Colin Lalouette
email: lalouette@irit.fr

Bernard Pavard
email: pavard@irit.fr

Enhancing inter-organizational resilience by loose coupling concept and complexity paradigm

During a co-design project, we modeled formal and informal cooperation which are expressions of tight and loose couplings. Our findings confirm that loose couplings are crucial since they enable selforganization and emerging processes which often underlie success of codesign. We offer new insight into management and organization theories by presenting an inter-organizational resilience model which explains how non-deterministic couplings can enhance inter-organizational resilience.

INTRODUCTION

To achieve a long-term competitive success, firms need to work with several partners to have the capacity of generating common knowledge and applying it in the form of innovation. By this way, architecture of design in aeronautical domain has become more and more complex in recent years and its management is no longer confined to the inside of the firm since linkages cross its boundaries [START_REF] Lalouette | KM of an aircraft manufacturer within extended enterprise: ECKM 2007[END_REF]. For implementing resilience between organizations, both project level cooperation and firm level linkages need to be taken into consideration. The aim of this article is to enhance interorganizational resilience by proposing a conceptual framework which combines loose coupling [START_REF] Weick | Educational organization as loosely coupled systems[END_REF] and organizational learning [START_REF] Argyris | Organizational learning: A theory of action perspective[END_REF] concepts within the complexity paradigm. To this end, we show how formal and informal cooperation are expressions of tight and loose couplings within a complex sociotechnical system. Loose coupling and organizational learning underlie the reputation of HRO, the High Reliability Organizations school [START_REF] Weick | Managing the unexpected: Resilient performance in an age of uncertainty[END_REF]: when they are enabled the resilience is enhanced [START_REF] Bierly | Culture and high reliability organizations: The case of the nuclear submarine[END_REF]. Unlike tight couplings, the outcomes of loose couplings are non-deterministic. How can non-deterministic couplings enhance resilience? This question is controversial for management and organization theories which deal classically with deterministic models. After an analysis of empirical data, we present an argument for an inter-organizational resilience model which answers this question by using a systemic approach. First, we proposed a way to improve the loose coupling conceptualization to assist with our specific research objectives. Then, we examined a co-design project (i.e. a common design of joint partners) and conducted semi-directed interviews by employing a qualitative analysis method on the information and knowledge flows. After that, we used our loose coupling conceptualization to instantiate loose couplings that we have recorded. Finally we modeled co-design in order to understand relationships between loose couplings and their outcomes. The empirical part of this study concerns a co-design from an aeronautical company and one of its risk sharing partners. Our findings confirm that loose couplings are crucial in complex socio-technical systems since they enable selforganization and emerging processes which often underlies success of co-design.

RELATION TO EXISTING THEORIES AND WORKS

Summing up prior studies, Williams points out that inter-organizational cooperation lies mainly in the sustained contractual linkages and social relationships among partners [START_REF] Williams | Cooperation by design: Structure and cooperation in interorganizational networks[END_REF]. Co-design is a specific inter-organizational cooperation which enables products to emerge from multiple design interactions between organizations. During a co-design, actors from different organizations work within a single spatial locationcommonly called a plateau -whose aim is to enable informal cooperation. Examining such projects during the past decade, we observe a significant increase in uncertainties, project risks and complexity [START_REF] Choi | The supply base and its complexity: Implications for risks and innovation[END_REF][START_REF] Williams | Cooperation by design: Structure and cooperation in interorganizational networks[END_REF]. We mobilize the concept of loose coupling as a way of studying complexity of such projects. Loose coupling has been mainly developed in Weick's work on loosely coupled systems [START_REF] Weick | Educational organization as loosely coupled systems[END_REF]. More recently this latter phrase was more clearly conceptualized by [START_REF] Orton | Loosely coupled systems: A reconceptualization[END_REF]. The loose couplings include implicit and nondeterministic interactions [START_REF] Rochlin | Defining HRO in practice: A taxonomic prologue[END_REF], flexible routines [START_REF] Grote | Rules management as source for loose coupling in high-risk systems[END_REF] or selforganizations and emerging processes [START_REF] Pavard | Underlying concepts in robustness and resilience and their use in designing sociotechnical systems[END_REF]. As opposed to loose coupling, the tight coupling concept is characterized by strong dependencies between elements of a system [START_REF] Perrow | Normal Accidents: Living With High-Risk Technologies[END_REF]. The tight couplings include explicit and deterministic procedures, official reviews or contractual commitment. We try to understand how loose couplings enable organizational learning; and particularly learning across multiple organizations [START_REF] Chena | Inter-organizational knowledge management in complex products and systems: Challenges and an exploratory framework[END_REF]. Organizational learning is a characteristic of an adaptive organization whose actors are able to sense changes in signals from their environment. Actors try to change organizational functions and structures of their organization according to these signals. Three level of organizational learning have been considered. First, single-loop learning is a simple error-andcorrection process. Then, double-loop learning is an error-and-correction process modifying organization's underlying norms, policies or objectives. Finally, deuterolearning is learning about how to carry out single-loop and double-loop learning. Organizational phenomena are sometimes discussed in terms of complex systems because the complexity paradigm is the only theoretical framework which is able to explain self-organization and emerging processes [START_REF] Pavard | Underlying concepts in robustness and resilience and their use in designing sociotechnical systems[END_REF]. By definition, complex systems are non-linear and non-deterministic: their elements interact in a systemic way with both positive and negative feedback which can lead to strong and unforeseen effects in other parts of the system [START_REF] Weick | Managing the unexpected: Resilient performance in an age of uncertainty[END_REF]. When organizations are complex, research suggests that there is no simple way to take control over development. To hope that more formalization could resolve this issue can be rather fruitless. This is why managers need to accept and to cope with complexity: a wiser strategy might ensure more organizational learning that could in turn enhance resilience.

RESEARCH APPROACH

We conducted a literature review to establish the state-of-the-art and to propose an improved conceptualization of the loose coupling according to four parameters:

1. The cause(s)2 of the loose coupling (e.g: authority delegation or culture).

2. The consequence(s) 2 (e.g: innovation or information buffering).

3. The category 2 (e.g: intra-organizational or inter-organizational). 4. The organizational learning level (from single-loop one to deutero-learning). For documenting formal and informal cooperation, and to study tight and loose couplings, we employed a qualitative analysis method on the information and knowledge flows [START_REF] Wybo | Méthodologie de retour d'expérience des actions de gestion des risques[END_REF]. This methodology is to closely examine tasks, activities and work of the actors in order to determine: a) the actions inside and between organizations; b) the links between the sequences of events; c) the sense-making of actors concerning artifacts, events and environment. Our corpus of gathered empirical data includes: a) discourse from semi-directed interviews; b) pictures and notes from field observations (contexts, actions, behaviors, etc.); c) and official companies documentation such as legal contracts and procedures. We analyzed the data according to the three spheres of continual interaction existing within socio-technical systems: the technical, the human and the organizational spheres. Data then has been treated according to two modeling dimensions. First, the inter-organizational modeling allowed us to represent where and how the actors worked and networked. Then, the co-design workflow modeling allowed us to reconstitute the various steps of the co-design between organizations. Finally we instantiated loose couplings according to parameters determined based on our conceptualization. During an observation on a plateau, 30 semi-directed interviews, lasting approximately one hour each, were conducted with engineering and management executives of the aeronautical company and its risk sharing partner under study.

FINDINGS

The empirical data enabled us to identify tight couplings, to instantiate loose couplings and then to describe the relationships between theses couplings and their outcomes.

Inter-organizational and co-design workflow modeling

Hereafter we describe data as examples of part of the corpus that we have analyzed. Ex. A -Interview with a stress engineer: "Due to the size of the organizations [both partners], to look for and find -then to talk with -the right person is more and more difficult. We haven't other choice: we use our personal network to find the information we need, even if we have always to overstep hierarchical and organizational marks." Ex. B -Observation of an informal management meeting: A says "You know that your team shall be organized as a mirror of ours?", B replies: "We shall… but we can't work with a work package organization as you. We can't change a life long way of working! Our overall thought is definitely component-focused, not package-focused.", A concludes: "OK, OK, so that means we'll just have to coordinate differently together." Ex. C -Interview with a stress engineer: "When a guy from our partner has to ask us a question, my boss [the stress leader and official responsible] always says to him to go directly to talk with me. We gain so much time without this hierarchical relationship." Ex. D -Interview with a design engineer: "Even if it's not my job, when they have an idea that we have already test, I say to them 'Hey, we've try this way but without success because (…). I would forget it if I were you'. Plateau is done for this kind of action." Ex. E -Interview with a program manager: "The PPM -the Project Progress Meetingis a weekly but unofficial meeting. It's written nowhere to do a PPM; you can't find any information about PPM since it's not expected by contract, nowhere. However we wished to build it -together -to have a brief overview of where we are / where we go." Ex. F -Interview with a design engineer: "I know it's the beginning… but too many designers of our partner work outdoors so that means that we do twice the same work." Analysis of these examples shows empirical evidences about loose couplings outcomes:

A) An inter-organizational social network emerges to cope with the complexity of the joint organizations: simple but powerful practices shortcuts official boundaries. B) An organizational interface is collectively built by project managers to articulate cooperation: the formal organization is modified and enables actors to converge. C) An informal settlement is agreed between partners to be more efficient: actors do not modify formally their hierarchical policy but they learn the point in delegating. D) Knowledge and advises are freely shared because a membership feeling appears: this outcome customarily found within plateau is the most basic but efficient one. E) Events are self-organized according to the inter-organizational coordination needs:

this meeting is become a quasi-official event thanks to its short-term benefits. F) Cooperation opportunities are rather inexistent and the work is done twice: actors of both organizations work more -for less results -and each in his own way. The instantiated loose couplings for both modeling are summarized in Tab. 1 and Tab. 2.

