De Gennaro
email: degennar@cermes.enpc.fr

P Delage

Y.-J Cui

Lecturer, Ph.D V De Gennaro

ON THE COLLAPSE BEHAVIOUR OF OIL RESERVOIR CHALK

Keywords: chalk, compaction, laboratory tests, offshore engineering, soft rocks, suction

INTRODUCTION

In the last two decades, problems related to the seabed subsidence in the Ekofisk oilfield in the North Sea (about 10 m, [START_REF] Nagel | Ekofisk geomechanics monitoring[END_REF]) required a substantial revision in the production planning, as well as an important structural rehabilitation of the offshore platforms [START_REF] Hermansen | Experiences after 10 years of waterflooding the Ekofisk Field, Norway[END_REF]. Although it is now widely accepted that the main cause of the seabed settlement is the compaction of the 150 m thick layer of reservoir chalk (n = 30-48%) located at a 3000 m depth below seafloor, the origin of the compaction is still an open issue.

Early studies that related the compaction to increased effective stresses due to reservoir depletion [START_REF] Johnson | Compaction behaviour of Ekofisk chalk as a function of stress[END_REF][START_REF] Jones | Compaction and flow of porous rocks at depth[END_REF][START_REF] Leddra | Compaction and shear deformation of a weakly-cemented, high porosity sedimentary rock[END_REF] were soon questioned [START_REF] Jones | Pore pressure change and compaction in North Sea chalk hydrocarbon reservoirs[END_REF]. The depletion phase (1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986) was followed in 1987 by an enhanced oil recovery procedure in which cold seawater was injected (waterflooding). Although pressure depletion was stalled, resulting in a constant effective stress, seabed subsidence continued.

Since the early eighties, the effect of the nature of the pore fluids, of their mutual interaction and of their interaction with the rock skeleton were examined to better interpret the origin of compaction [START_REF] Newman | The effect of water chemistry on the laboratory compression and permeability characteristics of some North Sea chalks[END_REF][START_REF] Monjoie | Characterisation and Inhibition of Chalks[END_REF][START_REF] Piau | Mechanical effects of water injection on chalk reservoirs[END_REF][START_REF] Schroeder | Water/chalk (or collapsible soil) interaction: Part II. Results of tests performed in laboratory on Lixhe chalk to calibrate water/chalk models[END_REF][START_REF] Risnes | Chalk-fluids interactions with glycol and brines[END_REF]. It was proposed to adopt a coupled hydro-mechanical framework taken from the mechanics of unsaturated soils (containing water and air as a non wetting fluid) and to adapt it to reservoir chalks (containing water and oil as a non wetting fluid) [START_REF] Delage | Subsidence and capillary effects in chalk[END_REF][START_REF] Collin | Mechanical behaviour of Lixhe chalk partly saturated by oil and water : experiment and modeling[END_REF][START_REF] De Gennaro | Time-dependent behaviour of oil reservoir chalk: a multiphase approach[END_REF]. In this framework, it was demonstrated that the compaction induced by waterflooding bore strong similarities with the collapse of unsaturated soils when wetted under a constant load. In both cases, water was considered to located in menisci in the smaller pores close to the inter-grain contacts, remaining the largest available porosity to the non wetting fluid (air or oil).

In this framework, the oil-water suction s o was defined by s o = u o -u w (u o and u w being the oil and water pressures respectively). As in unsaturated soils [START_REF] Coleman | Stress strain relations for partly saturated soils[END_REF][START_REF] Fredlund | Stress state variables for unsaturated soils[END_REF], two independent stress variables were considered, namely the oil-water suction s o and the mean net stress p -u o . An extended experimental program including suction controlled oedometric and triaxial tests was developed from 1997 to 2003 within the framework of two European projects (Pasachalk1, 2001;Pasachalk2, 2004). Suction control was achieved by using both the oil overpressure (or axis translation) technique [START_REF] Richards | A pressure-membrane extraction apparatus for soil solution[END_REF][START_REF] Hilf | An investigation on pore-water pressure in compacted cohesive soils[END_REF] and the osmotic technique (Kassiff & Benshalom, 1971;[START_REF] Delage | Suction controlled testing of non saturated soils with an osmotic consolidometer[END_REF]. Among other things, the effects of physico-chemical chalk-water interactions as a complement of capillarity were evidenced. Finally, a constitutive "Pasachalk" model, derived from the Barcelona Basic Model [START_REF] Alonso | A constitutive model for partially saturated soils[END_REF]) with time effects added, was adapted to reservoir chalks and successfully used in reservoir simulations [START_REF] Charlier | Constitutive modeling of chalk -application to waterflooding[END_REF]Collin et al., 2002).

In this note, some results of oedometer tests carried out on chalk samples under constant (oil-water) suction are presented. Particular emphasis is given to the effect of suction on the compression behaviour. Collapse due to waterflooding (i.e. decreasing the oil-water suction by replacing oil by water) under a constant load is also presented and discussed.

TESTED MATERIAL

Blocks of an outcrop chalk from Belgium called "Lixhe chalk", corresponding to the same geological layer than the Ekofisk reservoir chalk (Hod formation of the Upper Campanian level, Cretaceous period) were used in this study [START_REF] Schroeder | Du coccolithe au reservoir petrolier[END_REF]. SEM observation highlighted remains of coccolithes (skeletal debris of unicellular algae) which are present in small plates of about 1 to 10 microns dimensions (Fig. 1). Between the calcite grains, the voids (dimensions 1 to 5 microns) represent about half of the total volume, with an average porosity of about 40 %. This value was corroborated by a series of mercury intrusion porosimetry (MIP) tests that characterised a quite well defined population of large pores with an average entrance radius of about 0.37 µm (Fig. 2). In the natural deposit, voids are filled with water in chemical equilibrium with the chalk, saturated in CaCO 3 . In the oil reservoir, chalk was initially filled by water a long time ago (35 millions years for Cretaceous chalks) and oil has afterwards infiltrated part of the pore space, expelling part of the water.

Constant head permeability measurements (Pasachalk1, 2001) gave a value of intrinsic permeability K of about 1x10 -14 m 2 (corresponding to water and oil permeability respectively equal to k water ≅ 1x10 -8 ms -1 , k oil ≅ 7x10 -9 ms -1 ).

A non polar and non toxic immiscible organic liquid called Soltrol 170 ® (C12-C14 isoalkanes, Phillips Petroleum Co.) was used in this study to simulate oil. Soltrol 170 ® has also been selected for its very low solubility in water (<< 1mg/l at 20°C) and very low volatility in air (<< 4x10 -2 mm 3 /h at 20°C). Soltrol 170 ® has a dynamic viscosity η o = 2.028 cP and a density ρ o = 0.78 Mg m -3 .

EXPERIMENTAL INVESTIGATION

The pressure discontinuity (u o -u w ) through the interface separating the two immiscible fluids (oil and water) gives rise to the capillary pressure (Laplace, 1806;[START_REF] Morrow | Physics and Thermodynamics of capillary[END_REF], that depends on the fluid interfacial tension and on the pore geometry. In clayey soils, additional physico-chemical fluid-mineral interactions exist. Both capillary and physico-chemical interactions are included in the definition of a potential energy called suction (Statement of the advisory panel 1965). This concept is considered to be valid in multiphase chalk.

The control of suction was accomplished using the osmotic technique [START_REF] Delage | Suction controlled testing of non saturated soils with an osmotic consolidometer[END_REF][START_REF] Dineen | A new approach to osmotically controlled oedometer testing[END_REF]Cui & Delage, 1996). This technique consists in putting the sample in contact with a regenerated cellulose semi-permeable membrane behind which a solution of large molecules of polyethylene glycol (PEG) is circulated. Since the large PEG molecules cannot go through the semi-permeable membrane, an osmotic suction that increases with the PEG concentration is imposed on the sample through the membrane. Note that direct suction measurements carried out by [START_REF] Dineen | A new approach to osmotically controlled oedometer testing[END_REF] using the IC suction sensor [START_REF] Ridley | A new instrument for measurement of soil moisture suction[END_REF] on samples in which the suction was osmotically imposed showed some deviations from the standard calibration of [START_REF] Williams | An evaluation of polyethylene glycol PEG 6000 and PEG 20000 in the osmotic control of soil water matric potential[END_REF]. Some preliminary tests showed an excellent behaviour of the semi-permeable membrane when put in contact with Soltrol, with no apparent chemical reaction, no membrane damage and no resulting PEG leaks through the membrane. This was confirmed by careful examination made on the sample at the end of the tests, where no evidence of PEG infiltration (PEG infiltration in samples due to membrane breakdown are clearly apparent) was observed.

The validity of the osmotic technique was particularly interesting in the case of oedometer testing, where the use of the osmotic technique is easier than that of the overpressure technique. Due to the difficulty of a simultaneous direct measurement of suction, the [START_REF] Williams | An evaluation of polyethylene glycol PEG 6000 and PEG 20000 in the osmotic control of soil water matric potential[END_REF] calibration curve was used. This will probably result in an uncertainty at high suction levels, estimated at a maximum value of about 200 kPa when considering the [START_REF] Dineen | A new approach to osmotically controlled oedometer testing[END_REF] measurements for suction values ranging between 0 MPa and 1.5 MPa. However, as will seen further on, the range of this uncertainty will not significantly affect the conclusions regarding suction effects on the compression behaviour of the chalk.

