Judicaël Aubry
email: judicael.aubry@bretagne.ens-cachan.fr

Hamid Ben

Member, IEEE Bernard Multon

H Ben Ahmed

Sizing Optimization Methodology of a Surface Permanent Magnet Machine-Converter System over a Torque-Speed Operating Profile : Application to a Wave Energy Converter

Keywords: Design optimization, energy efficiency, fluxweakening control, pareto optimization, permanent magnet machines, power electronic converters, variable speed drives, wave energy conversion

This paper sets forth a sizing optimization methodology of a surface permanent magnet machine-converter system over a torque-speed operating profile. The two optimization objectives are to minimize the cost of the machine-converter system and to minimize (or maximize) electrical energy consumption (or generation). The optimization parameters serve to describe both the machine geometry and the electrical ratings of the electronic power converter. Each operating point of the profile is treated independently, and current control is optimized at every operating point in order to not only minimize machine drive losses but also satisfy several constraints and then implicitly considering fluxweakening possibility. This optimization methodology is generic and is applied to a particular case: a direct-drive conversion chain for a wave energy converter. We show that taking into account both the sizing parameters of the converter and the fluxweakening control, in addition to the classical sizing parameters of the machine, has a strong impact on the machine-converter system optimal results. Moreover, the strong coupling with the wave energy converter through damping parameters, plays also a crucial role on the sizing results.

Thermal resistance S conv Apparent power of the power electronic converter T i Electromagnetic torque of the i th operating point T p Spectral peak period of the sea state U DC DC bus voltage V 0,x Threshold voltage of x (diode or igbt) component V rated Rated voltage of the power electronic converter

The geometric parameters of the electromagnetic structure of the machine are defined in Table II.

I. INTRODUCTION

T HIS article proposes to develop and apply a sizing optimization methodology of a surface permanent magnet machine(SPM)-converter system over a torque speed operating profile. The term "operating profile" refers herein to a series of torque-speed operating points denoted (T i , Ω i ). From the moment that variable speed is required and even more if field weakening too, the sizing process of a machine-converter system must not only include the machine dimensions but also the power electronic converter ratings. Furthermore, performances (e.g. losses) of the machine-converter system must be calculated over the whole operating profile. These two facts compel us to adopt an original sizing process.

The first original feature is to deal with the more realistic operating profile. Indeed in the literature, a broad majority of sizing methods are only based on one typical torque-speed operating point [START_REF] Boules | Design optimization of permanent magnet DC motors[END_REF]- [START_REF] Laskaris | Internal Permanent Magnet Motor Design for Electric Vehicle Drive[END_REF], which can be difficult to define for variable-speed applications [START_REF] Dorrell | A Review of the Design Issues and Techniques for Radial-Flux Brushless Surface and Internal Rare-Earth Permanent Magnet Motors[END_REF]. Some others approaches are based on a base point and a flux weakening point [START_REF] Bianchi | Unified approach to the analysis and design of an AC motor drive for flux-weakening operations[END_REF]. This is not necessarily easier to define.

The second original feature is to consider the machine and the power electronic converter as a whole. Indeed, the sizings and ratings of each component are strongly interdependent [START_REF] Lovelace | Impact of saturation and inverter cost on interior PM synchronous machine drive optimization[END_REF]. For example, the flux-weakening capability of the machine will have a high impact on the ratings of the converter, especially if the operating profile presents a constant power speed range [START_REF] Figueroa | Relative Sizing of Inverter and Surface Mount PM Motor for Traction Applications[END_REF]. That is why the proposed methodology will include a current control strategy (direct and transverse axis current) in order to contribute to the extension of the constant speed power range [START_REF] Jahns | Flux-Weakening Regime Operation of an Interior Permanent-Magnet Synchronous Motor Drive[END_REF], [START_REF] Morimoto | Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity[END_REF] but also the minimization of losses [START_REF] Morimoto | Loss minimization control of permanent magnet synchronous motor drives[END_REF]- [START_REF] Cavallaro | Efficiency Enhancement of Permanent-Magnet Synchronous Motor Drives by Online Loss Minimization Approaches[END_REF]. This consideration will take the form of an (i d , i q ) optimization to minimize losses at each operating point of the profile respecting some constraints (voltage, current, demagnetization...) [START_REF] Chedot | Integrated Starter Generator: The Need for an Optimal Design and Control Approach. Application to a Permanent Magnet Machine[END_REF]. Research to date have been limited to optimizing the control strategy and machine geometry (excluding the converter) [START_REF] De La Barrière | PM Axial Flux Machine Design for Hybrid Traction[END_REF], or optimizing the control-convertermachine system while focusing on just a single criterion (e.g. the machine mass [START_REF] Kreuawan | Optimal design of permanent magnet motor using multidisciplinary design optimization[END_REF] or total cost of the system [START_REF] Lindstrom | Design of high-efficiency electrical motors for a hybrid electric vehicle[END_REF], [START_REF] Tessarolo | A system-level approach to the optimal dimensioning of induction-motor variable-frequency drives[END_REF]).

In the proposed methodology, the sizing parameters of the machine and the current rating of the power electronic converter (∝ silicon area) are optimized together according two objective functions. The first optimization objective is the minimization of the machine-converter system cost, which is here considered as the sum of the cost of raw materials mass for the active parts of the machine and the cost of the power electronic converter. The calculation of the average system losses over the operating profile enables to determine the second optimization objective which is the electrical energy. All the operating points of the profile are taken into account to determine objectives and satisfy constraints.

The first part of the paper will present the sizing methodology of the machine-converter system on an operating profile. In the second part, we will apply this approach and consider a direct drive generator and its power electronic converter of a wave energy converter (WEC) as an example. A strong coupling is shown between the optimization of damping parameters of the WEC and the sizing parameters of the machine-converter system. This paper constitutes a follow-up of the conference article [START_REF] Aubry | Bi-Objective Sizing Optimization of a PM Machine Drive on an Operating Profile[END_REF]. This methodology proves to be generic and applicable to any system in which a machineconverter system is operating at variable speed, like for electric traction or renewable energy conversion.

II. PRESENTATION OF THE OPTIMIZATION PROBLEM

An optimization problem consists in defining one or more objectives, depending on one or more parameters, subjects to one or more constraints.

A. Optimization Objectives

1) First Objective : Cost of the machine-converter system: In order to evaluate the cost of the machine-converter system C drive , we consider the sum of the power electronics cost (converter, filters, control circuits) and machine cost:

C drive = C conv + C mach (1)
Our assumption is that the cost of the converter is a function of its apparent power S conv ( 2) (stemming from observations). Values of coefficients α and γ remain valid for a given power range and conversion structure. These coefficients for an AC-DC-AC IGBT (NPT) three-phase bridge are provided for the application example further below. As for the machine cost, only the sum of costs of different raw materials for active parts have been taken into account [START_REF] Messine | Optimal design of electromechanical actuators: a new method based on global optimization[END_REF], with numerical values being listed in Table I. These costs are very sensitive to market prices and the values considered here are given in Table I for example purposes only.

C conv = αS conv γ (2)
C mach = c N dF eB M N dF eB + c F e M F e + c Cu M Cu (3)
where c x and M x are respectively the specific cost and the total mass of the material x. 2) Second Objective : Electrical Energy: Depending on the specific application, whether motor or generator, the electrical energy may be either consumed or generated. The losses must be added to the mechanical power in motor case and subtract in generator case. Electrical energy E elec is expressed as follows:

E elec = i (T i Ω i ± P loss,i )d i (4)
where P loss,i are the total machine-converter system losses at operating point (T i , Ω i ) with a cumulated duration d i over all the operating profile.

B. Optimization Parameters

The system to be optimized is an SPM machine-converter system. The optimization parameters thus need to describe the two physical components making up this system: machine and converter.

Let's assume the DC bus voltage U DC to be constant then the rated current I rated of the power electronic converter will then be parameterized by the apparent power S conv with S conv = 3V rated I rated and V rated = U DC /(2 √ 2) i.e. without accounting injection of third harmonic.

