Hadj Mahboubi
email: hmahboubi@eric.univ-lyon2.fr

Kamel Aouiche
email: kaouiche@eric.univ-lyon2.fr

Jérôme Darmont
email: jdarmont@eric.univ-lyon2.fr

Materialized View Selection by Query Clustering in XML Data Warehouses

Keywords: Materialized views, XML, Data warehouses, Clustering, Complex data

XML data warehouses form an interesting basis for decision-support applications that exploit complex data. However, native XML database management systems currently bear limited performances and it is necessary to design strategies to optimize them. In this paper, we propose an automatic strategy for the selection of XML materialized views that exploit a data mining technique, more precisely the clustering of the query workload. To validate our strategy, we implemented an XML warehouse modeled along the XCube specifications. We executed a workload of XQuery decision-support queries on this warehouse, with and without using our strategy. Our experimental results demonstrate its efficiency, even when queries are complex.

Introduction

Decision support applications nowadays exploit heterogeneous data from various sources. Furthermore, the development of the Web and the proliferation of multimedia documents contributed to the analysis of so-called complex data [START_REF] Darmont | An architecture framework for complex data warehouses[END_REF]. For instance, analyzing medical data may lead to exploit jointly information under various forms: patient records (classical database), medical history (text), radiographies, echographies (multimedia documents), physician diagnoses (texts or audio recordings), etc.

In this context, we have used XML in the process of integrating and warehousing complex data for analysis [START_REF] Darmont | Web multiform data structuring for warehousing[END_REF]. However, decision-support queries are generally complex because they involve several join and aggregation operations. In addition, native XML database management systems (DBMSs) present poor performances when the volume of data is very large and the queries are complex. Thus, it is crucial to design XML data warehouses that guarantee the best performance when accessing data. Indexing and view materialization are the most frequently used optimization techniques for this sake [START_REF] Gupta | A report on XML data indexing techniques[END_REF].

Materialized views are physical structures that improve data access time by precomputing intermediary query results. Then, end-user queries can be processed efficiently from the data stored within these views and do not need access the original data any more. Nevertheless, the use of materialized views requires additional storage space and induces some refreshing process overhead. So it is crucial to select only pertinent views.

In the context of relational data warehouses, several studies have been proposed to resolve the materialized view selection problem [START_REF] Agrawal | Automated selection of materialized views and indexes in SQL databases[END_REF][START_REF] Baralis | Materialized views selection in a multidimensional database[END_REF][START_REF] Baril | Selection of materialized views: a cost-based approach[END_REF][START_REF] Gupta | Selection of views to materialize in a data warehouse[END_REF][START_REF] Gupta | Selection of views to materialize in a data warehouse[END_REF][START_REF] Harinarayan | Implementing data cubes efficiently[END_REF][START_REF] Nadeau | Achieving scalability in OLAP materialized view selection[END_REF][START_REF] Shukla | Materialized view selection for multicube data models[END_REF][START_REF] Smith | A wavelet framework for adapting data cube views for OLAP[END_REF][START_REF] Uchiyama | A progressive view materialization algorithm[END_REF][START_REF] Valluri | View relevance driven materialized view selection in data warehousing environment[END_REF][START_REF] Zhang | An evolutionary approach to materialized view selection in a data warehouse environment[END_REF]. The views that are relevant to materialize are selected to minimize the processing time of a given workload. This optimization is achieved under maintenance cost or storage space constraints [START_REF] Kotidis | Dynamat: A dynamic view management system for data warehouses[END_REF]. The existing studies differ in several points:

1. the way of determining candidate views; 2. the framework used to capture relationships between candidate views; 3. the use of mathematical cost models vs. calls to the query optimizer; They syntactically analyze the workload to enumerate the relevant candidate views [START_REF] Agrawal | Automated selection of materialized views and indexes in SQL databases[END_REF]. By calling the query optimizer, they greedily build a configuration of the most pertinent views. A materialized view selection based on clustering has also been proposed [START_REF] Aouiche | Selection of views to materialize based on query clustering[END_REF]. This proposal exploits query clustering to determine a set of candidate views and cost models to choose pertinent views to materialize.

To the best of our knowledge, no such view materialization approach exists in XML databases and XML data warehouses in particular. Hence, we propose in this paper an adaptation of the query clustering-based relational view selection approach [START_REF] Aouiche | Selection of views to materialize based on query clustering[END_REF] to the XML context. Our approach clusters XQuery queries (instead of SQL queries) and builds candidate XML views that can resolve multiple similar queries belonging to the same cluster. New XML-specific cost models are used to define the XML views that are pertinent to materialize. To validate our proposal, we implemented an XML data warehouse in a native XML DBMS. It is indeed interesting to check whether native XML DBMSs could someday be able to compete with XML-compatible, relational DBMSs. Then, we measured the execution time of a decision-support query workload with and without using our strategy. Our experimental results show that the use of our strategy greatly improves query performance.

The remainder of this paper is organized as follows. We first present the context of this study in Section 2. Then we detail our materialized view selection strategy in Section 3. In order to validate our strategy, we present some experimental results in Section 4. Finally, we conclude and outline some research perspectives in Section 5.

Study context 2.1 XML data warehouse specification

Several studies have been proposed for designing and building XML data warehouses. For instance, Pokorny modeled a star schema in XML by defining dimension hierarchies as a set of logically connected collections of XML data, and facts as XML data elements [START_REF] Pokorny | Modelling Stars Using XML[END_REF][START_REF] Pokorny | XML Data Warehouse: Modelling and Querying[END_REF].

Park et al. also proposed an XML multidimensional model in which each fact is described by a single XML document and dimension data are grouped into a repository of XML documents [START_REF] Park | XML-OLAP: A Multidimensional Analysis Framework for XML Warehouses[END_REF].

Finally, Hummer et al. designed XCube, a family of templates allowing the description of a multidimensional structure, dimension and fact data for integrating several data warehouses into a virtual or federated data warehouse [START_REF] Hummer | XCube: XML for data warehouses[END_REF]. The federated templates are not directly related to XML warehousing, but they can be used to represent XML star schemas. XCube is organized as a set of modules or formats:

XCube Schema, XCube Dimensions and XCube Facts, which respectively formalize the schema, the dimensions and the facts according to a star schema.

These studies use XML documents to manage or represent the facts and dimensions of an XML data warehouse. They actually help logically modeling a data warehouse. This allows the native storage of documents and their easy interrogation based on XML languages.

In this paper, we selected the XCube specification to model a reference XML data warehouse and apply our strategy. Indeed, in XCube, the authors proposed a simple structure for representing facts and dimensions in a star schema. They use one XML document to represent dimensions and one XML document to represent facts. In addition, they use another XML document representing warehouse metadata. The other proposals do not use XML documents for representing warehouse schema. However, we need these metadata to compute our cost models.

Thus, our data warehouse is composed of the following XML documents:

• Schema.xml specifies the data warehouse metadata; • Dimensions.xml defines all the dimensions characterized by their attributes and values; • Facts.xml specifies the facts, i.e., the identifiers of dimensions and the description of measures.

Figure 1. XCube warehouse specification 2.2 XML data warehouse interrogation

We selected the XQuery language [START_REF] Boag | XQuery 1.0: An XML Query Language[END_REF] to formulate our decision-support queries because, unlike simpler languages such as XPath, it allows complex queries, including join queries over multiple XML documents, to be expressed with the FLWOR syntax. However, in our implementation, we had to extend FLWOR expressions with explicit Group by clauses to be able to formulate the decisionsupport queries we needed. Thus, we added the functions Group by (attribute list) and Aggregation (aggregation operations, measure list) to the XQuery syntax. Figure 2 provides an example of decision-support query with a multiple Group by clause. The architecture of our materialized view selection strategy is depicted in Figure 3. We assume that we have a workload composed of representative queries for which we want to select a configuration of materialized views in order to reduce their execution time. The first step is to build, from the workload, a clustering context. Then we define similarity and dissimilarity measures that help clustering together similar queries.

For each cluster, we build a set of candidate views. The last step exploits cost models that evaluate the cost of accessing data using views and the cost of their storage to build a final materialized view configuration.

Query workload analysis

The workload that we consider is a set of selection, join and aggregation queries. Figure 4 gives a snapshot of this workload. The first step consists in extracting from the workload the representative attributes for each query. We mean by representative attributes those are present in Where (selection predicate attributes) and Group by clauses. We store the relationships between the query workload and the extracted attributes in a "query-attribute" matrix. The matrix lines are the queries and the columns are the extracted attributes. A query i q is then seen as a line in the matrix that is composed of cells corresponding to representative attributes. The general term ij q of this matrix is set to one if extracted attribute i a is present in query i q , and to zero otherwise. This matrix represents our clustering context. Table 1 shows the query-attribute matrix that is built from the workload snapshot from Figure 4.

Building the candidate view configuration

In practice, it is hard to search all the syntactically relevant views (candidate views) because the search space is very large [START_REF] Agrawal | Automated selection of materialized views and indexes in SQL databases[END_REF]. To reduce the size of this space, we propose to cluster the queries. Hence, we group in a same cluster all the queries that are similar. Similar queries are the one having a close binary representation in the query-attribute matrix. Two similar queries can be resolved by using only one materialized view. We define similarity and dissimilarity measures that ensure that queries within a same cluster are strongly related to each others whereas queries from different clusters are significantly different.

Similarity and dissimilarity measures

A query is described by the attributes extracted in the query analysis phase. We thus describe a query i q by a vector

{ } pi i i i q q q q ,..., , 2 1 =
, where p is the number of attributes in the matrix. This description allows query comparison. We define similarity (respectively, dissimilarity) between two queries i q and j q regarding attribute ) .. 1 ( p k a k = in Formula 1 (respectively, Formula 2).