Sample preparation

Chalk samples were cored from a block of chalk and then shaped on a lathe at the required size. Samples of about 50 mm diameter and 15 mm high were used for the oedometer tests (Table 1). For the retention tests, samples had a diameter of about 20 mm and their height ranged between 20 to 25 mm [START_REF] De Gennaro | Time-dependent behaviour of oil reservoir chalk: a multiphase approach[END_REF]. All the samples were oven dried at 105°C, put under vacuum (approximately -94 kPa for 24 hours) and oil saturated under vacuum. The oil saturated state is to be related to a "dry" state of the chalk (with no water inside) with very high values of suction s o .

Subsequent wetting down to controlled values of suction was made using the osmotic technique. Samples full of oil were inserted in a cylinder-shaped semi permeable membrane that was subsequently plunged in a PEG solution at the desired concentration (see Cui & Delage, 1996). When doing so, a good contact between the membrane and the sample should be ensured. Due to the higher surface tension of water as compared to that of oil, water coming through the membrane progressively infiltrated the sample, giving rise to oil expulsion out of the sample. Visual observation showed that the expelled oil remained inside the membrane. This technique of imposing a suction when no stress application is required appeared quite convenient and inexpensive to treat many samples at the same time. Note that the infiltration of water in an oil saturated chalk is comparable to the waterflooding carried out in the oil reservoir chalk to enhance oil recovery.

Retention properties of Lixhe chalk

The wetting path of the retention curve of the Lixhe chalk containing oil and water is presented in Fig. 3 in a Log s o : S rw diagram, where S rw is the degree of saturation in water. At high suctions (s o higher than 0.5 MPa), large changes in suction induce small changes in expelled oil volume, whereas same suction changes at lower suction involves significantly larger expelled volume, leading to a residual degree of saturation in water of 70% (average) at zero suction. This high residual degree of saturation in water shows the high water wettability of this chalk. Similar data are used in the Amott quantification of water wettability of reservoir rocks [START_REF] Amott | Observations relating to the wettability of porous rock[END_REF]. Other North Sea chalks, like for instance in the Valhall oilfield (Andersen et al. 1992), present a hydrophobic behaviour. The origin of such a behaviour can be either adsorption of organic molecules along the coccolithe surfaces, due to the contact that occurred between oil and chalk minerals during a very long period of time of the reservoir history at elevated temperature (between 130 °C and 150 °C) and pore pressure (44.5 MPa at 2400 m depth), or surface alteration due to oil-based drilling mud. It is most probable that the degree of wettability or non wettability to water of chalks is of utmost importance in the coupled hydro-mechanic behaviour of chalks.

Suction controlled oedometer

The samples were tested in the osmotic oedometer cell presented in Fig. 4. In this device, the bottom of the sample is in contact with a semi-permeable membrane below which a solution of polyethylene glycol (PEG) is circulated (Kassiff & Benshalom, 1971;[START_REF] Delage | Suction controlled testing of non saturated soils with an osmotic consolidometer[END_REF].

Water exchanges through the membrane are monitored through visual observation of the water level in the graduated tube placed in the bottle that contains the PEG solution. Water exchanges were in general very slow and it was observed that a period of time of about 15 days was necessary to reach equilibrium after imposing the desired suction.

In order to reach the desired net vertical stress, the sample was loaded using a high pressure oedometer frame with a double lever arm that allowed a maximum vertical stress of approximately 60 MPa to be applied to a 50 mm diameter sample [START_REF] Marcial | On the high stress compression of bentonites[END_REF]. A standard step loading procedure was adopted. At each stage, the stabilisation of the PEG level in the tube was checked.

TEST RESULTS AND DISCUSSION

Figure 5 shows the results of 4 compression tests performed on chalk samples submitted to various oil-water suctions, namely: 0.1, 0.4 MPa (Fig. 5(a)) and 0.8 MPa and dry sample (Fig.

5(b))

. Due to the overall importance of the initial void ratio on the compression behaviour, compression curves have been grouped according to their initial void ratio to facilitate comparisons. Data of samples with higher initial void ratios (0.715 at 0.1 MPa and 0.702 at 0.4 MPa) are presented in Fig. 5(a) and that with lower void ratios (0.665 at 0.8 MPa and 0.649 in dry state) in Fig. 5(b). All samples were loaded up to 10 MPa, submitted to an unloading-reloading cycle, and subsequently loaded up to a maximum vertical stress which was selected depending on the suction applied (20 MPa for the sample at s o = 0.1 MPa, 30 MPa for the sample at s o = 0.4 MPa, 40MPa for the sample at s o = 0.8 MPa and for the dry sample). The corresponding void ratio was calculated from the volumetric strain obtained after 24 hours of applied constant loading.

The initial water saturation degrees (S rw ) of the samples can reasonably be estimated from the retention curve of Fig. 3, giving respectively S rw = 50%, 20% and 10%, for the samples at 0.1, 0.4 and 0.8 MPa respectively.

It can be observed in Fig. 5 that the yield stress (i.e. the maximum past consolidation stress) increases with increasing suction, i.e. with lower degrees of saturation in water (S rw ).

These results are in accordance with well established results showing a higher yield stress observed on chalk full of oil as compared to chalk full of water [START_REF] Schroeder | Water/chalk (or collapsible soil) interaction: Part II. Results of tests performed in laboratory on Lixhe chalk to calibrate water/chalk models[END_REF][START_REF] Delage | Subsidence and capillary effects in chalk[END_REF]. They are also compatible with the water weakening effect. However, the results of Fig. 5 complete these observations by also accounting for the gradual effect of partial saturation in both fluids under a controlled suction. In this regard, the change in yield stress with suction is compatible with the conclusions drawn on unsaturated soils by [START_REF] Alonso | Special problem soils. General Report[END_REF][START_REF] Alonso | A constitutive model for partially saturated soils[END_REF] and that founded the notion of a LC (Loading Collapse) curve. Note that, the results of the four tests presented here cannot be plotted together to determine a LC curve because of the effects of the change in void ratios, and increased density having also a significant effect on the yield stress. However, unlike in unsaturated soils, the slope in the plastic zone does not appear to be suction dependent. Conversely, like in unsaturated soils, the elastic response investigated by the unloading-reloading sequences, does not show any significant suction effect.

The collapse phenomenon of an oil saturated chalk sample due to waterflooding has been investigated in the framework of unsaturated soil mechanics by infiltration of water under a vertical load of 10 MPa, as shown in Fig. 6. In this test, the initial (theoretically) infinite oil-water suction was reduced to zero. In the absence of an available water saturated compression test at the same initial void ratio, a test at low suction (0.1 MPa) has been plotted together with the collapse test. As mentioned earlier, the initial degree of water saturation of this sample is about 5%, as compared to the average value of 70% observed on samples saturated under a zero suction (see Fig. 3).

Water was infiltrated using the same system that allowed to circulate PEG solutions during suction controlled tests (Fig. 4). Thus, the circulation of pure water at the bottom of the chalk sample was ensured by the peristaltic pump shown in Fig. 4. However, with respect to the apparatus layout shown in the same figure, neither PEG solution nor cellulotic semipermeable membrane were necessary. The final point in Fig. 6 (point B) has been obtained after one week of continuous water circulation, and defines a total decrease of 0.025 in void ratio (path AB). This variation of the void ratio corresponds to a compressive volumetric strain of about 1.5%. Some creep may also have affected this volume decrease [START_REF] Ruddy | Rock compressibility, compaction and subsidence in a high porosity chalk reservoir: a case study of Valhall Field[END_REF][START_REF] De Gennaro | Time-dependent behaviour of oil reservoir chalk: a multiphase approach[END_REF]. It is worth noting that the induced volumetric strain due to wetting results from a natural infiltration process, developing from the bottom to the top of the sample. Unlike in waterflooding, during which the soft rock is soaked by water injection under pressure and suction may attain negative values (i.e. u w > u o , forced imbibition) and the residual oil saturation, infiltration requires much more time to achieve the water saturation degree corresponding to the complete suction release down to zero (i.e. S rw of about 70%).

Consequently, it is believed that higher volumetric strain would have been induced if water was injected at constant pressure. Nevertheless, the collapse observed in Fig. 6 is significant and comparable to earlier data of [START_REF] Newman | The effect of water chemistry on the laboratory compression and permeability characteristics of some North Sea chalks[END_REF] on chalk samples from Cora, Dan and Gorm North Sea oilfields. The comparison with the 0.1 MPa compression curve shows that the point B is not located on or below the 0.1 MPa compression curve, as could have been expected referring to well established results in unsaturated soils as shown through the double oedometer approach of [START_REF] Jennings | The additional settlement of foundations due to collapse of sandy soils on wetting[END_REF] and the state surface of [START_REF] Matyas | Volume change characteristics of partially saturated soils[END_REF]. This difference is, however, often observed in natural soils and is not surprising in this natural chalk.

In unsaturated soils, collapse is interpreted as a breakdown of an open porous metastable granular structure whose stability was ensured in the unsaturated state by capillary menisci at inter-granular contacts. Here, some questions arise due to the initial dry state of the chalk before oil saturation and to the existence of capillary menisci in such conditions. It seems more probable that the strongest inter-granular links existing in the oil saturated sample (which, if not capillary, have a significant physico-chemical component due to the high reactivity of carbonate) are progressively weakened by the infiltration of water through the smallest pores (i.e. at the inter-grain contacts) giving rise to collapse.

