Michel Schneider Limos

Blaise

A general model for the design of data warehouses

Keywords: multidimensional, data warehouse, general model, relational mapping 1

Design and implementation of data warehouses remain delicate tasks which are led by experts. Nevertheless it would be interesting to allow the users to define and to build themselves their system through a simple and flexible process. In particular, in the field of production systems, exists the need to integrate data from various sources and to analyze them in order to extract knowledge for optimizing these systems. Traditionally the design of a data warehouse is based on an adequate representation of facts on one hand and dimensions of analysis on the other hand. We show in this article that an unified representation can be envisaged and that the problem comes down to that of the choice of a hierarchy of criteria adapted to the necessities of analysis. Our proposition leans on a graphic representation which offers a visual help to the user.

structures; section 6 shows the ability of our model to describe realistic cases; section 7 discusses relational mappings; sections 8 illustrates SQL queries on the relational form of well-formed structures; section 9 discusses some improvements of our model and concludes.

Modelling facts

A fact is used to record measures or states concerning an event or a situation. Measures and states can be analyzed through different criteria organized in dimensions.

A fact type has the following structure :

fact_name[(F), (fact_key), (list_of_reference_attributes), (list_of_fact_attributes)]

where -fact_name is the name of the type ; -F is a mark for the fact type ; -fact_key is a list of attribute names ; the concatenation of the values of these attributes identifies each instance of the type ;

-list_of_reference_attributes is a list of attribute names ; each attribute has a value which is either an atomic value (degenerated case) or a reference to a member instance in a dimension or a reference to another fact instance ;

-list_of_fact_attributes is a list of attribute names ; each attribute is a measure for the fact type (such an attribute will also be called a measure attribute).

The set of referenced dimensions comprises the dimensions which are directly referenced through the list_of_reference_attributes, but also the dimensions which are indirectly referenced through other facts.

Each fact attribute can be analyzed along each of the referenced dimensions. Analysis is achieved through the computing of aggregate functions on the values of this attribute.

There may be no fact attribute; in this case a fact records the occurrence of an event or a situation. In such cases, analysis consists in counting occurrences satisfying a certain number of conditions.

For the needs of an application, it is possible to introduce different fact types sharing certain dimensions and having references between them.

Two dimensions are independent if there is no relationship between a member of the first and a member of the second.

A dimension is degenerated in a fact type if its reference attribute is replaced by a value attribute. In other words the analysis is achieved by direct use of the values of this attribute.

Definition 1 (well-formed fact type).

A fact type is well-formed if each referenced dimension is either degenerated or points to a legal entry in a dimension (a legal entry, as it is defined further, is a key of any member in a dimension).

Example 1. As an example let us consider the following fact type for memorizing the sales in a set of stores.

Sales[(F), (ticket_number, product_key), (time_key, product_key, store_key), (price_per_unit, quantity)]

The key is (ticket_number, product_key). This means that there is an instance of Sales for each different product of a ticket. There are three references to dimensions: time_key, product_key, store_key. There are two fact attributes: price_per_unit, quantity. The fact attributes can be analyzed through aggregate operations by using the three dimensions. Since each of the three references points to a root in a dimension, this fact type is well formed.

Example 2. Consider now the same fact type but with another reference to the dimension product (the key category_key of the member category).

Example 3. Consider again the fact type Sales and another reference to the dimension product (weight of a product).

Sales[(F), (ticket_number, product_key), (time_key, product_weight, store_key), (price_per_unit, quantity)]

Since product_weight is not a legal entry in a dimension, this fact type is not well-formed. We will see in section 3.6 that such an attribute is a property attribute which cannot be used to organize the multi-dimensional analysis.

In some models, it is imposed that measure attributes are independent from each others. This will clarify their analysis. The independence can be expressed by using functional dependencies: it must not exist any functional dependence between measure attributes. To be general, we do not impose a priori such a constraint.

Modelling dimensions

Member of a dimension

The different criteria which are needed to conduct analysis along a dimension are introduced through members. A member is a specific attribute (or a group of attributes as we will see in section 3.6) taking its values on a well defined domain. For example, the dimension TIME can include members such as DAY, MONTH, YEAR, … . Analysing a fact attribute A along a member M means that we are interested in computing aggregate functions on the values of A for any grouping defined by the values of M. In the paper we will also use the notation M ij for the j-th member of the i-th dimension.

Hierarchical organization of members

Members of a dimension are generally organized in a hierarchy which is a conceptual representation of the hierarchies of their occurrences. Hierarchies in dimensions is a very useful concept that can be used to impose constraints on member values and to guide the analysis. Hierarchies of occurrences result from various relationships which can exist in the real world: categorization, membership of a subset, mereology. Figure 1 illustrates typical situations which can occur.

Cases (a) and (b) represents the same members but organized differently. In case (a) there are hierarchical relationships between time_key and month and between month and year. Time_key, for example, is a date which encodes the day, the month and the year; the month has values such as February/02 which identifies each month from all the months of the total period. In these conditions, the amount of sales for all the months of all the years, is obtained with a group_by just on the month. In case (b) month and year are both hierarchically dependent of time_key but are independent of each other (month, for example, is a value such as January identifying a month independently from the value of year). With such a structure we can make groupings by using only values of month, or only values of year, or both values of month and year. The expression of the previous query would involve a group_by on month+year. Case (c) represents a hierarchy where the two paths are alternative. They share the same root type (time_key) and the same leaf type (year). Starting from time_key, groupings are possible by using either the values of week or either the values of month (but not both). This configuration has precise semantics: for a given occurrence of time_key, whether the week path or the month path is used, one always obtains the same occurrence of year. This means that, using either the first path or the second path, we obtain the same result when continuing the aggregations with the year element. In this case we said that alternatives paths satisfy the path coherence constraint. We use dotted arrows to represent alternative paths.

We will model these different cases according to a hierarchical relationship (HR) which links a child member M ij (i.e. week) to a parent member M ik (i.e. year) and we will use the notation M ij M ik . For the following we consider only situations where a child occurrence is linked to a unique parent occurrence in a type. However, a child occurrence, as in case (b) or (c), can have several parent occurrences but each of different types. Existence of this HR is very important since it means that the members of a dimension can be organized into levels and correct aggregation of fact attribute values along levels can be guaranteed.

Cover graph of a dimension

For the following, we suppose that HR is anti-symmetric and transitive. To justify these properties we can refer to the notion of part-whole relationship. This kind of relationship is often appropriate to apprehend real situations [START_REF] Abello | Understanding Analysis Dimensions in a Multidimensional Object-Oriented Model[END_REF]. There exist different semantics for part-whole-relationships and most of them verify these two properties. Thanks to the transitivity property we introduce the notion of cover graph of a dimension. The idea behind the notion of cover graph is to remove in a dimension graph all redundant directed edges and paths.

Definition 2 (cover graph of a dimension).

Consider the directed graph defined by the HR between the members of a dimension. A cover graph of this dimension is a minimal sub-graph obtained by removing all the directed edges resulting from the transitivity property. In our dimension graph, we do not introduce the member type "ALL" which represents the upper level of aggregation. This member specifies that all the occurrences of a fact type which point to a same dimension can be aggregate together. However, this upper aggregation will always be possible with our model.

Well-formed dimension Definition 3 (well-formed dimension).

A dimension is well-formed relatively to a cover graph when this graph has a unique connected component and is acyclic and when the path coherence constraint is satisfied for alternative paths.

Restricting the cover graph to a unique component is very important in practice. If the graph comprises, for example, two components, the dimension must be divided into two distinct dimensions. We do not impose that the cover graph has a unique root. In real situations we can encounter different dimensions which share a common part.

Example 5. Let us consider the dimensions illustrated in figure 1. They are all well-formed since their cover graphs have a unique component and are acyclic (in case (c) it is supposed that the path coherence constraint is satisfied). Example 6. In figure 3 we illustrate a dimension graph with two roots. In this case it appears that two dimensions which are priori different (supplier dimension and customer dimension) share a same part.

Fig. 3. A dimension graph with two roots

Remark (relaxing the transitivity property for the HR). Definition 2 can be easily extended to the more general case where the transitivity property is not satisfied by the HR. In this case, the cover graph is replaced in the definition by the initial graph of the dimension or by an equivalent non redundant graph. A non-redundant graph is obtained by removing directed edges which can be derived by using some rule.

