Adrian Mihai Sandu

Helmut Gnaegi

Johannes J L Mulders

Henny W Zandbergen

Keywords: dislocations, EBSD, TEM, SEM ultramicrotomy, electron backscattering diffraction, transmission electron microscopy, dislocations Comment [A1]

Ultramicrotomy reveals the crystallographic information on the sectioned surface of the metallic block specimen

Introduction

Microstructure is analyzed using classic techniques such as imaging a mechanically polished surface or a thin section in an optical (OM), scanning (SEM) and/or transmission electron microscope (TEM). However, many parameters of the complex microstructural features, such as connectivity, spatial distribution and true size and shape, cannot always be determined accurately from two-dimensional (2D) images [1] and require a three-dimensional (3D) approach.

Many of 3D visualization methods were initially developed by life sciences community, whereby they combined the ex-situ serial sectioning by ultramicrotomy with successive TEM imaging [2,3]. This laborious 3D technique was simplified when the serial ultramicrotomed block-face was directly imaged with an optical microscope. Surface imaging microscopy (SIM) [4] facilitated 3D sample reconstruction for larger volumes than those obtained by TEM. An increase in the resolution for both for biological and non-metallic materials, was achieved with the use of serial block-face scanning electron microscopy (SBFSEM) [5,6] which couples conventional SEM with in-situ ultramicrotome. The primary tools for serial sectioning of metallic specimens are mechanical polishing [7,8] and recently, the focused ion beam (FIB) [9,10]. The latter was recently employed and can be coupled with electron backscattering diffraction (EBSD) analysis which, however, requires a high-quality finish for the specimen surface since topographical features and/or preparation induced deformation may alter the Kikuchi pattern quality [11]. FIB sectioning delivers high surface finish for EBSD [9,10,12] but the procedure itself is time consuming when compared to the high data acquisition speed of the new [13-16] EBSD cameras.

Ultramicrotomy performs accurate serial sectioning over larger areas, while not subjecting the sectioned block-face to ion beam influences [17]. Here, we introduce ultramicrotomy sectioning as a fast sample preparation method that exposes the block-face microstructure of metallic specimens in just a few seconds and directly facilitates EBSD investigation. In particular what was investigated was whether the cutting artefacts hamper the EBSD analysis or lead to an undesired surface roughness. Also, we analyzed whether the cutting process produces microstructural surface features that can further speed up the 3D analysis process. For instance if grain boundaries can be displayed in SEM imaging then only a fraction of the sample surface needs to be analysed by EBSD because the shape of the grains can be determined from the grain boundary locations. We show, based on TEM and EBSD results, that most of the knife-induced strain is limited to the uppermost region of the blockface. Furthermore, we show that grain boundaries are well displayed in SEM and optical microscopy and that some cutting effects can be used to quickly assess their deformation resistance in respect to the cutting direction. We theorize that all these can speed up the 3D grain analysis by a factor of 10 3 , allowing for 3D analysis of large volumes (e.g. 200 3 µm 3 ) instead of the ~30 3 µm 3 that can be obtained using a FIB for sectioning.

Experimental procedure

A laboratory elaborated 6016 aluminium alloy containing 0.25-0.6 wt.% Mg, 1-1.5 wt.% Si was subjected to ultramicrotomy sectioning. The sample sectioning employed a Leica EM UC6 ultramicrotome using a Diatome ultra 35º diamond knife with a cutting speed of 30 mm/s. Rectangular specimens with the base parameter of 1 mm were polished to form a fine tip. 50 serial sections with 500 nm depth of cut were performed until a surface of the desired size was obtained at an undisturbed depth from the previous polishing. Afterwards, each specimen was sectioned with depths of cut of 30, 100, 500, 1000 and 5000 nm, respectively.

The average roughness (R a ) of the ultramicrotomed block-faces was measured with a Veeco WYKO 3300 interferometer. The SEM investigations were performed using a FEI Strata 235 DB operated at 10 kV. The EBSD analysis was carried out at an accelerating voltage of 25 kV with a scan step size of 250 nm on a sample tilted 70º. Electron transparent lamellas for TEM observations were prepared via the focused ion beam method and investigated with a Philips CM30T microscope operated at 300 kV.

Results and discussion

Scanning electron microscopy / electron backscattered diffraction investigations

Figure 1(a) shows a SEM micrograph for the block-face specimen after ultramicrotomy sectioning at a feed (depth of cut) of 30 nm. The EBSD scanned area (40 x 10 µm 2 ) is marked with a white rectangle which includes a knife-induced groove and a few fine scratches (the white arrows). Figure 1(b) exhibits the EBSD orientation map from three grains marked as "A", "B", "C" revealing the existence of sharp grain boundaries. The groove position is indicated by the high number of randomly indexed points. Figure 1(c Figure 2(a) shows the SEM micrograph for the block-face specimen after ultramicrotomy sectioning at a feed of 1 µm. The EBSD scanned area (48 x 18 µm 2 ) is marked with a white rectangle and includes a wave-like feature as indicated by the white arrow. In the orientation map (Fig. 2(b)), five grains were identified: "D", "E" -area marked by white arrow in Fig. 2(a), "F", "G" and "H" respectively. The IQ map (Fig. 2(c)) also exhibits easily identifiable grain boundaries since, as mentioned before, they have lower IQs than the grains. The IQs for grains "E" and "F" exhibit a cyclic variation from lighter to darker grey with a wavelength of 1 µm. These "waves" are oriented perpendicular to the cutting direction and their arrangement resembles the wave-like feature indicated in Fig. 2(a).

They may be associated to the local internal strains found within 40 nm below the sample surface which constitutes the diffraction volume [START_REF] Randle | [END_REF]. The diffraction volume is a function of the electron beam diameter, the applied accelerating voltage, the specimen atomic number and its tilt angle during EBSD analysis. Typically, the specimen surface makes a 20° angle in respect to the incident beam. For this high tilt, the depth reached by the electron probe is between 10 to 40 nm [START_REF] Randle | [END_REF]. Therefore, the backscattered electrons that generate the Kikuchi patterns, escape the specimen surface relatively undeviated after few inelastic scattering events [START_REF] Randle | [END_REF]. In the case of grain "H", the relatively high IQ values suggest a rather limited knife-induced strain at the cutting interface and hence also in the sampled diffraction volume.

Light interference microscopy investigations

The topography of the block-face specimen after ultramicrotomy sectioning at a feed of 30 nm is investigated in Fig. 3(a) by light interference analysis. The average roughness (R a ) is 11 ±13 nm which is comparable to lapping [START_REF] Ashby | Materials Selection in Mechanical Design: Third Edition[END_REF] ~10 nm, electrolytic abrasion (~25 nm) or super finishing [21]. Some grains ("B" and "C") exhibit different heights with respect to each other, therefore a surface profile measurement was performed (black line in Fig. 3(a)). In Fig 3(b), the left side of the plot represents the surface profile of grain "B" which exhibits most of its values above the reference line (P h = 0). The right side of the plot originates from grain "C" and most of its values are under the reference line. The average difference in height between these grains is 13 nm. A bulge-dimple feature is marked at the grain boundary by the black triangle in Fig. 3(b). The height difference between the top of the bulge (grain "B" side) and the bottom of the dimple (grain "C" side) is 30 nm. The width of the dimple is ~2 µm.

The topography of the block-face specimen after ultramicrotomy sectioning at a feed of 1 µm is exhibited in Fig. 3(c). The R a is 8 ± 14 nm and is comparable with the one obtained after sectioning at a feed of 30 nm. The grains boundaries can be identified along with some wave-like features marked with white arrows. Figure 3(d) presents the line profile of a wavelike feature (indicated by the black line in Fig. 3(c)) while the positions of the grain boundaries are indicated by black triangles. Between the grain boundaries there appears a pronounced rippling of the grain surface which corresponds to the wave-like pattern. The wave has a wavelength of ~1 µm and the peak-valley difference varies from ~ 5 nm to ~ 20 nm. Similar fluctuations [START_REF] Ahlers | [END_REF] were reported in thin TEM sections of aluminium prepared by ultramicrotomy. A periodic change of the section's thickness with a wavelength of approximately 1 µm was observed.

Analysis of the knife-induced cutting artefacts

Studies on the microcutting of aluminium single crystals [23][24][25][26] have shown that a change in cutting direction with respect to crystal orientation leads to a change in the values of the cutting forces that dictate the surface finish. For instance, the cutting force was lower when cutting was performed parallel to {001} planes along [010] direction, compared to cutting along the [110] direction [START_REF] Ahlers | [END_REF]. One may interpret these results as a change in the deformation resistance of the single crystal with respect to the cutting direction. Hence, given that our specimens are polycrystalline materials, one may expect each grain to have different cutting behaviour. We can analyze this process through a simple shear deformation, whereby each grain is considered as a single crystal with respect to cutting direction. The orientation of a given crystal, in regards to the cutting direction, can be described by an orientation factor [START_REF] Hirth | Theory of Dislocations -2 nd edition[END_REF] m whose higher absolute values show for what specific slip system the grain deforms easier:

α α sin 2 cos sin cos cos cos * Θ * + * Θ * = k k m (1)
where: k is the angle between the slip direction of the considered crystallographic system in the grain and the direction of the applied stress, Θ is the angle between the normal to the shear plane and the axis perpendicular to the sample surface (or grain surface in this case) and α is the angle between the applied stress direction and one of the axes of the sample coordinate system. Now, considering that α is zero i.e. the applied stress direction is parallel to sample surface, the formula becomes:

Θ * - = cos cos k m (2)
The analysis of the m values (see Supplementary information -Table 1) after sectioning at a feed of 30 nm revealed that grain "C" deformed the easiest, followed by grain "A" and grain "B". This analysis shows that the larger height of the grain "B" is related to an regarding nanometric cutting [START_REF] Komanduri | [END_REF]. Moreover, the dimple is on the "softer" grain "C" side, while the bulge is on the "harder" grain "B" side (Fig 3(a)). This effect is also observed in steels, at the interface between the harder pearlite and the softer ferrite [29]. The analysis of m after sectioning at a feed of 1 µm indicated that grain "E" opposed more to the deformation than grain "F". Therefore, the wave-like features occurred predominantly in the grains with a higher deformation resistance (white arrows in Fig. 3(c)). This is an indication that the high dislocation density at the cutting interface does not change significantly the overall lattice orientation of the bulk grain which is sampled by the electron probe during EBSD analysis.