CONCLUSIONS

An interpretation of the collapse mechanism induced by waterflooding in chalk reservoir rocks has been proposed in this note, based on the use of a framework taken from the mechanics of unsaturated soils. The relevant developments allowing for chalk mechanical testing under oil-water suction control have been described. As in unsaturated soils, the elastic behaviour of chalk is not affected by suction.

Conversely, increasing suction induce an increase of the vertical stress at yielding. Suction decrease has been recognised to play a major role in interpreting the collapse due to wetting under constant load. This situation is comparable to that encountered in oilfields when waterflooding is used to enhance oil production. Water weakening effects and chalk compaction (collapse) seem likely to occur through the loss of strength of the inter-granular links existing in the oil saturated sample. The nature of these links includes both capillary and physico-chemical fluids-chalk interactions, and is well represented by the oil-water suction.

On the other hand, some differences can be mentioned in comparison with unsaturated soil behaviour, namely: (i) the lack of dependence of the slope of the virgin compressibility curve of the chalk on the suction values and (ii) the stress independence of the collapse phenomenon.

Time-dependent behaviour of oil reservoir chalks, including the analysis and elucidation of suction effects on creep, are currently the object of further research in this area.

  The osmotic technique has been used to control oil-water suction during retention tests following a wetting path. Its reliability in controlling suction in chalk has been verified. A series of suction controlled tests in the osmotic oedometer cell, performed on chalk samples having different relative saturation in oil and water, provided information on the mechanical behaviour of multiphase chalk under K o conditions and controlled suction. Due to the presence of two immiscible pore fluids (oil and water) of different surface tension properties, the volume change behaviour of oil reservoir chalk appears to present various similarities with that of unsaturated soils. Experimental results highlight the influence of oil-water suction on the mechanical response of the material.

Figure 1 :Figure 2 :Figure 3 :Figure 5 :Figure 6 :

 12356 Figure 1 : SEM pictures of Lixhe chalk at various magnifications : (a) 10µm, (b) 1 µm

Table 1 .

 1 Physical properties of chalk samples (oedometric tests)

	Sample	D (mm) H (mm) W s (g)	W sat (g) S rw (%) e o	(1)	s o (MPa)
	1	49.89	17.11	52.41	63.26	98.6	0.704	Oil sat.
	2	49.84	13.64	43.11	-	-	0.649	Dry
	3	49.91	13.46	42.23	50.47	98.3	0.665	0.8
	4	49.84	14.19	43.43	52.28	97.4	0.702	0.4
	5	49.47	12.51	37.43	45.31	98.7	0.715	0.1
	(1) calculated with G s = 2.71

ACKNOWLEDGEMENTS

The results presented in this note have been obtained within the framework of the European projects PASACHALK 1 (contract n° JOF3CT970033) and PASACHALK 2 (contract n° ENK6-2000-00089) carried out jointly by the University of Liege (Dpt. GeomaC, Belgium), the Ecole Nationale des Ponts et Chaussées (ENPC, Dpt. CERMES, Paris, France) and TotaFinaElf oil company (Drs. Ph. Keul and A. Onaisi). The collaboration of Dr. B. Chen during his Ph.D. stage at CERMES is also acknowledged.


Sophie Giffard-Roisin

Lauren Fovargue

Jessica Webb

Roch Molléro

Jack Lee

Hervé Delingette

Nicholas Ayache

Reza Razavi

Maxime Sermesant

Estimation of Purkinje Activation from ECG: an Intermittent Left Bundle Branch Block Study

Keywords: Electrophysiology, Electrophysiological Model, Forward EP Model, Parameter Estimation, Purkinje System

Modelling the cardiac electrophysiology (EP) can help understand pathologies and predict the response to therapies such as cardiac resynchronization. To this end, estimating patient-specific model parameters is crucial. In the case of patients with bundle branch blocks (BBB), part of the Purkinje system is often affected. The aim of this work is to estimate the activation of the right and left Purkinje systems from standard non-invasive techniques: magnetic resonance imaging (MRI) and 12-lead electrocardiogram (ECG). As it is difficult to differentiate the contribution of the Purkinje system, this work relies on a particular intermittent left BBB (LBBB) case where both LBBB and absence of LBBB (ALBBB) were recorded on different 12-lead ECGs. First, an efficient forward EP model is proposed by coupling a Mitchell-Schaeffer cardiac model with a current dipole formulation that simulates the ECG. We used the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm to optimize the 3 parameters by minimizing the error with the real ECG. The estimation of conduction velocity (CV) parameters for LBBB and ALBBB shows a good agreement on the myocardial CV (0.39m/s for ABBB, 0.40m/s for LBBB), while the estimation of the left Purkinje CV seems to identify the pathology (1.32m/s for ALBBB, 0.49m/s for LBBB). Finally, the plots of the simulated 12-lead ECGs together with the ground truth ECGs indicate similar shapes.

Introduction

Modelling the cardiac electrophysiology (EP) can help understanding pathologies and predicting the response to therapies such as cardiac resynchronization therapies (CRT). To this end, estimating patient-specific model parameters is crucial. In the case of patients with bundle branch blocks (BBB), part of the Purkinje system is often affected. The Purkinje fibers are located just beneath the endocardium and are able to conduct cardiac action potentials quickly and efficiently: typical conduction velocity (CV) ranges from 2 to 3m/s while it ranges from 0.3 to 0.4m/s for myocardial cells [START_REF] Durrer | Total excitation of the isolated human heart[END_REF]. Stimulus arrives from the atrioventricular node through the His bundle and separate the network in two branches, the left bundle and the right bundle. When a block occurs in a bundle (LBBB for left, RBBB for right), the Purkinje system is not as efficient and the contraction of the ventricles isn't synchronized.

Some studies have been focusing on the understanding of LBBB patterns by simulating ECGs with different parameters from precise cardiac and torso models [START_REF] Lorange | A computer heart model incorporating anisotropic propagation[END_REF][START_REF] Potse | Similarities and differences between electrocardiogram signs of left bundle-branch block and left-ventricular uncoupling[END_REF]. Because of their complexity, we defined a simpler model for the estimation of patient-specific parameters. A study has also recently proposed an EP parameter estimation from ECG data [START_REF] Zettinig | Data-driven estimation of cardiac electrical diffusivity from 12lead ECG signals[END_REF]. It uses two features from the 12lead ECG to recover 3 electrical diffusivity parameters using a boundary element method forward model and a polynomial regression. As it is difficult to differentiate the contribution of the Purkinje system, our work relies on a particular intermittent LBBB case where both LBBB and absence of LBBB (ALBBB) are recorded on 12-lead ECGs. First, an efficient forward EP model is proposed by coupling a 3-parameter cardiac EP model based on the Mitchell-Schaeffer model with a current dipole formulation. We used the CMA-ES algorithm to optimize the 3 parameters by minimizing the error with the ECG signals.

Materials and Methods

Clinical Data

In this study, we considered cardiac imaging data from MRI and electrical data from the 12-lead ECG. The MRI acquisition allows a precise myocardial geometry at end diastole. The 12-lead ECG represents the cardiac electrical activity recorded from 9 body surface electrodes. Because the locations of the electrodes were not registered, we manually position them guided by the conventional ECG placement (Figure 1(a)). The 12 standard Einthoven, Goldberger and Wilson leads (12-lead ECG) measures the potential differences between selected electrodes.

Pre-processing

The myocardial mesh was generated using the VP2HF platform [START_REF] Groth | Robust left ventricular myocardium segmentation for multi-protocol MR[END_REF] and the VP2HF meshing pipeline1 creating a tetrahedral mesh with roughly 90K tetrahedra. Rule-based fibre directions were estimated with an elevation angle between -70 • and 70 • . The right and left Purkinje regions were manually delineated (Figure 1(b)). The 12-lead ECG were digitized using the opensource Engauge Digitizer followed by a resampling at a rate of 1kHz. Only the 200ms following the Q wave were used (QRS window).

Forward EP Model

Mitchell-Schaeffer Cardiac Model: We simulated the electrical activation of the heart using the monodomain version of the Mitchell-Schaeffer's EP model [START_REF] Mitchell | A two-current model for the dynamics of cardiac membrane[END_REF]. The monodomain formulation considers that the extra-cellular and intracellular anisotropies are proportional and therefore we can solve directly the transmembrane potential. It is governed by:

C m ∂v ∂t + I ion = ∇ • σ∇v (1)
with v the transmembrane potential, C m the membrane capacitance and I ion the current through the cell membrane per unit of area. The anisotropic conduction tensor σ is defined as σ = σ • diag(1, r, r) where the anisotropy ratio r enables conduction velocity in the fibre direction to be larger than in the transverse plane (we used r = (1/2.5) 2 ). The conductivity σ is a local parameter that depends on the capability of the tissue to propagate the electrical activation. σ can be written in terms of intracellular and extracellular conductivities:

σ = σ i σ e σ i +σ e
The reduction of the monodomain model implies σ i = λσ e for some scalar λ resulting in a linear relationship between σ and σ i . The diffusivity d (in m 2 s -1 ) can be expressed as a conductivity σ (in Ω.m) by using σ = C m β d with C m the membrane capacitance and β the surface-to-volume ratio. Finally, the diffusion d is linked to the conduction velocity c in m/s by c = k √ d, where the constant k was estimated numerically in our simulations as 0.35 s -1/2 .

