Xiaotao Wu

Claude H Moog

Yueming Hu

Modelling and Linear Control of a Buoyancy-Driven Airship

We describe the modelling and control of a newkind airship which is propelled by buoyancy. Based on the Newton-Euler equations and Kirchhoff equations, and referred to the models of underwater gliders and aircraft, a 6DOF nonlinear mathematical model of a buoyancy-driven airship is derived, with features distributed internal mass, and no thrust, elevators and rudders. The attitudes are controlled by the motion of internal mass. The performances of the airship are studied in the vertical plane. A linear feedback controller is derived for the nonlinear model. The results of simulation display robustness properties of the controllers to disturbances.

I. INTRODUCTION

Stratospheric platforms or high altitude platforms, which locate 17-22 km above the ground, and keep quasigeostationary positions, attract an increasing research interest for these recent ten years. Such a platform has the potential capability to serve as a wireless communication relay station and as a high resolution observing station [START_REF] Elfes | Project AURORA: development of an autonomous unmanned remote Monitoring Robotic Airship[END_REF], [START_REF] Tozer | High-altitude platforms for wireless communications[END_REF], [START_REF]Lighter Than Air Systems for Future Naval Missions Briefing: Flag Officers and Senior Executive Service[END_REF].

A high altitude unmanned airship as this platform has the following features; driven by solar power makes it longendurance in high altitude, and generally this platform can take 1000 kg to 3000 kg payload which is a low cast methods to carry out similar functions of satellites. A conventional airship is driven forward by propulsors along the hull, the attitude is controlled by elevators and rudders or vectorpropulsors. Buoyancy-driven airships move forward by a cyclic change of the net buoyancy of the craft and of the position of ballast. This concept of airship comes from underwater gliders who replace traditional thrust propulsion by a cyclic This work was supported by CSC X. WU is with Institut de Recherche en Communications et Cybernétique de Nantes, 1 rue de la Noë, 44321, Nantes, France, and South China University of Technology xiaotao.wu@irccyn.ec-nantes.fr C. H. MOOG is with Institut de Recherche en Communications et Cybernétique de Nantes, claude.moog@irccyn.ec-nantes.fr Y. HU is with South China University of Technology, auymhu@scut.edu.cn change of the net buoyancy and of the position of the centroid, which has been proved to be efficient in water [START_REF]Nonlinear gliding stability and control for vehicles with hydrodynamic forcing[END_REF]. Underwater gliders cruise for long distances consumed little power. The structure of this new-kind airship see Figure 1. The blower is used to fill an impermeable inner bladder with ambient air, and the valve is used to release the inner air. The ballast can move in the horizontal plane. The mechanism of operating this kind of airship is as follows. When releasing air from ballonets, the mass of the airship reduces, the lift becomes positive. Accompanying the ballast moves to the tail, the airship gets a positive pitch angle θ, and moves upward and forward, see Figure 2. Oppositely, when pumping air into ballonets, the airship mass increases, the lift decreases and becomes minus. Accompanying the ballast moving to the head, the airship gets a negative pitch angle θ, and moves downward and forward, see The environment of high altitude is quite different from underwater. Comparing with incompressible water, air is compressible. The density, temperature, and pressure of atmosphere is changing with the change of altitude. All of this make high altitude airship have some differences from underwater gliders, and more difficult to control.

At present, most research on airship control is based on airships with actuators-thrusts and elevators [START_REF] Beji | Position and attitude control of an underactuated autonomous airship[END_REF]- [START_REF] Gomes | Airship dynamic modeling for autonomous operation[END_REF]. Almost no paper discusses the possibility of airship driven by buoyancy, just as underwater gliders. The only monograph available on buoyancy-driven airship is the doctoral disserta-tion [START_REF] Purandare | A buoyancy-propelled airship[END_REF]. This pioneering study includes the effect of various atmospheric conditions. However, the complete mathematical model of 6DOF is not given, and the control method also needs to be improved.

The contributes in the rest of this paper are as follows. The complete equations of 6DOF motion are given for the first time for a high altitude airship only driven by buoyancy. It includes the modelling of the ballast and the ballonets. This full model is derived from the model of the underwater glider. Dynamic performances have been studied, and a linear controller have been tested.

In section II, the mathematical model of a high altitude buoyancy-driven airship is derived. In section III, the model is specialized to the vertical plane. Then the nonlinear model has been linearized, the static stability and controllability has been analysed. In section IV, a LQR controller has been derived for the nonlinear system and the simulations are presented.

II. AIRSHIP DYNAMIC MODELLING

A. Kinematics

Figure 1 shows the assignment of the two frames. The body frame {O, e 1 , e 2 , e 3 } is assigned with the reference point O at the center of hull, overlapped with the center of buoyancy CB. The inertial {G, i, j, k} frame is fixed to the earth, with the axis k along the direction of gravity [START_REF] Gomes | Airship dynamic modeling for autonomous operation[END_REF].

To reduce the drag of the body, the hull of airship is designed to have a high volume/surf ace -area ratio. The shape comes from revolving of an airfoil profile. The airfoil profile can be chosen from NACA series of US. A ellipsoid has been used to represent that special shape for simple in this paper, and given that the equatorial radii and the polar radius are 7 m, 3 m and 3 m respectively.

The rotation matrix between the body frame and the inertial frame is represented by R 1 which is composed by the pitch angle θ, the yaw angle ψ and the roll angle φ The position of the airship in the inertial frame is represented by vector b = (x, y, z) T ∈ 3 , see Figure 1. R 1 ∈ SO(3), SO(3) is 3×3 special orthogonal matrix, defined as follows:

SO(3) = {R 1 ∈ 3×3 |RR T = I, detR = 1}
here I denotes a 3 × 3 identity matrix. The attitude and position of the airship is decided by (R 1 , b). So the configuration space of the system is defined as: 3) can be represented by homogeneous coordinates, as follows: 3) is a rotation matrix group. For example, if G ∈ SE( 3), then G is a transformation matrix of the rigid body from body frame to the inertial frame [START_REF] Leonard | Stability of a bottom-heavy underwater vehicle[END_REF].

SE(3) = {(b, R 1 )|b ∈ 3 , R 1 ∈ SO(3)} = 3 × SO(3) SE(
R 1 b 0 1 ∈ SE(3) SE(
Let V = (v 1 , v 2 , v 3 ) T and Ω = (Ω 1 , Ω 2 , Ω 3
) denote the velocity and the angular velocity in the body frame respectively. So the position and the attitude of the airship can be described by the Lie algebra of SE( 3), denoted as the group se [START_REF]Lighter Than Air Systems for Future Naval Missions Briefing: Flag Officers and Senior Executive Service[END_REF]. It is as follows:

Ω V 0 0 ∈ se(3)
Define the operator ∧ for a vector 3), where so( 3)is the Lie algebra of SO [START_REF]Lighter Than Air Systems for Future Naval Missions Briefing: Flag Officers and Senior Executive Service[END_REF]. The kinematics of the airship are given by The airship described in this paper is driven by the buoyancy and the ballast, just like some underwater gliders [START_REF] Leonard | Model-based feedback control of autonomous underwater gliders[END_REF]. To set up the mathematical model, The entire mass of airship have to be splited into several terms. Let m h denote the uniformly distributed hull mass, m b is the variable mass of ballonets, m is the mass of the inside movable ballast, and m w denotes other inside fixed masses whose centroid offset from CB. r p = (r p1 , r p2 , r p3 ) T , r b and r w are the vectors from CB to the mass points of ballast, the ballonet and m w , see Figure 4.

x = (x 1 , x 2 , x 3 ) T ∈ 3 , x =   0 -x 3 x 2 x 3 0 -x 1 -x 2 x 1 0   and x ∈ so(
Ṙ1 ḃ 0 0 = R 1 b 0 1 Ω V 0 0 (1)

B. Mass Distribution and Definition

The mass m s is the total stationary mass, thus m s = m h + m b + m w . The total mass of the vehicle is m v , so we have:

m v = m s + m = m h + m b + m w + m. Let m = ρ a ∇
is the buoyancy of the airship with volume ∇. Thus, the net buoyancy of the airship is m 0 = m v -m. In this paper, m h = 269 kg, m = 30 kg, and m w , r b and r w are neglected.

C. Fluid Inertia Forces and Added Mass

The inertia of airships with a large V olume/M ass ratio is much more significant in comparison with conventional airplanes. So, fluid inertial forces should be considered.

In the case of the motion of a rigid body in an ideal fluid with velocity v i in the direction i, the force acted on the rigid body by the fluid in the direction j is R j = -m ij vi and the parameter m ij is called the added mass. There are 36 added masses for a rigid body in motion; the matrix M add including those added masses is called the inertia matrix [START_REF] Beji | Position and attitude control of an underactuated autonomous airship[END_REF].

M add = M f * * J f
M f is the symmetric 3 × 3 added mass matrix; J f is the added inertia matrix; and the other two blocks are added cross terms which are neglected. Here, It is supposed that the airship is centrosymmetric, so only elements on the diagonal are nonzero, other elements are zero because of symmetry. So, M f = diag{m 11 m 22 m 33 } and J f = diag{m 44 m 55 m 66 }. In this paper, m 11 = 0.8m h , m 33 = m h and m 55 = 1.3J yy . J yy is the moment of inertia of the airship around y axis, and approximately,

J yy = m(a 2 + b 2 )/5 ≈ 3500 kg • m 2 .
In an ideal fluid, the kinetic energy T add of fluid disturbances is

T add = 1 2 6 i=1 6 j=1 m ij ζ i ζ j = 1 2 (m 11 v 2 1 + m 22 v 2 2 +m 33 v 2 3 + m 44 Ω 2 1 + m 55 Ω 2 2 + m 66 Ω 2 3 )
here

ζ 1 = v 1 , ζ 2 = v 2 , ζ 3 = v 3 , ζ 4 = Ω 1 , ζ 5 = Ω 2 , ζ 6 = Ω 3 . The momenta B = (B 1 , B 2 , B 3 ) T and moments of momentum K = (B 4 , B 5 , B 6 )
T of fluid disturbances are related to the kinetic energy T add :

B i = ∂T add ∂ζ i (i = 1, 2, • • • , 6) So, B = M f v K = J f Ω
So, the inertial forces F I and moments M I acting on the airship are as follows

F I = - dB dt = -( d B dt + Ω × B) = -M f v + M f v × Ω (2)
M I = - dK dt = -( d K dt + Ω × K + v × B) = -J f Ω + J f Ω × Ω + M f v × v (3)
here, dB dt , dK dt denote the time-derivative of momentum B and angular momentum K with respect to the inertial frame,

D. Aerodynamic forces and moments

Different pneumatic pressures are distributed on the surface of a vehicle flying in the atmosphere. The effect of those pneumatic pressures can be presented by aerodynamic forces F a and moments M a as follows,

F a = (X a , Y a , Z a ) M a = (L a , M a , N a )
The aerodynamic forces are contributing by the forces and moments on the hull and fin and act on the center of buoyancy CB. By convention, the decomposed aerodynamic forces lie in the velocity frame (also called the wind frame), and the moments are decomposed in the body frame [START_REF] Mueller | Development of an aerodynamic model and control law design for a high altitude airship[END_REF].