Co-design workflow and inter-organizational models

From this data analysis, we observed that loose couplings have positive (Ex. A to E) or negative consequences (Ex.

Inter-organizational resilience model

From the whole analysis of our corpus, we found empirical evidences about tight couplings and loose couplings. By formalizing organizational structures and functions, tight couplings enable employees -and especially managers -to foresee process outputs and to plan projects in an idealistic optimized way: they clearly improve co-design effectiveness. By enabling informal cooperation, self-organization and emerging processes, loose couplings often underlie the success of formal cooperation; they clearly improve co-design efficiency. Loose couplings are the foundation for co-design performance, from day-to-day work to resolution of complex problems, since they ensure more organizational learning that in turn enhances resilience. In fact, organizational structures and functions evolve thanks to both kinds of coupling: this provides the balance between control and freedom required during co-design. Besides, we can notice that deutero-learning is also implemented within the studied plateau by at least two means: a lessons learnt process whose aim is to improve expected technical issues for further programme and a learning organization process whose aim is to do continuous improvement about unexpected organizational issues for current programme. These organizational learning are respectively long-cycled and medium-cycled; we define them foreseen resilience (i.e. resilience for adaptation). On the other hand, very few things are done within plateau to promote and spread short-cycled organizational learning; we define it emerging resilience (i.e. resilience for adaptability). We consider all these findings into an inter-organizational resilience model for co-design (cf. Fig. 3).

Fig. 3. Inter-organizational resilience model

CONCLUSION

Inter-organizational cooperation is getting complex and complex: to manage holistically becomes merely impossible. Unplanned events often take place during co-design and, in most cases, only relying on the existing knowledge basis cannot develop appropriate problem-solving solutions. In this study, we explained that loose couplings create self-organization and emerging processes enabling actors of different organizations to make functional and structural regulations. The model that is introduced goes beyond a mere description of the system by offering a new insight into cooperation and management: this model shows why managers have to increase loose couplings. Actually, partners of an extended enterprise need to freely learn relevant knowledge from each other. To this end, they need to combine their knowledge by a distributed and bottom-up control to improve organizational learning and ensure decision-making. But how can we theoretically combine a top-down centralized control with a bottom-up distributed cooperation? Our next step will be to provide dialectic thanks to complexity paradigm on this different comment about organization theories. After the completion of this final step, we will develop and test the application on co-design of newly developed material and process artifacts, with specific outcome objectives, informed by the holistic understanding of loose couplings. Actors will be able to use these artifacts at their discretion, according to their operational needs and opportunities [START_REF] Pavard | Context dependant mobile interfaces for collaboration in extreme environment[END_REF].

  Fig. 1. Inter-organizational model Fig. 2. Co-design workflow model

Table 1 .

 1 Instantiated loose coupling for the inter-organizational modeling

	Ex. Cause	Consequence	Category	Organizational learning
	A	Complexity	Hierarchical shortcuts	Inter-organizational	Single-loop
	B	Needed convergence	Behavioral discretion	Inter-organizational	Double-loop
	C	Authority delegation	Efficiency	Intra-organizational	Single-loop

Table 2 .

 2 Instantiated loose coupling for the co-design workflow modeling

	Ex. Cause	Consequence	Category	Organizational learning
	D	Membership feeling	Increased advices	Inter-organizational	Single-loop
	E	Needed coordination	Ensured cooperation	Inter-organizational	Double-loop
	F	Limited cooperation	Ineffectiveness	Inter-organizational	Ø

This work was supported by the Foundation for an Industrial Safety Culture (FonCSI)

This parameter comes from the conceptualization of Orton & Weick[START_REF] Orton | Loosely coupled systems: A reconceptualization[END_REF]


Lionel Leroux

Betty Descamps

Nancy Ferreira Tojais

Benjamin Séguy

Pierre Oses

Catherine Moreau

Danièle Daret

Zoran Ivanovic

Jean-Michel Boiron

Jean-Marie Daniel Lamazière

Pascale Dufourcq

Thierry Couffinhal

Cécile Duplàa
email: cecile.duplaa@inserm.fr

Hypoxia Preconditioned Mesenchymal Stem Cells Improve Vascular and Skeletal Muscle Fiber Regeneration After Ischemia Through a Wnt4-dependent Pathway

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

INTRODUCTION

Bone marrow mesenchymal stem cells (MSC) can be isolated from bone marrow-derived mononuclear cells (MNC), expanded in vitro and have been shown to possess functional multi lineage differentiation capacity [START_REF] Pittenger | Multilineage potential of adult human mesenchymal stem cells[END_REF]. MSC have been shown to differentiate into pericytes [2], vascular endothelial cells [START_REF] Dufourcq | Secreted frizzled-related protein-1 enhances mesenchymal stem cell function in angiogenesis and contributes to neovessel maturation[END_REF][START_REF] Muguruma | Reconstitution of the functional human hematopoietic microenvironment derived from human mesenchymal stem cells in the murine bone marrow compartment[END_REF] and cardiomyocytes [START_REF] Oswald | Mesenchymal stem cells can be differentiated into endothelial cells in vitro[END_REF], and their transplantation has improved recovery from ischemia in rat hindlimb and swine dilated cardiomyopathy models [START_REF] Toma | Human mesenchymal stem cells differentiate to a cardiomyocyte phenotype in the adult murine heart[END_REF]. Their precocious role in the formation and the maintenance of neo vessels has been studied extensively [2,[START_REF] Nagaya | Transplantation of mesenchymal stem cells improves cardiac function in a rat model of dilated cardiomyopathy[END_REF]. Such reports have led to the hypothesis that MSC may be used in the treatment of ischemic cardiovascular pathologies. One major limitation demonstrated in both animal and human experiments has been the inability to maintain a large number of cells after grafting into hypoxic sites. In the current study we employed a strategy of low oxygen (O2)-preconditioning of MSC before tissue implantation. We hypothesized that creating this hypoxic environment might mimic the stem cell niche microenvironment in vivo which others have hypothesized to likely create a hypoxic cavity [START_REF] Abramsson | Endothelial and nonendothelial sources of PDGF-B regulate pericyte recruitment and influence vascular pattern formation in tumors[END_REF]. We chose to study 1% O2 concentration since it has been reported as the level found in vivo in bone marrow stem cell niche areas [START_REF] Moore | Stem cells and their niches[END_REF]. Moreover, data from animal studies have demonstrated a role of hypoxic gradients in stem cell trafficking in ischemic tissue [START_REF] Chow | Modeling pO(2) distributions in the bone marrow hematopoietic compartment. II. Modified Kroghian models[END_REF]. On the molecular level, temporary oxygen deprivation is known to regulate gene transcription and differentiation of stem cells [START_REF] Ceradini | Progenitor cell trafficking is regulated by hypoxic gradients through HIF-1 induction of SDF-1[END_REF]12].

Several reports suggest that the Wnt pathway plays a role in maintaining hematopoietic stem cell self-renewal and pluripotency [START_REF] Reya | A role for Wnt signalling in self-renewal of haematopoietic stem cells[END_REF][START_REF] Malhotra | Wnt-related molecules and signaling pathway equilibrium in hematopoiesis[END_REF]. The Wnt family of genes encodes over twenty cysteine-rich secreted glycoproteins to regulate canonical and non canonical signaling pathways [START_REF] Bhanot | A new member of the frizzled family from Drosophila functions as a Wingless receptor[END_REF]. The canonical Wnt pathway regulates gene expression due to the stabilization and nuclear localization of J3 catenin. We have previously demonstrated that MSC have a structural role in forming a precocious network and facilitating neovessel recruitment in an angiogenic model and reported that overexpression of a soluble modulator of Wnt functions, sFRP-1, in MSC, enhanced their angiogenic capacities [2]. Experimental manipulation of a pluripotent mouse embryonal carcinoma stem cell line via another secreted Wnt modulator, sFRP2, identified the Wnt pathway in cardiomyogenic differentiation [START_REF] Zhang | Secreted frizzled related protein 2 protects cells from apoptosis by blocking the effect of canonical Wnt3a[END_REF]. Wnt3a activation modulated proliferation and differentiation of human MSC and murine embryonic mesenchymal cells [START_REF] Boer | Effects of Wnt signaling on proliferation and differentiation of human mesenchymal stem cells[END_REF][START_REF] Derfoul | Differential regulation of osteogenic marker gene expression by Wnt-3a in embryonic mesenchymal multipotential progenitor cells[END_REF]. Recently, another study demonstrated a role of the Wnt signaling pathway in the acquisition of the invasion property of human MSC [START_REF] Neth | The Wnt signal transduction pathway in stem cells and cancer cells: influence on cellular invasion[END_REF]. These data have been particularly important to help elucidate the molecular mechanism that enables MSC to contribute to tissue regeneration under ischemic conditions.

