as well as their high sensitivity, light weight and large workspace make them suitable for rehabilitation tasks. Sophia-3 is a 2-DOF cable driven parallel robot used for the upper limb rehabilitation [START_REF] Zanotto | Sophia-3: A semiadaptive cable-driven rehabilitation device with a working plane[END_REF]. This simple device in terms of kinematics and cost can, assure shoulder rehabilitation exercises instead of complex and 3-D exoskeletons.

Passive cable devices such as CATRASYS and Milli-CATRASYS have been proposed since early '90s for the determination of the pose and orientation of mechanisms' end-effector, [START_REF] Hernández-Martínez | Characterization of a Cable-Based Parallel Mechanism for Measurement Purposes[END_REF]. A recent work of Varela et al. [START_REF] Varela | A kinematic characterization of human walking by using CaTraSys[END_REF] proposed an experimental approach using CATRASYS to characterize human walking. CUBE, proposed by Cafolla et al. [START_REF] Cafolla | CUBE , a Cable-driven Device for Limb Rehabilitation[END_REF], consists of 5 DOF parallel robot driven through 6 cables dedicated to clinical exercises for both upper and lower limbs. NeReBot is an upper limb neurorehabilitation device proposed by Fanin et al. [START_REF] Fanin | NeRebot: A Wire-based Robot for Neurorehabilitation[END_REF]. It uses 3 cables to suspend the patient upper limb. Clinical tests by Rosati et al. [START_REF] Rosati | On the Use of Cable-Driven Robots in Early Inpatient Stroke Rehabilitation[END_REF] show that patients treated with the additional protocol of NeReBot are recovering faster than others treated with a classical protocol.

Dimensional synthesis is one of the challenging tasks in the design process of a mechanical system. It consists of searching for the "best dimensions" of the mechanism to fulfill the required performances. Kelaiaia et al. [START_REF] Kelaiaia | Multiobjective optimization of a linear Delta parallel robot[END_REF] proposed two different approaches for dimensional synthesis: the Atlas approach and the cost function approach. The most used technique is the cost function [START_REF] Kelaiaia | Multiobjective optimization of a linear Delta parallel robot[END_REF]- [START_REF] Bilel | Multi-objective robust design optimization of a mechatronic system with uncertain parameters, using a polynomial chaos expansion method[END_REF], where an optimization problem is formulated in order to minimize an objective function subject to constraint functions. Design approaches of CDPRs depend on their applications and the desired specifications, such as workspace, speed, compliance. A recent work of Laribi et al. [START_REF] Amine | On the Optimal Design of Cable Driven Parallel Robot with a Prescribed Workspace for Upper Limb Rehabilitation Tasks[END_REF] proposed a multi-criteria optimization of LAWEX, a CDPR dedicated to upper limb rehabilitation. The problem formulation consists in the minimization of cables tensions distribution, while following a prescribed trajectory. The solution was given using a Genetic Algorithm method implemented under MATLAB software. Lamine et al. [START_REF] Lamine | Design Study of a Cable-based Gait Training Machine[END_REF] developed a discrete algorithm for the design optimization of a Cable Driven Leg Trainer; for gait rehabilitation. The objective of this optimization is to minimize cables tensions considering the height's difference among patients. Cables tensions of all heights have been calculated to compute the optimum power of the robot's actuators. A different optimization model was proposed by Hernandez et al. [START_REF] Hernandez | Design Optimization of a Cable-driven Parallel Robot in Upper Arm Training-Rehabilitation Processes[END_REF] for the design of a CDPR used for patients with shoulder problems. A prescribed workspace was defined using the upper limb possible movements. A kinematic and wrench analyses have been carried out to determine the Jacobian matrix. The considered objective function was for the optimization of cables tensions. The problem was solved using the Estimation of Distribution Algorithm. In most the cases, the cables are considered as massless, however, in some mechanisms, long cables' masses cannot be neglected. Liu et al. [START_REF] Liu | Tension Optimization for a Cable-Driven Parallel Robot with Non-Negligible Cable Mass[END_REF] proposed a tension optimization iterative algorithm to avoid sags of long cables. This work proposed an optimization approach of a cable driven parallel robot intended for rehabilitation of human upper limb. The paper is structured as follows: Section 2 presents the difference between our CDPR design process and the commonly used robotic mechanism design processes. The following section deals with the search of the topological structures for the CDPRs. Different characteristics and performances of cable robots are analyzed in section 4. Section 5 introduces the proposed case of study on the synthesis of LAWEX, a CDPR intended for rehabilitation tasks. A concurrent design approach combining type and dimensional synthesis is proposed and carried out. The last section presents some conclusions.

The proposed design approach

The mechanical design process has been the object of several works in the literature such as, just for example, [START_REF] Parada Puig | A methodology for the design of robotic hands with multiple fingers[END_REF]- [START_REF] Nouaille | Design process for robotic medical tool guidance manipulators[END_REF]. The procedure described in Fig. 1 represents the proposed general conceptual design as based on the fulfillment of specific requirements or needs. Determine mechanism dimensions based on the functional requirements

• CAD model • Prototype construction • Experimental tests
-Phase 1: Topological synthesis, which requires decisions on the main design choices concerning the number of DOFs, the actuation nature, the degree of redundancy. -Phase 2: Dimensional synthesis related to the mechanism dimensions, where an optimization problem could be formulated to identify the best design parameters for a given required task of the mechanism.

As shown in Fig. 1, the classical design process is a sequential one, where the topological synthesis comes first followed by the dimensional synthesis. In the present work, a concurrent design approach is proposed, where the topology and dimensions of the mechanism are optimized simultaneously.

The objective of this novel design approach is to select the suitable manipulator architecture with optimized dimensions for a given task. The proposed methodology combines the type and the dimensional optimization in the same operation. The problem formulation depends on the desired application, which will define the objectives, the constraints, and the decision parameters.

Optimal topology search strategy

Most of the literature works on synthesis of cable driven parallel robots are interested only on dimensional optimization. However, the number of cables, the positions of the cables exit points and the positions of the cable anchor points on the moving platform, define the robot design and affects the number of DOFs as well as the device performances.

Generally, according to the number of DOFs and the number of cables , two main cases of CDPRs can be defined, under constrained and fully constrained CDPRs. A necessary condition but not sufficient to define an under-constrained CDPR is ≤ . Typically, the end-effector of an underconstrained CDPR is still movable when actuators are locked so that external forces are necessary for static equilibrium. A CDPR is defined as fully constrained if all its DOFs can be controlled, it requires at least + 1 cables. Redundancy of CDPRs was addressed by Merlet [START_REF] Merlet | On the Redundancy of Cable-Driven Parallel Robots[END_REF]. Despite the advantage of increasing drastically the robot's workspace, redundancy affects the kinematics and cables tensions distribution. Maintaining a positive cable tension in redundant structures, is one of the most challenging addressed issues in the literature [START_REF] Khosravi | Robust PID control of fully-constrained cable driven parallel robots[END_REF].

An additional issue of cables that can affect the robot motion is the distribution of attachment points on the end-effector. Fig. 3 shows two different end-effectors with different attachment points. The first configuration uses an end-effector with two anchor points. In this case, the controllable motions of the end effector are limited to just 3 translations. In the second case, the end-effector contains one anchor point for each cable. This feature gives the robot an additional mobility in rotation, 3 translations and one rotation are possible. The number of anchor points is related to the required movements of the end effector and the number of cables. A full measure of the moving object pose, i.e., position and orientation, requires 3 nonaligned points, however reducing the number of attachment points reduces the risk of cable wrapping issue. For example, for translational devices, only one attachment point is sufficient to define the pose of the end effector.

Optimal dimensional synthesis strategies

Dimensional synthesis deals with the determination of the mechanism dimensions according to the required performances by the designer.

A general optimization problem is formulated in order to minimize or to maximize an objective function subject to constraint functions as stated below:

Minimize/Maximize ( ) Subject to . / ( ) ≤ 0 1 23 4 , . . , 3 6 7 3 89: ; 3 ; 3 8<=

(1) where ( ) is the objective function defining the criteria to optimize. . / ( ) are constraint functions. 1 23 4 , . . , 3 6 7 is the design vector defined by the set of design variables and (3 89: , 3 8<= ) the search domain for each design variable 3 . Depending on the application requirements, the performance criteria of an optimization problem are determined, some of them will be fixed as objectives to optimize and others as constraints. In the following, some of the mainly used performance criteria for CDPRs are introduced.

Workspace

Workspace analysis remains one of the active research items for parallel robots and especially for CDPRs. A general definition of the workspace is given by the region of space reachable by the moving platform. CDPRs have potentially a large workspace compared to the classic parallel robots. However, there is an additional constraint for CDPRs since the robot's cables can only pull on the end-effector, which requires the cables tensions to always be positive. Additional conditions can be added to the workspace, which lead to different workspaces types.

The first researches on CDPRs' workspace have been interested in wrench closure workspace (WCW) and wrench feasible workspace (WFW). WCW refers to the main characteristics of CDPRs, which is the positive tension in the cables [START_REF] Gouttefarde | Analysis of the wrench-closure workspace of planar parallel cabledriven mechanisms[END_REF]. A given pose belongs to WCW if it is able to generate positive cables tensions. However, WFW is defined by the maximum and the minimum of acceptable tensions, [START_REF] Heo | Workspace and stability analysis of a 6-DOF cable-driven parallel robot using frequency-based variable constraints[END_REF] [START_REF] Loloei | Wrench feasible workspace analysis of cable-driven parallel manipulators using LMI approach[END_REF].

The evaluation of parallel manipulators workspace remains an important research field. Discretization approaches presented in Fig. 4 have been widely used for workspace analysis [START_REF] Castelli | A fairly general algorithm to evaluate workspace characteristics of serial and parallel manipulators[END_REF]. The general principle consists of discretizing the 3-D space, calculate the inverse kinematic problem (IKP) at each point and check the constraints conditions. This method is easy to implement and can be applied to any robot type, however the computational time could be high, especially for robots with complex kinematic equations. Laribi et al. proposed an analytical method by determining the mathematical equations of the boundaries of the robot's workspace [START_REF] Laribi | Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace[END_REF]. This method presented in Fig. 5 is based on the shape of the sub-workspace of each leg (or cable) of the robot. This formulation was used for several optimization problems [START_REF] Amine | On the Optimal Design of Cable Driven Parallel Robot with a Prescribed Workspace for Upper Limb Rehabilitation Tasks[END_REF], [START_REF] Ben Hamida | Geometric Based Approach for Workspace Analysis of Translational Parallel Robots[END_REF], [START_REF] Laribi | Geometric and Kinematic Performance Analysis and Comparison of Three Translational Parallel Manipulators[END_REF].

