Flavie Przybylski

Yinoussa Adagolodjo

Anna Mîra

Giulio Cerruti

Jérémie Dequidt

Christian Duriez

Pierre Berthet-Rayne

Przybylski Flavie

Adagolodjo Yinoussa

M Îra

Cerruti Giulio

Dequidt Jérémie

Berthet-Rayne Pierre

3D Kinematics and Quasi-Statics of a Growing Robot Eversion

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

I. INTRODUCTION

In the last couple of years, the field of research in robotics has significantly evolved, going from well-known rigid structures toward articulated [START_REF] Berthet-Rayne | The i²snake robotic platform for endoscopic surgery[END_REF], flexible [START_REF] Abdelaziz | X-ray to mr: the progress of flexible instruments for endovascular navigation[END_REF] and now soft structures [START_REF] Laschi | Soft robotics: Technologies and systems pushing the boundaries of robot abilities[END_REF]. Soft robotics revisits the concepts of traditional rigid robotics with the objective of expanding its capabilities for various purposes such as exploring environments, enhancing agricultural practices, and advancing medical treatments [START_REF] Calisti | Fundamentals of soft robot locomotion[END_REF], [START_REF] Elfferich | Soft robotic grippers for crop handling or harvesting: A review[END_REF], [START_REF] Garcia | The[END_REF].

Inspired by the process of plant expansion, growing robots reinvent locomotion in robotics by creating a continuous forward motion, growing from the tip, called eversion. Growing robots can navigate in constrained and unconstrained environments, while conforming their shape to the environment without direct friction [START_REF] Hawkes | role of soft robotic micromachines in the future of medical devices and personalized medicine[END_REF], [START_REF] Coad | Vine robots: Design, teleoperation, and deployment for navigation and exploration[END_REF], [START_REF] Berthet-Rayne | Mammobot: A miniature steerable soft growing robot for early breast cancer detection[END_REF]. Eversion is achieved through an inverted membrane that is pressurized at its tip, which lengthens the apparent distal part of the robot. While the concept seems simple, the underlying mechanical behavior is challenging to model [START_REF] Blumenschein | Modeling of bioinspired apical extension in a soft robot[END_REF]. Previous work has proposed geometric and physical simulations to model the behavior of the growing robot and its interaction with the environment [START_REF] El-Hussieny | Development and evaluation of an intuitive flexible interface for teleoperating soft growing robots[END_REF], [START_REF] Jitosho | A dynamics simulator for soft growing robots[END_REF], [START_REF] Greer | Robust navigation of a soft growing robot by exploiting contact with the environment[END_REF]. These simulations are based on models involving a series of rigid bodies, connected or not by joints or springs, and implementing the elongation 1 Caranx Medical, Nice, France 2 Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 CRIStAL, Lille, France 3 3IA Affiliate Chair, INRIA Sophia Antipolis, France corresponding author: flavie.przybylski at caranx-medical.com phenomenon by the incremental addition of small segments of fixed length. In a recent study [START_REF] Wu | Towards a physicsbased model for steerable eversion growing robots[END_REF], the SOFA software was used to model a steerable growing robot, with the robot body represented by a 2D planar thin-walled conical mesh.

The model takes into account parameters to simulate the incompressible eversion behavior that is specific to the robot application. However, previous simulations of growing robots have not fully considered the eversion phenomenon, a critical aspect of their behavior. To gain a better understanding, it is necessary to account for various properties, including the packing and storing method of the robot material inside itself, the impact of internal pressure on the membrane during deployment, the potential self-collision of the inner membrane, and finally the deformation of the outer membrane in response to encountered obstacles. A geometric description of the translation of the inner membrane towards the eversion zone is required to reproduce the 3D kinematics of the growing robot. Additionally, other membrane parameters such as deformation, pressure exertion, and potential selfcollision leading to internal friction must be considered to fully describe the motion. By modeling and integrating these factors into the kinematics, critical parameters for successful navigation in complex environments can be identified, and the robot's adaptability can be assessed in different environments. This knowledge can also contribute to the optimization and design of soft robots for practical applications. This paper proposes a new approach to soft robot modeling by combining the Cosserat and FEM models and is depicted in Fig. 1. The use of local coordinates allows a direct description of the eversion kinematics, while global coordinates allow a detailed understanding of the force balance between membrane stresses and wall pressure. Thanks to this approach, it is possible to provide a first parameterization and a first geometrical representation of the initial physics involved in the eversion process of growing robots. Although the presented work does not introduce an experimental validation, the proposed approach represents a crucial first step in the understanding of the complex mechanics of growing robots and their potential applications in various fields of robotics. The proposed model is described in detail in section II and III, and the numerical results are reported in section IV.