In this work, we considered 3 different domains with uniform conduction velocities: the myocardial cells (MC), the left Purkinje system (LP) and the right Purkinje system (RP). The MC was modelled as one single domain for simplification reasons and because the patient was non-ischaemic. We modelled the LP and RP as a thin layer covering the endocardial surfaces. By considering that the Purkinje geometry is unknown, this simplification to a layer allows also a rapid computation. Concretely, the layer is composed of all the tetrhedra connected to the endocardial surface.

We manually selected the onset activation locations on the septum near the valves, see Figure 1(b). This was driven by the fact that the electrical wave arrives from the His bundle to the left and right bundles located on the septum.

From Cardiac Simulations to BSPM, Current Dipole Formulation: We computed simultaneously the cardiac electrical sources and body surface potentials. Our forward method is based on a simplified framework composed of sources and sensors in an infinite and homogeneous domain. As in [START_REF] Chávez | Inverse problem of electrocardiography: Estimating the location of cardiac ischemia in a 3d realistic geometry[END_REF], we modelled every myocardium volume element (tetrahedron) as a spatially fixed but time varying current dipole. The equivalent current density j eq writes as:

j eq = -σ i ∇v (2)
j eq is a current dipole moment per unit of volume and the local dipole moment p in the volume V writes as p = V j eq dV .

According to the volume conductor theory, the electric potential at a distance R in a homogeneous volume conductor of conductivity σ T is:

Ψ (R) = 1 4πσ T V j eq • ∇( 1 R )dV (3)
The infinitesimal dipole moment of the volume dV X located at position X is defined as p X = j eq,X dV X = -σ i X ∇v X dV X . As we use linear tetrahedra in the FEM discretization of the myocardium, the potential v is linear and ∇v is constant over the tetrahedron. We get the following formulation of the dipole moment of the charge in the volume V H of tetrahedron H of the myocardial mesh: p H = -σ i H ∇v H V H . From [START_REF] Delingette | Nicholas: Soft tissue modeling for surgery simulation[END_REF], the gradient of the electric potential in tetrahedron H can be computed from the potentials v(X k H ) at the nodes X k H , and the contribution Ψ H of the tetrahedron H to the potential field calculated at position X T is:

Ψ H (X T ) = 1 4πσ T σ i H V H (∇v H • --→ HT ) --→ HT 3 (4)
with --→ HT the vector from centre of the tetrahedron H to the torso electrode location T . Finally, we sum over the whole mesh to get the potential field at X T . The implementation was performed using the SOFA platform2 , with a direct coupling to the Mitchell-Schaeffer model. One iteration of the model is computed in 0.1ms (dual-Xeon X6570 with 12 cores at 2.93GHz).

Parameter Estimation using CMA-ES Algorithm

We estimated the 3 conduction parameters using a Covariance Matrix Adaptation Evolution Strategy (CMA-ES) [START_REF] Hansen | The CMA evolution strategy: a comparing review[END_REF]. It is a derivative-free and stochastic algorithm that is suited for non-convex continuous optimization problems. At each iteration, new candidate solutions are sampled from a multivariate normal distribution whose covariance matrix is adapted according to the ranking between the candidate solutions of the previous iteration. We define the score of a simulation S as its error to the ground truth 12-lead ECGs Ψ GT :

f (S) = T t=0 1 N N i=1 |Ψ GT (i, t) - Ψ GT Ψ S Ψ S (i, t)| (5)
with N the number of leads (N = 12), T the final time (T = 200ms), Ψ GT (i, t) the ground truth difference of potential of the lead i at time t and Ψ S (i, t) the simulated difference of potential of the lead i at time t. We used a population of 100 simulations per generation and optimized over 20 generations. We initialized the algorithm by a multivariate distribution of mean x 0 = (0.6, 0.6, 0.6)m/s and standard deviation std = 0.1m/s in each direction. We fix the parameter searching range at [0.05, 2.5]m/s to avoid non-physical solutions. The best score vs, the number of iterations for a parameter estimation is plotted on

Evaluation on an Intermittent LBBB Patient

Intermittent LBBB Patient Data

As an evaluation of the proposed method, a patient with intermittent LBBB was chosen. The data has been acquired at St Thomas Hospital (London) as part of the VP2HF project. Both LBBB pattern and absence of LBBB (ALBBB) were documented on two 12-lead ECG, the ALBBB being recorded after the LBBB.

The parameters were estimated separately for the LBBB and ALBBB. Only the right onset location was activated for the LBBB whereas both right and left were activated for ALBBBm because in an LBBB the left bundle is not active.

Results

Table 1 shows the CV before the parameter estimation, after the LBBB parameter estimation and after the ALBBB parameter estimation. First, all Purkinje CV are higher than myocardial CV which is to be expected. We can see that the myocardial cells CV (as for the right Purkinje) is very similar between the LBBB and the ALBBB estimations. For the left Purkinje, we found 0.49m/s for LBBB and 1.32m/s for ALBBB, indicating that the model seems to identify the LBBB pathology (affected LP system). Moreover, the MC CV values lie in the myocardial CV range found in the literature [START_REF] Durrer | Total excitation of the isolated human heart[END_REF]. The RP CV (as well as the LP CV for the ALBBB) is close to the Purkinje CV range found in the literature. Figure 3 shows the simulation results after parameter estimation. Figure 3(a) represents the true (black) and simulated (blue) 12-lead ECG for the LBBB case and Figure 3(b) the corresponding cardiac activation map. We can see that the shape of the ECG is coherent with the ground truth and especially the clear notched R wave on leads V5 and V6, indicator of an LBBB pathology. Figures 3(c) and 3(d) depict the results for the ALBBB, where both QRS on ECG and activation times are shorter than for the LBBB. The real and simulated ECG for ALBBB have similar shapes even though we can notice the notched V2 and V3 R waves (so RV and LV are not perfectly synchronous). It may indicate that our Purkinje zone delimitation could be improved.

Discussion

We have shown a promising parameter estimation based on common non-invasive procedures and identified the activation of the Purkinje system. The fact that the RP and LP conductions are smaller than the literature range could be due to the fact that we model the Purkinje system as a layer (and not a small fiber network). For consitency reasons, we initialized the LBBB with only the right onset. However, it leads to different initial settings between ALBBB and LBBB parameter estimation. That is why we also ran our algorithm using both onsets for the LBBB: we found a similar left Purkinje CV. Because of the simplicity of the 12-lead ECG, we made some strong assumptions as the location of the onset activation and of the torso electrodes. This could lead to important errors and may not allow to identify more model parameters. We can think of two ways to avoid this problem. The first consists in using BSPM data with more electrodes and recorded locations. The second includes the processing of more patient data to identify the error distribution.

Conclusion

We have shown a method for estimating the activation of the left and right Purkinje system of the EP cardiac model based on the 12-lead ECG. The estimation of CV parameters for LBBB and ALBBB (same patient) shows a good agreement for the myocardium CV (0.39m/s for ABBB, 0.40m/s for LBBB), while the estimation of the left Purkinje CV seems to identify the pathology (1.32m/s for ALBBB, 0.49m/s for LBBB). Moreover, the plots of the simulated 12-lead ECGs and the real ECGs indicate similar shapes. We believe this work to be an interesting first step for understanding and modelling BBB pathology.

Fig. 1 .

 1 Fig. 1. (a) The 9 ECG electrodes and the cardiac mesh. (b) Long axis view of the cardiac mesh with delineated regions: Myocardial cells region (blue), right Purkinje system region (orange) and left Purkinje system region (beige). The red dots are the modeled right and left onset activation locations.

Figure 2 Fig. 2 .

 22 Fig.2. Best score versus the number of iterations of the CMA-ES algorithm. The score is identified as the mean error between the simulated and real 12-lead ECG, in mV.

Fig. 3 .

 3 Fig. 3. Simulation results after parameter estimation. LBBB: (a) Real 12-lead ECG (black) and estimated (blue) during the 200 ms after onset activation. (b) Estimated activation map. ALBBB: (c) Real 12-lead ECG (black) and estimated (blue) during the 200 ms after onset activation. (d) Estimated activation map.

Table 1 .

 1 Estimated Conduction Velocities for LBBB and ALBBB.

	CV (m/s)	myocardium left Purkinje right Purkinje
	Initially	0.6	0.6	0.6
	LBBB	0.39	0.49	0.95
	Absence of LBBB	0.40	1.32	1.22

VP2HF is a European Seventh Framework Program, http://www.vp2hf.eu/. The VP2HF meshing pipeline is based on CGAL, VTK, ITK and VMTK opensources libraries.

SOFA is an Open Source medical simulation software available at http://www.sofaframework.org

Acknowledgments. The research leading to these results has received funding from the Seventh Framework Programme (FP7/2007-2013) under grant agreement VP2HF n • 611823.


Bingyao Sun
email: bingyao@vt.edu

Rolando Burgos

Dushan Boroyevich

Remi Perrin
email: remi.perrin@insa-lyon.fr

Cyril Buttay

Bruno Allard

Nicolas Quentin

Marwan Ali

Two Comparison-Alternative High Temperature PCB-Embedded Transformer Designs for a 2 W Gate Driver Power Supply

Keywords: GaN, PCB-embedded transformer, high integration converter, inter-capacitance, high temperature

With fast power semiconductor devices based on

GaN and SiC becoming more common, there is a need for improved driving circuits. Transformers with smaller interwinding capacitance in the isolated gate drive power supply helps in reducing the conducted EMI emission from the power converter to auxiliary sources. This paper presents a transformer with a small volume, a low power loss and a small intercapacitance in a gate drive power supply to fast switching devices, such as GaN HEMT and SiC MOSFET. The transformer core is embedded into PCB to increase the integration density. Two different transformer designs, the coplanar-winding PCB embedded transformer and the toroidal PCB embedded transformer, are presented and compared. The former has a 0.8 pF inter-capacitance and the latter has 85% efficiency with 73 W/in 3 power density. Both designs are dedicated to a 2 W gate drive power supply for wide-band-gap device, which can operate at 200 C ambient temperature.