Drag : X a = 1 2 ρ a V 2 (S h C x1 + S f C x2 ) Sidef orce : Y a = 1 2 ρ a V 2 (S h C y1 + S f C y2 ) Lif t : Z a = 1 2 ρ a V 2 (S h C z1 + S f C z2 ) Roll moment : L a = 1 2 ρ a V 2 (S h l h1 C l1 + S f l f 1 C l2 ) P itch moment : M a = 1 2 ρ a V 2 (S h l h2 C m1 + S f l f 2 C m2 ) Y aw moment : N a = 1 2 ρ a V 2 (S h l h3 C n1 + S f l f 3 C n2 )
here, ρ a is the density of ambient air, S h and S f are the reference areas of hull and fin, l h1 , l h2 , l h3 and l f 1 , l f 2 , l f 3 are the distances from the CB to the aerodynamic center of the hull and fin. The C i 's are the aerodynamic coefficients which are computed from wind tunnel experiments. Those coefficients do mainly depend on the angle of attack α and the sideslip angle β.

Since F a is respected to the velocity frame, F a is transferred to the body frame, which denotes by F at .

F at =   cos α cos β cos α sin β -sin α -sin β cos β 0 sin α cos β sin α sin β cos α   F a = R 2 F a ( 4
) where R 2 the transfer matrix from the velocity frame to the body frame. M a is respected to the body frame, so,

M at = M a (5)

E. Gravity and Buoyancy

In the inertial frame, the composite effect of gravity and buoyancy along the axis of inertial frame is denoted by F GB as follows,

F GB = m 0 gk
where, k is a unit vector pointing in the direction of gravity. F GB is transferred to the body frame as follows,

F GBt = R T 1 F GB = m 0 gR T 1 k (6)
It is assumed that the centroid of the stationary mass m s is on CB. So there is no moment which is caused by m s and the buoyancy of the airship. Only the ballast have moments since r p is not zero. In the inertial frame, the moment is

M GB = m 0 gr s × k
which is transferred to the body frame as follows,

M GBt = R T 1 M GB = m 0 gR T 1 r s × k (7)

F. Dynamics of the Ballast

Let r p be the position of the ballast in the body frame. If the airship is rotating with angular velocity Ω. According to the relation between the absolute velocity and the relative velocity, the absolute velocity of the ballast in the body frame v p is as follows,

v p = v + ṙp + Ω × r p
Let B p = (B p1 , B p2 , B p3 ) T denote the momentum of the ballast, and u = (u 1 , u 2 , u 3 ) T denote the total external force acting on the ballast. Both B p and u are with respect to the body frame. So that,

B p = mv p = m(v + ṙp + Ω × r p ) (8) Ḃp = u (9)
From ( 8), one gets,

ṙp = 1 m B p -v -Ω × r p (10)

G. Model

Let B total and K total be the total momentum and the total moment of momentum of the airship. one gets,

B total = m s v + B p (11) K total = J s Ω + r p × B p (12)
here J s is the matrix of the moment of inertia of the airship. Let F total and M total be the total external force and the total moment of the airship. From equation ( 2) to [START_REF] Ouyang | Research on modeling and control of an unmanned airship[END_REF], F total and M total be computed as follows, 2) and (3), F total and M total are derived from [START_REF] Leonard | Model-based feedback control of autonomous underwater gliders[END_REF] and (12) as follows,

F total = F I + F at + F GBt (13) = -M f v + M f v × Ω + +m 0 gR T 1 k + F at M total = M I + M at + M GBt (14) = -J f Ω+ J f Ω × Ω+ M f v × v + m 0 gR T 1 r s × k + M at Similar to equation (
F total = dB total dt = d Btotal dt + Ω × B total M total = dK total dt = d Ktotal dt + Ω × K total + v × B total
Substituted (9), ( 11) and (12) into above equations, then,

F total = m s v + u + m s Ω × v + Ω × B p ( 15
)
M total = J s Ω + ṙp × B p + r p × u -J s Ω × Ω -m s v × v + Ω × (r p × B p ) + v × B p (16)
Substituted ( 10) into ( 16), then gets,

M total = J s Ω -Ω × r p × B p + r p × u -J s Ω × Ω -m s v × v -r p × B p × Ω (17)
v is derived from ( 13) and (15) as follows,

v = M -1 (M v + B p ) × Ω + m 0 gR T 1 k + R 2 F a -u (18) where, M = m s I + M f = diag(m 1 , m 2 , m 3 ). I is the 3 × 3 identity matrix.
Similarly, Ω is derived from ( 14) and ( 17) as follows,

Ω = J -1 ((J Ω + r p × B p ) × Ω + Ω × r p × B p + M v × v + mgr p × R T 1 k + M a -r p × u) (19) where, J = J s + J f = diag(J 1 , J 2 , J 3 ).
As the airship is driven by change of buoyancy, it is necessary to control the mass of ballonets, through the input u 4 , as

ṁb = u 4 (20)
Combining with equations ( 1), ( 18), ( 19), ( 10), ( 9) and ( 20) , the mathematical model of a buoyancy-driven airship is obtained as

          Ṙ1 ḃ v Ω ṙp Ḃp ṁb           =           R 1 Ω R 1 v M -1 F J -1 M 1 m B p -v -Ω × r p u u 4           (21)
where, M is a moment matrix, and F is a force matrix. The values of M and F is as follows,

M = (J Ω + r p × B p ) × Ω + Ω × r p × B p +M v × v + mgr p × R T 1 k + M a -r p × u F = (M v + B p ) × Ω + m 0 gR T 1 k + R 2 F a -u

III. A SPECIAL CASE OF THE AIRSHIP DYNAMICS

A. Dynamics in the Vertical Plane

This mathematical model ( 21) has many complex couplings, which make it difficult to analyse by conventional ways as decoupling of the longitudinal plane and the lateral plane through decoupling [START_REF] Beji | Position and attitude control of an underactuated autonomous airship[END_REF]. Thus, we restrict the airship in the vertical plane.

The airship has to be driven by a periodic change of net buoyancy. The airship moves in a saw-tooth pattern path. So the most ideal and simplest condition is that the airship only moves in the vertical plane e 1 -e 3 and it is assumed not to be disturbed by the wind and the atmosphere. Thus, it is assumed that there is no wind, and the density, pressure, temperature of atmosphere are constant; the vertical plane of the body frame and the inertial frame do coincide.

Since the airship only flies in the vertical plane, some states are set to zero. Thus, attitude angles ψ = φ = 0, position y = 0, velocity v 2 = 0, angular velocities Ω 1 = Ω 2 = 0. And we also suppose the ballast only move in the vertical plane, so r p2 = 0, B p2 = 0 and u 2 = 0.

Substituting the above restricted conditions into the mathematical model ( 21), the motion equations in the vertical plane reduce to,

θ =Ω 2 (22) Ω2 = 1 J 2 ((m 3 -m 1 ) v 1 v 3 -(r p1 B p1 + r p3 B p3 )Ω 2 + M a -mg(r p1 cos θ + r p3 sin θ) + r p1 u 3 -r p3 u 1 ) (23) v1 = 1 m 1 (-m 3 v 3 Ω 2 -B p3 Ω 2 -m 0 g sin θ + X a cos α -Z a sin α -u 1 ) (24)
v3 = 1 m 3 (m 1 v 1 Ω 2 + B p1 Ω 2 + m 0 g cos θ + X a sin α + Z a cos α -u 3 ) (25) ṙp1 = 1 m B p1 -v 1 -r p3 Ω 2 (26) ṙp3 = 1 m B p3 -v 3 + r p1 Ω 2 (27) Ḃp1 =u 1 (28) Ḃp3 =u 3 (29) ṁb =u 4 (30)
Here, the drag, lift and pitch moment in the vertical plane are simplified as follows,

X a = 1 2 ρ a ∇ 2/3 v 2 (C x0 + C α x α 2 ) Z a = 1 2 ρ a ∇ 2/3 v 2 (C z0 + C α z α) M a = 1 2 ρ a ∇v 2 (C m0 + C α m α)

B. A Nonlinear Feedback Controller

To keep control of the attitude and velocity of the airship, let new control input ũ = (ũ 1 , ũ2 , ũ3 ) T . Differentiating (22), with (24) and (25), then gives

  θ v1 v3   =   ũ1 ũ3 ũ4   = -P + C   u 1 u 3 u 4   (31)
Form differentiating ( 22), ( 24) and (25), matrices P and C can be derived. Thus, we can get nonlinear state feedback from (31),

  u 1 u 3 u 4   = C -1     ũ1 ũ3 ũ4   + P   (32)
which linearizes θ, v1 and v3 with respect to the new input ũ. Substitute (32) into (24)-(30), and get the motion equations of the airship with a nonlinear states controller in the vertical plane. Results of (31) will be published elsewhere.