Cables tensions

A cable can only pull on the attachment point due its flexible nature. This limitation adds an extra constraint when designing cable robots. Therefore, for the cable robot to function properly, the tensions in the different cables have to be maintained positive, at all times. In practice and to be on the safe side, the tension in any cable of the robot is always maintained greater than a non-zero minimum tension.

The optimization consists of minimizing the cables tensions values and consequently minimize the power consumption of the manipulator.

Under static conditions, the relation between cables' tensions and the wrench applied at the platform is given by Newton-Euler formulation.

> ? 1 > @ (2) Where > ∶ is the structure matrix (6 × ) > 1 D E F E F × @ F .. E G E G × @ G
H; E is the vector of the i th cable direction and @ is the vector from the i th attachment point to the inertia center of the end-effector. ? 1 2 4 … J 7 K is the vector of all cables' tensions > @ 1 2L K M K 7 K is the external wrench applied on the end-effector.

In case of redundant actuation, the vector tension is given by the summation of the particular and homogeneous solutions as follows: Where > N : is the under-constrained Moore-Penrose pseudoinverse of >.

? 1 > N > @ + ( O -> N >)Q (3)
O : is the × identity matrix. Q: is an arbitrary m-vector

? S 1 > N > @ 1 2 ̅ 4 … ̅ J 7 U is the particular solution however V 1 ( G -> N >)Q
is the homogeneous solution. To maintain positive tension on all cables, the homogeneous solution V is fixed to guarantee a minimum required tension J/6 (see Fig. 6) [START_REF] Khosravi | Robust PID control of fully-constrained cable driven parallel robots[END_REF].

Fig. 6. Adjustable motor control

For mechanism synthesis problems, an objective function for the minimization of cable tensions was proposed in [START_REF] Amine | On the Optimal Design of Cable Driven Parallel Robot with a Prescribed Workspace for Upper Limb Rehabilitation Tasks[END_REF]. This function is expressed by:

( ) 1 1 (max(?)) W (? K . ?) (4)
Where ? 1 2 4 , W , . . , J 7, is the number of cables of the manipulator / is the tension of the i th cable

Cables sagging

In general, the studies on CDPRs consider the cables to be massless. However, in some cases with long-span cables, the aspect of sagging cables has to be taken into account. As shown in Fig. 7, a cable with a non-negligible mass has tendency to sag under its proper weight.

Cables sagging issue was addressed first by Jeong et al. [START_REF] Jeong | Development of a parallel wire mechanism for measuring position and orientation of a robot end-effector[END_REF] where an analytical expression of the longitudinal deformation of a cable was established and then a compensation factor of the cable deformation was proposed and validated through experimental tests.

Liu et al. [START_REF] Liu | Tension Optimization for a Cable-Driven Parallel Robot with Non-Negligible Cable Mass[END_REF] proposed a tension optimization approach for a cable driven parallel robot with large dimensions. The mathematical model for sagged cable layout proposed in [START_REF] Kozak | Static analysis of cable-driven manipulators with non-negligible cable mass[END_REF] is used and then an iterative approach was applied to compute the cables tensions. The compactness is a geometric criterion that characterizes the robot's size. There is no general formulation of this criterion. Essomba et al. [START_REF] Essomba | Optimal synthesis of a spherical parallel mechanism for medical application[END_REF] used the notion of local compactness function to optimize a spherical parallel manipulator. The index is given by the most inclined axis for a given configuration, then a global index is proposed through a discrete approach. For the same robot, Nelson et al. [START_REF] Nelson | Optimization of a Redundant Serial Spherical Mechanism for Robotic Minimally Invasive Surgery[END_REF] proposed a compactness criterion as the sum of the angular design parameters. A different approach, proposed in [START_REF] Ben Hamida | Comparative Study of Design of a 3-DOF Translational Parallel Manipulator with Prescribed Workspace[END_REF], considers the robot's compactness as the ratio of a desired workspace by the entire volume occupied by the robot. The calculation of the occupied volume by the robot depends on the base geometric shape, it could be a cube, a prism or a cylinder. Table 1 presents examples of different basic geometric shapes. Cube

X 1 Y W Z
Where Y: is the horizontal position of the motors Z: is the height of the robot

CUBE [9] Prism X 1 Y W 2 Z
Where Y: is the horizontal position of the motors Z: is the height of the robot FAST [START_REF] Tang | An Overview of the Development for Cable-Driven Parallel Manipulator[END_REF] Cylinder

X 1 \ ] W Z
Where R: is the radius of the platform Z: is the height

Singularity

Singular configurations correspond to the poses of the end-effector where the robots' performances degenerate and the control is lost. The determination of these configurations is essential in order to avoid them in the robot's trajectory. Generally, singularities can be identified through the examination of the Jacobian matrix. However, the Jacobian matrix considers all cables as rigid links. Therefore, the analysis of the Jacobian matrix becomes of no use if there is a slack in one of the robot's cable. Accordingly, two singularity cases can be distinguished [START_REF] Diao | Singularity analysis of planar cable-driven parallel robots[END_REF]; the Jacobian singularity and force closure singularity, depending if the Jacobian matrix is singular or not and the force-closure condition is violated or not. Recently, J-P Merlet [START_REF] Merlet | Singularity of cable-driven parallel robot with sagging cables: Preliminary investigation[END_REF] investigated the singularity of cable driven robots in case of sagging cables.

In this case, the singularity analysis showed, in counter to rigid parallel robots, CDPRs present two class of singularities: inverse kinematic and forward kinematic singularities.

To describe the overall kinematic behavior of the robots, we use the error amplification factor, which is calculated using the inverse of the condition number ( ), introduced by Gosselin [START_REF] Gosselin | A Global Performance Index for the Kinematic Optimization of Robotic Manipulators[END_REF].

1 1 ( ) (5)
Where ( ) 1 ‖ ‖. ‖ _F ‖ : is the Jacobian matrix of the robot at a given location

In the case of redundant actuation, the Jacobian matrix is a non-square matrix. The pseudo-inverse of the Jacobian matrix N , is used instead of its inverse. The condition number can be understood as a measure of how sensitive the related function is to changes or errors in its entries. A large condition number also means that the matrix is getting close to being singular.

The condition number, in this case, is calculated as

( ) 1 ‖ ‖. ‖ N ‖
To evaluate the global dexterity within the desired workspace, a global conditioning index ranging between 0 and 1 is defined in Eq. ( 6)

1 ∑ a b4 c ( 6
)
Where c is the discretization parameter of the desired workspace. The best kinematic performance is reached when = 1

The use of the condition number is not appropriate for manipulators having translational and rotational DOF and the normalization of the Jacobian matrix will be needed.

Safety

Safety issues are of a great importance in the design of robotic devices. The human-robot interaction has been investigated in several works mainly for medical devices, where the user is in direct physical contact with the manipulator. The increase of use of medical robots, requires the definition of specific safety standards since the safety measures of medical and industrial robots should be different. The « IEC 80601-2-78:2019» is a recent ISO standard applies to the general requirements for basic safety and essential performance of medical robots that physically interact with a patient with an impairment to support or perform rehabilitation, assessment, compensation or alleviation [START_REF] Robotics | Particular requirements for basic safety and essential performence of medical robots for rehabilitation, assessment, compensation or alleviation[END_REF]. Since the workspace in these situations is shared by the robot and the patient, conventional measures requiring a safety zone cannot be applied. The « IEC 80601-2-78:2019» standards evokes the risk management and situation awareness due to mechanical and electrical hazards. Different situations have been tackled as Energy release, exceeding the patient's movement limits, misalignment and collisions.

Carbone et al. [START_REF] Giuseppe | Design Issues for an Inherently Safe Robotic Rehabilitation Device[END_REF] have highlighted 3 aspects that affect patient's safety during a rehabilitation task:

-Operation ranges: when the robot moves the patient limb outside its operation space.

-Operation modes: when the robot speed is greater than the patient safe speed.

-Operation forces/torques: when the robot exercises an important effort on the human limb.

To ensure that the robot's works on a safety mode, the knowledge of the human operation ranges, modes and forces is required.

Another safety measure has been investigated in literature, which is the detection of cable failure. In fact, an emergency stop is often used with classical rigid robots however due to the flexibility of cables, the braking of motors could be not enough to stop the robot. Boschetti et al. [START_REF] Boschetti | Cable Failure Operation Strategy for a Rehabilitation Cable-Driven Robot[END_REF] proposed an operational strategy for cable failure that consists in generating an opposite wrench in case of failure, which leads the end-effector to a safe position. Another criterion that have been introduced in a previous work [START_REF] Ben Hamida | Novel Safety Criterion for Synthesis of Cable Driven Parallel Robots[END_REF] is the minimum distance between the cables and the patient during the rehabilitation task as presented in Fig. 8. The approach consists in discretizing the cables' line into t points and calculate the distance between each point and the cylinder surrounding the patient. The cylinder surrounding the patient with diameter d, the shoulder width, and centered on its spine is presented in Fig 9 . The objective of this method is to maximize this distance to avoid any risk of collision between the user and the robot. The distance Y between a given point e (3 , f , g ) on the cable and the cylinder, the safety area of the patient, is given by the following equation.

Y 1 h i3 -3 j k W + if -f j k W - d 2 (7)
Where 3 j , f j , g j are the coordinates of a point from the cylinder axis ( g j 1 g ).

Overview

Table 2 presents an overview of the presented criteria. As it can be seen, some of them could be considered as constraints or/and objectives.