(1) 0

1 1 ) , ( ⎩ ⎨ ⎧ = = = otherwise q q if q q kj ki kj ki sim δ (2) 0 1 ) , ( ⎪ ⎩ ⎪ ⎨ ⎧ ≠ = = kj ki kj ki kj ki dissim q q if q q if q q δ
Two queries i q and j q are similar regarding attribute k a if and only

if 1 = = kj ki q q
, i.e., k a is present in both queries. They are dissimilar if and only if kj ki q q ≠ , i.e., one of the two queries does not contain attribute k a . These measures can be extended to a set A composed of p attributes such that we get the degree of global similarity and dissimilarity between two queries. We thus define the similarity (respectively, dissimilarity) between two queries i q and j q according to all the matrix attributes k a in Formula 3 (respectively, Formula 4). p q q sim q q q q sim j i p j lj ki sim j i

≤ ≤ = ∑ = ) , ( 0 (3) ) , ( ) , ( 1 δ p q q dissim q q q q dissim j i p j lj ki dissim j i ≤ ≤ = ∑ = ) , ( 0 (4) ) , ( ) , ( 1 δ
Thus, the closer ) , ( j i q q sim (respectively, ) , (

j i q q dissim
) is to p , the more i q and j q are considered similar (respectively, dissimilar).

We also define similarity (respectively, dissimilarity) measures between two query sets and within a query set. These measures are defined by Formulas 5, 6, 7 and 8.

p C card C card C C sim q q C C sim a a b a C q C q l k sim b a b l a k × × ≤ ≤ = ∑ ∈ ∈ ) ( ) ( ) , ( 0
(5) ) , ( ) , ( , δ p C card C card C C dissim q q C C dissim a a b a C q C q l k dissim b a b l a k × × ≤ ≤ = ∑ ∈ ∈ ) ( ) ( ) , ( 0 (6) ) , ( ) , ( , δ 2 ) ( ) ( ) ( 0 (7) ) , ( ) ( ,
, p C card C card C sim q q C sim a a a l k C q C q l k sim a b l a k × × ≤ ≤ = ∑ < ∈ ∈ δ 2 ) ( ) ( ) ( 0 (8) ) , ( ) ( , , p C card C card C dissim q q C dissim a a a l k C q C q l k dissim a b l a k × × ≤ ≤ = ∑ < ∈ ∈ δ

Clustering

Clustering consists in determining a socalled natural partition nat P composed of objects (here, queries) that reflects the internal structure of data. This partition must be such as its clusters are composed of objects with high similarity and objects from different clusters present a high dissimilarity.

Based on the previously defined functions, a clustering quality measure ) ( h P Q can be built, formula 9.

∑ ∑

< = = = + = b a z b z a z a a b a h C disim C C sim P Q , ... 1 , ... 1 1 (9) )) ( ) , ( ( ) (
This measure permits to capture the natural aspect of a partition. Hence, ) ( h P Q measures simultaneously similarities between queries within the same cluster of partition h P and dissimilarities between queries within different clusters. Thus, we can define ) ( h P Q as an homogeneity function for the same class and an heterogeneity function for different classes. Therefore, the partitions presenting a high intra-cluster homogeneity and a high intercluster disparity have a weak value of ) ( h P Q and thereby appear as the most natural.

We have selected the Kerouac algorithm [START_REF] Jouve | Kerouac: An algorithm for clustering categorical data sets with practical advantages[END_REF] for the clustering phase. This algorithm indeed bears several interesting properties:

1. its computational complexity is quite low (log linear regarding the number of queries and linear regarding the number of attributes); 2. it can deal with a high number of objects (queries); 3. it can deal with distributed data; 4. it allows to integrate constraints within the clustering process. This last characteristic is particularly interesting, since it provides us with a way to integrate constraints concerning the view merging process.

Cost models

The number of candidate views is generally as high as the input workload is large. Thus, it is not feasible to materialize all the proposed views because of storage space constraints. To circumvent this limitation, we propose to use cost models allowing to keep only the most pertinent views.

Figure 5 shows the typical structure of an XML view. In our context, it is composed of Cell elements. Each Cell is itself composed of dimension elements that contain Group by attributes and fact elements corresponding to the aggregate results. We propose cost models that estimate the size and storage cost of a given XML view.

Figure 5. XML view structure

We estimate the size of a view by its number of elements. The number of Dimension and Fact elements in each Cell is the same. Indeed, the number of elements in a given view is estimated by the number of Cell elements. To compute it, we first estimate the maximum number of Cell elements (Formula 10). Golfarelli et al. [START_REF] Golfarelli | A methodological framework for data warehouse design[END_REF] proposed to estimate the number of tuples in a given view v by using Yao's formula [START_REF] Yao | Approximating block accesses in database organizations[END_REF]. We also use this formula to estimate the number of Cell elements in v (Formula 12). ( 12

) 1 ) ( 1 ) ( 1 ) ( 1 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + - + - × - × = ∏ = Cell i i Cell ms i c Cell ms v ms v . ) ( 1 1 v ms c - = If ) ( ) ( v ms
Cell ms is large enough, this formula is well approximated by Cardena's formula [START_REF] Cardenas | Analysis and performance of inverted data base structures[END_REF]. Hence, we obtain Formula 13. ( 13) ) (

1 1 1 ) ( ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - - × = Cell v ms v ms v
Cardenas and Yao's formulas are based on the assumption that data are uniformly distributed. The size, in bytes, of a view v is equal to the number of Cell elements multiplied by the average size needed to store one element. Thus, we estimate the size of a view as shown in Formula 14.

Objective functions

We describe in this section three objective functions that help evaluating the variation of query execution cost induced by adding a new view. The query execution cost is assimilated to the number of Cell elements in the document Facts.xml, if no view is used; or to the number of Cell elements in the view(s) if they are exploited. The workload execution cost is obtained by adding the execution costs of each query within this workload.

The first objective function advantages the views providing more profit while executing queries. The second one advantages the views providing more benefit while occupying the smallest storage space. The third one combines the first two in order to first select all the views providing more profit and then retain only those occupying less storage space when this resource becomes critical. The first function is useful when the space storage is not limited, the second one is useful when storage space is small and the third one is interesting when storage is reasonably large.

Profit objective function

Let { } m v v V ,..., 1 =
be the candidate view set, S the final view set and

{ } n q q Q ,..., 1 =
a query set (workload). The profit objective function, noted P, is defined in Formula 15.

S ) (v v C Q C Q C v P j j update vj S S j S ∉ - - = ∪ (15) ) ( ) ( ) ( ) ( / / / β ) ( / Q C S
denotes the query execution cost when all the views in S are used. If this set is empty,

F Q Q C × = ) ( Ø /
because all the queries are resolved by accessing fact F . When a view i v is added to S ,

∑ = ∪ = Q k j k Vi S v q C Q C 0 / ) , ( ) (
denotes the query execution cost for the views that are in

i v S ∪ . If query k q exploits i v , cost ) , ( j i v q C is then equal to vj C (number of tuples in j v . Otherwise, ) , ( j i v q C
is equal to the maximum value between F and value of

) , ( v q C i (executing cost of i q exploiting S v ∈ with j v v ≠ ). Coefficient ) ( i v p Q = β

) ( j update v C

represents the maintenance cost for view j v .

Profit/space ratio objective function

If view selection is achieved under a space constraint, the profit/space objective function from Formula 16 is used. This function computes the profit provided by j v in regard to the storage space ) ( j v size it occupies.

Hybrid objective function

The constraint on storage space may be relaxed if this space in relatively large. The hybrid objective function H does not penalize space-greedy views if the ratio space storage space remaining -is lower or equal than a storage-space given threshold 1 0 , ≤

< α α

, where remainingspace and storage-space are respectively the remaining space after adding i v and the allotted space needed for storing all the views. This function is computed by combining the two functions P and R as shown in Formula 17.

(17) otherwise ) (

) ( ) ( / / / ⎪ ⎩ ⎪ ⎨ ⎧ - = j S j S j S v R space storage space remaining- if v P v H

View selection algorithm

Our view selection algorithm (Algorithm 1) is based on a greedy search within the candidate view set V. The objective function F must be one of the functions P, R or H described in the previous section. If R is used, we add to the algorithm's input the storage space M allotted for views. If H is used, we also add threshold α as input.

In the first algorithm iteration, the values of the objective function are computed for each view within V. The view max v that minimizes F, if it exists (

0 ) ( max / > v F S
), is then added to S. If R or H is used, the whole storage space M is decreased by the amount of space occupied by max v .

The function values of F are then computed for each remaining view in S V -, since they depend on the selected views present in S. This helps taking into account the interactions that probably exist between the views.

We repeat these iterations until there is no improvement (

0 ) ( / ≤ v F S
) or until all the views have been selected ( Ø

= -S V

). If functions R or H are used, the algorithm also stops when storage space is full.

Experiments

In order to validate our approach for XML materialized view selection, we generated an XML data warehouse, modeled according to the XCube specifications. This classical test data warehouse is composed of sales facts characterized by the amount and quantity measures. The facts are stored in the document Facts.xml (4,92 MB). They are described by five dimensions: channels, promotions, customers, products and times that are stored in the document Dimensions.xml (3.77 MB). This data warehouse has been implemented within the eXist native XML DBMS [START_REF] Meier | eXist: An Open Source Native XML Database[END_REF], which is a free tool that allows the storage of large documents and supports the XQuery language. We ran our tests on a Pentium 2 Ghz PC with 1 GB main memory and an IDE hard drive.