Transmission electron microscopy observations on cross sections of microtomed surfaces

TEM observations revealed that for a "smooth" area, the knife-induced strain (such as dislocation pile-ups) is located beneath the depth of the diffracting volume for EBSD and does not affect the quality of the Kikuchi patterns. Therefore, the EBSD image quality map does not exhibit any variation of the grey levels, as it was also seen after 30 nm sectioning in Fig. 1. In the case of the "wave-like feature" the dislocations pile-ups accommodate part of the induced strain close to the cutting interface. They do not form a continuous damaged region and their depth also varies, in some cases being within the diffracting volume for EBSD. Thus, the strain sensitive IQ map exhibits periodic features, as shown in Fig. 2(c) for the grains "E", "F" and "G".

Conclusions

We have shown that EBSD maps can be obtained directly from the aluminium block-face specimens sectioned on an ultramicrotome for depths of cut up to 1 µm and were not hampered by inherent cutting artefacts. They are related to the relative orientation of the grains with respect to the cutting direction. The grain boundaries are clearly visible and this facilitates a precise control of the depth of the subsequent serial sectioning when removing grain/grains with certain orientations, in the particular case of aluminium alloys. TEM observations showed the "smooth" surfaces exhibit pile-up dislocations at a depth of 200 -300 nm whereas the wave-like features consist of pile-up dislocations within 150 nm from the cutting interface, influencing the IQ maps. The mechanical properties of the grains can be readily assessed for low depth of cut based on the height difference with respect to each other. Table 1 Orientation factor (m) for grains "A", "B" and "C" after 30 nm sectioning and for grains, "D", "E", "F", "G" and "H" after 1 µm sectioning 270x203mm (96 x 96 DPI)

5 [ 18 ]

 518 ) shows the image quality (IQ) map which describes the sharpness of the Kikuchi bands. The patterns may become diffuse due to distortions of the crystal lattice induced by dislocations or precipitates . In this experiment the analyzed grains exhibit light grey to white IQ values indicating high quality of the Kikuchi patterns, with the grain boundaries showing up as dark grey to black since they exhibit lower IQs. This is related to the diffraction volume at the grain boundary which contains the crystal lattices of the neighbouring grains and hence a mix of the two patterns.

  the knife passing its position, as seen in other investigations

Figure 4 (

 4 a) exhibits a bright field TEM micrograph of the top region of the sample after ultramicrotomy sectioning at a feed of 500 nm revealing a relatively low dislocation density in its bulk. Some dislocations that exceed 1.5 µm in length (white single-headed arrows) originate close to the knife-specimen interface and are oriented parallel to <2 -2 0> Al directions. Figure4(b) presents the knife-specimen interface of an area containing some wave-like features. This interface exhibits a high density of dislocation pile-ups aligned parallel to the cutting direction. They are discontinuous along the cutting interface at depths ranging between 75 to 150 nm. Other pile-up dislocations run parallel to the cutting interface at depths between 200 and 300 nm (double-headed arrows in Fig.4(a-d)) on the entire length of the TEM specimen.

Figure 4 (

 4 Figure4(d) exhibits a relatively "flat" top-region of the specimen with a lower density of dislocations close to the cutting interface when compared to the wave-like feature region.Dislocation pile-ups aligned parallel to the top surface are found at a depth of ~ 200 nm with no dislocations running along <2 -2 0> Al directions are present. Thus, it may be inferred that the line dislocations are associated to the presence of the wave-like features presence. The overall assessment of the knife-induced strain in the sample's bulk is given by the selected

  (the inset in Fig.4(d)) which exhibits sharp and undistorted reflections.

10 ForFigure 1

 101 Figure captionsFigure 1 SEM/EBSD investigations for the block-face specimen after ultramicrotomy sectioning at a feed of 30 nm: (a) SEM micrograph tilted 70º indicating the scanned area by EBSD (white rectangle) and marking some knife induced scratches (white arrows); the difference in image contrast is given by electron beam contamination of the sample surface such as the circular features; (b) tilt corrected orientation map [001]; (c) tilt corrected IQ map. The black line indicates the cutting direction.

Figure 2

 2 Figure 2 SEM/EBSD investigations for the block-face specimen after ultramicrotomy sectioning at a feed of 1 µm: (a) Series of three consecutive (the white triangles mark the stitching lines) SEM micrographs tilted 70º indicating the scanned area by EBSD (white rectangle); some regions with different contrasts are given by electron beam contamination of the sample surface; (b) tilt corrected orientation map [001]; (c) tilt corrected IQ map. The black line indicates the cutting direction.

Figure 3

 3 Figure 3 Light interference micrograph and the line profile analysis for the block-face specimens after ultramicrotomy cutting: (a) 3D reconstruction of the sample surface after ultramicrotomy sectioning at a feed of 30 nm; (b) line profile of an area crossing a grain boundary (black bar in (a)); (c) 3D reconstruction of the sample surface after specimen after ultramicrotomy sectioning at a feed of 1 µm; (d) line profile of an area containing a wave-like feature (black bar in (c)). The black lines indicate the cutting direction.

Figure 4 Figure 1 Figure 2 Figure 3 Figure 4

 41234 Figure 4 TEM investigations for the block-face specimen after ultramicrotomy sectioning at a feed of 500 nm: (a) bright field micrograph of the cross-sectioned area; (b) high magnification TEM micrograph of a "wave-like feature"; (c) simplified sketch of dislocations distribution in (b) where light grey is Pt layer, black is 6016 Al alloy and white are the dislocations; (d) high magnification TEM micrograph of a "flat" area and selected area diffraction pattern as inset (e -// [001] Al ) of the areas in (a), (b) and (d).

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Acknowledgments

This research was carried out under the project number MC7.05209 in the framework of the Research Program of the Materials innovation institute M2i (www.m2i.nl). The authors would like to thank Prof. Leo Kestens and Dr. Jurij Sidor (TU Delft) for supplying the study material. A.M.S acknowledges the helpful discussions with Dr. Octav Paul Ciuca of the Toyohashi University of Technology / National Institute for Materials Science, Japan.


Garcia Rodriguez

Luis Alberto

Angel Lanas
email: alanas@unizar.es

Luis A García-Rodríguez

Mónica Polo-Tomás

Marta Ponce

Enrique Quintero

Maria Angeles Perez-Aisa

Javier P Gisbert

Luis Bujanda

Manuel Castro

Maria Muñoz

Dolores Del-Pino

Santiago Garcia

Xavier Calvet

The changing face of hospitalization due to gastrointestinal bleeding and perforation

Keywords: Peptic ulcer disease < Disease-based, Diverticular disease < Disease-based, Stomach and duodenum < Organ-based, Epidemiology < Topics, NSAIDs peptic ulcer, bleeding, perforation, angiodysplasia, diverticulum

Background: Temporal changes in the incidence of cause-specific gastrointestinal (GI) complications may be one of the factors underlying changing medical practice patterns. Aim: To report temporal changes in the incidence of five major causes of specific gastrointestinal (GI) complication events. Methodology: Population-based study of patients hospitalized due to GI bleeding and perforation from 1996-2005 in Spain. We report crude rates, and estimate regression coefficients of temporal trends, severity, and recorded drug use for 5 frequent GI events. GI hospitalization charts were validated by independent review of large random samples. Results: The incidence per 100,000 person-years of hospitalizations due to upper GI ulcer bleeding and perforation decreased over time (from 54.6 and 3.9 in 1996 [R 2 =0.944] to 25.8 and 2.9 in 2005 [R 2 =0.410], respectively). On the contrary, the incidence per 100,000 person-years of colonic diverticular and angiodysplasia bleeding increased over time (3.3 and 0.9 in 1996 [R 2 =0.443] and 8.0 and 2.6 in 2005 [R 2 =0.715], respectively). A small increasing trend was observed for the incidence per 100,000 person-years of intestinal perforations (from 1.5 to 2.3 events). Based on data extracted from the validation process, recent recorded drug intake showed an increased frequency of anticoagulants with colonic diverticular and angiodysplasia bleeding, whereas NSAID and low-dose aspirin use were more prevalent in peptic ulcer bleeding and colonic diverticular bleeding respectively. Conclusions: From 1996-2005, hospitalizations due to peptic ulcer bleeding and perforation have decreased significantly, whereas the number of cases of colonic diverticular and angiodysplasia bleeding have increased.

Major therapeutic advances in the treatment and prevention of peptic ulcer diseases have been implemented in the past decade, which should contribute to a significant decrease in the incidence and mortality due to peptic ulcer diseases. Opposing trends in peptic ulcer complications such as bleeding or perforation have been reported in different countries, and no decrease or increase in hospitalizations due to peptic ulcer bleeding complications have been observed [START_REF] Sung | Systematic review. The global incidence and prevalence of peptic ulcer disease[END_REF][START_REF] Sonnenberg | Time trends of ulcer mortality in Europe[END_REF][START_REF] Post | Declining incidence of peptic ulcer but not of its complications: a nation-wide study in The Netherland[END_REF][START_REF] Ohmann | Time-trends in the epidemiology of peptic ulcer bleeding[END_REF][START_REF] Kang | Recent trends in hospital admissions and mortality rates for peptic ulcer in Scotland 1982-2002[END_REF][START_REF] Paimela | Current features of peptic ulcer disease in Finland: incidenceof surgery, hospital admissions and mortality for the disease during the past twenty-five years[END_REF]. More recently, two studies from different geographical areas suggested that there has been a marked decrease in the incidence of upper GI complications and a slight increase in the incidence of lower GI complications [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF][START_REF] Zhao | Hospitalizations for Gastrointestinal Bleeding in 1998 and[END_REF]; however, the specific lesions leading to these changes have not been analyzed. Furthermore, the time trends for bleeding and perforation may not be parallel, since the underlying pathogenic mechanisms and risk factors could diverge [START_REF] Bardhan | Time, change and peptic ulcer disease in Rotherham, UK[END_REF][START_REF] Paimela | Surgery for peptic ulcer today. A study on the incidence, methods and mortality in surgery for peptic ulcer in Finland between 1987 and 1999[END_REF]. Additionally, the exact source of lower GI complications are often more difficult to identify than upper GI complications because of the anatomic complexity of the lower gut and available diagnostic tests. Among the causes of lower GI bleeding, colonic diverticuli and angiodysplasia are two lesions which could explain, at least in part, the recent trends, since age was found to be one of the main risk factors for hospitalizations [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF]. However, the time trends and clinical characteristics of hospitalizations owing to these two lesions have not been reported.