A Case of Study

Requirements and constraints for forearm rehabilitation tasks

CDPRs achieved interesting results regarding physical rehabilitation of post-stroke patients. Among the physiotherapy exercises for post stroke patients is the Elbow flexion/extension planar movement shown in Fig. 10 [42], [START_REF] Rahman | Exoskeleton robot for rehabilitation of elbow and forearm movements[END_REF], [START_REF] Rahman | Modeling and control of a 7DOF exoskeleton robot for arm movements[END_REF]. It consists of an arc of center the elbow of the patient and radius the length of the forearm. To define the workspace required for this particular exercise several measures of 10 normal subjects of different ages (25 -70 years) and gender, have been carried out. The results are given in Table 3. According to the obtained movements ranges, a desired workspace, presented in Fig. 11, was defined as a surface limited by two arcs corresponding to the maximal and minimum forearm lengths. LAWEX robot, shown in Fig. 12, is a rehabilitation device built in LARM in Cassino [START_REF] Giuseppe | Design Issues for an Inherently Safe Robotic Rehabilitation Device[END_REF]. It consists of 4 motors controlling the lengths of 4 flexible cables attached to a circular end-effector. The used cables are thin with negligible weights so that sagging issue can be considered as negligible. As a rehabilitation device, LAWEX operates at low speed. The weight of the moving part is estimated to be equal to 1.5 Kg, including the average weight of a human hand and forearm, as it is reported in [START_REF] Plagenhoef | Anatomical Data for Analyzing Human Motion[END_REF].

Fig. 12. LAWEX robot

This section aims at the study and the comparison of four different designs of LAWEX robot (see Fig. 13). The objective is to select the optimal design and the optimal parameters of the robot having the best tension distribution along the prescribed trajectory and occupying the smallest volume.

By assuming that the orientation of the end-effector during the rehabilitation task is constrained, we consider only the forces generated by the cables' tensions and the moments are neglected. This design consists of a suspended cable driven robot with 3 cables attached in the same point of the end-effector. The inverse geometric model of a cable driven parallel robot defines the lengths of cables according to the end-effector position. The position of the end effector is given by the vector @ 1 23, f, g7 K . The motors positions according to Fig. 14 are given by the following equations.

l F 1 2Y 4 , 0, Z7 K l m 1 20 , 0 , Z7 K l n 1 20, Y W , Z7 K (8)
The inverse kinematic model (IKM) is obtained by the closed-loop equation of each cable defined in the following equation.

@ 1 l F + E F 1 l m + E m 1 l n + E n (9)
here E o : is the vector from the i th motor to the end-effector.

3, f, g: are the coordinates of the end-effector.

p E F 1 @ -l F E m 1 @ -l m E n 1 @ -l n ( 10
)
The IKM is given by the length of the 3 cables

q r 4 1 ‖@ -l F ‖ 1 s(3 -Y 4 ) W + f W + (g -Z) W r W 1 ‖@ -l m ‖ 1 s3 W + f W + (g -Z) W r t 1 ‖@ -l n ‖ 1 s3 W + (f -Y W ) W + (g -Z) W (11) u r 4 r W r t v 1 w s(3 -Y 4 ) W + f W + (g -Z) W s3 W + f W + (g -Z) W s3 W + (f -Y W ) W + (g -Z) W x ( 12
)
The cables tensions are given by the Newton Euler formulation as follows

> ? 1 > y (13)
Where ? 1 2 4 , W , t 7 K > y 1 20 0z { 7 K , z : end-effector mass, {: gravitational acceleration

> 1 2 4 , W , t 7 , | o 1 D @ × H , U 9 = - E r / ~
@ : is the vector connecting the reference point on the moving platform @ to the anchor point of the i th cable.

The Jacobian Matrix of the LAWEX robot is given by

1 > • 1 € • • • ' 3 -Y 4 r 4 f r 4 g -Z r 4 3 r W f r W g -Z r W 3 r t f -Y W r t g -Z r t ƒ " " " … (14)

Design (b), fully constrained CDPR

For this design, four cables are used to control the end-effector pose. However, we consider the orientation of the end-effector to be constrained due to a fixed support of the patient elbow. In this case, the LAWEX robot is a fully constrained mechanism where the end-effector position is defined by the length of the 4 cables. The considered parameters are given in Fig. 15. The IKM of the fully constrained CDPR is given by Eq [START_REF] Botello-Aceves | Evaluating concurrent design approaches for a Delta parallel manipulator[END_REF].

w r 4 r W r t r † x 1 € • • ' s(3 -Y 4 ) W + f W + (g -Z) W s3 W + f W + (g -Z) W W + (f -Y W ) W + (g -Z) W s3 W + f W + g W ƒ " " … (15)
The cables tensions are obtained, as in the previous case, through Newton-Euler formulation.

> ‡ 1 > @ (16)
where ? 1 2 4 , W , t , † 7 K > @ 1 20 0z { 7 K , z : end-effector mass, {: gravitational acceleration

> 1 2 4 , W , t , † 7 , > 1 D @ × H , = - E r / ~
Since the mechanism is over constrained, there is an infinite number of solutions of the tension vector. The vector tension is given by the following equation.

? 1 ‡ S + ˆ ‰ (17)
where ? S 1 > N > y : is the particular solution of Eq [START_REF] Amine | On the Optimal Design of Cable Driven Parallel Robot with a Prescribed Workspace for Upper Limb Rehabilitation Tasks[END_REF] where > N is the Moore-Penrose pseudoinverse of > ‰: is the Kernel vector of > ˆ: is an arbitrary scalar chosen so that / (Š 1 1. .4) is greater than the minimum desired tension.

In our case, we fix J/6 1 0.5 N. The value of 0.5 N has been selected by referring to the maximum loading conditions of LAWEX (1.5 Kg) and to the mass of the LAWEX cables (nylon cables, whose weight is about 5 grams per meter). Accordingly, a ten times higher cable tension value provides a negligible sagging effect. This is also discussed in [START_REF] Boschetti | Cable Failure Operation Strategy for a Rehabilitation Cable-Driven Robot[END_REF]. For this design, four cables are used to control the end-effector pose. In this case, the LAWEX robot is a redundant mechanism where the end-effector position is defined by the length of the 4 cables. The considered parameters are given in Fig. 16.

The IKM of the over constrained CDPR is given by Eq [START_REF] Bilel | Multi-objective robust design optimization of a mechatronic system with uncertain parameters, using a polynomial chaos expansion method[END_REF].

w r 4 r W r t r † x 1 € • • ' s(3 -Y 4 ) W + f W + (g -Z) W s3 W + f W + (g -Z) W s3 W + (f -Y W ) W + (g -Z) W s(3 -Y 4 ) W + (f -Y W ) W + (g -Z) W ƒ " " … (18)
Cables tensions are given through the Newton Euler formulation (Eq [START_REF] Amine | On the Optimal Design of Cable Driven Parallel Robot with a Prescribed Workspace for Upper Limb Rehabilitation Tasks[END_REF])

> ? 1 > y (19)
Where ? 1 2 4 , W , t , † 7 K > @ 1 20 0z { 7 K , z : end-effector mass, {: gravitational acceleration

> 1 2 4 , W , t , † 7 , > 1 D @ × H , = - E r / ~
The tension vector is obtained by summation of the particular and a homogeneous solution as defined in Eq [START_REF] Essomba | Optimal synthesis of a spherical parallel mechanism for medical application[END_REF] of the previous case.

Design (d), fully constrained CDPR

In this design, four cables are distributed above and below the platform as shown in Fig. 17. The motors positions are given in the following Equations: The IKM of the fully constrained CDPR is given by Eq.( 20)

l F 1 20, 0, Z7 K l m 1 2Y W , Y W , Z7 K l n 1 2Y 4 , 0,07 K l Ž 1 20, Y W , 07 K
The cables tensions are obtained through Newton-Euler formulation and the solution is defined as in the previous two cases

Mathematical formulation of the optimization problem

The objective of this optimization is to select the best LAWEX design (a , b, c, or d) and the best set of design parameters that guarantee the best compromise between cables tension and the compactness criterion for a prescribed rehabilitation trajectory.

Given:

-Trajectory of the patient wrist Objectives:

-Include the prescribed trajectory; -Minimize the occupied volume by the robot; -Minimize the maximum cables tensions.

A mathematical formulation of the optimization problem is given as follows:

Minimize ( ) 1 • 4 ( ) W ( ) Subject to . / ( ) ≤ 0 1 23 4 , . . , 3 6 7 3 J/6 ; 3 ; 3 Jz• [START_REF] Hernandez | Design Optimization of a Cable-driven Parallel Robot in Upper Arm Training-Rehabilitation Processes[END_REF] where

w r 4 r W r t r † x 1 € • • ' s3 W + f W + (g -Z) W s(3 -Y 4 ) W + (f -Y W ) W + (g -Z) W s(3 -Y 4 ) W + f W + g W s3 W + (f -Y W ) W + g W ƒ " " … (20)
4 ( ) and W ( ) are the objective functions defining the robot's size and the cables tensions, respectively. . / ( ) are the constraint functions describing the prescribed trajectory. 1 23 4 , . . , 3 6 7 is the decision vector defined by the set of design variables and 3 J/6 , 3 Jz• the search domain for each design variable 3 .

The proposed solving algorithm approach

A novel approach for mechanism synthesis is proposed in Fig. 18. It aims to expand the Nondominated Sorting Genetic Algorithm (NSGA-II) [START_REF] Deb | A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II[END_REF] allowing the synthesis of more than one architecture.

The NSGA-II optimization algorithm is an evolutionary elitist algorithm inspired from the natural evolutionary process. The strength of this metaheuristic is highlighted especially with complex problems involving several objectives and/or constraints.

Two types of coding, discrete and real, can be used to represent individuals (solutions) of the Genetic Algorithm. The Main contribution of this approach is to combine both coding types in the same formulation. The design vector is composed of two parts: a discrete part handling the design type and a continuous part handling the set of design parameters of the studied manipulator.

Starting for a randomly generated initial population, the individuals are evaluated, selected and then genetical operators are applied (Crossover and mutation). born by applying selection operator. From each generation, a parallel selection is made to select the non-dominated solutions which will appear in the Pareto front. The same steps are repeated with new generations until achieving one of the stopping criteria. The considered stopping criterion is the maximum number of generations. The decision vector of the proposed approach is composed of two parts, a discreate variable (Y'' 1 1,2,3,4) referring to the selected design a, b, c or d and a design vector composed of continuous design parameters of the robot. The decision vector is given by:

The decision vector

1 2Y'', Y 4 , Y W , Z, ", g • 7 K (22)
where: Y'' 1 1, 2, 3,4 ∶ assigns the design type (see Fig. 13) Y 4 , Y W , Z : design parameters of the robot " 1 3 • √2 1 f • √2 3 • , f • , g • : position of the patient elbow as shown in Fig. 19.

