P Chapelle
email: pierre.chapelle@univ-lorraine.fr

B Tezenas

A Jardy

B Tezenas Du Montcel

C Creusot

Arc appearance and cathode spot distribution in a long gap high-current vacuum arc controlled by an external axial magnetic field

Keywords: Vacuum arc, axial magnetic field, long gap, arc appearance, cathode spot distribution, experimental study

An experimental study of a high-current vacuum arc (VA) generated between two static CuCr25 contacts spaced 20 or 30 mm apart was conducted to characterize the arc appearance and the cathode spot (CS) distribution. The arc was ignited from the lateral surface of the cathode and controlled using an external axial magnetic field. Under the investigated experimental conditions, three distinct arc modes have been observed: multiple arc, diffuse and diffuse columnar modes. The latter appeared at low B AMF /I arc values, typically below 4 mT/kA. The temporal evolutions of the spot spatial distribution and of the associated distribution of the current density were analyzed by processing high-speed video images of the cathode. Various types of distribution depending mainly on current were identified. At low currents (up to 13 kA), CS distribution covered only a fraction of the cathode surface. At intermediate currents (in 17.2 -31.1 kA range), CSs were present on the whole circumference of the cathode and the CS distribution included a closed region without spot. The latter was progressively filled by CSs, yet it totally disappeared before the end of arcing only when its location was off-centered with respect to the cathode axis. At high currents (up to 36.3 kA), the whole cathode surface was occupied by CSs at current peak. The azimuthally averaged radial distribution of the current density was found to be relatively uniform in the regions occupied by CSs. An average spot current of 36.5A ± 2.5 A has been estimated.

I. INTRODUCTION

ACUUM interrupter is nowadays the most widely used switching technology for medium voltage applications, whereas SF 6 interrupter is the dominant technology in high voltage applications. In an attempt to develop SF 6 free alternative circuit breakers owing to environmental considerations, research efforts are currently being made to increase the voltage rating of vacuum interrupters [START_REF] Zhang | Axial magnetic field strength needed for a 126-kV single break vacuum circuit breaker during asymmetrical current switching[END_REF][START_REF] Hartmann | AMF vacuum arcs at large contact separation[END_REF]. As a result, the behavior of a vacuum arc (VA) for contact gap above 10 mm needs to be better understood. Studies on this latter point are still limited. Most of the published papers on this topic are focused on vacuum arcs controlled with an axial magnetic field (AMF). Studies have been carried out for the case of large (10-40 mm) and very large (40-60 mm) contact gaps. Cheng et al. [START_REF] Cheng | The discharge development and arc modes in vacuum at a long gap distance in vacuum interrupters[END_REF] investigated VAs with current up to 14.25 kA between 50 mm diameter electrodes spaced 40 mm apart. Instable arc modes for the highest currents were mentioned for this configuration. Xiu et al. [START_REF] Xiu | Study of distortion of a vacuum arc at a long-gap distance[END_REF] have studied into more detail these instabilities for VAs with current up to 11 kA for 75-100 mm diameter electrodes with gaps in 20-60 mm range. They classified them into two groups (normal and spiral distortions) and correlated their apparition with a magnetohydrodynamic criterion. Recently, Wang et al. [START_REF] Wang | Experimental investigation on vacuum arc behaviors subjected to larger diameter cup-shaped and coil-shaped axial magnetic field electrode[END_REF] have studied the increase of the plasma constriction near the anode, within a 10 to 40 mm contact gap range, for applied current up to 28 kA and using either 90 mm diameter cup-shaped electrodes or 110 mm diameter coil type electrodes. Besides the behaviour of the interelectrode plasma, the appearance of VAs at the anode has also been investigated by a few researchers. Cheng and Wang [START_REF] Cheng | Study on high-current vacuum arc characteristics under self-generated axial magnetic field of contact at a long contact gap for highvoltage vacuum interrupters[END_REF] have analyzed the anode phenomena for VAs with very large gaps for 100 mm diameter single coil type electrodes. Considering drawn arcs between 100 mm diameter 2/3 coil type electrodes, Yao et al. [START_REF] Yao | Anode mode diagram: a determination of opening displacement curve for a 126 kV vacuum circuit breaker[END_REF] have investigated, for large and very large gaps, the various modes of existence of the arc at the anode (passive anode, footpoint and anode spot) according to the current and arc length.

In VA, the plasma is emitted at the cathode surface by tiny, mobile cathode spots (CSs). Their motion and spatial distribution have a significant influence on the arc aspect and the plasma parameters [START_REF] Chaly | Cathode spot dynamics on pure metals and composite materials in high-current vacuum arcs[END_REF]. CS motion is influenced by numerous factors, such as surface conditions, magnetic field intensity and plasma density [START_REF] Jüttner | The retrograde motion of arc cathode spots in vacuum[END_REF][START_REF] Song | Influence of AMF on the expansion speed of cathode spots in high-current triggered vacuum arc[END_REF]. To determine the spatial distribution of CSs over the cathode surface, Afanas'ev et al. [START_REF] Afanas'ev | Computer-aided reconstruction of cathode images obtained by high speed photography of high current vacuum arcs[END_REF] developed an original processing method, based on post-treatment of cathode images (previously) recorded with a high-speed camera. In this method, the position of CSs is extracted by filtering light intensity contours. Moreover, the method allows estimating the distribution of current density at the cathode from the reconstructed CS distribution. Up to now, the method was employed to investigate VAs with small gap spacing (from 2 to 16 mm) with a current of 3 to 25 kA and contacts of 30 -50 mm diameter [START_REF] Song | Influence of AMF on the expansion speed of cathode spots in high-current triggered vacuum arc[END_REF][START_REF] Chaly | High-current vacuum arc appearance in nonhomogeneous axial magnetic field[END_REF][START_REF] Chaly | High-current vacuum arc in a strong axial magnetic field[END_REF][START_REF] Shi | The influence of axial magnetic field distribution on high-current vacuum arc[END_REF]. Moreover, it should be noted that all of these studies were performed for static contacts, the arc triggering being carried out with an auxiliary electrode placed at the cathode center.

This study aims to investigate experimentally the behavior of AMF controlled VAs with large gap distance (20 mm or 30 mm) triggered with an auxiliary electrode placed close to the cathode outer diameter. First, arc visualization results are presented, describing arc mode and the interelectrode plasma appearance. Then, the temporal evolutions of CS distribution and current density are described, applying a similar spot detection method as proposed by Afanas'ev et al. [START_REF] Afanas'ev | Computer-aided reconstruction of cathode images obtained by high speed photography of high current vacuum arcs[END_REF].

II. EXPERIMENTAL

A. Setup

Experiments have been conducted in a demountable vacuum chamber with a pumping system capable of maintaining a vacuum ranging from 10 -7 Pa to 10 -5 Pa, as depicted in Fig. 1. A pair of static electrodes was disposed inside the chamber with a controlled gap. The contacts were 70 mm diameter hollow cylinders of OFHC copper, surmounted by 2 mm thick CuCr25 alloy disks. A sixteen turns Helmholtz coil pair was installed outside the chamber to generate an AMF in the contact gap region. The arc was triggered with the help of an auxiliary electrode located close to the cathode outer diameter and connected to a High-Voltage (20 kV) pulsed power supply. The arc and Helmholtz coils were powered from two independent 50 Hz generators. Current and voltage were measured at different locations of the electrical circuit. Four shunts were installed to measure the injected current I BT , the output current I arc , the leakage current I leak and the current in the Helmholtz coils I coils . The arc voltage U arc was obtained by measuring the potential difference upstream and downstream the chamber using two voltage dividers. Measured data were recorded on an acquisition bay with a sample frequency of 1 MHz. The electric arc was filmed with a highspeed camera Photron SA5 with an exposure time of 369 ns and a frame rate of 15000 or 20000 frames/s. Fig. 2 shows the radial profiles of the AMF intensity and the time delay between the AMF intensity and the coil current measured at mid-distance between the two contacts (spaced 25 mm apart) using a Hall probe placed on a mobile support. It can be seen that there is an important effect of the contacts upon the two parameters. The radial profile of the AMF has a saddle shape with values in 9.6-17.1 mT/kA range inside the contact gap region, while the time delay between the AMF intensity and the coil current has a bell-shaped profile with values in 3.4-5.2 ms range inside the contact gap region. As illustrated on Fig. 3, the arc was triggered when the voltage between the contacts reached a peak value and interrupted after a half-wave of current. The current injection in the Helmholtz coils was triggered 3.4 ms before the arc ignition in order to synchronize the peak of arc current with the AMF peak at the edge of the cathode. Moreover the current half-wave in the coil had a duration of 14 ms to maintain an intense AMF between the contacts during most of the arc lifetime. The coil current was finally interrupted using an auxiliary circuit breaker.