In the current study, we compare the ability, of hypoxic preconditioned murine MSC (HypMSC) and non-preconditioned MSC (NormMSC), to engraft into ischemic tissue and assessed the ability of these cells to participate in skeletal tissue and vascular regeneration. A sub acute murine limb ischemia model was used to mimic the clinical setting of critical limb ischemia in patients. Our results demonstrate that HypMSC have a greater capacity for engraftment in ischemic tissue compared to NormMSC. HypMSC also improved skeletal muscle regeneration and induced more neoangiogenesis, and elicited significant improvement in blood flow as compared to NormMSC. Localization of HypMSC compared to NormMSC suggests that HypMSC participate in the remodeling of the stromal environment via structural interactions, first in encircling necrotic myocytes and then shaping a tight network around endothelial cells along growing neovessels. This preferential localization led us to speculate that MSC could functionally interact via paracrine effectors with myocytes and endothelial cells (EC). Our data demonstrates that MSC express Wnt4 and in vivo Wnt4 transcripts were significantly increased in ischemic muscles engrafted with HypMSC while in muscle engrafted with NormMSC no significant increase was detected. We tested the biological activity of Wnt4 in vitro and found that it could stimulate EC migration, myogenic differentiation and MSC proliferation but had no effect on EC proliferation. Importantly, inhibition of Wnt4 expression in MSC abrogated HypMSCinduced vascular regeneration. Our data provides strong evidence that Wnt signaling could be an important factor in the mechanism by which MSC contribute to tissue regeneration, as well as vessel formation and stabilization. As such, hypoxia preconditioning of MSC could be an attractive therapeutic approach for the treatment of ischemic vascular diseases.

RESULTS

Vascular and muscle regeneration of the ischemic hindlimb was improved after transplantation of HypMSC vs NormMSC

We examined the comparative effectiveness of transplanted murine HypMSC vs NormMSC for vascular and ischemic muscle regeneration after femoral ligation in C57BL/6J mice. Three groups were set up: a control sham group receiving saline injection, a NormMSC group receiving by intramuscular injection 0.5x10 6 MSC cultured in normoxia (20% O2) and a HypMSC group transplanted with 0.5x10 6 MSC pretreated during 36 hours in a reduced oxygen tension (1% O2).

HypMSC enhanced vascular response

Blood flow recovery in the limb of HypMSC-treated animals was significantly improved when compared with sham-treated animals or NormMSC-treated animals (Figs. 1a,b).

The therapeutic action of HypMSC was also evident at the angiogenic level, as evidenced by quantification of only viable muscle, excluding angiogenesis involved in an inflammatory response to granulation tissue. At day 15, there was an increase in CD31-positive capillary number in HypMSCtreated muscles compared respectively with that in sham-treated control (P<10 -5 ) and in NormMSC groups (P< 10 -3 ) at day 15 ( Figs 1c-f). These results suggest a potent role of HypMSC in new-vessel formation. Consistent with improved limb perfusion and capillary density, micro scanner (mCT) analysis of the whole arterial network revealed the global impact of HypMSC on vessel formation in the hindlimb after ischemia. Images showed a greater number of vessels in HypMSC-treated hind limb compared to NormMSC or sham-treated injected hindlimb at day 8 after the insult (Figs 1g-k).

We calculated a 2 fold increase in the vessel number (number of vessels/μm 3 , P<0.01) and a 1.7 fold increase in their connectivity and branching (P<0.01) in the HypMSC-treated hindlimb compared with sham-treated control animals while NormMSC-treated animals were at an intermediate level (P<0.05) (Figs 1 j-k).

HypMSC enhanced muscle regeneration

Histological evaluation of muscle tissue, performed to analyze the impact of HypMSC transplantation on the repair process, revealed that administration of either HypMSC or NorMSC accelerated the repair process. At day 7, almost no overt necrotic area was found in either of the MSC-treated groups, while necrotic muscle fibers were markedly observed in sham treated muscles (25% out of total muscle surface). However, HypMSC engraftment had a significant beneficial effect on muscle regeneration when compared with NormMSC-treated group. Less than 10% of the histological area in the ischemic muscle were still actively regenerating in HypMSC-treated tissue while in the NormMSC treated group, the process was delayed with over 21% of the total muscle surface was still actively regenerating (Figs 1l-q).

Hypoxic pretreatment modified MSC engraftment in ischemic hindlimb

MSC were infected with a lentivirus encoding for the GFP gene (GFP-MSC) and expression was followed as a marker of viable GFP-positive MSC [2]. HypMSC robustly engrafted the adductor and tibial muscles in large patches, as revealed by direct fluorescence at day 7 (Figure S1a) or antiGFP immunohistochemistry at day 14 (Figure S1b).

Hypoxic treatment improved MSC survival capacities in vivo

Real time RT-PCR was performed using total RNA obtained from HypMSC and NormMSC injected muscles at day 7 after injury to determine the percentage of remaining GFP expression, and demonstrated that hypoxic pre-treatment contributes to effective enhancement of MSC recruitment in vivo. In the HypMSC group, there was a significant increase in MSC engraftment at day 7 (150% of initially engrafted HypMSC) where as in NormMSC group, the total number of MSC was not maintained after transplantation (63% of initially engrafted NormMSC) (Fig. 2a). At day 7, caspase 3 labeling showed apoptotic muscle fibers surronding by surviving Hyp and Norm GFP-MSC (Fig. 2b).

Double BrdU/GFP labeling revealed that BrdU incorporation rate was significantly increased in

HypMSC group compared to NormMSC group (16.3 ± 8.1 vs 13.1 ± 6.6 BrdU/GFP + cells/mm 2 P<0.05) (Figs 2c-d).

HypMSC were widespread in hypoxic zones and may play a macrophage-likefunction

HypMSC appeared to have a different pattern of engraftment as compared to NormMSC. To better understand this, we evaluated the scattering of MSC in hypoxic zones using the 2-nitroimidazole hypoxia marker, pimonidazole. Hypoxic sections of muscle produced a mottled staining with a characteristic hypoxic brown center. At day 7, a large number of GFP-positive HypMSC were evenly distributed in deep hypoxic zones around necrotic myocytes whereas GFP-positive NormMSC were consistently detected at the periphery of ischemic zones (Fig 3a andFigure S2). The distribution of MSC around necrotic myocytes suggested a potential macrophage-like, phagocytic function for these cells. GFP immunofluorescent staining revealed that MSC harbor a phenotype with long filopodial protusions that can encircle and penetrate into dead myocytes (Figs 3b-d). To evaluate the phagocytic capacity of MSC in regards to myocytes, in vitro experiments were conducted.

Fluorescent microscopy examination revealed that GFP-MSC co-cultured with necrotic cell bodies of PKH-labeled murine myoblasts (red) were able of robustly engulf part of the myoblast cell membranes (Figs 3f,g). GFP-MSC co-cultured with non-necrotic PKH-labeled murine myoblasts (red) did not have this property (Fig. 3e). At day 15, HypMSC appeared to be preferentially associated with capillaries and microvessels, behaving as perivascular cells shaping along the whole length of the vessel, covering growing CD31-forming tube-like structures, as mural cells (Figure S3).

HypMSC paracrine Wnt dependent effect on angiogenesis and muscle regeneration

The effects of temporary hypoxia on Wnt factor expression were also investigated. Several studies have demonstrated a role of the Wnt pathway in vascular development [START_REF] Zerlin | Wnt/Frizzled signaling in angiogenesis[END_REF] as well as stem cell proliferation and maintenance [START_REF] Reya | A role for Wnt signalling in self-renewal of haematopoietic stem cells[END_REF]. We hypothesized that MSC express Wnt and use the Wnt pathway as a mechanism for activation of muscle regeneration processes. Screening by RT-PCR for the expression of different Wnt transcripts revealed that MSC express Wnt4, 5A, 5B and 11. In vivo, Wnt4 transcripts were significantly increased in HypMSC injected muscles (ratio Wnt4/P0: 15.6±5.2, P=0.01 vs control tissues) while NormMSC implantation did not significantly increase Wnt4 transcripts (ratio Wnt4/P0: 3.8±1.8, P=NS vs control tissues) (Fig. 4). Wnt5A, 5B and 11 expressions were not significantly modified in either HypMSC and NormMSC injected muscles compared with control muscle at day 7 after ischemia. Corroborating evidence was found in vitro where a specific strong up-regulation of Wnt4 was detected after exposing MSC to hypoxia for 36 hours compared to normoxia-treated MSC (Wnt4/P0: 4.78±1.8, P=0.01 in comparison to control) (Figure S4). In parallel, we report preconditioning effects on angiogenic growth factor expressions by HypMSC (Figure S4 ac).

Functional validation of HypMSC secreted factors on cell functions

To further elucidate the functional paracrine and autocrine role of HypMSC secreted factors in vascular response and muscle regeneration enhancement, we studied the effect of ex vivo incubationof the different cellular components namely EC, muscle fibers and MSC with HypMSC and Wnt4 conditioned medium (HypCM and Wnt4 CM, respectively).

HypMSC secretedfactors and Wnt4 played a role on EC migration but not on EC proliferation

Transwell filters revealed that HypCM and Wnt4 CM induced significantly more migration of EC than did respectively CM from NormMSC (NormCM) and control CM (P<0.05). Moreover, addition of a secreted Wnt antagonist, rb sFRP-1, blocked the HypCM-induced migration suggesting that Wnt dependent factors are the major active factors present in HypCM. (Fig 5a and Figure S5). It is worth noting that rb sFRP-1 enhanced migration of both NormCM-treated EC and control EC, which is in agreement with previous reports [START_REF] Dufourcq | FrzA, a secreted Frizzled Related Protein, induced angiogenic response[END_REF]. Interestingly, HypCM had no effect on EAhy926 proliferation compared with CM from NormMSC (NorCM) (data non shown). Taken together, these results support a role of HypCM and Wnt4 on EC migration.