II. METHODOLOGY

Our approach combines a Cosserat-type model with a 3D finite element analysis. The Cosserat model is based on reduced bending and torsion coordinates, which allows a more efficient and accurate description of the complex deformations involved in the eversion process. Specifically, the growing robot membrane, possessing a tubular shape, is represented as a bundle of distributed Cosserat fibers, which captures the local curvature observed in the eversion zone. However, this model alone cannot fully capture the selfcollision and pressure effects that occur during the eversion process. To address this limitation, a second local analysis at the tip of the robot is applied, based on 3D finite elements. This allows to consider external collisions, as well as to accurately capture self-collision and pressure effects. Finally, a coupling between the two models is defined to apply appropriate boundary conditions to the FEM model and simplify its computation.

A. Discrete Cosserat Modeling with local coordinates

Cosserat models are often used to accurately model the deformation of thin structures during large transformations. These models assume no cross-sectional deformations, with each section of the continuum represented by a rigid body. In the paper [START_REF] Renda | Discrete cosserat approach for soft robot dynamics: A new piece-wise constant strain model with torsion and shears[END_REF], a piecewise constant deformation (PCS) formulation of the Cosserat model is proposed to model soft and thin robots. The PCS formulation is based on the use of reduced coordinates in the deformation space, which makes it easy to define the types of deformations that is allowed. For example, if no elongation is defined in the coordinate space, the model is perfectly inextensible. Furthermore, the deformation space is a vector space, which can be easily interpolated to reduce the coordinate space [START_REF] Renda | A geometric variable-strain approach for static modeling of soft manipulators with tendon and fluidic actuation[END_REF].

Although these models can reproduce the behavior of a large class of continuum robots, it is more difficult to fit them directly to growing robots. Some assumptions, such as no cross-sectional deformation, are not applicable to buckling zones. In addition, these models cannot represent the complexity of the eversion phenomenon, which is due to surface deformation.

However, if we consider the behavior of a growing robot with straight eversion and no interaction with its environment Fig. 2. The representation of the growing robot under the Cosserat model is based on its 1D structure. The robot consists of several sections, labeled S n , which are connected by nodes labeled N n . The base of the robot is represented by the section S 0 and the node N 0 . The eversion of the robot is represented by the section s e , the beginning of the eversion being represented by the node N e , and the end of the eversion by the node N e+ j . Fig. 3. Representation of the hybrid model of the growing robot, which includes the fibers (a) that give it its shape and the entire membrane (b). These fibers begin at node N 0 associated with section S 1 and are described by node N e at N e+ j associated with section S e during eversion.

(see Fig. 2), we can assume that the section representing a segmented element of the beam is undeformable. It is therefore possible to divide the robot body into several constant sections from S 0 to S n , connected by nodes from N 0 to N n+1 . The resulting configuration is reduced coordinates of the nodes according to their torsional or bending deformation state.

B. 3D Finite Element Method with global coordinates

The finite element method (FEM) is a numerical technique used to solve partial derivative problems. In the context of deformation modeling, FEM allows capturing the 3D geometry of the structure through a mesh. Moreover, the weak formulation facilitates the expression of boundary conditions, such as pressure or contact conditions. In practice, FEM balances the forces at the nodes of the mesh in global coordinates, which simplifies the management of contact forces, for example. The FEM calculation can be used to model soft robots, both directly and inversely [START_REF] Coevoet | Software toolkit for modeling, simulation, and control of soft robots[END_REF].