C. Static Stability Analysis

As Figure 5, the airship driven by buoyancy flies along an oblique line with angle ξ e during equilibrium cruise. At a time t, the airship is at the position (x, z) in the vertical plane with respect to the inertial frame, and (x , z ) in the coordinate i -G -k . According to the rotation matrix, the distance from the airship to the desired path is as follows, see Figure 6, z = -sin ξ e x + cos ξ e z (33)

Differentiating (33) and substituting v 1 , v 3 and θ into it. The perpendicular velocity to desired path is

ż = -sin ξ e (v 1 cos θ + v 3 sin θ) + cos ξ e (-v 1 sin θ + v 3 cos θ) (34)
During the equilibrium cruise, equations ( 24)-( 30) and ( 33) are all equal to zero. Through those equations, the equilibrium states x e = (θ e , Ω 2e , v 1e , v 3e , r p1e , r p3e , B p1e , B p3e , m be , z e ) T and input u e = (u 1e , u 2e , u 3e ) T during cruise under desired path angle ξ e and speed V e can be got.

The nonlinear model ( 22)-( 30) can be simulated directly in MATLAB through the principle of digital integration, but the relation between parameters and performances of the system can not be clear revealed from the nonliear model. Thus, as conventional [START_REF] Beji | Position and attitude control of an underactuated autonomous airship[END_REF], small disturbance method is used to linearize the mathematical model around the equilibrium. The static stability of the airship around the equilibrium can be studied through the linearized model.

The motion of airship can be splited into two motions, the benchmark motion x e and u e which are the values on the equilibrium, and the disturbing motion ∆x and ∆u which are the values away from the equilibrium. Substituting x = x e + ∆x and u = u e + ∆u into (22)-( 30) and (34), the result only keep the first-order of ∆x and ∆u, neglected high-order terms. Then, the linearized model is as follows,

∆ ẋ = A∆x + B∆u (35)
where, A is a 12 × 12 constant system matrix, and B is a 12 × 3 input matrix.

Given that the airship is desired to fly with the angler ξ e = 15 • and the volecity V e = 10 m/s. After computered the values of states on that equilibrium and linearization, the values of matrix A and B can be got. The eigenvalues of the system are not totally stable, but the system is controllable.

IV. LQR CONTROLLER OF THE AIRSHIP

In this section, we design a simple linear feedback controller for the nonlinear system ( 22)-(30), and demonstrate the performance of that controlled flying in the vertical plane. This simple linear controller is not good enough with large initial errors, and which need improve. The linear quadratic regulator (LQR) is a well-known design technique that provides practical feedback gains. It is assumed that all the 10 states ∆x are available for the controller. The infinite horizon cost function is defined as,

J = ∞ 0 ∆x T Q∆x + ∆u T R∆u dt
The weight matrices Q and R are tuning parameters and their choice will decide about the performance of the closed loop system. In this simulation, Q = (2, 1, 2, 2, 1, 1, 1, 1, 0.5, 1) T , R = (0.1, 0.1, 0.1) T .

The feedback gain is a matrix K, implemented as,

∆u = -K(x-x desired ) = -K(x-x e ) = -K∆x (36)
where, K is easily computed by MATLAB. Substitute the linear feedback controller (36) into nonlinear equations in the vertical plane ( 22)-(30). Given ξ e = 15 • and the volecity V e = 10 m/s, so α e = -10 • , v 1 = 9.8 m/s and v 3 = -1.7 m/s. If there is a abrupt wind led up to +2 m/s offset of v 1 . Figure 6 is the simulation of the nonlinear system with controller (36) under that initial errors, and Figure 7 is the flying path of the airship in this situation.

The system can converge to the equilibrium after 15 seconds with that LQR controller. But the system will be unstable with larger initial errors.

V. CONCLUSION

In this paper, A novel airship has been studied, which is driven by a cyclic changing the net buoyancy of the airship, and the attitude is controlled by moving the internal ballast. There are not conventional thrusts, elevators and rudders.

Referred to the model of underwater glider, a full 6DOF nonlinear model of the airship has been derived with the ballast and the ballonet being considered separately. The mathematic model is similar to the model of underwater sliders, but it is derived by a general aerial way [START_REF] Gomes | Airship dynamic modeling for autonomous operation[END_REF], [START_REF] Leonard | Model-based feedback control of autonomous underwater gliders[END_REF]. The dynamics in the vertical plane has been derived. A Compared to most of the prevalent high-altitude airship researches, this paper give out a novel concept of the highaltitude airship. Compared to the conventional engine-driven airship, the new kind airship is driven by buoyancy. This driving method aims at making the airship cruise long distant with consuming little energy.

Future research perspectives include the effects of the various atmospheric density, temperatures and pressure with the change of altitude based on this model, and the design of a better performance nonlinear controller. The dynamics in the lateral plane also need be considered.

Fig. 1 .

 1 Fig. 1. Structure of Buoyancy-Driven Airship

Fig. 2 .

 2 Fig. 2. Ascent of the Buoyancy-Driven Airship

Figure 3 .

 3 If the ballast is moving to side, then the airship will roll. Due to the coupling of roll and rotation moments, the airship flies to the right or the left.

Fig. 3 .

 3 Fig. 3. Descent of the Buoyancy-Driven Airship

Fig. 4 .

 4 Fig. 4. Mass Distribution

K

  dt denote the time-derivative in the body frame.

Fig. 5 .

 5 Fig. 5. Flying Sketch

Fig. 6 .

 6 Fig. 6. Simulation Result

Fig. 7 .

 7 Fig. 7. Flying Path


Maartje F A Verploegen

Rosa Vargas-Poussou

Stephen B Walsh

Harika Alpay

Atefeh Amouzegar

Gema Ariceta

Bahriye Atmis

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Tom Nijenhuis
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Parathyroid hormone and phosphate homeostasis in patients with Bartter and Gitelman syndrome

Keywords: Bartter syndrome, Gitelman syndrome, parathyroid hormone, phosphate, salt losing tubulopathies

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INTRODUCTION

Bartter and Gitelman syndrome are genetically distinct hereditary salt-losing tubulopathies that are characterized by hypokalaemic metabolic alkalosis secondary to impaired reabsorption of sodium chloride (NaCl) in different segments of the renal tubule [START_REF] Seyberth | Bartter's and Gitelman's syndrome[END_REF][START_REF] Besouw | Bartter and Gitelman syndromes: questions of class[END_REF]. Bartter syndrome is further classified into different subtypes. Bartter syndrome type I and II are caused by biallelic mutations in the SLC12A1 gene encoding the NKCC2 sodium-potassium-chloride cotransporter and by biallelic mutations in the KCNJ1 gene encoding the ROMK potassium channel, respectively, both of which are expressed in the thick ascending limb of the loop of Henle (TAL). Bartter syndrome type III results from biallelic mutations in the CLCNKB gene, which encodes the ClC-Kb chloride channel. Bartter syndrome type IV is caused by biallelic mutations in the BSND gene that encodes Barttin, or by molecular abnormalities affecting the two adjacent CLCNKA (encoding the chloride channel ClC-Ka) and CLCNKB genes. Barttin and ClC-Kb are expressed in the TAL and distal convoluted tubule (DCT); ClC-Ka is only expressed in the TAL. Finally, a transient X-linked form of Bartter syndrome (type V Bartter syndrome) has been described in male patients harbouring mutations in the MAGED2 gene, which alters the expression of the NKCC2 and NCC, the sodium chloride cotransporter. Gitelman syndrome is caused by biallelic mutations in the SLC12A3 gene, encoding the NCC, of which the expression is restricted to the DCT.

While Bartter and Gitelman syndromes share similarities, including hypokalaemia, metabolic alkalosis, hyperreninemic hyperaldosteronism and low/normal blood pressure, differences in the tubular segments where NaCl reabsorption is compromised produce different clinical pictures [START_REF] Besouw | Bartter and Gitelman syndromes: questions of class[END_REF]. Patients with Gitelman syndrome usually present in late childhood or early adulthood. Typically, patients with Gitelman syndrome have hypomagnesemia and hypocalciuria. Conversely, type I and II Bartter syndrome patients usually present antenatally with polyhydramnios and postnatally with severe polyuria, hypercalciuria and early onset nephrocalcinosis. Patients with type III Bartter syndrome have variable phenotypes that, in some cases, are difficult to distinguish from Gitelman syndrome. The large phenotypic spectrum of Bartter III patients is most likely explained by variable expression of the pathogenic gene product in the TAL and DCT and by the possibility of partial compensation by other chloride channels, in particular, ClC-Ka in the TAL.