B. Operating parameters

The parameters used for the tests are presented in Table I. Exp. 1 to 7 were performed with a gap of 20 mm and with arc peak current values varying between 4.9 kA and 43.3 kA. Exp. 8 to 11 were performed with a gap of 30 mm and with arc peak current values varying between 8.9 kA and 24.9 kA. All experiments were realized with an AMF of about 143 mT oriented towards the cathode, except Exp. 7 during which the AMF was oriented towards the anode and its intensity was fixed at 269 mT. Note that Exp. 1-6 and 8-11 were realized one after the other with the same contacts whereas a new pair of similar contacts was used during Exp. 7.

C. Image processing method

The image processing method employed to detect CSs on the cathode image is inspired by the work of Afanas'ev et al. [START_REF] Afanas'ev | Computer-aided reconstruction of cathode images obtained by high speed photography of high current vacuum arcs[END_REF]. The first step of the method consists in the detection, selection and density computing of iso-contours of light intensity on the image of the cathode front surface. The contours are selected according to their intensity, to eliminate the darkest contours, as well as according to their size, to reject too long and too short contours which cannot surround a single spot. Next, we calculate the centroid position of each selected contour and then the number of iso-contour centroid on each pixel. Above a certain threshold of iso-contour number, a pixel is marked and considered as a spot location. A limitation of this approach is that the same spot may end up to be detected on several adjacent pixels. To solve such a situation, only the centroid of each connected pixel region is conserved. Finally, the few false spots associated to a local minimum of light intensity, which may be detected after the complete processing procedure, are excluded based on an additional threshold filtering. The result of these successive operations is illustrated on Fig. 4. CS coordinates need then to be corrected to take into account the deformation of the cathode surface caused by the tilting of the camera. This can be done using a projective transformation relating the spot coordinates on the deformed image (x,y) to the spot coordinates on the rectified image (x',y') [START_REF] Jagannathan | Perspective correction methods for camera-based document analysis[END_REF]:

(1)
The transformation involves eight coefficients h i,j . Those coefficients were determined from four reference points taken from a 10 mm-square reticle grid which was disposed after the tests on the front surface of the cathode and shot with the same viewing angle as the one used during the experiments.

The projective transformation is also applied to the points defining the contour of the cathode surface. Due to experimental uncertainties, the cathode contour obtained after this step is still elliptic with an eccentricity below 0.4. Thus, a final correction step is needed to make the contour perfectly circular. The radial coordinate of the points located on the cathode contour, measured from the center of the ellipse obtained after the projective transformation, is replaced by the minor radius of the ellipse. Similarly, the radial coordinate of a CS, defined with respect to the center of the ellipse obtained after the projective transformation, is replaced by the following expression 1 cos

, where e is the eccentricity of the ellipse and is the spot angular position with respect to the major axis of the ellipse emanating from the center of the ellipse. From the CS map, the distribution of the current density at the cathode was reconstructed by partitioning the cathode surface into Voronoi cells, each cell enclosing a single spot. The current density in each cell was considered to be inversely proportional to the cell area. Next, an azimuthally averaged radial profile of the cathode current density was determined. This profile was calculated using a harmonic mean formula (instead of an arithmetic mean) in order to be less sensitive to extreme values, which may occur when several CSs are located very close to each other, leading to very small Voronoi cells.

III. ARC COLUMN

In this section, we first describe the evolution of the arc appearance during the current wave for two different peak values with a gap of 20 mm. Then, we detail the various arc modes observed for the range of conditions investigated in the present study.

Fig. 5 presents an example of the currents and arc voltage as a function of time measured during Exp. 3 and 6, which were carried out with the same gap length of 20 mm and with a peak current of 25.7 kA and 36.3 kA respectively. The AMF intensity and the overall plasma luminosity, defined as the integration of light intensity in the contact gap region are also represented on this figure. For both cases, a leakage current (up to 3 kA), that matches with the difference between I arc and I BT , exists during most of the first half wave of the arc current, meaning that a fraction of CSs is located on the walls of the chamber, while no significant leakage current is detected during the second half wave of the arc current. As will be seen below, the existence of a significant leakage current during the first half-wave of current is due (partly if not completely) to the location of spots on the lateral surface of the cathode immediately after arc ignition. Those spots may cause significant leaks of plasma out of the interelectrode space, which may enhance the apparition of CSs on the walls of the chamber. In contrast, during the second halfwave of current, most of the CSs are located on the front surface of the cathode, reducing the current leaks. A very high spike of the arc voltage is observed at the instant of ignition of the arc. Afterward, the variations of U arc are heavily influenced by the impedance of the experimental circuit. Fig. 6 shows images of the arc column every millisecond during Exp. 3 and 6. As seen in Fig. 6a, after arc ignition, CSs are localized on the edge of the cathode, covering only a fraction of the circumference. From 1 to 6 ms, the spots spread from the edge to the center of the cathode covering almost completely the cathode surface at the peak current. Individual plasma jets produced by the spots are clearly visible in the near cathode region. As the current increases, the plasma jets mix progressively and form a relatively homogeneous interelectrode plasma, which is characteristic of an arc operating in a diffuse mode. From 7 to 11 ms, during the current decrease phase, the luminosity of the interelectrode plasma decreases gradually. As seen in Fig. 5a, the overall luminosity of the plasma is roughly proportional to the arc current. As shown in Fig. 6b, the evolution of the arc appearance at higher current is significantly different. Until 4 ms, the arc develops similarly to that observed in Fig. 6a. However, contrary to Fig. 6a, from 5 to 8 ms the plasma distribution is strongly non uniform. A very bright plasma axial column emerges and grows from the central part of the contacts, surrounded by a diffuse plasma column. This corresponds to the so called diffuse columnar mode. The presence of this bright column is responsible for a strong increase of the overall luminosity of the plasma as observed in Fig. 5b. At 9 ms, the arc appears diffuse again. Then the plasma becomes darker with the decrease of the arc current. While the central column luminosity decreases, the column radius changes only a little. Note that contrary to Fig. 6a, the CSs occupy completely the cathode surface at the current peak value. After the arc extinction, the optical inspection of the contacts revealed no traces of melting on the anode surface, which indicates that the anode remained passive during arcing. Fig. 7 and Fig. 8 show the arc appearance at the peak of current for all the performed experiments. Fig. 7 refers to a gap of 20 mm, while Fig. 8 refers to a gap of 30 mm. When the gap is positioned at 20 mm, essentially three different arc modes can be observed. For currents lower than 4.9 kA (Fig. 7a), the arc operates in a multiple arc mode. In this mode, the plasma jets emitted by the CSs do not overlap. At currents higher than 17.2 kA (Fig. 7b-e), the arc becomes diffuse. The mixing of the plasma jets produces a quite uniform plasma. Moreover, with the current increase, the mixing of the plasma jets tends to take place closer to the cathode. Finally, for current higher than 36.3 kA (Fig. 7f), the arc appears as a diffuse columnar arc, with the formation of a bright plasma column in the central part of the contacts. Note that, while the arc current in Exp. 7 (Fig. 7g) was higher compared to that in Exp. 6 (Fig. 7f), the arc remains diffuse in Exp. 7 because the applied AMF is stronger. In Figure 7b-e, a counterclockwise inclination of the plasma jets is clearly visible. The inclination becomes more pronounced when the current increases. As discussed by Jia et al. [START_REF] Jia | Vacuum arc under axial magnetic fields: experimental and simulation research[END_REF], the flow direction of the jets is dependent on that of the composite magnetic field resulting from the superposition of the AMF and the azimuthal self-generated magnetic field. The inclination of this composite magnetic field gets stronger when the current increases, giving a more pronounced inclination of the jets. In accordance with this explanation, it is observed that the plasma jet inclination becomes clockwise in Exp. 7 (Fig. 7g) due to the reversal of the AMF direction.