The selected objective functions • Compactness

This criterion aims to reduce the occupied volume by the robot. It is computed as the ratio of the cuboid robot's volume by the volume of the actual design (see Fig. 12).

4 (-) 1 Y 4 × Y W × Z X ˜™š•› 23)
Where X ˜™š•› : is the volume of the built prototype at LARM Cassino. The design parameters of this prototype are given in Table 4. The solutions having a compactness index greater than 1 in the Pareto front are the solutions with a bulkier design than LARM prototype.

Discontinuity of the Pareto front along cables tension index axis can be explained by heterogeneity of the studied designs where the compactness index is a common function of all designs and cables tension function is specific for each design. To examine the point of discontinuity, both solutions of the gap point of the Pareto front are identified (Table 5) and presented in Fig. 23.

Fig. 23 shows that the occupied volume of both solutions is very close however a considerable difference of the maximal cable tension is recorded along the desired trajectory. The distinction of motors position from a design to another affects the static equilibrium of the end-effector and then the applied efforts.

Pareto front selection approach

To select a single solution from the set of the Pareto front, a novel criterion is proposed. The decision process is performed relatively to the patient safety. We consider the approach presented previously in Fig. 8. It consists in evaluating the minimum distance between the cables and the user, ¦ points are selected on each cable at equal distance and then the distance from a point § / to the patient is calculated where Š 1 1. . and ¨1 1. . ¦. To simplify the model, we consider the axis centered on the spine of the patient. To evaluate patient safety, the minimum distance between cables and the patient is computed.

© 1 Š (e / ) (28)
Where e / 1 h i3 / -3 j k

W + if / -f j k W - ª W
is the distance from the point § / to the cylinder 3 / , f / : are the coordinates of the point § /

The safety function is computed for all Pareto solutions. The ranking of Pareto solutions reveals that the design «d» is safer for the patient than solutions of design «c» with a minimum distance equal to 10cm during desired trajectory. The solution which guarantee the maximal distance between cables and patient is selected. Design parameters of this solution are given in Table 6.

Results show that a 2-2 topology is the best topology for the selected optimality criteria. Also, the dimensional synthesis provide feasible sizes for fulfilling the desired design requirements in terms of optimal tradeoff between occupied robot volume, cable tensions and the user safety. Design parameters of the existing LAWEX rehabilitation device (Fig. 12) are given in Table 7. The index of cables tension on the Pareto front of design «d» solutions is greater than 1 which attested a maximal cables tension slightly greater than LAWEX prototype maximal cables tension. Fig. 24 shows a difference going from 2 to 4 N along the prescribed trajectory between both designs. Fig. 25 presents the CAD models of LAWEX prototype and the selected solution. A significant difference on the occupied volume by both designs can be noticed. An evaluation of the occupied volume and maximal cables tension are given in Table 8. Results demonstrate a 2-2 topology as being the most effective in terms of the selected optimality criteria with optimal tradeoff between occupied robot volume, cable tensions and the user safety. Namely, it has been possible to achieve a reduction of the occupied volume of about 85% while maximum cable tension has been reduced by 2%. In terms of safety, the actual prototype is still 38% safer than the selected solution due to the position of exiting points which are secluded from the patient position.

Maximal cable tension

Conclusion

First part of this paper focuses at fundamental characteristics related to topological and dimensional performances of CDPRs with a general discussion on their type and dimensional synthesis, which are currently done in sequential order. Then, authors propose a concurrent optimization approach specific for CDPRs, which is combining their type and dimensional synthesis. A specific case of study is carried out by referring to LAWEX a 3DOFs CDPR rehabilitation device for the human forearm. The reported case of study proposes concurrent multi-objective optimization by taking into account cables tensions and occupied volume alongside with desired workspace and motion performances. Topology search has been considering four different topology designs of LAWEX. The topology and dimensions of the mechanism are optimized, simultaneously. In addition to the design parameters, the decision vector of the GA contains a discrete variable to define the selected topology among the four proposed architectures. A Pareto front has been obtained showing the set of feasible optimal solutions. An additional safety criterion is implemented for identifying an optimal solution among the set of solutions in the obtained Pareto front. This has allowed to identify the desired optimal solution. Results demonstrate a 2-2 topology as being the most effective in terms of the selected optimality criteria with optimal tradeoff between occupied robot volume, cable tensions and the user safety.

Fig. 1 .

 1 Fig. 1. Mechanical design processFirst, a problem definition based on the required functional criteria by the user should be identified. A mathematical formulation of the design problem is then established for the mechanism synthesis, which is processed in two phases:

Fig. 2 .

 2 Fig. 2. Different configurations of CDPRs Fig. 2 presents three possible designs of the CDPRs. The first case (a) presents an under constrained robot with 3 cables for 3 DOFs. The gravity is used in this case, to ensure positive tensions in the cables. The second case (b) is a fully constrained CDPR, which uses 4 cables to ensure the same number of DOFs as the first case. The third robot, case (c), is an over constrained CDPR, as it is using 5 cables to ensure 3 DOFs.

Fig. 3 .

 3 Fig. 3. Different shapes of end-effector

Fig. 4 . 5 .

 45 Fig. 4. Discretization Approach Fig. 5. Power point function Approach

Fig. 7 .

 7 Fig. 7. Sagging cable in its vertical plane

Fig. 8 .

 8 Fig. 8. Safety criterion

Fig. 9 .

 9 Fig. 9. Dimension and position of the cylinder surrounding the patient

Fig. 10 .

 10 Fig. 10. Flexion movement of upper arm Fig. 11. Desired workspace

Fig. 13 . 5 . 2 . Geometric and kinematic modellings for different topologies 5 . 2 . 1 .

 1352521 Fig. 13. Different designs of LAWEX robot: (a) Under-constrained suspended CDPR (b) Fully constrained CDPR (c) underconstrained suspended CDPR and (d) Fully constrained CDPR 5.2. Geometric and kinematic modellings for different topologies 5.2.1. Design (a), Under-constrained suspended CDPR

Fig. 14 .

 14 Fig. 14. Geometric Parameters of design (a)

Fig. 15 .

 15 Fig. 15. Geometric Parameters of Design (b)

5. 2 . 3 .Fig. 16 .

 2316 Fig. 16. Geometric parameters of design (c)

Fig. 17 .

 17 Fig. 17. Geometric Parameters of design (d)

Fig. 18 .

 18 Fig. 18. Flow chart of the proposed approachThe initial population is created randomly with an arbitrary number of each design type then evaluation, ranking and sort of the individuals according to the crowding distance, are performed. After combination of the old population and the new individuals obtained through crossover and mutation operators, the set is raked and sorted according to the crowding distance. A new generation is

Fig. 19 .

 19 Fig. 19. Design parameters of the design approach

Fig. 20 .Fig. 21 .

 2021 Fig. 20. Evolution of solutions type through generations

Fig. 22 .

 22 Fig. 22. Pareto front Fig. 22 presents the set of non-dominated optimal solutions called Pareto front of the optimization process. The first and second designs, «a» and «b», are excluded from the Pareto front since their solutions are dominated solutions. The minimum cables tension is obtained for the third design «c» where the end-effector is suspended by four cables while the best compactness values are presented by design «d», where the cables are fairly distributed below and above the end-effector. We called this design 2-2 topology.

Fig. 23 .

 23 Fig. 23. CAD and maximal tension distribution of the two selected solutions from the Pareto front

Fig. 24 .

 24 Fig. 24. Maximal cables tension of LAWEX prototype in N: (a) LAWEX prototype, (b) selected optimal solution

Fig. 25 .

 25 Fig. 25. (a) CAD of the built LAWEX prototype, (b) CAD of the proposed solution

Table 1 .

 1 Different bases shape

	Robot	Occupied volume
	LAWEX
	[19]

Table 2 .

 2 Summary of the CDPR criteria

		Constraint	Performance
	Workspace
	Compactness	x
	Dexterity	x
	Singularity		x
	Payload and weight
	Cables tensions
	Safety
	Cables interferences		x
	Cables sagging		x
	Power consumption

Table 3 .

 3 Elbow mouvement mesures

		Forearm length (cm)	Lower limit (°)	Upper limit (°)
	1	27	0	125
	2	21	0	130
	3	30	5	150
	4	27	0	130
	5	25	0	120
	6	32	0	125
	7	30	0	140
	8	23	5	135
	9	28	0	150
	10	31	0	130

Table 4 :

 4 Design parameters of LARM Prototype

	Y 4 ˜™š•› 0.6 m	Y W ˜™š•› 0.6 m	Z ˜™š•› 0.65 m	X ˜™š•› 0.234 m t

Table 5 .

 5 Two selected solutions from the Pareto front

	I	Design 4 3	Y 4 0.3 m 0.3 m	Y W 0.3 m 0.302 m	Z 0.404 m 0.405 m	" 0.281 m 0.281 m	g ¤ 0.05 m 0.05 m

Table 6 :

 6 Design parameters of the selected solution

	5.4.2.	I	Design 4	Y 4 0.3 m	Y W 0.3 m	Z 0.386 m 0.284 m "	g ¤ 0.053 m

Comparison of the obtained solutions with the LAWEX prototype

Table 7 .

 7 Design parameters of the existing LAWEX prototype

	³l>´µ	d 4 ¬-®¯° 0.6 m	d W ¬-®¯° 0.6 m	h ¬-®¯° 0.65 m	r ¬-®¯° 0.29 m	z ¯ ¬-®¯° 0.22 m

Table 8 .

 8 Performances comparison of LAWEX prototype and the proposed solution

	LAWEX prototype	Proposed solution	% improvement
	Occupied volume

X ˜™š•› 1 0.234 m t X ©•¸1 0.0347 m t X ˜™š•› -X ©•X ˜™š•› % 1 85%

Acknowledgment

This work is supported by the "Poitiers Université Foundation".