In recent years, several investigators have observed abnormal levels of parathyroid hormone (PTH) and serum phosphate in patients with Bartter and Gitelman syndrome [START_REF] Bettinelli | Phosphate homeostasis in Bartter syndrome: a case-control study[END_REF][START_REF] Gross | Antenatal Bartter syndrome presenting as hyperparathyroidism with hypercalcemia and hypercalciuria: a case report and review[END_REF][START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF][START_REF] Leonhardt | Calcium homeostasis and hypercalciuria in hyperprostaglandin E syndrome[END_REF][START_REF] Li | Association of mutations in SLC12A1 encoding the NKCC2 cotransporter with neonatal primary hyperparathyroidism[END_REF][START_REF] Wongsaengsak | A novel SLC12A1 gene mutation associated with hyperparathyroidism, hypercalcemia, nephrogenic diabetes insipidus, and nephrocalcinosis in four patients[END_REF][START_REF] Zuo | Eight novel KCNJ1 variants and parathyroid hormone overaction or resistance in 5 probands with Bartter syndrome type 2[END_REF][START_REF] Akhtar | A rare case of Gitelman's syndrome with hypophosphatemia[END_REF][START_REF] Ali | A case of Gitelman syndrome with severe hyponatraemia and hypophosphataemia[END_REF][START_REF] Katopodis | Hypophosphataemia in a patient with Gitelman's syndrome[END_REF][START_REF] Vigano | Renal phosphate handling in Gitelman syndrome-the results of a case-control study[END_REF]. Patients with Bartter syndrome tend to have a high PTH [START_REF] Bettinelli | Phosphate homeostasis in Bartter syndrome: a case-control study[END_REF][START_REF] Gross | Antenatal Bartter syndrome presenting as hyperparathyroidism with hypercalcemia and hypercalciuria: a case report and review[END_REF][START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF][START_REF] Leonhardt | Calcium homeostasis and hypercalciuria in hyperprostaglandin E syndrome[END_REF][START_REF] Li | Association of mutations in SLC12A1 encoding the NKCC2 cotransporter with neonatal primary hyperparathyroidism[END_REF][START_REF] Wongsaengsak | A novel SLC12A1 gene mutation associated with hyperparathyroidism, hypercalcemia, nephrogenic diabetes insipidus, and nephrocalcinosis in four patients[END_REF][START_REF] Zuo | Eight novel KCNJ1 variants and parathyroid hormone overaction or resistance in 5 probands with Bartter syndrome type 2[END_REF]. However, the prevalence and pathophysiology of hyperparathyroidism in these Bartter patients are unclear. Furthermore, data have been in part contradictory since a tendency towards both hyper-and hypophosphatemia has been described in Bartter syndrome [START_REF] Bettinelli | Phosphate homeostasis in Bartter syndrome: a case-control study[END_REF][START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF]. In patients with Gitelman syndrome, high PTH levels have only been described in patients that had parathyroid adenoma [START_REF] Rego | Gitelman syndrome and primary hyperparathyroidism: a rare association[END_REF][START_REF] Wen | An unusual case of Gitelman's syndrome with hypercalcemia[END_REF], while hypophosphatemia has been reported in several small studies [START_REF] Akhtar | A rare case of Gitelman's syndrome with hypophosphatemia[END_REF][START_REF] Ali | A case of Gitelman syndrome with severe hyponatraemia and hypophosphataemia[END_REF][START_REF] Katopodis | Hypophosphataemia in a patient with Gitelman's syndrome[END_REF][START_REF] Vigano | Renal phosphate handling in Gitelman syndrome-the results of a case-control study[END_REF] and has been attributed to renal phosphate wasting [START_REF] Katopodis | Hypophosphataemia in a patient with Gitelman's syndrome[END_REF][START_REF] Vigano | Renal phosphate handling in Gitelman syndrome-the results of a case-control study[END_REF].

To verify whether these observations from case reports and small series are prevalent in Bartter and Gitelman syndromes or just incidental findings, we analysed PTH and phosphate levels in a very large cross-sectional cohort of patients with Bartter and Gitelman syndrome collected across Europe, including both paediatric and adult subjects.

MATERIALS AND METHODS

On behalf of the European Rare Kidney Diseases Reference Network (ERKNet) Tubulopathies Working Group and European Society for Paediatric Nephrology (ESPN) Working Group on Inherited Renal Disorders, members of the ERKNet and ESPN were invited to provide retrospective clinical and laboratory data on patients with Bartter and Gitelman syndrome. Patients had either signed an informed consent form, allowing an anonymized transfer of clinical data within the ERKNet network, or consent was obtained according to local regulations and under the responsibility of local investigators. The data collection form included 38 items, of which some were mandatory, in particular those related to kidney function, PTH levels, and calcium-phosphate metabolism (Supplementary data, Table S1). To minimize biases in estimating the prevalence of signs and symptoms, data collection was cross-sectional and centres were asked to provide only information corresponding to the last available patient visit. For example, if a given patient had transiently developed high PTH in the past, this information would not be captured to avoid overestimating the prevalence of hyperparathyroidism.

Laboratory data were converted to SI units. Outlier data were identified and verified with the referring clinician. Patients with incomplete data on creatinine or PTH were excluded from the analysis. To preclude measuring the effects of low GFR on phosphate and PTH levels, patients with decreased kidney function were excluded. Since estimated GFR (eGFR) data were not available, patients were excluded based on serum creatinine. To this end, we excluded all patients aged >15 years with serum creatinine >100 μmol/L and patients aged ≤15 years with serum creatinine levels above an arbitrary value calculated with the following formula: 2.7 x age (years) + 60. Using these conservative cut-off values, we estimated by preliminary testing that most patients with eGFR < 65 mL/min/1.73m 2 have been excluded. Overall, we excluded 76 patients with elevated creatinine (Figure 1). A data completeness list is provided in Supplementary data, Table S2.

Serum phosphate, alkaline phosphatase and TmP/GFR are strongly influenced by age in the paediatric population. To be able to compare these variables in all patients, standard deviation scores (SDS) were calculated based on age-related reference values [START_REF] Ardeshirpour | Evaluation of bone and mineral disorders[END_REF][START_REF]KDOQI Clinical Practice Guideline for Nutrition in Children with CKD: 2008 update. Executive summary[END_REF][START_REF] Zierk | Pediatric reference intervals for alkaline phosphatase[END_REF]. We used the following formula to calculate SDS for phosphate, alkaline phosphatase and TmP/GFR: SDS = levelmean level for age /SD for age.

Each formula was based on published age-related reference values for phosphate, alkaline phosphatase and TmP/GFR. (Supplementary data and methods, Tables S3 andS4, Figure S1-S3).

PTH and phosphate homeostasis in Bartter and Gitelman syndrome Patients were stratified into 4 groups, based on the underlying genetic cause. These include patients with Bartter syndrome type I or II (n = 107), Bartter syndrome type III (n = 88), Bartter syndrome 'not otherwise specified' (NOS) including patients with Bartter syndrome for which genetic data were not available (n = 90) and Gitelman syndrome (n = 304). Patients with Bartter syndrome type IV (n = 9), type V (n = 4), or Gitelman syndrome NOS (n = 32) were excluded from the final analysis because these tests were severely underpowered (Figure 1). Data were analysed using IBM SPSS Statistics Version 25. Categorical data are described as numbers and %. Continuous data are presented as median with interquartile range (IQR). Data were analysed using Chi-squared test, Fisher's exact test, Mann-Whitney U test, and Kruskal-Wallis test as appropriate. Spearman's rank correlation was used for the analysis of the correlation between variables. Univariable and multivariable logistic regression were used to identify variables associated with elevated PTH; variables that reached a P-value < .10 at the univariable level were used in the multivariable model.

RESULT S

Overall characteristics

After excluding subjects with incomplete data, with serum creatinine above the threshold, or underpowered subgroups of patients, 589 patients from the original 770 patients collected were included for analysis (Figure 1).

Patient characteristics are in agreement with the known phenotypic characteristics of the diseases and are detailed in Table 1. The median age was 16.6 years (IQR 8.2-33.5). Patients with Bartter syndrome were significantly younger than patients with Gitelman syndrome [median age 9.5 years (3.5-16.3) versus 28.8 years (16.4-43.9) respectively; P < .001). Sex distribution was not significantly different in the four subgroups (P = .113). Overall, 52% of the patients were female. Nephrocalcinosis was reported more frequently in patients with Bartter syndrome type I and II compared to type III, with a prevalence of 89 and 18% respectively and very rarely in patients with Gitelman syndrome, as expected. On average, patients with Bartter syndrome had higher urinary calcium/creatinine ratios than Gitelman patients (P < .001) and patients with Gitelman syndrome had lower serum magnesium levels than patients with Bartter syndrome (P < .001). Indomethacin or other nonsteroidal anti-inflammatory drugs (NSAIDs) were prescribed more often to patients with Bartter syndrome than Gitelman syndrome (P < .001).

Elevated PTH levels were observed in a significant proportion of patients. Hyperparathyroidism (iPTH >7.0 pmol/L) was present in 23% of patients (Supplementary data, Table S5). Patients with Bartter syndrome type I and II had the highest median intact parathyroid hormone (iPTH) levels [7.5 pmol/L (4.8-11.2)] (Table 1; Figure 2) and the prevalence of hyperparathyroidism was 56% in this group. Conversely, Gitelman patients had the lowest prevalence of hyperparathyroidism (7%) and even showed a 20% prevalence of hypoparathyroidism (iPTH < 2.0 pmol/L).

All disease subgroups had a negative median phosphate-SDS, demonstrating that median serum phosphate was lower in all subgroups than median age-specific serum phosphate levels (Table 1; Figure 2). Patients with Bartter syndrome type III had the lowest median phosphate-SDS of -1.34 (-2.31 to -0.15), which was significantly lower compared to phosphate-SDS in Bartter syndrome type I and II and Gitelman syndrome (P = .032 and P = .011 respectively; Figure 2). No differences were observed in tubular reabsorption of phosphate (TRP) (P = .254) between different disease subgroups. TmP/GFR-SDS was lowest in patients with Gitelman syndrome [-0.98 (-1.47 to -0.46); Figure 2]. This was significantly lower compared to Bartter syndrome type I and II (P = .006).

Median and IQR of serum calcium were within the normal range for all subgroups (Table 1; Figure 2). Serum calcium was significantly higher in patients with Bartter syndrome compared to Gitelman syndrome (P < .001). No significant differences in serum calcium were observed between Bartter syndrome subtypes.

Although data were available only in part of the entire cohort (Supplementary data, Table S2), 25-hydroxy vitamin D (25OH vitamin D) levels were lower in patients with Bartter syndrome compared to Gitelman syndrome (P = .001) and patients with Bartter syndrome used vitamin D supplements more often (P < .001; Table 1). No difference in serum calcium levels was found between patients who used vitamin D supplements and non-supplemented patients (data not shown).