Aggregation levels in a well-formed dimension

Since the cover graph of a well-formed dimension is acyclic, it is possible to distribute its members into levels. Each level represents a level of aggregation. Each time we follow a directed edge, the level increases (by one or more depending on the used path). This action corresponds to a ROLLUP operation (corresponding to the semantics of the HR) and the opposite operation to a DRILL DOWN. Starting from the reference to a dimension D in a fact type F, we can then roll up in the hierarchy of dimension D by following a path of the cover graph of D.

Property attributes in a dimension

As in other studies [START_REF] Hùsemann | Conceptual Data Warehouse Design[END_REF], we consider property attributes in a dimension. Such attributes are used to describe the members. A property attribute is linked to its member through a functional dependence, but does not introduce a new member and a new level of aggregation. For example a member town in a dimension may have property attributes such as population, administrative position, … . These attributes are not interesting to specify groupings but they can be useful in the selection predicates of queries to filter certain groups.

Member type

We now define the notion of member type, which incorporates the different features presented above. A member type has the following structure:

member_name[(M), (member_key), (list_of_reference_attributes), (list_of_property_attributes)]

where -member_name is the name of the type; -M is a mark for the member type; -member_key is a list of attribute names; the concatenation of these attributes identifies each instance of the type;

-list_of_reference_attributes is a list of attribute names where each attribute is a reference to the successors of the member instance in the cover graph of the dimension; alternatives are represented by using a sub-list in nested parentheses;

-list_of_property_attributes is a list of attribute names where each attribute is a property for the member.

Only the member_key is mandatory. Note that the two reference attributes week_key and month_key are represented in a sublist since they are the origin of two alternative paths.

Here is an occurrence of the week type :

week [(M), (w1_03), ( 2003), (holiday)].

Entries and roots in a dimension

Each member_key of a member in a dimension can be an entry for this dimension i.e. can be referenced from a fact type or from another member type. This possibility is very important since it means that dimensions can be shared between several fact types in various ways. In particular, it is possible to reference a dimension at different levels of granularity. A root represents a standard entry in a dimension. The cover graph can have several roots. For the three dimensions in figure 1, there is a single root. However, definition 3 authorizes several roots.

Handling many-to-many relationships in a dimension

In certain situations, a many-to-many relationship exists between two members of a dimension hierarchy. For example a Project can be connected with several Groups (possibly zero) and conversely a Group can collect several Projects (at least one). Within the framework of an analysis of purchases (purchase is so a fact type), a dimension can incorporate projects. Problem arises so how to elaborate the hierarchy with the Projects and the Groups. One supposes that a purchase for a project depends on the group to which this project belongs. A simple solution consists in two separated hierarchies, a one around a member Project and the other one around a member Group (Figure 4(a)). It is then possible to make aggregations, either on the projects separately, or on the groups separately, or simultaneously on projects and groups by crossing the two dimensions. Another solution consists in a single dimension with a member Project-Group which points towards members Project and Group (Figure 4(b)). This solution offers the same possibilities of aggregation as the previous one but it materializes the relationship between the Projects and the Groups through the instances of the member Project-Group. It becomes then possible to materialize aggregates at the level of Project-Group. In this second solution, if a project is isolated (it does not belong to any group), it is possible as in [START_REF] Mansmann | Extending Visual OLAP for Handling Irregular Dimensional Hierarchies[END_REF] to introduce an artificial instance for Group.

A unified way for modelling elements (facts or members)

A fact type has a very similar structure to that of a member type. Moreover, property attributes of a member can be seen as fact attributes and can be analyzed along the successors of this member acting as roots of partial dimensions. For example, suppose that in a dimension we have a member town with a property attribute population which references the member region. One can analyze population by using region : one can calculate aggregates on population with groupings on region_name.

An element is a type which has the following structure : where -element_name is the name of the type; -T is a mark for the type (F or M); -element_key identifies each instance of the type; -list_of_references is composed of sub-lists of attribute names; each attribute references another element ; these references determine the multidimensional structure of the data warehouse;

-list_of_specific_attributes is a list of attribute names; each attribute is a measure for a fact or a property for a dimension member.

The list of references determines the dimensions along which the element can be analyzed. Each specific attribute can be analyzed along each of these dimensions. Analysis is achieved through the computing of aggregate functions on the values of this attribute. The aggregation is specified through the values of the chosen members in the dimensions. Recall that the notion of sub-list is used to mark alternative paths.

Well-formed structures

Various structures for data warehouses

In this section we explain how with our unified model fact types and member types can be interconnected in order to model various data warehouse structures.

First, a fact can directly reference any member of a dimension. Usually a dimension is referenced through one of its roots (as we saw above, a dimension in our model can have several roots). But it is also interesting and useful to have references to members other than the roots. This means that a dimension can be used by different facts with different granularities. For example, a fact can directly reference town in the customer dimension and another can directly reference region in the same dimension. This second reference corresponds to a coarser granule of analysis than the first. Moreover, a fact F 1 can reference any other fact F 2 . This type of reference is necessary to model certain situations (see section 6). This means that a fact attribute of F 1 can be analyzed by using the key of F 2 (acting as the grouping attribute of a normal member) and also by using the dimensions referenced by F 2 .

To formalise the interconnection between facts and dimensions, we thus suggest extending the HR relationship of section 3 to the representation of the associations between fact types and the associations between fact types and member types. This gives a very uniform model since fact types and member types are considered equally. To maintain a traditional vision of the data warehouses, we also ensure that the members of a dimension cannot reference facts.

Fig. 5. Typical data warehouse structures

Figure 5 illustrates the typical structures we want to model. Case (a) corresponds to the simple case, also known as star-snowflake structure, where there is a unique fact type F 1 and several separate dimensions D 1 , D 2 , … . Cases (b) and (c) correspond to the notion of facts of fact. Case (d) corresponds to the sharing of a whole dimension. In cases (e) and (f) only the members which are at the intersection of D 1 and D 2 are shared. An illustration of case (e) is given further in Fig. 7.

Data Warehouse Graph (DWG) and well-formed structures

To represent data warehouse structures, we suggest using a graph representation called DWG (data warehouse graph). It consists in representing each type by a node containing the main information about this type, and representing each reference by a directed edge. Alternative paths in dimensions are represented by dotted lines.

We are now able to introduce the notion of well-formed structures.

Definition 4 (well-formed data warehouse structures).

A data warehouse structure is well-formed when the following conditions are satisfied : 1) the fact types are well-formed ;

2) the dimensions are well-formed ; 3) a fact type is a root or all its predecessors in the graph are fact types ; 4) the DWG has a unique component and is acyclic.

Cut in the DWG

D 1 F 1 F 2 D 1 D 2 F 2 F 3 D 2 D 3 F 1 F 1 D 1 D 2 D 1 F 1 D 2 D 1 (b) (c) (e) (a)
(f)

F 2 F 1 D 1 (d) D 2 F 2 F 2 F 1
We introduce now the notion of cut in the DWG in order to characterise the legal groupings when making an analysis.

Definition 5 (Cut of a sub-graph in a DWG).

Let SG be a sub-graph of a well-formed DWG with root R. A cut of SG is a sub-set S={e 1 , e 2 , …, e k ) of edges of SG such that two different edges e i , e j of S does not appear in a same path or in two alternative paths.

Property 1. Each cut of a sub-graph of a well-formed DWG defines a legal grouping (i.e. the elements pointed by the edges of the cut can be legally combined to make an aggregation on the occurrences of the root of the sub-graph).

This important property permits to use the DWG in order to situate the different possibilities of aggregations. This ability is illustrated in the next section.

Illustrating the modelling of realistic cases with well-formed structures

In this section we show how different realistic cases can be described with well-formed structures.

Star and snowflake structures

We have a star or snowflake structure when :

-there is a unique fact type; -each dimension has a unique root; -each reference in the fact type points towards the root of a dimension. Our model does not differentiate star structures from snowflake structures. The difference will appear with the mapping towards the relational model (see section 7). The DWG of a starsnowflake structure is represented in figure 6. This representation is well-formed. Such a representation can be very useful to a user for formulating queries. Facts are clearly differentiated from members, reference to dimensions are shown explicitly, analysis criteria appear immediately.

We can illustrate on this structure several cuts as defined previously. For example (e 1 , e 2 , e 6 ) is a cut, also (e 1 , e 5 , e 6 ). So groupings on (e 1 , e 2 , e 6 ) or (e 1 , e 5 , e 6 ) are legal. But (e 3 , e 4 , e 5 ) or (e 2 , e 5 , e 6 ) are not cuts. So groupings on (e 3 , e 4 , e 5 ) or (e 2 , e 5 , e 6 ) are not legal.