In order to effectively describe the machine, let's identify just the geometric parameters shown in Fig. 1 andlisted

C. Optimization Constraints

To complete the description of this optimization problem, several constraints still need to be defined. Some constraints must be satisfied at each operating point (T i , Ω i ). They can be qualified as instantaneous constraints:

• Rated voltage: ∀i, v 2 d,i + v 2 q,i ≤ √ 3V rated • Rated current: ∀i, i 2 d,i + i 2 q,i ≤ √
3I rated where voltage and current in d-and q-axis are calculated from equivalents circuits on Fig. 2.

• Saturation ∀i, max(B i ) ≤ B sat
which must be respected in each part of the machine (stator and rotor yoke and in teeth). This constraint only has to ensure the validity of the linear magnetic model.

• Demagnetization ∀i, H i ≥ -H k + _ + _ + _ + _ + _
Fig. 2. d-and q-axis equivalent circuits of the SPM machine Other geometrical constraints however must be satisfied for each machine, they can be qualified as global constraints:

• e > 0.2 + 3 √ r s l s (mm) [2] • r s + h slot + h stat ≤ r max • r s -e -h mag ≥ h rot
Lastly, the thermal constraint must be treated with special attention. The temperature rise of the hottest point relative to ambient temperature must be calculated strictly by means of a transient thermal model. The maximum value over the entire temperature rise profile must therefore remain below a threshold value : max(∆Θ(t)) ≤ ∆Θ max

In order to avoid a temporal transient simulation which will increase excessively the optimization process computation time, only one steady-state thermal model may be used but only in two cases:

• When thermal time constants of the machine are large relative to the loss variation periods, the temperature rise constraint can be calculated based on average machine losses value. If we denote ∆Θ i the steady-state temperature rise for each operating point, the temperature rise constraint in this case can be rewritten :

i ∆Θ i d i / i d i < ∆Θ max •
When the thermal time constants are small relative to the loss variation periods, temperature rise may be considered as instantaneous and the corresponding constraint appears on the least favorable operating point: max(∆Θ i ) < ∆Θ max Depending on the application and level of power under consideration, one of these two cases may be envisaged. Otherwise, it would be necessary to calculate the temperature rise profile on the basis of a temporal resolution with a transient thermal model, which could cause higher computation time.

The constraint parameters used in the example further below are listed in the Table III.

D. Local Current Vector Control Optimization

In order to evaluate system losses P loss,i at each operating point (T i , Ω i ), the direct axis current i d,i still needs to be determined. The transverse axis current i q,i , in case of a nonsalient machine, is completely defined by the torque T i to be supplied.

As said previously, the field weakening can be very influent on the sizing of each component. It can improve the performance of the machine-converter system in two ways:

• The extension of the constant power speed range. In several articles [START_REF] Jahns | Flux-Weakening Regime Operation of an Interior Permanent-Magnet Synchronous Motor Drive[END_REF], [START_REF] Morimoto | Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity[END_REF], it is shown that electronic flux weakening (through modification of the leading angle) makes it possible, for given converter ratings, to extend i q,i Rated voltage limit (depends on Ω i )

Required torque (depends on T i )

Demagnetization limit

Saturation limit

Unconstrained range of d-axis current i d,i . What is the best value of id,i for this operating point? i d,i

Rated current limit the operating speed range of a machine-converter system with respect to a conventional control (i.e. an i d = 0 control).

• The minimization of losses [START_REF] Morimoto | Loss minimization control of permanent magnet synchronous motor drives[END_REF]- [START_REF] Cavallaro | Efficiency Enhancement of Permanent-Magnet Synchronous Motor Drives by Online Loss Minimization Approaches[END_REF]. By restricting losses to just copper losses, then loss minimization at each operating point necessitates a so-called "maximum torque per ampere" control, which within the scope of non-salient machines, may be expressed very simply as i d = 0. By adding other losses (magnetic, converter) to this formulation, the control law for minimizing losses at each point becomes more complex, while still remaining feasible.

Then the values of currents i d,i at each operating point should constitute strictly optimization parameters to the same extent as machine-converter system sizing parameters. Over an operating profile containing a large number of points however, this rigorous approach is infeasible since it leads to an excessive increase in the number of optimization parameters. The alternative approach adopted herein consists of locally optimizing the value of current i d,i for each operating point. Let's assign the minimization of total machine and converter losses P loss as the optimization criterion, which in turn contributes to optimizing one of the two global sizing objectives, namely electrical energy E elec .

As indicated in the previous paragraph however, some instantaneous constraints must be satisfied at each operating point (T i , Ω i ): voltage, current, saturation and demagnetization. An illustration of these constraints is presented in Fig. 3. The value i d,i must therefore be optimized subject to these constraints. Should no optimization solution exist, i.e. no i d,i value found to satisfy all four instantaneous constraints, then the particular operating point cannot be reached. A new constraint will now be defined that encompasses the four mentioned above: each operating point (T i , Ω i ) have to be reached (equivalent to a i d,i shall exist for each operating point

(T i , Ω i )).
In practice, this constrained optimization routine is per-formed by systematically computing several discrete values lying within the interval [-I rated ; 0] (a reduction of this interval is possible by calculating the corresponding d-axis current of intersection points between the iso-torque line and the constraints limits). The selected i d,i value is the one that minimizes losses while satisfying constraints. The number of computed discrete values will be established on the basis of a compromise between level of accuracy and computation time.

III. MACHINE-CONVERTER SYSTEM MODELIZATION

A. Electrical Machine Model

The equivalent circuits in both axes are depicted in Fig. 2. Iron losses are taken into account in the sum of system losses. But they are not include in the calculation of electrical values. That is why the equivalent resistance R f is drawn in dotted line and does not appear in ( 5) and [START_REF] Dorrell | A Review of the Design Issues and Techniques for Radial-Flux Brushless Surface and Internal Rare-Earth Permanent Magnet Motors[END_REF].

The decomposition into d-q axis has been chosen so that the RMS current value per phase and the RMS phase to neutral voltage are both expressed as follows:

√ 3I = i 2 d + i 2 q (5) √ 3V = √ (Rsi d -(Lm+L l )ωiq) 2 +(Rsiq+ω((Lm+L l )i d +Φ f )) 2 (6)
The electromagnetic torque equals:

T = pΦ f i q (7)

B. Model of machine-converter system losses

The resistance R s of one phase is determined from the set of geometric parameters. Copper resistivity is set at the maximum allowable temperature(@130 • C). The dependence of resistivity or other physical quantities on temperature could be incorporated by means of an iterative calculation, yet computation time would rise excessively. Total copper losses are then expressed as follows :

P copper,i = R s (i 2 d,i + i 2 q,i ) (8)
Iron losses are calculated in the first harmonic hypothesis. The consideration of harmonic losses in the model would not cause any additional difficulties. Equation ( 9) is used to calculate loss densities:

p iron,i = 2k H π |Ω i | Bi 2 + α p (pΩ i Bi ) 2 2 ( 9
)
where Bi is the local flux density peak value for i th operating point. This value depends on the part of the machine. Loss coefficients α p and k H are detailed in Table IV. Total iron losses are derived from (9) by summing total losses in both the teeth and stator yoke. Loss densities are considered to be homogeneous in each of these two parts (rotor losses are assumed to equal zero for this model in the first harmonic under steady-state mode). Losses in the electronic power converter are composed of the sum of conduction losses [START_REF] Jahns | Flux-Weakening Regime Operation of an Interior Permanent-Magnet Synchronous Motor Drive[END_REF] and switching losses [START_REF] Morimoto | Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity[END_REF] within both the diodes and transistors (in this case IGBT). Equivalent thermal conductivity of winding 0.5

P cond,x = V 0,x I av,x + R d,x I 2 RM S,x (10)
W.m -1 .K -1 λ F e
Radial thermal conductivity of laminations

30 W.m -1 .K -1 h Convective heat transfer coefficient 10 W.m -2 .K -1
where x is the component under consideration (diode or IGBT), V 0,x the threshold voltage of the device x and R d,x its dynamic resistance. I av,x and I RM S,x are respectively the average and RMS current passing through the device x. It depends on the RMS current per phase I and voltage V but also on the phase difference between these two quantities. Switching losses are assumed to be proportional to the switched current:

P sw = f sw (B sw,rec )I RM S √ 2/π (11)
where B sw,rec is the switching and recovery losses coefficient in the IGBT and diode. The hypothesis will be adopted whereby for a given maximum voltage rating (here 3300 V), this coefficient remain independent of the maximum current rating of the switch. Observations from manufacturers' documentation enable deducing, for a given maximum voltage rating (here 3300 V), the scale law as a function of the maximum current rating of the two components: V 0,x and B sw,rec are assumed as constants (12)

R d,x = r d,x /( √ 2I rated )(∝ silicon area -1 ) (13)

C. Magnetic machine model

An expression of the magnetizing inductance L m is shown in [START_REF] Cavallaro | Efficiency Enhancement of Permanent-Magnet Synchronous Motor Drives by Online Loss Minimization Approaches[END_REF] for a diametral winding with one slot per pole and per phase:

L m = 3 2 4 π µ 0 K c e + h mag n 2 s r s l u p 2 (14)
where K c is Carter's coefficient [START_REF] Gieras | Permanent magnet motor technology: design and applications[END_REF].