C. Combination

Recent research [START_REF] Adagolodjo | Coupling numerical deformable models in global and reduced coordinates for the simulation of the direct and the inverse kinematics of soft robots[END_REF] has demonstrated the possibility of combining the Cosserat and FEM models to better capture the behavior of flexible robots. Specifically, the FEM model is used to represent the global 3D geometry of the robot structure, while the Cosserat model is used to describe the behavior of flexible elements in local coordinates. This combination allows a more accurate simulation of the robot behavior, especially when considering complex deformations and interactions with the environment.

This study proposes a new hybrid modeling framework for the growing robot by combining the Cosserat model and the FEM model, building on the previous ability to combine these two models for accurate modeling of soft robots.

III. IMPLEMENTATION

Our methodology is based on a dual modeling system that combines two models for the eversion process of the growing robot (see Fig. 3). The first model represents the membrane using a system of curves (called "fibers") regularly positioned along the tube formed by the membrane. The motion of the fibers is parameterized using local coordinates, as in the discrete Cosserat model described above. This model is used to support a kinematic model of the eversion process.

The second model focuses on the balance of forces in the eversion zone, using a finite element method to model the membrane in global coordinates.

A. Eversion kinematics based on the strain based reduced coordinates

To model the kinematics of the growing robot eversion, we represent the shape of its membrane tube as a series of parallel fibers of size L. Each fiber is sampled in sections S i , i ∈ [0, n], with local coordinates q i that provide their curvature. We adopt the use of angular velocity parameters (bending and twisting angles per unit length) as in [START_REF] Renda | Discrete cosserat approach for soft robot dynamics: A new piece-wise constant strain model with torsion and shears[END_REF] to simplify the calculation. The different sections are connected by N i nodes along the beam.

At the base of each fiber, there is a reference frame F defined on the node N 0 , which is mechanically fixed in space. Each reference frame is rotated so that the x-axis is oriented in the direction of the tube, with the y-axis and z-axis normal and tangent to the membrane surface, respectively.

To describe the eversion phenomenon, a first node N e is placed at the curvilinear abscissa representing the beginning of the eversion zone and a second node N (e+ j) at the end. Although multiple s e sections can be added to each fiber in the eversion zone, we found that one section per fiber was sufficient for our implementation (s e = 1).

To capture the eversion process, we use the local coordinates corresponding to the bending along the Z axis for each fiber.

q z e = -(s e /l e ) * π (1)
The length of the eversion along the fiber is the distance between N e and N (e+ j) along the curvilinear abscissa, and determines the shape of the U-turn made by the fiber in the eversion region. Depending on the value of l e , the U-turn can be either sharp (for a small l e ) or smooth (for a large l e ). To model a non-homogeneous eversion geometry at the end, each fiber can have its own parameters for N e and N (e+ j) . If more than one section is used between N e and N (e+ j) , the curvature need not be constant. In this case, it is sufficient to ensure that the curvature created by the succession of bent sections creates a U-turn:

j ∑ i=0 q z e+i * l e+i = -π (2)
Here l e+i is the length of the section e + i To recreate the revolution geometry of the growing robot, we project the desired number of fibers n times into the reference frame. The same transformations as in Cosserat's theory [START_REF] Renda | Discrete cosserat approach for soft robot dynamics: A new piece-wise constant strain model with torsion and shears[END_REF] are applied along each fiber to obtain the global position p of the fibers from the local coordinate space q. In practice, in the global space, the points are uniformly spaced p k = (x k , y k , z k ) along each fiber. Thus, due to the rotational motion, all fibers create a mesh of points that represents the surface of the membrane.

To create growing motion (see Fig. 4), we shift the curvilinear abscissas of N e and N (e+ j) (increase to move forward and decrease to move backward) and update the discretization of each fiber accordingly. Since the p points of the membrane are distributed along each fiber according to their curvilinear abscissa, moving the U-shaped bending region forward or backward along this abscissa for each fiber results in eversion motion of the membrane. In practice, the use of three sections S i for each fiber is sufficient to model the kinematics, with S 1 representing the section before eversion, S 2 representing the eversion region, and S 3 representing the section after eversion. However, to model the curvatures before, during and after the eversion zone, the fiber modeling approach must be enriched.