• Cables tensions

To guarantee a minimal cables tension along the prescribed trajectory, the objective function is given as a ratio of the calculated maximal tension at a point from the trajectory by the maximal tension of the existing prototype

The defined constraint functions

The proposed optimization problem is subject to two constraints:

-The belonging of the desired trajectory to the robot workspace -A positive cables' tension

To examine if a given point (3, f, g) from the trajectory is inside the workspace or not, the power point function is used as follows:

To ensure a positive cables tension, the Moore-Penrose inverse, presented in section 4.2, is used

where ? S 1 > N > @ , > N : is the under-constrained Moore-Penrose pseudoinverse of >.

A penality function is considered to ensure that the problem constraints are respected and it is given as bellows:

Here, is a large positive constant.

Numerical implementation and results

The described optimization problem is solved using MATLAB software. The modified NSGA-II algorithm was implemented with the following inputs: population size = 500, and number of generations =100.


Céline Stutz

Fareeha Batool

Catherine Petit

Marion Strub

Sabine Kuchler-Bopp

Nadia Benkirane-Jessel

Olivier Huck
email: o.huck@unistra.fr

Prof Olivier Huck

Influence of parathyroid hormone on periodontal healing in animal models: a systematic review

Keywords: inflammation, infrabony defect, parathyroid hormone, periodontal regeneration, periodontitis

Objectives:

The purpose of this systematic review was to determine the potential interest of parathyroid hormone as an adjunct to periodontal treatment based on studies performed in rodents.

Materials & methods: Electronic databases (MEDLINE, Web of Science) were searched up to December 2019. Studies assessing the impact of PTH administration in experimental periodontitis in rodents have been identified.

Results: Amongst the 247 identified articles, 10 met the inclusion criteria and were included in this systematic review. Experimental periodontitis was mainly induced by ligature placement or surgically with a dental bur. All studies considered bone healing after PTH administration at different frequencies as primary outcome. Results showed that an intermittent administration of PTH promoted bone healing and neovascularization. Nevertheless, a decrease of soft tissue inflammation was also observed.

Conclusion:

Intermittent administration of PTH appears to enhance significantly periodontal healing and to promote alveolar bone regeneration. However, due to the risk of side effects, the development of scaffolds allowing its local and time-controlled delivery is of importance.

Introduction

Periodontal diseases are inflammatory diseases of infectious origin with a high prevalence worldwide [START_REF] Kinane | Periodontal diseases[END_REF]. Amongst them, periodontitis, is characterized by inflammation and destruction of tooth supporting tissues and was linked to several systemic diseases such as cardiovascular diseases [START_REF] Huck | Evaluating periodontal risk for patients at risk of or suffering from atherosclerosis: recent biological hypotheses and therapeutic consequences[END_REF], diabetes [START_REF] Chapple | Diabetes and periodontal diseases: consensus report of the Joint EFP/AAP Workshop on Periodontitis and Systemic Diseases[END_REF], obesity [START_REF] Keller | The Association Between Periodontal Disease and Overweight and Obesity: A Systematic Review[END_REF] and rheumatoid arthritis [START_REF] Fuggle | Hand to Mouth: A Systematic Review and Meta-Analysis of the Association between Rheumatoid Arthritis and Periodontitis[END_REF]. Its impact on oral health-related quality of life and masticatory function [START_REF] Pereira | Treatment of chronic periodontitis and its impact on mastication[END_REF][START_REF] Sulaiman | Impact of Severe Chronic Periodontitis on Oral Health-related Quality of Life[END_REF] emphasizes the need of efficient treatment. Currently, periodontal treatment aims to control periodontal inflammation through restoration of an imbalance between periodontal flora and host-response. It consists of mechanical removal of supra and sub-gingival biofilms with potential adjunct of chemotherapy such as the use of antibiotics, antiseptics or anti-inflammatory drugs through systemic or local delivery in most severe cases [START_REF] Agossa | Systemic Application of Anti-inflammatory Agents in Periodontal Treatment[END_REF][START_REF] Pretzl | Administration of systemic antibiotics during non-surgical periodontal therapy-a consensus report[END_REF][START_REF] Quirynen | Topical antiseptics and antibiotics in the initial therapy of chronic adult periodontitis: microbiological aspects[END_REF]. Current periodontal strategies are, in most of the clinical scenario effective, however, in severe cases with presence of infrabony defects, non-surgical periodontal treatment outcomes may be decreased and correlated with the establishment of a long junctional epithelium rather than ad integrum regeneration of periodontal tissues [START_REF] Lsf Sculean | Wound models for periodontal and bone regeneration: the role of biologic research[END_REF].

To achieve periodontal regeneration and to improve treatment outcomes, new pharmacological approaches have been suggested. Indeed, the local administration of signaling molecules such as growth factors, anti-cytokines or hormones has been evaluated due to their modulating effects on inflammation and bone metabolism [START_REF] Oortgiesen | Periodontal regeneration using an injectable bone cement combined with BMP-2 or FGF-2[END_REF][START_REF] Del Amo | Biologic Agents for Periodontal Regeneration and Implant Site Development[END_REF]. An increasing interest has also been made on parathyroid hormone (PTH) or parathyroid hormone-related protein (PTHrP) based on clinical evidences demonstrating interactions between thyroid disorders and periodontal diseases [START_REF] Zahid | The effects of thyroid hormone abnormalities on periodontal disease status[END_REF]. Endogenous PTH and PTHrP play a crucial role in the development of trabecular bone mass and cartilaginous growth plate especially in the fetus and the neonate [START_REF] Goltzman | Studies on the mechanisms of the skeletal anabolic action of endogenous and exogenous parathyroid hormone[END_REF]. PTH is secreted by the parathyroid glands and is considered as one of the major systemic regulator of calcium metabolism and bone remodeling [START_REF] Goltzman | Physiology of the Calcium-Parathyroid Hormone-Vitamin D Axis[END_REF]. PTH structure includes 84 amino acids with its biological activity associated to the NH2-terminal 34 residues ). This NH2terminal domain interacts with a G-protein-coupled receptor called the PTH/PTHrP receptor type 1 (PTHR-1) expressed notably in bone [START_REF] Taylor | From parathyroid hormone to cytosolic Ca2+ signals[END_REF] (Figure 1). PTH binding to this receptor activates different types of G protein subclasses, Gαs and Gαq/11 resulting in the activation of protein kinase A or protein kinase C respectively [START_REF] Goltzman | Physiology of the Calcium-Parathyroid Hormone-Vitamin D Axis[END_REF], both contributing to the modulation of bone metabolism associated pathways involving RANK/RANKL/OPG, Wnt/β-catenin [START_REF] Silva | Catabolic and anabolic actions of parathyroid hormone on the skeleton[END_REF] and MAPK [START_REF] Miao | Parathyroid hormone-related peptide stimulates osteogenic cell proliferation through protein kinase C activation of the Ras/mitogen-activated protein kinase signaling pathway[END_REF]. PTH is physiologically involved in the regulation of RANKL secretion via the PI3K/AKT/STAT5 signaling pathway [START_REF] Sun | Endogenous parathyroid hormone (PTH) signals through osteoblasts via RANKL during fracture healing to affect osteoclasts[END_REF]. Bone remodeling is a physiological process which occurs constantly throughout human life, orchestrated notably by RANKL/OPG ratio. The modification of the bone remodeling cycles could lead to bone destruction as observed in the context of periodontitis [START_REF] Xu | Disturbed bone remodeling activity varies in different stages of experimental, gradually progressive apical periodontitis in rats[END_REF][START_REF] Yan | Substance P participates in periodontitis by upregulating HIF-1α and RANKL/OPG ratio[END_REF]. Endogenous PTH is mainly involved in the bone formation phase by regulating the expression of transcriptional regulator of osteoblastic differentiation factors such as RUNX2 [START_REF] Goltzman | Studies on the mechanisms of the skeletal anabolic action of endogenous and exogenous parathyroid hormone[END_REF]. The anabolic role of endogenous PTH and PTHrP on bone remodeling process was demonstrated in animals deficient in PTH or/and PTHrP as they exhibit skeletal abnormalities [START_REF] Siddiqui | Physiological Bone Remodeling: Systemic Regulation and Growth Factor Involvement[END_REF].

Based on its properties, this hormone has already been approved as an anabolic treatment for osteoporosis by Food & Drug Administration [START_REF] Wojda | Parathyroid hormone for bone regeneration[END_REF]. Its administration stimulates bone remodeling and reduces the risk of vertebral and non-vertebral fractures especially in postmenopausal osteoporotic women [START_REF] Leder | Parathyroid Hormone and Parathyroid Hormone-Related Protein Analogs in Osteoporosis Therapy[END_REF]. Interestingly, PTH has two opposite effects depending on the frequency of administration. Intermittent administration increases bone formation and promotes bone mineral density. At contrary, continuous administration of PTH increases bone resorption through regulation of RANKL and OPG. Such catabolic effect is correlated to an increased risk of vertebral and hip fracture [START_REF] Silva | Parathyroid hormone: anabolic and catabolic actions on the skeleton[END_REF]. As alveolar bone is a major component of periodontium and is significantly destroyed during periodontitis, PTH administration has been suggested to be used in periodontal lesion management. This systematic review aims to evaluate the effect of PTH administration on periodontal healing in experimental periodontitis induced in rodents to determine the therapeutic potential of PTH and the most effective route and protocol of administration.

Materials and methods

Focused question

In this systematic review, the following question was addressed:

• Is PTH influencing periodontal healing in experimentally induced periodontitis in rodent models?

Screening and selection criteria

The results of this systematic review were reported following the PRISMA guidelines [START_REF] Moher | Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement[END_REF]. Studies were identified independently by two blinded researchers from the following databases: MEDLINE and Web of Science up to December 2019. An additional hand search was also performed in references list of included articles and reviews. The following strategy was used in the search using Boolean operators and an asterisk symbol (*) as truncation to identify papers using MesH, keywords and other free terms: ((PTH) OR (parathyroid hormone) AND (periodontitis OR alveolar bone OR periodontal treatment OR periodontal healing OR periodontal destruction)) AND (mouse OR rat). Only articles published in English language have been considered. After titles and abstracts screening by two reviewers (C.S., O.H.), studies were categorized as suitable or not for inclusion. Full-texts were then evaluated to allow clear decision and disagreements between reviewers were resolved after discussion.