Figure 7. Experimental results

We executed on our data warehouse a workload composed of ten XQuery decision-support queries, with and without using our strategy. The selected views are stored in an independent collection. This collection is targeted by rewritten queries according to view data. We plotted in Figure 7 the execution time of our query workload on the original XML documents and on the materialized views we generated. The X-axis represents the ten queries and the Y-axis the corresponding execution time. The Y-axis is represented in logarithmic scale to highlight the difference between the execution costs. On an average, our XML view materializing strategy improves response time by a factor 24,700.

Conclusion and perspectives

In this paper, we have presented a strategy for materialized view selection in XML data warehouses. Our strategy exploits the results of clustering applied on a given workload to build a set of syntactically relevant candidate views. With the help of cost models we specifically designed for the XML model, we retain only the most advantageous candidate views. These models estimate data access cost using materialized views and storage cost for these views. We have also proposed three objective functions: profit, profit/space ratio and hybrid that exploit our cost models to evaluate the execution cost of the workload. These functions are themselves exploited by a greedy algorithm that recommends a pertinent configuration of materialized views. This allows our strategy to respect the storage space constraint.

Finally, note that our strategy is independent from the warehouse model and the DBMS it is stored in. Though we used an XCube-based reference data warehouse, our strategy could easily be applied on any other model. In the same way, any DBMS could be used instead of eXist, including relational, XML compatible DBMSs.

The first experimental results we achieved are very encouraging, and show that our strategy guarantees a substantial gain in performance. However, our first perspective is to complement these results with other tests, possibly on other systems than eXist, and to assert in each configuration the gain in performance vs. the overhead for generating and refreshing the materialized views.

This work also opens two other axes of research perspectives. First, it is blatantly crucial to adapt or develop highly efficient optimization techniques in native XML DBMSs if they are to approach the performances of relational systems. XML indices are getting more and more efficient, but there is still room for improvement (e.g., multidocument join indices). The generalized exploitation of materialized views could also be very beneficial. Thus, a rewriting query engine and refreshing strategies should be devised.

Our second research axis is even more specific to XML data warehouses. Decision-support queries bear specific needs in terms of operators. For instance, we had to extend XQuery to allow multiple Group by clauses to be able to implement our decision-oriented workload within eXist. Similar extensions do exist already, but it could be interesting to further extend XQuery to support OLAP operators such as Cube, Rollup or Drill down.

Figure 2

 2 Figure 2. Decision-support XQuery example

Figure 3 .Figure 4 .

 34 Figure 3. Materialized view selection strategy

1 ,

 1 cardinality of the dimension characterizing the Cell element. d is the number of dimensions in the document Dimensions.xml. Let ) (v ms be the maximum size of view v that is composed of dimensions k d d ,..., where k is the number of dimensions in the view and

  the size, in bytes, of dimension i d from v and k the number of dimensions.

  of updating vs. querying the data warehouse.


Guillaume Mornieux
email: guillaume.mornieux@univ-lorraine.fr

Anja Hirschmüller

Albert Gollhofer

Norbert P Südkamp

Dirk Maier

Multimodal assessment of

Keywords: glenohumeral instability, overhead sports, proprioception, joint position sense, perturbation, internal impingement, injury, prevention

come

Introduction

Evaluation of sensorimotor shoulder function is of major importance for guidance of sportsspecific training, injury prevention and rehabilitation of sports-specific shoulder disorders, e.g. shoulder instability and functional impingement syndromes. The musculoskeletal sensorimotor system maintains functional joint stability by complex interaction of afferent, efferent, peripheral and central integration and processing components coordinating agonist and antagonist muscular activity. [START_REF] Riemann | The sensorimotor system, part I: the physiologic basis of functional joint stability[END_REF] For instance, patients with anterior shoulder instability exhibit deficits of both afferent proprioception and efferent motor response. [START_REF] Myers | Sensorimotor contribution to shoulder stability: effect of injury and rehabilitation[END_REF] Mihata et al. showed that muscular imbalance and anterior capsular laxity lead to an increase of posterior superior glenohumeral contact pressures. [START_REF] Mihata | Effect of rotator cuff muscle imbalance on forceful internal impingement and peel-back of the superior labrum: a cadaveric study[END_REF][START_REF] Mihata | Effect of anterior capsular laxity on horizontal abduction and forceful internal impingement in a cadaveric model of the throwing shoulder[END_REF] Alterations of shoulder kinematics in anterior shoulder instability may lead to clinically symptomatic posterior superior impingement (PSI) syndrome causing structural lesions, e.g. superior labrum anterior to posterior (SLAP) lesions and tears of the posterior superior labrum as well as the rotator cuff. [START_REF] Mihata | Effect of rotator cuff muscle imbalance on forceful internal impingement and peel-back of the superior labrum: a cadaveric study[END_REF][START_REF] Walch | Impingement of the deep surface of the supraspinatus tendon on the posterosuperior glenoid rim : an arthroscopic study[END_REF] PSI is known to be a common source of functional shoulder pain ("thrower's shoulder") in throwing athletes. [START_REF] Liu | Posterior superior impingement of the rotator cuff on the glenoid rim as a cause of shoulder pain in the overhead athlete[END_REF] Pathogenesis of the "thrower's shoulder" involves complex structural and kinematic alterations, most importantly a relative deficiency of internal rotation strength. Edouard et al. [START_REF] Edouard | Shoulder strength imbalances as injury risk in handball[END_REF] found muscular imbalances of internal and external rotation strength in asymptomatic, high-level handball players which were associated with a higher risk for subsequent shoulder injuries. Such muscular imbalance impairs sensorimotor shoulder function and may lead to clinically symptomatic functional disorders such as PSI and glenohumeral internal rotation deficit (GIRD) syndrome. [START_REF] Mihata | Effect of rotator cuff muscle imbalance on forceful internal impingement and peel-back of the superior labrum: a cadaveric study[END_REF][START_REF] Guney | The effect of glenohumeral internal-rotation deficit on functional rotator-strength ratio in adolescent overhead athletes[END_REF][START_REF] Myers | The role of the sensorimotor system in the athletic shoulder[END_REF] Proprioception plays an important role within the sensorimotor system. [START_REF] Riemann | The sensorimotor system, part I: the physiologic basis of functional joint stability[END_REF] Subjects with unstable shoulders show decreased proprioceptive ability and mechanoreceptor dysfunction due to structural lesion of the capsuloligamentous complex. [START_REF] Warner | Role of proprioception in pathoetiology of shoulder instability[END_REF] However, evaluation of proprioception alone, e.g., using joint position sense testing and detection of passive motion tests, [START_REF] Aydin | Shoulder proprioception: a comparison between the shoulder joint in healthy and surgically repaired shoulders[END_REF][START_REF] Lephart | Proprioception of the shoulder joint in healthy, unstable, and surgically repaired shoulders[END_REF][START_REF] Safran | Shoulder proprioception in baseball pitchers[END_REF] does not provide sufficient information for comprehensive assessment of sensorimotor shoulder function because evaluation of efferent motor response is lacking.

Literature reports shoulder range of motion tests [START_REF] Wilk | Current concepts in the rehabilitation of the overhead throwing athlete[END_REF][START_REF] Zheng | Shoulder rotational properties of throwing athletes[END_REF] and isokinetic strength evaluation in handball players [START_REF] Edouard | Shoulder strength imbalances as injury risk in handball[END_REF][START_REF] Andrade | Profile of isokinetic eccentric-to-concentric strength ratios of shoulder rotator muscles in elite female team handball players[END_REF] and patients with anterior shoulder instability. [START_REF] Edouard | Rotator cuff strength in recurrent anterior shoulder instability[END_REF][START_REF] Saccol | Shoulder rotator strength and torque steadiness in athletes with anterior shoulder instability or SLAP lesion[END_REF] However, few studies focused on sensorimotor function of the shoulder joint. [START_REF] Edouard | Sensorimotor control deficiency in recurrent anterior shoulder instability assessed with a stabilometric force platform[END_REF][START_REF] Laudner | Upper extremity sensorimotor control among collegiate football players[END_REF][START_REF] Myers | Proprioception and neuromuscular control of the shoulder after muscle fatigue[END_REF][START_REF] Padua | The effect of select shoulder exercises on strength, active angle reproduction, single-arm balance, and functional performance[END_REF][START_REF] Tripp | Recovery of upper extremity sensorimotor system acuity in baseball athletes after a throwing-fatigue protocol[END_REF] While the latter focused on 3D analysis of upper extremity position reproduction during functional movement, others investigated glenohumeral sensorimotor control using an upper limb weight-bearing condition. Edouard et al. found impaired postural sensorimotor control in patients with anterior shoulder instability. [START_REF] Edouard | Sensorimotor control deficiency in recurrent anterior shoulder instability assessed with a stabilometric force platform[END_REF] The experimental set-up with the lower part of the body being supported on a table does not only target the shoulder joint but the entire upper body part and does not consider functional testing such as a throwing task.

To date, there is no experimental set-up that evaluates all relevant components of sensorimotor shoulder function including proprioception, dynamic neuromuscular control, muscle strength and functional performance.

The aim of the present study therefore was to evaluate feasibility and results of such multimodal assessment of sensorimotor shoulder function in patients with untreated anterior shoulder instability and asymptomatic recreational handball players. Both groups are prone to muscular imbalance and alteration of sensorimotor function potentially leading to functional shoulder disorders such as PSI and the "thrower's shoulder". Using combined proprioceptive, dynamic and functional testing, a shoulder-specific sensorimotor index (S-SMI) was designed as a novel diagnostic tool for multimodal assessment of sensorimotor shoulder function. We hypothesized 1) an impaired sensorimotor function of the dominant unstable shoulder compared to the non-dominant healthy shoulder in patients and 2) a superior sensorimotor function of the dominant throwing shoulder compared to the non-dominant shoulder in handball players.