When the gap is positioned at 30 mm, only two arc modes are observed. The multiple arc mode is observed again at low current (Fig. 8a), while the arc is diffuse at currents higher than 13 kA (Fig. 8b-d). In contrast to the experiments with a 20 mm gap, the arc exhibits no diffuse columnar mode. This may be related to lower values of the arc current investigated for a 30 mm gap (24.9 kA instead of 36.3 kA under a similar AMF intensity). The lowest value reached by the ratio B AMF /I arc for a 30 mm gap is 5.7 mT/kA. This value remains larger than the one for Exp. 6 with a 20 mm gap, during which a diffuse columnar arc mode was observed. Note that besides the influence of the ratio B AMF /I arc we cannot exclude effects related to the increase of the gap length on the arc operating mode. As it was observed for a 20 mm gap, the plasma jets exhibit again a counterclockwise inclination, which gets stronger with the rise of the current.

Fig. 9 illustrates the evolution of the arc mode observed during Exp. 5 to 7 as a function of the instantaneous current and AMF magnitude. As the identification of the transition between the multiple arc mode and the diffuse arc mode is not straightforward (and based on visual criterion), the boundary between these two modes is not represented in Fig. 9. This figure suggests a linear relationship between the critical current and the critical AMF magnitude separating the existence domain of the diffuse mode and the diffuse columnar mode: 0.1 #$%. &' ( )* +,-. 17 #$%)

(2) This criterion is close to that deduced from the diagram presented by Schade and Shmelev (cf. Fig. 1 in [START_REF] Schade | Numerical simulation of high-current vacuum arcs with an external axial magnetic field[END_REF]) given for 55 mm diameter copper contacts spaced 10 mm apart. It is also interesting to note that the curves relative to Exp. 5 and 7 remain below the derived boundary between the diffuse and diffuse columnar modes, in accordance with the observations made on the arc images.

IV. CATHODE SPOTS

In this section, the evolution of the spatial distributions of CSs and current density is studied on the cathode images posttreated with the previously presented CS detection method. Afterward, an estimation of the average current carried by a single spot is also presented.

A. Cathode spot distribution

First, the initial propagation of CSs after arc ignition is described. As illustrated in Fig. 10 for the case of Exp. 3, because of the lateral trigger system, the first CSs appear on the lateral surface of the cathode. These spots exhibit a very fast anticlockwise rotation motion around the cathode under the influence of the AMF [START_REF] Jüttner | The retrograde motion of arc cathode spots in vacuum[END_REF]. From about 100 µs, some CSs reach the front surface, emerging at various locations along the circumference of the cathode. These spots are much slower than the spots established on the lateral surface. They begin to effectively spread over the cathode surface from about 700 µs. Finally, CSs established on the lateral surface of the cathode disappear totally at around 1 ms for that particular experiment. 11d, CSs appear first along large sections of the circumference of the cathode, before spreading across the entire cathode surface. At the current peak, the whole cathode surface is occupied by the CSs. After the current peak, CSs tend to align along spiral arms originating from the center of the cathode. For intermediate values of current (from 17.2 kA to 31.1 kA for the present conditions, i.e. in Exp. 2 to 5, 10 and 11), the CS distribution exhibits two different behaviors. Similarly to the case at high current, a CS empty region within the spatial distribution of CSs is formed during the rise of current as a result of the expansion of the CSs from the edge towards the center of the contact. The empty region may either be eventually totally filled and disappear as in Fig. 11b or persist, although its size decreases while the current rises, until the end of arcing as in Fig. 11c. As seen in Fig. 11 and confirmed by the observations made in the other experiments of Table I, it seems that the evolution of the CS empty region depends on its location with respect to the axis of symmetry of the cathode. The empty region eventually disappears in the case of an off-centered location, whereas it remains always present when its location is relatively centered.

Note that in all cases, during the decrease of the arc current, the disappearance of CSs seems to happen homogeneously over the cathode surface. Our results do not reveal any noticeable effect of the gap length on the CS distribution. Moreover, the presence of a bright plasma column at the center of the contacts in Exp. 6 seems to have no influence on the CS distribution.

B. Cathode spot average current

Fig. 12 shows an estimation of the average current carried by a CS, which was computed by dividing the instantaneous total arc current by the number of spots detected at that instant. The quite high values of the spot current during the first milliseconds in some experiments can be explained by the presence of an important proportion of spots on the lateral surface of the cathode. Our processing method discards those spots. The number of spots being underestimated, the spot current is hence overestimated. Similarly, the number of spots may be slightly underestimated (hence the spot current will be slightly overestimated) during most of the arc lifetime, because of the ejection of spots out of the front surface of the cathode as a result of repulsive forces between spots. This effect is expected to weaken when the current decreases during the second half of the current wave, which explains the decreasing trend of the computed spot current values observed in Figure 12 and the converging trend of the curves associated to the different experiments. Therefore, it is believed that the most reliable spot current value are those at the end of arcing (~ 1 ms before arc extinction), yielding to an average value of the current emitted by a spot of 36.5±2.5 A. When averaging the data presented in Fig. 12, the data of Exp. 2 has been excluded, since video images of the arc reveal an ejection of CSs out of the front surface still important at the end of arcing. This was interpreted as a consequence of a poor control of the arc due to the lower magnitude of the AMF at the end of arcing. AMF magnitude was lower at the end of arcing because arc ignition was exceptionally long during this experiment. The value of the average CS current obtained here is similar to the spot current measured by Yu et al. [START_REF] Yu | High-current vacuum arc phenomena of nanocrystalline CuCr25 contact material[END_REF] for nanocrystalline CuCr25 contact material.

Radial profile of the cathode current density

Azimuthally averaged radial profiles of the cathode current density have been calculated from the position of CSs according to the procedure exposed in section II.C. Fig. 13 shows typical examples of those profiles for the same four experiments, whose CS distributions were presented in Fig. 11. At low current (Fig. 13a), except at the beginning of arcing, the current density decreases from the center to the edge of the cathode. At higher currents (Fig. 13b-d), because of the initial repartition of CSs on the edge of the cathode, the current density exhibits a peak at the cathode edge during the first milliseconds. Next, as the current increases and spots expand on the cathode surface, the peak widens and the front of current density moves towards the center of the cathode. It is interesting to note that the current density at the edge of the cathode shows only slight variation during the propagation of the front. At the current peak, when CSs occupy completely the cathode surface, such as in Exp. 4 and 6, the current density is approximately evenly distributed. In contrast, in Exp. 5, because of the persistence of a central CS empty region, the current density at the current peak is non uniform, with minimum values reached naturally near the center of the cathode. For all experiments, after the current peak, the current density tends to decrease uniformly over the surface. Note that the very large values of the current density observed close to the cathode center at 7 ms and 9 ms in Exp. 6 are believed to be computation artefacts, induced by a small number of spots averaged close to the center.