It is clear that any subset of a cut is also a cut.

Fig. 6. The DWG of a star-snowflake structure

Constellation structure (sharing of a dimension)

The constellation structure appears when: -there are at least two different root types (each root acts as a fact type); -a fact type does not reference another fact type.

Note that in such a structure, there exists at least one element in the hierarchy which can be reached from the two roots.

Using the notion of DWG, figure 7 shows an example with the fact type manufacturing from figure 6 and a new fact type stock memorizing stock facts. Stock has a reference to the member town of the dimension factory. So, the dimension factory is shared partly between the two fact types. The two other dimensions are completely shared.

The DWG clearly shows how the two fact types can be exploited separately or simultaneously. We can explore the graph from one of its two roots and use it as a single rooted graph. We can also simultaneously exploit the two fact types. For example, to the node town, one can associate different aggregates from the stock occurrences and use them for the analysis of the manufacturing facts, or vice-versa. Fig. 7. The DWG for a constellation data warehouse

Facts of fact with a unique root

Sometimes one fact type, called primary fact type, can be characterized by several other fact types, called secondary fact types. Let us consider for example the case of a manufacturing of a product. It is characterized by primary fact attributes such as quantity, cost, ... . An instance of manufacturing is created each time a product is manufactured. A manufacturing is in fact composed of several operations on machines. Secondary fact attributes are associated to each operation such as the duration of the operation with a given machine. It is not adequate to memorize these secondary facts in the primary type (there is a many-to-many association between operations and manufacturing). One solution consists in placing them in a secondary fact type referencing the primary fact type. Our model caters for the description of such a solution. It consists in specifying two different fact types manufacturing and operation, and installing in operation a reference to manufacturing (figure 8). It should also be noted that operation has a normal reference to the root of the machine dimension. There is an instance of operation for each different operation in a manufacturing. Note that a serial number is used in the primary key of the operation type to mark the order of an operation in the sequence of a manufacturing. So an operation can occur several times in a manufacturing. The key of the operation type is composed of the operation name, the serial number, the manufacturing key. For example a welding operation can be associated to the manufacturing M100, a first time with serial number 2, and a second time with serial number 4. This means that this operation occurs in position 2 and in position 4 in the sequence of operations for the manufacturing M100. So two instances with respective keys (welding, 2, M100) and (welding, 4, M100) appear for the operation type. With this representation it is possible to analyze the duration of an operation by using the serial number (for example : what is the average ratio between the duration of a welding operation and the total duration of a manufacturing when the welding occurs in position 2) or not (for example : what is the average ratio between the duration of the welding operations and the total duration of a manufacturing).

For the secondary fact type, the primary fact type acts as a multi-dimension. So, all the dimensions of the primary type can be also used as dimensions of the secondary type. This clearly appears in the DWG of the global structure (figure 8). For example, quantity can be analyzed using the time and product dimensions and duration can be analyzed using machine dimension but also time and product dimensions. The operation fact can also be analyzed using manufacturing_key alone acting as a degenerated dimension. For example we can calculate the average duration of an operation per manufacturing. For the previous example we wish now to analyze the component parts which are needed for a manufacturing and which are necessary to buy in advance to suppliers outside the company. For a given manufacturing, several component parts are involved. We introduce so another secondary fact type component_part which references the manufacturing type. The measure attribute quantity of the component_part type can be so analyzed not only according to the component dimension (for example: which is the supplier who have supplied the largest number of component parts) but also according to manufacturing (for example: how much a manufacturing requires of component parts on average) and of the dimensions product and time (for example: total number of component parts which were furnished by a given supplier for each month in year 2005). 7 Mapping to the relational model One way to implement data warehouses is to use relational DBMS. So it is necessary to be able to map our well-formed structures in accordance with the relational model. In this section we provide a certain number of guidelines for this mapping. In the framework of [START_REF] Czarnecki | Classification of model transformation approaches[END_REF], our proposal is related to relational approaches.

Relational mapping with split dimension

This solution, which is straightforward, consists in mapping each type P i (fact type or member type) into a table T i . The key of P i becomes the primary key of T i . References between types are implemented via foreign keys. This solution offers a simple way to memorize precalculated aggregates by adding supplementary attributes in element types. Its drawback is well-known: navigating through the hierarchy necessitates many joins which can burden the performances. For a structure like the one described in figure 6, this solution leads to the relational snowflake data warehouse structure as represented below (primary keys are marked in bold, foreign keys in italics).

manufacturing(manufacturing_key, time_key, product_key, factory_key, quantity, cost_per_unit) time_root(time_key, A1$week_no, A1$month_no, …) week(week_no, year_no, …) month(month_no, year_no, …) year(year-no, …) product_root(product_key, category_no,…) category(category_no, family_name, …) family(family_name, …) factory_root(factory_key, town_name, …) town(town_name, region_name, ...) region(region_name, …)

Note that the two references in town for the first (and unique) alternative are marked with the special prefix A1$. If a second configuration of alternative paths would exist in the same dimension, we can use the special prefix A2$, and so on.

Relational mapping with regrouped dimensions

This solution is only possible when the DWG has a unique root. First the root type is mapped into a specific table. Then we create a number of tables equal to the number of references in the root type. All the elements which can be reached from one reference are grouped in the same table. For a structure like the one described in figure 6, this solution leads to the relational star data warehouse structure as represented below.

manufacturing(manufacturing_key, time_key, product_key, factory_key, quantity, cost_per_unit) time_root(time_key, …, A1$week_no, …, A1$month_no, …, year_no, …) product_root(product_key, …, category_no,…, family_name, …) factory_root(factory_key, …, town_name, …, region_name, …)

With this mapping the structure of the dimension hierarchies is not represented. It is embedded in the data.

Hybrid relational mapping

The previous mapping is not possible when an element can be reached from different roots. This is because this element acts as an entry and must be the key of a table in order to install the references correctly. The hybrid mapping thus consists in inserting each element entry into a specific table. Elements which are accessible only from one entry can be stored in the table of this entry. Others must be stored in separate tables.

For the structure of figure 7, this mapping gives the following tables :

manufacturing(manufacturing_key, time_key, product_key, factory_key, ..., town_name, quantity, cost_per_unit) stock(time_key, product_key, warehouse_key, ..., town_name, quantity) time_root(time_key, …) product_root(product_key, …) town(town_name,…, region_name, ...)

Note that the attributes of the element types factory_root, warehouse_root, region have been encapsulated into the tables manufacturing, stock, town respectively.

Performances of theses mappings

These various mappings do not offer the same performances as regards the execution of queries by the relational engine. The most efficient mapping is the one that requires a minimum of joins that is the second mapping. But this mapping, as we underlined it, does not explicitly represent relationships between the dimension members. It is more difficult for the end user to separate the legal groupings and the not legal groupings. The first mapping well represents these relations but it is the least efficient. In practice it will so be necessary to choose a hybrid mapping.

It is important to notice that almost every relational DBMS offer now functions to calculate the day, the month, the year from any date. As a consequence it is useless to represent the corresponding members in the time dimension which can be so considerably simplified. In a majority of cases the time dimension can be degenerated and represented only by an attribute of type DATE in the fact tables.

Automatic generation of theses mappings

Indeed the descriptions of the different types (facts and members) contain all the necessary information for generating the relational schema. It is not difficult to design an algorithm which ensures this generation. The problem is how to produce the descriptions of the different types from a DWG. We can imagine a software component with a graphical interface which permits a user to draw the DWG. This component must control at each step the properties and the constraints of the DWG and must verify that the structure is well-formed. It is this constituent which has to offer a function for generating the descriptions of the types. Such a constituent would be very useful to allow the users to be involved in the design of the data warehouse. But its elaboration is not so easy and represents a main objective of our future work.

Illustrating SQL queries on the relational forms of well-formed structures

In this section we show how the DWG can help the design of aggregation queries on the relational forms defined previously. This query corresponds to the cut represented in Figure 10 (edges of the cut are marked in bold). The DWG permits to identify immediately the different elements involved in the query (in grey in the figure). Note that we do not select the year element and the category element since the attributes we need are included as foreign keys in the week table and in the product_root table.