Materials and Methods

Study population

Using data from the literature evaluating proprioceptive and isokinetic strength parameters in patients with shoulder instability [START_REF] Lephart | Proprioception of the shoulder joint in healthy, unstable, and surgically repaired shoulders[END_REF][START_REF] Edouard | Rotator cuff strength in recurrent anterior shoulder instability[END_REF] and overhead athletes, [START_REF] Safran | Shoulder proprioception in baseball pitchers[END_REF][START_REF] Andrade | Profile of isokinetic eccentric-to-concentric strength ratios of shoulder rotator muscles in elite female team handball players[END_REF] the sample size was estimated to achieve 80% statistical power with an alpha level of 0.05. Nine patients (PAT; 8 males and 1 female; body height = 180 ± 7 cm; body mass index (BMI) = 25 ± 4 kg.m 2 ; age = 22 ± 4 years) with untreated anterior instability exclusively of their dominant shoulders and 15 asymptomatic, recreational handball players (HB; 11 males and 4 females body height = 180 ± 10 cm; BMI = 24 ± 3 kg.m 2 ; age = 21 ± 2 years) participated in the study. All patients had experienced at least one but a maximum of five shoulder dislocations with magnetic resonance imaging proven Bankart lesions of the anterior inferior labrum. Patients with bony involvement and associated injuries were excluded. The minimum time period between the last event of dislocation and multimodal testing was two months to ensure painless and full range of motion. None of the patients had received a specific rehabilitation program prior to testing. Patients suffered from subjective shoulder instability during overhead activities but must not have experienced habitual dislocations in daily routine. The clinical diagnosis of symptomatic, unidirectional anterior glenohumeral instability without ligamentous hyperlaxity (B2 according to Gerber and Nyfeller [START_REF] Gerber | Classification of glenohumeral joint instability[END_REF] ) was confirmed by an experienced orthopaedic surgeon. All patients showed clearly positive anterior apprehension signs but no clinical signs of ligamentous hyperlaxity. Participants in the HB group were recruited to match the PAT group concerning body height, BMI and age. Handball players studying at the sport university and playing in the 3rd -5th league, as well as their teammates were asked to participate in the study. They constituted a homogeneous group, with over 10 years handball experience and on average 6.5 ± 1.5 hours/week of training. The regular training program was maintained during testing. 13 players were right-handed and two were left-handed. All participants were free from any upper extremity pain at the time of testing and did not report any history of shoulder pain or injury over the 12 months prior to the measurements. In addition, players were excluded if they reported any history of shoulder dislocation, fracture or surgery.

Written consent was obtained prior to study participation. The study was approved by the local ethics committee (approval 195/12) and was conducted according to the ethical principles for medical research involving human subjects (Declaration of Helsinki).

Procedure

Participants were asked to perform proprioceptive joint position sense (JPS_prop) and dynamic stabilisation (Stabi_dyn) tests on an isokinetic device (IsoMed2000, D. & R. Ferstl GmbH, Hemau, Germany) in a seated position with 45° of shoulder abduction in the scapular plane, 90° of elbow flexion and 10° of shoulder external rotation (Figure 1). Trunk and arm were firmly fixed with straps so that participants could not move these segments during measurements. The rationale for this testing position was the high reliability reported for isokinetic strength parameters. [START_REF] Edouard | Reliability of isokinetic assessment of shoulder-rotator strength: a systematic review of the effect of position[END_REF] For JPS_prop testing, the shoulder was first placed in 10° of internal rotation (IR) or 10° of external rotation (ER). After 10 sec. the shoulder was turned to the neutral position. From that reference position, participants had to passively reposition their arm to the 10° IR or ER positions, respectively. During the entire proprioception test, participants were blindfolded.

For Stabi_dyn testing, participants had to maintain their shoulder position as close as possible to the reference position, while sustaining random displacements in both IR and ER directions. Intensity of displacements was set at different percentage levels of the maximal voluntary isometric torque (MVIT) measured in both IR and ER prior to testing. Additionally, instantaneous visual feedback of the arm position in relation to the reference position was provided on a screen. Two attempts at different levels of force (25%, 50 and 75% MVIT) were allocated and each measurement lasted 54 seconds. Reliability of this new Stabi_dyn test was evaluated by means of the intraclass correlation coefficient (ICC2,1). Therefore, among the 24 participants, 18 performed the test twice on 2 different days. Across the 3 intensity levels, this test showed acceptable reliability for internal and external rotations (ICC=0.87 and ICC=0.75, respectively). [START_REF] Hopkins | Measures of reliability in sports medicine and science[END_REF] In addition, participants conducted a functional throwing test to determine their individual performance index (FTPI_func) reflecting throwing accuracy. [START_REF] Davies | Neuromuscular testing and rehabilitation of the shoulder complex[END_REF] Subjects were asked to throw a ball towards a 0.3m 2 target area on the wall from a 4.6m distance as many times as possible during a time period of 30 seconds. The examiner records the number of throws and the number of throws hitting the target area.

Finally, isokinetic strength testing was performed at 2 angular velocities: 90°/s and 180°/s with 5 and 10 repetitions respectively. Participants were asked to progressively increase their effort in order to reach their peak strength during the last 2 repetitions.

All tests were performed for both the dominant (Do) and non-dominant shoulder (randomly assigned over all participants). Thus, the healthy non-dominant side (N-Do) provided intraindividual reference values for each participant. Few days prior to this multimodal assessment, participants became familiar with the testing procedure during a specific training session.

Data analysis

Mean reposition errors (in °) with respect of the 10° IR or 10° ER were assessed for JPS_prop testing. Mean position errors (in °) related to the reference position were calculated over the 54 seconds test duration for IR and ER direction, respectively. FTPI_func (in %) was calculated as the ratio between the number of accurate throws and the total number of throws during the 30 seconds test.

In order to further evaluate the sensorimotor function of the shoulder, a shoulder-specific sensorimotor index (S-SMI, expressed in %) was calculated as follows:

Mean values ( ) of each of the three tests accounted for one third of the value of the S-SMI.

For that purpose, all test results were expressed as percentages. For JPS_prop and Stabi_dyn measurements, 0 up to 10 degree deviation corresponded to percentage values ranging from 100% to 0%, respectively.

During the isokinetic movements, dynamic strength of internal rotators and external rotators were evaluated by means of peak torque values normalized to body mass (Nm.kg -1 ). Side-toside differences (%) were calculated at each angular velocity and represented dominant side strength deficit/superiority compared with non-dominant side.

Statistical analysis

The best out of two attempts of JPS_prop (two dependent variables), Stabi_dyn (six dependent variables) testing, FTPI_func, S-SMI and the peak torque values for IR and ER at each angular velocity were selected for both Do and N-Do shoulders for statistical analysis.

Present data did not follow normal distribution for four variables (Shapiro-Wilk test).

Accordingly, non-parametric tests were applied. Descriptive statistics used median, interquartile range as well as minimal and maximal values. The influence of shoulder dominance (Do vs. N-Do) on dependent variables within each participant group was analysed using the Wilcoxon test. The level of significance was set at 0.05.

Results

PAT showed no significant difference between Do and N-Do shoulders for JPS_prop, Stabi_dyn and FTPI_func testing (Table I). Moreover, median (interquartile range) values for S-SMI were not significantly different between Do (44.7% (15.5%)) and N-Do (45.7% (6.1%)) shoulders (P=0.59).

HB achieved significantly superior Stabi_dyn scores for external rotation, at 25% level of force intensity for their Do compared to N-Do shoulders (P=0.004). FTPI_func was significantly higher for Do than N-Do shoulder in handball players (P<0.001). Table II lists the detailed results of all variables for JPS_prop, Stabi_dyn and FTPI_func testing for HB. Moreover, S-SMI for Do (56.9% (8.8%)) was significantly higher than for N-Do (45.4% (8.2%)) shoulders (P=0.002; Figure 2).

Internal and external rotator isokinetic peak torque values and external to internal rotator ratios (ER/IR) values for PAT and HB are presented in Table III. Moreover, side-to-side differences (Do vs. N-Do) for these values are provided in Table III. IR values were not significantly different between Do and N-Do. For instance, HB demonstrated comparable IR values between Do and N-Do at 90°/sec and 180°/sec (P=0.59 and P=0.22, respectively). ER for Do was significantly higher than for N-Do shoulders for both PAT (P=0.01) and HB (P=0.005) at 90°/sec. The same was true at 180°/sec (P=0.012 and P=0.02, respectively). ER/IR ratios were also significantly higher for Do than for N-Do shoulders for both PAT (P=0.02) and HB (P=0.03) at 90°/sec. At 180°/sec, ER/IR ratio was significantly higher for Do than for N-Do shoulders for PAT (P=0.01), but not HB (P=0.05).

Discussion

Multimodal assessment of the glenohumeral sensorimotor function revealed 1) successful and valid measurements in both patients with shoulder instability and handball players, 2) comparable sensorimotor function of unstable dominant shoulders compared to healthy contralateral shoulders and 3) superior sensorimotor function of the dominant shoulder of handball players compared to their non-dominant side.