The leakage inductance L l is obtained from a calculation of the magnetic energy stored in a single slot (end windings and tooth tips have been neglected herein), which yields:

L l = 2µ 0 n 2 s l u p 2 h slot 3w slot (15)
where w slot = (2π(r s + h slot /2)k slot )/(6p) is the width of the slot (neglecting curvature effects).

D. Thermal machine model [START_REF] Boglietti | Evolution and modern approaches for thermal analysis of electrical machines[END_REF] The equivalent thermal circuit of the machine is displayed in Fig. 4. Due to symmetry considerations, only one half of a tooth pitch has been examined. The curvature effects are neglected. The expression for thermal resistances is detailed for the slot only as follows:

R th slot,rad = 1 λ Cu h slot l u w slot 2 (16)
R th slot,tg = 1 λ Cu w slot 2 l u h slot (17)
P copper,slot corresponds to copper losses produced inside a half-slot. λ Cu corresponds to the equivalent thermal conductivity of the stator winding (copper + insulation), and it is considered constant set equal to 0.5 W.m -1 .K -1 . The value of the temperature rise constraint ∆Θ is calculated inside the winding; it corresponds to the temperature rise between the hottest point of the slot and the ambient temperature. For simplification concerns, a thermal model of the electronic power converter was not developed since maximum current ratings have been established on the basis of manufacturer guidelines; moreover, it can be considered that cooling will be sized in order to maintain the junction temperature at an acceptable value.

IV. SIZING OPTIMIZATION FLOWCHART

This article has demonstrated how to evaluate and optimize the performance of a given machine-converter system over an operating profile. Fig. 5 offers the optimization flowchart. The cost of the electric chain, along with the geometric constraints, may be directly assessed from the parameters presented. Losses enable to calculate the objective electrical energy and the thermal constraint. If for a given operating point no solution exists that optimizes i d,i , then the corresponding set of optimization parameters will not be selected as part of the overall sizing optimization.

The multi-objective optimization algorithm is based on particle swarm [START_REF] Hasanien | Particle Swarm Design Optimization of Transverse Flux Linear Motor for Weight Reduction and Improvement Thrust Force[END_REF]. It is a self implemented version of MOPSO [START_REF] Coello Coello | Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art[END_REF] (Multi Objective Particle Swarm Optimization). The size of the swarm has been set at 2,000, and 500 iterations were chosen. Total computation time lasted roughly 1,000 s on an octo-core PC. To ensure good convergence, the process was run 10 times. The results discussed below represent a combination of the results from each run.

V. APPLICATION TO THE SIZING OPTIMIZATION OF A DIRECT-DRIVE GENERATOR-CONVERTER SYSTEM FOR A WAVE ENERGY CONVERTER

A. Presentation of the SEAREV Wave Energy Converter

SEAREV (French acronym for Autonomous Electrical System of Wave Energy Conversion) is a wave energy converter (WEC) composed of a float actuated by swell movement. Inside this device, an eccentric mass wheel oscillates relative to the float.

An electric generator (SPM) operating in direct drive converts the mechanical energy of the pendular wheel into electrical energy, thereby causing damping of the relative motion between these two parts. The power electronic converter on the generator side allows the damping torque to be controlled. Because of direct electrical conversion, an electrical energy storage system (ESS) can be placed on the DC-bus to smooth the output electrical power. The SEAREV system therefore provides an application example of this optimization method over a cycle in power generation mode.

B. Damping torque control strategy

One possible strategy for controlling the conversion torque consists of generating, via the associated machine-converter system, a viscous friction torque, i.e. introducing a resistant torque proportional to the angular velocity in addition to a levelling of the converted mechanical power [START_REF] Ruellan | Design Methodology for a SEAREV Wave Energy Converter[END_REF]. The idea behind this levelling is to downsize the electronic power converter without an excessive loss of produced energy potential. Indeed, without levelling, the power can be very high but during very few time. It will induced cost overrun without increasing the income. For each operating point, torque T i can thus be correlated with angular velocity Ω i by [START_REF] Lindstrom | Design of high-efficiency electrical motors for a hybrid electric vehicle[END_REF].

T i = βΩ i if βΩ 2 i < P lev P lev Ωi if βΩ 2 i ≥ P lev ( 18
)
where β is the viscous damping coefficient and P lev is the mechanical levelling power. We refer herein as "Damping Parameters" the set (β, P lev ).

C. Numerical modelization

The hydrodynamic and mechanical numerical modelization of the SEAREV has been developed at the Ecole Centrale de Nantes [START_REF] Babarit | Optimization and Time-Domain Simulation of the SEAREV Wave Energy Converter[END_REF]. This model permits to compute torque and angular velocity time series of the direct drive electrical generator. Because of strong hydro-mechanical coupling, they depend on the two damping parameters β and P lev previously defined. Others parameters have to be provided for the numerical simulation such as the sea state in the form of two values H 1/3 (the significant height) and T p (the spectral peak period). Simulations are conducted over 1256 s with a time-step of 0.1 s. The computation time of such a simulation is about 30 s. Fig. 7 gives examples of angular velocity and mechanical torque time series (between t = 500 s and t = 800 s) corresponding to β = 4.10 6 N.m.s -1 and P lev = 1 M W and for typical sea state (H s = 3 m,T p = 8 s). Fig. 8 shows the corresponding operating cycle in the torque-speed plane. The area of each plotted point is proportional to its mechanical energy (the cumulated duration of the operating point multiply by its mechanical power T i Ω i d i ).

D. Sensitivity of the damping parameters

Values of each damping parameters have a strong influence on the torque speed operating profile and therefore on the mechanical recoverable energy. To illustrate this fact, Fig. 9 shows the average mechanical power (recoverable energy before electrical conversion) over the operating profile according to the two damping parameters β and P lev for the sea state (H s = 3 m,T p = 8 s). It can be seen that the mechanical maximum power to convert can be limited up to 1.2 M W without excessive loss of average power (energy potential).

For each value of P lev , there is one value of β maximizing the average mechanical power. Values of damping parameters have also an influence on the maximum mechanical torque over the operating profile which is equal to T max = √ βP lev (cf Fig. 8) . It is then very difficult to find a priori the best sets of damping parameters. That is why, they have to be optimized in the same way as the machine-converter system sizing parameters. A comparison between two optimizations is presented in the following (cf Fig. 10). The first one is with β and P lev taken into account in the optimization parameters. The second one is with fixed damping parameters.

E. Numerical application to SEAREV WEC

The level of power being considered (∼1 MW) allows adopting the hypothesis previously described on transient thermal states, with the temperature rise constraint then being calculated on the basis of the average value of copper and iron losses. The losses coefficients for the power electronic Fig. 9. Recoverable mechanical average power (before electrical conversion) in Watt according to the mechanical levelling power and the viscous damping coefficient converters were given previously for a maximum voltage rating of 3,300 V.

In this example, the direct axis current is optimized at each operating point in order to minimize total machine-converter system losses. The numerical method employed to perform this constrained optimization has been described in Section II-D. The number of discrete values tested for i d has been fixed at 100 in the bounded interval [-I rated ; 0].

Because the solutions with a cost higher than 1 MA C will never be cost effective, a constraint has been added to limit the cost below this threshold.

The optimization results are presented on Fig. 10. These two Pareto fronts indicate the sets of best solutions relative to both the machine-converter system cost and average produced electrical power on the sea state (H s = 3 m,T p = 8 s). More thorough studies should take into account all the encountered sea states and their probability of appearance on a specific wave site.