D. Discussion

CS motion (which is a random walk when no magnetic field is present) is strongly influenced by a magnetic field. In presence of a tangential magnetic field, it is well known that a CS is subjected to a directional "retrograde" motion, which is in the direction opposite to that given by the Lorentz force 0 1 ∧ * 31 . The velocity of this directional motion depends on the material of the cathode and the magnetic field magnitude [START_REF] Jia | Vacuum arc under axial magnetic fields: experimental and simulation research[END_REF]. Superposing an axial magnetic field to the tangential magnetic field causes an additional angular drift with respect to the retrograde direction (called the Robson drift) [START_REF] Robson | The motion of a low-pressure arc in a strong magnetic field[END_REF]. The deflection angle was found to be proportional to the angle formed by the total magnetic field with the cathode surface [START_REF] Jia | Vacuum arc under axial magnetic fields: experimental and simulation research[END_REF]:

4 5 atan * +,-* ⁄ (3) where the coefficient η depends among others on the cathode material. In a high current VA, as many CSs are present simultaneously on the cathode surface, the retrograde motion of CSs under the combined effect of the self-magnetic fields generated by every spot results in self-repulsion between CSs and the expansion of CSs over the cathode surface [START_REF] Jia | Vacuum arc under axial magnetic fields: experimental and simulation research[END_REF].

The analysis of the CS distributions in section IV.A showed that the presence of an empty region within the CS distribution until the end of arcing, leading to only a partial occupation of the cathode surface, seems to correlate with the relatively centered location of the empty region, this characteristic being itself linked to the initial repartition of CSs along the cathode circumference. In the following, an interpretation of this result by examining the direction of the retrograde motion of the whole CSs is proposed. The direction of retrograde motion of CSs was calculated from the CS map presented above, following a similar approach to that employed by Jia et al. [START_REF] Jia | Investigations on the motion of high-current vacuum-arc cathode spots under a magnetic field[END_REF]. The tangential magnetic field produced by the current of a spot i at the location of a spot n is given by:

* 31 : ;<= > ? @ ;A BCDE F 1 G =∧ 1 HIJ ‖ 1 HIJ ‖ (4)
where 1 :(L is the displacement vector from the location of spot i to the location of spot n. Then, the direction of the retrograde motion of spot n is given by:

M A BCDE @N BCDE 1 O P ∧ ∑ * 31 : ;<= R BCDE :S > ? @ A BCDE N BCDE ∑ 1 HIJ ‖ 1 HIJ ‖ R BCDE :S (5)
Due to the presence of an AMF, one needs also to take into account the angular deflection with respect to that direction caused by the AMF, the deflection angle being determined from equation (3). Based on the AMF magnitude profile presented in Figure 2 and considering a spot current of 36.5 A, a spot radius of 50 µm [START_REF] Jüttner | Cathode spots of electric arcs[END_REF] and a typical value of the parameter η equals to 0.8 (similar to that given for CuCr30 contacts in [START_REF] Chaly | Low-current vacuum arcs with short arc length in magnetic fields of different orientations. A review[END_REF]), the direction of the retrograde motion of every CS can thus be calculated from the CS location map using equation [START_REF] Wang | Experimental investigation on vacuum arc behaviors subjected to larger diameter cup-shaped and coil-shaped axial magnetic field electrode[END_REF]. Fig. 14 shows an example of calculation results at three particular time instants during Exp. 4 and 5. When the CS empty region is off-centered as in Exp. 4, it is observed that part of the CSs (essentially those close to the center of the cathode) have a motion directed towards the inside of the empty region and contribute to the decrease of the size of the empty region. Between 4 and 5 ms, the area of the empty region falls by half. At 6 ms, the empty region disappears and the cathode is fully occupied by CSs.

In contrast, when the CS empty region is relatively well centered as in Exp. 5, very few CSs exhibit a motion directed towards the inside of the empty region. Therefore, the empty region although decreasing in size remains present until the end of arcing. At 6 ms, it represents about 10 % of the cathode surface. Thus, the correlation observed between the persistence of the empty region inside the CS distribution and the centered position of the empty region in the case of moderate arc current may be explained by the CS motion direction, which does not favor the filling of the empty region.

V. CONCLUSION

VAs between CuCr25 static contacts spaced 20 and 30 mm apart with a range of peak current between 3.9 and 43.3 kA and under a peak value of AMF of 143 mT or 269 mT were studied with a high speed camera to characterize the arc appearance and the CS distribution.

For a 20 mm gap, three arc modes were successively observed with increasing arc current, respectively a multiple arc mode, a diffuse arc mode and a diffuse columnar arc mode. The diffuse columnar arc mode occurred for a value of the B AMF /I arc ratio of around 4 mT/kA. For a 30 mm gap, the maximum current investigated was smaller (yielding to a minimum value of the B AMF /I arc ratio of around 6 mT/kA). No diffuse columnar arc mode was observed; the arc exhibiting either a multiple arc mode or a diffuse mode.

Various types of CS distribution have been identified, which are to some extent dependent on the specific arc ignition procedure on the lateral surface of the cathode used in the present work. At low currents, after reaching the front surface of the cathode, the CSs form a distribution without empty region, which covers only a fraction of the cathode surface. At moderate currents, a closed region unoccupied by CSs forms within the CS distribution during the development of the arc. This empty region, although decreasing in size, remains present until the end of arcing, when its location is centered with respect to the cathode axis. In contrast, the empty region was found to be eventually totally filled by CSs when its location is off-centered. An explanation of this behavior was proposed in terms of the direction of the retrograde motion of CSs located at the periphery of the empty region. When the current is further increased, due presumably to the increase of CS density, the cathode surface is always fully occupied by CSs at the current peak. No significant modification of the CS distribution with the gap length was observed. An average spot current of 36.5 ± 2.5 A was estimated. Our results suggest that the current density is relatively uniform in the regions occupied by CSs.

Fig. 1 .

 1 Fig. 1. Experimental setup.

Fig. 2 .

 2 Fig. 2. Radial profiles of the AMF intensity and the time delay ∆t between BAMF and Icoils measured at mid-distance between the two contacts. The symbol rc on the x-axis refers to the radius of the contacts.

Fig. 3 .

 3 Fig. 3. Example of experimental procedure illustrating the synchronization of the arc and coil currents.

Fig. 4 .

 4 Fig. 4. (a) Example of cathode image, (b) the same image with cathode spots detected using the numerical treatment.

Fig. 5 .

 5 Fig. 5. Time evolutions of Iarc, IBT, Ileak, Uarc, BAMF and the overall plasma luminosity during Exp. (a) 3 and (b) 6.

Fig. 6 .

 6 Arc image every millisecond during Exp. (a) 3 and (b) 6.

Fig. 7 .Fig. 8 .

 78 Fig. 7. Arc image at the current peak under a gap of 20 mm. Exp. (a) 1, (b) 2, (c) 3, (d) 4, (e) 5, (f) 6 and (g) 7.

Fig. 9 .

 9 Fig. 9. Arc modes as a function of the instantaneous current and AMF magnitude during Exp. 5-7.

Fig. 10 .