I. INTRODUCTION

Fast-switching power devices, such as GaN HEMT and SiC MOSFET, have enabled converters to achieve higher switching frequency, higher efficiency, and higher power density. The fast switching transient results in low switching losses though it tends to aggravate EMI. To enhance the EMI immunity of the whole system, the transformer in the isolated gate drive power supply should have a small inter-winding capacitance. High power density and high efficiency are also another important factors in terms of converter design.

The integration of passive components is a key enabler for high-power-density power supply [START_REF] Yipeng | High frequency integrated Point of Load (POL) module with PCB embedded inductor substrate[END_REF] [START_REF] Arturi | High frequency models of PCB-based transformers[END_REF]. The low-cost printed circuit board (PCB) is the most widely used substrate material in electronic applications [START_REF] Su | Design and evaluation of a high-frequency ltcc inductor substrate for a three-dimensional integrated dc-dc converter[END_REF] [START_REF] Artillan | Integrated lc filter on silicon for dc-dc converter applications[END_REF]. The PCB material selected as the substrate material to integrate a high power-density converter is mainly because of its capability for high-volume production using standard lamination process.

This study details a comparative work of two ways to embed magnetic into PCB. Two different transformer structures are both optimized to have a PCB thickness as thin as possible. This point is motivated to limit the delamination issue due to a too high PCB stack [START_REF] Coombs | The Printed Circuits Handbook[END_REF] and to have a converter size as small as possible. The magnetic material of the both designs is carefully selected, guaranteeing a lower transformer loss [START_REF] Inoue | Low loss MnZn-ferrites: frequency dependence of minimum power loss temperature[END_REF] and holding the mechanical pressure during the PCB lamination process. The high temperature PCB material R-1515, is selected and suggests the potential to use the transformer in high temperature application, holding 200 C. This work interest is multiple. First the resonant active clamp flyback topology is selected according to the high-temperature low-power power supply requirement. The two corresponding PCB embedded transformer designs dedicated to this topology is processed with optimizations. The transformer performances between the two PCB-embedded designs are compared afterwards with the high frequency converter.

II. TOPOLOGY: ACTIVE-CLAMP FLYBACK

The gate drive power supply is dedicated to support one phase-leg of 600 V, 30 A GaN devices. The specific requirements of the power supply are listed in Table I. There are two isolated outputs in order to support both the switches of the phase leg. The inter-winding capacitance is required to be as small as possible, ideally lower than 5 pF. The switching frequency is limited to 1 MHz due to the gate driver hightemperature integrated chip used for this converter.

The active-clamp flyback is a better choice in this application, compared with the classic flyback and the LLC converter. Fig. 1 shows the simplified circuit model of the With the active-clamp circuit, the energy stored in the leakage inductance can be used for both outputs and the two switches T S1 and T S2 can achieve soft switching, contributing a high efficiency. With the PCB-embedded transformer, the leakage inductance can represent 30% ~ 50% in the total primary inductance. Due to this large leakage inductance, the main switch in the classic flyback would experience very large turnoff voltage spike. In simulation with same devices, the active clamp flyback can achieve 88% efficiency, 19% higher than that of the classic flyback. In the other words, the active-clamp circuit offers the advantage of minimizing the power stored in the transformer. That allows the use of a smaller transformer compared to the classic flyback converter with comparable characteristics.

Compared with LLC converters, the selected topology is still a better candidate. It contains fewer transformer windingsthree windings for two outputs. The LLC converter needs five windings and two more output diodes, which increase the transformer size significantly, and make it difficult to embed into PCB. On the other hand, the LLC brings higher efficiency (as high as 90%), but it is a small benefit compared with 88% efficiency based on the active clamp flyback.

As such, active clamp flyback topology was selected. In the following, two transformer designs are evaluated to assess their performance in this topology.

III. COPLANAR-WINDINGS TRANSFORMER DESIGN

A. Transformer design

This design is based on a commercially available ferrite core, (Ferroxcube ER-9.5), with the central leg of th E core machined to form a U, as shown in Fig. 2b. The main target is to reduce the inter-windings capacitance drastically, so primary and secondary windings are jept separated, as visible in Fig. 2a. This structure has the advantage to not superimpose the primary and the secondary windings. The common area between primary and secondary is resume to the PCB copper thickness. The transformer design is based on the dead-time optimization for GaN transistors phase-legs, as explained below.

B. Design Method

During the dead time a current circulates between drain and source to charge and discharge the GaN parasitic capacitance. The equations are as follows and summarize the elements to calculate the primary magnetizing inductance L m . V in is the input voltage, V o is the output voltage, D is the duty cycle, f is the switching frequency, L r is the leakage inductance of the transformer, P is the output power, C S1/2 is the total capacitance of the switch junction capacitors, n is turn number ratio, and t DT is the dead time between the two switches. In a high frequency soft-switching half-bridge, the dead-time control is a key point to reduce parasitic oscillations on the drain-source voltage responsible for EMI and switching losses. In a GaN HEMT half-bridge, it is not necessary to use external diode due to the 'body-diode' available in the HEMT structure. Nevertheless, this 'body diode' has an important voltage drop (2~3.1 V) which leads to conduction losses because of the resonant current. That is why a solution, experimentally verified, to set precisely the dead-time duration is proposed for a diode-less GaN half-bridge [START_REF] Perrin | High Temperature GaN Active-Clamp Flyback Converter with Resonant Operation Mode[END_REF]. During deadtimes, there is a capacitive transition in the half-bridge, where the current is flowing through the drain-source intrinsinc capacitor. There is a relation between the magnetizing inductance and the required current to charge and discharge the drain-source capacitors. Indeed by a proper choice of the deadtime in [START_REF] Arturi | High frequency models of PCB-based transformers[END_REF] and the current at switching in (1), the transistor losses can be more reduced even further. In Fig. 3, by using the Q3D software, the distance between the primary and the secondary windings (in order to reduce the isolation capacitance as low as possible) was optimized. This curve has to be balance by the width of each winding that means more or less copper losses.

2 0 2 0 2 ( ( ) ) 2(2 ( ( ) )) in r Lr in m r L r in D P D V L i t V f f f L P D L i t V f f - + = + (1) 0 1 / 2 ( ) 2 o in Lr S DT V V n i t C t + ≥ (2) (1 ) o m r in m V D L L n DV L - + = (3)
A comparison was between two different ferrite sizes. This study allowed us to check if any improvement can be made on the volume but also for the losses. Two transformers were made, one transformer design with ER14.5 core, and one with an ER9.5 core. In Fig. 4 two 3D curve graphics show the chosen design point between volumes, primary inductance given in (2) and air-gap. The corresponding losses (copper and core) calculated for both designs using the Maxwell for two Ferroxcube magnetic materials with high Curie temperature point: 3C92 and 3F45. The high Curie temperature point is a requirement, as the final converter should be able to operate at 200°C.

Based on Fig. 4 and Table II the following conclusions can be drawn: first the efficiency of the converter is barely affected by the transformer loss with respectively 8 and 11% for ER14.5 and ER9.5 core of the total converter efficiency. In another hand the volume is dividing by two when we are using a smaller core. Therefore, the density of the converter will be higher with the ER9.5 core with a small increase of the loss. For the material 3C92 is not a high frequency material and the losses are higher than with 3F45 for a 1 MHz switching frequency.

In this practical case, the transistor used has an equivalent drain-source capacitor of 50 pF for 30 V drain voltage. The current, in (1), has to be more than 102.6 mA if the dead-time value is 110 ns. In these conditions the magnetizing inductance in (2) has to be less than 5.4 μH. The transformer ratio is designed by the equation (3).

C. Experimental results

Fig. 5b shows a cross-section view of the PCB embedded transformer with different layers. In Fig. 5a the ferrite core and coplanar winding were embedded into the PCB (Panasonic R-1515W) to implement the transformer. All other components including active transistor devices were mounted on the top surface of the PCB substrate. The volume of this fabricated converter is 23 mm x 18 mm x 2.8 mm with an intercapacitance measured of 0.77 pF, shown in Fig. 6. The global efficiency of the converter is about 74 % at 25°C. The losses are mainly affected by the voltage drop in the output rectifiers.

IV. TOROIDAL PCB-EMBEDDED TRANSFORMER DESIGN

A. Transformer design

A different design, named toroidal PCB-embedded transformer, is proposed, shown in Fig. 7. The toroidal core is placed in x-y plane and three copper windings -one primary and two secondary -wrap the core. The planar copper on the top and bottom sides layouts as PCB traces. The z-direction copper winding connection can be realized by via-holes or copper pins.