For the relational snowflake representation the corresponding SQL query is the following :

Select sum(quantity) from manufacturing m, time_root t, product_root p, time_root t, week w where m.time_key=t.time_key and m.product_key=p.product_key and t.A1$week_no=w.week_no and w.year_no=2004 group by t.A1$week_no, p.category.no;

For the relational star representation the query is slightly shorter (since the week table is embedded into the time_root table) :

Select sum(quantity) from manufacturing m, time_root t, product_root p where m.time_key=t.time_key and m.product_key=p.product_key and t.year_no=2004 group by t.A1$week_no, p.category_no;

Query 2 (using results analysis coming from another fact when a same dimension is shared)

For the data warehouse represented in Figure 7 we want to elaborate the total quantity of product 40 manufactured in the towns where there exists a stock greater than 200 for this product on the 12 December 2004.

Also in this case the DWG can be very useful to help in identifying the different elements involved in the query (see figure 11). We use the hybrid relational mapping of section 7 for expressing the SQL query. In a first step we elaborate the stock for the product 40 on the 12 December 2004 for each town and we incorporate the result in the corresponding town instance using a property attribute.

Towards an automatic generation of queries

The DWG can be used to support a graphic interface so as to allow a user to specify its aggregation queries. For a simple query, without filtering conditions, it is necessary to select the measure attribute and to indicate the cut (one saw in sections 6 and 8 how a cut of the DWG allows to specify the legal groupings). For a more complex query, with filtering conditions, it is necessary also to be able to specify graphically these conditions. From these graphic specifications one can rather easily design an algorithm which allows generating the SQL code of the query by taking into account the mapping which was used to generate the data base.

Conclusion

In this paper we propose a model which unifies the notion of fact and dimension member. This model can describe various data warehouse structures. It extends existing models for sharing dimensions and for representing relationships between facts. It allows for different entries in a dimension corresponding to different granularities. A dimension can also have several roots corresponding to different views and uses. It is possible to apprehend the concept of facts of fact which is very frequently encountered in the real world. Based on this model, the schema of the data warehouse is graphically represented through a graph called Data Warehouse Graph (DWG). Thanks to the DWG, we define the notion of well-formed data warehouse structures which guarantees desirable properties.

We have shown how well-formed structures can be mapped to the relational model in different ways. To represent the references we have used values of reference attributes. Instead, we can adopt an object-oriented model. Identifiers and references would then be represented through OIDs. This would make it possible to define mappings towards the object relational model.

We showed also how the DWG could be used to help in the specification of aggregation queries, by using notably the notion of cut in the graph. Moreover, the model which we propose allows queries which use aggregates resulting from various facts. For example it is possible to use an aggregate which results from a fact table F1 to filter aggregates resulting from another fact table F2.

The DWG can also be very helpful for the design of a data warehouse. An end user can easily express his decision-making needs by specifying with our model the multi-dimensional schema which seems the most appropriate. It is then possible to envisage automatic techniques to look for the compatibility of this schema with those from the available sources. The semantics problems can be solved by leaning on the techniques of the semantic Web. Incompatibilities will be solved through a dialogue between the user and the system. The schema being strengthened then definitively, it is possible to use approaches by materialized views (as in [START_REF] Theodoratos | View selection for designing the global Data Warehouse[END_REF]) to make the connection between the sources and the repository and to solve the problems of data refreshment.

We think that such facilities would permit an end user to handle himself the design and the manipulation of his data warehouse. In many domains there exist multiple needs for constructing a data warehouse and for extracting knowledge from the data. With our approach end users have the opportunity to be freed from the technical constraints.

We think that our model can be enriched in different ways. We are investigating extensions to allow specializations in dimensions ( [START_REF] Lechtenbôrger | Multidimensional Normal Forms for Data Warehouse Design[END_REF], [START_REF] Mansmann | Extending Visual OLAP for Handling Irregular Dimensional Hierarchies[END_REF]) and to handle so the cases of null values. We envisage also the possibility for defining a reflexive relation on a member type in order to take into account the hierarchies of data of various levels. Handling mixed-granularity hierarchies ( [START_REF] Mansmann | Extending Visual OLAP for Handling Irregular Dimensional Hierarchies[END_REF]) is another important extension we have in project. In all cases it would be necessary to fit out the relational mappings in order to propose adequate representations which can be exploited with the relational engine.

Other extensions are less immediate because they suppose to introduce specific operations through an algebra. For example for the extension in the treatment of qualitative data as in [START_REF] Huang | Models of multi-dimensional analysis for qualitative data and its application[END_REF], it would be necessary to introduce operations to scan efficiently the selected data. The situation is the same for the dynamic treatment of data for which it is a question of tracking down the changes which occurred during a time interval.

As far as our model permits to exploit simultaneously data stemming from several cubes, it would be also interesting to think about operations which allow to get back an aggregate of a cube to use it in another cube (in a condition of filtering for example as in section 8.2). For this purpose, the relational mapping could be adapted to allow the materialization of aggregates, either in the tables of the dimension members, or by using materialized views. This last solution would be doubtless more interesting because it could exploit the well-known rewritings techniques of queries from views for generating efficient execution plans.

It would be also interesting to establish mappings for implementation on other OLAP engines. We think that our model can be used in various OLAP environments to help the design of data warehouses.

Fig. 1 .

 1 Fig. 1. Different types and data hierarchies in dimensions

Fig. 2 .Example 4 .

 24 Fig. 2.A graph of a dimension and its cover graph.

Example 7 .

 7 Using this model, the representation of the members of the dimension represented in figure 1(c) is the following: time_root[(M), (time_key), ((week_key, month_key)), ()] week[(M), (week_key), (year_key), (week_type)] month[(M), (month_key), (year_key), ()] year[(M), (year_key), (), (year_type)]

Fig. 4 .

 4 Fig. 4. Handling a many-to-many relationship in a dimension

  element_name[(T), (element_key), (list_of_references), (list_of_specific_attributes)]

  ),(category_no), …] manufacturing[(F), (manufacturing_key), (time_key, product_key, factory_key), (quantity, cost_per_unit)] month[(M), (month_no),...]

  F), (time_key, product_key, warehouse_key), (time_key, product_key, warehouse_key), (quantity)] warehouse_root [(M),(warehouse_key), ....]

Fig. 8 .Fig. 9 .

 89 Fig. 8. Modelling facts of fact with a unique root

  time_root product_root operation[(F), (operation_name, serial_number, manufacturing_key), (machine_key, manufacturing_key), (duration)] machine_root[(M), (machine_key), …] manufacturing[(F), (manufacturing_key), (time_key, product_key), (quantity)] product_root time_root operation[(F), (operation_name, serial_number, manufacturing_key), (machine_key, manufacturing_key), (duration)] machine_root[(M), (machine_key), …] manufacturing[(F), (manufacturing_key), (time_key, product_key), (quantity)] component_part[(F), (component_key, manufacturing_key), (component_key, manufacturing_key), (quantity)] component_root[(M), (component_key), …] supplier[(M), (supplier_key), …]

Fig. 10 .8. 1

 101 Fig. 10. The marking of the DWG for illustrating Query 1

  ),(category_no), …] manufacturing[(F),(manufacturing_key), (time_key, product_key, factory_key), (quantity, cost_per_unit)] month[(M), (month_no),...]

Fig. 11 .

 11 Fig. 11. The marking of the DWG for illustrating Query 2

  In a second step, we can specify the final query by using the new attribute sum_stock in the town table.

	Select m.town_name, sum(quantity) from manufacturing m, town t
	where m.town_name=t.town_name and m.time_key= "12 December 2004"and
	m.product_no=40 and t.sum_stock>200
	group by m.tow_name;
	manufacturing[(F), (manufacturing_key),	stock[(F), (time_key, product_key,
	(time_key, product_key, factory_key), (quantity,	warehouse_key), (time_key, product_key,
	cost_per_unit)]		warehouse_key), (quantity)]
	time_root product_root	factory_root [(M), (factory_key),…]	warehouse_root [(M), (warehouse_key), ....]	time_root product_root
		town
		[(M), (town_name),…]
		region
		[(M), (region_name),...]
	Create view v(sum_stock, town_name) as
	select sum(quantity), town_name from stock
	where time_key= "12 December 2004"and product_no=40
	group by town_name;

Alter table town add (sum_stock number(6) default 0). Update town t set sum_stock=(select sum_stock from v where v.town_name=t.town_name);

Sales[(F), (ticket_number, product_key), (time_key, category_key, store_key), (price_per_unit, quantity)]

International Journal of Production Economics, Volume 112, Issue 1, March 2008, Pages 309-325 Elsevier, doi:10.1016/j.ijpe.2006.11.027

Acknowledgements

The author is grateful to the reviewers for their very useful and helpful comments.