Hyperparathyroidism and hypophosphatemia

Analysis of the entire cohort. The characteristics and laboratory data of patients according to the absence or presence of hyperparathyroidism are shown in Supplementary data, Table S6. Overall, 84% of patients with elevated iPTH had Bartter syndrome. Notably, 45% of the patients with hyperparathyroidism were patients with Bartter syndrome type I and II, while this disease subtype comprises only 18% of patients in the entire cohort. Several parameters, among which urinary calcium/creatinine ratio and serum magnesium, were significantly different when comparing patients with and without hyperparathyroidism (Supplementary data, Table S6) and iPTH was correlated with several parameters (Supplementary data, Table S7). However, these analyses appear markedly influenced by the unequal prevalence of hyperparathyroidism among different disease subgroups, and therefore, may reflect differences related to the underlying disease, rather than differences related to high iPTH. The same limitation applies to the multivariable logistic regression reported in Supplementary data, Table S8 and is underscored by the finding that the strongest predictor for hyperparathyroidism is the Bartter syndrome type I and II sub-class (OR: 3.20, 95% CI 1.68-6.08; P < .001). Other significant factors associated with hyperparathyroidism included higher serum magnesium [OR: 18.47 (2.67-127.93) per mmol/L, P = .003], lower serum calcium [OR: 0.03 (0.01-0.21) per mmol/L, P < .001), higher alkaline phosphatase-SDS [OR: 1.260 (1.11-1.431) per SDS, S9). The prevalence of hypophosphatemia was 19% in patients with Bartter syndrome type I and II, 32% in patients with Bartter syndrome type III, and 16% in patients with Gitelman syndrome. Patients with hypophosphatemia had higher serum calcium and lower TmP/GFR-SDS (Supplementary data, Table S10). Phosphate-SDS correlated with TRP (r s = 0.201; P = .004) and with TmP/GFR-SDS (r s = 0.699; P < .001) (Supplementary data, Table S11). To exclude an effect of age and/or the necessary modulation of serum phosphate to SDS score to be able to compare paediatric age groups and adults, we also evaluated serum phosphate only in adults. Hypophosphatemia was observed in 14.3% of adult patients (Supplementary data,

S12

). The prevalence of hypophosphatemia was 7% in patients with Bartter syndrome type I and II, 5% in patients with Bartter syndrome type III, and 15% in patients with Gitelman syndrome. However, patient numbers in the Bartter subtype groups were low.

We finally performed a sensitivity analysis, demonstrating that the overall results of Bartter patients were not significantly influenced by the inclusion of the Bartter syndrome NOS cohort (data not shown). Overall, patients included in the NOS subgroup tended to resemble more patients with type I and II Bartter syndrome, especially if they had elevated PTH.

Analysis of disease subgroups. When restricting the analysis to patients with Bartter syndrome type I and II, patients with hyperparathyroidism had lower serum calcium levels (2.42 versus 2.49 mmol/L; P = .038) and higher alkaline phosphatase-SDS (1.08 versus 0.27; P = .010) (Table 2). No differences were observed in serum creatinine, phosphate-SDS, 25OH vitamin D, TmP/GFR-SDS, urinary calcium/creatinine ratio, or the prevalence of nephrocalcinosis. No differences were observed in the prescription of NSAIDs or vitamin D supplements between patients with and without hyperparathyroidism.

In this cohort of patients with Bartter syndrome type I and II, a correlation was observed between iPTH and alkaline phosphatase-SDS (r s 0.268, P = .015) and an inverse correlation between iPTH and calcium (r s -0.253, P = .009) (Table 3; Figure 3). No correlation was observed between iPTH and phosphate-SDS, TmP/GFR-SDS, or urinary calcium/creatinine ratio. By multivariable logistic regression analysis, higher alkaline phosphatase-SDS [OR: 1.54 (1.09-2.19) per SDS, P = .015] was associated with high iPTH (Table 4). A trend was observed for lower serum calcium [OR: 0.025 (0.001-1.16) per SDS, P = .059], which did not reach statistical significance. In the Gitelman cohort, we observed a significant correlation between iPTH and serum magnesium (r s = 0.191, P = .001) and an inverse correlation between iPTH and 25OH vitamin D (r s = -0.207, P = .004) (Supplementary data, Table S13).

In addition, as in the entire cohort, a significant correlation was observed between serum phosphate-SDS and TmP/GFR-SDS in patients with Bartter syndrome type III (r s = 0.744; P < .001) and Gitelman syndrome (r s = 0.845; P < .001) (Figure 4).

DISCUSSION

This cross-sectional study analysed PTH and phosphate homeostasis in patients with Bartter and Gitelman syndrome. We observed high PTH (>7.0 pmol/L) in 56% of patients with type I and II disease. All disease subgroups, particularly patients with Bartter syndrome type III, had a tendency towards lower serum phosphate levels and a significant proportion of patients had overt hypophosphatemia (phosphate-SDS < -2).

To date, hyperparathyroidism in these disorders has only been described in case reports and small series [START_REF] Bettinelli | Phosphate homeostasis in Bartter syndrome: a case-control study[END_REF][START_REF] Gross | Antenatal Bartter syndrome presenting as hyperparathyroidism with hypercalcemia and hypercalciuria: a case report and review[END_REF][START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF][START_REF] Leonhardt | Calcium homeostasis and hypercalciuria in hyperprostaglandin E syndrome[END_REF][START_REF] Li | Association of mutations in SLC12A1 encoding the NKCC2 cotransporter with neonatal primary hyperparathyroidism[END_REF][START_REF] Wongsaengsak | A novel SLC12A1 gene mutation associated with hyperparathyroidism, hypercalcemia, nephrogenic diabetes insipidus, and nephrocalcinosis in four patients[END_REF][START_REF] Zuo | Eight novel KCNJ1 variants and parathyroid hormone overaction or resistance in 5 probands with Bartter syndrome type 2[END_REF]. For example, Landau et al. observed high PTH levels in 10/14 patients with Bartter syndrome type II [START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF]. Additional small studies did not include genetic characterization [START_REF] Bettinelli | Phosphate homeostasis in Bartter syndrome: a case-control study[END_REF][START_REF] Leonhardt | Calcium homeostasis and hypercalciuria in hyperprostaglandin E syndrome[END_REF], while others included only type I and II Bartter syndrome [START_REF] Gross | Antenatal Bartter syndrome presenting as hyperparathyroidism with hypercalcemia and hypercalciuria: a case report and review[END_REF][START_REF] Li | Association of mutations in SLC12A1 encoding the NKCC2 cotransporter with neonatal primary hyperparathyroidism[END_REF][START_REF] Wongsaengsak | A novel SLC12A1 gene mutation associated with hyperparathyroidism, hypercalcemia, nephrogenic diabetes insipidus, and nephrocalcinosis in four patients[END_REF][START_REF] Zuo | Eight novel KCNJ1 variants and parathyroid hormone overaction or resistance in 5 probands with Bartter syndrome type 2[END_REF]. Owing to the large number of patients that were recruited, we were able to analyse subgroups of patients, demonstrating that hyperparathyroidism developed primarily in patients with Bartter syndrome type I and II and to a lesser degree, in patients with Bartter syndrome type III. A major confounding factor when analysing PTH levels is kidney function. To prevent overestimating hyperparathyroidism, we excluded from the analysis all patients with elevated creatinine, using a very conservative threshold. In addition, we observed no correlation between PTH and creatinine levels. We did not observe age-dependent changes in PTH. The aim of this study was to evaluate the prevalence of hyperparathyroidism and phosphate homeostasis abnormalities in patients with Bartter and Gitelman syndrome. To this end, we designed a cross-sectional study, favouring collection of data on a very large number of patients, over collecting longitudinal data on fewer patients which would have been more informative on pathophysiology, but would have limited our ability to estimate disease prevalence. However, some hypotheses on the pathophysiology and possible clinical implications can be proposed and discussed.

It has previously been hypothesized that hypercalciuria, a characteristic feature of patients with Bartter syndrome type I and type II, may contribute to increased PTH secretion, as a physiological response to maintain serum calcium within the normal range despite excessive renal calcium loss [START_REF] Gross | Antenatal Bartter syndrome presenting as hyperparathyroidism with hypercalcemia and hypercalciuria: a case report and review[END_REF][START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF][START_REF] Li | Association of mutations in SLC12A1 encoding the NKCC2 cotransporter with neonatal primary hyperparathyroidism[END_REF][START_REF] Gasongo | Effect of nonsteroidal antiinflammatory drugs in children with Bartter syndrome[END_REF]. Indeed, in our whole cohort, a correlation between urinary calcium excretion and PTH was found. Calciuria is a crucial distinction between Bartter and Gitelman syndrome and our observational study cannot distinguish between a causative role of calciuria for hyperparathyroidism or a simple association because of other differences between Bartter and Gitelman syndrome. As expected, hypercalciuria was a consistent feature in patients with Bartter syndrome type I and II, but no correlation between urinary calcium excretion and PTH levels were observed in this subgroup. However, the crosssectional design of the study and significant heterogeneity of patient treatments, do not allow excluding a possible role of hypercalciuria in promoting PTH secretion. Patients with hyperparathyroidism in this subgroup had on average lower serum calcium levels and, as expected, serum calcium was negatively correlated with PTH. These findings are concordant with the reports by Landau et al. and Bettinelli et al. [START_REF] Bettinelli | Phosphate homeostasis in Bartter syndrome: a case-control study[END_REF][START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF]. The cause of this lower serum calcium and whether it is sufficient to trigger PTH secretion in these patients remains undetermined.

In our study, high PTH levels in type I and II Bartter syndrome patients were not associated with lower serum phosphate or with higher urinary excretion of phosphate, as also observed by Landau et al. [START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF]. Taken together, these findings raise the possibility of renal hyporesponsiveness to PTH, which could contribute to PTH secretion. Yet, with renal hyporesponsiveness increased serum phosphate could be expected, which we did not observe.

Hyperparathyroidism in Bartter syndrome could also be secondary to prostaglandin secretion [START_REF] Gross | Antenatal Bartter syndrome presenting as hyperparathyroidism with hypercalcemia and hypercalciuria: a case report and review[END_REF][START_REF] Li | Association of mutations in SLC12A1 encoding the NKCC2 cotransporter with neonatal primary hyperparathyroidism[END_REF]. Patients with type I and II disease produce large amounts of prostaglandins due to decreased intracellular NaCl concentration in the macula densa caused by impaired salt reabsorption via the NKCC2 pathway [START_REF] Leonhardt | Calcium homeostasis and hypercalciuria in hyperprostaglandin E syndrome[END_REF][START_REF] Reinalter | Role of cyclooxygenase-2 in hyperprostaglandin E syndrome/antenatal Bartter syndrome[END_REF][START_REF] Seyberth | Bartter-and Gitelman-like syndromes: salt-losing tubulopathies with loop or DCT defects[END_REF]. Treatment of Bartter syndrome patients with NSAIDs reduces renal calcium excretion [START_REF] Gasongo | Effect of nonsteroidal antiinflammatory drugs in children with Bartter syndrome[END_REF][START_REF] Reinalter | Role of cyclooxygenase-2 in hyperprostaglandin E syndrome/antenatal Bartter syndrome[END_REF][START_REF] Reinalter | Evaluation of long-term treatment with indomethacin in hereditary hypokalemic salt-losing tubulopathies[END_REF][START_REF] Restrepo De Rovetto | Hypercalciuria with Bartter syndrome: evidence for an abnormality of vitamin D metabolism[END_REF] and in one report, reduces PTH levels [START_REF] Gasongo | Effect of nonsteroidal antiinflammatory drugs in children with Bartter syndrome[END_REF]. It is unclear in this latter study, if NSAIDs directly inhibit the parathyroid glands, or reduce PTH secretion indirectly, by inhibiting renal calcium excretion. In our study, we did not observe an association between NSAID prescription and PTH levels, nor between NSAID prescription and urinary calcium excretion.