It is shown on Fig. 10 that the simultaneous optimization of the machine-converter system and the damping parameters of the SEAREV WEC enable to extend the set of non dominated solutions, compared to the optimization with fixed values of β and P lev . For the first optimization (coupled), β and P lev vary respectively in the bounded intervals precised in Tab. V. As for the second optimization (uncoupled), β and P lev are fixed at (5 M N.m.s -1 , 1 M W ).

For the highest costs solutions of the coupled optimization, damping parameters are chosen in such a way that the incoming average mechanical power is maximum (here 260 kW cf Fig. 9) regardless of the peak mechanical power : (β = 4.5 * 10 6 N.m.s -1 , P lev = 3 M W cf Fig. 11). With the system cost decrease, P lev is the first damping parameter to decrease until it arrives in the vicinity of 1.5 M W . The average mechanical power is almost not affected by the levelling power above this value, but the mechanical peak power decreases greatly. That is why in this part of the Pareto front, the average produced electrical power does not decrease a lot, whereas the cost falls significantly. Below the value of 1.5 M W , the two damping parameters decrease simultaneously and the mechanical incident power as well. A claimed originality of the presented methodology of sizing is to take into consideration the local constrained optimization of the d-axis current i d,i for each operating point (cf section II-D). This step allows to take some constraints into account but also ratings of the power electronic converter and then implicitly flux-weakening possibility. Figure 12 compares the Pareto front obtained with the presented method (i.e. with flux-weakening) and these obtained with an optimization where the d-axis current is always set to 0 (i.e. without fluxweakening). Solutions without flux weakening exhibit always higher system cost for the same average produced electrical power. This cost overrun is mainly due to the power electronic converter cost. Indeed, the levelling of the mechanical incident power via the damping parameter P lev , can be achieve by flux-weakening without an important oversizing of the power electronic converter as it can be seen on Fig. 13 (on the bottom) where S conv /P lev ∼ 1. Otherwise (i.e. without fluxweakening possibility), the required apparent power of the power electronic converter is more related to the product of the maximum torque by the maximum speed (corner power) of the operating cycle as it can be seen on Fig. 13 (on the top S conv /(T max Ω max ) ∼ 1). Then, decrease the mechanical levelling power without permitting a flux-weakening is not interesting to reduce the cost of the power electronic converter because it increases the corner power. The sizing parameters of five specific solutions (denoted A,B,C,D and B') are detailed in Tab. VI. Fig. 14 shows the power-speed operating areas of B and B' solutions along with the operating profile corresponding to their damping parameters in the mechanical power-speed plane. The area of each plotted operating point of the cycle is proportional to its cumulated duration multiply by its mechanical power (T i Ω i d i ). The gray scale indicates the daxis current contour plot of the machine-converter system for each feasible operating point. On the left, this current is always set to 0 because flux-weakening is not permitted. On the right, d-axis current is optimized according to the total system losses criterion. These two solutions produce the same average electrical power but B' solution, which is optimized without flux-weakening possibility, costs twice as much as B solution (cf. Table VI). The mechanical power levelling is slighter for B' solution because a lower levelling would have increase the corner power and then the apparent power of the converter. For B solution, mechanical power levelling is more significant because flux-weakening is permitted and the apparent power is no more related to the corner power but to the levelling power. VI. CONCLUSION This paper has presented a machine-converter system optimization methodology applied over an operating profile with a strong coupling between the machine and the power electronic converter. The aim was optimizing the sizing of an all-electric conversion chain for a wave energy conversion system. This methodology proves to be applicable to any system in which a machine-converter system is operating at variable speed, like for electric traction or renewable energy conversion. A number of simplifying hypotheses were adopted, primarily to save computation time, yet the integration of more complex models would not pose a problem from a methodological standpoint. A machine model based on finite elements could even be used to more accurately calculate magnetic losses, particularly under conditions of considerable flux weakening, although computation time would rise substantially. A transient thermal model could also improve quality of results especially for applications where thermal time constants of the machine are near from the loss variation periods. Finally, taking the cost of manufacturing process and these of inactive parts into account in the cost of the machine could lead to different optimal solutions [START_REF] Mcdonald | modelling and optimisation of novel topologies of electromagnetic actuators and generators, and the optimisation of renewable energy systems[END_REF].

Fig. 3 .

 3 Fig. 3. Illustration of the d-axis current constrained optimization problem

Fig. 4 .

 4 Fig. 4. Equivalent thermal lumped circuit of one half of a tooth pitch of the SPM machine

Fig. 5 .

 5 Fig. 5. Optimization flowchart

Fig. 6 .

 6 Fig. 6. Schematic diagram of the SEAREV WEC operating principle

Fig. 7 .Fig. 8 .

 78 Fig. 7. Examples of operating time series (angular velocity and torque time series) extract of 200 s of a total time cycle equals 1,256 s. Damping parameters are β = 4.10 6 N.m.s -1 and P lev = 1 M W , then the maximum torque is 2 MN.m

Fig. 10 .Fig. 11 .Fig. 12 .

 101112 Fig. 10. Pareto fronts with and without damping parameters optimization

Fig. 13 .Fig. 14 .

 1314 Fig.[START_REF] Mademlis | Loss minimization in surface permanent-magnet synchronous motor drives[END_REF]. Sconv/P lev and Sconv/(TmaxΩmax) ratios according to to the average produced electrical power for the optimization without flux-weakening (on the top) and with flux-weakening (on the bottom)

  C mach Cost of the machine d i Cumulated duration of the i th operating point E elec Electrical energy converted f sw Switching frequency of the converter H i Local field intensity for the i th operating point H s Significant wave height of the sea state I rated Rated current of the power electronic converter L l Leakage inductance per phase L m Magnetizing inductance per phase M x Total mass of the material x (iron ,magnet, copper) P average Average produced electrical power P cond Power electronics conduction losses P copper Copper losses P iron Iron losses

	P lev	Levelling power of the WEC
	P loss Machine-converter system losses
	P sw	Power electronics switching losses
	R d,x	Dynamic resistance of x (diode or igbt) component
	R f	Equivalent iron loss resistance
	R s	Armature resistance per phase
	R th

  in TableII. The design range of each parameter is also precised for the application further below.

	h mag		hstat
		hrot
	r s	2π 3p	k slot π 3p
		e	h slot
	Fig. 1. Geometric parametrization of the SPM machine

TABLE IV CONSTANT

 IV PARAMETERS USED FOR THE APPLICATION FURTHER BELOW

	Symbol	Description	Value
	V 0,IGBT Threshold voltage for each device V 0,diode	2 V 1.7 V
	r d,IGBT Dynamic resistance for each	1500 mΩ.A -1
	r d,diode	component per ampere-rating	1000 mΩ.A -1
	Bsw,rec	Switching and recovery losses coefficient	3 mJ.A -1
	fsw	Switching frequency	2 kHz
	Br	Remanent induction of permanent magnet	1 T
	k f ill	Slot-filling coefficient	0.4
	k H	Hysteresis loss coefficient	90 A.m.V -1 .s -1
	αp	Eddy current loss coefficient	0.065 A.m.V -1
	ρ Cu	Copper resistivity @130 • C	2.5.10 -8 Ω.m -1
	λ Cu


PSATTT 2011: International Workshop on Proof Search in Axiomatic Theories and

Preface

This volume contains the papers presented at PSATTT-11: International Workshop on Proof-Search in Axiomatic Theories and Type Theories held on July 31, 2011 in Wroclaw. This workshop continues the series entitled "Proof Search in Type Theories" (PSTT at CADE'09, FLOC'10), and enlarges its scope to encompass proof search in axiomatic theories as well.

Generic proof-search in propositional and first-order logic (even second-order, higher-order) are fields that already benefit from a long research experience, spanning from techniques as old as unification to more recent concepts such as focusing and polarisation.

More adventurous is the adaptation of generic proof-search mechanisms to the specificities of particular theories, whether these are expressed in the form of axioms or expressed by sophisticated typing systems or inference systems.

The aim of this workshop is to discuss proof search techniques when these are constrained or guided by the shape of either axioms or inference/typing rules. But it more generally offers a natural (and rather informal) venue for discussing and comparing techniques arising from communities ranging from logic programming to type theory-based proof assistants, or techniques imported from the fields of automated reasoning and SMT but with an ultimate view to build proofs or at least provide proof traces.