Wnt4 induced skeletal myoblast differentiation

To explore the potential role of Wnt4 on skeletal muscle differentiation, intact primary murine skeletal myoblasts were cultured in the presence of Wnt4 CM for 16 hours and compared with myoblasts treated with control CM. The results revealed that the number of myogenin-expressing cells was significantly increased in Wnt4-treated myoblast culture compared to control condition (P<0.01) (Fig. 5b).

Autocrine role of Wnt4 promoted MSC proliferation, migration and Wnt canonical ß-catenin pathway activation

We then tested the hypothesis that enhancement of HypMSC engraftment could be due in part to Wnt4 upregulation. The role of Wnt4 as a potent inducer of MSC migration was demonstrated (Fig. 5c).

In addition, data revealed an effect of Wnt4 on the number of MSC but only under hypoxic conditions (Fig. 5d). Moreover, Wnt4 was able to activate the canonical Wnt pathway as shown by T-Cell factor (TCF) -dependent transcriptional activity measured under hypoxic conditions; transfection of MSC with a plasmid coding for Wnt4 provoked a 15-fold increase in luciferase activity (Fig. 5e). No activation was seen by using the corresponding control reporter with mutated TCF binding sites.

Inhibition of Wnt signaling using rb sFRP1 also effectively suppressed TopFlash luciferase reporter activities in response to Wnt4. Our data are consistent with the interpretation that Wnt4 signals are transduced via the canonical branch of the Wnt pathway and reveal that MSC respond to Wnt4 stimuli in a hypoxic environment.

Suppression of Wnt4 expression in HypMSC prevented the vascular regenerative response induced by hypoxia pre treatment

An in vivo model of Wnt4 suppression was employed to demonstrate the importance of Wnt4 as a key paracrine factor mediating pro-angiogenic effects of HypMSCs. As such, we treated HypMSC with two siRNA against Wnt4 (Fig. 6a) and transplanted them into the mouse ischemic hindlimb model. We showed that siControl (siCtl) treated HypMSC compared to siCtl treated NormMSC enhanced significantly the blood flow (P<0.05) (Fig. 6b), and vascular density (P<0.05) and connectivity (P<0.05) (Fig. 6 c-d). Treatment of HypMSC with siRNA against Wnt4 abrogated the difference between HypMSC and NormMSC groups; either blood flow or vascular density and connectivity were not significantly different between siWnt4 treated HypMSC and siCtl treated NormMSC groups.

DISCUSSION

The influence of temporary hypoxic preconditioning of MSC on the stimulation of angiogenesis and muscle regeneration was investigated and the data revealed that ex vivo hypoxic preconditioning of MSC plays a unique role in the enhancement of vessel formation and repair of the necrotic zone after a hindlimb ischemia via a Wnt dependent pathway.

We hypothesized that the 1% oxygen atmosphere in which MSC were maintained could condition them to survive in a hypoxic environment in vivo as reported in vitro [START_REF] Kim | Ischemic preconditioning augments survival of stem cells via miR-210 expression by targeting caspase-8-associated protein 2[END_REF][START_REF] Jin | Mesenchymal stem cells cultured under hypoxia escape from senescence via down-regulation of p16 and extracellular signal regulated kinase[END_REF]. Oxygen tension in bone marrow compartments has been reported to be very low as in injured tissue, suggesting that tissue hypoxia may be a fundamental mechanism governing stem cell recruitment and retention [START_REF] Chow | Modeling pO(2) distributions in the bone marrow hematopoietic compartment. II. Modified Kroghian models[END_REF]. As a result, we demonstrated that hypoxic pre-treatment can more effectively overcome the hurdle of cell death after implantation than normoxic conditioning, promoting MSC survival and proliferation in situ.

HypMSC engrafted robustly in ischemic tissue and their proliferation index in ischemic sites was superior to that of NormMSC. The decline MSC number that has been previously described could be due to cytokine secretion and tissue remodeling [START_REF] Wu | Mesenchymal stem cells enhance wound healing through differentiation and angiogenesis[END_REF] or immune rejection by the host as they expressed GFP a well-known immunogen [START_REF] Andersson | Engraftment of retroviral EGFP-transduced bone marrow in mice prevents rejection of EGFPtransgenic skin grafts[END_REF].

MSC have been successively administered as a treatment in both animal studies [START_REF] Toma | Human mesenchymal stem cells differentiate to a cardiomyocyte phenotype in the adult murine heart[END_REF][START_REF] Wu | Mesenchymal stem cells enhance wound healing through differentiation and angiogenesis[END_REF][START_REF] Derval | Epicardial deposition of endothelial progenitor and mesenchymal stem cells in a coated muscle patch after myocardial infarction in a murine model[END_REF] and human clinical trials [START_REF] Horwitz | Transplantability and therapeutic effects of bone marrow-derived mesenchymal cells in children with osteogenesis imperfecta[END_REF][START_REF] Wollert | Intracoronary autologous bone-marrow cell transfer after myocardial infarction: the BOOST randomised controlled clinical trial[END_REF]. Studies showed their possible contribution to vascular structures and skeletal muscle in vivo. For example, injection of MSC in a rat model of dilated cardiomyopathy revealed that some of the MSC were differentiated into cardiomyocytes [START_REF] Toma | Human mesenchymal stem cells differentiate to a cardiomyocyte phenotype in the adult murine heart[END_REF]. The application of MSC improves wound healing regeneration through differentiation [START_REF] Wu | Mesenchymal stem cells enhance wound healing through differentiation and angiogenesis[END_REF]. Recent studies suggest that monocytes under activation could express EC markers and form tube-like structures [START_REF] Chen | Pleiotrophin produced by multiple myeloma induces transdifferentiation of monocytes into vascular endothelial cells: a novel mechanism of tumor-induced vasculogenesis[END_REF]. The setting of hypoxic preconditioning in this study did not enhance cell differentiation into EC, as HypMSC kept their pericyte-like properties and behaved as perivascular cells as reported [2,[START_REF] Au | Bone marrow derived mesenchymal stem cells facilitate engineering of long-lasting functional vasculature[END_REF]. Their tissue localization led us to hypothesize a potential macrophage-like role in which they participate in phagocytosis of necrotic muscle fibers. Our data indicates that MSC have the ability to participate in the phagocytic process of muscle fibers in vitro and to encircle and send extensions into necrotic muscle fibers in vivo, which could indicate that these cells participate in clearing skeletal muscle cellular debris. This process has similarities with previously published data which demonstrated that macrophages reorganize their actin cytoskeleton to form phagocytic lamellipodia structures to engulf apoptotic cells [START_REF] Nakaya | Spatiotemporal activation of Rac1 for engulfment of apoptotic cells[END_REF].

Moreover, at early timepoints, MSC appear to play a role in neovessel formation encircling endothelial cells in capillaries and microvessels and participating in their stabilization as previously described [START_REF] Tigges | FGF2 -dependent neovascularization of subcutaneous Matrigel plugs is initiated by bone marrow-derived pericytes and macrophages[END_REF][START_REF] Dufourcq | Regulation of endothelial cell cytoskeletal reorganization by a secreted frizzled-related protein-1 and frizzled 4-and frizzled 7-dependent pathway: role in neovessel formation[END_REF]. Our results support the notion that MSC play a cooperative role in both myocyte regeneration and vascular formation by structural and functional interaction with both myocytes and EC.

As MSC have been shown to secrete a large quantity of angiogenic factors [START_REF] Kasper | Mesenchymal stem cells regulate angiogenesis according to their mechanical environment[END_REF], we investigated the potential involvement of paracrine and/or endocrine factors produced by MSC. Previous reports have demonstrated that conditioned medium from MSC can promote EC migration, differentiation and survival [START_REF] Hung | Angiogenic effects of human multipotent stromal cell conditioned medium activate the PI3K-Akt pathway in hypoxic endothelial cells to inhibit apoptosis, increase survival, and stimulate angiogenesis[END_REF]. Our data indicate that conditioned medium from HypMSC is more effective than conditioned medium from NormMSC in inducing EC migration as well as MSC proliferation and migration. As the Wnt signaling pathway has been shown to play a role in stem cell fate [START_REF] Reya | A role for Wnt signalling in self-renewal of haematopoietic stem cells[END_REF],

muscle regeneration [START_REF] Polesskaya | Wnt signaling induces the myogenic specification of resident CD45+ adult stem cells during muscle regeneration[END_REF], vascular formation [START_REF] Ezan | FrzA/sFRP-1, a secreted antagonist of the Wnt-Frizzled pathway, controls vascular cell proliferation in vitro and in vivo[END_REF] and invasion capacity of MSC [START_REF] Neth | The Wnt signal transduction pathway in stem cells and cancer cells: influence on cellular invasion[END_REF], we hypothesized that this pathway may be involved in the mechanism involved in this process. Our study identified that Wnt4 was specifically over expressed in vitro in conditioned media from HypMSC and that, in vivo, injection of HypMSC into the ischemic hindlimb strongly induced Wnt4 expression. We also demonstrate that Wnt4 exerts an effect on myoblast differentiation, in vitro. We have established a role of Wnt4 as a potent mediator in vascular regeneration as it affects EC migration. It is worth noting that Wnt4 conditioned medium could affect MSC migration and proliferation but only under hypoxic conditions through a canonical J3 catenin dependent Wnt signaling. Thus, it is likely that, in situ, residual tissue hypoxia confers responsiveness of MSC to environmental signals. Moreover, Wnt4 signaling was shown to stimulate myogenic proliferation and differentiation during chick development [START_REF] Takata | Involvement of Wnt4 signaling during myogenic proliferation and differentiation of skeletal muscle[END_REF] and satellite cell proliferation in skeletal muscle in myostatin-knockout mice [START_REF] Steelman | Transcriptional profiling of myostatin-knockout mice implicates Wnt signaling in postnatal skeletal muscle growth and hypertrophy[END_REF].