There is only one air gap cut in the core, to keep the core as one piece, which makes the structure stronger during lamination process and reduces the magnetic flux leakage. If two or more air gaps are distributed on the core, the air gap cannot be precisely controlled to be the desired value due to the high pressure in the lamination process. Besides, the core is hard to be in the same x-y plane if it is cut into several pieces. As for the air gap position, it locates out of windings to avoid extra AC winding loss, and between the two secondary windings to keep two secondary windings symmetric. Core material is selected as P61 from ACME. It has relatively low power loss coefficient compared with other products [START_REF] Huang | Design consideration of MHz active clamp flyback converter with GaN devices for low power adapter application[END_REF].

B. Design method

An optimization is performed to have a smaller transformer volume, a smaller inter-capacitance and a smaller loss in this design, by optimizing the transformer dimension parameters in Fig. 7, listed in Table III. In order to do the optimization, first the boundary of the optimization input is clarified. To limited core size and to have an enough top circuit area, R o should be smaller than 6 mm and larger than 4 mm. w i , w o , and h w are required to be larger than 0.5 mm, 0.5 mm and 0.1 mm due the limited PCB manufacture ability. t w has two options: 1 oz (0.0343 mm) or 2 oz (0.0686 mm). In order to achieve softswitching, according to (1), ( 2), (3), the leakage inductance and magnetizing inductance has a limitation, with one more fact that leakage inductance takes 30% ~ 40% of the total primary inductance, found in the finished transformer samples. The outputs of the optimization are transformer volume, the total loss and the inter-capacitance.

Then the equations between the inputs and outputs are built. First the volume, it is can be calculated as follows taking a square surface on the top layer:

2 (2(
)) ( 2)

o o w V R w ww h h = + + + . ( 4
)
The loss can be separated into the core loss and the winding loss. The core loss can be calculated based on the estimated average magnetic field and the power loss coefficient P v at 1 MHz provided by the magnetic manufacture as follows:

P i i R R - - = + + . ( 8
)
i rms-pri and i rms-sec are calculated primary and secondary current under different magnetizing inductance. The equivalent winding AC loss R AC is estimated to a closed value from the FEA transient simulation. The loss model with the equations matches the FEA simulation within 10% error. The FEA simulation has 5% percent error from the experimentally transformer.

The inter-capacitance model is relatively complex to build compared with the loss model. There are two parts in the intercapacitance calculation. One is total impedance of the equivalent capacitance from winding to core, in series with the resistance from primary side to secondary side on the core, and with the capacitance from core to the winding. This can be described with some analytical equations. The other part is the capacitance between the two windings without core, which is descripted with curve-fitting method based on the Q3D simulation results. However the error between the Q3D simulation and final measurements can be up to 35% due to the measurement accuracy, which reduces accuracy of the whole optimization.

There are two transformer samples with 1.3 mm and 1.8 mm thickness to verify the loss model and three samples with different inter-winding-angle to verify the inter-capacitance model.

Using the optimization software CADES, and the built models, the optimization process runs with two steps to draw a 3D Pareto surface -volume, loss, and inter-winding capacitance. In the first step, one optimization runs with fixed volume number and inter-winding capacitance value to get the smallest loss, by optimizing inputs. In special conditions, there is no solution to solve a fixed volume with a fixed intercapacitance, and therefore it will give none under this condition. Once the solutions can output, the optimization runs within the solutions to find the smallest loss. The second step is to sweep the volume value and the inter-capacitance value to have the 3D Pareto surface in Fig. 8. Each point on this surface is an optimized result. One points is selected according to the requirement as 242 mW loss, 1 pF inter-capacitance and 242 mm 3 volume. The corresponding dimensions are listed in Table III.

C. Lamination and experimental results

The PCB material layer stack before the lamination process is shown in Fig. 9a and Fig. 9b, where the toroidal core is place in the center of four copper pins. The copper pins are used to fix the layer position during press process in case the core center misses alignment with the winding center. Fig. 9c and Fig. 9d exhibit the toroidal PCB-embedded transformer after the press cycle, where the core, its air gap, and winding via-holes are displayed. It is also seen in this figure that the core and the three windings are accurately aligned. The finished thickness of the transformer PCB is 2 mm. The measured inter-winding capacitance of the transformer is 1.6 pF, the primary magnetizing inductance is 3.5 µH and the leakage inductance is 1.7 µH.

In order to connect the transformer with the ACR flyback converter, the second lamination is processed as Fig. 9e shows, whose result is depicted in Fig. 9f. There are six via-holes to drill at the top converter layer, located at the exact winding input and output via-holes. The bottom of the transformer is also attached to a thin PCB layer to increase the transformer stability and isolation voltage. The final converter is illustrated in Fig. 10. The efficiency of the whole prototype is 85%, the volume 405 mm 3 (13 mm x 13mm x 2.4mm), and the power density 72.6 W/in 3 .

V. COMPARISON BETWEEN THE TWO DESIGNS

Table IV compares the three key characteristics of the two designs -coplanar and toroidal PCB-embedded transformer. The toroidal transformer core has a small size, compared with coplanar one. Therefore its total converter size is smaller, but with a larger inter-windings capacitance. The latter is mainly dominated by the distance between windings. If the core is larger, the primary and secondary can be placed with further distance, and as a result, the inter-winding capacitance is smaller. As for the converter efficiency, the toroidal design wins on the transformer loss, thanks to the core material with smaller loss coefficient to have less core loss. The toroidal design has 10 turns for each winding, and therefore a larger magnetizing inductance, then smaller current in the transformer and switches, which leads to smaller AC winding loss and smaller switch conducting loss.

For the high temperature consideration, first the curie temperature of the both cores is higher than 280 C. The PCB material is selected to hold a maximum point at 300 C. The thermal cycling test was performed to verify the stability of the transformers structure after 1000 cycles (30 min at 200°C and 30 min at -55°C with a slop of 10°C/min). Moreover, the coplanar windings method is to pot the ferrite with a dedicated layer for the winding in order to making the transformer. The winding is connected to the top circuit by pin connection. As a comparison, in the toroidal design, the conductive via-holes as winding is wrapped around the core. The reliability of the assembly against temperature variation is reduced due to the large number of winding via-holes. More prepreg layers in the structure help to exhaust air in the via-holes and the air gaps and to enhance the thermal reliability.

Besides, the open structure with the external windings in the toroidal design may generate a significant magnetic field emission, which may not fit with the aeronautical standard. In order to reduce the emission generation, one shielding layer can be placed between circuit layer and transformer, and one more shielding layer is added at the bottom layer. With the extra shield layers, the volume of the transformer will increase 20%. From the point on the isolated voltage, the two secondary winding in the coplanar are quite close, resulting in a smaller isolation voltage.

Compared with the state of the art, the coplanar transformer has much smaller inter-winding capacitance. As a comparison, for commercial products with close volume, have a capacitance of 2.1 pF between primary and secondary [START_REF] Power | NXE2 Series Isolated 2W Single Output SM DC/DC Converters[END_REF]. The toroidal design wins on the efficiency compared with 70%~75% efficiency in the commercial products [START_REF] Power | NXE2 Series Isolated 2W Single Output SM DC/DC Converters[END_REF]. Both designs have two isolated outputs, contributing to a larger equivalent power density compared with the similar products with single output.

VI. SUMARRY AND CONCLUSIONS

In the paper, the magnetic PCB-embedded technique is introduced to build a high-integration high-efficiency and low inter-capacitance converter. The coplanar transformer embeds the modified ER core into PCB and achieves a very small interwinding capacitance as 0.77 pF. The toroidal approach introduces the use of a toroidal-shape core inside PCB, and build a 3D Pareto surface based on an optimization, which brings a high efficiency of 85% at 2 W output, and a very small volume and small inter-winding capacitance.

Fig. 2 .Fig. 3 .Fig. 1 .

 231 Fig. 2. (a) Coplanar-windings transformer design; (b) Machine U-I shape ferrites.

Fig. 4 .Fig. 6 .Fig. 5 .

 465 Fig. 4. Comparative transformer design 3D curve between ER 14.5 and ER 9.5 ferrite.

10 ( 2 .Fig. 7 .

 1027 Fig. 7. Toroidal PCB-embedded transformer design.

Fig. 9 .Fig. 8 .

 98 Fig. 9. (a) PCB lamination layer stack illustration; (b) layer stack before lamination; (c) toroidal PCB-embedded transformer, whose core and air gap are highlighted; (d) toroidal PCB embedded transformer; (e) connection of the toroidal PCB-embedded transformer and the converter; (f) converter after final lamination.

Fig. 10 .

 10 Fig. 10. ACR flyback with the toroidal PCB-embedded transformer

TABLE I

 I

	.	GATE DRIVE POWER SUPPLY DESIGN REQUIREMENTS
		Parameter	Value
	Input Voltage	15 (±1 V) V
	Output Voltage	6 V (2 %), 2 channels
	Switching frequency	1 MHz
	Primary/Secondary Insulation	> 2.5 kV (1 min @50 Hz)
	Inter-windings Capacitance	< 5 pF
	Operating Temperature	[-55°C; +200°C]
	EMC requirement	DO160/MILSTD-461

active clamp flyback converter. This topology adds an activeclamp snubber in the conventional flyback converter, composed of an auxiliary switch T S2 and a clamp capacitor C r .