B. FEM model of the pressurized membrane at eversion

From a mechanical point of view, the quasi-static equilibrium at the eversion level comes from 4 types of forces (for a 3D position of the nodes x):

• Internal forces, noted F(x), which depend on the material used for the membrane, • Pressure forces, noted P(x) inside the structure that leads to the deployment of new material at the eversion point, • The self-collision forces of the membrane on itself and the associated friction, noted H t λ , • The boundary conditions B(x) are also very important.

In some vine robot designs [START_REF] Hawkes | role of soft robotic micromachines in the future of medical devices and personalized medicine[END_REF], a motor is placed at the base of the robot to counteract the eversion pressure and precisely control the eversion point. To determine the internal forces of the membrane, we use a FEM model based on triangular elements. In our Fig. 4. The fiber of the growing robot is divided into three sections: S 1 (pre-eversion), S 2 (eversion), and S 3 (post-eversion). To move the robot forward, we increase the curvilinear abscissa between N e and N (e+ j) . As a consequence, the section S 1 stretches (a), and the section S 3 shrinks (b). On the other hand, to make the robot move backwards, we decrease the curvilinear abscissa, which causes the section S 1 to shrink (c) and the section S 3 to stretch (d).

approach, we assume a linear elastic constitutive law, and the elements are designed to support large displacements while maintaining small deformations. We consider only in-plane forces for the membrane model, and each element can rotate freely relative to its neighbor along their shared segment, allowing for the natural flexibility of thin materials. However, this approach creates a dependence on the mesh. For future work, a more continuous approach to FEM analysis of the membrane could be considered. To distribute the pressure forces, we use the surface area of each triangle. We compute the self-collisions using the Lagrange multiplier constraints [START_REF] Coevoet | Software toolkit for modeling, simulation, and control of soft robots[END_REF]. Finally, the boundary conditions are defined by the coupling model (described below).

All these forces are computed in the 3D space of the FEM mesh nodes by solving the non-linear quasi-static equilibrium, i.e, finding x so that:

F(x) + P(x) + H T λ + B(x) = 0 (3)

C. Coupling model

The coupling approach exploits the strengths of both models to provide a complete description of the robot's behavior. Although the curved fiber model captures the 3D kinematics of the eversion motion, it lacks physical realism. Conversely, the FEM model of the pressurized membrane is complex and computationally demanding, and does not account for self- collisions within the robot, which are difficult to simulate and irrelevant to the eversion process. However, the FEM analysis at the end of the robot is useful for studying the effect of membrane properties on eversion. By combining the two models, we can obtain a more accurate and computationally efficient simulation of the robot behavior.

A coupling model is therefore proposed (see Fig. 5) for which the position of the membrane points is given by the kinematic model in the pre-and post-eversion zones (called kinematic zone), and by the FEM model in the eversion zone (called quasi-static zone). The kinematic model allows starting the FEM meshes in eversion position and to define realistic boundary conditions for the quasi-static analysis.

Both models use the same level of discretization, so each point k on the membrane has a position given by the kinematic model, denoted as p k , as well as a position from the static model, denoted as x k .

Some springs are defined between the two positions

B(x) = ∑ k k k (p k -x k ) (4)
In the kinematic zone, a high stiffness value is assigned to k k to ensure that the position of x k closely follows the position given by the kinematic model. In contrast, in the quasi-static zone, the value of k k is set to zero, allowing the membrane to follow the equilibrium of forces due to the membrane elasticity, pressure, and self-collision.

IV. RESULTS

In the previous sections, we presented a new method that integrates the Cosserat model and the FEM model to describe the eversion and the shape of growing robots. In this section, we present the simulation results obtained with our method, focusing on robots with various geometric properties and in different constrained environments.