It has also been hypothesized that higher PTH secretion in Bartter syndrome may be secondary to hyperaldosteronism [START_REF] Landau | Accentuated hyperparathyroidism in type II Bartter syndrome[END_REF]. Parathyroid glands express mineralocorticoid receptors allowing stimulation of PTH secretion by aldosterone [START_REF] Maniero | Primary hyperparathyroidism with concurrent primary aldosteronism[END_REF]. Accordingly, mild hyperparathyroidism has been reported in patients with primary hyperaldosteronism [START_REF] Tomaschitz | Aldosterone and parathyroid hormone interactions as mediators of metabolic and cardiovascular disease[END_REF] and PTH levels in these patients decrease after adrenalectomy [START_REF] Lenzini | PTH modulation by aldosterone and angiotensin II is blunted in hyperaldosteronism and rescued by adrenalectomy[END_REF]. This hypothesis seems unlikely in patients with salt-losing tubulopathies since patients with Gitelman syndrome, who typically have very high aldosterone levels, do not develop hyperparathyroidism. In addition, PTH levels in our cohort were not associated with treatment with aldosterone antagonists.

Finally, it has been suggested that hypokalaemia could cause hyperparathyroidism and that potassium supplementation could normalize PTH [START_REF] Bando | A case of pseudohypoparathyroidism (PHP) type II associated with Bartter's syndrome-restoration of phosphaturic response to parathyroid hormone (PTH) by treatment for hypopotassemia[END_REF]. Here again, we did not observe an inverse correlation between serum potassium and PTH. Moreover, Bartter and Gitelman syndromes are both characterized by hypokalaemia, whereas we observed hyperparathyroidism primarily in patients with Bartter syndrome.

Another noteworthy finding in our cohort was that 20% of patients with Gitelman syndrome had hypoparathyroidism. The calcium-sensing receptor signalling is known to be dependent on extracellular magnesium levels. Unlike calcium, PTH secretion is inhibited by supraphysiologically high magnesium levels via stimulation of the calcium-sensing receptor, but also by low magnesium concentrations [START_REF] Brown | Calcium, magnesium and the control of PTH secretion[END_REF]. This latter response is suggested to result from intracellular disinhibition of G-protein signalling downstream from the calcium-sensing receptor, precluding PTH release [START_REF] Quitterer | Paradoxical block of parathormone secretion is mediated by increased activity of G alpha subunits[END_REF]. Accordingly, decreased PTH secretion and decreased responsiveness of PTH to ionized calcium have been suggested in small cohorts of patients with Gitelman syndrome [START_REF] Bianchetti | Evidence for disturbed regulation of calciotropic hormone metabolism in Gitelman syndrome[END_REF][START_REF] Nicolet-Barousse | Inactivation of the NA-Cl co-transporter (NCC) gene is associated with high BMD through both renal and bone mechanisms: analysis of patients with Gitelman syndrome and NCC null mice[END_REF][START_REF] Blanchard | Resistance to insulin in patients with Gitelman syndrome and a subtle intermediate phenotype in heterozygous carriers: a cross-sectional study[END_REF]. In agreement with these data, we observed a significant correlation between PTH and serum magnesium in patients with Gitelman syndrome, suggesting that low serum magnesium might be, at least in part, responsible for hypoparathyroidism.

Hypophosphatemia was common in all disease subgroups, in particular in Bartter syndrome type III with a prevalence of 32%. The prevalence of hypophosphatemia in Bartter syndrome type III patients decreased in adulthood to 5%. In Gitelman syndrome, the prevalence of hypophosphatemia PTH and phosphate homeostasis in Bartter and Gitelman syndrome was not age-dependent. Low serum phosphate levels were associated with lower TmP/GFR in all subgroups, indicating that hypophosphatemia was most likely related to renal phosphate wasting. However, renal hypophosphatemia did not appear to be driven by hyperparathyroidism, since PTH did not correlate with phosphate-SDS or TmP/GFR-SDS. Furthermore, patients with Gitelman syndrome did not have high PTH levels, while they often had hypophosphatemia and renal phosphate wasting. The exact mechanism(s) of hypophosphatemia in these patients remains unclear. Notably, low serum phosphate levels have already been observed in anecdotal reports on Gitelman syndrome [START_REF] Akhtar | A rare case of Gitelman's syndrome with hypophosphatemia[END_REF][START_REF] Ali | A case of Gitelman syndrome with severe hyponatraemia and hypophosphataemia[END_REF][START_REF] Katopodis | Hypophosphataemia in a patient with Gitelman's syndrome[END_REF][START_REF] Vigano | Renal phosphate handling in Gitelman syndrome-the results of a case-control study[END_REF], including a possible link with lower renal tubular phosphate reabsorption [START_REF] Katopodis | Hypophosphataemia in a patient with Gitelman's syndrome[END_REF][START_REF] Vigano | Renal phosphate handling in Gitelman syndrome-the results of a case-control study[END_REF]. Interestingly, it has been hypothesized that chronic hypokalaemia can cause proximal tubular cell injury, resulting in a phosphate leak [START_REF] Bouchireb | Fanconi syndrome and severe polyuria: an uncommon clinicobiological presentation of a Gitelman syndrome[END_REF]. However, serum potassium and serum phosphate were not correlated in our cohort. Furthermore, FGF23 could play a role. Interestingly, a recent study demonstrated that in the NCC knockout mouse model for Gitelman syndrome, FGF23 levels were increased [START_REF] Pathare | Elevated FGF23 levels in mice lacking the thiazide-sensitive NACl cotransporter (NCC)[END_REF]. In contrast to our Gitelman cohort, these mice also showed increased PTH levels which, however, did not alter fractional phosphate excretion or serum phosphate levels.

We also observed significantly higher serum calcium levels in patients with Bartter syndrome, compared to patients with Gitelman syndrome. Theoretically, since patients with Gitelman syndrome have hypocalciuria, they are expected to have higher serum calcium levels than patients with Bartter syndrome that have hypercalciuria. Furthermore, compared to healthy controls, patients with Gitelman syndrome have higher serum calcium levels [START_REF] Vigano | Renal phosphate handling in Gitelman syndrome-the results of a case-control study[END_REF] and patients with Bartter syndrome tend to have lower serum calcium levels [START_REF] Bettinelli | Phosphate homeostasis in Bartter syndrome: a case-control study[END_REF]. Vitamin D supplementation may have influenced our results. Although supplements were prescribed more frequently to patients with Bartter syndrome, patients treated with vitamin D did not have significantly higher serum calcium levels, compared to nonsupplemented patients.

Whether in clinical practice hyperparathyroidism and hypophosphatemia require further diagnostic evaluation and treatments is unclear. In our cohort, high PTH was associated with higher alkaline phosphatase levels. This is likely due to increased bone turnover. Reduced bone mineral density has previously been observed in patients with Bartter syndrome [START_REF] Rodriguez-Soriano | Bone mineral density and bone turnover in patients with Bartter syndrome[END_REF][START_REF] Shoemaker | Calcium kinetics in the hyperprostaglandin E syndrome[END_REF]. It may therefore be appropriate that Bartter syndrome patients undergo a regular assessment of their bone density to detect incipient osteopenia or osteoporosis, particularly if they have high PTH. Since vitamin D deficiency stimulates PTH secretion, supplements could be prescribed in patients with low vitamin D levels, keeping in mind that they may worsen hypercalciuria in patients with Bartter syndrome. Of note, 25-OH vitamin D concentrations are usually normal in patients with Bartter syndrome [START_REF] Restrepo De Rovetto | Hypercalciuria with Bartter syndrome: evidence for an abnormality of vitamin D metabolism[END_REF], while high levels of 1,25-OH vitamin D have been reported [START_REF] Restrepo De Rovetto | Hypercalciuria with Bartter syndrome: evidence for an abnormality of vitamin D metabolism[END_REF][START_REF] Shoemaker | Calcium kinetics in the hyperprostaglandin E syndrome[END_REF]. The use of calcimimetics in patients with hyperparathyroidism associated with Bartter syndrome has been described in five patients [START_REF] Li | Association of mutations in SLC12A1 encoding the NKCC2 cotransporter with neonatal primary hyperparathyroidism[END_REF][START_REF] Wongsaengsak | A novel SLC12A1 gene mutation associated with hyperparathyroidism, hypercalcemia, nephrogenic diabetes insipidus, and nephrocalcinosis in four patients[END_REF]. In four of them, PTH levels normalized. However, all had high-normal or even high serum calcium levels. In theory, normocalcemic patients with Bartter syndrome could be at increased risk of developing symptomatic hypocalcemia if treated with calcimimetics, since they have metabolic alkalosis, which decreases the proportion of ionized calcium. It is unknown whether hypophosphatemia, especially if associated with bone changes, should be treated with phosphate supplementation.