Neither singular sensorimotor tests nor S-SMI were significantly influenced by glenohumeral instability of dominant shoulders. Edouard et al. [START_REF] Edouard | Sensorimotor control deficiency in recurrent anterior shoulder instability assessed with a stabilometric force platform[END_REF] found a significant sensorimotor control deficiency of 20-25% in patients with unstable dominant shoulders compared to healthy contralateral shoulders. However, they employed a static, weight-bearing experimental set-up, that rather measured postural stability of both the upper body than glenohumeral sensorimotor function. To our knowledge, the present study is the first to assess the influence of shoulder stability on dynamic sensorimotor shoulder function and adds valuable information to exclusive muscular strength analysis. Numerous studies showed significant isokinetic strength differences between unstable and stable shoulders. [START_REF] Edouard | Rotator cuff strength in recurrent anterior shoulder instability[END_REF][START_REF] Saccol | Shoulder rotator strength and torque steadiness in athletes with anterior shoulder instability or SLAP lesion[END_REF][START_REF] Tsai | Shoulder function in patients with unoperated anterior shoulder instability[END_REF] However, only Edouard et al. [START_REF] Edouard | Rotator cuff strength in recurrent anterior shoulder instability[END_REF] investigated rotator cuff strength profile in glenohumeral instability, while ensuring that instability was only present on the dominant side, as we did in the present study. These authors found a significant reduction of up to 9% of isokinetic peak torque values for external rotation but no significant difference for internal rotation in unstable compared to contralateral stable shoulders. [START_REF] Edouard | Rotator cuff strength in recurrent anterior shoulder instability[END_REF] The lack of internal rotation difference between both shoulders has also been reported in the present study. On the other hand, the literature consistently reports significant higher internal (up to 15%) and external (up to 12%) rotation strength of healthy dominant compared to healthy non-dominant shoulders. [START_REF] Edouard | Shoulder strength imbalances as injury risk in handball[END_REF][START_REF] Edouard | Rotator cuff strength in recurrent anterior shoulder instability[END_REF][START_REF] Mayer | Normal values of isokinetic maximum strength, the strength/velocity curve, and the angle at peak torque of all degrees of freedom in the shoulder[END_REF] Present findings cannot be directly compared with previously published studies. Most importantly, there exist no reference data for dynamic stabilisation testing with perturbation.

In contrast, sensorimotor shoulder function was assessed using a novel dynamic perturbation model in the present study. Based on existent knowledge, one would assume significant superiority of about 15% of sensorimotor function of the dominant shoulder joint. In the present study, untreated anterior shoulder instability led to a loss of this dominance-related effect indicating a significant decrease of sensorimotor function.

Handball players demonstrated superior dynamic stabilization of their dominant shoulder joints for external rotation at the lowest level of force intensity (25% MVIT), a higher functional throwing ability and an increased S-SMI compared to the non-dominant side.

Superior sensorimotor control for external rotation at the lowest force level might be explained by intensive functional training of dominant, throwing shoulders. However, this effect was not consistently present and could not be detected for higher force levels and internal rotation. This new dynamic stabilisation test combines proprioceptive and functional testing, is reliable and can be performed at individual force levels. Different experimental settings (e.g., lower force levels) should be explored to detect instability-related and sportsspecific deficits and imbalances. This comprehensive sensorimotor evaluation showed comparable internal rotator peak torques for both shoulders, and adds substantial knowledge to findings from conventional isokinetic strength studies. In contrast, other studies on elite handball players observed significantly higher isokinetic internal rotation strengths for dominant, throwing shoulders. [START_REF] Edouard | Shoulder strength imbalances as injury risk in handball[END_REF][START_REF] Clarsen | Reduced glenohumeral rotation, external rotation weakness and scapular dyskinesis are risk factors for shoulder injuries among elite male handball players: a prospective cohort study[END_REF][START_REF] Andrade | Profiling the isokinetic shoulder rotator muscle strength in 13-to 36-year-old male and female handball players[END_REF][START_REF] Ellenbecker | The application of isokinetics in testing and rehabilitation of the shoulder complex[END_REF] We explained this discrepancy by the lower level of training intensity and competition of recreational compared to high-level professional athletes.

The functional throwing test showed that dominant shoulders of handball players reached a 60% FTPI value corresponding to the top of the range reported for healthy shoulders. [START_REF] Davies | Neuromuscular testing and rehabilitation of the shoulder complex[END_REF] Moreover, non-dominant shoulders as well as unstable shoulders reached a poor FTPI level of below 30%. These findings indicate that instability-caused impairment of shoulder sensorimotor function might be effectively detected by functional tasks such as throwing, which are performed at low force levels.

Increased functional throwing ability combined with superior dynamic stabilisation for external rotation at a low force level yielded a superior S-SMI for dominant compared to nondominant shoulders of handball players.

Passive joint position sense was neither improved in dominant shoulders of handball players nor reduced in unstable dominant shoulders compared to non-dominant healthy shoulders. Although patients showed a 2° less accurate unstable shoulder for internal rotation, this value did not reach statistical significance. Our results were in accordance with joint position sense values found by Lephart et al. [START_REF] Lephart | Proprioception of the shoulder joint in healthy, unstable, and surgically repaired shoulders[END_REF] Consistently, Safran et al. [START_REF] Safran | Shoulder proprioception in baseball pitchers[END_REF] reported symmetry of shoulder proprioception in overhead athletes. Our study did not detect side-specific differences for shoulder proprioception using joint position sense testing, while combined functional and dynamic testing (FTPI_func and Stabi_dyn) enabled comprehensive evaluation of sensorimotor function of the shoulder joint.

This study represents a novel approach of comprehensive multimodal evaluation of sensorimotor function of the shoulder joint comprising sensory, motor and functional qualities. The use of an isokinetic dynamometer to perform dynamic stabilisation tests further shows the considerable potential of this technology. But several limitations need to be considered. Most importantly, normative values of sensorimotor function need to be defined by assessment of representative control cohorts. Dynamic sensorimotor testing at lower force levels might enable the detection of significant differences and the inclusion of patients with higher grades of shoulder instability.

From a clinical perspective, the combination of relative internal rotation weakness and anterior capsular laxity in untreated shoulder instability entails a substantial risk for posterior superior glenohumeral impingement and subsequent structural lesions, e.g. articular-sided rotator cuff and labral tears. [START_REF] Mihata | Effect of rotator cuff muscle imbalance on forceful internal impingement and peel-back of the superior labrum: a cadaveric study[END_REF][START_REF] Mihata | Effect of anterior capsular laxity on horizontal abduction and forceful internal impingement in a cadaveric model of the throwing shoulder[END_REF][START_REF] Walch | Impingement of the deep surface of the supraspinatus tendon on the posterosuperior glenoid rim : an arthroscopic study[END_REF][START_REF] Warner | Patterns of flexibility, laxity, and strength in normal shoulders and shoulders with instability and impingement[END_REF] Interestingly, this was also true for dominant shoulders of recreational handball players. Overhead athletes such as handball players are prone to symptomatic posterior superior impingement due to a relative weakness of internal rotation strength and glenohumeral internal rotation deficit (GIRD). [START_REF] Mihata | Effect of rotator cuff muscle imbalance on forceful internal impingement and peel-back of the superior labrum: a cadaveric study[END_REF][START_REF] Walch | Impingement of the deep surface of the supraspinatus tendon on the posterosuperior glenoid rim : an arthroscopic study[END_REF][START_REF] Liu | Posterior superior impingement of the rotator cuff on the glenoid rim as a cause of shoulder pain in the overhead athlete[END_REF][START_REF] Guney | The effect of glenohumeral internal-rotation deficit on functional rotator-strength ratio in adolescent overhead athletes[END_REF] Though, all included handball players were clinically asymptomatic, dominant internal rotation weakness represents a risk factor for occurrence of symptomatic posterior superior impingement syndrome. In this context, specific training of internal rotation strength appears beneficial for both patients with untreated shoulder instability and recreational handball players performing at lower levels of competition.

Conclusions

The present study proves feasibility of multimodal assessment of shoulder sensorimotor function in high-demand overhead athletes, healthy individuals and patients with symptomatic

Tables and Figures captions

Table I The dominant side in the patients group corresponds to the unstable shoulder.

* indicates significant differences between Do and N-Do.

  anterior shoulder instability. Untreated shoulder instability led to a loss of dominance-related superiority indicating functional internal rotation strength deficiency. Dominant shoulders of handball players showed a superior overall sensorimotor function but weakness of dominant internal rotation constituting a risk factor for occurrence of posterior superior impingement syndrome. The S-SMI, including proprioception, dynamic stabilisation and functional throwing ability, may serve as a diagnostic tool for guidance of sports-specific training, injury prevention and rehabilitation of shoulder instability and possibly other sports-specific shoulder disorders. Internal rotation training appears beneficial for both patients with untreated anterior shoulder instability and handball players performing at a recreational level.

  : Median, interquartile range (IQR), minimal and maximal values of proprioception (JPS_prop) and dynamic stabilisation (Stabi_dyn) scores for internal (IR) and external shoulder rotation (ER) and the three force levels (25, 50, 75%), as well as functional throwing (FTPI_func) scores for the dominant unstable (Do) and non-dominant (N-Do) shoulders in the patients group. Table II: Median, interquartile range (IQR), minimal and maximal values of proprioception (JPS_prop) and dynamic stabilisation (Stabi_dyn) scores for internal (IR) and external shoulder rotation (ER) and the three force levels (25, 50, 75%), as well as functional throwing (FTPI_func) scores for the dominant (Do) and non-dominant (N-Do) shoulders in the handball players group. * indicates significant differences between Do and N-Do.TableIII: Median (interquartile range) values for internal rotator and external rotator peak torque and external to internal rotator ratios (ER/IR) for patients with anterior instability and handball players.

*

  indicates significant differences between Do and N-Do.

Figure 1 :

 1 Figure 1: Schematic view of the setup during the joint position sense and sensorimotor tests

Figure 2 :

 2 Figure 2: Boxplot of the differences in the shoulder-specific sensorimotor index between

Table I :

 I Differences in glenohumeral sensorimotor function between dominant and non-dominant shoulders for patients with anterior instability.