 10 Fig. 10. Arc images every 200 µs during Exp. 3 just after arc ignition.

Fig. 11

 11 Fig. 11 presents typical time evolutions of the CS distribution that were observed depending on the arc peak current. Fig 11a shows that at low arc current (up to 13 kA for the present conditions, i.e. in Exp. 1, 8 and 9) CSs form a compact group (with no enclosed empty region) which occupies only a reduced fraction of the cathode surface. At high current (above 36 kA for the present conditions, i.e. in Exp. 6 and 7), as shown in Fig.11d, CSs appear first along large sections of the circumference of the cathode, before spreading across the entire cathode surface. At the current peak, the whole cathode surface is occupied by the CSs. After the current peak, CSs tend to align along spiral arms originating from the center of the cathode. For intermediate values of current (from 17.2 kA to 31.1 kA for the present conditions, i.e. in Exp. 2 to 5, 10 and 11), the CS distribution exhibits two different behaviors. Similarly to the case at high current, a CS empty region within the spatial distribution of CSs is formed during the rise of current as a result of the expansion of the CSs from the edge towards the center of the contact. The empty region may either be eventually totally filled and disappear as in Fig.11bor persist, although its size decreases while the current rises, until the end of arcing as in Fig.11c. As seen in Fig.11and confirmed by the observations made in the other experiments of TableI, it seems that the evolution of the CS empty region depends on its location with respect to the axis of symmetry of the cathode. The empty region eventually disappears in the case of an off-centered location, whereas it remains always present when its location is relatively centered.Note that in all cases, during the decrease of the arc current, the disappearance of CSs seems to happen homogeneously over the cathode surface. Our results do not reveal any noticeable effect of the gap length on the CS distribution. Moreover, the presence of a bright plasma column at the center of the contacts in Exp. 6 seems to have no influence on the CS distribution.

Fig. 11 .

 11 Fig. 11. Cathode spot distribution every millisecond during Exp. (a) 1 at 4.9 kA, (b) 4 at 26.7 kA, (c) 5 at 31.1 kA and (d) 6 at 36.3 kA.

Fig. 12 .

 12 Fig. 12. Estimated current carried by a single CS.

Fig. 13 .

 13 Fig. 13. Radial profiles of cathode current density for Exp. (a) 1, (b) 4, (c) 5, (d) 6.

Fig. 14 .

 14 Fig. 14. Calculated direction of the retrograde motion with Robson drift of CSs during Exp. (left column) 4 and (right column) 5 at three particular time instants.

ACKNOWLEDGMENT

This project was supported by the French Government in the framework of the "Investments for the Future" programme under the project reference (ANE-ITE-002-01). The authors would like to thank F. Catanese, F. Metral and P. Robin for their help in the experimental work.


Dr Antoine Netter
email: antoine.netter@gmail.com

Lisa Calderon

Anaïs Grob-Vaillant

Julien Mancini

Pascale Siles

Vincent Vidal

Aubert Agostini

Progression of adenomyosis magnetic resonance imaging features under ulipristal acetate for symptomatic fibroids BIOGRAPHY

Keywords:

The MRI features of adenomyosis seem to progress under a 3-month treatment course of daily 5 mg doses of ulipristal acetate (UPA). These findings do not encourage further research on the use of UPA as a treatment for adenomyosis.

INTRODUCTION

U lipristal acetate (UPA) has been approved for use in Europe for the treatment of symptomatic fibroids since 2012 [START_REF] Donnez | Liver safety parameters of ulipristal acetate for the treatment of uterine fibroids: a comprehensive review of the clinical development program[END_REF]. This drug has been proven to be efficient for reducing uterine bleeding and correcting anaemia prior to fibroid surgery (Donnez et al., 2012a(Donnez et al., , 2012b[START_REF] Donnez | Long-term treatment of uterine fibroids with ulipristal acetate✩[END_REF][START_REF] Donnez | Efficacy and safety of repeated use of ulipristal acetate in uterine fibroids[END_REF]. Approximately 765,000 patients had received this treatment between February 2012 and May 2018 when the European Medicines Agency issued new measures to restrict its use after reports of several cases of hepatic failure [START_REF] Donnez | Liver safety parameters of ulipristal acetate for the treatment of uterine fibroids: a comprehensive review of the clinical development program[END_REF]European Medicines Agency, 2018).

Selective progesterone receptor modulators (SPRM) such as UPA are used for their mixed progesterone agonist-antagonist properties on the myometrium and the endometrium in various contexts (i.e. contraception, abortion, uterine fibroids and endometriosis) [START_REF] Chabbert-Buffet | Selective progesterone receptor modulators and progesterone antagonists: mechanisms of action and clinical applications[END_REF]. However, also because of these properties, there is particular vigilance of the endometrial changes that UPA could potentially induce (Donnez et al., 2012a). Non-physiological histological endometrial changes are commonly observed immediately after a 3-month treatment course of UPA (Donnez et al., 2012a). Progesterone receptor modulator-associated endometrial changes (PAEC) are characterized by epithelial architectural distortion, by cystically dilated glands and, in one-third of cases, by extensive cyst formation [START_REF] Williams | Endometrial morphology after treatment of uterine fibroids with the selective progesterone receptor modulator, ulipristal acetate[END_REF]. These histological modifications, although benign and spontaneously reversible, have never been observed elsewhere, therefore suggesting a very specific effect of SPRM on the endometrium.

Adenomyosis is a uterine disorder defined by the presence of endometrial tissue within the myometrium [START_REF] Vannuccini | Pathogenesis of adenomyosis: an update on molecular mechanisms[END_REF]. The pathogenesis of adenomyosis has not been fully elucidated but the most likely theory would involve the invasion of the myometrium by the endometrium through a down-growth and an invagination [START_REF] García-Solares | Pathogenesis of uterine adenomyosis: invagination or metaplasia?[END_REF][START_REF] Vannuccini | Pathogenesis of adenomyosis: an update on molecular mechanisms[END_REF]. This process appears to be mediated by numerous pathogenic pathways, including a downregulation of progesterone receptors inducing progesterone resistance [START_REF] Nie | Promoter hypermethylation of progesterone receptor isoform B (PR-B) in adenomyosis and its rectification by a histone deacetylase inhibitor and a demethylation agent[END_REF]. Adenomyosis and uterine fibroids share similarities in terms of their symptomatology, (e.g. uterine bleeding, infertility and pain). For reasons that are not fully understood, both uterine pathologies are often concomitant (41-57%) [START_REF] Bazot | Role of transvaginal sonography and magnetic resonance imaging in the diagnosis of uterine adenomyosis[END_REF][START_REF] Brucker | Clinical characteristics indicating adenomyosis coexisting with leiomyomas: a retrospective, questionnaire-based study[END_REF][START_REF] Filip | Histological evaluation of the prevalence of adenomyosis, myomas and of their concomitance[END_REF]. Thus, given the widespread use of UPA in recent years, it is reasonable to assume that this treatment has been received by a large number of women who presented with adenomyosis. Despite this supposed exposure of adenomyotic women to UPA and its known influence on progesterone receptors that are also involved in the pathogenesis of adenomyosis, only two studies have investigated the effect of UPA on adenomyosis. [START_REF] Conway | Ulipristal acetate therapy increases ultrasound features of adenomyosis: a good treatment given in an erroneous diagnosis of uterine fibroids[END_REF] reported cases of six patients with adenomyosis erroneously treated by UPA. Their results, although limited by the small sample size, suggest that UPA worsens the symptoms and ultrasound features of adenomyosis. [START_REF] Gracia | Ulipristal Acetate Improves Clinical Symptoms in Women with Adenomyosis and Uterine Myomas[END_REF] conducted a retrospective analysis of 41 patients who were treated with UPA for uterine fibroids and who also presented with adenomyosis. They concluded that the UPA treatment led to a significant reduction of the symptoms of adenomyosis but did not report the evolution of the ultrasound features of adenomyosis. In addition, Olivier and Jacques Donnez recently reported the case of a 36-year-old woman with adenomyosis who was treated with UPA for 3 months. Both her symptoms and the MRI features of adenomyosis were aggravated by the treatment [START_REF] Donnez | Gonadotropinreleasing hormone antagonist (linzagolix): a new therapy for uterine adenomyosis[END_REF]. Thus, further studies are needed to determine the impact of UPA treatment on women presenting with adenomyosis.