Eligibility criteria

A study was considered eligible for inclusion in this systematic review if it met the following criteria: (1) in vivo study, (2) experimental induced periodontitis, (3) rodent model, (4) administration of PTH. Reviews, clinical trials in Humans and studies not focusing on periodontitis related outcomes were excluded. All the preselected articles were analyzed in accordance with the predefined eligibility criteria.

Outcomes

Quantitative and qualitative outcomes measurements relative to bone formation, bone loss and modulation of inflammatory markers were extracted from the included studies.

Risk of bias assessment

Risk of bias was determined using SYRCLE's RoB tool based on the Cochrane RoB tool [START_REF] Hooijmans | SYRCLE's risk of bias tool for animal studies[END_REF]. This tool contains 10 entries to assign a judgment of low, high or unclear risk of bias for each study. The tool provides a score based on the following questions:

Was the allocation sequence adequately generated and applied? Were the groups similar at baseline or were they adjusted for confounders in the analysis? Was the allocation to the different groups adequately concealed during the study? Were the animals randomly housed during the experiment? Were the caregivers and/or investigators blinded from knowledge which intervention each animal received during the experiment? Were animals selected randomly for outcome assessment? Was the outcome assessor blinded? Were incomplete outcome data adequately addressed? Are reports of the study free of selective outcome reporting? Was the study apparently free of other problems that could result in high risk of bias? Risk of bias was evaluated by two reviewers (C. S., O.H.). Disagreements between reviewers were resolved after discussion

Results

Studies selection

The flow diagram of the literature search is presented in Figure 2. Overall, 247 articles were identified by querying selected databases (Medline/Pubmed and Web of Sciences). After removal of duplicates, 183 articles were screened. 158 articles were excluded based on title and abstract. Amongst the 25 remaining articles, 10 were selected for full-text review. Three studies were excluded as they evaluated socket healing after teeth extraction, 8 because PTH was used in combination with other therapeutic modality or hormone and 4 were excluded because they were not focused on periodontal healing. Regarding the 10 included studies, 5 used a model of periodontitis induced by ligatures, 4 analyzed bone healing after a periodontal defect created by dental bur or orthodontic forces and one used streptozotocin-induced diabetic periodontitis.

Studies characteristics

All the identified studies were published between 2003 and 2019. Nine studies were performed in male rats aged 4 weeks to 3 months and one study used 8 weeks old male mice [START_REF] Barros | Parathyroid Hormone Protects against Periodontitis-associated Bone Loss[END_REF][START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF][START_REF] Lossdörfer | Anabolic effect of intermittent PTH(1-34) on the local microenvironment during the late phase of periodontal repair in a rat model of tooth root resorption[END_REF][START_REF] Otawa | Intermittent administration of parathyroid hormone ameliorates periapical lesions in mice[END_REF][START_REF] Tokunaga | Topical and intermittent application of parathyroid hormone recovers alveolar bone loss in rat experimental periodontitis[END_REF][START_REF] Vasconcelos | Intermittent Parathyroid Hormone Administration Improves Periodontal Healing in Rats[END_REF][START_REF] Wang | PTH/SDF-1α cotherapy induces CD90+CD34-stromal cells migration and promotes tissue regeneration in a rat periodontal defect model[END_REF][START_REF] Yoshida | Combined effects of systemic parathyroid hormone (1-34) and locally delivered neutral self-assembling peptide hydrogel in the treatment of periodontal defects: An experimental in vivo investigation[END_REF][START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF]. Otawa et al. have used mice mutant for lymphotoxin A (LTA) [START_REF] Otawa | Intermittent administration of parathyroid hormone ameliorates periapical lesions in mice[END_REF]. Characteristics of the included studies are presented in Tables 1234. Risk of bias amongst included studies ranged from 2 [START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF] to 6 [START_REF] Barros | Parathyroid Hormone Protects against Periodontitis-associated Bone Loss[END_REF] (Table 5).

Induction of periodontal defect

Several models have been used to induce periodontal destruction. In some studies, periodontal defects were surgically created with dental bur [START_REF] Vasconcelos | Intermittent Parathyroid Hormone Administration Improves Periodontal Healing in Rats[END_REF][START_REF] Wang | PTH/SDF-1α cotherapy induces CD90+CD34-stromal cells migration and promotes tissue regeneration in a rat periodontal defect model[END_REF][START_REF] Yoshida | Combined effects of systemic parathyroid hormone (1-34) and locally delivered neutral self-assembling peptide hydrogel in the treatment of periodontal defects: An experimental in vivo investigation[END_REF] (Table 1) while in two others, experimental periodontitis was induced by ligature placement [START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF] (Table 3). In Lossdörfer et al. study, an orthodontic force was applied on first and second molars to induce the development of an interdental defect [START_REF] Lossdörfer | Anabolic effect of intermittent PTH(1-34) on the local microenvironment during the late phase of periodontal repair in a rat model of tooth root resorption[END_REF] (Table 4). Interestingly, three studies evaluated the effect of PTH administration on alveolar bone loss in streptozotocin-induced diabetic rats [START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF][START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF] (Table 2).

Mode of PTH administration and dose

In included studies, PTH was in most of the cases administered by subcutaneous injections [START_REF] Barros | Parathyroid Hormone Protects against Periodontitis-associated Bone Loss[END_REF][START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF][START_REF] Lossdörfer | Anabolic effect of intermittent PTH(1-34) on the local microenvironment during the late phase of periodontal repair in a rat model of tooth root resorption[END_REF][START_REF] Otawa | Intermittent administration of parathyroid hormone ameliorates periapical lesions in mice[END_REF][START_REF] Vasconcelos | Intermittent Parathyroid Hormone Administration Improves Periodontal Healing in Rats[END_REF][START_REF] Wang | PTH/SDF-1α cotherapy induces CD90+CD34-stromal cells migration and promotes tissue regeneration in a rat periodontal defect model[END_REF][START_REF] Yoshida | Combined effects of systemic parathyroid hormone (1-34) and locally delivered neutral self-assembling peptide hydrogel in the treatment of periodontal defects: An experimental in vivo investigation[END_REF][START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF]. A local injection at the gingival level was performed solely in the study of [START_REF] Tokunaga | Topical and intermittent application of parathyroid hormone recovers alveolar bone loss in rat experimental periodontitis[END_REF]. Several concentrations of PTH were used ranging from 5 μg/kg [START_REF] Tokunaga | Topical and intermittent application of parathyroid hormone recovers alveolar bone loss in rat experimental periodontitis[END_REF] to 160 μg/kg [START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF].

Timing and duration of PTH administration

In all studies, intermittent protocol of administration was performed. However, the frequency of administration as well as the treatment duration varied between studies. Different timing and duration of PTH administration protocols have been used. Indeed, most of the studies injected PTH each 2 days [START_REF] Barros | Parathyroid Hormone Protects against Periodontitis-associated Bone Loss[END_REF][START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF][START_REF] Lossdörfer | Anabolic effect of intermittent PTH(1-34) on the local microenvironment during the late phase of periodontal repair in a rat model of tooth root resorption[END_REF][START_REF] Tokunaga | Topical and intermittent application of parathyroid hormone recovers alveolar bone loss in rat experimental periodontitis[END_REF][START_REF] Vasconcelos | Intermittent Parathyroid Hormone Administration Improves Periodontal Healing in Rats[END_REF][START_REF] Yoshida | Combined effects of systemic parathyroid hormone (1-34) and locally delivered neutral self-assembling peptide hydrogel in the treatment of periodontal defects: An experimental in vivo investigation[END_REF]. The duration of administration varies between 3 [START_REF] Wang | PTH/SDF-1α cotherapy induces CD90+CD34-stromal cells migration and promotes tissue regeneration in a rat periodontal defect model[END_REF] and 84 days [START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF].

Bone healing

In all included studies, bone healing after PTH administration was evaluated as primary outcome. Different methods were used to compare bone regeneration, such as Micro-CT analysis [START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Tokunaga | Topical and intermittent application of parathyroid hormone recovers alveolar bone loss in rat experimental periodontitis[END_REF][START_REF] Yoshida | Combined effects of systemic parathyroid hormone (1-34) and locally delivered neutral self-assembling peptide hydrogel in the treatment of periodontal defects: An experimental in vivo investigation[END_REF], histomorphometric analysis [START_REF] Barros | Parathyroid Hormone Protects against Periodontitis-associated Bone Loss[END_REF][START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Lossdörfer | Anabolic effect of intermittent PTH(1-34) on the local microenvironment during the late phase of periodontal repair in a rat model of tooth root resorption[END_REF][START_REF] Otawa | Intermittent administration of parathyroid hormone ameliorates periapical lesions in mice[END_REF][START_REF] Tokunaga | Topical and intermittent application of parathyroid hormone recovers alveolar bone loss in rat experimental periodontitis[END_REF], immunohistochemistry [START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Lossdörfer | Anabolic effect of intermittent PTH(1-34) on the local microenvironment during the late phase of periodontal repair in a rat model of tooth root resorption[END_REF][START_REF] Wang | PTH/SDF-1α cotherapy induces CD90+CD34-stromal cells migration and promotes tissue regeneration in a rat periodontal defect model[END_REF][START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF], enzymohistochemistry [START_REF] Vasconcelos | Intermittent Parathyroid Hormone Administration Improves Periodontal Healing in Rats[END_REF] and polarizing light microscopy [START_REF] Vasconcelos | Intermittent Parathyroid Hormone Administration Improves Periodontal Healing in Rats[END_REF]. In all studies, an increase of newly formed bone was measured independently of the duration of administration [START_REF] Wang | PTH/SDF-1α cotherapy induces CD90+CD34-stromal cells migration and promotes tissue regeneration in a rat periodontal defect model[END_REF] and up to 84 days of treatment [START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF]. Interestingly, Lossdörfer et al. have studied the effect of PTH administration during the early and late phase of periodontal repair in a rat model. They have shown that the re-establishment of the imbalance of OPG/RANKL ratio induced by intermittent injection of PTH promoted hard tissue repair [START_REF] Lossdörfer | Anabolic effect of intermittent PTH(1-34) on the local microenvironment during the late phase of periodontal repair in a rat model of tooth root resorption[END_REF] (Tables 1234).