	Patients Do the dominant unstable (Do) and non-dominant (N-Do) shoulders in the patients group.		Patients N-Do		effect Shoulder
		Median	IQR	Min	Max	Median	IQR	Min	Max	P value
	JPS_prop IR (°)	4	1	0	6	2	2	0	7	0.67
	JPS_prop ER (°)	5	5	2	15	6	3	0	13	0.73
	Stabi_dyn IR 25% (°)	2.5	0.9	2.1	3.8	3.2	0.9	1.9	4.1	0.17
	Stabi_dyn ER 25% (°)	2.8	0.8	1.8	5.1	3.9	1.8	2.4	5.3	0.21
	Stabi_dyn IR 50% (°)	4.5	0.1	3	5.9	4.5	1.7	3.3	6.2	0.62
	Stabi_dyn ER 50% (°)	3.7	2.4	2.7	7.5	4.8	0.6	3.8	8.3	0.11
	Stabi_dyn IR 75% (°)	6	1.1	4.3	10.1	5.9	2.1	4.1	11.6	0.94
	Stabi_dyn ER 75% (°)	6	3.4	4.1	13.3	7.2	3.4	5.6	11.8	0.37
	FTPI_func (%)	27.3	13.5	20	50	28.6	5.8	0	66.7	0.77

Table II :

 II Differences in glenohumeral sensorimotor function between dominant and non-dominant shoulders for handball players.

			Handball Players Do			Handball Players N-Do		Shoulder effect
		Median	IQR	Min	Max	Median	IQR	Min	Max	P value
	JPS_prop IR (°)	3	2	0	8	2	5	0	10	0.62
	JPS_prop ER (°)	5	5	2	11	6	7	1	11	0.89
	Stabi_dyn IR 25% (°)	2.6	0.7	1.8	3.4	2.9	0.7	1.9	3.3	0.36
	Stabi_dyn ER 25% (°)	3.1	0.6	2.3	3.9	3.7	0.7	2.7	5.9	0.004*
	Stabi_dyn IR 50% (°)	4	0.8	3.3	4.9	4.3	0.8	2..9	5.1	0.15
	Stabi_dyn ER 50% (°)	4.5	1.2	3.1	6	4.8	1.3	3.3	6.1	0.17
	Stabi_dyn IR 75% (°)	5.4	1.7	4.4	7.1	5.7	0.9	4.2	8.6	0.51
	Stabi_dyn ER 75% (°)	5.8	1.4	3.9	8.8	6	1.3	4.3	10.5	0.33
	FTPI_func (%)	60	10.4	43.8	85.7	31.3	13.5	9.1	46.2	< 0.001*

Table III :

 III Median (interquartile range) values for internal rotator and external rotator peak torque and external to internal rotator ratios (ER/IR) for patients with anterior instability and handball players

			Patients			Handball Players
		Do	N-Do	Do vs. N-Do (%)	Do	N-Do	Do vs. N-Do (%)
	Isokinetic 90°/sec (Nm/kg)
	Internal Rotators	0.49 (0.18)	0.52 (0.22)	-15.1 (9.8)	0.61 (0.26)	0.59 (0.22)	0.0 (18.3)
	External Rotators	0.37 (0.07)	0.29 (0.11) *	28.6 (30.0)	0.41 (0.15)	0.33 (0.15) *	46.9 (35.2)
	ER/IR ratio	0.82 (0.43)	0.57 (0.12) *	62.5 (40.8)	0.72 (0.43)	0.47 (0.28) *	58.0 (63.2)
	Isokinetic 180°/sec (Nm/kg)
	Internal Rotators	0.50 (0.17)	0.58 (0.16)	-14.3 (17.2)	0.61 (0.25)	0.66 (0.22)	-5.1 (13.4)
	External Rotators	0.40 (0.10)	0.30 (0.17) *	43.5 (65.9)	0.45 (0.20)	0.34 (0.18) *	40 (35.7)
	ER/IR ratio	0.86 (0.35)	0.53 (0.17) *	91.3 (75.9)	0.72 (0.37)	0.49 (0.38)	53.4 (53.2)

Acknowledgment and Conflict of Interest

Each author has participated to the study. The authors state that the article is original, has not been submitted elsewhere and that the study was approved by the ethics committee. No potential conflict of interest was reported by the authors.


Youri Duchene
email: youri.duchene@univ-lorraine.fr

Guillaume Mornieux

Arthur Petel

Gérome Philippe P Perrin

Duchene Youri

Mornieux Guillaume

Petel Arthur

Gauchard Gérome

The trunk's contribution to postural control under challenging balance conditions

Keywords: Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing -Original Draft, Visualization, Project administration. Guillaume Mornieux: Conceptualization, Methodology, Investigation, Writing -Original Draft, Visualization. Arthur Petel: Investigation, Writing -Reviewing Conceptualization, Writing -Reviewing Conceptualization, Methodology, Writing -Original Draft, Resources, Supervision Trunk control / Multijoint / Kinematics / Neuromuscular activity / Centre of force

come

The trunk's contribution to postural control under challenging balance conditions

Introduction

Postural control is a complex process in which the vertical projection of the center of mass (CoM) must be kept within the base of support during quiet stance. Displacements of the center of foot force (CoF) are commonly computed to assess postural control [START_REF] Paillard | Effects of general and local fatigue on postural control: A review[END_REF]. Postural control has also been widely described in terms of joint kinematics [START_REF] Horak | Postural strategies associated with somatosensory and vestibular loss[END_REF][START_REF] Riemann | Comparison of the ankle, knee, hip, and trunk corrective action shown during single-leg stance on firm, foam, and multiaxial surfaces[END_REF]. Nashner & McCollum's double inverted pendulum is the classical model of postural control in the frontal and sagittal planes [START_REF] Nashner | The organization of human postural movements: a formal basis and experimental synthesis[END_REF]. According to this model, postural control in the sagittal plane is first exerted around the ankle joint and then (if the postural challenge increases) by the hip joint [START_REF] Horak | Postural strategies associated with somatosensory and vestibular loss[END_REF][START_REF] Nashner | The organization of human postural movements: a formal basis and experimental synthesis[END_REF].

However, it has also been shown that the knee joint influences postural control by lowering the CoM [START_REF] Alexandrov | Feedback equilibrium control during human standing[END_REF] and triggering compensatory postural strategies [START_REF] Gauchard | On the role of knee joint in balance control and postural strategies: effects of total knee replacement in elderly subjects with knee osteoarthritis[END_REF]; this challenges the classic paradigm of anklehip synergy [START_REF] Kilby | Models of postural control: shared variance in joint and COM motions[END_REF]. Kilby et al.'s study of ankle, knee, hip and neck kinematics during balance tasks found that each of these joints had an active role in postural control. Moreover, an upper body strategy for maintaining balance during dynamic postural tasks has been described in the literature [START_REF] Boström | The contribution of upper body movements to dynamic balance regulation during challenged locomotion[END_REF]. As the trunk is the most inertial segment of the body, it is not surprising that trunk control might be involved in postural control -especially during challenging postural tasks or dynamic situations [START_REF] Massion | Movement, posture and equilibrium: interaction and coordination[END_REF]. Furthermore, the trunk might have an impact on balance by stabilizing the head and therefore the vestibular system [START_REF] Massion | Clinical Disorders of Balance, Posture and Gait[END_REF]. For instance, it has been reported that postural performance during dynamic, one-leg stance was improved following specific neuromuscular training of the trunk in healthy individuals [START_REF] Cosio-Lima | Effects of physioball and conventional floor exercises on early phase adaptations in back and abdominal core stability and balance in women[END_REF] and athletes [START_REF] Sandrey | Improvement in dynamic balance and core endurance after a 6-week corestability-training program in high school track and field athletes[END_REF]. It has also been reported that trunk sway during two-leg stance is greater for older adults [START_REF] Gill | Trunk sway measures of postural stability during clinical balance tests: effects of age[END_REF][START_REF] Granacher | The importance of trunk muscle strength for balance, functional performance, and fall prevention in seniors: a systematic review[END_REF] and patients with vestibular issues than in healthy people [START_REF] Allum | Trunk sway measures of postural stability during clinical balance tests: effects of a unilateral vestibular deficit[END_REF]. These findings emphasize the trunk's role in subjects known to have poor postural control. In the double inverted pendulum model, the hips and trunk are combined in a "hip strategy". However, Blackburn et al. [START_REF] Blackburn | Kinematic analysis of the hip and trunk during bilateral stance on firm, foam, and multiaxial support surfaces[END_REF] underlined the importance of distinguishing between the hips' and trunk's respective contributions to postural control; the researchers observed similar hip and trunk variances under several different postural control conditions and concluded that models of postural control should take account of the trunk segment as well as the hip joint. Although the trunk clearly appears to have a role in postural control, its contribution (relative to lower limb joints) to this process has not been precisely determined.

With a view to understanding the trunk's involvement in postural control, the segment's neuromuscular activity has been investigated during external balance perturbations [START_REF] Horak | Postural strategies associated with somatosensory and vestibular loss[END_REF], a non-loaded, imposed posture [START_REF] Snijders | EMG recordings of abdominal and back muscles in various standing postures: validation of a biomechanical model on sacroiliac joint stability[END_REF] or a loaded, imposed posture [START_REF] Calatayud | Core muscle activity in a series of balance exercises with different stability conditions[END_REF]. To the best of our knowledge, Donath et al. are the only researchers to have studied the trunk's overall neuromuscular activity during an unrestrained, bipedal balance task [START_REF] Donath | Leg and trunk muscle coordination and postural sway during increasingly difficult standing balance tasks in young and older adults[END_REF]. They showed that the trunk's neuromuscular activity varies with the difficulty of the postural challenge and with age; the greater co-activation of trunk muscles in young adults (vs. older adults) was considered to be a means of stiffening the trunk and adjusting for postural imbalance not controlled by an ankle strategy alone. However, Donath et al. did not record the joint kinematics and so did not have a comprehensive vision of the influence of the trunk's neuromuscular activity on postural control in general and trunk kinematics in particular. We therefore decided to measure both neuromuscular and postural parameters, with a view to determining how neuromuscular control of the trunk is involved in postural control.