TABLE II

 II

	.	LOSS COMPARATIVE RESULTS FOR 3F45 AND 3C92 MATERIALS.
				ER14.5	ER9.5
	Volume/ cm	3	0.614	0.265
	3C92 Total Losses (Copper+Core) /mW	65 +71	71+102
	3F45 Total Losses (Copper+Core) /mW	65 +182	71+295

TABLE III

 III

	DC R	=	2	N	ρ	copper	(	o R R w w i i o w w w t -+ + +	2	2 ) w ww h h + +	(7)	.	DIMENSIONS OF THE TOROIDAL PCB-EMBEDDED TRANSFORMER DESIGN
			winding	(	rms pri	2	2	rms	sec	2	) (	DC	AC	)	Transformer Description	Optimized Value
															Ri/mm	Core inner radius	3.7
															Ro/mm	Core outer radius	5.65
															h/mm	Core thickness	1.8
															lg/mm	Air gap width	0.1
															ww/mm	Turn width	0.2
															wi/mm	Space between winding and core at inner circle	0.5
															wo/mm	Space between winding and core at outer circle	0.5
															hw/mm	Space between winding and core in the vertical direction	0.1
															Θw/degree	Angle between turns	2.86
															tw/mm	Winding copper thickness	0.0343
															N	Turn number	10

TABLE IV

 IV

	.	COMPARISON BETWEEN TWO TRANSFORMERS
				Co-planar	Toroidal
	Volume/ mm	3	1159	405
	Inter-capacitance/pF	0.77	1.6
	Converter efficiency	74%	85%


Jesús M González-Barahona

Daniel Izquierdo-Cortázar

Gregorio Robles

Mario Gallegos
email: mgallegos@uca.edu.sv

Jesus M González-Barahona

Code Review Analytics: WebKit as Case Study

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction, motivation and goals

Code review is gaining importance in free, open source software (FLOSS) projects, as it started to gain relevance several years ago in proprietary software firms [START_REF] Ackerman | Software inspections and the industrial production of software[END_REF][START_REF] Ackerman | Software inspections: An effective verification process[END_REF]. Currently, most large FLOSS projects are using it in one way or another. Understanding how it is working, how it can be characterized with traceable, measurable parameters, and understating how it may affect to the relationships between actors in the project is becoming of great importance [START_REF] Rigby | Open source software peer review practices: a case study of the apache server[END_REF]. In this paper, we present a methodology that addresses these needs 1 . It starts by identifying traces from the review process in software development repositories such as source code management or issue tracking systems, and goes all the way to the characterization of performance and extension properties of the process. In particular, the following research questions are addressed: (Q1) To which extent can the review process based on traces in development repositories be characterized? (Q2) How can the evolution over time of the code review process be characterized?

The answer to Q1 is important because if those traces can be found, and automatically extracted from software development repositories, an automated or semiautomatic methodology could be designed, implemented and deployed to track the evolution of the main parameters of the code review process. This would be a first step to build an automated dashboard that allows to better understand the process and for the continuous follow-up of those aspects by any interested party [START_REF] Rigby | Understanding broadcast based peer review on open source software projects[END_REF]. Q2 is focused on identifying parameters as simple as possible to calculate, but that capture information about important aspects of the evolution of the code review process. Again, if this can be done, instead of using a large collection of complex parameters, a small number automatically computed could be used. In our case, we have checked these two questions in the well-known WebKit project.

The next section presents the WebKit code review process, and provides a qualitative answer to Q1. Then, the methodology for the data retrieval and postprocessing is described in Section 3, including a quantitative answer to Q1. The analysis itself, with the answer to Q2, follows in Section 4. Section 5 is devoted to discussion and the analysis of the main threats to validity. The paper concludes with a section presenting the conclusions.

The code review process, and its traces

In WebKit, most significant source code contributions must go through a review process. However, activities considered trivial, or very basic maintenance issues (such as minor fixes due peculiarities of one of the platforms) can be committed directly.

Code review: is it possible to follow it in detail?

Anyone may send a contribution to WebKit. But usually the contribution must go through a review process, and be accepted by a reviewer. Both committers and reviewers are selected by previous WebKit committers and reviewers by a meritocratic, peer-approval process 2 .

The contribution process3 is centered around the Subversion repository and the Bugzilla system. Developers start by choosing or opening a new ticket in Bugzilla. The ticket may correspond to a bug report, a feature request, or something else. While working on it, developers compose a patch in their local working copy of the Subversion repository, including entries in changelog files, describing the changes and identifying the ticket. Then, it is submitted to Bugzilla with another script, where it is attached to its ticket.

Usually, upon submission to Bugzilla, code review is requested. This can be done by flagging the attachment to the ticket (as "Review?"), but it can also be requested by other means, such as in the project IRC channel. Unfortunately, only the flagging in Bugzilla leaves traces. Fortunately, flagging the ticket is the most popular requesting method. The review request is not directed to a reviewer in particular, although the developer may try to get the attention of some of them by CCing them in the ticket update, or by directly addressing them somehow.

Reviewers deal with review requests according to their preferences. Once they have reviewed a contribution, they can decide to accept it, to ask for changes, or to reject it. Acceptance and rejection is signaled with a new flag ("Review+" or "Review-") to the ticket. When developers are asked for changes, they have to send a new patch for review with a new "Review?" flag. Changes may follow several iterations, which can in many cases be tracked by examining the review flags.

Once a contribution is accepted, it can be committed to the Subversion repository by any committer, or marked for automatic commit by the commitqueue bot. Therefore, only those developers who are also committers usually commit their own contributions. This means that the "committer" field in the Subversion commit record does not contain information about the real author or reviewer (and Subversion keeps no information about authorship).

Traces

Summarizing, the traces left by the code review process are:

-Changelog files in the Subversion repository. They include information for every commit, and at least author (usually including name and email address), Bugzilla identifier of the related ticket, and reviewer (if the commit was accepted after a code review process). -Commit records in the Subversion repository. The committer information is not reliable, but useful information can still be extracted from the committed changelog files. -Attachments and flags in the Bugzilla repository. Each contribution is usually submitted as an attachment to a ticket, and reviews are requested and granted usually setting flags in it. Detailed timing of all these operations is available, and some information about the person performing it. So, at least this information is available: time of review request ("Review+?") and results of the review process: acceptance ("Review+") or rejection ("Review-"), and Bugzilla identifier of those changing the state of the ticket.

Not always all of this information is available. However, commits with missing information is mainly from old reviews; since about 2005 a very large fraction of them have all data (see details in section 3). Using this information, a characterizations of the review process is possible:

-The most reliable information about authors and reviewers (i.e., name and email address) comes from the changelog files, since they are well documented. -Alternatively, authors and reviewers could also be determined from their identities in Bugzilla ticketsA manual examination of a random collection shows that both sources offer the same information, as usually scripts automatically include identities in both. -Timing information is obtained from Bugzilla. The review process starts when a developer flags an attachment to a ticket as "Review?". The end of the process occurs when a "Review+" flag is set. If there are several requests, the timing of each "Review?" flag can also be determined. -Authors and reviewers are linked to tickets thanks to the ticket identifier found in the changelog files.

With all this information the duration of reviews, and the number of iterations (number of review requests) can be tracked with great accuracy. Therefore, the answer to Q1 is, in principle, positive: the review process can be characterized with great detail at least in the above described terms. Some other aspects of the review process could be characterized with these data, such as the size of reviewed code (which could be extracted both from the commit record and the attachments to the ticket), the changes to code due to the review process (comparison of attachments to the ticket), etc.

Methodology

The methodology that we have used to characterize the code review process in WebKit is based on the following steps, similar to those described in [START_REF] Gonzalez-Barahona | On the reproducibility of empirical software engineering studies based on data retrieved from development repositories[END_REF]: data retrieval from development repositories into databases; clean-up, organization and sampling; and analysis. The first two steps are presented in this section.

Data sources and data retrieval

The study has been performed using data from the Bugzilla (issue tracking) system 4 , and from the Subversion (source code management) repository 5 of the WebKit project. In the case of the Subversion repository, it has been accessed through a git front-end6 which allows for complete access to all the information.

The git front-end to the Subversion repository was cloned on January 17th 2013 and includes information since August 24th 2001. Metainformation about all commit records (a total of 125,863) was obtained using CVSAnalY, from the MetricsGrimoire toolset 7 . This metainformation was used mainly for crossvalidation, but is not really a data source for this study. The git clone was also used to extract information from changelog files. These files, which are spread through the source code tree, were identified, and their relevant information extracted, using an ad-hoc script based in part in the webkitpy library 8 , maintained by the WebKit project itself. This script retrieves the complete list of commits from the git clone, identifying and parsing for each of them the modified changelog files. From these files, it extracts the relevant fields: author, reviewer and Bugzilla ticket. A total of 117,079 entries in changelog files were identified this way.

The exact strategy followed by the script to determine changelog entries starts by obtaining a list of all commit identifiers (hashes) directly from the git front-end. For each of them, changelog files added or modified are identified, and their diff information obtained. All entries in those diffs are considered to be related to the commit. The author, reviewer and Bugzilla ticket identifier are retrieved and stored.

Information for all changes to all Bugzilla tickets was retrieved on January 29th 2013 using Bicho, from the MetricsGrimoire toolset. A total of 100,221 issues, and 976,879 ticket state changes were retrieved, with the first ticket dating from June 1st 2005 (there is a single older ticket from 2000, which seems to be an error, and was not considered).

Cleaning and organizing the data

A quick observation of the retrieved dataset shows how, as expected, committer information in the Subversion repository is unreliable. 24,406 commit records were found to have a committer which is not the author, according to the changelog information. Many of those are submitted by bots, who perform automatic commits of already reviewed code, or of small maintenance changes. For example, during 2012 about 22% of commits (7,079 out of 31,923) were performed by bots.