The main limitations of our study relate to the crosssectional design and the relatively large group of Bartter NOS patients in the analysis. The cross-sectional design allowed us to assemble data on a very large number of patients to estimate the prevalence of PTH and phosphate abnormalities in these diseases. However, longitudinal follow-up of patients would provide additional information about the course of PTH and other variables throughout the years, which could have helped identify possible causal effects. Future studies should collect data at the initial presentation, thus pre-treatment and should also evaluate follow-up data of patients. An important opportunity to prospectively capture such data is by adding PTH and phosphate as variables to the ERKNet patient registry (ERKReg). The second main limitation is the relatively large group of patients with Bartter syndrome NOS, who lacked a genetic diagnosis and were diagnosed based on their phenotype. This subgroup was most likely composed of patients with mixed Bartter syndrome subtypes since their characteristics are intermediate between the type I and II and the type III subgroups. Sensitivity analyses performed removing the NOS subgroup showed that the inclusion of these patients did not modify our results.

Other limitations of our study are related to its retrospective, cross-sectional and multicentric design. The number of variables that could be reliably captured in the database was therefore limited. For example, active vitamin D, ionized calcium, cyclic AMP, FGF-23, aldosterone levels and data on bone metabolism were not available for most patients but could have been very instrumental in understanding the physiopathology of our findings. Treatments were decided by local physicians according to local protocols. Laboratory values were measured in different laboratories, which may have used slightly different methods and reference values. These latter aspects were probably well compensated for by the large size of our cohort. Since the age range of our patients spanned from small children to late adulthood, some values had to be normalized for age using reference data from the literature. This may have introduced some distortions in our data.

In conclusion, this cross-sectional study demonstrates that PTH is frequently elevated in patients with Bartter syndrome, especially in those with type I and II disease. The cause of hyperparathyroidism in this population remains unclear. Hypophosphatemia was observed in a significant proportion of patients with Bartter and Gitelman syndrome and appeared to be primarily related to a PTH-independent renal phosphate leak. Further studies are needed to understand better the pathophysiology and the clinical relevance of these observations.

FIGURE 1 :

 1 FIGURE 1: Patient cohort. NOS, not otherwise specified. Patients were grouped for analysis according to the genetic confirmation of disease (subtype). *Creatinine and PTH had to be provided. # 51 patients with Bartter syndrome type I and 56 patients with Bartter syndrome type II.

FIGURE 2 :

 2 FIGURE 2: Boxplots of iPTH, calcium, phosphate-SDS and TmP/GFR-SDS according to disease subtype iPTH, intact parathyroid hormone; phosphate-SDS, age-related phosphate standard deviation score; TmP/GFR-SDS, age-related ratio of tubular maximum reabsorption of phosphate to GFR standard deviation score; Boxplot graphs represent the median and IQR; the upper and lower whiskers represent data points within 25th percentile -1.5x IQR and 75th percentile + 1,5x IQR. Outliers are plotted individually. *P < .05; **P < .01; ***P < .001. A. iPTH in pmol/L; statistically significant difference in iPTH level between patients with Bartter syndrome type I and II and patients with Bartter syndrome type III, Bartter syndrome NOS and Gitelman syndrome. B. Calcium in mmol/L, statistically significant difference in calcium level between patients with Bartter syndrome type I and II and patients with Gitelman syndrome. C. Phosphate-SDS; statistically significant difference in age-adjusted phosphate level between patients with Bartter syndrome type III and patients with Bartter syndrome type I and II and Gitelman syndrome. D. TmP/GFR-SDS; statistically significant difference between Bartter syndrome type I and II and Bartter syndrome NOS and Gitelman syndrome.

FIGURE 3 :

 3 FIGURE 3: Scatterplots of calcium, urinary calcium/creatinine ratio, phosphate-SDS, TmP/GFR-SDS and alkaline phosphatase-SDS with iPTH of patients with Bartter syndrome type I and II. iPTH, intact parathyroid hormone; phosphate-SDS, age-related phosphate standard deviation score; alkaline phosphatase-SDS, age-related alkaline phosphatase standard deviation score; TmP/GFR-SDS: age-related ratio of tubular maximum reabsorption of phosphate to GFR standard deviation score; A. Scatterplot of calcium with iPTH. B. Scatterplot of urinary calcium/creatinine ratio with iPTH. C. Scatterplot of phosphate-SDS with iPTH. D. Scatterplot of TmP/GFR-SDS with iPTH. E. Scatterplot of alkaline phosphatase-SDS with iPTH.

Table 1 . Patient characteristics

 1 NSAIDs, nonsteroidal anti-inflammatory drugs; ACE inhibitors, angiotensin converting enzyme inhibitors; ARBs, angiotensin II receptor blockers. Categorical values are presented as number and % given in parentheses. Continuous values are presented as median with interquartile range (IQR) given in square brackets. Nota bene: some patients are using more than one NSAID according to the provided data.

		Bartter syndrome	Bartter syndrome	Bartter syndrome	Gitelman
		type I and II	type III	NOS	syndrome	Total
	Number of patients	107	88	90	304	589
	Characteristics
	Male: Female ratio, n (%)	51: 56 (48: 52)	50: 38 (57: 43)	48: 42 (53: 47)	133: 171 (44: 56)	282: 307 (48: 52)
	Age (years)	9.0 [3.5-16.0]	10.4 [3.3-17.2]	9.6 [3.6-16.3]	28.8 [16.4-43.9]	16.6 [8.2-33.5]
	Nephrocalcinosis, n (%)	90/101 (89)	15/85 (18)	46/82 (56)	4/257 (2)	155/525 (30)
	Laboratory results
	iPTH (pmol/L)	7.5 [4.8-11.2]	4.4 [3.0-6.7]	5.1 [2.9-8.3]	3.1 [2.3-4.0]	3.8 [2.5-6.6]
	Creatinine (umol/L)	55 [37-76]	43 [-62]	48 [-66]	58 [47-71]	55 [41-70]
	Sodium (mmol/L)	140 [138-142]	139 [137-141]	139 [137-140]	139 [138-141]	139 [138-141]
	Potassium (mmol/L)	3.6 [3.3-3.8]	3.2 [2.8-3.6]	3.4 [3.0-3.9]	3.0 [2.7-3.4]	3.2 [2.8-3.7]
	Chloride (mmol/L)	99 [97-101]	97 [92-100]	96 [93-101]	98 [95-100]	98 [95-100]
	Bicarbonate (mmol/L)	26.2 [24.3-28.1]	29.0 [26.3-32.0]	28.4 [27.0-30.7]	29.0 [27.0-31.0]	28.3 [26.3-31.0]
	Phosphate (mmol/L)	1.42 [1.21-1.63]	1.28 [1.09-1.44]	1.30 [1.12-1.53]	1.07 [0.92-1.25]	1.21 [0.99-1.42]
	Phosphate-SDS	-0.67 [-1.76-0.43] -1.34 [-2.31--0.15] -1.32 [-2.32-0.05]	-0.77 [-1.51-0.29]	-0.91 [-1.82-0.18]
	Calcium (mmol/L)	2.44 [2.37-2.53]	2.48 [2.40-2.58]	2.50 [2.38-2.60]	2.41 [2.31-2.50]	2.43 [2.34-2.53]
	Magnesium (mmol/L)	0.89 [0.80-0.97]	0.77 [0.68-0.85]	0.81 [0.75-0.95]	0.63 [0.56-0.71]	0.71 [0.61-0.84]
	Uric acid (μmol/l)	315 [246-405]	220 [162-319]	286 [190-409]	250 [190-321]	262 [190-350]
	Alkaline phosphatase (IU/L)	227 [161-287]	212 [114-274]	230 [160-303]	66 [51-136]	148 [62-245]
	Alkaline phosphatase-SDS	0.79 [-0.05-1.52]	0.21 [-0.50-0.99]	0.65 [-0.36-1.89]	-1.00 [-1.72-0.00]	-0.13 [-1.18-0.93]
	Total protein (g/L)	73 [70-77]	73 [69-76]	75 [71-78]	73 [69-76]	73 [70-77]
	Albumin (g/L)	46 [43-49]	45 [43-48]	46 [43-49]	46 [44-49]	46 [43-49]
	25OH vitamin D (nmol/L)	39 [-68]	40 [-82]	43 [-64]	61 [-85]	51 [-80]
	Urinary calcium/creatinine	1.55 [0.94-2.62]	0.33 [0.14-0.71]	0.55 [0.23-1.14]	0.08 [0.04-0.17]	0.21 [0.07-0.75]
	(mmol/mmol)
	TRP	0.90 [0.81-0.92]	0.90 [0.86-0.93]	0.88 [0.82-0.95]	0.91 [0.86-0.94]	0.90 [0.85-0.94]
	TmP/GFR (mmol/L)	1.41 [1.10-1.48]	1.17 [1.02-1.33]	1.11 [0.84-1.35]	0.95 [0.82-1.10]	1.04 [0.84-1.23]
	TmP/GFR-SDS
	Treatment
	NSAIDs, n (%)	69 (65)	52 (59)	55 (61)	26 (9)	202 (34)
	Indomethacin, n (%)	53 (50)	48 (55)	54 (60)	26 (9)	181 (31)
	Ibuprophen, n (%)	16 (15)	4 (5)	2 (2)	0 (0)	22 (4)
	Other NSAIDs, n (%)	5 (5)	7 (8)	4 (4)	1 (0.3)	17 (3)
	Potassium-sparing diuretics, n (%)	2 (2)	12 (14)	4 (4)	63 (21)	81 (14)
	Amilorid, n (%)	2 (2)	12 (14)	4 (4)	58 (19)	76 (13)
	Triamterene, n (%)	0 (0)	0 (0)	0 (0)	5 (2)	5 (1)
	Aldosterone antagonists, n (%)	5 (5)	17 (19)	23 (26)	54 (18)	99 (17)
	Eplerenone, n (%)	1 (1)	2 (2)	6 (7)	15 (5)	24 (4)
	Spironolactone, n (%)	4 (4)	15 (17)	16 (18)	37 (12)	72 (12)
	Canrenone, n (%)	0 (0)	0 (0)	1 (1)	2 (1)	3 (1)
	ACE inhibitors/ARBs, n (%)	4 (4)	5 (6)	0 (0)	6 (2)	15 (3)
	Hydrochlorothiazide, n (%)	3 (3)	0 (0)	6 (7)	0 (0)	9 (2)
	Potassium supplements, n (%)	71 (66)	83 (94)	76 (84)	280 (92)	510 (87)
	Sodium supplements, n (%)	28 (26)	44 (50)	21 (23)	43 (14)	136 (23)
	Magnesium supplements, n (%)	11 (10)	21 (24)	18 (20)	226 (74)	276 (47)
	Phosphate supplements, n (%)	0 (0)	2 (2)	3 (3)	1 (0,3)	6 (1)
	Proton pump inhibitors, n (%)	20 (19)	24 (27)	14 (16)	39 (13)	97 (17)
	Other gastric protectors, n (%)	12 (11)	10 (11)	8 (9)	11 (4)	41 (7)
	Oral contraceptive, n (%)	1 (1)	1 (1)	1 (1)	20 (7)	23 (4)
	Vitamin D supplements, n (%)	41 (38)	20 (23)	17 (19)	26 (9)	104 (18)
	P < .001] and the use of NSAIDs [OR: 1.88 (1.08-3.28);
	P = .026].