Hence, the main objectives of the present study were to (i) determine the trunk's contribution (relative to lower limb joints) to postural control during a challenging balance task and (ii) analyze the associated neuromuscular control processes. We hypothesized that in a challenging balance task, the trunk kinematic variables' contribution to CoF control would be at least as great as that of hip kinematic variables. Lastly, we explored the association between trunk muscle activation and trunk motion.

Materials and methods

Participants

Thirty-six healthy male adults participated in the study (mean (standard deviation (SD)) age: 23.3 (5.0); height: 1.83 (0.07) m; body weight = 79.4 (10.1) kg). This sample size was estimated based on a power analysis to achieve 80% power at an alpha criterion level of 0.05 during linear multiple regressions with four predictors analyses. All participants attended at least 3 training sessions a week and had over 10 years of experience in their respective sporting disciplines (handball, karate, and long jump). We chose these three sporting disciplines in order to study a broad range of postural control and footwork abilities. All participants reported that they had been free of lower limb or trunk injuries for the previous two months.

All participants gave their written informed consent prior to participation. The study was approved by the institutional review board (Comité de Protection des Personnes Sud Méditerranée III; reference: 2018.07.03 bis).

Material

Participants stood on a dual platform that consisted of two connected footplates supported by four strain gauges mounted symmetrically on a supporting force platform (EquiTest®, Neurocom, Clackamas, OR, USA). Vertical force data were sampled at 100 Hz. Given that the experimental perturbations were applied in the sagittal plane, the CoF was calculated in the anteroposterior direction, as follows: CoF=[((LF+RF)-(LR+RR))/(LF+RF+LR+RR)]*10.668, where left front (LF), right front (RF), left rear (LR) and right rear (RR) were the vertical forces and 10.668 (in cm) was the documented distance between the load cells and the center of the force platform.

Whole-body kinematics were measured using inertial measurement units (IMUs; CAPTIV, Tech Ergo Appliquées SARL, Vandoeuvre-lès-Nancy, France). The IMUs were placed on the left foot over the 3 rd metatarsal, laterally on the middle of the left shank, laterally on the middle of the left thigh, between the posterior superior iliac spines, and on the 6 th thoracic vertebrae. Before the static trial, the magnetometer's reading was checked and set to zero with the participant in quiet stance. Data were collected with a sampling rate of 64 Hz and resampled at 1000 Hz. Quaternions were converted into angles by using the CAPTIV system's software. The system had a resolution of 0.1°. Electromyographic activity (EMG) was recorded after the skin had been shaved and cleaned (baseline at rest: ≤5 µV). Wireless surface electrodes (Trigno™, Delsys, Natick, MA, USA) were attached parallel to the muscle fibers over the following muscles, bilaterally: the rectus abdominis (RA), the external obliquus (EOB) and the erector spinae (ES), in line with the SENIAM project's recommendations. RA electrodes were placed 2 cm laterally from the umbilicus, EO electrodes were placed at 15cm laterally from the umbilicus and ES electrodes were placed about 2 cm of the L1 spinous process.

Procedure

Participants performed three different bipedal postural tasks on a force platform. They were asked to remain as still as possible with their knees slightly flexed and their arms at their sides, while looking straight ahead. The foot position was standardized. Firstly, the participants were asked to remain still for 40 seconds with their eyes open (EO) (the static trial). Secondly, two non-static, challenging balance tasks were performed under EO and then "eyes closed" (EC) conditions. The ground support (i.e. the force platform) was tilted in the sagittal plane by twice the estimated anteroposterior sway of the CoM [START_REF] Nashner | Dynamic posturography in the diagnosis and management of dizziness and balance disorders[END_REF] (Figure 1). For example, a 1° forward or backward sway in the CoM around the ankle resulted in a 2° platform tilt in the same direction. The angle between CoM and center of foot support is calculated by the Equitest® as follows: θ = arcsin (PCoM/HCoM)-2.3 where PCoM is the distance between the center of force and the center of foot support, HCoM is 55.27% of the person's height. The 2.3 degrees is the correction applied by the system to correct anterior position of the CoM. The participants performed a warm-up consisting in 10 trials with different degrees of postural control difficulty to get familiar to unusual perturbations. Each trial lasted 20 seconds with 30 seconds rest in-between. After the warm-up, each participant performed two 20-second experimental trials (EO and then EC). Eight trials (7 during EC) were stopped and redone because subjects lost their balance and had to step off the platform.

Data analysis

The CoF's anterior-posterior maximum amplitude (CoF-AMP, in mm), sway path (CoF-SP, in mm) and SD (CoF-SD, in mm) were determined and provided respectively some information about postural accuracy, the magnitude of CoF displacement, and the variability of the postural control system [START_REF] Paillard | Techniques and methods for testing the postural function in healthy and pathological subjects[END_REF][START_REF] Cavanaugh | A nonlinear dynamic approach for evaluating postural control: new directions for the management of sport-related cerebral concussion[END_REF]. We also calculated the AMP, SP and SD for the ankle, knee, hip and trunk-pelvis joints angles (in °). Data on kinetics and kinematics were low-pass filtered with a 15Hz fourth-order Butterworth filter.

EMG data were sampled at 1000 Hz and band-pass filtered from 10Hz to 500 Hz. For the RA and EOB signals, the heart's electrical activity was filtered out with a 30 Hz Butterworth high-pass filter. The root mean square (RMS) EMG amplitudes were computed and normalized against the value from the static trial. Lastly, the left and right normalized EMG-RMSs were averaged.

We analyzed the data recorded during the middle 15 seconds of each trial. Each dependent variable was averaged over the two trials. Data were analyzed using MATLAB software (version 9.2, MathWorks, Inc., Natick, MA, USA).

Statistical analysis

Means and SDs were calculated for all measured variables. To determine the respective contribution (β-weight coefficients) of joint kinematics and EMG-RMS in postural control and trunk control, we performed multiple linear regression analyses of (i) joint kinematic variables as predictors of CoF variables, and (ii) EMG-RMSs as predictors of trunk kinematics. To check for multicollinearity, we examined the variance inflation factor (VIF) for each regression model. Normal distributions of quantitative data and residuals were checked with a quantile-quantile plot. Statistical analyses were performed with Statistica software (version 13, StatSoft, Inc., Tulsa, OK). The threshold for statistical significance was set to p<0.05.

Results

The values of CoF-AMP, CoF-SP, and CoF-SD were significantly higher in the EC condition than in the EO condition (Figure 2).

Likewise, joint kinematics were influenced by the postural task. For the ankle, knee, hip, and trunk, the respective AMP, SP and SD values were significantly higher in the EC condition than in the EO condition (p<0.001 for all; see Figure 3 for the trunk). Furthermore, the trunk muscles were significantly more activated in the EC condition than in the EO condition (p<0.001). The EC -EO difference (in %, relative to the static condition) was greater than 50% for the EOB (108±55% for EC vs. 51±17% for EO) and ES (181±93% vs. 115±46%, respectively) and close to 100% for the RA (150±140% vs. 53±29%, respectively).

The trunk relative weight in postural control

In all the regression models, the VIF was always below 5.0; we were therefore confident that multicollinearity was not a significant confounding factor. The results of the multiple linear regressions (i.e. joint kinematic variables as predictors of CoF variables) are summarized in Table 1. In the EO condition, the linear combination of joint kinematic variables accounted for between 60% and 75% of the variance (R²: 0.60-0.75; p<0.001) in the corresponding CoF variable. In the EC condition, the joint kinematic variables accounted for between 33% and 57% of the variance (R²: 0.33-0.57; p<0.05).

In the EO condition, β-ankle was a significant predictor of all the CoF variables, and β-trunk was a significant predictor of CoF-SP (p≤0.05). β-Ankle had the highest values (0.70 -0.80), followed by βtrunk (0.08 -0.27), β-knee (0.04 -0.15), and β-hip (0.03 -0.11). In the EC condition, only β-ankle was a significant predictor of CoF-SP and CoF-SD. Again, β-ankle had the highest values for each CoF variable, followed by β-hip (the second best predictor of CoF-AMP and CoF-SD) and β-trunk (the second best predictor of CoF-SP).

Trunk neuromuscular control

In all the regression models of the EMG data, the VIF was always below 5.0. The EMG variables did not significantly account for trunk kinematics under the EO condition. However, the linear combination of the EMG variables accounted for between 21% and 35% of trunk kinematics variance in the EC condition (R²: 0.21 -0.35; p≤0.05). For each kinematic variable, the ES had the highest β-coefficient (0.44 -0.57), followed by the EOB (0.10 -0.13) and the RA (-0.05 --0.01). β-ES was the only significant predictor of trunk kinematic variables.

Discussion

The present study's objectives were to determine the weight of trunk (relative to the lower limb joints) in postural control in athletes performing a challenging balance task and to analyze the neuromuscular control of the trunk. Our main findings were that (i) the trunk's contribution to postural control is at least as important as the hip's in the present task, and (ii) trunk motion during postural control seems to involve more the ES muscles than the surface abdominals.

Here, a challenging postural task was carried out on a tilting platform under EO and EC conditions. The greater difficulty under EC conditions (vs. EO) was evidenced by the significantly higher values of the CoF variables. Likewise, trunk motion and neuromuscular activity were higher under EC conditions.