Papers were solicited on topics that includes (but are not limited to):

invertibility of deductive rules, polarity of connectives and focusing devices, more generally, development and application of theorems establishing the existence of normal forms for proofs, explicit proof-term representations and dynamic proof-term construction during proof-search, use of meta-variables to represent unknown proofs to be found, use of failure and backtracking in proof search, integration of rewriting or computation into deductive systems, as organised by e.g. deduction-modulo integration of domain-specific algorithms into generic deductive systems transformation of goals into particular shapes that can be treated by domainspecific tactics or external tools externalisation of some proof searching tasks and interpretation of the obtained outputs (justifications, execution traces...) more generally, interfaces between cooperating tools importation of automated reasoning techniques and SMT techniques to proofconstructing frameworks quantifier instantiation in SMT techniques, arbitrary alternation of forall/exists quantifiers unification in particular theories or in sophisticated typing systems II More generally, contributions about the following topics are welcome proof search strategies, their complexity and the trade-off between completeness and efficiency, searching for proofs by induction, finding well-founded induction measures, strengthening goals to be proved by induction, etc, reasoning on syntaxes with variable binding (in e.g. quantifiers or data structures), termination, computational expressivity of related programming paradigms, user interaction and interfaces, systems implementing any of the ideas described Synthesising some of the above aspects into unifying theories is a concern of our research theme that aims at bringing together research efforts of different communities, enhancing their interaction. Contributions made in a spirit of synthesis are thus particularly welcome.

The organization of the workshop relied on the use of the EasyChair system, which was very useful. The workshop was partially funded by the Agence Nationale pour la Recherche, under the project entitled Proof-Search control in Interaction with domain-specific methods. The workshop organizers would like to thank the program committee for their work, the organizers of the PxTP workshop for a very fruitful partnership, as well as the organizers of the CADE conference.

July 2011

Stéphane Lengrand

Organization

The workshop was organized by


Belen Ruiz-Antorán

Antònia Agustí Escasany

Imma Antoni Vallano Ferraz

Danés Carreras

Neus Riba
email: nriba@clinic.ub.es

Silvia Mateu Escudero

Mª Joan Costa

Blanca Sánchez Santiago

Leonor Laredo

José Antonio Durán Quintana

Antònia Agustí

Antoni Vallano Ferraz

Imma Danés

Silvia Mateu
email: smateu@fundacio-puigvert.es

Blanca Sánchez
email: bsanchez@humv.es

Juan Ramón

Francisco Abad-Santos

Payares Concepción

Belén Herrera

Díaz Sádaba
email: bsadaba@unav.es

Eugenio Gómez De Rada

Ontañón

I Danés Carreras

M B Sánchez Santiago

J R Castillo

C Payares Herrera

B Sádaba Díaz De Rada

E Gómez Ontañón

Use of non-specific intravenous human immunoglobulins in Spanish hospitals; need for a hospital protocol

Keywords: Intravenous immunoglobulin, Drug utilization study, Off-label use, Compassionate use, Cost

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

Introduction

Intravenous immunoglobulin (IVIG), a plasma protein derivative employed in the treatment of a number of conditions, has been increasingly used in medicine over the last two decades [START_REF] Farrugia | Intravenous immunoglobulin: regulatory perspectives on use and supply[END_REF]. However, only some indications have been authorised by the Spanish Medicines Agency on the basis of contributed evidence. IVIG is also used for a number of conditions not included in the regulatory approvals but for which substantial clinical evidence exists [START_REF] Farrugia | Intravenous immunoglobulin: regulatory perspectives on use and supply[END_REF]. There has been a significant increase in the price per unit of IVIG, due to the increased complexity of manufacturing processes, including safety enhancements and stringent regulatory requirements [START_REF] Jolles | Clinical uses of intravenous immunoglobulin[END_REF][START_REF] Dalakas | The use of intravenous immunoglobulin in the treatment of autoimmune neuromuscular diseases: evidence-based indications and safety profile[END_REF][START_REF] Siegel | The product: all intravenous immunoglobulins are not equivalent[END_REF][START_REF] Chapel | Safety and availability of immunoglobulin replacement therapy in relation to potentially transmissable agents. IUIS Committee on Primary Immunodeficiency Disease. International Union of Immunological Societies[END_REF]. The capacity to fractionate IVIG from plasma is finite, and regulatory stringency has resulted in major recalls of the product by many of the important worldwide manufacturers. These factors, together with the increase in utilisation, have resulted in significant worldwide shortages of IVIG in the last few years [START_REF] Jolles | Clinical uses of intravenous immunoglobulin[END_REF][START_REF] Dalakas | The use of intravenous immunoglobulin in the treatment of autoimmune neuromuscular diseases: evidence-based indications and safety profile[END_REF][START_REF] Siegel | The product: all intravenous immunoglobulins are not equivalent[END_REF][START_REF] Chapel | Safety and availability of immunoglobulin replacement therapy in relation to potentially transmissable agents. IUIS Committee on Primary Immunodeficiency Disease. International Union of Immunological Societies[END_REF].

The use of this medicine in non-approved indications, the increase in consumption and its high cost have already promoted the rationalisation of its use through a consensus in other countries. Non-specific IVIG has been the object of a revision from the European Medicines Agency (EMA), and certain indications have been accepted on the basis of contributed evidence and as a result of the companies' request [START_REF]Core SPC for human normal immunoglobulin for intravenous administration (IVIg)[END_REF][START_REF]Committee for medicinal products for human use (CHMP) (2004) Core SPC for human normal immunoglobulin for intravenous administration (IVIg)[END_REF]. Different consensuses and guidelines have attempted to establish priorities and to optimise the use of IVIG with the result that several audits of its usage in a number of different countries have already been published [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF][START_REF] Chen | A multicenter drug use surveillance of intravenous immunoglobulin utilization in US academic health centers[END_REF][START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF][START_REF] Darabi | Current usage of intravenous immune globulin and the rationale behind it: the Massachusetts General Hospital data and a review of the literature[END_REF][START_REF] Perayre | Changes in the pattern of intravenous immunoglobulin use over a 5-year period[END_REF].

In Spain, according to the legislation that was in force at the time of this study, any drug use outside the conditions established by the Spanish Medicines Agency on the authorised label should be considered "compassionate use." Therefore, off-label drug use should follow all the requirements to get the corresponding authorisation and to be reimbursed by the National Health Service as a nonauthorised medicinal product when prescribed for an individual patient [13].

In this regulatory/legal setting, the Spanish Society of Clinical Pharmacology considered it to be of interest to carry out a study describing the utilisation of IVIG in Spain. The purpose of this study was to describe the use of IVIG in a number of Spanish hospitals and to evaluate the justification/rationale behind that use, according to a set of previously established criteria. Secondary objectives were to describe the different administrative patterns in the different situations faced (whether informed consent was obtained, if the corresponding authorisations for compassionate use were obtained, among others), the adverse events profile, the economic quantification of IVIG use, and the variability of use among different hospitals. The main hypotheses of the study were that a considerable percentage of IVIG prescriptions would be for off-label indications, especially for nonapproved non-accepted indications, suggesting unnecessary health expenditure. A certain variability in IVIG prescriptions between hospitals was expected.

Methods

An observational, prospective and multicentre drug utilisation study was carried out in 13 tertiary Spanish hospitals. Data were collected in each centre over a period of 3 months between July of 2004 and January of 2005.

All patients who received any of the IVIG drugs (Flebogamma®, Endobulin®, Gammagard®) were included in the study regardless of their age, sex, reason for the prescription, dose and duration of treatment, or concomitant drugs.

By means of a structured questionnaire, information on patient's demographics, indication for IVIG use, dosage regimen, adverse drug reactions, reasons for treatment withdrawal and requested informed consent were gathered from the medical records. Other data about administrative parameters, authorisation of compassionate use and batch identification as well as the cost of IVIG use were supplied by the pharmacy service of every hospital participating in the study. In addition, data of the participant hospitals were recorded.