Prevention strategies and optimization of hospital resources require a clear understanding of the type of pathology causing hospitalization. In a previous report, we presented the overall time trends of hospitalizations due to GI complications, [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF] which were obtained from a data-base including information provided by 10 Spanish general hospitals representative of the entire country [START_REF] Lanas | Investigators of the Asociación Española de Gastroenterología (AEG). A nationwide study of mortality associated with hospital admission due to severe gastrointestinal events and those associated with nonsteroidal antiinflammatory drug use[END_REF]. Now, as part of the pre-specified analysis plan, we aim to characterize and analyze in detail the time trends for hospitalizations due to five specific major causes of GI complications; namely, peptic ulcer bleeding, peptic ulcer perforation, intestinal perforation, colonic diverticular bleeding, and bleeding caused by angiodysplasia. We believe that these data are needed since, as discussed above, the available literature for some of these causes and

Methods:

Setting and data collection

The study [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF] was approved by the Institutional Review Board of Aragón and was carried out in 10 Spanish general hospitals distributed across the entire country, serving a population of 3,281,973 people in 1996 and 3,681,822 in 2005. Based on previous reports [START_REF] Lanas | Investigators of the Asociación Española de Gastroenterología (AEG). A nationwide study of mortality associated with hospital admission due to severe gastrointestinal events and those associated with nonsteroidal antiinflammatory drug use[END_REF], the population covered by these hospitals was representative of the whole country, where the majority (80%) of the population uses the Spanish NHS, which provides open access free-to-all healthcare services including hospitals, drugs, and diagnostic and therapeutic procedures.

The methodology of data collection was described in our first report of this study [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF]. Each hospital provided data from January 1, 1996 to December 31, 2005 on patients identified with a primary discharge diagnosis, coded according to the International Classification of Diseases (9 th revision, Clinical Modification [ICD9]), for the 5 specific diagnoses investigated in this study [START_REF] Sung | Systematic review. The global incidence and prevalence of peptic ulcer disease[END_REF].

The codes used were as follows: [START_REF] Sung | Systematic review. The global incidence and prevalence of peptic ulcer disease[END_REF] The primary discharge diagnosis was considered to be the cause leading to hospitalization based on the clinical judgment of the physician who managed the patient. In this way, each hospitalization event is unequivocally classified according to the main diagnosis together with other variables [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF]. We only included bleeding or perforation events that occurred in the community and excluded those that developed after hospitalization, since they probably represent a group different from our target population. The type and number of variables provided by each hospital were the same and were introduced in a common database specifically designed for this study.

Validation process

In brief and as described previously [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF], we validated around 10% of events with specific codes. However, since there was no experience or previous report on the accuracy of some undefined events from the lower GI tract codes, we undertook a more extensive validation process for intestinal perforation to study the exact location of the perforation event (e.g. small vs. large bowel). The selection of episodes available in each centre was carried out using the "SAMPLE" procedure available in the SPSS program (SPSS, Chicago, IL USA). This information was introduced into a second database along with other variables which included the original diagnosis code (ICD9) undergoing validation and the final diagnosis after the validation process. Data were coded anonymously. The process of validating the codes and chart review was carried out by gastroenterologists or trained GI residents with experience in these types of studies [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF][START_REF] Lanas | Investigators of the Asociación Española de Gastroenterología (AEG). A nationwide study of mortality associated with hospital admission due to severe gastrointestinal events and those associated with nonsteroidal antiinflammatory drug use[END_REF]. These investigators ensure the appropriate interpretation of data and tests carried out during the hospitalization event. In addition to validation of the diagnostic codes, this process allowed us to collect additional information including death outcome, number of days of hospitalizations, number of comorbidities, lowest Hb level detected, number of units of blood transfusions, and recorded drug use. The severity and burden of the events for this report were based on the following variables: (a) death rate, (b) days of during hospitalization, and (g) number of blood units transfused as described elsewhere [START_REF] Harris | Medicare Severity-Refined DRGs: An Improved System[END_REF].

We considered only recent use of drugs when they were taken by patients within 7 days before the date of hospitalization. The data entry was carried out by staff trained and experienced in managing databases, which was designed to minimize the data entry errors. One in five questionnaires was completely checked, and virtually no data entry errors were found.

Management and analysis of data

The data obtained from each hospital was entered in the two databases; one included the information gathered from the Minimum Basic Data Set (MBDS) and the other contained the information collected during the validation process. Time trends were reported based on the first database (MBDS), whereas data reported for severity of events and drug use was based on the database obtained from the validation and chart review process. A data analysis plan was pre-determined in advance for each database. Estimates of the actual frequencies were based on the validation process. Outcome variables are reported as rates, mean (SD), and 95% confidence interval (CI) depending on the type of variable. Rates were calculated overall, by year, and by source of the event. We estimated both crude and age-and sex-adjusted incidence rates with 95% CI for the five GI events. However, since the number of events was not large enough in 4 of the 5 codes to provide accurate age-and sex-adjusted rates, we report only crude rates. Wherever it may apply, data from different years (mean ± SD) were analyzed by one-way analysis of variance followed by unpaired Student's t-test. Additionally, we estimated regression coefficients of the incidence trend line from 1996 to 2005 with the ordinary least squares method. Categorical data were analyzed by Chi-square, and logistic regression analysis was performed to estimate the effect of a number of risk factors comparing upper versus lower GI events. Because of the multiple comparisons made for some of the analyses, values were considered statistically significant

Results

Time trends of events

Data obtained from the database collecting the MBDS information provided by the participant hospitals showed a statistically significant decrease in the incidence rate of peptic ulcer bleeding as well as ulcer perforation from 1996 to 2005 (Figures 1 and2). These decreasing trends were seen for both gastric and duodenal ulcer bleeding and perforations (data not shown). On the contrary, the trends for both colonic diverticular and bleeding due to colonic angiodysplasia showed a statistically significant increase over the same time period (Figures 1 and2). Intestinal (lower GI) perforations showed a nonsignificant increase over the same time period. Validation of codes showed > 90% accuracy for the 5 GI complications (Table 1). Incidence rates were adjusted according to the confirmation obtained with the manual chart review.

Based on the validation process of the 5 diagnostic codes identified in 2082 cases, 53.7% of intestinal perforations were located in the large bowel and 39% in the small bowel, whereas the remaining 7.2% were ascribed to the lower GI tract without further site specification. Validation of codes for peptic ulcer perforation showed that 6.5% of cases were indeed intestinal perforations.

Among cases coded as diverticular bleeding, the validation process showed that 1% of cases were actually upper GI bleeding events, and another 1% were unconfirmed events. Among those with angiodysplasia, 2.9% were upper GI bleeding events and in 1.4% of cases the source could not be ascribed to any cause. Finally, among peptic ulcer bleeds, only 1.5% were lower GI bleeding events and in 0.3% of cases the source could not be identified.

The age and gender distribution was markedly different across the 5 causes of hospitalization (Table 2). Patients with bleeding from the colonic diverticuli or angiodysplasia were older than those with other causes for hospitalization, whereas males were predominant among those with peptic ulcer perforation and bleeding. Very similar results were found in the validation random sample (data not shown). Overall, the case fatality rates were higher for perforation than for bleeding events (intestinal perforation > peptic ulcer perforation > bleeding angiodysplasia > peptic ulcer bleeding > diverticular bleeding). Overall mortality trends did not change over time during the period studied for intestinal or peptic ulcer perforation or angiodysplasia or diverticular bleeding (specific information concerning these mortality trends can be seen on-line in "Supporting Information Table 1").

Severity of events and drug use

The review of charts provided an opportunity to collect a number of variables that described the severity of the different types of events. The case fatality rate was similar to that reported above in the overall sample. The length of hospitalization was longer in patients with perforation than for those with bleeding events, and the weight of DRG (an indirect measure of hospitalization costs for each type of event) was higher for complications in the lower GI tract when compared with those from the upper GI tract. The number of comorbidities was greater in patients with colonic diverticular bleeding and angiodysplasia bleeding compared with the other type of lesions studied. As expected, hemoglobin decline and the number of blood units transfused were higher in patients with bleeding events than in those with perforations (specific information concerning the severity of events based on chart validation can be seen on-line in "Supporting Information Table 2

").

Detailed recorded drug use concerning nonsteroidal anti-inflammatory drugs (NSAIDs), proton pump inhibitors (PPI), and anti-platelet agents can be seen on-line in "Supporting Information Table 3". Peptic ulcer and diverticular colonic bleeding had the highest NSAID/aspirin drug use compared with cases of perforation and even bleeding from GI angiodysplasia. PPI use was more frequently recorded in patients with colonic and angiodysplasia bleeding events.

Recorded anticoagulant use was high in patients with diverticular bleeding and in patients with angiodysplasia.

Discussion

This study shows that hospitalizations due to both peptic ulcer bleeding and perforations progressively and importantly decreased from 1996 to 2005. These trends were not observed for other types of bleeding or perforation events from the lower GI tract. In fact, we found that the incidences of colonic diverticular bleeding or angiodysplasia are increasing, whereas the rate of intestinal perforation remains virtually stable with a slight increase over the study period.