0.23 [-0.46-0.78] -0.62 [-1.48-0.44] -0.66 [-2.03-0.14] -0.98 [-1.47--0.46] -0.86 [-1.54--0.02]

iPTH, intact parathyroid hormone; phosphate-SDS, age-related phosphate standard deviation score; alkaline phosphatase-SDS, age-related alkaline phosphatase standard deviation score; 25OH vitamin D, 25-hydroxy vitamin D; TRP, tubular reabsorption of phosphate; TmP/GFR, ratio of tubular maximum reabsorption of phosphate to GFR; TmP/GFR-SDS: age-related TmP/GFR standard deviation score; Hypophosphatemia (phosphate-SDS < -2) was observed in 22% of patients (Supplementary data, Table

Table

  PTH and phosphate homeostasis in Bartter and Gitelman syndrome 2479 Downloaded from https://academic.oup.com/ndt/article/37/12/2474/6523371 by guest on 27 February 2023

Table 2 . Characteristics of patients with Bartter syndrome type I and II with and without hyperparathyroidism

 2

	Variable	Hyperparathyroidisim	No hyperparathyroidism	P-value
	Number of patients, n (%)	60 (56)	47 (44)
	Characteristics
	Age (years)	9.6 [3.8-16.3]	8.9 [2.7-15.5]	0.476
	Sex (male)	27 (45)	24 (51)	0.563
	Nephrocalcinosis, n (%)	49/57 (86)	41/44 (93)	0.340
	Laboratory results
	iPTH (pmol/L)	10.7 [8.6-14.0]	4.5 [3.2-5.6]	NT
	Creatinine (μmol L)	54 [-71]	55 [37-77]	0.863
	Sodium (mmol/L)	140 [138-142]	140 [138-143]	0.838
	Potassium (mmol/L)	3.6 [3.2-3.8]	3.6 [3.3-3.9]	0.538
	Chloride (mmol/L)	99 [97-102]	99 [97-101]	0.390
	Bicarbonate (mmol/L)	26.0 [24.0-28.0]	26.4 [24.8-28.8]	0.414
	Phosphate-SDS	-0.66 [-1.56-0.47]	-0.82 [-1.94-0.21]	0.418
	Calcium (mmol/L)	2.42 [2.34-2.51]	2.49 [2.39-2.60]	0.038
	Magnesium (mmol/L)	0.90 [0.81-0.98]	0.89 [0.79-0.98]	0.651
	Alkaline phosphatase-SDS	1.08 [0.17-1.89]	0.27 [-0.28-1.09]	0.010
	Uric acid (μmol/L)	315 [240-403]	327 [262-421]	0.697
	Total protein (g/L)	74 [72-78]	72 [68-75]	0.147
	Albumin (g/L)	46 [43-48]	47 [43-50]	0.321
	25OH vitamin D (nmol/L)	40 [24.5-62.9]	35 [-94]	0.761
	Urinary calcium/creatinine (mmol/mmol)	1.46 [0.91-2.42]	1.73 [1.02-2.76]	0.452
	TRP	0.87 [0.79-0.93]	0.91 [0.81-0.93]	0.673
	TmP/GFR-SDS	-0.13 [-1.26-0.67]	0.56 [-0.36-0.90]	0.481
	Treatment
	Indomethacin or other NSAID, n (%)	37 (62)	32 (68)	0.545
	Potassium-sparing diuretics, n (%)	2 (3)	0 (0)	0.503
	Aldosterone antagonists, n (%)	2 (3)	3 (6)	0.652
	ACE inhibitors/ARBs, n (%)	2 (3)	2 (4)	1.000
	Hydrochlorothiazide, n (%)	2 (3)	1 (2)	1.000
	Potassium supplements, n (%)	42 (70)	29 (62)	0.413
	Sodium supplements, n (%)	17 (28)	11 (23)	0.660
	Magnesium supplements, n (%)	9 (15)	2 (4)	0.108
	Phosphate supplements, n (%)	0 (0)	0 (0)	N/A
	Proton pump inhibitors, n (%)	10 (17)	10 (21)	0.621
	Other gastric protectors, n (%)	5 (8)	7 (15)	0.360
	Oral contraceptives, n (%)	1 (2)	0 (0)	1.000
	Vitamin D supplements, n (%)	26 (43)	15 (32)	0.238

iPTH, intact parathyroid hormone; phosphate-SDS, age-related phosphate standard deviation score; alkaline phosphatase-SDS, age-related alkaline phosphatase standard deviation score; 25OH vitamin D, 25-hydroxy vitamin D; TRP, tubular reabsorption of phosphate; TmP/GFR-SDS, age-related ratio of tubular maximum reabsorption of phosphate to GFR standard deviation score; NSAID, nonsteroidal anti-inflammatory drug; ACE inhibitors, angiotensin converting enzyme inhibitors; ARBs, angiotensin II receptor blockers; NT, not tested; N/A, not applicable Categorical data is presented as number and % and was analysed by Fisher's exact test. Continuous data is presented as median and interquartile range and was analysed by Mann-Whitney U test.

Table 3 . Correlation coefficients of iPTH in patients with Bartter syndrome type I and II

 3

	Variable	N	r s	P-value
	Sex (male)	107	-0.056	0.569
	Age	107	0.116	0.236
	Nephrocalcinosis	101	-0.064	0.526
	Creatinine	107	0.171	0.078
	Sodium	104	0.003	0.974
	Potassium	107	-0.112	0.249
	Chloride	98	-0.027	0.792
	Bicarbonate	99	0.044	0.663
	Phosphate-SDS	104	0.104	0.293
	Calcium	105	-0.253	0.009
	Magnesium	93	0.014	0.897
	Uric acid	56	0.002	0.987
	Alkaline phosphatase-SDS	82	0.268	0.015
	Total protein	48	0.115	0.435
	Albumin	75	-0.126	0.283
	25OH vitamin D	60	-0.044	0.739
	Urinary calcium/creatinine ratio	82	-0.083	0.459
	TRP	17	-0.409	0.103
	TmP/GFR-SDS	17	-0.085	0.747
	Indomethacin or other NSAID	107	-0.095	0.331
	Potassium-sparing diuretics	107	0.137	0.158
	Aldosterone antagonists	107	-0.115	0.239
	ACE inhibitors/ARBs	107	-0.049	0.619
	Hydrochlorothiazide	107	-0.003	0.978
	Potassium supplements	107	0.102	0.295
	Sodium supplements	107	0.042	0.668
	Magnesium supplements	107	0.175	0.072
	Proton pump inhibitors	107	0.010	0.918
	Other gastric protectors	107	-0.083	0.393
	Oral contraceptives	107	0.108	0.266
	Vitamin D supplements	107	0.102	0.294
	iPTH, intact parathyroid hormone; phosphate-SDS, age-related phosphate standard
	deviation score; alkaline phosphatase-SDS, age-related alkaline phosphatase standard
	deviation score; 25OH vitamin D, 25-hydroxy vitamin D; TRP, tubular reabsorption
	of phosphate; TmP/GFR-SDS, age-related ratio of tubular maximum reabsorption of
	phosphate to GFR standard deviation score; NSAID, nonsteroidal anti-inflammatory
	drug; ACE inhibitors, angiotensin converting enzyme inhibitors; ARBs, angiotensin II
	receptor blockers.
	r s, Spearman's rank correlation coefficient.

Table 4 . Multivariable logistic regression of patients with Bartter syndrome type I and II for hyperparathyroidism (PTH >7.0 pmol/L)

 4

	Variable	Units N OR	95% CI P-value
	Calcium	mmol/L 80 0.03 0.001-1.16 0.059
	Phosphate-SDS		80 1.29 0.93-1.81 0.128
	Alkaline phosphatase-SDS		80 1.54 1.09-2.19 0.015
	Indomethacin or other NSAID	Yes	80 1.12 0.38-3.34 0.833
	Vitamin D supplements	Yes	80 1.34 0.49-3.66 0.566
	Phosphate-SDS, age-related phosphate standard deviation score; alkaline phosphatase-
	SDS, age-related alkaline phosphatase standard deviation score; NSAID, nonsteroidal anti-
	inflammatory drug; OR, Odds ratio; 95% CI, 95% confidence interval.

M. F. A. Verploegen et al. Downloaded from https://academic.oup.com/ndt/article/37/12/2474/6523371 by guest on 27 February 2023

M. F. A. Verploegen et al.

M. F. A. Verploegen et al.

PTH and phosphate homeostasis in Bartter and Gitelman syndrome

DATA AVAIL ABILIT Y STATEMENT

The data underlying this article will be shared on reasonable request to the corresponding author.

SUPPLEMENTARY DATA

Supplementary data are available at ndt online.

ACKNOWLED GEMENT S

This project has been supported by the European Reference Network for Rare Kidney Diseases (ERKNet), which is partly co-funded by the European Union within the framework of the Third Health Programme 'ERN-2016-Framework Partnership Agreement 2017-2021' . This work is generated within the European Society for Paediatric Nephrology working group on inherited renal disorders. This work was supported by an Innovation Grant 19OI06 from the Dutch Kidney Foundation (to T.N.).

C ONFLICT OF INTEREST STATEMENT

The authors have no conflicts of interest to declare.