This study sought to determine the effect of a 3-month treatment course of daily 5 mg doses of UPA on the evolution of the MRI features of adenomyosis in patients treated prior to surgery for uterine fibroids.

MATERIALS AND METHODS

Study design

This was a prospective pilot study conducted between January 2014 and December 2017 in the Department of Medical Imaging at La Timone Hospital, Marseille, France. The study was approved by an independent ethics committee on 8 February 2015 (CEROG 2014-GYN-1103).

Study population

The study population partly overlaps with the one described in a previous paper reporting the variation in the volume of fibroids subsequent to UPA treatment [START_REF] Netter | Predictors of uterine fibroid volume reduction under ulipristal acetate: a prospective MRI study[END_REF]. All premenopausal patients who presented for consultation for symptomatic uterine fibroids received detailed information about the study and the UPA treatment. Women willing to undergo delayed surgery after a 3-month treatment course of daily 5 mg doses of UPA were considered for inclusion and were requested to provide written consent. Patients were eligible for inclusion if they had uterine bleeding and/or abdominal pain and/or other symptoms that could be attributed to uterine fibroids. The exclusion criteria were contraindications to magnetic resonance imaging (MRI) (e.g. ferromagnetic implants, claustrophobia), contraindications to UPA treatment (e.g. pregnancy, previously known hypersensitivity), interruption of treatment within 3 months or fibroid surgery before the end of the 3 months, previous fibroid treatment with either gonadotrophin-releasing hormone (GnRH) agonists or UPA, previous fibroid or uterine surgeries, and an inability to provide written consent.

MRI assessment of adenomyosis

Patients underwent pelvic MRI shortly before (pre-MRI) and after (post-MRI) treatment (not more than 1 month before and after treatment) at the Women's Health Imaging Department at La Timone Hospital in Marseille, France. MRI were performed with an MRI Siemens Spectra 3.0T device (Siemens AG, Munich, Germany). The MRI protocol was T2weighted sagittal and axial (± coronal) sequences and axial T1-and T1FSweighted sequences. Sagittal T2-weighted sequences were acquired with a field of view of 250 mm and 4 mm sections with a 1.4 mm intersection gap using a 320 × 320 matrix.

Every MRI was independently interpreted after the end of the study period by two experienced radiologists (LC and AG-V) who did not know whether the MRI had been performed before or after treatment. In cases of disagreement about the presence of adenomyosis, the MRI at issue could be re-examined jointly by the two radiologists to reach consensus.

The diagnosis of adenomyosis on MRI was defined by the observation of at least one of the following features: (i) intramyometrial cysts represented by cystic cavities (small high signal intensity foci on T2-weighted sequences) and/ or haemorrhagic foci within these cystic cavities (small high signal intensity foci on T1-weighted sequences) and/or (ii) a thickening of the junctional zone >12 mm [START_REF] Bazot | Ultrasonography compared with magnetic resonance imaging for the diagnosis of adenomyosis: correlation with histopathology[END_REF][START_REF] Dueholm | Magnetic resonance imaging and transvaginal ultrasonography for the diagnosis of adenomyosis[END_REF][START_REF] Reinhold | Diffuse adenomyosis: comparison of endovaginal US and MR imaging with histopathologic correlation[END_REF]. The junctional zone was identified on T2-weighted sequences as the distinct inner lower signal area that separates the central endometrium (high signal intensity) from the outer myometrium (intermediate signal) [START_REF] Brown | Uterine junctional zone: correlation between histologic findings and MR imaging[END_REF][START_REF] Scoutt | Junctional zone of the uterus: correlation of MR imaging and histologic examination of hysterectomy specimens[END_REF]. The maximal thickness of the junctional zone was defined by the greatest antero-posterior dimension measured on sagittal T2-weighted sequences and only in areas without fibroids. When the junctional zone could not be accurately measured and if no intramyometrial cyst was identified, then the diagnosis of adenomyosis was not retained.

The progression of adenomyosis after the UPA treatment was defined by the presence at least one of the aforementioned criteria of adenomyosis on the pre-MRI and by at least one of the following on the post-MRI: (i) increased thickness of the junctional zone ≥20% and/or (ii) increased number of intramyometrial cysts. The appearance of adenomyosis was defined by the absence of the aforementioned criteria of adenomyosis on the pre-MRI and the presence of at least one of these criteria on the post-MRI.

The pre-and post-MRI were classified by subtypes based on the localization of adenomyosis according to the classification suggested by [START_REF] Kishi | Four subtypes of adenomyosis assessed by magnetic resonance imaging and their specification[END_REF], which was enhanced by Bazot and Daraï ( 2018): (i) intrinsic or internal adenomyosis (focal or diffuse) when adenomyosis was limited to the inner layer of the uterus in direct connection to the junctional zone without affecting the outer structures; (ii) extrinsic or external adenomyosis when limited to the outer shell of the uterus without connection to the junctional zone; (iii) intramural adenomyosis when occurring alone unrelated to the junctional zone or the serosa; and (iv) indeterminate when adenomyosis did not meet the criteria for any of the aforementioned subtypes or when adenomyosis was only diagnosed by an isolated thickening of the junctional zone >12 mm [START_REF] Bazot | Role of transvaginal sonography and magnetic resonance imaging in the diagnosis of uterine adenomyosis[END_REF][START_REF] Kishi | Four subtypes of adenomyosis assessed by magnetic resonance imaging and their specification[END_REF].

Through a secondary unblinded interpretation by both radiologists, the aspect of the endometrium was compared between the pre-and post-MRI. PAEC was suspected when the endometrium was thicker after the treatment and presented new cystic dilatations [START_REF] Williams | Endometrial morphology after treatment of uterine fibroids with the selective progesterone receptor modulator, ulipristal acetate[END_REF]. The suspicion of PAEC was retained only when both radiologists agreed on the presence of these aforementioned criteria.

End-points

The primary end-points were the percentage of patients for whom adenomyosis progressed among the patients presenting adenomyosis on the pre-MRI and the percentage of patients for whom adenomyosis appeared after UPA treatment among patients who did not present adenomyosis on the pre-MRI. The secondary end-point was the percentage of patients for whom a PAEC was suspected on the post-MRI among patients who presented a progression or an appearance of adenomyosis.

Statistical analysis

Due to the absence of prior data regarding the evolution of adenomyosis under UPA treatment, no sample size could be estimated for this pilot study. All patients who were treated with UPA during the study period and who met the selection criteria were included.

The baseline characteristics of the patients are reported as the mean ± SD or the median (minimum-maximum) for quantitative variables and as counts (percentages) for categorial variables.

Categorical variables were compared using Fisher's exact test. Variations before and after the MRI were compared using McNemar's test for qualitative variables and the paired Wilcoxon test for quantitative variables. The comparison of suspicion of PAEC between progressive adenomyosis and non-progressive adenomyosis was performed using Pearson's chi-squared test.

All statistical analyses were two-tailed, and results were considered significant when P-values <0.05 were obtained. These analyses were performed using SPSS Statistics for Windows, Version 20.0 (IBM Corp., Armonk, NY, USA).

RESULTS

Population

Between January 2014 and December 2017, 73 patients were considered for inclusion. After the exclusion of one patient who underwent surgery before the end of the UPA treatment, 72 patients were included in the final analysis. The mean age was 39.4 ± 5.8 years. The median gravidity and parity were 2 (0-8) and 1 (0-7), respectively.