There is wide agreement that hospitalizations due to uncomplicated peptic ulcer are decreasing over time [START_REF] Sung | Systematic review. The global incidence and prevalence of peptic ulcer disease[END_REF][START_REF] Sonnenberg | Time trends of ulcer mortality in Europe[END_REF], but there were discrepancies between hospitalizations on rates due to complicated peptic ulcers. Our results agree with data from Sweden [START_REF] Sadic | Bleeding peptic ulcer -time trends in incidence, treatment and mortality in Sweden[END_REF][START_REF] Hermansson | Decreasing incidence of peptic ulcer complications after the introduction of the proton pump inhibitors, a study of the Swedish population from 1974-2002[END_REF] and the USA [START_REF] Zhao | Hospitalizations for Gastrointestinal Bleeding in 1998 and[END_REF] showing that hospitalizations due to peptic ulcer bleeding are decreasing. However, these data are not in agreement with reports from other European countries [START_REF] Post | Declining incidence of peptic ulcer but not of its complications: a nation-wide study in The Netherland[END_REF][START_REF] Ohmann | Time-trends in the epidemiology of peptic ulcer bleeding[END_REF][START_REF] Kang | Recent trends in hospital admissions and mortality rates for peptic ulcer in Scotland 1982-2002[END_REF][START_REF] Paimela | Current features of peptic ulcer disease in Finland: incidenceof surgery, hospital admissions and mortality for the disease during the past twenty-five years[END_REF][START_REF] Bak Andersen | Time Trends for peptic ulcer disease in Danmark, 1981-1993. Analysis of hospitalization register and mortalitydata[END_REF], which show either no decrease or even an increase in hospitalizations for this type of event. The reasons for these discrepancies are unclear, since a decrease of H. pylori infection among the population, increasing H. pylori eradication therapy, and increasing PPI use across Europe should be accompanied by a progressive decrease in peptic ulcer complications [START_REF] Sadic | Bleeding peptic ulcer -time trends in incidence, treatment and mortality in Sweden[END_REF][START_REF] Hermansson | Decreasing incidence of peptic ulcer complications after the introduction of the proton pump inhibitors, a study of the Swedish population from 1974-2002[END_REF][START_REF] Pérez-Aisa | Clinical trends in ulcer diagnosis in a population with high prevalence of Helicobacter pylori infection[END_REF]. The variability in the use of low-dose aspirin (ASA) and gastro-protective treatments between countries may partly explain these differences [START_REF] Lanas | Education-based approach to addressing non-evidence-based practice in preventing NSAID-associated gastrointestinal complications[END_REF][START_REF] Sturkenboom | Underutilization of preventive strategies in patients receiving NSAIDs[END_REF], but our study and those reporting decreasing peptic ulcer bleeding rates collected data from more recent years and were population-based [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF][START_REF] Zhao | Hospitalizations for Gastrointestinal Bleeding in 1998 and[END_REF].

Our data also show very low rates of mortality due to peptic ulcer bleeding, which is consistent with other studies [START_REF] Zhao | Hospitalizations for Gastrointestinal Bleeding in 1998 and[END_REF][START_REF] Sadic | Bleeding peptic ulcer -time trends in incidence, treatment and mortality in Sweden[END_REF][START_REF] Hermansson | Decreasing incidence of peptic ulcer complications after the introduction of the proton pump inhibitors, a study of the Swedish population from 1974-2002[END_REF]. The lack of improvement in case fatality rates is usually linked to a progressively aging population with increasing numbers of co-morbidities, despite data that show better bleeding management strategies associated with reduction in the risk of rebleeding and a reduced need for surgery [START_REF] Barkun | Endoscopic hemostasis in peptic ulcer bleeding for patients with high-risk lesions: a series of metaanalyses[END_REF]. In any case, our data agree with a recent USA report [START_REF] Zhao | Hospitalizations for Gastrointestinal Bleeding in 1998 and[END_REF] that shows an overall decrease (absolute numbers) Time trends on peptic ulcer perforation are rarely reported and those available show no change or small changes overtime [START_REF] Bardhan | Time, change and peptic ulcer disease in Rotherham, UK[END_REF][START_REF] Paimela | Surgery for peptic ulcer today. A study on the incidence, methods and mortality in surgery for peptic ulcer in Finland between 1987 and 1999[END_REF][START_REF] Bardhan | Admission rates for peptic ulcer in the trent region, UK, 1972--2000. changing pattern, a changing disease?[END_REF]. Here we report a clearly decreasing trend (∼ 50%) in peptic ulcer perforation from 1996 to 2005, which is consistent with a decrease in the overall incidence of peptic ulcer and peptic ulcer complications. The decrease in incidence of hospitalizations owing to peptic ulcer perforation was not associated with a decrease in case fatality rates over this time.

Other studies have reported time trends for peptic ulcer bleeding or perforation, but not other sources of GI bleeding or perforation. In our first overall report of this study [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF], we pointed out that the ratio of hospitalizations for upper vs. lower GI complications has changed from a 4:1 to 1.4:1. Here we report that two common reasons for hospitalizations, colonic diverticular and angiodysplasia bleeding, are more frequent today than 10 years ago. A progressively aging population and the increasing use of NSAIDs and low-dose ASA may explain, at least in part, these results. [START_REF] Lanas | Risk of upper gastrointestinal ulcer bleeding associated with selective cyclooxygenase-2 inhibitors, traditional non-aspirin non-steroidal anti-inflammatory[END_REF]. PPI use was more frequently recorded in patients hospitalized with diverticular bleeding and bleeding due to angiodysplasia than in those with peptic ulcer bleeding. This could support the concept that PPI use is associated with the prevention of upper GI but not lower GI complications, but age and its accompanying greater number of co-morbidities could also explain the observed higher prevalence of PPI use. Eventually, it must be noted that anticoagulant use, a growing clinical practice, is especially associated with bleeding events and overall with diverticular and angiodysplasia bleeding.

Trends on intestinal perforation are rarely reported. Here we report overall intestinal (small and large bowel) perforation rates and found that these rates remained stable over time, although with a numerical tendency to increase in agreement with the data reported from the UK on diverticular perforation (23). Our study has strengths and limitations. A strength is that we carried out an extensive validation of events. This is especially important for intestinal perforation, and diverticular and bleeding from angiodysplasia lesions. Contrary to peptic ulcer bleeding and perforation, these have rarely been reported in the literature. Therefore, these ICD-9 codes have rarely been validated in observational studies. This is of major importance since the diagnostic process of diseases from the lower GI tract is more complex than those used in the upper GI tract.

The study also has limitations. First, undefined codes such as "GI bleeding" may include patients with both peptic ulcer bleeding and bleeding from diverticular disease and angiodysplasia lesions. This means that the reported incidence and trends reflect minimum rates, since it is possible that a proportion of patients with the events studied here may not be counted because of misclassification under undefined codes. In our previous report, we observed that this proportion was constant over time [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF]. Another limitation refers to data on drug use, which relies on data recorded in charts and are subject to reporting bias in the clinical history. Ascertainment of NSAID, ASA, and PPI use may be more frequently searched in patients with peptic ulcer complications than in diverticular or angiodysplasia bleeding events. Finally, our mortality rates refer to in-hospital mortality, as we could not provide 30-day mortality, since most patients were discharged from hospital before this window of time.

In summary, our study shows that, over the past decade, there has been a significant decrease in hospitalization rates for peptic ulcer bleeding and perforation, but an increase for colonic diverticular and angiodysplasia bleeding, with virtually no change in intestinal perforation. These data show a clear change in the incidence of hospitalizations due to GI complications over time, with upper GI events decreasing and lower GI events increasing. Since the severity of these events are very different, these data should be of interest for improving clinical practice in terms of preventive strategies and to better address the increasing prevalence of lower GI events, specifically the increase in colonic diverticular and angiodysplasia bleeding.

F o r P e e r R e v i e w

Supporting Information Table 2. Severity of events using several measures, by type of lesion based on the chart validation. Reply: The manuscript was submitted to a professional English medical editing service for correction and revision of the English language (www.sanfranciscoedit.com).

Lesion

b) Please would you make Table 3 to be Supporting Information Table 1, and label the two duplicate Tables 4 &5 as Supporting Information Tables 2 and3. [Supporting Information is available to readers on-line. The important / significant results should be mentioned in the text, and the supporting information referred to in the text. This is explained in the Author Guidelines at www.APandT.org or at http://authorservices.wiley.com/bauthor/suppmat.asp ].

Reply: We made this change and incorporated the main data from Tables 3,4, and 5 into the text. These Tables have been converted to Supporting Information Tables 1, 2 and 3.

c) Can you really look at your paper, and make it clear what's new -in addition to your already well-cited earlier paper?

Reply: We reworked the introduction and discussion to clarify what it is new in this manuscript. Below is the list of the new information provided: a) time trends for hospitalizations due to peptic (gastric and duodenal) ulcer bleeding and its contrast with peptic ulcer perforation b) time trends for intestinal perforation c) time trends for colonic diverticular bleeding d) time trends for bleeding due to angiodysplasia e) mortality rates of these events f) description of severity characteristics of these lesions g) recorded drug use for each of these entities. We outlined the association between anticoagulant use with both diverticular bleeding and angiodysplasia, which we believe is of utmost importance. 1. The first sentence is vague, and could mean anything: "Gastrointestinal complications are major causes of GI hospitalization." In any case, they need to make it clear that GI is an abbreviation of gastrointestinal in this sentence.

Reply: We revised the sentence accordingly, and defined the abbreviation. We believe the sentence specifies a clear and important fact, which is essential to our paper.

2. The statement on two occasions in the Introduction that "…no cause specific analyses were performed" as part of their previous study (reference [START_REF] Lanas | Time trends and impact of upper and lower gastrointestinal bleeding and perforation in clinical practice[END_REF], and that "…trends for the specific cause of lower GI complications were not reported" as part of their previous study again leaves me with the feeling that this is a post hoc analysis of data in an attempt to obtain another publication from the same piece of work. Why weren't these analyses performed in the prior publication if, as the authors presumably believe, this is important information?

Reply: We now make clear that this piece of information was not reported. As we responded to the editor, the data presented are new and it well know that databases with extensive data can provide important information that cannot always be included in a single publication.

Methods

1. Page 6, line 42/43. I think the authors mean that "…gastroenterologists or trained GI residents with experience of these types of studies." rather than "…on this type of studies."

2. Page 6, line 56/57. There is now no mention whatsoever of what DRG is an abbreviation of. This needs to be added.

Reply:

We changed the text in accordance with these suggestions.

Results

1. Page 8, lines 7 to 10 don't make sense: "…information provided by the participant hospitals showed and statistically significant decrease…" The authors mean "…a statistically significant…" 2. Page 9, lines 19/20: "…length of hospitalization were higher…" should be "…was higher…" 3. Page 9, lines 24/25: "…from the lower GI tract when compared those…" should be "…when compared with those…"

Reply: The text was corrected by a professional editing service to improve the readability of the manuscript.

Discussion

The authors state on page 11, lines 8 to 11 that: "Time trends on peptic ulcer perforation are rarely reported and those available show no change or small changes overtime." They reference their previous study here. This makes it seem as though the results of the current study are at odds with those of the previous study, yet how can this be the case, as they are derived from the same dataset?!

Reply:

The referee is right. We included this reference because it reported overall trends, but clearly it should not be there. We have removed reference 7. Reply: We thank reviewer 2 for being comfortable with our previous reply.