Our results confirm Gill et al.'s report [START_REF] Gill | Trunk sway measures of postural stability during clinical balance tests: effects of age[END_REF] of greater trunk angular sway during more difficult postural tasks.

As the ankle had the highest β-coefficient of the four joints, our results confirm the well-known major role of the ankle in postural control [START_REF] Prieto | Characterization and modeling of postural steadiness in the elderly: a review[END_REF][START_REF] Aramaki | Reciprocal angular acceleration of the ankle and hip joints during quiet standing in humans[END_REF]. In the EO condition, 61% of the variance in CoF-AMP (i.e. postural accuracy) was accounted for by the amplitude of the joint kinematics. The trunk had an important, corrective role (-trunk: -0.18) in postural accuracy. In the EC condition, the joint kinematics only accounted for 33% of the variance in This low proportion might be due (at least in part) to the inclusion of extreme values in our calculation of the amplitude. Privation of vision might further increase the proportion of extreme values if the "safety zone" is explored so as to better estimate the CoM's position [START_REF] Krishnamoorthy | Joint coordination during quiet stance: effects of vision[END_REF]. Moreover, the joints' outlier values might not be time-synchronized with those of the CoF, as a result of antiphase joint patterns. The CoF-SP (i.e. the magnitude of CoF displacement) corresponds to the ability to stand as still as possible (i.e. steadiness) [START_REF] Cavanaugh | A nonlinear dynamic approach for evaluating postural control: new directions for the management of sport-related cerebral concussion[END_REF]. In the EO condition, 75% of variance in the CoF-SP was accounted for by the amplitude of joint displacement. The ankle was the most important joint in this respect, and was followed by the trunk. The knee and hip joints made rather small contributions. Interestingly, the trunk was the second-largest contributor factor in the EC condition -demonstrating that body steadiness is explained (at least in part) by the amount of trunk displacement. Our results underline the importance of trunk steadiness and thus head-trunk coordination, which would provide an effective support for the vestibular system [START_REF] Massion | Clinical Disorders of Balance, Posture and Gait[END_REF][START_REF] Nicholas | A link-segment model of upright human posture for analysis of head-trunk coordination[END_REF] and help to limit CoM accelerations [START_REF] Aramaki | Reciprocal angular acceleration of the ankle and hip joints during quiet standing in humans[END_REF]. CoF-SD was mostly accounted for by the ankle joint's SD. Surprisingly, the trunk did not appear to have an impact on CoF-SD. In view of the trunk's inertia, fast angular corrections through the ankle would certainly be more effective and would decrease the trunk's contribution to regulation of CoF-SD. The predominance of ankle variance over trunk variance under EC conditions has already been described in the literature [START_REF] Krishnamoorthy | Joint coordination during quiet stance: effects of vision[END_REF].

Overall, we found that the ankle was the main joint involved in posture control under challenging balance conditions. Although this was not unexpected (given the extensive literature [START_REF] Prieto | Characterization and modeling of postural steadiness in the elderly: a review[END_REF]), our results in a platform tilt paradigm further confirm the importance of this joint in balance. It is noteworthy that the trunk was more important than the hip in controlling postural accuracy and steadiness; this highlights the likely value of performing separate kinematic analyses of the trunk and hip [START_REF] Blackburn | Kinematic analysis of the hip and trunk during bilateral stance on firm, foam, and multiaxial support surfaces[END_REF]. The knee joint contributed less than other joints, indicating that the primary strategy used by the knee to lower the CoM might not be essential under challenging balance conditions. Overall, a multijoint analysis is likely to be more valuable than conventional single or double inverted pendulum models for understanding postural control. This suggestion is in line with Hsu et al.'s report [START_REF] Hsu | Control and estimation of posture during quiet stance depends on multijoint coordination[END_REF] that a six-joint model accounted for CoM variance better than the conventional inverted pendulum models did.

Although joint kinematics is the key factor for analyzing postural coordination, the present study's data on trunk neuromuscular activity provide a deeper understanding of the trunk's influence on postural control. In the EC condition, between 21% and 35% of the variance in trunk kinematic variables was accounted for by the three trunk muscles measured in the present study. The ES muscles made the largest contribution. With respect to anteroposterior body sway, it could be suggested that the ES may control trunk extension and flexion through concentric and eccentric contraction, respectively. In our task, the ES appeared to control the trunk's anteroposterior motion and the RA and EOB appeared to help stiffen the spine; this hypothesis might explain (at least in part) the low proportion of trunk motion variance accounted for by these muscles, and is in agreement with Stanton & Kawchuk's suggestion [START_REF] Stanton | The effect of abdominal stabilization contractions on posteroanterior spinal stiffness[END_REF] that the RA and EOB help to stabilize the spine. Interestingly, EMG activity for the abdominal muscles was lower during the EO condition than during the static trial. As ES are possibly the main muscles controlling anterior-posterior trunk tilt, RA and EOB might decrease their activity to reduce spine stiffness and therefore allow faster and more accurate trunk displacements during a challenging balance task. Furthermore, the analysis of "local" muscles (such as the transversus abdominis and the internal obliquus) might provide a more accurate view of trunk neuromuscular activity during postural control [START_REF] Donath | Leg and trunk muscle coordination and postural sway during increasingly difficult standing balance tasks in young and older adults[END_REF]. Lastly, the low percentage of variance accounted for by muscle activity might be due to inter-individual variability in muscle coordination and the intensity of trunk muscle contraction needed to stiffen the spine [START_REF] Cholewicki | Stabilizing function of trunk flexor-extensor muscles around a neutral spine posture[END_REF]. Difficulty in explaining trunk kinematics with EMG measurement has been reported for other tasks (such as changes of direction) in which neuromuscular activity was not associated with the trunk angle at initial foot-ground contact [START_REF] Jamison | The effects of core muscle activation on dynamic trunk position and knee abduction moments: Implications for ACL injury[END_REF]. Trunk muscle activity did not account for trunk motion in the EO condition. This could be explained by limited trunk motion with respect to the pelvis with the eyes open (e.g. AMP=2°). Indeed, the perturbations caused by platform movements induce displacements of the trunk; these displacements might be regulated by the trunk muscles themselves or by lower leg joints action that stabilize the trunk. The lack of correlation between kinematics and muscle activation observed in the present study suggests that trunk motion is controlled by the lower limb joints and that trunk muscle activation stiffens the spine and helps to maintain balance [START_REF] Donath | Leg and trunk muscle coordination and postural sway during increasingly difficult standing balance tasks in young and older adults[END_REF].

We acknowledge several limitations in this study. First of all, different balance tasks induce different skills in order to maintain balance [START_REF] Kümmel | Specificity of balance training in healthy individuals: a systematic review and meta-analysis[END_REF]. Therefore, the present results cannot be generalized to each challenging balance task and every healthy or active population. However, this study helps to underline the importance of the trunk in a challenging situation, confirming literature on other tasks [START_REF] Blackburn | Kinematic analysis of the hip and trunk during bilateral stance on firm, foam, and multiaxial support surfaces[END_REF]. Then, all trunk and pelvis muscular activity could not be taken into account, as only main surface muscles connecting thorax or spine to the pelvis were measured. Moreover, the modelling of the trunk as a rigid segment might not accurately reflect its kinematics [START_REF] Preuss | Musculature and biomechanics of the trunk in the maintenance of upright posture[END_REF], blurring the links between muscle activations and spine kinematics. Although the Captiv IMU system has been validated in the literature [START_REF] Peeters | Full body three dimensional joint angles validation using TEA ergo inertial measurement units[END_REF], the use of this methodology might reduce the accuracy of joint angles measurements compared to gold standard motion capture systems.

Figure 1 :

 1 Figure 1: Representation of the balance task with the tilting platform in (A) the "eyes open" (EO) and (B) eyes closed (EC) conditions (EquiTest®, Neurocom, Clackamas, OR, USA).

Figure 2 :

 2 Figure 2: CoF amplitude (AMP), sway path (SP) and standard deviation (SD) under "eyes open" (EO) and "eyes closed" (EC) conditions.

Figure 3 :

 3 Figure 3: Trunk amplitude (AMP), sway path (SP), and standard deviation (SD) under "eyes open" (EO) and "eyes closed" (EC) conditions.

Table 1 :

 1 Results of the multiple linear regressions for each kinematic variable (amplitude (AMP), sway path (SP), and standard deviation (SD)) under "eyes open" (EO) and "eyes closed" (EC) conditions. R² = coefficient of determination, F= Fisher distribution, *p≤0.05

		AMP		SP		SD
		EO	EC	EO	EC	EO	EC
	R²	0.61	0.33	0.75	0.57	0.60	0.43
	F	12.0	3.85	23.8	10.1	11.5	5.91
	p	<0.001	<0.001	0.012	<0.001	<0.001	0.001
	β-Ankle	0.70*	0.34	0.72*	0.50*	0.80*	0.59*
	β-Knee	0.15	0.02	0.06	0.16	0.04	-0.08
	β-Hip	0.11	0.21	-0.04	-0.06	-0.03	0.15
	β-Trunk	-0.18	0.11	0.27*	0.27	-0.08	0.03

Acknowledgements

This work was promoted by the Université de Lorraine, France. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Conclusion

When compared with the double inverted pendulum model, a multijoint analysis provided a better understanding of postural control. We found that during a highly challenging balance task, the trunk was the second most important segment or joint (after the ankle) in the control of postural accuracy and steadiness. Although the trunk muscles' EMG activity accounted for a relatively small proportion of the variance in trunk motion, our present results demonstrated that the ES seems to have an important role in controlling trunk anteroposterior motion, while the RA and EOB might tend to stiffen the spine.

Conflict of interest

The authors declare that they have no conflict of interest.