Finally we demonstrate here that, knockdown of Wnt4 expression resulted in inhibition of the beneficial impact of HypMSC on vascular regeneration compared with that induced by NormMSC. Collectively, these results strongly support the hypothesis that Wnt4 secreted by MSC is an important factor in mediating tissue regeneration in the setting of ischemia.

In conclusion, we have demonstrated that hypoxic preconditioning of MSC prior to transplantation could be a potent strategy in overcoming the current limitations in the field of regenerative medicine. This study suggests that many of the cellular functions associated with the ability of MSC to regenerate ischemic tissue are often not expressed constitutively by MSC but rather only transiently. MSC respond to contextual signals according to their microenvironment. [2,[START_REF] Derval | Epicardial deposition of endothelial progenitor and mesenchymal stem cells in a coated muscle patch after myocardial infarction in a murine model[END_REF] were treated for 36 hours at 1% O2 in a hypoxia chamber (HypMSC) (C21 Proox chamber, BioSpherix, New York) or maintained at 20% O2 (NormMSC) before being injected into a mouse ischemic hind limb. Mice were randomly assigned to three treatment groups. One group underwent sham treatment (i.e., aperture and saline injection) (control group). The other groups received injection of either 0.5 x10 6 NormMSC or HypMSC. Detailed description of materials, animal procedures, MSC preparation, hindlimb ischemia model, tissue collection and preparation for biochemical assays, Laser Doppler Perfusion Imaging (LPDI), microCT analysis, immunoshistochemistry, macrophagic assays, and in vitro cell functional assays can be found in the Online Data Supplement. Vessel numbers were calculated after CD31 immunolabelling (c-f) in the control, NormMSC and HypMSC groups. 'K, P<0.00001 vs. control; $, P<0.001 vs NormMSC.

Materials and Methods

MSC

Reconstructed micro-CT images of control, NormMSC or HypMSC injected hindlimb 7 days after ischemia in age-and gender-matched mice (g-i) (tm 3 resolution). Note marked increase in vessel number (j) and in connectivity (k) in HypMSC treated mice versus NormMSC treated mice and control mice. Data are % ± S.E.M.; 'K, P <0.05 and 'K'K, P<0.001 vs. control; $, P<0.05 vs.

NormMSC. n=6 in each group.

Repaired surface measurement of control and MSC group (n=6 in each group) in hindlimb ischemic mice. Representative repaired surface and necrotic area were quantified as ratio of necrotic or in repair or repaired surface out of total muscle area (l-q). NormMSC. N=9 in each group.

SUPPLEMENTAL FIGURE LEGENDS

Figure 1 :

 1 Figure 1: augmented vascular regeneration by intramuscular transplantation of MSC in a hindlimb ischemia model.

Figure 2 :

 2 Figure 2: Engraftment, survival and proliferation of MSC in ischemic hindlimb tissues:

Figure 3 :

 3 Figure 3: HypMSC engraftment sites could assist MSC in their macrophagic-like role (a) At day 4, hindlimb muscles transplanted with either NormMSC or HypMSC have large hypoxic

Figure 4 :

 4 Figure 4: effects of HypMSC transplantation on Wnt gene expressions. Wnt4, 5A, 5B and 11

Figure 5 :

 5 Figure 5: effect of HypCM and Wnt4 CM on cell properties

Figure 6 :

 6 Figure 6: effect of Wnt4 knock down on NormMSC or HypMSC treated with siControl

Figure S1 :

 S1 Figure S1: MSC detection: (a) cell patches at day 7 were found in whole muscle by direct

Figure S2 :

 S2 Figure S2: double immunolabelling of GFP and CD31 in ischemic tissues at day 7 and day 15 after

Figure S3 :

 S3 Figure S3: MSC harbored a pericyte like phenotype after implantation in ischemic muscle at day 7.(a)

Figure S4 :

 S4 Figure S4:

Figure S5 :

 S5 Figure S5: effect of HypCM or Wnt4 CM on EC wound migration. Wnt4 CM and HypCM


Dr Stephane Avril
email: avril@emse.fr

Stéphane Avril

Laura Bouten

Laura Dubuis

Sylvain Drapier

Jean-François Pouget

Stéphane Avril

Mixed experimental and numerical approach for characterizing the biomechanical response of the human leg under elastic compression

Keywords: soft tissues, elastic compression, image warping, mechanical identification, FE modelling

Elastic compression is the process of applying an elastic garment around the leg, supposedly for enhancing the venous flow. However, the response of internal tissues to the external pressure is still partially unknown. In order to improve the scientific knowledge about this topic, a slice of a human leg wearing an elastic garment is modelled by the finite-element method. The elastic properties of the tissues inside the leg are identified thanks to a dedicated approach based on image processing. After calibrating the model with MRI scans of a volunteer, the pressure transmitted through the internal tissues of the leg is computed. Discrepancies of more than 35% are found from one location to another, showing that the same compression garment cannot be applied for treating deficiencies of the deep venous system or deficiencies of the large superficial veins. Moreover, it is shown that the internal morphology of the human leg plays an important role. Accordingly, the approach presented in this paper may provide useful information for adapting compression garments to the specificity of each patient.

INTRODUCTION Introduction

The major function of veins is to return blood back to the heart. In the leg, when veins fail to work properly, the classical therapy is elastic compression (EC): an elastic garment is applied around the leg. It is supposed to help the venous return, to decrease venous pressure, to prevent venous stasis and deterioration of venous walls, and to efficiently relieve aching and heavy legs [START_REF] Belcaro | Hémodynamique veineuse des membres inférieurs[END_REF].

Classically, the compression is prominent at the ankle and decreases going up the leg. This principle was established in reference to the Poiseuille's law in fluid mechanics which states that steady flow in a cylindrical pipe is always proportional to the opposite of pressure gradients. However, applying this principle to EC is arguable. Indeed, strong pressures at the ankle only affect the venous flow very superficially as ankles are mostly bony. Pressures at the ankle may even be painful and hamper the garment to be slipped on. Conversely, large pressures onto the calf muscle are essential, as confirmed by clinical studies [START_REF] Ducrozet | Un nouveau concept de contention-compression veineuse évalué par un essai randomisé en double aveugle: contention progressive versus contention classique dans l'insuffisance veineuse légère: l'étude booster[END_REF] or medical studies based on Magnetic Resonance Imaging (MRI) and ultrasounds [START_REF] Blanchemaison | Relation entre veines et muscles du mollet chez le sportif et le sujet sédentaire : étude échographique et conséquences physiopathologiques[END_REF][START_REF] Pouget | Nuclear magnetic resonance (NMR) study of leg venous drainage in men with and without elastic compression socks (traditional and new BVSport c concept)[END_REF][START_REF] Couzan | Un nouveau concept de contention-compression : apport de l'écho-doppler couleur avec prise des pressions veineuses et de l'IRM[END_REF][START_REF] Couzan | Study of the athletes venous system by doppler scan with pressures measurement and the perfecting of a new elastic compression concept[END_REF].

From a biomechanical point of view, no numerical model has ever been developed for reproducing the action of compression garments on legs and henceforward for helping to their design. Studies regarding the biomechanical effect of compression stockings on legs are limited to fluid mechanics [START_REF] Maton | Intramuscular pressure and surface EMG in voluntary ankle dorsal flexion: Influence of elastic compressive stockings[END_REF][START_REF] Downie | Effects of elastic compression stockings on wall shear stress in deep and superficial veins of the calf[END_REF]. They have never addressed the essential question of pressure transmission through the leg tissues.

The finite-element (FE) method can give a proper response to this mechanical issue. However, FE models considering the soft tissues of the human leg are quite scarce. Studies about the heel pad [START_REF] Gefen | Stress analysis of the standing foot following surgical plantar fascia disease[END_REF], the thigh tissues of amputees [START_REF] Portnoy | Internal mechanical conditions in the soft tissues of a residual limb of a trans-tibial amputee[END_REF][START_REF] Lee | Using computational simulation to aid in the prediction of socket fit: A preliminary study[END_REF] or the buttock [START_REF] Linder-Ganz | Assessment of mechanical conditions in sub-dermal tissues during sitting: A combined experimental-MRI and finite element approach[END_REF] can be cited. However, the relevancy of such models is always conditioned by the accuracy of constitutive properties. Such properties are still very difficult to identify in vivo, even using recent techniques such as elastography [START_REF] Ophir | Optical and acoustical imaging of biological media: Elastography[END_REF][START_REF] Park | Shear modulus reconstruction in dynamic elastography: time harmonic case[END_REF][START_REF] Barbone | Elastic modulus imaging: some exact solutions of the compressible elastography inverse problem[END_REF].