Amiard Jc
email: alain.geffard@univ-reims.fr

BIOACCUMULATION OF METALS IN SEDIMENT ELUTRIATES AND THEIR EFFECTS ON GROWTH, CONDITION INDEX AND METALLOTHIONEIN CONTENTS OF OYSTER LARVAE

Keywords: Sediment elutriates, Crassostrea gigas larvae, Larval growth, Metal bioaccumulation, Metallothionein

The bioavailability of Cd, Cu, Zn and Pb from two metal-contaminated sediment (Bidassoa and Dunkerque) was studied using Crassostrea gigas larvae exposed to sediment elutriates. The metal contents within the sediments, the larvae and larval growth, the condition index, and the induction of metallothionein in the larvae were measured. The larval growth and condition index were only affected after exposure to the highest elutriate concentration (5 to 25%) from the most contaminated sediment (Dunkerque). Bioaccumulation of all metals was observed in larvae exposed to Dunkerque elutriatre and only Cu bioaccumulation was observed in the case of Bidassoa elutriate. The compilation of results from larvae exposed to both sediment elutriate show a strongly correlation between bioaccumulated metal considered individually or combined and metallothionein level in larvae presenting no detrimental effect.

In contrary, in the case of larvae exposed to the highest Dunkerque elutriate concentration and showing the highest metal body burdens, we observed a drop of the metallothionein level.

These results indicate that metallothionein is a more sensitive indicator of heavy metal pollution, compared to physiological endpoints taking into account in bioassays and could be proposed as precocious biomarker of metals exposure in larvae. However, it must be take care to the "fault control" due to toxicological effect on larvae metabolism in the case of important contaminant exposure.

INTRODUCTION

Marine and coastal areas are constantly subjected to the introduction of natural and anthropogenic pollutants, which are mostly adsorbed by suspended particles and subsequently accumulated in the sediments. Sediments can accumulate metals at concentrations 10,000 times higher than in the overlying water column [START_REF] Förstner | Metal pollution assessment from sediment analysis[END_REF], constituting an important source of contamination and risk for living organisms. Coastal and estuarine areas serve as reproductive and nursery grounds for many invertebrate and fish species and should be preserved.

Benthic and epibenthic species are the most exposed to contaminants of sedimentary origin, to those which are adsorbed on sedimentary particles as well as to those which are dissolved in interstitial water. Pelagic organisms are equally exposed to sediment-bound contaminants either via the food web and/or after the remobilization of contaminants into the sea water (Chapman and Long 1983[START_REF] Fichet | Experimental studies of impacts of harbour sediment resuspension on marine invertebrate larvae: Bioavailability of Cd, Cu, Pb and Zn and toxicity[END_REF][START_REF] Miller | An assessment of the contamination and toxicity of marine sediments in the Holy Loch, Scotland[END_REF]. The contamination of water column occurs by diffusion and when the sediments are resuspended by natural factors such as bioturbation (Burgess et al. 1993[START_REF] Peterson | Effects of bioturbation on metal-sulfide oxidation in surficial freshwater sediments[END_REF], Ciarelli et al. 1999[START_REF] Borgmann | Methods for assessing the toxicological significance of metals in aquatic ecosystems: bio-accumulation-toxicity relationships, water concentrations and sediment spiking approaches[END_REF], storms, wave and tide action and by human activities, such as dredging operations in particular (Chapman et al. 1998). When sediments are resuspended, the amounts of heavy metals, released into the sea water, are relatively low [START_REF] Kwan | Development of reference sediment samples for solid phase toxicity screening tests[END_REF]Dutka 1996, Van den berg et al. 2001) and do not generally induce short term toxicity. Long-term toxicity assessment of these low contamination levels requires development of sensitive and early warning biological tools. Elutriate tests allow to assess the toxicity of sedimentary metals released in water column when sediments are resuspended [START_REF] Thompson | Relationship between sediment contamination and toxicity in San Francisco Bay[END_REF].

Chemical analyses allow to characterize the contamination level of the medium (water or sediment), but they are inadequate to assess the biological quality of a studied zone. Only living systems are able to integrate the various complex effects of contaminants that are really bio-available (Chapman and Long 1983). Numerous bioassays, standardized to varying degrees, have been developed during the two last decades (see Review Burton 1992;[START_REF] His | The assessment of aquatic contamination: bioassays with bivalve embryos and larvae[END_REF]. Bivalve embryo is one of the most sensitive organisms and has been used in numerous environmental toxicology studies [START_REF] Taylor | A summary of the data on the toxicity of various materials to aquatic life[END_REF], Carr et al. 1996[START_REF] Mcpherson | Copper effects on potential sediment test organisms: the importance of appropriate sensitivity[END_REF]. Instead of the endpoints considered in bioassays, larval growth test is most difficult to perform but it is more sensitive (Geffard et al. 2002a) and allows to assess the bioavailability and toxicity of both soluble contaminant fraction and contaminants adsorbed on suspended particles (Geffard et al. 2002a).

Bioassays allow evaluating the toxicity of contaminants that are really bio-available and therefore constitute a useful tool to study the biological quality of estuaries and coastal areas.

However, physiological endpoints of these tests are not early-warning biological responses.

When deleterious effects are observed, the biological quality of the studied area is not good and the contamination levels have already marked and irreversible effects on living organisms. Moreover, bioassays do not allow identifying the compounds inducing the observed biological effects.

The bio-availability of contaminants depends on several factors such as physico-chemical properties of the contaminant itself, the characteristics of the environment and that of the organism used in the bioassay [START_REF] Borgmann | Methods for assessing the toxicological significance of metals in aquatic ecosystems: bio-accumulation-toxicity relationships, water concentrations and sediment spiking approaches[END_REF]. One of the recognized methods to assess the bio-availability of contaminants is to observe their accumulation in the test organisms. This method takes into account all factors that control their bioavailability [START_REF] Connell | Importance of Internal Biotic Concentrations in Risk evaluations with Aquatic Systems[END_REF][START_REF] Borgmann | Methods for assessing the toxicological significance of metals in aquatic ecosystems: bio-accumulation-toxicity relationships, water concentrations and sediment spiking approaches[END_REF]. Recently, for several compounds, some authors have determined critical body burden concentrations above which biological effects could be observed. However, this approach cannot be used with essential metals (Cu, Zn) and metabolized compounds such as PAHs.

Biomarkers could also be used to study the bio-availability of contaminants, such as metallothionein for metal exposures. Many studies have shown that metallothionein, a lowmolecular-weight cytosolic protein, is induced by metal contamination in numerous taxa, including mammals, fish [START_REF] Hamza-Chaffai | Metallothionein-like protein: it is an efficient biomarker of metal contamination? A case study based on fish from the Tunisian coast[END_REF]) and marine invertebrates [START_REF] Bebianno | Comparison of metallothionein induction in response to cadmium in the gills of the bivalve molluscs Mytilus galloprovincialis and Ruditapes decussates[END_REF][START_REF] Bebianno | Metallothioneins in the clam Ruditapes decussatus: an overview[END_REF][START_REF] Mouneyrac | Metallothionein-like proteins in Macoma balthica : effects of metal exposure and naturals factors[END_REF], 2002). It is generally admitted that the primary role of metallothionein is the homeostasis of essential metals such as Cu and Zn, but this protein is also involved in the detoxification of non-essential metals such as Ag, Cd and Hg (Roesijadi 1992[START_REF] Amiard | Metallothioneins in aquatic invertebrates : their role in metal detoxication and their use as biomarkers[END_REF]. Metallothionein-like protein has also been detected in bivalve larvae of Mytilus galloprovincialis [START_REF] Pavicic | Embryo-larval tolerance of Mytilus galloprovincialis, exposed to elevated seawater metal concentrations-1. Toxic effects of Cd, Zn and Hg in relation to the metallothionein level[END_REF] and Crassostrea virginica [START_REF] Ringwood | Expression of constitutive and metal-inducible metallothioneins in oyster embryos (Crassostrea virginica)[END_REF][START_REF]Surveillance du milieu marin. Travaux du R.N.O, IFREMER, Edition 1995 Roesijadi G[END_REF][START_REF] Roesijadi | Concentration-response relationships for Cd, Cu, and Zn and metallothionein mRNA induction in larvae of Crassostrea virginica[END_REF]). However, the inductions are observed for studies using metallic salts and experimental doses unrealistic compared to environmental concentrations present even in metal-rich areas. More recently, metallothionein-like protein induction was detected in veligers of M. galloprovincialis exposed to natural contaminated sediment (Geffard et al. 2002c). However, these authors used freeze-dried sediment known to be more toxic than the fresh sediment (Geffard et al. 2002b[START_REF] Geffard | Effects of storage method and duration on the toxicity of marine sediments to embryos of oyters Crassostrea gigas[END_REF].