Interobserver agreement

Among the 72 patients included, the radiologists disagreed about the presence of adenomyosis only for three patients (4.2%). The radiologists disagreed about the presence of adenomyosis on the pre-MRI for one patient. The presence of adenomyosis was ruled out for this patient after a secondary analysis by both radiologists. Adenomyosis was also absent on the post-MRI for this patient. The radiologists disagreed about the appearance of adenomyosis on the post-MRI for two patients. The presence of adenomyosis was confirmed for these two patients after a secondary analysis.

The agreement between observers regarding the count of intramyometrial cysts and the measurement of the junctional zone was excellent (Cohen's kappa = 0.947 and 0.838, respectively; P < 0.001 for both).

Evolution of adenomyosis under UPA

Among the 72 patients included, 15 were diagnosed with adenomyosis on the pre-MRI (TABLE 1).

Twelve of these 15 patients (80.0%) had an increased number of intramyometrial cysts after the UPA treatment than before. The median number of intramyometrial cysts was significantly greater after treatment (10 [2-30]) than before (2 [0-10]; P = 0.002). In three patients, who only presented a thickening of the junctional zone >12 mm without intramyometrial cysts on the pre-MRI, intramyometrial cysts were observed on the post-MRI (FIGURE 1).

The median thickness of the junctional zone was similar before (13.5 [2-21] mm) and after the UPA treatment (11.0 [5-21] mm; n = 14; P = 0.640). Only three patients had an increased thickness of the junctional zone ≥20%, all of whom also had an increased number of intramyometrial cysts.

Appearance of adenomyosis under UPA

Adenomyosis was not observed on the pre-MRI for 57 of the 72 patients included (TABLE 2). Among these 57 patients, the appearance of adenomyosis was observed on the post-MRI for 15 patients (26.3%). The appearance of adenomyosis after treatment was exclusively represented by emerging intramyometrial cysts (FIGURE 2). The median number of intramyometrial cysts among these patients on the MRI after treatment was 3 (2-20). The median thickness of the junctional zone was the same before (7.0 [3-11] mm; n = 12) and after treatment (7.5 [3-13] mm; n = 13; P = 0.670).

Classification of adenomyosis

Eleven of the 15 patients (73.3%) who were diagnosed with adenomyosis on the pre-MRI had internal adenomyosis (TABLE 1). These 11 patients still had internal adenomyosis on the post-MRI; for nine of these patients, the intramyometrial cysts increased in number after treatment. One patient a Only the statistical analyses to compare the number of intramyometrial cysts and the thickness of the junctional zone before and after the treatment were conducted. was diagnosed with an intramural adenomyoma, which remained unchanged on the post-MRI. Three patients were diagnosed with an isolated thickening of the junctional zone >12 mm without any direct criteria. Internal adenomyosis appeared on the post-MRI for all three of these patients.

Fourteen of the 15 patients (93%) for whom adenomyosis appeared on the post-MRI had internal diffuse adenomyosis (TABLE 2). For one patient, who was not diagnosed with adenomyosis on the pre-MRI, external adenomyosis was observed on the post-MRI.

Association with the suspicion of PAEC PAEC were suspected on the post-MRI in 24 of the 72 patients included (33%). Among the 30 patients who either had a progression or an appearance of adenomyosis, 14 (46.7%) presented a suspicion of PAEC on the MRI after UPA treatment. Among the 42 patients who presented neither a progression nor an appearance of adenomyosis, PAEC was suspected for 10 (23.8%; P = 0.042).

DISCUSSION

This is the largest study to report the evolution of adenomyosis in response to a 3-month treatment course of 5 mg daily doses of UPA on prospectively collected MRI. The results suggest that UPA induces either a short-term progression or an appearance of typical intramyometrial adenomyotic cysts in a large proportion of the patients treated. A progression was assessed in 12/15 (80%) of patients who already had adenomyosis, and an appearance Only the statistical analyses to compare the number of intramyometrial cysts and the thickness of the junctional zone before and after the treatment were conducted.

occurred for 15/57 (26%) of patients who did not have adenomyosis before the treatment. Although the intramyometrial cysts seem to increase in number, the junctional zone does not seem to be impacted by the UPA treatment. PAEC were more frequently suspected in patients for whom adenomyosis either progressed or appeared. As these MRI modifications are involved in distinct layers of the uterus, they are unlikely to be confused with one another. However, it was not possible to verify the presence of PAEC with histological data for this study and therefore the strength of the association between PAEC and the emergence or progression of adenomyosis cannot be accurately reported. Nevertheless, this concomitant emergence of endometrial (PAEC) and myometrial (intramyometrial cysts) observations on MRI suggest that UPA treatment exerts the same effect on both eutopic and ectopic endometrium.

According to this hypothesis, the progression of MRI features of adenomyosis under UPA treatment observed in this study would only be an illustration of PAEC occurring in the intramyometrial endometrium.

Only two other studies have investigated the effect of UPA on adenomyosis. [START_REF] Gracia | Ulipristal Acetate Improves Clinical Symptoms in Women with Adenomyosis and Uterine Myomas[END_REF] retrospectively compared 41 patients who underwent a 3-month treatment course of 5 mg daily doses of UPA for symptomatic fibroids and who also presented ultrasound features of adenomyosis to 122 patients who only had uterine fibroids without adenomyosis. They concluded that UPA treatment was even more effective for treating pelvic pain and uterine bleeding in patients who presented with adenomyosis and uterine fibroids than in patients who only presented with uterine fibroids. They did not report any data on the evolution of adenomyosis features on ultrasound.

The retrospective nature of this study and the statistical arrangements of data are major impediments to interpretation of their results. [START_REF] Conway | Ulipristal acetate therapy increases ultrasound features of adenomyosis: a good treatment given in an erroneous diagnosis of uterine fibroids[END_REF] reported a case series of six patients who erroneously received a 3-month treatment course of 5 mg daily doses of UPA for adenomyosis. All six patients presented worsened symptoms of adenomyosis (dysmenorrhoea, pelvic pain, dyspareunia and bowel symptoms) after the treatment than before. However, these symptoms were retrospectively assessed, as recalled by the patients, which impairs the reliability of the results. The sonographic features were reportedly enhanced after the UPA treatment in comparison with the ultrasounds before the treatment, which were not performed in their unit. More recently, Olivier and Jacques Donnez reported the case of a patient presenting with adenomyosis who received a 3-month treatment course of UPA [START_REF] Donnez | Gonadotropinreleasing hormone antagonist (linzagolix): a new therapy for uterine adenomyosis[END_REF]. [START_REF] Bazot | Role of transvaginal sonography and magnetic resonance imaging in the diagnosis of uterine adenomyosis[END_REF]. Studies comparing imaging and histological outcomes have reported that intramyometrial cysts are only observed in half of the MRI when adenomyosis is assessed histologically [START_REF] Bazot | Ultrasonography compared with magnetic resonance imaging for the diagnosis of adenomyosis: correlation with histopathology[END_REF][START_REF] Reinhold | Diffuse adenomyosis: comparison of endovaginal US and MR imaging with histopathologic correlation[END_REF]. As stated by [START_REF] Bazot | Role of transvaginal sonography and magnetic resonance imaging in the diagnosis of uterine adenomyosis[END_REF], measurement of the junctional zone is perilous, particularly with the presence of uterine fibroids, and should therefore not be used as a sole criterion to diagnose adenomyosis. Indeed, in the current study, the junctional zone was not measurable in 29% of MRI. Using the two criteria instead of only one criterion increases sensitivity with a minimal loss of specificity because intramyometrial cysts are pathognomonic and a junctional zone >12 mm is fairly specific for adenomyosis [START_REF] Bazot | Role of transvaginal sonography and magnetic resonance imaging in the diagnosis of uterine adenomyosis[END_REF][START_REF] Champaneria | Ultrasound scan and magnetic resonance imaging for the diagnosis of adenomyosis: systematic review comparing test accuracy[END_REF]. However, interpretation of the results must be measured by a few considerations. Firstly, this study only provides imaging information, and whether any patients presented symptoms of adenomyosis before treatment or how these symptoms evolved after treatment cannot be stated. The most common symptoms of adenomyosis are uterine bleeding and pelvic pain [START_REF] Chapron | Diagnosing adenomyosis: an integrated clinical and imaging approach[END_REF].