Reviewer: 2 Comments for Transmission to the Authors None

3 Background

 3 Gastrointestinal (GI) complications are major causes of hospitalization.

  among them are sparse or absent. Additionally, we also describe the severity characteristics and recorded drug use for each of these entities.

  c) number of diagnostic procedures, (d) weight of diagnosisrelated groups (DRG), (e) number of comorbidities, (f) lowest Hb level recorded

  values were < 0.01. All statistics were carried out with Excel (Microsoft Office 2000), SPSS (Chicago, IL USA), and STATA (StataCorp, 2005, TX USA).

  hospital deaths linked to GI bleeding diagnoses between 1998 and 2006, owing to a decrease in the number of hospitalizations.

  and combinations. Gut. 2006 Dec;55(12):1731-8. Epub 2006 May 10. 23. Humes DJ, Solaymani-Dodaran M, Fleming KM, Simpson J, Spiller RC, West J. A population-based study of perforated diverticular disease incidence and associated mortality. Gastroenterology. 2009 Apr;136(4):1198-205.

Figure 1 :

 1 Figure1: Estimated number of peptic ulcer, colonic diverticular, and angiodysplasia bleeding events per 100,000 person-years based on the adjudication of events in the validation process. Regression coefficients of temporal trends were: R 2 = 0.944 (p<0.0001) for peptic ulcer bleeding rates; R 2 = 0.443 (p = 0.03) for colonic diverticular bleeding rates; R 2 = 0.715 (p = 0.002) for angiodysplasia bleeding rates.

Figure 2 :

 2 Figure 2: Estimated number of perforations per 100,000 person-years based on the adjudication of events in the validation process. Regression coefficients of temporal trends were: R 2 = 0.410 (p = 0.04) for peptic ulcer perforation; R 2 = 0.091 (p = 0.395) for intestinal perforation rates.

Table 1 :

 1 Accuracy of codes for the final diagnosis after validation of clinical history for five major causes of specific gastrointestinal complication events.

	Recorded discharge diagnosis code before validation	Number of patients	Cases validated n (%)	Actual diagnosis after validation n (%)
	Peptic ulcer Bleeding	13616	1241 (9.1%)	1218 (98.1%) = peptic ulcer bleeding 23 (1.8%) = Other
				129 (93.5%) = peptic ulcer
	Peptic Ulcer Perforation	1655	138 (8.3%)	perforation 9 (6.5%) = Other
	Diverticulosis or			189 (97.9%) = colonic
	Diverticulitis with	2130	193 (9.1%)	diverticular bleeding
	bleeding			4 (2%) = Other
	Angiodysplasia Bleeding	597	69 (11.6%)	66 (95.7%) = intestinal (lower GI) angiodysplasia 3 (4. 3%) = Other
				422 (95.7%) = intestinal
	Intestinal perforation	759	441 (58.1%)	perforation 26 (5.9%) = Other
	Total (5 causes)	18757	2082 (11.1%)	2024 (97.2 %) = Accurate 58 (2.85) = Other

Table 2 :

 2 Age and gender distribution by lesion type.

	a)
		n	Age (Mean, SD)	Male Gender (n, %)
	Peptic ulcer bleeding	13616	63.50 (16.7)	9615 (70.6%)
	Peptic ulcer perforation	1655	55.13 (19.1)	1050 (69.5%)
	Diverticulosis or Diverticulitis with bleeding	2130	75.91 (10.2)	950 (44.6%)
	Angiodysplasia Bleeding	597	73.32 (11.6)	333 (55.9%)
	Intestinal perforation	759	63.37 (18.6)	414 (54.5%)
	Mean comparison among categories: p-value < 0.001

Table 1 :

 1 Time trends of case fatality by lesion type (n =18757). No statistical differences were found for any of the 5 types of lesions over time.

	Supporting Information Year Mortality 1996 1997 1998 1999 2000 2001 2002	2003	2004	2005	Total
	Peptic Ulcer	n	46	59	57	53	41	29	45	40	39	18	427/13616
	Bleeding	%	2.5	3.5	3.2	3.2	3.1	2.2	4.0	3.7	4.2	1.9	3.1
	Peptic ulcer	n	19	19	16	21	21	16	17	15	10	10	164/1655
	perforation	%	9.5	8.2	8.9	11.4	13.5 10.0	10.3	10.6	7.6	9.2	9.9
	Diverticular	n	0	3	6	5	5	6	5	4	5	4	43/2130
	Bleeding	%	.0	1.8	2.5	2.5	2.8	2.7	2.1	1.6	2.3	1.3	2.0
	Angiodysplasia	n	2	2	1	4	2	3	9	1	2	4	30/597
	Bleeding	%	6.7	5.7	2.4	11.1	4.5	4.6	9.1	1.3	2.8	4.0	5.0
	Intestinal	n	11	22	29	24	28	24	22	20	22	30	232/759
	perforation	%	21.2	36.1	36.3	30.8	30.1 28.2	25.9	30.3	31.0	34.1	30.6

Table 3 :

 3 NSAID, Low-Dose Aspirin, PPI use recorded in the charts by lesion type

		N		Mortality	Hospital Stay (days)	Number of diagnostic tests performed	DRG Weight	Number of Comorbidities	Lowest Hemoglobin level	Blood units transfused
	Peptic Ulcer Bleeding	Mean (%) 1218 95% CI [0.96, 2.43] [6.54, 7,32] [1,03, 1,06] [1.09, 1.18] [1.50, 1.60] 1.69 6.93 1.04 1.13 1.55	9.18 [9.05, 9.30]	1.51 [1.40, 1.63]
	Peptic Ulcer Perforation 129	Mean (%) 95% CI [0.10, 8.69] [8.74, 14.38] [1.04, 1.36] [2.52, 3.61] [1.23, 1.56] 4.40 11.56 1.20 3.06 1.40	12.25 [11.65, 12.85]	1.16 [0.25, 2.08]
	Diverticular Bleeding	189	Mean (%) 95% CI [0.36, 5.32] [8.32, 10.36] [1.20, 1.41] [1.15, 1.41] [1.92, 2.22] 2.84 9.34 1.31 1.28 2.07	10.14 [9.76, 10.53]	1.28 [0.95, 1.61]
	Angiodysplasia	66	Mean (%) 95% CI	1.56 [0, 4.68] [6.58, 11.10] [1.04, 1.64] [1.06, 1.29] [2.41, 3.00] 8.84 1.34 1.17 2.70	8.31 [7.78, 8.85]	2.02 [1.54, 2.50]
			Mean (%)	28.66	21.78	0.99	4.04	1.85	10.96	0.91
	Intestinal perforation	422	95% CI	[23.58, 33.75]	[19.21, 24.35]	[0.92, 1.05] [3.64, 4.43] [1.73, 1.97]	[10.66, 11.27]	[0.59, 1.24]
	Comparisons among categories:
	• Mortality:
	o Intestinal perforation vs. Any other lesion: p < 0.001
	o Peptic Ulcer Bleeding vs. Peptic Ulcer Perforation: p = 0.363 (NS)
	• Hospital stay: Peptic Ulcer Bleeding vs. Peptic Ulcer Perforation: p < 0.001
	• Number of diagnostic tests performed:
	o Angiodysplasia vs. Peptic Ulcer Bleeding: p < 0.001
	o Angiodysplasia vs. Peptic Ulcer Perforation: p = 0.019 (NS)
	o Angiodysplasia vs. Diverticular Bleeding: p = 0.905 (NS)
	o Angiodysplasia vs. Intestinal perforation: p < 0.001
	o Diverticular Bleeding vs. Peptic Ulcer Bleeding: p < 0.001
	o Diverticular Bleeding vs. Peptic Ulcer Perforation: p = 0.012 (NS)
	o Diverticular Bleeding vs. Intestinal perforation: p < 0.001
	• Number of Comorbidities:

Reply to comments from the Editor and Referees 1. EDITOR'S COMMENTS TO AUTHOR:

	a) Please can you work on the standard of English -it is sub-optimal.

Acknowledgements:

The study was supported by Pfizer Inc. Pfizer had no role in the conduct of the study, or the analysis or interpretation of the data.

Statements of interest

Conflict of interest:

Angel Lanas is member of the adjudication Committee of the international multicenter CONDOR trial, sponsored by Pfizer, and has received honoraria for lecturing at Pfizer-and AstraZeneca-sponsored symposiums.

Xavier Calvet has received honoraria for participating in advisory boards and for lecturing at AstraZeneca-sponsored symposiums. Javier P. Gisbert has received honoraria for lecturing at AstraZeneca-and Pfizer-sponsored symposiums. Luis Bujanda has received small honoraria for lecturing at Pfizersponsored symposiums.

The other study authors have no conflicts of interest to report.


Sebastian Haag

Jane M Andrews

Judith Gapasin

Guido Gerken

Andreas Keller

Prof Gerald Holtmann
email: gerald.holtmann@uk-essen.de

NATION POPULATION SURVEY OF UPPER GASTROINTESTINAL SYMPTOMS: PREVALENCE OF SYMPTOMS AND SOCIOECONOMIC FACTORS

Keywords:

Background:

We aimed to determine the prevalence of upper gastrointestinal (UGI) symptoms in 13 European countries and the association between socioeconomic factors and symptoms using a standardised method.

Methods: A representative age-and gender stratified sample of 23.110 subjects (aged 18-69 years) was surveyed.

Results:

The prevalence of UGI symptoms was 38%. UGI symptoms were most prevalent in Hungary (45.3%, 95% confidence interval (CI) 42.2-48.4) and lowest in the Netherlands (23.6%, 95%CI 21.0-26.2). UGI symptoms were more prevalent in females (39%, 95%CI 38.4-39.6) vs. males (37%, 95%CI 36.4-37.6).

Heartburn (24%, 95%CI 23.4-24.6) and acidic reflux (14%, 95%CI 13.6-14.4) were most common. With age, the prevalence of UGI symptoms decreased (e.g. 18-29 yrs: 42.8%, 95%CI 41.4-44.3 vs. 50-69yrs: 33.4%, 95%CI 32.3-34.4); in contrast, the frequency of symptom episodes/year increased with age (e.g. . Socioeconomic status as measured by gross domestic product was inversely associated with symptoms and in total, socioeconomic factors, gender, body mass index, smoking habits and alcohol consumption explained 83.4% of the variance of UGI symptoms.

Conclusions:

There are marked differences in the country specific prevalence of UGI complaints. Socioeconomic factors are closely associated with the prevalence of UGI symptoms.

INTRODUCTION

Upper gastrointestinal (UGI) symptoms such as heartburn, acidic reflux, indigestion, epigastric pain and/or discomfort are common and widely prevalent.