A. Shape of eversion

We evaluated the capability of our initial attempts at geometric eversion simulation by testing them on three commonly observed eversion shapes in real life, which are determined by the way the growing robot body expands on itself: random (see Fig. 6.b), triangular (see Fig. 6.d), and linear (see Fig. 6.f). These shapes can be categorized as either a free geometric shape, in which all fibers initially bend uniformly and produce a consistent revolution, or an imposed geometric shape, in which the fibers are initially bent to match a desired shape and produce a modified revolution.

We defined a motion for the local coordinates over three sections (pre-eversion, eversion, post-eversion) in these three examples, accepting slight variations in the curvilinear abscissa. To create a simulation close to reality, we assigned the membrane elasticity parameters similar to those of the low-density polyethylene (LDPE) material, applied a small pressure, and activated the self-collision of the membrane on itself.

Our first analysis focused on a free geometry, here associated with a random shape (see Fig. 6.a), allowing the membrane to bend freely during the eversion process without any constraints on its shape. The results showed that the material had a tendency to form folds in a seemingly random fashion, resulting in a unique and interesting pattern. This behavior is not surprising, as the fibers that make up the membrane are free to bend in any direction. The results are consistent with real-world observations and can provide important information about the behavior of the material when not under specific stress, highlighting the natural tendency of the material to take on unique shapes and structures.

The second part of our analysis involved implementing a geometric shape imposed on the membrane during the eversion process, representing triangular (see Fig. 6.c) and linear (see Fig. 6.e) shapes. We found that the eversion process complies with the previously established preforming conditions by imposing specific values of the curvilinear abscissa during the revolution. During the simulation, the eversion process maintains the imposed shape and the selfcollisions of the membrane on itself remain present, although varying with the shape and the applied pressure. This results in different maximum induced pressures for each shape.

B. Constrained environment

In this section, we propose a model to study the eversion behavior of a growing robot in a narrow space, which has been explored in previous studies [START_REF] Hawkes | role of soft robotic micromachines in the future of medical devices and personalized medicine[END_REF]. The robot's pressurized membrane, which constantly inflates from the inside out, allows it to stretch and adapt to its environment (at least when the pressuring media is air). When the robot encounters a narrow space, the pressurized membrane on its front edge deforms and slides along the edges of the space, reducing the robot's diameter to pass through. Once the robot has passed through the gap, the pressurized membrane returns to its original shape and diameter.

To investigate how the robot behaves in a restricted space, we conducted tests by introducing two narrow slots that constrain the robot's expansion. In these experiments, we used the same simulated robot parameters as in our previous tests, which included dividing the fibers into three sections (pre-eversion, eversion, post-eversion) and using an LPDE membrane.

Our model provides insight into how the growing robot behaves during eversion and responds to environmental stresses. Our analysis indicates that the robot's pressurized membrane, with relaxed springs, is sensitive to external forces and can adapt to the constraints it faces. When the pressurized membrane encounters an obstacle such as a narrow gap, the eversion tip responds to the balance of forces, causing the membrane to deform, which reduces the diameter of the robot according to the size of the gap, allowing it to pass. Once the eversion tip passes through the gap, the pressurized membrane returns to its original diameter and the robot maintains the membrane deformation in the previously constrained region (see Fig. 7).

V. CONCLUSION AND FUTURE WORK

In conclusion, this study presented a new approach that combines the Cosserat model and the FEM model to simulate the eversion behavior of a growing robot. Our simulations demonstrated the effectiveness of this approach in capturing the complex eversion of the robot in various shapes and under different environmental conditions. However, it is Fig. 7. Simulation results of the eversion constrained by external obstacles. As the robot passes through the narrowing, the membrane exerts a pressure on the planes, which is proportional to the contact force F applied and depends on the type of constriction (high, medium, or small). The vertical section V s of the membrane undergoes deformation, causing a reduction in diameter equal to that of the constriction, while the horizontal section H s , which does not encounter any constriction, remains unchanged. important to note that these results represent only a first step towards understanding and modeling the eversion behavior of growing robots.