Although the PEARL studies clearly demonstrated that UPA was effective in reducing these symptoms in the context of uterine fibroids, the particular population of women affected by both uterine fibroids and adenomyosis was not investigated (Donnez et al., 2012a(Donnez et al., , 2012b)). Thus, the clinical evolution of these patients remains unresolved. The myometrial MRI changes described in this study should not be overly interpreted as a sign of aggravation of adenomyosis on their own, and clinical evaluation remains paramount. Secondly, MRI were conducted immediately after the UPA treatment for this study and it is therefore impossible to determine whether the emerging intramyometrial cysts would spontaneously regress as has been described for PAEC (Donnez et al., 2012a(Donnez et al., , 2012b)). The evaluation of the long-term evolution would have required a third MRI months after the end of the UPA treatment, which was not conceivable for this study given that the vast majority of the patients underwent surgery shortly after the end of treatment. Thirdly, adenomyosis was not histologically confirmed and although intramyometrial cysts are fairly specific of adenomyosis, other intramyometrial changes specific to UPA cannot be ruled out, especially because the thickness of the junctional zone remained unchanged after treatment. Finally, this being a pilot study on a limited number of patients that could not be calculated beforehand, and given the paucity of the scientific literature on this specific matter, generalization of the conclusions remains uncertain.

The pathogenesis of adenomyosis, while still debated, involves sex steroid hormone aberrations with an increase of oestrogen receptor activity and a downregulation of progesterone receptors [START_REF] Kitawaki | Progesterone induction of 17beta-hydroxysteroid dehydrogenase type 2 during the secretory phase occurs in the endometrium of estrogen-dependent benign diseases but not in normal endometrium[END_REF][START_REF] Nie | Promoter hypermethylation of progesterone receptor isoform B (PR-B) in adenomyosis and its rectification by a histone deacetylase inhibitor and a demethylation agent[END_REF][START_REF] Oehler | Functional characterization of somatic point mutations of the human estrogen receptor alpha (hERalpha) in adenomyosis uteri[END_REF][START_REF] Vannuccini | Pathogenesis of adenomyosis: an update on molecular mechanisms[END_REF]. These hormonal modifications have been described as the primary elements of a cascade of reactions involving numerous molecular pathways and resulting in the invasion of the myometrium by endometrial tissue [START_REF] Vannuccini | Pathogenesis of adenomyosis: an update on molecular mechanisms[END_REF]. The association between selective oestrogen receptor modulators (SERM) such as tamoxifen, which is prescribed for breast cancers in postmenopausal women, and the presence of adenomyosis has long been described [START_REF] Cohen | Estrogen and progesterone receptors of adenomyosis in postmenopausal breast cancer patients treated with tamoxifen[END_REF][START_REF] Mccluggage | Tamoxifen-associated postmenopausal adenomyosis exhibits stromal fibrosis, glandular dilatation and epithelial metaplasias[END_REF]. Similar data are missing for SPRM. In 2017, an observational study with histological and molecular analyses of endometrial samples to determine the effect of UPA on the endometrium was conducted [START_REF] Whitaker | Selective progesterone receptor modulator (SPRM) ulipristal acetate (UPA) and its effects on the human endometrium[END_REF]. The UPA treatment altered the expression of mRNA encoding sex steroid receptors. Progesterone receptors were expressed in differential manners within the endometrium, with a down-regulation within the stroma and an up-regulation within the glandular epithelium. These altered gene expressions could somehow explain the emergence or the progression of adenomyosis that were observed in the present study.

Thus, the results of this study suggest that a 3-month treatment course of daily 5 mg doses of UPA could provoke a short-term progression or an emergence of typical adenomyosis intramyometrial cysts on MRI exams. Although no clinical data about the evolution of symptoms is reported, these results do not encourage further research on the use of UPA as a treatment for adenomyosis.

FIGURE 1

 1 FIGURE 1 Example of a progression of adenomyosis after ulipristal acetate (UPA) treatment on T2-weighted sagittal sequences. (A) Magnetic resonance imaging (MRI) before UPA treatment; (B) MRI after UPA treatment.

FIGURE 2

 2 FIGURE 2 Example of an appearance of adenomyosis after ulipristal acetate (UPA) treatment on T2-weighted sagittal sequences. (A) Magnetic resonance imaging (MRI) before UPA treatment; (B) MRI after UPA treatment.

TABLE 1 MRI CHARACTERISTICS OF PATIENTS FOR WHOM ADENOMYOSIS WAS DIAGNOSED ON THE MRI BEFORE THE UPA TREATMENT (N = 15) MRI before UPA treatment MRI after UPA treatment P-value a

 1

	Diagnosis of adenomyosis
	Junctional zone >12 mm	15	8/15 (53)	6/15 (40)	-
	type="Other" Presence of intramyometrial cysts	15	12/15 (80)	15/15 (100)	-
	Classification of adenomyosis
	Focal internal adenomyosis	15	10/15 (67)	10/15 (67)	-
	Diffuse internal adenomyosis	15	1/15 (7)	4/15 (27)	-
	Intramural adenomyoma	15	1/15 (7)	1/15 (7)	-
	External adenomyosis	15	0/15 (0)	0/15 (0)	-
	Isolated thickening of the junctional zone	15	3/15 (20)	0/15 (0)	-
	Number of intramyometrial cysts, median (minimum-maximum)	15	2 (0-10)	10 (2-30)	0.002 **
	Thickness of the junctional zone (mm), median (minimum-maximum) 14	13.5 (2-21)	11.0 (5-21)	0.640
	Progression of adenomyosis	15	-	12/15 (80)	-
	Increased thickness of the junctional zone ≥20%	14	-	3/14 (21)	-
	Increased number of intramyometrial cysts	15	-	12/15 (80)	-
	PAEC	15	-	9/15 (60)	-

Data are presented as n (%). ** P-value ≤0.01. MRI = magnetic resonance imaging; PAEC = progesterone receptor modulator-associated endometrial changes; UPA = ulipristal acetate.

TABLE 2 MRI CHARACTERISTICS OF PATIENTS FOR WHOM ADENOMYOSIS APPEARED AFTER THE UPA TREATMENT (N = 15) n MRI before UPA treatment n MRI after UPA treatment P-value

 2

	Diagnosis of adenomyosis
	Junctional zone >12 mm	-	-	15	2/15 (13)	-
	Presence of intramyometrial cysts	-	-	15	15/15 (100)	-
	Classification of adenomyosis
	Focal internal adenomyosis	-	-	15	14/15 (93)	-
	Diffuse internal adenomyosis	-	-	15	0/15 (0)	-
	Intramural adenomyoma	-	-	15	0/15 (0)	-
	External adenomyosis	-	-	15	1/15 (7)	-
	Isolated thickening of the junctional zone	-	-	15	0/15 (0)	-
	Number of intramyometrial cysts, median (minimum-maximum)	-	-	15	3 (2-20)	-
	Thickness of the junctional zone (mm), median (minimum-maximum) 12	7.0 (3-11)	13	7.5 (3-13)	0.670
	PAEC	-	-	15	5/15 (33)

Data are presented as n (%). MRI = magnetic resonance imaging; PAEC = progesterone receptor modulator-associated endometrial changes; UPA = ulipristal acetate. a