They present with a broad spectrum of intensity and/or frequency While chronic or relapsing UGI symptoms including symptoms of gastrooesophageal reflux (GOR) are most frequently due to so called functional gastrointestinal disorders or gastroesophageal reflux disease (GORD), they significantly impair health-related quality of life and cause a significant burden to society due to reduced work productivity and increased health-care resource utilization [START_REF] Eslick | Gastroesophageal reflux disease (GERD): risk factors, and impact on quality of life-a population-based study[END_REF][START_REF] Rey | Impact of gastroesophageal reflux symptoms on health resource usage and work absenteeism in Spain[END_REF][START_REF] Nocon | Prevalence and sociodemographics of reflux symptoms in Germany--results from a national survey[END_REF][START_REF] Wiklund | Gastroesophageal reflux symptoms and wellbeing in a random sample of the general population of a Swedish community[END_REF][START_REF] Gschossmann | Epidemiology and clinical phenomenology of visceral pain[END_REF]. Studies from specific countries and post-hoc analyses reported that the prevalence of dyspepsia, (upper) abdominal pain and the severity of reflux symptoms decreases with advancing age [START_REF] Agreus | Natural history of gastroesophageal reflux disease and functional abdominal disorders: a population-based study[END_REF][START_REF] Kay | Epidemiology of abdominal symptoms in a random population: prevalence, incidence, and natural history[END_REF][START_REF] Johnson | Heartburn severity underestimates erosive esophagitis severity in elderly patients with gastroesophageal reflux disease[END_REF][START_REF] Gschossmann | Epidemiological trends of functional gastrointestinal disorders[END_REF]. However, despite their decreasing overall prevalence, more serious GORD-complications like complicated ulcers (i.e. life-threatening bleeding) and adenocarcinoma [START_REF] Vizcaino | Time trends incidence of both major histologic types of esophageal carcinomas in selected countries, 1973-1995[END_REF] appear to occur predominantly in elderly patients [START_REF] Eguchi | Gastric cancer in young patients[END_REF].

The prevalence of GORD is currently estimated to be in the range from 10-20% [START_REF] Vakil | The Montreal definition and classification of gastroesophageal reflux disease: a global evidence-based consensus[END_REF], but a recent systematic review suggested significant geographic variations [START_REF] Dent | Epidemiology of gastrooesophageal reflux disease: a systematic review[END_REF]. Other studies suggest an increase of GORD prevalence in recent years (14;15). However, studies on the influence of age and gender on GORD and GOR symptoms have yielded inconsistent results (13;16-18) and a low 4 socioeconomic status has been reported to be associated with upper GI symptoms in some countries (3;19). Therefore we aimed to assess the prevalence of upper GI symptoms and the influence of age and gender on upper gastrointestinal symptoms in 13 European countries using a standardized previously validated methodology. Furthermore we assessed the influence of socioeconomic variables (individual income, individual education level as well as gross domestic productivity, use of telephones [main lines, cell phones], internet use, and electricity consumption) on the prevalence of UGI symptoms in these countries.

METHODS

Subjects

Data were assessed by an online survey with a total of 23.110 interviews taken in a panel of overall 662.700 subjects which represent age-and gender stratified cohorts that are representative for the respective 13 countries. Subjects were members of a fixed panel, and a subset of panellists (n=33135, 5%) was invited to participate in this survey by mail, randomly selected from a telephone directory from the overall panel. To take part in this study, an internet access was required; however, subjects were free to enter this study at any computer with internet access. Predefined numbers of subjects for the various age-strata were included and upon achievement of the predefined numbers, strata were closed. Thus, even if all invited panellist would possibly be interested to take part in this and Switzerland. To ensure a sufficient statistical power, sample size were > 1.000 per country, while the five largest European countries (France, Germany, Italy, Poland, and Spain) had samples of more than 3.000 subjects each.

The individual highest achieved educational level and actual income were also documented. Data on gross domestic product (GDP) and GDP per capita (purchase power parity); mean body mass index (BMI, kg/m 2 ), current tobacco use in adults >15yrs; per capita alcohol consumption (litres of pure alcohol) in adults >15yrs; use of telephones [main lines in use, mobile cellular] (million); internet users (million) and electricity consumption (billion kWh) in the various countries were acquired from available sources (20;21).

Upper gastrointestinal symptom questionnaire

The questions were designed by a group of experts in the field. Internal consistency was reviewed by a steering committee consisting of natives from all countries involved in this trial. After testing for test-retest reliability, the questions were utilized. Two days after study begin, a plausibility check was done to test for responsiveness and construct validity. In the questionnaire, the following definitions were used to assess the key UGI symptoms. Heartburn was defined as a restrosternal burning sensation (behind the breastbone). Stomach acid complaints were defined as symptoms (pain, burning sensation) between the region of the umbilicus and lower end of the sternum, marked by the medioclavicular lines. Reflux/ acid taste in the mouth was defined as regurgitation of liquid gastric content into the oesophagus/ mouth. Dyspepsia was defined as pain or discomfort in the upper abdomen.

Assessment of the predominant upper gastrointestinal symptom

Statistical analysis

Demographical data are reported as the mean and standard deviation for numerical factors and as percentages and 95% confidence intervals (CI) for discrete characteristics. Initial bivariate categorical associations were tested for using the chi-squared test and continuous data by the Student's t-test or nonparametric tests when appropriate. All p-values calculated were two-tailed and the α-level was set at 5%. After testing for distribution, multivariate correlation analysis was performed. Two multiple linear regression models assessed the associations of age, gender and socioeconomic variables with the prevalence of any UGI symptom (model 1) and dyspeptic symptoms (model 2). The associations are reported using partial r 2 values, adjusted for all other variables in the model. All analyses were performed with the Statistical Package for the Social Sciences 17.0 (SPSS Inc., Chicago, IL, USA).

RESULTS

F

Prevalence of upper GI symptoms across countries

While upper gastrointestinal and dyspeptic symptoms were highly prevalent in all thirteen countries (overall 37.8%, 95%CI 37.2-38.4 and 11.8%, 95%CI 11.4-12.2), there were marked differences in the prevalence of symptoms, e.g. dyspeptic symptoms ranging from 23.6% in the Netherlands up to 45.3% in Hungary (table 1). The predominant symptoms in all countries were heartburn and symptoms of gastrointestinal reflux (table 1). In subjects with heartburn, symptoms occurred on average 16.5±41.2 times during the previous 12 months (figure 1).

The influence of age and gender on upper GI symptoms

Overall, females reported a greater prevalence of UGI symptoms than men (table 1). Interestingly, this was not true in all countries with men in Belgium and Poland, having a higher prevalence of UGI symptoms than females. Women also generally experienced a greater frequency of UGI symptoms compared to men (figure 2). Twenty-seven percent of women (95%CI Overall, the prevalence of UGI symptoms decreased from 42.8% in the group of subjects between 18-29 yrs to 32.9% in the 50 to 69yrs old group (p<0.001). The age related decrease of symptoms was in particular clear for heartburn and dyspepsia while reflux and stomach acid complaints were not affected by age (figure 3).

The influence of socioeconomic variables on upper GI symptom prevalence

In the bivariate analyses UGI symptoms and dyspepsia were significantly and negatively correlated with GDP per capita (r=-0.579, p=0.004, figure 4), highest achieved level of education (r=-0.397, p=0.02), number of phones (main lines in use, r=-0.122, p=0.02) and internet use (r=-0.152, p=0.02) as indirect markers of a high socioeconomic status and positively with body mass index (r=0.180, p=0.04), smoking habits (r=0.176, p=0.33), alcohol consumption (r=0.334, p=0.01), proportion of subjects with a monthly income of less than €1500 (r=0.507, p=0.01, figure 5). After adjusting for age, gender and body mass index, smoking and alcohol consumption were no longer significantly associated with either UGI symptoms or dyspepsia (table 2). However, there was a trend for alcohol consumption being associated with dyspepsia, but it failed to reach statistical significance. Similar associations were found for dyspepsia (data not shown).

The per capita GDP was negatively correlated with UGI symptoms and dyspepsia. After stratification for individual income, subjects with a monthly income of less than 1500€/month reported higher rates of UGI symptoms or

DISCUSSION

In our study, utilising a large age and gender stratified sample from thirteen countries, the overall prevalence of upper gastrointestinal symptoms was 38% with a marked inter-country variation. However, our data clearly support the notion that there are marked geographic differences in the prevalence of UGI symptoms. Even more importantly besides well recognised risk factors such as BMI and alcohol or nicotine consumption, dyspepsia and the prevalence of UGI symptoms are inversely associated with the GDP per capita and other indicators of wealth such as education, electricity consumption per capita and other markers. This association was still evident after adjusting for potential confounding factors.

In all countries, acidic reflux and heartburn were the most prevalent symptoms.

All symptoms were more prevalent in females. While the proportion of subjects with symptoms decreased with age, symptom episodes were more frequent in the elderly. Relationships between age and gastrointestinal symptoms have been previously reported (3;22). However, different studies have found different relationships between aging and the prevalence of UGI symptoms, with some studies finding an increasing prevalence with age until the age of 69 or 55 years, from which point the trend was reversed (3;13), whereas in the Kalixanda study the prevalence decreased even for subjects above 34 years [START_REF] Aro | Valid symptom reporting at upper endoscopy in a random sample of the Swedish adult general population: the Kalixanda study[END_REF], and others who did not report an association of GOR symptoms with age [START_REF] Ponce | Prevalence of gastro-oesophageal reflux disease in Spain and associated factors[END_REF]. The reasons for the variation between studies and countries, in this relationship amongst ageing and UGI symptoms, are still unknown and need to be elucidated further.