Future work will involve improving the accuracy of our model by incorporating more complex physical effects and optimizing its computational speed by reducing the membrane model in the reduced space. In addition, we plan to validate our model against physical experiments to confirm its applicability to real-world scenarios.

The successful validation of our model would have important implications for the development of growing robots. By providing a more accurate representation of the eversion process, our method could contribute to a better understanding of how growing robots navigate dynamic environments.

In summary, our results highlight the potential of the Cosserat-FEM model to advance the study and design of growing robots. By accurately simulating the eversion behavior of these robots, we can gain a better understanding of their capabilities and limitations, and ultimately develop more effective and efficient designs for a wide range of applications.

Fig. 1 .

 1 Fig. 1. Modeling of the eversion of a growing robot by combining the Cosserat rod model with FEM simulation using the SOFA framework [15].

Fig. 5 .

 5 Fig. 5. The coupling model is represented by the curved fiber model associated with the pressurized membrane. The coupling is done by means of rigid springs (a) in the kinematic zone and relaxed springs (b) in the quasi-static zone.

Fig. 6 .

 6 Fig. 6. Comparison between the simulated (a) (c) (e) and real geometries (b) (d) (f) of the growing robot in the free and imposed cases. The simulated free geometry is represented by a randomly shaped membrane (a), while the simulated imposed geometry is represented by a triangular (c) and linear shape (e). The simulations capture the complex shapes of the free and imposed geometries by initializing the fiber length along the curvilinear abscissa.


B Nottelet

E Pektok

* D Mandracchia

J.-C Tille

B Walpoth

R Gurny

M Mo ¨ller

Factorial design optimization and in vivo feasibility of poly(e-caprolactone)-micro-and nanofiber-based small diameter vascular grafts

Keywords: biodegradable polymers, polycaprolactone, vascular grafts, electrospinning, nanofibers, in vivo study

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

INTRODUCTION

Cardiovascular diseases are the leading cause of mortality in western countries and are becoming the main one in developing countries. In a single decade (1990-2000), the number of acute myocardial infarction increased about 6% for women and 13% for men across the world. [START_REF] Avendano | Socioeconomic status and ischaemic heart disease mortality in 10 western European populations during the 1990s[END_REF][START_REF] Ounpuu | The impending global epidemic of cardiovascular diseases[END_REF] Most ischaemic diseases like atherosclerosis require a revascularisation procedure. Normally, they are either treated by percutaneous coronary intervention with or without stent placement, or by bypass surgery. [START_REF] Rodengen | Coronary artery disease and treatment options[END_REF] For bypass surgery, autologous graft material, mainly arteries, is preferable, since it leads to good long-term results. [START_REF] Tomizawa | Vascular prostheses for aortocoronary bypassgrafting-A review[END_REF] However, for cases with pre-existing vascular disease or prior surgery, alternative graft materials have to be used. [START_REF] Emery | North American experience with the perma-flow prosthetic coronary graft[END_REF] While homografts can be used, they are limited in number and only recommended for special indications. [START_REF] Brockbank | Cryopreserved vein transplantation[END_REF] On the other hand, synthetic and biostable vascular grafts made of poly(tetrafluoro ethylene) (PTFE) or Gore-Tex 1 are widely used to overcome these limitations. Advantageously, they are shelf-ready and widely available for large blood vessels replacement, but they carry the severe risks of early thrombosis and late intimal hyperplasia, which are even more pronounced with small diameters grafts (Ø < 6 mm). [START_REF] Teebken | Tissue engineering of small diameter vascular grafts[END_REF] Two main strategies were developed to avoid these problems. The first one tries to compensate the lack of tissue compatibility by coating biostable grafts with heparin [START_REF] Walpoth | Improvement of patency rate in heparin-coated small synthetic vascular grafts[END_REF] or growth factors [START_REF] Walpoth | VEGF 121 induced enhancement of cellular coverage of ePTFE grafts in the chronic pig model[END_REF][START_REF] Crombez | Improving arterial prosthesis neo-endothelialization: Application of a proactive VEGF construct onto PTFE surfaces[END_REF] in order to create a non-thrombogenic or bio-active inner surface. Although this improved some cases, the use of biostable material is not preferable, since long-term residence of foreign material leads to late complications. [START_REF] Suma | The right gastroepiploic artery graft-Clinical and angiographic midterm results in 200 patients[END_REF][START_REF] Stock | Dynamics of extracellular matrix production and turnover in tissue engineered cardiovascular structures[END_REF] The second approach uses biodegradable polymers for in vitro tissue engineering, that is a combination of a degradable scaffold with cells and mediators. Several approaches have been pursued, such as in vitro formation of a novel vessel. [START_REF] Kadner | Human umbilical cord cells for cardiovascular tissue engineering: A comparative study[END_REF][START_REF] Mcfetridge | Endothelial and smooth muscle cell seeding onto processed ex vivo arterial scaffolds using 3D vascular bioreactors[END_REF][START_REF] Nasseri | Dynamic rotational seeding and cell culture system for vascular tube formation[END_REF][START_REF] Williams | Perfusion bioreactor for small diameter tissue-engineered arteries[END_REF] Unfortunately, this strategy relies on a personalized graft that must be ''customized'' with each patients own cells. As a consequence, this approach is inefficient, since many intermediate steps are required before implantation. Moreover these grafts are neither shelf-ready nor cheap. For this reason, it is of great interest to develop an in vivo colonizable and simultaneously degradable polymeric graft for promoting tissue regeneration, which would be suitable for a direct implantation.