An ad hoc appropriateness analysis of IVIG indications was performed according to IVIG indications established by the EMA [START_REF]Core SPC for human normal immunoglobulin for intravenous administration (IVIg)[END_REF][START_REF]Committee for medicinal products for human use (CHMP) (2004) Core SPC for human normal immunoglobulin for intravenous administration (IVIg)[END_REF], recommendations of expert panels for offlabel use and the published scientific evidence [14 -32]. For the aforementioned analysis, the indications were classified in three groups: authorised by the EMA (group 1), nonauthorised indications with scientific evidentiary support (level A (Oxford Centre for Evidence-based Medicine): at least one controlled and randomized clinical trial that was appropriately designed supports IVIG use) (group 2) (Table 1) and finally the others were considered as nonauthorised and non-accepted indications (group 3). For the last two groups, informed consent and the Spanish compassionate use procedure were required. The definition of compassionate use in Spain is a special and unique requirement that applies to drug use [START_REF] Farrugia | Intravenous immunoglobulin: regulatory perspectives on use and supply[END_REF] in patients outside a clinical trial with an investigational medicinal product and (2) for indications or conditions different from those authorised in the summary product characteristics ("off-label" use) [13].

The cost of IVIG use was calculated from the price information supplied by the financial department of every hospital participating in the study.

The study was conducted according to international ethics recommendations. In accordance with the national directives in relation to post-authorisation studies, the study was approved by the Ethics Committee of Clinical Investigation of the coordinating hospital and additionally by the remaining hospitals whenever required.

Statistics analysis Data were entered in a relational database (Microsoft Access, Microsoft, Redmond, WA). Descriptive analysis of continuous variables was performed by means of mean, standard deviation, median and range. The statistical analysis was performed using SAS version 9 statistical package.

Results

During the study period, data from the 554 patients treated in the participating hospitals were collected. Patients had a mean age of 52 years (±16), and 54% were female. It should be noted that the patient population included a group of 87 children and adolescents (15.7%).

A total of 1,287 prescriptions were administered during the study period, representing 2,352 days of treatment. The average number (SD) of days of treatment was 1.7 (1.4), with a median of 1 day (range 1-11 days). The average number (SD) of prescriptions per patient during the study period was 2.3 (1.6), with a median of 2 prescriptions (range 1-13). A total of 238 patients (43%) received one IVIG prescription, 99 patients (17.9%) two prescriptions, 96 (17.3%) three prescriptions, 82 (14.8%) four prescriptions, and 39 (7%) five or more prescriptions. The treatment with IVIG was initiated during the study period in 174 (31.4%) patients, before the study period in 344 patients (62.1%) and in 36 patients (6.5%) the timing was unknown.

The most frequently prescribed IVIG was Flebogamma (654, 50.8%), followed by Endobulin (583, 45.3%) and Gammagard (50, 3.9%). The mean (SD) daily dose was 24 (14.8) g, with a median of 22.5 g (range 0.6-90 g). The IVIG were most frequently prescribed by the neurology (131 patients and 187 prescriptions), haematology (125 patients and 332 prescriptions) and pneumology (104 patients and 365 prescriptions) services.

Overall, 335 patients (60%) were prescribed IVIG for labelled indications authorised by the EMEA (group 1), while 219 (40%) received them for off-label indications (groups 2 and 3). In the off-label indications, 86 patients (39.2%) were included in group 2 (non-authorised indications with scientific evidentiary support), and 133 patients (60.7%) in group 3 (non-authorised and non-accepted indications) There were 953 (74%) prescriptions of IVIG for authorised indications, 137 (11%) for non-authorised 2. The most frequently authorised indications were primary (30.5% of patients and 43% of total prescriptions) and secondary immunodeficiencies (16.8% of patients and 21.4% of total prescriptions). The levels of IG were measured in 255 (46%) of a total of 554 prescriptions for primary immunodeficiencies. Of these prescriptions, in 79 (30%) cases, IG levels were below the recommended range (<600 mg/dl) for IVIG administration.

The non-authorised indications with scientific evidentiary support (group 2) are presented in Table 3. The most frequent were motor multifocal neuropathy (3.8% of patients and 3.3% of total prescriptions), myasthenia gravis (4.5% of patients and 2.6% of total prescriptions) and chronic inflammatory demyelinating polyradiculopathy (3.4% of patients and 2.1% of total prescriptions).

The non-authorised and non-accepted indications (group 3) are presented in Table 4. The most frequent non-accepted indications were multiple sclerosis (2.7% patients and 1.6% of total prescriptions), bullous dermatosis (1.8% patients and 1.4% of total prescriptions) and transplanted organ complications (1.8% patients and 1.2% of total prescriptions).

According to Spanish legislation, 219 of the 554 patients included in the study needed an informed consent to comply with the compassionate use procedure. However, informed consent was requested in 26 patients (12%) and the compassionate use procedure was only followed in 12 (5.5%) of these patients. In only 592 (46%) of the prescriptions was the administered lot number recorded in the clinical history of the patient.

At least one adverse drug reaction was described in 119 patients (21.4%). In 28 patients (5%) it was a serious adverse drug reaction, and in 16 patients the IVIG treatment was discontinued or the regimen modified due to the adverse drug reaction. The most commonly reported adverse effects were general disorders and events at the administration site, followed by nervous system disorders, gastrointestinal disorders, musculoskeletal and connective tissue disorders, and skin and subcutaneous tissue disorders. The most frequent serious adverse drug reactions were headache, pyrexia, malaise, nausea, vomiting, asthenia, and back pain. In nine patients (1.6%), IVIG treatment was withdrawn for lack of effectiveness. The total budget for IVIG treatment during the period of the study was 1,794,494 €. The mean (SD) cost of IVIG treatment per patient in the study was 3,260.6 € (2,435.7 €) and per prescription was 1,398.7 € (1,502.4 €). Table 5 shows the cost of IVIG use according to the appropriateness of indications. The mean (SD) cost of IVIG per prescription and per patient for group 2 and group 3 was higher than for group 1. The indications with highest mean cost per prescription were Guillain-Barré syndrome, followed by dermatomyositis, chronic inflammatory demyelinating polyneuropathy and motor multifocal neuropathy.

Table 6 shows the differences in IVIG prescriptions between hospitals. A great variability was observed among the number of treated patients, number of prescriptions and the appropriateness of indications between hospitals. The mean (SD) cost per prescription between hospitals ranged from 919.4 € (1,158 €) to 4,223.8 € (1,490.2 €). The recording of lot numbers also ranged from some settings in which it was 100%, down to hospitals where the lot number was never registered.

Discussion

The results of the study show that 40% of patients treated with IVIG and almost a third of prescriptions were for offlabel indications. Figures for the non-authorised and nonaccepted indications were 24 and 15% respectively of the total treated patients and prescriptions. Other IVIG utilisation studies have been reported, but this particular study has the highest number of included patients.

The percentage of IVIG use for off-label indications described in other multicentre drug utilisation studies ranged from 62.9 to 20% [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF][START_REF] Chen | A multicenter drug use surveillance of intravenous immunoglobulin utilization in US academic health centers[END_REF][START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF]. In a study where IVIG use was monitored over a period of 2 years (2003)(2004)(2005) in 339 patients from four Canadian Atlantic provinces, 62.9% prescriptions were for off-label indications [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF]. This rate was 52% in another study from 12 U.S. academic health centres [START_REF] Chen | A multicenter drug use surveillance of intravenous immunoglobulin utilization in US academic health centers[END_REF], where data from 251 patients were prospectively collected during 8 months in 1996, and it was only 20% in a retrospective study from four Toronto teaching hospitals carried out in 429 patients over a 6-year period (1995-2000) [START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF]. At the same time, the percentage of non-authorised and non-accepted IVIG prescriptions described in the present study was higher than that described in the American study (14% of treated patients) [START_REF] Chen | A multicenter drug use surveillance of intravenous immunoglobulin utilization in US academic health centers[END_REF] and in the study from four teaching hospitals in Canada (8.4% of the indications) [START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF].

These differences cannot be explained by a variance in the prevalence of the diseases between countries. The lack of a well established treatment for the majority of these severe diseases could explain the use of drugs with scarce evidence in settings where a consensus protocol is not available.

In this study, as in those mentioned above, the neurologists and the haematologists were the leading prescribing specialists of IVIG [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF][START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF]. However, in our study a relevant difference was the high prescription of IVIG by pneumologists.