Avril -BIO-09-1119

The aim of this paper is to set up a patient-specific FE model of the human leg under the action of compression garments. For solving the issue of identifying the elastic properties for the soft tissues, a dedicated approach based on image processing has been developed. After detailing the FE model and the identification approach, results obtained on a volunteer are presented.

Materials and methods

Subject and images

Image acquisition

MRI scans of the leg cross section are necessary for this study. The scans were acquired with a 1.5 T MRI scanner on a volunteer, a 25-year-old woman without venous pathology, following informed consent and according to a protocol approved by the local institutional ethics committee. Scans were acquired in the natural state (without compression) of the leg, as shown in Fig. 1(a), but also while wearing compressive socks, as shown for example in Fig. 1(b). T1-weighted images of 5 mm thick slices were acquired under a spin echo sequence with a repetition time (TR) of 772 ms and an echo time (TE) of 13 ms [START_REF] Macrobbie | MRI: From Picture to Proton[END_REF], with a pixel size of about 0.36×0.36 mm 2 . The cross section shown in Fig. 1 is located where the perimeter of the calf is the largest. It was segmented for defining the contours of the tibia and fibula bones, the adipose tissue (fat) and the muscle tissue. A T1-weighted sequence was employed here because it provides a good contrast between these tissues. Segmentation was achieved using the Matlab R software [START_REF]Matlab R[END_REF] with a custom made routine.

Image warping

In order to identify the material properties of soft tissues, an image processing approach based on image warping (also called image registration) was used [START_REF] Amunts | Analysis of neural mechanisms underlying verbal fluency in cytoarchitectonically defined stereotaxic space -the role of Brodmann areas 44 and 45[END_REF]. The principle of image warping is the following. Let I 1 be the image to be warped, in our case Avril -BIO-09-1119 the image of the leg wearing compressive socks (Fig. 1(b)). Let I denote the warped image, i.e. a synthetic image derived from I 1 by mathematical operations. Actually, the mathematical operations consists here in applying onto I 1 a geometric deformation.

The principle is the following:

1. Let u(x, y) and v(x, y) be respectively the horizontal and vertical components of the geometric deformation; x and y denote the plane coordinates of a pixel of the warped image where the grey level has to be estimated. Let i(x, y) denote this gray level.

2.

Assuming that the grey level of each material point remains constant between the unloaded and loaded states, it can be stated that i(x, y) should be the same as

i 1 (x + u, y + v), i 1 (x + u, y + v) denoting the grey level at (x + u, y + v) in I 1 .
3. As (x + u, y + v) is usually not the exact position of a pixel in I 1 , i(x, y) is derived by linear interpolation from the grey levels of the pixels surrounding (x + u, y + v)

in I 1 .
Eventually, the objective is that I matches as much as possible the target image, denoted I 0 , which is the image of the uncompressed leg in our case. Image warping was achieved using the Matlab R software [START_REF]Matlab R[END_REF] with a custom made routine.

Computational modeling

A FE model of a leg was developed in this study. FE modelling consists in a number of components:

1. computational mesh generation, 2. specification of boundary conditions, [START_REF] Blanchemaison | Relation entre veines et muscles du mollet chez le sportif et le sujet sédentaire : étude échographique et conséquences physiopathologiques[END_REF]. specification of material properties, [START_REF] Pouget | Nuclear magnetic resonance (NMR) study of leg venous drainage in men with and without elastic compression socks (traditional and new BVSport c concept)[END_REF]. calibration of the material properties using experimental data (this step is only mandatory when the material properties are unknown),

simulation and results

Avril -BIO-09-1119

MATERIALS AND METHODS

Computational modeling

FE analyses were run on a software called Zebulon R [19]. Large deformations were considered in the resolution by taking into account geometric nonlinearities. The model was 2D, representing a slice of the leg. Accordingly, the plane strain assumption was considered.

Mesh generation

The geometry of the internal tissues constituting the leg was deduced from the MRI scans of the leg cross section. The whole geometry was meshed with 400 displacementbased linear triangular elements (Fig. 2), which appeared to be satisfactory for the soft tissues considered here [START_REF] Bouten | In-vivo identification of soft biological tissues using MR imaging[END_REF]. The mesh was created directly after the image segmentation, still using the Matlab R software [START_REF]Matlab R[END_REF] with a custom made routine. Then, the mesh was exported to Zebulon R .

Boundary conditions

Boundary conditions were of two types:

-Dirichlet, by fixing all the degrees of freedom along the contours of the tibia and fibula bones, as both bones are assumed to be infinitely rigid (their elastic properties are nearly 1000 times larger than the ones of soft tissues).

-Neumann along the external contour of the leg. A normal pressure was applied along this contour. Locally, the pressure value, denoted p, is computed as a function of the local tension in the garment, denoted T (defined as the force per unit width), and the local radius of curvature, denoted r (evaluated in the deformed configuration of the leg during the FE computations), following the Laplace's law:

p = T /r (1)
Friction of the garment on the leg is neglected, which means that no tangential pressure is applied. Consequently, for simple mechanical balance arguments, the T Avril -BIO-09-1119 value is assumed as constant along the contour of the leg. Thanks to the segmentation of the MRI scan of the leg before and after wearing the compression garment, it is possible to evaluate the perimeter of the leg in both uncompressed and compressed states. Then the stretch of the garment in the circumferential direction can be deduced. Thus, the T value in Eq. 1 is deduced by characterizing previously the elastic response of the garment.

Garment characterization

A non destructive system, shown in Fig. 3, has been devised for the mechanical characterization, reproducing loading conditions similar to the ones observed in the circumferential direction of the leg when the garment is worn. This system and the related tests result from an original methodology for characterizing the biaxial behaviour of elastomeric textiles [START_REF] Gaied | Experimental assessment and analytical 2d predictions of the stocking pressures induced on a model leg by medical compression stockings[END_REF][START_REF] Gaied | Identification strategy for orthotropic knitted elastomeric fabrics under large biaxial deformations[END_REF]. This methodology is based on a specific experimental set-up for applying biaxial loadings to the garment, and on an optical system for measuring the deformation of the garment during its loading [START_REF] Gaied | Identification strategy for orthotropic knitted elastomeric fabrics under large biaxial deformations[END_REF].

Thanks to this system, the value of T was estimated with an accuracy of about 10%. A complementary study was also carried out for verifying the relevancy of the Laplace's law [START_REF] Gaied | Experimental assessment and analytical 2d predictions of the stocking pressures induced on a model leg by medical compression stockings[END_REF].

Material properties

Image segmentation has yielded different zones in the images: one corresponding to the muscle tissues, another one corresponding to adipose tissues, and the others being the bones. In the model, the zones of the muscle and adipose tissues were assumed as homogeneous in terms of elastic properties. Each tissue is figured by a different colour in Fig. 2. The skin, the veins and the arteries are not modelled. The skin is included in the fat zone. Similarly, veins and arteries are included in the muscle or adipose tissue.

In terms of elastic properties, it is assumed that the veins and arteries contribute to the average elastic behaviour of the tissue where they sit (fat or muscle). The assumption Avril -BIO-09-1119

2 MATERIALS AND METHODS

Computational modeling

of homogeneity in both tissues provides a sufficient accuracy for evaluating the strains and stresses inside the leg, as this will be shown in Section 4.2.

The response of the soft tissues of the leg is assumed as compressible hyperelastic.

Compressibility is justified by observing a diminution of about 4.5% of areas in the MRI scans when comparing scans before and after wearing the garment (Fig. 1). As the finite deformations of the soft tissues remain relatively small (<5%), a simple Neo-Hookean strain energy function is justified [START_REF] Fung | Biomechanics: mechanical properties of living tissues[END_REF]. This strain energy function can be written:

W = C 10 (I 1 -3) + K v [(J 2 -1)/2 -ln(J)] (2)
where J = det(F ) and I 1 = J -2tr( t F.F )/3 with F being the deformation gradient and tr the trace of a matrix.

The elastic behaviour of each tissue is driven by two parameters: C m 10 and K m v for the muscle tissue and C f 10 and K f v for the fat. The model is therefore driven by 4 parameters. There is a very large variability of the values reported for the elastic parameters of soft tissues in the literature [START_REF] Portnoy | Internal mechanical conditions in the soft tissues of a residual limb of a trans-tibial amputee[END_REF][START_REF] Lee | Using computational simulation to aid in the prediction of socket fit: A preliminary study[END_REF][START_REF] Linder-Ganz | Assessment of mechanical conditions in sub-dermal tissues during sitting: A combined experimental-MRI and finite element approach[END_REF][START_REF] Gefen | A biomechanical model of peyronie's disease[END_REF]. One objective of this paper is to propose a methodology for calibrating the 4 parameters as realistically as possible with regard to the in vivo response of any patient's leg.