The aim of this study was to use the larval growth test and the metallothionein concentration as a sensitive and early warning tool to assess the bioavailability and the toxicity of metals released into the water column when sediments are re-suspended. For this, fertilized eggs and larvae of Crassostrea gigas were exposed to elutriate obtained from natural sediments. Two metal rich sediments have been selected, one from a coastal zone (Bidassoa Estuary, French-Spanish border) and the second from the port of Dunkerque (North of France). The final aim of this study was to establish links between biochemical response (metallothionein), metal accumulation, larval growth and the condition index of larvae.

Materials and Methods.

Sampling and conservation of sediment.

Sediments were sampled in July 1999. At the Bidassoa estuary, only the top 2 cm of the surface were scraped using a plastic blade. Sediments from the port of Dunkerque were collected with a stainless steel Van Veen grab. All sediments were wet-sieved at 2 mm to eliminate debris, homogenized and stored in glass bottles at 4°C in darkness for less than one week prior to bioassays.

Elutriate preparation.

Elutriates were prepared using a modification of Melzian's method (1990). Sediments were shaken mechanically (multi-wirst shaker, 500 rpm) in filtered seawater (FSW) at a ratio of 1:4 (sediment: water) for 8 h and allowed to settle for another 8 h before recovery of the supernatant (elutriate). Elutriate was diluted with FSW to concentrations of 0 (control), 5, 10, 25 and 50% for Bidassoa and 0 (control), 1, 5, 10 and 25% for Dunkerque. These concentrations have been selected because they do not previously induced abnormal effects on the embryonic development of Crassostrea gigas. The maximum concentrations tested correspond to the No Observed Effect Concentrations (NOEC; Geffard et al. 2002b).

Larval rearing.

Mature oysters were collected in Arcachon Bay (French) which is extensively used for oysters farming based on Pacific oysters Crassostrea gigas and was thus assumed to have a good 'biological quality' (Geffard et al. 2002b). The procedure to obtain embryos was described in detail by Geffard et al (2001aGeffard et al ( , 2002c)). Fertilized eggs were counted and placed in 2-liter bakers (60,000 l -1 ) filled with the different media to be tested (3 replications per treatment).

After the first 24 h, veligers maintained in rearing status were placed in 2-liter beakers (10,000 larvae l -1 , 3 replications) and fed with Isochrysis galbana (150 algae µl -1 ). All experimental solutions were renewed at 48-h intervals, using elutriates prepared some hours before. At this time, larvae were photographed with a Canon camera fitted to an inverted microscope and larval height of 50 individuals per replicate (distance between the umbo and the ventral valve margin, Galtsoff 1964) was measured. The growth test was stopped after 10 days for Bidassoa elutriate. On contrary, Dunkerque elutriate had severe effects on C. gigas growth, so much so that experiments were respectively stopped on day 5 for the highest concentration and on day 7 for another. At the end, larvae were recovered through a sieve (32µm), rinsed with 0.9% aqueous ammonium formiate (to eliminate the salt), freeze-dried, weighed and stored at 4° C in hermetic bag before being used for analysis. Condition index (CI) of larvae from each replicate was determined using the following equation: Aliquots (3 replicates of 0.5 g) of each fresh sediment were taken from the well-homogenized total sample and placed in acid-washed glass tubes. These samples were then dried and weighed to determine metal concentration as a function of dry weight. Hot mineralisation (95°C) was performed by addition of 5 ml of HNO 3 and 3 ml of HCl. This process was conducted until dryness, and the residues were then suspended again in 10 ml of 1N HCl for metal analysis.

Extraction of metals and metallothionein from larvae. Geffard et al (2002c) descrived the process for tissular compartmentalization of metals and partial purification of metallothionein. Each replication of lyophilized larvae was homogenized in Tris-NaCl buffer and the Cytosolic (S1) and insoluble (P1) fractions were separated by initial centrifugation (25,000 g, 55 min at 4°C). The insoluble fraction is constituted by all cellular and tissular debris plus shells of larvae. Metallothionein was isolated from an aliquot (50µl) of the S1 fraction by a second centrifugation (15,000g, 10 min at 4°C) after being subjected to heat (75°C, 15 min). This second supernatant (S2) containing metallothionein was frozen at -80°C prior to be used for metallothionein analysis. Before metal analysis, an acid digestion step was required for soluble (S1) and insoluble (P1) fractions, using a procedure described in Geffard et al (2002c). After acid digestion, the solution obtained were supplemented to a known volume (2 ml) with deionised water. The three replications of each exposure condition were treated separately with the exception of the larvae exposed to 5, 10 and 25% of Dunkerque elutriate, where larval growth and the weight of larvae was low. The three replicate samples were mixed together to prevent problems of sensitivity related to the analytical tools.

Metal assays.

Following the acid digestion phase (for sediment and cytosolic (S1) and insoluble (P1) fraction of larvae), metals were analyzed by flame atomic absorption spectrophotometry (AAS) for Cu in sediment and Zn in sediment and larvae fraction. We used electrothermal AAS with Zeeman effect (Hitachi Z8200) for Cu in larvae fractions and for Cd and Pb in larvae fractions and sediment. The analytical method was previously described by [START_REF] Amiard | Application de la spectrométrie d'absorption atomique Zeeman aux dosages de huit éléments traces (Ag, Cd, Cr, Cu, Mn, Ni, Pb et Se) dans les matrices biologiques solides[END_REF]. To eliminate matrix effect, standard addition analysis was performed in an isomedium, and the concentration of each element were +125, 250 and 500 ng ml -1 for Zn and Cu in flame AAS and +12.5, 25 and 50 ng ml -1 for Cu, +0.25, 0.50 and 1 ng ml -1 for Cd and 6.25, 12.5 and 25 for Pb in electrothermal AAS. The assays were validated using certified samples of sediments (SD-M-2/TM IAEA) and mussel tissues (BCR, 278R). The total bioaccumulation of metals (Cd, Cu, Zn and Pb) in larvae was calculated by summing up the amounts that were measured in the soluble (S1) and insoluble (P1) fractions.

Assay of larval metallothionein.

The metallothionein assay was performed in the S2 fraction by differential pulse polarography. The thiol groups (SH) were determined using Brdicka reagent (1933) according to the method of [START_REF] Thompson | An improved electrochemical method for the quantification of metallothionein in marine organisms[END_REF]. Measurements were performed at a constant temperature (4°C) on a polarograph using a PAR Model 174 analyser, a PAR/EG&G Model 303 electrode in SMDE mode, and a RE0089 type X-Y reorder. The metallothionein amounts measured were determined by a standard addition using metallothionein rabbit liver metallothionein standard (Sigma Chemical Co., St Louis, MO, USA) (no metallothionein standard exists for oysters). The validity of this method was confirmed by [START_REF] Olafson | Electrochemical detection of metallothionein[END_REF].

Statistical analysis.

For each series of results, the comparison of values was tested by one-way ANOVA (Statistica software). Significant differences (at the 95% level) were then determined by Tukey's test, except for larvae exposed to 5, 10 and 25% of Dunkerque elutriate because there were only one value per tested elutriate concentration.

Results.

Sediment contamination

Metal concentrations in each sample of studied sediments are indicated in the Table 1. For comparison, Table 2 gives the French Géode classification system, which defines sediment quality according to the degree of contamination with PCBs and eight metals (Lamy 1996).

"Géode background" denotes the natural concentrations, and "Géode median" is calculated from the samples taken at various ports in France. Sediments having values lower than double the median (termed "level 1") are allowed to be dumped offshore. Sediments having values higher than four times the median (termed "level 2") should not be dumped offshore.

Sediments with intermediate values require further analyses, including bioassays, before a decision is taken. Dunkerque sediments were more highly contaminated than the Bidassoa ones. In the sediments from Dunkerque, Cd and Zn levels and Cu and Pb levels respectively surpassed the level 1 and level 2. Bidassoa sediments were characterized by a Cu contamination with value higher than the level 1.

Larval biometry

Condition index (CI) of larvae exposed to Bidassoa elutriate was not significantly different depending on the exposure (p = 0.274; Table 3). For Dunkerque, the CI significantly (p = 0.000064) decreases between the control and the lowest concentration (1% elutriate). The CI of larvae exposed between 5 and 10% of elutriate was lower than of the CI of controlled ones.