Primary and secondary immunodeficiencies were the most frequently labelled indications in this study. It is generally agreed that IVIG is useful for these conditions and their administration is recommended when plasma levels of IG are below 600 mg/dl [START_REF]Core SPC for human normal immunoglobulin for intravenous administration (IVIg)[END_REF][START_REF]Committee for medicinal products for human use (CHMP) (2004) Core SPC for human normal immunoglobulin for intravenous administration (IVIg)[END_REF]. During the study period, IG plasma levels were measured quite frequently but IVIG was often administered even if the IG levels were above the levels for which IVIG administration is recommended. In the American and Canadian studies, immunodeficiencies also represented the most frequent labelled indications, but idiopathic thrombocytopenic purpura was the most frequent [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF][START_REF] Chen | A multicenter drug use surveillance of intravenous immunoglobulin utilization in US academic health centers[END_REF][START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF]. In this condition IVIG therapy was established as an immunomodulatory alternative when steroids fail to increase the platelet count [START_REF] Jolles | Clinical uses of intravenous immunoglobulin[END_REF].

The neurological conditions (motor multifocal neuropathy, myasthenia gravis and chronic inflammatory demyelinating polyradiculopathy) were the most frequent non-authorised indications with scientific support in the study. In several randomized controlled trials, IVIG therapy improved some features of these conditions and was increasingly preferred to steroids or plasma exchange, especially for motor multifocal neuropathy and chronic inflammatory demyelinating polyradiculopathy therapy [START_REF] Jolles | Clinical uses of intravenous immunoglobulin[END_REF]. However, the EMEA is requesting further clinical studies for approval of IVIG use in these immunomodulatory indications [START_REF] Farrugia | Intravenous immunoglobulin: regulatory perspectives on use and supply[END_REF]. In the American and the Canadian studies, chronic inflammatory demyelinizing polyradiculopathy was the most frequent non-authorised indication with scientific support [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF][START_REF] Chen | A multicenter drug use surveillance of intravenous immunoglobulin utilization in US academic health centers[END_REF][START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF]. Guillain-Barré syndrome was another frequent non-authorised indication with scientific support in the US and Canadian studies [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF][START_REF] Chen | A multicenter drug use surveillance of intravenous immunoglobulin utilization in US academic health centers[END_REF][START_REF] Pendergrast | Changes in intravenous immunoglobulin prescribing patterns during a period of severe product shortages, 1995-2000[END_REF][START_REF] Darabi | Current usage of intravenous immune globulin and the rationale behind it: the Massachusetts General Hospital data and a review of the literature[END_REF]. However, Guillain-Barré syndrome is a label indication in Europe, and therefore, in this study was included as an authorised indication. Multiple sclerosis, bullous dermatosis and transplanted organ complications were the most frequent non-authorised and non-accepted indications in this study. The percentage of patients with IVIG therapy for non-authorised and nonaccepted indications described in our study was higher than that reported in the other studies. However, the percentage of non-authorised and non-accepted indications per prescription was lower due to the high proportion of patients with immunodeficiencies in the study and the elevated frequency of IVIG administration in these patients throughout the study. All these conditions, with the exception of multiple sclerosis, which was classified as a non-authorised indication with scientific support in the Canadian studies [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF], also appeared on the list of the most frequently non-authorised and non-accepted indications in the other studies. A Cochrane review of IVIG in multiple sclerosis concluded that while there is some scientific evidence to support its use in relapsing-remitting disease, there is a need for further studies to establish more robust conclusions [START_REF] Van Schaik | Intravenous immunoglobulin for multifocal motor neuropathy[END_REF].

The relevance of IVIG prescriptions for non-authorised and non-accepted indications lies in the increase that has been described over the last few years; the situation is dramatic when a period of product shortage occurs [START_REF] Jolles | Clinical uses of intravenous immunoglobulin[END_REF][START_REF] Dalakas | The use of intravenous immunoglobulin in the treatment of autoimmune neuromuscular diseases: evidence-based indications and safety profile[END_REF][START_REF] Siegel | The product: all intravenous immunoglobulins are not equivalent[END_REF][START_REF] Chapel | Safety and availability of immunoglobulin replacement therapy in relation to potentially transmissable agents. IUIS Committee on Primary Immunodeficiency Disease. International Union of Immunological Societies[END_REF]. On the other hand, IVIG is a haemoderivative product and its administration for these conditions submits patients to some risk [START_REF] Jolles | Clinical uses of intravenous immunoglobulin[END_REF][START_REF] Dalakas | The use of intravenous immunoglobulin in the treatment of autoimmune neuromuscular diseases: evidence-based indications and safety profile[END_REF][START_REF] Siegel | The product: all intravenous immunoglobulins are not equivalent[END_REF][START_REF] Chapel | Safety and availability of immunoglobulin replacement therapy in relation to potentially transmissable agents. IUIS Committee on Primary Immunodeficiency Disease. International Union of Immunological Societies[END_REF]. Finally, the economic consequences are also relevant. In our study, the mean cost per prescription and per patient was higher for the non-authorised indications with scientific support and the non-authorised and non-accepted indications than for the authorised indications. The economic implications of IVIG use have only been assessed in a few studies. Constantine et al. reported that a 4.2% reduction in unlabelled IVIG use in indications not supported by evidence was associated with a $153,799 reduction in cost during their 2-year project [START_REF] Constantine | Intravenous immunoglobulin utilization in the Canadian Atlantic provinces: a report of the Atlantic Collaborative Intravenous Immune Globulin Utilization Working Group[END_REF]. In our study, if IVIG had not been prescribed for the non-authorised and non-accepted indications, then a reduction in cost of 459,973.52 € (25.6% of the total budget) would have been produced during the study period. In another study from the Massachusetts General Hospital, the annual cost of IVIG use for chronic neuropathies (chronic inflammatory demyelinating polyneuropathy and multifocal motor neuropathy) exceeded $50,000 per patient [START_REF] Darabi | Current usage of intravenous immune globulin and the rationale behind it: the Massachusetts General Hospital data and a review of the literature[END_REF]. In our study, the mean cost per patient for these diseases was less, being 5,445.1 € (1,779.6 €) to treat chronic inflammatory demyelinating polyneuropathy and 6,854.0 € (3,782.2 €) to treat multifocal motor neuropathy over the 3 months of the study.

On the other hand, only on a few occasions was informed consent requested and compassionate use regulations followed in cases where Spanish legislation made this necessary. This behaviour may involve some legal consequences for medical doctors, especially if an adverse reaction appears with the administered haemoderivative product for an unlabelled indication without scientific support. Nevertheless, the Spanish legislation for compassionate use has recently changed and now includes only the requirement for compliance with the protocol for uses of an investigational medicinal product in a patient outside a clinical trial.

Finally, great variability was observed in the IVIG prescription appropriateness between hospitals. It is interesting to note that two appropriateness patterns of prescription were observed. In some hospitals most of the IVIG prescriptions were for authorised indications, and in other hospitals the percentage of IVIG prescriptions for authorised and non-authorised indications was similar. A study carried out in a single tertiary Spanish hospital, and not included in our study, reported a percentage of prescriptions for labelled indications of 85.8%, similar to one of the prescription patterns mentioned above, and most were for primary immunodeficiencies [START_REF] Perayre | Changes in the pattern of intravenous immunoglobulin use over a 5-year period[END_REF]. This hospital variability may be due, at least in part, to the heterogeneity of the hospitals (i.e. size of the hospitals, medical specialities and treated pathologies). Unfortunately, no information on IVIG prescription differences between hospitals was included in the other multicentre published studies.

One of the main limitations of our study is whether the results are representative of IVIG prescription in Spain, as a random sample of hospitals was not selected. However, IVIG are usually used in tertiary hospitals similar to those included in our study. Another limitation is the variability in the categories where some indications are classified. Guillain-Barré syndrome and multiple sclerosis are classified as non-authorised indications with scientific support in some recommendations [START_REF] Ratko | Recommendations for off-label use of intravenously administered immunoglobulin preparations. University Hospital Consortium Expert Panel for off-label use of polyvalent intravenously administered immunoglobulin preparations[END_REF][START_REF]Present and future uses of IVIG. A Canadian multidisciplinary consensus building initiative[END_REF]. In our study, these misclassifications would have slightly increased the percentage of IVIG prescriptions for the non-authorised indications with scientific support to 23.4% per patient and 15.4% per prescription and slightly decreased the corresponding percentages for the authorised indications to 56% per patient and 72.4% per prescription, and the nonauthorised and non-accepted indications to 21% per patient and 13.4% per prescription, respectively. In addition, another limitation may be that the study was conducted 5 years ago; however, the findings are still in line with the present situation because significant changes regarding IVIG use have not happened in Spanish hospitals during this period.