Different methods can be applied to prepare polymeric vascular grafts. However, the chosen method has a great influence on both the mechanical properties and the micro-and nanostructures of the resulting product. On the one hand, the ideal artificial graft should be mechanically compatible with the natural arteries and the surrounding tissue. On the other hand, it should also mimic the extracellular matrix morphology; it should have a nanoscale topography (5 to 500 nm) with high porosity and adequate pore sizes (5-500 lm) in order to enhance cell attachment and proliferation for the regeneration of the natural tissues. [START_REF] Lanza | Principles of Tissue Engineering[END_REF][START_REF] Stevens | Exploring and engineering the cell surface interface[END_REF] One process which has attracted much attention in recent years is the use of melt or solution electrospinning. Melt or solution electrospinning allows the simple preparation of 3D highly porous polymeric scaffolds composed of nanofibers. [START_REF] Ashammakhi | Tissue engineering: A new take-off using nanofiber-based scaffolds[END_REF][START_REF] Li | Electrospinning of nanofibers: Reinventing the wheel?[END_REF][START_REF] Huang | A review on polymer nanofibers by electrospinning and their applications in nanocomposites[END_REF][START_REF] Chew | The role of electrospinning in the emerging field of nanomedicine[END_REF][START_REF] Xu | Electrospun nanofiber fabrication as synthetic extracellular matrix and its potential for vascular tissue engineering[END_REF] Some natural degradable materials, like collagen, [START_REF] Boland | Electrospinning collagen and elastin: Preliminary vascular tissue engineering[END_REF][START_REF] Buttafoco | Electrospinning of collagen and elastin for tissue engineering applications[END_REF] hyaluronic acid, [START_REF] Remuzzi | Vascular smooth muscle cells on hyaluronic acid: Culture and mechanical characterization of an engineered vascular construct[END_REF][START_REF] Arrigoni | The effect of sodium ascorbate on the mechanical properties of hyaluronan-based vascular constructs[END_REF] sodium alginate, [START_REF] Lee | Development and characterization of an alginate-impregnated polyester vascular graft[END_REF][START_REF] Lu | Electrospinning of sodium alginate with poly(ethylene oxide)[END_REF] or fibrinogen, [START_REF] Wnek | Electrospinning of nanofiber fibrinogen structures[END_REF][START_REF] Morton | Electrospun fibrinogen and fibrin nanofibers for angiogenesis in vitro[END_REF] have been electrospun. Unfortunately, they show poor mechanical properties compared to synthetic degradable polymers and are most commonly used as coatings on biostable grafts. Several synthetic degradable polymers have been proposed, mainly aliphatic biodegradable polyesters like poly(lactic-co-glycolic acid) (PLGA), [START_REF] Miller | Endothelial and vascular smooth muscle cell function on poly(lactic-coglycolic acid) with nano-structured surface features[END_REF][START_REF] Iwai | Biodegradable polymer with collagen microsponge serves as a new bioengineered cardiovascular prosthesis[END_REF] poly(lactic acid) (PLA), [START_REF] Boland | Electrospinning of bioresorbable polymers for tissue engineering scaffolds[END_REF][START_REF] Li | Fabrication and characterization of six electrospun poly(a-hydroxy ester)-based fibrous scaffolds for tissue engineering applications[END_REF][START_REF] Patel | A combined strategy to reduce restenosis for vascular tissue engineering applications[END_REF][START_REF] Bacakova | Adhesion and growth of rat aortic smooth muscle cells on lactide-based polymers[END_REF] but also polycarbonate derivatives [START_REF] Buttafoco | Porous hybrid structures based on P(DLLA-co-TMC) and collagen for tissue engineering of small-diameter blood vessels[END_REF][START_REF] Zhang | Engineering of vascular grafts with genetically modified bone marrow mesenchymal stem cells on poly (propylene carbonate) graft[END_REF] or polydioxanone, [START_REF] Cikirikciouglu | Biodegradable poly-dioxanone grafts for replacement of the abdominal aorta in the rat model[END_REF] since they are already in use in some biomaterial and drug delivery applications. The main problem encountered with these synthetic biodegradable polymers is their rapid loss of mechanical properties, which is due to an accelerated in vivo biodegradation of the nanofibers as a direct consequence of their very high surface/ volume ratio. For example, nanofibers of PLGA have been reported to degrade within a few days, [START_REF] Zeng | Enzymatic degradation of poly(L-lactide) and poly (epsilon-caprolactone) electrospun fibers[END_REF] which is rather unsuitable for the application as vascular prosthesis. Furthermore, the nanostructure of the envisioned grafts can lead to an increased ''pre-degradation'' induced by the necessary sterilization. In contrast, poly(e-caprolactone) (PCL) is well known for its very good mechanical properties, and the in vivo degradation of PCL occurs mainly by a very slow hydrolytic process. Some studies have shown a degradation time of several months for electrospun PCL fibers, [START_REF] Huang | Encapsulating drugs in biodegradable ultrafine fibers through co-axial electrospinning[END_REF][START_REF] Bolgen | In vitro and in vivo degradation of non-woven materials made of poly(e-caprolactone) nanofibers prepared by electrospinning under different conditions[END_REF] which is reasonable for vascular applications.