The CI of larvae exposed to 25% of Dunkerque elutriate was not indicated because the recovered larvae were only 5 days old.

Bidassoa elutriate induces a weak inhibition of the larval growth at the highest concentrations and on day 10 (Fig. 1), but the difference with the control value was not significant (p = 0.07).

On the contrary, Dunkerque elutriate had deleterious effects on C. gigas growth (Fig. 1). The growth of larvae reared in 25% of elutriate was significantly reduced (p = 0.0003) from day 3 to the end of the experiment. The same phenomenon occurred at the all concentrations on day 5 (p < 0.0006).

Metallothionein concentrations

For Bidassoa elutriate, metallothionein contents in larvae significantly increase (p = 0.0001) for a concentration higher than 5 %. Metallothionein values ranged from 864 mg kg -1 for controls to 1,430 mg kg -1 in larvae exposed to 50% of elutriate (Fig. 2). The concentration ratio of exposed to control larvae ranged from 1.2 to 1.7 depending on the degree of contamination. For Dunkerque elutriate (Fig. 2), metallothionein concentration significantly increased between the control and the concentration attaining 1 % elutriate (p < 0.05), while the concentration rapidly decreased for the highest concentrations. The significant decrease of metallothionein between the control and concentration of 5, 10 and 25 could not be tested because of the lack of replicates. However, metallothionein concentrations in larvae exposed to 5, 10 and 25 % elutriate were three or four times lower than those observed in larvae reared in control sea water and 1 % elutriate. Metallothionein concentration in 7 day-old control larvae (Dunkerque experiment) were significantly lower (p < 0.0001) than this in 10 days-old control larvae (Bidassoa experiment).

Metal bioaccumulation

Metal levels of larvae reared in the presence of the different elutriates were showed in figure 3. For the Bidassoa elutriate, no significant (0.108 < p < 0.9938) bio-accumulations of Cd, Zn and Pb was observed in larvae. Only Cu levels significantly (p = 0.0001) increased for elutriate concentration higher than 5%. The Cu concentration ratio of exposed to control larvae ranged from 1.1 to 1.8 depending on the degree of contamination. Larvae exposed to Dunkerque elutriate show contamination levels higher than those exposed to Bidassoa (except in Zn). Cd and Cu concentrations increased according to the elutriate concentration. However, the lack of replicates did not allow to test if this increase is significant. With Zn and Pb, significant (p < 0.108) accumulations were observed for the lowest tested concentration (1 %). The concentration ratio of exposed to control larvae were ranged from 1.6 and 2 for the Zn and from 2 to 20 for the Pb.

Cytosolic fractions showed similar contamination patterns than those previously observed in raw organism (Fig. 4), except for the Cd at the highest concentration of Bidassoa elutriate, where the accumulation was significant and for the Pb with the Dunkerque elutriate where accumulation was not observed.

Metallothionein is a cytosolic heat-stable protein. Consequently it should be preferable to examine the relationship between metal and metallothionein levels, taking into account metal concentrations in the supernatant S2 obtained after heat denaturation of the cytosol.

(However, the fate of metals during heating is a matter of question, since metal analysis of chromatographic fractions obtained from raw cytosol (S1) and heat-denaturated cytosol (S2) revealed differences in metal binding to cytosol ligands [START_REF] Bragigand | Some methodological aspects of metallothionein evaluation[END_REF]).

Consequently, relationships between metallothionein and S1 metal concentrations were studied. As all studied elements could be binding to metallothionein and might therefore contribute concomitantly to metallothionein induction, the relationship between metallothionein and metal levels (S1) was examined taking into account the metals individually or combined. For relationship, all data were taking into account except with the highest elutriates concentration from Dunkerque (5, 10 and 25%) (Fig. 5), where deleterious effects are noticed (growth inhibition). Positive and significant relationships were observed for Cu, Zn and for all combined elements.

From a biomonitoring point of view and aiming to use metallothionein as a biomarker of metal contamination, metallothionein has to reflect the gross metallic concentration. Thus relationship between total metal (S1+P1) and metallothionein levels was equally examined.

Results were similar than those previously observed with cytosolic metal concentrations.

Relationships between metal and metallothionein concentrations were significant for the Cu and Zn and in the case of all elements combined (not shown).

Discussion

According to Geffard et al. (2002a), Bidassoa and Dunkerque sediments are heavily contaminated by metals. In comparison with the French Géode classification system, Dunkerque sediment is characterized by a Cu and Pb contamination and is more contaminated than the Bidassoa one which is only Cu-enriched. Dunkerque sediments are equally highly contaminated by polycyclic aromatic hydrocarbons (Geffard et al. 2002b).

Physical and chemical characteristics of the Bidassoa and Dunkerque elutriates have been

shown in a previous paper (Geffard et al. 2002a). The metal contamination of the controlled sea water was in the same range of magnitude as the metal levels observed in waters from uncontaminated areas (Campanella et al. 2001, Prego and[START_REF] Prego | Cadmium, copper and lead contamination of the seawater column on the Prestige Shipwreck (NE Atlantic Ocean)[END_REF] and lower than those of the Gulf of Gaeta, Tyrrhenian Sea (central Italy), known to be slowly contaminated (Conti and Cecchetti 2003). Metal contents of the Bidassoa and Dunkerque elutriates were approximately 10 times more concentrated than the controlled seawater, with values in the same range of magnitude as metal contaminations currently observed in impacted coastal and estuary areas (RNO 1995[START_REF] Martino | Resuspension, reactivity and recycling of trace metals in the Mersey Estuary, UK[END_REF]. Cu levels in Bidassoa and Dunkerque elutriates exceeded environmental quality standard [START_REF] Matthiessen | Sources and Potential Effects of Copper and Zinc Concentrations in the Estuarine Waters of Essex and Suffolk, United Kingdom[END_REF].

According to [START_REF] Slotten | Heavy metals in intact and resuspended sediments of a Califronia reservoir, with emphasis on potential bioavailability of copper and zinc[END_REF] and [START_REF] Van Den Berg | Dredgingrelated mobilisation of trace metals: a case study in the Netherlands[END_REF], these results showed that resuspending sediments induce an increase of the total seawater metal contamination.

Bio-availability of contaminants may be determined using bio-accumulation test. With Bidassoa elutriates, only the copper was bio-available and accumulated by the larvae. For Dunkerque, all studied metals were bio-available and accumulated by larvae. These results are in agreement with metal contamination levels of these sediments. However, highest metal contaminations (difference between control and exposed larvae) were observed in larvae exposed to the Dunkerque elutriates, whereas the contamination level of the highest tested concentration (25 %, that is to say 0.019µg Cd.l -1 , 1.78µg Cu.l -1 , 6.88µg Zn.l -1 and 3.6 µg Pb.l -1 , estimated according metals concentration in raw elutriate published in Geffard et al. 2002a) was lower than the level of Bidassoa elutriates (50 %, 0.054µg Cd.l -1 , 5.65µg Cu.l -1 , 13.65µg Zn.l -1 and 4.5µg Pb.l -1 ). These observations show that bio-availability of metals from the Dunkerque elutriates was higher than those from Bidassoa one (Geffard et al., 2002a).

According to [START_REF] Fichet | Experimental studies of impacts of harbour sediment resuspension on marine invertebrate larvae: Bioavailability of Cd, Cu, Pb and Zn and toxicity[END_REF] and Geffard et al. (2002a) parts of the heavy metals released in the water, when sediments are suspended again, and / or are bio-available, could be accumulated and toxic. According to [START_REF] Borgmann | Methods for assessing the toxicological significance of metals in aquatic ecosystems: bio-accumulation-toxicity relationships, water concentrations and sediment spiking approaches[END_REF], contamination level in larvae is a better indicator of potential biological impact than the contamination levels of medium.

In our previous study (Geffard et al. 2002a), no observed concentration effect of Bidassoa and Dunkerque elutriates on C. gigas embryogenesis was respectively 50 and 25 %. Bidassoa elutriate concentration of 50 % did not induce deleterious effects on the growth and condition index of larvae, after 10 day exposure. On the contrary, with Dunkerque elutriate larval growth test was highly more sensitive than the embryotoxicity test. Growth and CI inhibition were observed at the lowest elutriate concentration (1%). These results are in accord to those of [START_REF] His | The assessment of aquatic contamination: bioassays with bivalve embryos and larvae[END_REF] who found that larval growth is the most sensitive life stage in this organism. The decrease of CI indicates that in exposed larvae, the inhibition of weight was more important than the inhibition of the height. CI constitutes an interesting and early warning marker of contaminant effects on larvae. These observations show that released sediment-bound contaminants may affect physiology and metabolism of oyster larvae. The resuspending of sediments constitutes really a risk for pelagic species.