Very recently one study by Gururatsakul et al. [START_REF] Gururatsakul | The ageing gut: diminished symptom response to a standardized nutrient stimulus[END_REF], demonstrated diminished sensory responses in elderly patients with peptic ulcer disease and elder healthy controls as compared to younger patients and controls. Thus the decrease in the prevalence of dyspeptic symptoms in the elderly might be explained by diminished sensory responses (or a decreased prevalence of functional GI disorders). The decrease of symptoms in the elder subjects thus occurs despite of the well known fact, that the prevalence of H. pylori is higher in the elderly as compared to younger subjects. In additions elderly are more likely to be on medications that may cause dyspepsia (e.g., non-steroidal anti-inflammatory drugs, bisphosphonates) that increase their risk for dyspeptic symptoms and acid-related disorders [START_REF] Holtmann | Do changes in visceral sensory function determine the development of dyspepsia during treatment with aspirin?[END_REF][START_REF] Ruszniewski | Nonsteroidal anti-inflammatory drug use as a risk factor for gastro-oesophageal reflux disease: an observational study[END_REF][START_REF] Wallander | Dyspepsia in general practice: incidence, risk factors, comorbidity and mortality[END_REF]. On the other hand, difference in the H. pylori prevalence and differences in the alcohol consumption -while not specifically assessed in our study -might be potential. In our study, the associations between symptoms and smoking or alcohol consumption did not yield significance. On the other hand, an association with GORD symptoms and smoking has been reported previously (22;29), while the results of an association of GORD symptoms with alcohol consumption are still controversial. The Georgia Medicaid study identified a significant association between a GORD diagnosis and alcohol consumption with an OR 1.8 (95% CI 1.4-2.4). Another study, also, found an association between GORD and alcohol consumption, but only if it was judged excessive [START_REF] Mohammed | Genetic influences in gastro-oesophageal reflux disease: a twin study[END_REF]. In contrast, alcohol consumption did not significantly affect the risk of a first time diagnosis of GORD in data from the UK GP database study [START_REF] Ruigomez | Natural history of gastro-oesophageal reflux disease diagnosed in general practice[END_REF]. An excess body mass/ higher body mass index has been reported to be associated with the prevalence of GORD (18;30;31), although the OR was small (OR 1.3 (95%CI 1.2-1.4) for BMI >25 and OR 1.3 (95%CI 1.2-1.5) for BMI >30) [START_REF] Ruigomez | Natural history of gastro-oesophageal reflux disease diagnosed in general practice[END_REF].

In our study, upper GI symptom prevalence was inversely associated with educational level. This is in line with some data from El Serag et al. [START_REF] Serag | Gastroesophageal reflux among different racial groups in the United States[END_REF] and Isolauri et al. [START_REF] Isolauri | Prevalence of symptoms suggestive of gastrooesophageal reflux disease in an adult population[END_REF]. However, neither the lowest, nor the highest achieved level of education but rather, graduation from senior high school, was negatively associated with upper GI symptom and dyspepsia prevalence in our study. However, this association was observed in the univariate analysis, but did not significantly affect the upper GI symptom prevalence in the multivariate analysis.

The reason for this finding might be the correlation of educational level and monthly income, which also ultimately affect nutritional factors, which were not 12 assessed in this study. We furthermore analyzed the association of individual monthly income with the prevalence of symptoms and demonstrated that a monthly income of less than €1499 was associated with higher rates of upper GI symptoms, while an income exceeding €1500/month was negatively associated with these symptoms. There was also a significant negative association between gross domestic productivity and the reported prevalence of upper GI symptoms and dyspepsia.

To determine whether a higher social status/ income may also result in an increased intake of antacids, we assessed the individual medication taken for upper GI symptoms in various countries. However, we did not find a significant association of PPI use with a decreased rate of upper GI symptoms or dyspepsia, while the use of H2RAs and antacids were associated with higher rates of upper GI symptoms and dyspepsia. Due to the nature of the study, individual co-medication as well as current or past medical history were not assessed. However, it is unlikely that these potential confounders significantly influenced our results.

While our results are based on very large stratified cohorts, there are some limitations of this study that need consideration. The nature of online surveys requires internet access. However, since the subjects were randomly selected from a telephone directory and received their invitation per mail, a personal internet access which may cause bias, was not necessarily required but the questionnaire could have been assessed and answered from any computer with internet access. In our study, predefined numbers of subjects for the various agestrata were included and upon achievement of these predefined numbers, the strata were closed. Therefore data on response rates are not available. [START_REF] Harris | Lottery incentives did not improve response rate to a mailed survey: a randomized controlled trial[END_REF]. The questionnaire only included four predominant upper gastrointestinal symptoms (heartburn, stomach acid complaints, reflux/ acid taste in the mouth and dyspepsia). Whilst focusing on these core symptoms appears justified by the results of a recent factor analytic study that revealed that these as main factors for the assessment of upper GI symptoms [START_REF] Talley | Gastrointestinal symptoms and subjects cluster into distinct upper and lower groupings in the community: a four nations study[END_REF], it is possible that the lack of assessment of other symptoms has limited our understanding of all UGI symptomatology. In our study, for example, we did not assess extra-oesophageal symptoms. On the other hand it can be argued that members of a panel for questionnaire studies are likely to talk about their health and we may thus have overestimated the prevalence of UGI symptoms. We found various associations between sociodemographic and ecologic data and GI symptoms. While it is very unlikely that e.g. the number of mobile phones per 1000 directly affects GI symptoms or underlying disease, there are many factors that might be correlated with mobile utilization that ultimately affect the symptom manifestation. However, the key finding of our study is the fact that beyond reasonable doubt, environmental factors are associated with symptoms. Thus, the ecologic "indicators" tested are indeed linked with the prevalence of symptoms. However, despite these limitations, our findings are in accordance with population-based studies from various Western nations (3;7;18;24;34-36).

In summary, there are marked differences in the country specific prevalence of upper GI complaints. These differences are associated with socioeconomic indicators such as the GDP per capita. Whether these socioeconomic factors and the prevalence of UGI symptoms are linked via specific environmental factors (e.g. nutritional) needs to be elucidated further.

  further study entry was possible. All completed interviews were gratified with a voucher, valued €5. Countries included were Austria, Belgium, Denmark, Finland, France, Germany, Hungary, Italy, Netherlands, Poland, Portugal, Spain

  those with a monthly income > 1500€/month. The overall numbers of phones (main lines in use) as well as internet use were negatively correlated with UGI symptoms in general, and along with electricity consumption were negatively correlated with dyspepsia in particular.

  Incentives are often used to maximize study participation in epidemiological studies which in turn raises the question of selection bias. Because bias is the value of the incentive, we have rewarded study participation with a €5 voucher to compensate potential costs associated with study participation only, as previous studies have demonstrated that low-price vouchers are not causing a significant selection bias

Figure 3 :

 3 Figure 3: Age-and gender-specific prevalence of upper gastrointestinal symptoms

Figure 4 :

 4 Figure 4: Correlation of Gross Domestic Productivity per capita in $ with prevalence of upper GI symptoms. (• = small countries, sample size n=1000; • = large countries, sample size n=3000). r=-0.58, p=0.004.

23 Figure 5 :

 235 Figure 5: Correlation of income/ month below €1500 with prevalence of upper GI symptoms. (• = small countries, sample size n=1000; • = large countries, sample size n=3000). r=0.51, p=0.01

Table 1 :

 1 Prevalence rates of upper gastrointestinal symptoms (%, 95%CI) Episodes of heartburn in the previous 12 months (***p<0.001), stratified by age and gender.

	Overall	Austria	Belgium	Denmark	Finland	France	Germany
	(n=23.163)	(n=1.000)	(n=1.010)	(n=1025)	(n=1014)	(n=3.020)	(n=3.000)
	Any upper GI
	symptom

yrs 1 to 3 times 4 to 6 times 7 to 12 times 13 times and more Figure 2:

  Frequency of upper gastrointestinal symptoms reported in the previous 12 months stratified by age and gender.

				15%	14%
	12%	10%	14%			12%
				14%	15%		9%
	14%	14%	14%			14%
							14%
				14%	14%
	13%	13%	13%			13%
							12%
	24%	24%	24%	27%	28%	24%	20%
	F o Total male	female	18-
		r
		P
			e e r
				R e v i e w
							22

29 yrs 30-39 yrs 40-49 yrs 50-69 yrs Heartburn Stomach acid complaints Reflux/ acid taste in the mounth Dyspepsia

Acknowledgements:

This work was supported by an unrestricted grant from Nycomed GmbH.

Haag, MD, MSc and Gerald Holtmann, MD, MBA are the guarantors of this article. All investigators contributed to the design, interpretation of data and to the writing and critical revision of the manuscript. A.K. dealt with data collection and S.H. and G.H. performed the analysis. All authors have read and approved the manuscript. Sebastian Haag has received research support, speaker's fees or travel support from Essex Pharma, Ferring, Abbott Inc., and Nycomed. Jane M Andrews has received research support, speaker's fees, travel support or honoraria from Abbott, AstraZeneca, Ferring, Fresenius Kabi, J&J, Nycomed, Orphan, Pharmatel, and Schering-Plough. Judith Gapasin has received speaker's fees and travel support from Nycomed. Guido Gerken has nothing to declare. Andreas Keller is an employee from Nycomed GmbH. Gerald Holtmann has received research support, speaker's fees, travel support or honoraria from Abbott, Ardeypharm, AstraZeneca, Bayer, J&J, Nycomed, and Steigerwald.

F o r P e e r R e v i e w

Any upper GI symptom Dyspeptic symptoms

Variable R


Manamiary Bruno Andriamiarina
email: manamiary.andriamiarina@loria.fr

Dominique Méry
email: dominique.mery@loria.fr

Stepwise Development of Distributed Vertex Colouring Algorithms (Abstract)

Introduction

Verifying distributed algorithms is non trivial. A promising methodology is based on the Event B language and the refinement process ( [START_REF] Abrial | Modeling in Event-B: System and Software Engineering[END_REF]) : it consists in redeveloping the algorithms by targeting a collection of required properties, using the refinement of models which preserves the properties of an abstract one in concrete ones. This approach has already been followed by Abrial et al for their work on the IEEE 1394 protocol ( [START_REF] Abrial | A mechanically proved and incremental development of ieee 1394 tree identify protocol[END_REF]). Our goal is to integrate probabilities into this approach. It appears that there are other proposals for dealing with this problem ( [START_REF] Hallerstede | Qualitative probabilistic modelling in event-b[END_REF][START_REF] Morgan | The challenge of probabilistic event b -extended abstract[END_REF][START_REF] Morgan | Probabilistic predicate transformers[END_REF][START_REF] Duffy | Complexity analysis of a decentralised graph colouring algorithm[END_REF]). This paper presents an illustration of our approach through the study of vertex coloring algorithms, based on an algorithm cited by Métiver et al ( [START_REF] Métivier | An analysis of an optimal bit complexity randomised distributed vertex colouring algorithm (extended abstract)[END_REF]), and preliminary elements of a global methodology on realistic distributed algorithms.