Despite these limitations, the results of this study show that in Spain, a significant percentage of IVIG prescriptions are for indications without scientific support. This fact is even more important because the administration of IVIG is associated with some risks, its production is very limited with recurrent periods of shortage, and it has a high cost. Therefore, the Spanish Society of Clinical Pharmacology considers the elaboration of protocol agreements of IVIG use to be of great interest and believes that the results of this study, which describes IVIG utilisation in our country, are essential and confirm that a consensus statement is needed. A proposed consensus committee would imply the involvement of the following interested parties: health authorities, prescribing physicians (haematologists, neurologists, internal medicine specialists), pharmacists and clinical pharmacologists.

To provide an example, national Clinical Guidelines for IVIG use have been available in the United Kingdom since 2007, have been recently revised in a second edition [START_REF] Provan | Clinical guidelines for immunoglobulin use[END_REF], and local hospitals are required to complete audit forms for monitoring the use of IVIG according to the Clinical Guidelines. The goal of this interesting initiative, supported by the Department of Health, is to provide guidance on appropriate use, to manage demand and to ensure supply for patients for whom IGIV is life-saving.

In conclusion, this extensive nationwide study on IVIG prescribing describes a high proportion of off-label prescriptions and highlights the need to provide national clinical guidelines for IVIG use.

Table 1

 1 Classification of indications according to the authorisation by the EMEA and scientific evidentiary support

	Authorised indications by the EMEA	Non-authorised indications with scientific evidentiary support
	Primary immunodeficiencies	Myasthenia gravis
	Secondary immunodeficiencies	Chronic inflammatory demyelinating polyradiculopathy
	Chronic lymphoid leukaemia	Motor multifocal neuropathy
	Multiple myeloma	Dermatomyositis
	Medulla osseous transplant	Pure red cell aplasia parvovirus B19
	Idiopathic thrombocytopenic purpura	Lambert-Eaton syndrome
	Kawasaki syndrome	Thrombocytopenia refractory to transfusions
	Guillain-Barré syndrome	Interstitial pneumonia CMV, in BMT patients
	Isoimmunization
	Children with congenital AIDS and recurrent infections
	BMT: Bone Marrow Transplantation

Table 3

 3 IGIV prescriptions in non-authorised indications with scientific evidentiary support

	Indications	Patients		Prescriptions
		Non-authorised indications with	All indications	Non-authorised indications with	All indications
		scientific evidentiary support	(n=554) (%)	scientific evidence support	(n=1,287) (%)
		(n=86) (%)		(n=137) (%)
	Motor multifocal neuropathy	24.4	3.8	30.7	3.3
	Myasthenia gravis	29.1	4.5	24.8	2.6
	Chronic inflammatory demyelinating	22.1	3.4	19.7	2.1
	polyradiculopathy
	Dermatomyositis	14.0	2.2	13.1	1.4
	Pure red cell aplasia parvovirus B19	2.3	0.4	5.1	0.5
	Interstitial pneumonia CMV in BMT	4.6	0.7	3.6	0.4
	patients
	Thrombocytopenia refractory to	2.3	0.4	2.2	0.2
	transfusions
	Lambert-Eaton syndrome	1.2	0.2	0.7	0.1
	BMT: Bone Marrow Transplantation

Table 2

 2 IGIV prescriptions in the authorised indications

	Indications	Patients		Prescriptions
		Authorised indications	All indications	Authorised indications	All indications
		(n=335) (%)	(n=554) (%)	(n=953) (%)	(n=1,287) (%)
	Primary immunodeficiencies	50.4	30.5	58.1	43.0
	Secondary immunodeficiencies a	27.8	16.8	28.9	21.4
	Idiopathic thrombocytopenic purpura	10.1	6.1	6.3	4.7
	Kawasaki syndrome	0.9	0.5	0.3	0.2
	Guillain-Barré syndrome	7.2	4.3	2.8	2.1
	Isoimmunization	0.9	0.5	0.3	0.2
	Congenital AIDS	2.7	1.6	3.3	2.4

a Chronic lymphoid leukaemia, multiple myeloma and medulla osseous transplant indications with scientific support and 197 (15%) for nonauthorised and non-accepted indications.

The authorised indications group (group 1) is presented in the Table

Table 4

 4 IGIV prescriptions in the most frequent non-accepted indications

	Indications	Patients		Prescriptions
		Non-authorised non-accepted	All indications	Non-authorised non-accepted	All indications
		indications (n=133) (%)	(n=554) (%)	indications (n=197) (%)	(n=1,287) (%)
	Multiple sclerosis	11.3	2.7	10.6	1.6
	Bullous dermatosis	7.5	1.8	9.1	1.4
	Transplanted organ complications	7.5	1.8	7.6	1.2
	Rheumatoid arthritis and other	3.7	0.9	6.6	1.0
	inflammatory polyarthropathies
	Other malignant neoplasias: histiocytic	3.7	0.9	4.6	0.7
	and lymphoid tissues
	Purpura and other haemorraghic	5.3	1.3	4.6	0.7
	conditions
	Peripheral neuropathy: hereditary and	5.3	1.3	4.6	0.7
	idiopathic
	Horn cells disease	4.5	1.1	4.6	0.7
	Chronic glomerulonephritis	3.7	0.9	3.5	0.6
	Immune disorders	5.3	1.3	3.5	0.5
	Encephalitis, myelitis and	4.5	1.1	3.5	0.5
	encephalomyelitis

Table 5

 5 Cost of IVIG use according to the appropriateness of indications

	Indications

The total budget for IVIG treatments for the authorised indications was of 884,932.6 € (49.3%), for the non-authorised indications with scientific support 451,216.8 € (25.1%) and for the non-authorised and non-accepted indications 459,973.5 € (25.6%).

Table 6

 6 Characteristics of IVIG prescription across the hospitals

	Hospital no.	Authorised	Non-	Non-authorised	Total
	(n patients)	indications,	authorised	and non-	prescriptions,
		n (%)	indications	accepted	n (%)
			with	indications,
			evidentiary	n (%)
			support,
			n (%)
	1 (60)	134 (82.2) 3 (1.8)	26 (16.0)	163 (100)
	2 (173)	423 (82.5) 9 (1.8)	81 (15.8)	513 (100)
	3 (51)	62 (49.2) 37 (29.4) 27 (21.4)	126 (100)
	4 (44)	102 (75.6) 14 (10.4) 19 (14.1)	135 (100)
	5 (11)	6 (46.2)	3 (23.1)	4 (30.8)	13 (100)
	6 (23)	17 (53.1) 8 (25.0)	7 (21.9)	32 (100)
	7 (25)	35 (85.4) 4 (9.8)	2 (4.9)	41 (100)
	8 (40)	29 (46.0) 13 (20.6) 21 (33.3)	63 (100)
	9 (11)	0 (0.0)	13 (92.9) 1 (7.1)	14 (100)
	10 (42)	53 (62.4) 15 (17.6) 17 (20.0)	85 (100)
	11 (8)	9 (75.0)	2 (16.7)	1 (8.3)	12 (100)
	12 (26)	28 (66.7) 5 (11.9)	9 (21.4)	42 (100)
	13 (40)	24 (50.0) 11 (22.9) 13 (27.1)	48 (100)

Eur J Clin Pharmacol (2010) 66:633-641

Appendix

The following persons participated in the study: Maria Oliveras Arenas, Aurora Fernández Polo, Xavier Carné, Nuria Cruz, Francesc Jané Carrencà, Anna Vaqué, Anabel Barriocanal, Cristina Campo Hoyos, Marta Valero Domínguez, Antonio Portoles, Aithana Calvo, Mª Ángeles Geniz Clavijo, José Luis Hernández Galán, Carmen María Jiménez, Mónica Saldaña, María Laura Peregrina, Lourdes Cabrera García, Arantxa Sancho López, Maria José Pedrosa Martinez, Isabel Salcedo de Diego, José Ramón Azanza Perea, Julia Nazco Casariego, Mar García-Sáiz.