Inflammation response and vascularization

As periodontitis is an inflammatory disease, the influence of adjunctive treatment, i.e PTH administration, on soft tissue inflammation and inflammatory cytokines secretion is of importance. A decrease in inflammatory cell infiltration was observed following PTH treatment [START_REF] Barros | Parathyroid Hormone Protects against Periodontitis-associated Bone Loss[END_REF][START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Otawa | Intermittent administration of parathyroid hormone ameliorates periapical lesions in mice[END_REF]. Indeed, low, middle and high doses of PTHrP (1-34) could prevent upregulation of IL-1β and IL-6 secretion [START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF].

Interestingly, PTH may prevent or reverse the pro-inflammatory effects associated with lipopolysaccharide (LPS) stimulation emphasizing its anti-inflammatory properties [START_REF] Barros | Parathyroid Hormone Protects against Periodontitis-associated Bone Loss[END_REF].

Vascularization is a key phenomenon of wound healing as blood supply and development of micro-vascularization are mandatory. In the included studies, PTH administration induced an increase of VEGF-positive cells near blood vessels within the connective tissues and capillary ingrowth [START_REF] Yoshida | Combined effects of systemic parathyroid hormone (1-34) and locally delivered neutral self-assembling peptide hydrogel in the treatment of periodontal defects: An experimental in vivo investigation[END_REF].

Diabetes and PTH

Three studies have evaluated the influence of PTH treatment in bone healing in diabetics rats (streptozomicin-induced diabetes model) [START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF][START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF]. In this specific model, periodontitis was induced by ligature placement [START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF][START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF] or solely associated with the diabetes development [START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF]. Results

showed that PTH administration could decrease the periodontal damage caused by ligature placement and streptozocin-induced diabetes. Moreover, PTH injections seemed to decrease osteoclastogenesis in the alveolar bone tissue in periodontally-affected diabetic rats. Indeed, the number of osteoclasts in the diabetic group was more important than in control independently of the dosage of PTH [START_REF] Zhang | Parathyroid hormone-related peptide (1-34) reduces alveolar bone loss in type 1 diabetic rats[END_REF] (Table 2).

Discussion

This systematic review demonstrated that administration of PTH in the context of experimental periodontitis could be an interesting host-modulatory therapy that may be used as an adjuvant to periodontal treatment. However, mode and frequency of administration influence significantly the periodontal healing outcomes as PTH displays both anabolic (bone formation) and catabolic (bone resorption) properties.

PTH plays a role in several physiological mechanisms such as tooth eruption, and in periodontal tissue formation, emphasizing its potential application as a therapeutic agent [START_REF] Ono | Parathyroid hormone receptor signalling in osterix-expressing mesenchymal progenitors is essential for tooth root formation[END_REF]. PTH is already employed in the management of post-menopausal, male and cortisonic osteoporosis owing to its anabolic properties [START_REF] Dang | Local pulsatile PTH delivery regenerates bone defects via enhanced bone remodeling in a cell-free scaffold[END_REF]. In osteoporotic patients, administration of PTH and PTHrP analogs has already demonstrated its ability to promote bone formation through release of growth factors from the skeletal matrix and by decreasing apoptosis of osteoblasts [START_REF] Leder | Parathyroid Hormone and Parathyroid Hormone-Related Protein Analogs in Osteoporosis Therapy[END_REF]. Such anabolic effect is mainly related to the activation of cAMPprotein kinase signaling pathway associated with the induction of pro-osteogenic factors' expression [START_REF] Yoshida | Combined effects of systemic parathyroid hormone (1-34) and locally delivered neutral self-assembling peptide hydrogel in the treatment of periodontal defects: An experimental in vivo investigation[END_REF] (Figure 1). Moreover, PTH has also an inhibitory effect on the induction of sclerostin, consequently, contributing to bone formation [START_REF] Kim | Intermittent PTH administration improves alveolar bone formation in type 1 diabetic rats with periodontitis[END_REF]Zhang et al., 2020). Thus, pulsatile administration of PTH increases osteoblastic activity and decreases osteoclastic activity. PTH also reduces the RANKL/OPG ratio [START_REF] Chen | Intermittent administration of parathyroid hormone ameliorated alveolar bone loss in experimental periodontitis in streptozotocin-induced diabetic rats[END_REF]. A new synthetic analog of PTH and PTHrP, named abaloparatide, has been used for the management of osteoporosis [START_REF] Iolascon | Pharmacological Therapy of Osteoporosis: What's New?[END_REF]. The pharmacokinetics profile of PTH, PTHrP and abaloparatide are similar, and an intermittent administration is required for all [START_REF] Hattersley | Binding Selectivity of Abaloparatide for PTH-Type-1-Receptor Conformations and Effects on Downstream Signaling[END_REF]. These three molecules share many of their amino acid residues and abaloparatide exhibits 41% and 76% homology to PTH and PTHrP respectively [START_REF] Tella | Profile of Abaloparatide and Its Potential in the Treatment of Postmenopausal Osteoporosis[END_REF]. Intermittent administration is essential to obtain an anabolic response, resulting in an increase in osteoblast number. Indeed, this type of administration is similar to the physiological cycles of systemic PTH secretion [START_REF] Jilka | Molecular and cellular mechanisms of the anabolic effect of intermittent PTH[END_REF]. Such pulsatile administration of PTH induces a peak of Runx2 expression and anti-apoptotic signaling at each injection. Therefore, it activates short bursts of survival signaling causing repeated delay in apoptosis with an eventual reduction in the prevalence of damaged osteoblasts [START_REF] Jilka | Molecular and cellular mechanisms of the anabolic effect of intermittent PTH[END_REF]. At contrary, continuous PTH administration blocks osteoblastic differentiation (Wang et al., 2004) as observed in primary and secondary hyperthyroidism [START_REF] Rajkumar | Normocalcemic Hyperparathyroidism[END_REF]. This disease leads to skeletal deformities, bone pain and pathological fractures [START_REF] Bandeira | Bone disease in primary hyperparathyroidism[END_REF] associated to increased bone resorption and hypercalcemia [START_REF] Maruyama | Low bone mineral density due to secondary hyperparathyroidism in the Gla tm Tg(CAG-A4GALT) mouse model of Fabry disease[END_REF].

Furthermore, intermittent administration of PTH has already shown its efficiency in calvarial defect healing with a significant increase in bone mineral density (Silva et al., 2015).

Based on the beneficial properties of PTH and positive clinical outcomes obtained in the context of osteoporosis management, the use of PTH was evaluated for periodontal treatment purposes.

To our knowledge, only one randomized clinical trial was performed in Humans [START_REF] Bashutski | Teriparatide and Osseous Regeneration in the Oral Cavity[END_REF]. In this regard, 40 patients with severe chronic periodontitis were treated with periodontal surgery and concomitant teriparatide or placebo administration for 6 weeks. All of them received oral calcium and vitamin D supplementation during the treatment. The group treated with PTH displayed a faster bone healing compared with that of the placebo group. A significant bone gain was observed after 6 months and 1 year (29% in teriparatide treated group and 3% in placebo group). Periodontal probing depth and clinical attachment level were also improved with PTH treatment [START_REF] Bashutski | Teriparatide and Osseous Regeneration in the Oral Cavity[END_REF]. In this systematic review, we focused only on studies performed in experimental periodontitis induced in rodents. All included studies demonstrated a beneficial effect of PTH administration on periodontal and bone healing.

Interestingly, regardless of the periodontal defect, PTH was able to increase bone formation and to limit alveolar bone loss induced by periodontitis, even in case of diabetes. Moreover, PTH had an impact on soft tissue inflammation illustrated by a decrease in inflammatory cells infiltration.

The underlying mechanisms induced by the action of PTH on inflammation remain unclear.

However, PTH seems to cause a rapid decrease in the expression of inflammatory cytokines such as IL-1, IL-6, and TNF-α [START_REF] Dohke | Teriparatide rapidly improves pain-like behavior in ovariectomized mice in association with the downregulation of inflammatory cytokine expression[END_REF]. Such effect was also observed in a model of tooth extraction in rats, where intermittent PTH administration suppressed inflammation, promoted collagen synthesis and induced new blood vessels formation in addition to its pro-osteogenic properties [START_REF] Kuroshima | Distinctive toothextraction socket healing: bisphosphonate versus parathyroid hormone therapy[END_REF].

The use of PTH is associated to potential side effects such as nausea, vomiting, hypertension, dizziness and allergic reaction [START_REF] Valderrama | Evaluation of Parathyroid Hormone Bound to a Synthetic Matrix for Guided Bone Regeneration Around Dental Implants: A Histomorphometric Study in Dogs[END_REF]. A mild hypercalcemia could also be observed inducing the need of plasmatic calcium level monitoring [START_REF] Thiruchelvam | Teriparatide Induced Delayed Persistent Hypercalcemia[END_REF]. Therefore, mode of PTH administration appears to be of high importance. In the context of periodontal treatment, local administration appears the most promising due to increased anabolic effect on bone while reducing the risk of side effects [START_REF] Dang | Local pulsatile PTH delivery regenerates bone defects via enhanced bone remodeling in a cell-free scaffold[END_REF]. For local application, the relatively short half-life of PTH (8 minutes) induces the need of quick release of active molecule from the scaffold [START_REF] Dang | Local pulsatile PTH delivery regenerates bone defects via enhanced bone remodeling in a cell-free scaffold[END_REF]. Several strategies have been developed and evaluated to obtain a local delivery of the hormone in large bone defects [START_REF] Lopes | Bone physiology as inspiration for tissue regenerative therapies[END_REF] or around dental implants for bone regeneration [START_REF] Valderrama | Evaluation of Parathyroid Hormone Bound to a Synthetic Matrix for Guided Bone Regeneration Around Dental Implants: A Histomorphometric Study in Dogs[END_REF]. In these studies, new scaffolds such as hydrogel matrix and membranes were synthesized that induced significant bone regeneration [START_REF] Dang | Local pulsatile PTH delivery regenerates bone defects via enhanced bone remodeling in a cell-free scaffold[END_REF][START_REF] Wojda | Thiolene Hydrogels for Local Delivery of PTH for Bone Regeneration in Critical Size defects[END_REF]. Recently, a biodegradable 3D nanofibrous scaffold was developed to deliver locally the PTH intermittently for 21 days. This local pulsatile delivery decreased the risk of side effects, commonly observed in case of systemic administration and induced bone healing in a critical size calvarial defect [START_REF] Dang | Local pulsatile PTH delivery regenerates bone defects via enhanced bone remodeling in a cell-free scaffold[END_REF].