The Graph Coloring Problem

Fig. 1: Overview of the development Figure 1 presents our methodology. We begin by defining an abstract model, and end with three concrete models which are three different vertex coloring algorithms. Specification of the graph coloring problem -This is done in the machine COL-ORING1. A simple graph GRAPH is given over a set of vertices NODES. Using results of the graph theory, the vertices of GRAPH can be colored in such a way that no two adjacent vertices of GRAPH share the same color. The vertices of GRAPH are colored by a statement in the machine. The next step is to define an inductive coloring function which associates different colors to the adjacent vertices of GRAPH.

Computing the coloring function -In the machine COLORING2, we define an inductive coloring function, which assigns the vertices their colors, which are different from the ones given to their neighbors. This model does not take into account the notion of ill-chosen colors and multiple tentatives of color choices. The vertex coloring algorithms (COLORING3, COLORING5, COLORING6) -The algorithms defined in COLORING3, COLORING5, COLORING6 introduce the notion that a node might make multiple color choices before finding the right one. COLORING3 -This model presents a synchronous algorithm divided into steps : in a first round, all the vertices which have no color or are not correctly colored choose a color, then in a second round, all the vertices which have chosen colors, update the graph by deleting the edges between them and their neighbours which have chosen different colors, and finally the vertices verify if they are still linked to some neighbours; if it is the case, they restart choosing colors otherwise they stop executing the algorithm.

COLORING5 and COLORING6 -These models present asynchronous algorithms. The behavior of these algorithms are the same as the one defined in COLORING3, except the fact that the vertices do not have to wait for all the others to choose their colors, update the links between them and their neighbours or restart choices. Behavior verification -The visualisation and simulation of the algorithms are done with the software ViSiDiA ( [START_REF] Derbel | A brief introduction to visidia[END_REF][START_REF] Tounsi | A Refinement Approach for Proving Distributed Algorithms : Examples of Spanning Tree Problems[END_REF][START_REF] Sellami | Des calculs locaux aux algorithmes distribués[END_REF]). Probabilistic arguments -Our analysis shows that the probabilistic aspects of these algorithms lie within the random choice of a color by a vertex. Probabilities can be distributed over of the elements of the set of available colors for a vertice or over the set of the events which are parts of the global event "choice of a color by a node" : the event when a node chooses a correct color happens with a certain probability, and the event when it chooses a wrong one has a certain probability attached to it, too. The next step is to analyse these aspects using probabilistic formal tools like PRISM ( [START_REF] Kwiatkowska | PRISM: Probabilistic symbolic model checker[END_REF]).

Conclusion and Further Developments

The current stepwise development focuses on algorithms which require probabilistic arguments to achieve termination. We have derived these vertex coloring algorithms from an abstract specification of the graph coloring problem. They have in common the integration of possible errors during the choice of colors by vertices and this is the point where probabilistic arguments can be handled. As we have mentioned in the introduction, this paper presents preliminary elements of a global methodology for handling the correct-by-construction refinement-based approach applied to distributed algorithms and further work is needed to adapt technique and tools. It is also a first step towards our goal of obtaining a development framework, integrating probabilistic arguments and refinement, for distributed algorithms. This framework can be an extension of the Event B method ( [START_REF] Hallerstede | Qualitative probabilistic modelling in event-b[END_REF][START_REF] Morgan | The challenge of probabilistic event b -extended abstract[END_REF]) or, in our case, a combination of the Event B method and other formal methods (see figure Fig. 1).


Manamiary Bruno Andriamiarina
email: manamiary.andriamiarina@loria.fr

Stepwise Development of Distributed Algorithms (Research Abstract)

We study distributed algorithms using the "correct-by-construction process", which involves the Event B method and the refinement process. These algorithms integrate non-functional requirements like probabilistic aspects. Therefore, it appears that the correct-by-construction process should integrate probabilistic arguments to be considered as a development and verification framework for distributed algorithms. We present here preliminary elements of a global approach on how to take into account probabilistic arguments during the development of distributed algorithms, and we illustrate this approach with the study of distributed coloring algorithms.

Introduction

Overview -Verifying distributed algorithms is non trivial. A promising methodology is based on the Event B language and the refinement process ( [START_REF] Méry | Refinement-based guidelines for constructing algorithms[END_REF]): it consists in redeveloping the algorithms by targeting a collection of required properties, using the refinement of models which is preserving the properties of an abstract one in concrete ones. However, this approach called "correct-by-construction process" does not handle probabilistic arguments. Therefore, we propose in this paper a way of handling probabilities and integrating them into the process, and we illustrate our approach through the study of vertex coloring algorithms, which have strong features related to probabilistic statements.

Related works -

The correct-by-construction approach has already been followed by Abrial et al during their redevelopment of the tree identification protocol IEEE 1394 ( [START_REF] Abrial | A mechanically proved and incremental development of ieee 1394 tree identify protocol[END_REF]), leading to an algorithm which does not integrate probabilistic arguments. In this paper, we are considering the integration of probabilistic aspects into the development of distributed algorithms and the refinement process. It appears that there are other proposals for dealing with probabilisitic choices in algorithmic systems and we cite the works of McIver and Morgan ( [START_REF] Mciver | Probabilistic predicate transformers[END_REF]), and the approach of Hoang et al ( [START_REF] Hallerstede | Qualitative probabilistic modelling in event-b[END_REF][START_REF] Abrial | The challenge of probabilistic event b -extended abstract[END_REF]) which is integrated into the Event B methodology. We choose graph coloring algorithms to illustrate our topic, because of their strong ties to probabilities. The probabilistic aspects of these algorithms have already been studied by several researchers, such as Métivier et al ( [START_REF] Métivier | An analysis of an optimal bit complexity randomised distributed vertex colouring algorithm (extended abstract)[END_REF]), who analysed a coloring algorithm using random bits exchanges between the vertices of a graph, Kubale et al ( [START_REF] Hansen | Distributed largestfirst algorithm for graph coloring[END_REF][START_REF] Kubale | A better practical algorithm for distributed graph coloring[END_REF]), who analysed coloring algorithms based on the use of random numbers for the choice of colors by the vertices, and Duffy et al ( [START_REF] Duffy | Complexity analysis of a decentralised graph colouring algorithm[END_REF]), who proposed an algorithm in which probabilities are distributed over the set of colors a vertex can choose. In fact, there is no or little verification of the safety correctness of these algorithms. The main contribution is yet the analysis of complexity, which can be done later on our final models.

Summary of the paper -Section 2 contains our methodology and the development and study of the graph coloring problem. Section 3 concludes and discusses the issues of this problem and the development of probabilistic distributed algorithms.

The Graph Coloring Problem 2.1 Development methodology

The figure Fig. 1 presents the methodology we used to develop our algorithms. We begin by developing an abstract model and end with three concrete models which can be translated into three different algorithms.

Specification of the graph coloring problem

The specification of the graph coloring problem is done in the machine COLORING1. A simple graph GRAPH is given over a set of vertices NODES. Using results of the graph theory, the vertices of GRAPH can be colored in such a way that no two adjacent vertices of GRAPH share the same color (see figure Fig. 2). The vertices of GRAPH are colored by a statement in the machine.

Fig. 2: A proper coloring of a graph

The next step is to define an inductive coloring function which associates different colors to the adjacent vertices of GRAPH.

Induction step : Computing the coloring function

In the machine COLORING2, we define an inductive coloring function, which assigns the vertices their colors, which are different from the ones given to their neighbors (see figure Fig. 3) . Fig. 3: The coloring function This model does not take into account the notion of ill-chosen colors and multiple tentatives of colors choices. Next section will solve this question.

The vertex coloring algorithms

The algorithms defined in the machines COLORING3, COLORING5, COLORING6 introduce the notion that a node might do multiple color choices before finding the right one (see figure Fig. 4) . Fig. 4: The algorithms general behavior COLORING3 -This model presents a synchronous algorithm divided into steps : in a first round, all the vertices which have no color or are not correctly colored choose a color, then in a second round, all the vertices which have chosen colors, update the graph by deleting the edges between them and their neighbours which have chosen different colors, and finally the vertices verify if they are still linked to some neighbours; if it is the case, they restart choosing colors otherwise they stop executing the algorithm.

COLORING5 and COLORING6 -These models present asynchronous algorithms. The behaviors of these algorithms are the same as the one defined in COLORING3, except the fact that the vertices don't have to wait for all the others to choose their colors, update the links between them and their neighbours or restart choices.

Behavior verification -The visualisation and simulation of the algorithms are done with the software ViSiDiA ( [START_REF] Derbel | A brief introduction to visidia[END_REF][START_REF] Hadj-Kacem | A Refinement Approach for Proving Distributed Algorithms : Examples of Spanning Tree Problems[END_REF][START_REF] Sellami | Des calculs locaux aux algorithmes distribués[END_REF]).

Integration of Probabilistic Arguments

Our analysis shows that the probabilistic aspects of these algorithms lie within the random choice of a color by a vertice. Probabilities can be distributed over of the elements of the set of available colors for a vertice or over the set of the events which are parts of the global event "choice of a color by a node" : the event, when a node chooses a right color, happens with a certain probability, and the event when, it chooses a wrong one, has a certain probability attached to it, too. The next step is to analyse these aspects using probabilistic formal tools like PRISM ( [START_REF] Kwiatkowska | PRISM: Probabilistic symbolic model checker[END_REF]).

Conclusion and Further Developments

The current stepwise development is focusing on algorithms wich require probabilistic arguments to achieve termination. We have derived these vertex coloring algorithms from an abstract specification of the graph coloring problem. They have in common the integration of possible errors during the choice of colors by vertices and this is the point where probabilistic arguments can be handled. As we have mentioned in the abstract, this paper is presenting preliminary elements of a global methodology for handling the correct-by-construction refinement-based approach applied to distributed algorithms and further work is needed to adapt technique and tools. It is also a first step towards our goal to obtain a development framework, integrating probabilistic arguments and refinement, for distributed algorithms. This framework can be an extension of the Event B method ( [START_REF] Hallerstede | Qualitative probabilistic modelling in event-b[END_REF][START_REF] Abrial | The challenge of probabilistic event b -extended abstract[END_REF]) or, in our case, a combination of the Event B method and other formal methods (see figure Fig. 5).

Acknowledgment

We want to thank the supervisor of this doctoral work, Dominique Méry 1 ([4]), for his help, suggestions, advices and the discussions about this article for improvements.

Fig. 1 :

 1 Fig. 1: The development methodology

Fig. 5 :

 5 Fig. 5: A framework for the development of distributed algorithms