Calibration against experimental data

After checking convergence of the FE model on representative materials, the problem of identifying C m 10 , K m v , C f 10 and K f v from real experimental data was addressed. Using the MRI scans as experimental data, this entailed using image processing algorithms such as digital image correlation (DIC) [START_REF] Schreier | Systematic errors in digital image correlation due to undermatched subset shape functions[END_REF], or image warping (also called image registration) [START_REF] Amunts | Analysis of neural mechanisms underlying verbal fluency in cytoarchitectonically defined stereotaxic space -the role of Brodmann areas 44 and 45[END_REF]. DIC proved not to be suited to such in vivo identification [START_REF] Bouten | In-vivo identification of soft biological tissues using MR imaging[END_REF]. On the contrary, the use of image registration applied to medical images for identifying the elastic properties of soft tissues was already used in different studies [START_REF] Linder-Ganz | Assessment of mechanical conditions in sub-dermal tissues during sitting: A combined experimental-MRI and finite element approach[END_REF][START_REF] Augenstein | Estimation of cardiac hyperelastic material properties from MRI tissue tagging and diffusion tensor imaging[END_REF][START_REF] Chabanas | Comparison of linear and non-linear soft tissue models with post-operative CT scan in maxillofacial surgery[END_REF][START_REF] Azar | Methods for modeling and predicting mechanical deformations of the breast under external perturbations[END_REF][START_REF] Chung | A biomechanical model of mammographic compressions[END_REF].

Avril -BIO-09-1119

Let I 0 be the image of the leg in the unloaded state (Fig. 1

M(C m 10 , K m v , C f 10 , K f v )
. The measure of mismatch can be of different types, defined for example on the basis of cross correlation products, or otherwise by the distance separating the same markers on both images. This second option has been chosen here, using the contours of the fat and muscle zones as markers (Fig. 1). This option has been chosen instead of using correlation products because, for the correlation products, the contrast of MRI images is too poor.

For each pixel of the contours in I, of coordinates (x k , y k ), the closest pixel belonging to a contour of fat or muscles in I 0 is found, and the distance between them is denoted d k . Graphical plots of d k 's are shown in Fig. 4(a) and in Fig. 4(b). This type of graphical plots shows where the mismatch is the largest, which can help to interpret the relevancy of the FE model. Eventually, the measure of mismatching

M(C m 10 , K m v , C f 10 , K f v
) is defined as the sum of all the (d k ) 2 's for all the pixels belonging to a contour.

The optimal registration is reached when the four parameters C m 10 , K m v , C f 10 and

K f v minimize M(C m 10 , K m v , C f 10 , K f v )
. Such minimization is achieved by running the Nelder Mead algorithm in the Matlab R software [START_REF]Matlab R[END_REF]. In this algorithm, evaluations

of the cost function M(C m 10 , K m v , C f 10 , K f v )
are required through an iterative scheme.

For each evaluation of the cost function here, a new FE analysis is required, with new inputs of the elastic properties of the muscle and adipose tissues. In the Matlab R software, a routine was developed for running these FE analyses, saving the results

Avril -BIO-09-1119 8

(displacement fields u and v), and using them for achieving image registration and

update M(C m 10 , K m v , C f 10 , K f v ).
Dialogue between Matlab R and Zebulon R was achieved by including prompt commands in the Matlab R routines that order the jobs to the Zebulon R software. Before each new job, the data file containing the material properties of the FE model required by Zebulon R was updated with the new values of C m 10 , K m v , C f 10 and K f v for which a new evaluation of the cost function is needed.

Statistical approach

An alternative approach has been used to determine mechanical properties. This alternative approach does not provide a unique value for the material properties but it provides intervals within which the material properties are likely to be.

M(C m 10 , K m v , C f 10 , K f v
) is computed and the material properties leading to a value of M lower than a given threshold are kept.

3 Results

Elastic properties of tissues

The elastic properties of the soft tissues were identified by applying the approach described in section 2. Using the statistical approach presented in section 2.

Pressure evaluation with central values of elastic properties

As the veins have a small size compared with the size of the fat and muscle areas in the scans (Fig. 1), it can be assumed that the presence of a vein in the fat or muscle tissues does not drastically modify the local stresses computed by our model. Therefore, the pressure that tissues will apply onto the vein walls can be approximated by the local hydrostatic pressure (first invariant of the stress tensor) evaluated in the fat or muscle tissues by our model.

The obtained distribution of pressure is shown in Fig. 5, computed with the central values of elastic properties reported in Tab. [START_REF] Ducrozet | Un nouveau concept de contention-compression veineuse évalué par un essai randomisé en double aveugle: contention progressive versus contention classique dans l'insuffisance veineuse légère: l'étude booster[END_REF]. A special attention has been paid to the results at five positions (Fig. 5) which may have an interest for physicians (results for these five locations are reported in the first column of Tab. 3):

-position 1 is located in the hypodermis, close to the tibia bone.

-position 2 is located in the deep venous system near the twin veins.

-position 3 is located where the maximum pressure is usually observed by our FE model.

-position 4 is located near the greater saphenous, which is the large superficial vein on the inner side of the human leg.

Avril -BIO-09-1119 10

DISCUSSION

-position 5 is located near the small saphenous vein, which is a large vein of the superficial posterior leg.

The maximum pressure computed is of 5.3 kPa (40.3 mmHg), it is obtained at the back of the leg, at the interface between the fat and the muscle tissues. The minimum pressure is of 0.9 kPa (6.8 mmHg), it is obtained near the tibia bone. The first important conclusion is that the spatial variations of pressures are significant and consequently, it cannot be assumed that the same pressure is applied onto the whole veins. The variation between the pressures computed at position 2 and position 3 is more than 35%.

Discussion

Material properties

The bounds reported in Tab. 2 for C m 10 , K m v , C f 10 and K f v are in agreement with the range order of values known for the properties of soft tissues like fat or muscles [START_REF] Portnoy | Internal mechanical conditions in the soft tissues of a residual limb of a trans-tibial amputee[END_REF][START_REF] Lee | Using computational simulation to aid in the prediction of socket fit: A preliminary study[END_REF][START_REF] Linder-Ganz | Assessment of mechanical conditions in sub-dermal tissues during sitting: A combined experimental-MRI and finite element approach[END_REF][START_REF] Gefen | A biomechanical model of peyronie's disease[END_REF]. The fat properties found here are also similar to hypodermis elastic properties reported in the literature [START_REF] Tran | Propriétés mécaniques multi-couches de la peau humaine in vivo[END_REF][START_REF] Delalleau | Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test[END_REF]. This supports the simplification of merging the adipose tissues and the skin in the present model. Accordingly, there is not a unique set of material parameters ensuring a good agreement between the numerical and actual deformations of the leg. The consequence for the current approach is that the values of the pressures inside the leg cannot be computed deterministically. Pressures reported in the first column of Tab. 3 are mean values, and it can only be announced that the actual pressures may be scattered about these mean values.

In order to evaluate this scatter about the mean values, 30 computations were achieved with the FE model, each one using a set of elastic properties drawn randomly within the bounds reported in Tab. [START_REF] Ducrozet | Un nouveau concept de contention-compression veineuse évalué par un essai randomisé en double aveugle: contention progressive versus contention classique dans l'insuffisance veineuse légère: l'étude booster[END_REF]. This approach for characterizing uncertainty has the advantage of being statistically relevant and not very time consuming (15 minutes in total).

The coefficients of variation (ratio between the standard deviation and the mean value) of the 30 pressure values were systematically smaller than 5% (third column in Tab. 3). Therefore, this shows that the nonuniqueness of the identified material parameters has only a limited impact on the uncertainty of pressure computations.

Image processing

In this study, the contours of the fat and muscle zones were used as markers (Fig. 1(a)) instead of using correlation products because, for the correlation products, it must be assumed that the MRI signal received from each material point of the leg is constant between the unloaded and loaded states, and also because the contrast inside the fat or muscle tissues is poor. Different MRI modalities like MRI tagging may help to provide a better contrast inside the tissue. This would increase the number of markers and consequently improve the sensitivity of the cost function to the material properties.

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Effect of the leg morphology

Effect of the leg morphology

In our approach, the contours of the fat and the muscle tissues were deduced from the MRI scans. A T1-weighted sequence was employed because it provides a good contrast between these tissues. A question arises from this segmentation: is there also a contrast between these two zones in terms of mechanical properties?

Let us consider that the central value of intervals found for each property is their most probable guess. Therefore, regarding these values, the muscle tissue is significantly more compressible than fat. This is also in agreement with the variation of their respective area between Fig. 1(a) and Fig. 1(b). This means that EC has a larger effect on the muscle zone than on the fat zone. Therefore, it transpires that the proportion of fat inside the leg can play an important role in the efficiency of the compression process.

This analysis is in agreement with several medical studies about EC, which showed that most of the venous blood in the leg is located in venules of the calf muscle [START_REF] Pouget | Nuclear magnetic resonance (NMR) study of leg venous drainage in men with and without elastic compression socks (traditional and new BVSport c concept)[END_REF][START_REF] Couzan | Un nouveau concept de contention-compression : apport de l'écho-doppler couleur avec prise des pressions veineuses et de l'IRM[END_REF][START_REF] Couzan | Study of the athletes venous system by doppler scan with pressures measurement and the perfecting of a new elastic compression concept[END_REF].

The contrast of mechanical properties also induces a contrast of computed pressures. There is indeed a slight jump of pressure at the interface between the fat and the muscle tissues (Fig. 5), due to the difference of elastic properties. This effect shows that the fat has a "shielding" effect, lowering the pressures inside muscles. Therefore, this confirms that the internal leg morphology should be considered before the prescription of EC.

Uncertainty about the boundary conditions

A large source of uncertainty about pressure evaluation is induced by the uncertainty of the garment tension. Experimentally, tension T can only be assessed with a precision of about 10%. This includes the fact that the friction is neglected in the boundary conditions.