The analysis of the changelog files shows that they covered a very large fraction of all commits: only 8,784, or about 7% of the commits, are missing in the changelogs. The difference can be attributed in some cases to errors, but usually to minor maintenance commits, such as versioning commits, which are not considered to deserve an entry in changelog files. Although other approaches are possible, we considered only a single author for each commit. This meant that of the commits identified in changelog files, an additional 578 (about 0.5%) were ignored because they included information about more than one author (this usually happens when several developers collaborated in the code change).

The number of commits that included "Reviewed by" and similar entries was 74,290. On the other hand, the number of commits with changelog files that reference a Bugzilla ticket is 68,460. Both conditions (being reviewed and referencing a ticket) are fulfilled by only 60,991. Many of the commits that do not comply with both conditions correspond to the period before June 2005, when tickets were not introduced in the Bugzilla database. In some cases, a ticket is referenced in more than one commit: 55,649 unique tickets were found in changelogs. When looking for those tickets, some corresponded to non-public tickets (such as those used in some cases by Apple developers), being 54,501 the total number of tickets that we could use in our study.

The last step in selecting tickets is considering only those with complete information about the review process: we need to know when it was initiated, and when it finished. For that, we selected tickets flagged at least once as "Review?" (review request) and "Review+" (review approved).

Our study will consider tickets with review request after 2006 and before 2013. This will avoid the early days of the project when few information about code review is available in the Bugzilla system, and the final part of the sample, which would distort the final part of the evolution studies. For that period, we have a total of 75,179 commits marked as reviewed in the changelog files. Out of them, 61,867 (82%) reference a Bugzilla ticket, with 56,483 different tickets referenced. Of those, 55,303 (98%) are publicly available. Of those, 53,212 include at least one review request and approval: this is our final sample, which will be used for the following analysis.

Analysis over time

In order to characterize the evolution of the review process over time, after informal discussion with some WebKit developers, we have used the following parameters as they capture the most relevant aspects of how the code review process is changing:

-Bulk parameters: number of commits subject to code review, number of authors and reviewers involved, per month. They capture the "size" of the review process: how many actors are involved, how many actions ("review processes") they perform. -Performance parameters: number of iterations (review requests needed) per review, delay from review request to reviewed. They capture how much effort is put into the review process (measured by iterations), and how much delay the process is causing (by measuring time-to-review). Figure 1 shows the bulk parameters for authoring. The number of reviewed commits is increasing clearly over time (from less than 400 per month before mid-2009 to around 1,500 per month during 2012). The number of active authors per month is also increasing, following closely (although not always) the number of reviewed commits. In this case, the growth started a bit earlier than for commits, and shows what at first sight seems to be a linear trend. Fig. 2. Bulk parameters (reviewing). Total number of tickets corresponding to review processes, and of active reviewers (review approvers) per month. Time of review approved is used to determine the month for each ticket.

Bulk parameters for reviewing, shown in Figure 2, show very similar patterns. With a median delay of 151 minutes, times for asking for review and granting it are very close, which explains the almost equal shapes for commits. The growth in reviewers, on the contrary, is a bit slower than in the case of authors. While from 2008 to 2012 authors increased from around 50 to 250-300, reviewers grew only from about 20 to 80. Performance parameters tell about how the process is actually working over time. Figure 3 shows the evolution of the means: mean iterations and mean delay over time. In the case of iterations (number of cycles implying review requests) per ticket, although there is a lot of variance over time, a slowly growing trend seems clear. In early 2007, the mean number of iterations per ticket was of about 1.4, while in 2012 it remains around 1.8 most of the year.

Despite this increase in the number of iterations, the mean delay for tickets has been decreasing since mid 2008, after a couple of long peaks (in mid 2007 and mid 2008), for which we have found no apparent explanation. Looking at the general trend, it shows how, despite putting more effort in the review process (more iterations), the project is being able of reducing the time-to-review. This means that both reviewers are being more responsive to review requests by authors, but also that those have into account quickly the suggestions for changes, so that a new review cycle can start. Fig. 4. Performance parameters (quantiles per month). Delay (time from review request to review approval, in minutes) for "quick" (top) and "slow" (middle) reviews, and logarithm of the delay (bottom).

This said, it is important to signal that the distribution of delays is very skewed: while the median for delays is 151 minutes, the mean is 7,447 minutes. Therefore, we have considered convenient to offer also, in Figure 4, similar information, but now using quantiles. In the top chart in that figure we can see the maximum delay for the quickest closed tickets. For example, the .2 (green) line in that chart shows how the maximum delay for the 20% quickest review processes, over time. The .5 (black) line shows the evolution of the median delay.

For all the quantiles analyzed, the evolution of delay over time is quite similar, and consistent with the one found for the mean delay. Maybe the quickest tickets are reducing their delays, while the slower ones tend to be more stable. This can be seen in the middle chart, with the delays for 80% and 95% of the tickets, but more clearly in the bottom one, which shows the logarithm of delay over time: the red and blue lines shows a tendency to descend since 2008, while the black and green ones are almost horizontal. The bottom chart, taking into account the log scale, shows also the great skewness of the distribution of delays.

Discussion and threats to validity

In large projects where many different actors contribute, each with their own and usually competing interests, many software development processes are difficult, yet important to understand. In the case of our study, the code review process is specially important, because it controls what enters the code base, but also what is left out. It is a barrier that developers have to overcome for contributing. Therefore, understanding it is really important, and more when the stakeholders are companies competing in the marketplace, but collaborating in the project.

A pure qualitative understanding, based on the modeling of the mechanics of the process, is not enough. Quantitative information is needed to back discussions with data, to detect early problems, and to be able of evaluating solutions and new policies. In this respect, we have quantified several aspects of the process, and have validated them with WebKit developers.

The main contribution of our study, from this point of view, is a detailed methodology, that can be used in the WebKit project and, with some variations, in other projects too. The parameters and charts presented can be the basis for a specialized dashboard that tracks the details of how the review process is evolving. The parameters presented, and the way they are calculated, can also be the basis of a validation system for any quantitative model of the code review process.

There are several threats to the internal validity of the study. The main one is probably the validity of the parameters selected to characterize the code review process. In general, both practitioners and academics consulted agree on the validity and usefulness of them as they can be linked to important concepts such as effort or delay in actions. But more research is needed to really correlate them with other parameters, so that it becomes clear that they are really important for the review process. Other threats to internal validity are related to the actual data retrieval process, the validity of the analyzed sample, and the exact procedures for estimating the parameters. In general, all of them have been validated with developers from the project. Section 3, and the answer to Q1, have also tried to establish how the sample is good and large enough, as well as the process for estimating parameters from it. However, errors and conceptual problems may remain.

With respect to external validity, it is important to notice that this study does not try to state proprieties to be valid in other projects, nor even in the future of WebKit. We have only tried to determine techniques and artifacts that help to understand the review process, and not to determine general laws or models of how it works. This said, the methodology and the presented artifacts (charts, statistics) are meant to be valid for other projects, and therefore threats to external validity can be applied to them.

Conclusions

This paper has presented a detailed methodology for the quantitative analysis of the code review process in large software development projects, based on traces left in software repositories. The methodology has been tested with WebKit, a large and complex project with high corporate involvement. Some developers have given us assistance in the validation and understanding of the code review process, ensuring a higher usability of the results for its stakeholders.

We have answered the two research questions stated in the introduction of this paper. First of all, we have determined how there is enough information in the project repositories to characterize the code review process, and how it can be used, in fact, to calculate parameters that seem to be related to the extension and performance of the project (Q1). We have also characterized the evolution over time of the process using quantitative (bulk or performance) parameters, and have shown how they can be useful to understand such evolution (Q2).

By doing this we have characterized the review process of the WebKit project, and proposed the fundamentals for a dashboard that can serve to evaluate it. We have found that the importance and extension of code review is growing in the project, that reviewers are not growing as fast as authors -and although this has not supposed delays so far, it could cause bottlenecks in the future. On the contrary, the project is improving in the code review process over time, probably due to developers devoting more effort to it.

Fig. 1 .

 1 Fig.1. Bulk parameters (authoring). Total number of tickets corresponding to review processes, and of active authors (review requesters) per month. Time of review request used to determine the month for each ticket.

Fig. 3 .

 3 Fig.3. Performance parameters (mean per month). Number of iterations (review requests for the same ticket) and delay (time from review request to review approval, in minutes).

Reproduction information and data sources of the study, according to[START_REF] Gonzalez-Barahona | On the reproducibility of empirical software engineering studies based on data retrieved from development repositories[END_REF], are available at http://gsyc.es/ ~jgb/repro/2014-oss-webkit-review

http://www.webkit.org/coding/commit-review-policy.html

http://www.webkit.org/coding/contributing.html

https://bugs.webkit.org

http://www.webkit.org/building/checkout.html

http://trac.webkit.org/wiki/UsingGitWithWebKit

http://metricsgrimoire.github.com

https://trac.webkit.org/browser/trunk/Tools/Scripts/webkitpy

Acknowledgments

The work of Gonzalez, Robles and Izquierdo has been funded in part by the Spanish Gov. under SobreSale (TIN2011-28110) and Torres Quevedo (PTQ-12-05577). We thank the Webkit developers for their feedback and suggestions.