Rodents are often used to investigate molecular mechanisms involved in periodontitis and to validate potential treatment strategies [START_REF] Batool | Periodontal Tissues, Maxillary Jaw Bone, and Tooth Regeneration Approaches: From Animal Models Analyses to Clinical Applications[END_REF][START_REF] Graves | Animal models to study host-bacteria interactions involved in periodontitis[END_REF]. Indeed, their use can overcome the limitations associated with in vitro studies, especially, owing to their multicellular aspects and the lack of complexity in the mechanisms involved. In the context of PTH administration as adjuvant to periodontal treatment, several models were used in the identified studies. In most of the studies, periodontal lesion was induced either surgically or by mechanical trauma induced by ligature placement. Such models are of interest as they are well characterized and extensively used, however, they did not incorporate the infectious component found in periodontitis. Such parameter is of paramount importance as the presence of periodontal pathogens may alter the response to a potential treatment and bone regeneration as observed for Porphyromonas gingivalis [START_REF] Okumura | Experimental arthritis and Porphyromonas gingivalis administration synergistically decrease bone regeneration in femoral cortical defects[END_REF]. Nevertheless, a specific focus should be made on the PTH doses administered to the rodents. In the studies analyzing the impact of PTH on periodontal healing, PTH doses used ranged from 5 to 160 µg/kg. As observed in studies assessing the impact of PTH on long bone fracture healing in rats, the PTH doses used in these studies were high when compared to human equivalent doses. While using the Body Surface Area normalization method, 5, 40, 75, 80 and 160 µg/kg are comparable to 49, 390, 730, 778 and 1557 µg respectively for a human weighing 60 kg [START_REF] Reagan-Shaw | Dose translation from animal to human studies revisited[END_REF] which are high, considering the recommended dose for osteoporosis management (Tsai et al., 2019). As some studies demonstrated a dose-response effect, such parameter should be considered in future studies to allow translation of the results to Humans.

Nevertheless, this systematic review presents some limitations. Only few publications related to the evaluation of PTH in the context of periodontal treatment were available.

Moreover, the important variation of defect type and evaluation methods do not allow a metaanalysis.

Conclusion

Periodontal management of deep periodontal defects is challenging and new innovative adjuvant therapies should be developed to improve tissue regeneration. Within the limitations of this systematic review, intermittent administration of PTH appears to enhance significantly the periodontal healing and to promote alveolar bone regeneration. However, local cost-effective mode of intermittent PTH delivery should be developed and evaluated in Human randomized clinical trials.

Figures legends

Figure 1 :

 1 Figure 1: Implication of PTH and PTHrP on bone remodeling. PTHR-1 is expressed by osteoblast precursors and osteocytes. The binding of PTH to its receptor activates several intracellular pathways such as Gα/cAMP/PKA, Gαq/IPC/PLC, Gα12/13/RhoA/PLD. These signaling pathways lead to an increase in the expression of CREB, cFos, Runx2 and Osx involved in osteogenesis. Osteocytes synthetize ERK1/2 through the activation of MAPK pathways. ERK1/2 promote osteoblastic differentiation, decrease SOST/sclerostin leading to an increase of β-catenin that is involved in osteoblastic differentiation. The binding of PTH to PTHR-1 on osteoblast precursors results in an up-regulation of RANKL and a down-regulation of OPG expression inducing osteoclastic maturation. PTH is also involved in the recruitment of MSC at lesion site. AKT : Protein kinase B, cAMP : cyclic adenosine monophosphate, DAG : diacylglycérol, ERK : extracellular signal-regulated kinase, IP3 : inositol triphosphate, MAPK : mitogen-activated protein kinase, MSC : mesenchymal stem cells, OPG : osteoprotegerin, PKA : Protein kinase A, PKC : Protein kinase C, PI3K : phosphoinositide-3 kinase, PLC : phospholipase C, PTH : Parathyroid hormone, PTHrP : Parathyroid hormone related peptide, RANKL : Receptor activator of nuclear factor kappa-B ligand, SOST : sclerostin precursor, STAT5 : transducer and activator of transcription 5.

Figure 2 :

 2 Figure 2: Selection of the studies.

Table 1 :

 1 Studies evaluating the effect of PTH treatment after a periodontal defect surgically created with dental bur

	Tables
	Study	Species, Strain,	Test group(s) (n)	Test period	Type of	PTH / Control	Results
		Sex, Weight (g),		(days)	periodontal	(concentration)
		Age			defect	Administration
						mode
						Frequency
						Period (days)
	Yoshida et al.	Rats	PTH/SPG-178 (10)	14/28	Periodontal defect surgically created	PTH (1-34) 40 µg/kg	At 4 weeks, bone volume fraction is
		Wistar	PTH/Unfiled (10)		with dental bur	Combination	significantly
		Male	Saline/SPG-178		(1.8mm)	therapy	greater in the
		250-300g	(10)			Subcutaneous	PTH group
		10 weeks				injections	(p<0.0001).
						Intermittent	Approximately
						Every 2 days	30% increase in
						14 or 28 days	bone volume
							fraction.
							PTH improved
							bone formation
							PTH
							administration
							increased
							significantly
							VEGF-positive
							cells after 2 and 4
							weeks of
							treatment
							(p<0.05-0.0001
							)
	Wang et al.	Rats	SDF-1a only (15)	3/7/14/28/56	Periodontal defect	SDF-1a + PTH	At 2 weeks,
		Wistar	PTH only (15)		(length x height x	(1-34) (40 μg/kg)	increase in newly
		Male	PTH + SDF-1a		depth : 5mm x	Combination	formed bone with
		220-250g	(15)		4mm x 1mm)	therapy	PTH treatment
		8 weeks			surgically created	Intraperitoneal	(p<0.05)
					with dental bur	injection	PTH promotes the
						Intermittent	migration of
						3 days,7	CXCR4+ cells in
						days, 14 days,	periodontal
						28 days, 56days	defects (p<0.05)
	Vasconcelos et al.	Rats	Treated group	14/21	Periodontal defect	PTH (1-34) (40	PTH
		Wistar	T14 (8)		surgically created	μg/kg)	administration
		Male	Treated group		with dental bur	Subcutaneous	increases bone
		254+/-16,6g	T21 (8)		(2mm)	injections	formation
		8 weeks				Intermittent	(p<0.01) and
						administration	decreases
						Every 2 days,	remaining bone
						14 or 21 days	defect extension
							(p<0.01)

Table 2 :

 2 Studies evaluating the effect of PTH treatment in diabetic animals with periodontitis

	Study	Species, Strain, Sex, Weight(g), Age	Test group(s) (n)	Test period (day)	Type of periodontal defect	PTH / Control Period (day) (concentration) Frequency Administration mode	Results
	Otawa et al.	Mice Homozygous mutant for LTA (Jackson) Male 8 weeks	Periodontitis + VC (7) Periodontitis + PTH (7)	30	Pulp exposure the mandibular molar to assess the effect of plaque contamination Periapical lesions Ligature -periodontitis	PTH(1-34) (40 μg/kg/day) subcutaneous injections Intermittent Daily 21 days	PTH treatment reduced inflammation and protected against tissue destruction by periodontitis (p<0.001)
	Tokunag a et al.	Rats Fischer Male 8 weeks	PTH low dose (6) PTH high dose (6) Control (12)	35/70	Periodontitis -Ligature	PTH (1-34) Low dose (1μg/50μL) High dose (5 μg/50μL) Buccal gingiva injections Intermittent 3 times a week 35 or 70 days	PTH increased significantly mineralized area of bone nodule 56% and 29% of the total bone loss were reversed by treatment with low and high dose of PTH respectively (p<0.005)
			PTH + ligature
	Barros et al.	Rats Wistar Male 4 weeks	(105) PTH -ligature (10) Placebo + ligature (10)	30	Periodontitis -Ligature	PTH (1-34) (40 μg/kg) Subcutaneous injections Intermittent 3 times/week 28 days	Number of inflammatory cells decreased in PTH-treated group compared with placebo group (p<0.05)

Table 3 :

 3 Studies evaluating the effect of PTH treatment after periodontitis induced by ligature

Table 4 :

 4 Studies evaluating the effect of PTH treatment after orthodontic force induced periodontal lesion

	Study	Species, Strain, Sex, Weight(g), Age	Test group(s) (n)	Test period (d)	Type of periodontal defect	PTH / Control (concentration) Administration mode Frequency Period (d)
	Lossdör fer et al.	Rats Wistar Male 300g 3 months old	7 groups (10)	8/10/1 4/17/2 1/70	Orthodontic forces (5 days) Periodontal lesions -necrosis -root resorption	PTH (5 μg/kg) Subcutaneous injections Intermittent Every second day for 8,10,14,17,21, 56 and 70 days	PTH administration failed to alter OPG expression in the early phase of periodontal repair but enhanced it significantly in the late phase from day 21

Table 5 :

 5 Quality and risk of bias assessment

		Sequence	Baseline	Allocation	Random	Investigator	Random	Blinding	Incomplete	Selective	Ethical	Score
		generation	characteristics	concealment	housing	blinding	outcome	of	outcome	outcome	consideration
							assessment	outcome	data	reporting
	Yoshida et	U	Y	U	Y	U	U	U	Y	Y	Y	5
	al.
	Kim et al.	U	N	U	U	U	U	U	U	Y	Y	2
	Chen et al.	Y	Y	U	Y	U	U	U	U	Y	Y	5
	Zhang et al.	Y	N	U	U	U	U	U	U	Y	Y	4
	Wang et al.	Y	Y	U	U	U	U	U	U	Y	Y	4
	Otawa et al.	U	Y	U	U	U	U	U	Y	Y	Y	5
	Vasconcelos	U	Y	U	Y	U	U	U	Y	Y	Y	5
	et al.
	Tokunaga et	U	Y	U	Y	U	U	U	Y	Y	Y	5
	al.
	Lossdörfer	U	Y	U	Y	U	U	U	N	Y	Y	4
	et al.
	Barros et al.	Y	Y	U	Y	U	U	U	Y	Y	Y	6

Conflict of interest and source of funding statement

The authors have stated explicitly that there are no conflicts of interest in connection with this article. No specific funding was received for this review. This article does not contain any studies with human participants performed by any of the authors.