The increase or decrease of computed pressures due to a respective increase or decrease of tension is not linear, as increases or decreases range from 5 to 14% (Tab. 4).

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The nonlinearity is induced by the geometric nonlinearity of the FE model, especially by the fact that the Laplace's law is calculated with the deformed value of the local radius of curvature r. However, a rough estimate of about 10% can still be kept for characterizing the uncertainty of pressure evaluations induced by the uncertainty of tension evaluation.

Eventually, adding up the uncertainty of the elastic properties to the uncertainty of the garment tension, it can be concluded that the pressure inside the leg induced by EC can be assessed by our approach with a relative precision of about 15%. For classically prescribed pressures of about 20 mmHg, this corresponds to an uncertainty of 3 mmHg, which is a common tolerance for such medical prescriptions.

A natural improvement would be to include the garment in the numerical model, with contact elements between the garment and the leg. The question that arises is whether the time for running such model will be balanced by a worthwhile increase in accuracy. This question will be addressed in the near future.

Link with the blood pressure

An assumption is made to obtain the pressure applied onto the vein walls. The mechanical role of veins is neglected and the pressure is computed as the hydrostatic pressure in the surrounding tissues. It is a strong assumption, the limitations of which are not evaluated in the current study. A more sophisticated model involving fluid structure interactions will be set up in the future for addressing this issue. In the meantime, the current study still provides an answer to the general question of pressure transmission through the internal tissues. The current model shows that the spatial variations of pressures are significant inside the leg and consequently, pressure transmission through the internal tissues should be considered in medical treatments.

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3D effects

A strong assumption in our approach is the plane strain assumption. It means that the out of plane strains are zero. In solid mechanics, the plane strain assumption is employed when the dimension of a structure in one direction is very large in comparison with the dimensions of the structure in the two other directions. The leg can be assumed as such a structure.

In order to justify this assumption, a 3D FE model was set up. The geometry was deduced from the scans of all the cross sections of the whole leg using the Avizo R software [33]. The geometry was meshed with 718,937 tetraedric linear elements with 131,712 nodes. The material properties and the boundary conditions were similar to the ones used in 2D: the bones were clamped and pressure was applied onto the skin.

The mesh and the boundary conditions are shown in Fig. 6(a). Using this model, the deformation of the leg tissues was computed, as shown in Fig. 6(b).

Eventually, a comparison was made between the pressures at the five positions of Fig. 5 computed with the 2D or with the 3D model. The results are reported in Tab. [START_REF] Couzan | Un nouveau concept de contention-compression : apport de l'écho-doppler couleur avec prise des pressions veineuses et de l'IRM[END_REF].

It can be checked that the difference between the pressures of the 2D model and of the 3D model is low, less than 5%, which remains within the range of uncertainty of the approach reported before.

It must be emphasized that the computation speed with a 2D model is drastically reduced compared with a 3D model, especially with the material and geometric nonlinearities considered here. The main advantage of the 2D model presented here is that it can provide almost in real time the distribution of pressures inside the leg for any patient provided that the internal morphology of the leg is known (only 2 MRI scans are required). Regarding the uncertainties, the 2D model is able to predict the internal pressures with an uncertainty of 15%, which is still compatible with the requirements of medical prescriptions.

Avril -BIO-09-1119 an approach should now be validated on different sets of subjects in order to take into account the wide variations of properties from one subject to another. The effect of venous pathologies onto the approach should also be investigated.

Conclusion

In order to improve the scientific knowledge about the mechanical response of a human leg under elastic compression, a FE model was developed, under the assumption of plane strains. A methodology for calibrating the model in a patient specific way has been presented and the uncertainty of the results provided by the model has been characterized.

Using the model, it has been shown that the spatial variations of pressures are significant inside the leg. Discrepancies of more than 35% were reported from one location to another, showing that the same compression garment cannot be applied for treating deficiencies of the deep venous system or deficiencies of the large superficial veins. Moreover, the internal morphology of the human leg (muscle properties, thickness of subcutaneous fat) affects the pressure transmission through the internal tissues of the leg. A clinical validation is now required on a significant number of patients.

In the meantime, a more realistic model will also be implemented for analyzing the effects of the computed pressures onto the venous return. A 3D model has been set up, considering a more accurate description of the leg components. Blood flow in the veins of the compressed leg will be considered, based on different approaches of the literature [START_REF] Maton | Intramuscular pressure and surface EMG in voluntary ankle dorsal flexion: Influence of elastic compressive stockings[END_REF][START_REF] Downie | Effects of elastic compression stockings on wall shear stress in deep and superficial veins of the calf[END_REF]. Avril -BIO-09-1119

  (a)), and let I 1 be the image of the leg in the loaded state (Fig. 1(b)). Let I be the processed image deduced from I 1 after warping, by applying the deformation computed by the FE model, as explained in section 2.1.2. Therefore, the warped image I only depends on C m 10 , K m v , C f 10 and K f v as these four parameters drive the response computed by the FE model. Let M be the measure of mismatching between the original image I 0 and the warped image I. M only depends on the unknown constitutive parameters and it can be denoted as a function of them:

2 . 5 . 9 3. 2

 2592 It was observed that, whatever the values of C m 10 , K m v , C f 10 and K f v chosen within a broad range (Tab. 1) for initializing the iterative scheme, the minimization always converged, though yielding different results. This means that the cost function has several minima. Accordingly, it was decided to use another approach for the minimization. It was observed that when the value of the cost function passed below 3.4, the variations of the cost function with respect to the values of C m 10 , K m v , C f 10 and K f v become very Avril -BIO-09-1119 Pressure evaluation with central values of elastic properties 3 RESULTS irregular and they can not be controlled. Therefore, all the values of C m 10 , K m v , C f 10 and K f v that provide cost function values below 3.4 are considered as satisfactory. It is shown in Section 4.2 that the nonuniqueness of the solution has only a limited impact on the uncertainty of pressure computations.

2 . 5 ,

 25 it was found that the values of C m 10 , K m v , C f 10 and K f v that provide cost function values below 3.4 are located in intervals delimited by an upper bound and a lower bound. Out of these bounds, the material parameters yield too large values of the cost function. The bounds of these intervals along with the central values are reported in Tab. 2.

4. 2

 2 Irregularity of the cost function and nonuniqueness of the solution of the inverse problem It was observed that when the value of the cost function passed below 3.4, the variations of the cost function with respect to the values of C m 10 , K m v , C f 10 and K f v become very irregular and they can not be controlled. The irregularity of the cost function can be understood by observing the local mismatch between the warped image and the target image. Indeed, using values of C m 10 , K m v , C f 10 and K f v located within the bounds reported in Tab. 2, it was noticed that when the local mismatch is minimized on one part of the contours, it is always increased elsewhere. For example, Fig. 4(a) Avril -BIO-09-1119 and Fig. 4(b), obtained with two different sets of elastic properties, show some minor registration errors located at different locations, whereas they both correspond to cost function values located below 3.4.

4. 8 of patients 5 CONCLUSION 4 . 8

 8548 Number Number of patientsThe results shown in this paper prove the feasibility of a FE model of the human leg under elastic compression where the material parameters of the FE model are identified from in vivo data. This was shown on a single subject without venous pathology. Such

Table 1

 1 Results obtained in the minimization process for different initial values. C f 10 and K f v are the material constants of fat, C m 10 and K m v are the material constants of the muscle tissue. C 10 is the constant corresponding to the contribution of the strain first invariant in the Neo-Hookean strain energy function, Kv is the constant corresponding to the contribution of compressibility in the Neo-Hookean strain energy function.

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Table 3

 3 Pressure variations and uncertainty due to the approximation of tissue elastic properties.

		Average tension	Average tension +10 %	Average tension -10 %
		Pressure (kPa)	Pressure (kPa) Deviation (%) Pressure (kPa) Deviation (%)
	position 1	3.4	3.77	11	2.94	14
	position 2	2.72	2.95	8.4	2.46	9.5
	position 3	4.38	4.66	6.4	4.13	5.7
	position 4	4.15	4.48	8	3.74	10
	position 5	4.28	4.71	10	3.83	10.5

Table 4

 4 Pressure variations and uncertainty due to the approximation of the garment tension.

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ACKNOWLEDGEMENT

Moreover, it should be emphasized that in the model used here, the reduction of volume in the muscle zone is fully attributed to the compressibility of the muscle tissue. This is likely to be abusive and a biphasic model considering the calf muscle as a wet "sponge", made of "real" muscle tissues and dense blood capillaries, would be more realistic. Future improvements of our model will go into this direction.

The recent progresses of the spatial resolution in medical imaging techniques and/or the combination of different MRI sequences may be the key for improving the accuracy of our in vivo identification methodology based on image registration. Moreover, such identification from in vivo data may have a lot of other applications outside the study of EC, since the mechanical characterization of soft tissues remains one of the most complicated issues in biomechanics.

When all the on-going improvements and validations are completed, the approach presented in this paper may become a useful tool in practice for adapting compression garments to the specificity of each patient.

Acknowledgement

The authors are grateful to the Rhone-Alpes Regional Council for funding the PhD grant of Laura Dubuis. This work is also part of the Imandef project (Grant ANR-08-JCJC-0071) funded by the ANR (French National Research Agency).

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List of Tables

List of Tables

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List