Larval growth test in C. gigas is a sensitive bioassay and allows to assess the toxicity of bioavailable contaminants, constituting a useful tool to study the biological quality of sediments. However, they do not allow identifying the compounds inducing the observed biological effects.

Metallothionein level in larvae exposed to Bidassoa elutriates increased with increasing degree of contamination. Metallothionein is thought to be produced in response to increased intracellular levels of free metal to prevent or reverse potentially detrimental, non specific binding of metals to other ligands [START_REF] Roesijadi | Cadmium-induced metallothionein expression during embryonic and early larval development of the mollusc Crassostrea virginica[END_REF]. These observations confirm that released metals from Bidassoa sediment were really bio-available. Ringwood andBrower (1993, 1995) and [START_REF] Roesijadi | Cadmium-induced metallothionein expression during embryonic and early larval development of the mollusc Crassostrea virginica[END_REF] have also showed metallothionein inductions in C. gigas larvae exposed to metallic salts under laboratory conditions. However, they found that first induction occurred at a Cd concentration of 0.6 µg.l -1 , which is 30 fold higher than the Bidassoa elutriate concentrations of 10 % (0.018µg Cd.l -1 ) that carry out a significant metallothionein induction in this study. The precocity of metallothionein response to metals bioaccumulation, according to the degree of exposure, compared to the responses of other physiological endpoints taken into account in this study (growth and CI) authorize to define a scale of sensitivity of biological and biochemical responses in C. gigas larvae:

Metallothionein>larval growth = CI>abnormal embryogenesis

Similar observations were made by several authors in an other species of bivalve, Mytilus galloprovincialis [START_REF] Pavicic | Embryo-larval tolerance of Mytilus galloprovincialis, exposed to elevated seawater metal concentrations-1. Toxic effects of Cd, Zn and Hg in relation to the metallothionein level[END_REF], Geffard et al. 2002c).

For Dunkerque elutriates, metallothionein levels slowly increased between the control and the elutriate concentration of 1%, and then highly decreased. These observations could be explained by the poor physiological state of larvae (condition index and growth lower than controls). These results are good examples of a situation which have previously been mentioned as 'spillover' (Brown and Parsons 1978). This is the saturation of detoxification mechanisms, carrying out the first harmful effects. This phenomenon has been described in several species in laboratory, the fish Pleuronecta platessa (Georges and Olsson 1994), copepods, Tigriopus brevicornis [START_REF] Barka | Influence of different essential and non-essential metals on MTLP levels in the copepod Tigriopus brevicornis[END_REF]) and bivalve larvae Mytilus galloprovincialis (Geffard et al. 2002c).

According to the previous results and the good relationships observed between the most bioaccumulated metals (Cu and Zn) and metallothionein concentrations indicated that metallothionein level reflect : 1 -the cytosolic metal charge was the most toxicologically important [START_REF] Wallace | Subcellular compartmentalization of Cd and Zn in two bivalves. I. Significance of metal-sensitive fractions (MSF) and biologically detoxified metal (BDM)[END_REF] , 2 -the gross metallic concentrations (S1+P1) suggested the possible use as metal exposure biomarker. The absence of relationship between metallothionein and cadmium concentrations could be explained by the very low bioaccumulation of this metal by larvae. Concerning the lead, the total bio-accumulated metal due to the elutriate exposure was found in the insoluble fraction (P1), suggesting a poor implication of metallothionein in the detoxification of this element and equally a low induction of metallothionein synthesis by lead. As shown with other species (Mytilus edulis larvae, Geffard et al. 2002c) oyster larvae could be used as biological matrix to determined metallothionein as biomarker of metallic pollution. The highest advantage to use the larvae stage of bivalve as biological matrix compared to adult stage, is due to the higher sensitivity of this stage to different contaminants family [START_REF] His | The assessment of aquatic contamination: bioassays with bivalve embryos and larvae[END_REF]. The potential use of the determination of metallothionein as biomarker in bivalve larvae in biomonitoring programs could be realised during in situ tests as developed by Geffard et al (2001b).

Larvae exposed to the highest Dunkerque elutriate concentrations (5, 10 and 25%) had the highest metal body burden and corresponded to the lowest metallothionein level. These individuals constitute "fault controls" not due at low contaminants levels exposure, but inversely at very high contaminants level exposure, which induce detrimental effects and the phenomenon of spill over as described above. In biomonitoring programs, in order to avoid these fault controls, it is important to use several biochemical biomarkers more or less specific to a contaminants family as proposed by several authors [START_REF] Narbonne | Scale of classification based on biochemical markers in mussels: application to pollution monitoring in European coasts[END_REF][START_REF] Lafontaine De | Biomarkers in zebra mussels (Dreissena polymorpha) for the assessment and monitoring of water quality of the St Lawrence River (Canada)[END_REF], Cajaraville et al. 2000) including easily measurable global physiological markers as condition index.

These results showed that Dunkerque sediments constitute a biological hazard when they are suspended again (example: dredging). Moreover the present study, using metal concentrations similar to those found in the natural environments, showed an early (low-dose) metallothionein response as compared to the time that abnormalities appeared. Thus, the determination of metallothionein in oyster larvae could be use as biomarker of metal exposure, which represents an important ecological factor because the successful breeding is necessary to maintain the population. Brown DA, Parsons TR (1978)

List of tables

Table 1: Heavy metals (mean µg g -1 dry weight ± SD) contents of Dunkerque and Bidassoa sediments.

Table 2: French "Géode" classification of sediment quality (Md = median of metal concentrations µg g -1 dry weight).

  of sediments for metal analysis.

  Figure captions

Figure 1 :

 1 Figure 1: Growth (µm; mean ± SD) of Crassostrea gigas larvae exposed to Bidassoa (A) and

Figure 2 :

 2 Figure 2: Metallothionein contents (mean ± SD, n = 3) in larvae after ten days (Bidassoa,

Figure 3 .

 3 Figure 3. Total metal concentrations (mean ± SD, three replications) in larvae after ten days

Figure 4 .

 4 Figure 4. Cytosolic metal concentrations (mean ± SD, three replications) in larvae after ten

Figure 5 .

 5 Figure 5. Relationships between cytosolic (S1) metal (individual or combined) and MT

Figure 1 Figure 2 Figure 3 Figure 4 :Figure 5

 12345 Figure 1 Growth (µm; mean ± SD) of Crassostrea gigas larvae exposed to Bidassoa (A) and

Table 3 .

 3 Condition index (CI, mean; ± SD between bracket)of larvae recovered after 10 (Bidassoa) or 7 (Dunkerque) days of rearing in medium containing different percentage of elutriate. No CI was calculate in the case of 25% of Dunkerque elutriate because rearing was stopped after 5 days. * indicate a significant difference at 95% level of the CI compare to the control (0%) for each sediment tested

Table 1 .

 1 Heavy metals (mean µg g -1 dry weight ± SD) contents of Dunkerque and Bidassoa sediments.

	Site	Cd	Cu	Zn	Pb
	Dunkerque	2.2 (0.05)	158 (10)	542 (36)	391 (24)
	Bidassoa	0.8 (0.1)	70 (11)	268 (31)	74 (9)

Table 2 .

 2 French "Géode" classification of sediment quality (Md = median of metal concentrations µg g -1 dry weight).

		PCB a	As Cd Cr Cu Hg Ni Pb Zn
	Géode background	0	4.4 0.5 45 35 0.2 20 47 115
	Géode median	0.00025 12.5 0.6 45 22.5 0.2 18.5 50 138
	a PCB = polychlorinated biphenyl

Table 3 .

 3 Condition index (CI, mean; ± SD between bracket)of larvae recovered after 10 (Bidassoa) or 7 (Dunkerque) days of rearing in medium containing different percentage of elutriate. No CI was calculate in the case of 25% of Dunkerque elutriate because rearing was stopped after 5 days. * indicate a significant difference at 95% level of the CI compare to the

	control (0%) for each sediment tested
	Site	Parameter	0%	1%	5%	10%	25%	50%
	Bidassoa	CI	0.52		0.68	0.44	0.50	0.46
	(Day 10)		(0.10)		(0.09)	(0.31)	(0.17)	(0.08)
	Dunkerque	CI	0.39	0.24*	0.16*	0.23*	/
	(Day 7)		(0.006)	(0.02)	(0.0008)	(0.006)