To date, electrospinning studies of PCL have mostly focused on process parameters, in order to control the morphology of pure electrospun PCL fibers and to evaluate their effect on degradability. [START_REF] Bolgen | In vitro and in vivo degradation of non-woven materials made of poly(e-caprolactone) nanofibers prepared by electrospinning under different conditions[END_REF][START_REF] Linnemann | Electrospinning: Nanofiber from polycaprolactone (PCL)[END_REF][START_REF] Jeun | Study on morphology of electrospun poly(caprolactone) nanofiber[END_REF][START_REF] Hsu | Nano-sized beads and porous fiber constructs of poly(e-caprolactone) produced by electrospinning[END_REF] A few other studies have focused on their histocompatibility using different type of cells, [START_REF] Li | Biological response of chondrocytes cultured in three-dimensional nanofibrous poly(epsilon-caprolactone) scaffolds[END_REF][START_REF] Li | Multilineage differentiation of human mesenchymal stem cells in a three-dimensional nanofibrous scaffold[END_REF][START_REF] Venugopal | In vitro study of smooth muscle cells on polycaprolactone and collagen nanofibrous matrices[END_REF][START_REF] Venugopal | In vitro culture of human dermal fibroblasts on electrospun polycaprolactone collagen nanofibrous membrane[END_REF][START_REF] Serrano | In vitro biocompatibility assessment of poly(epsilon-caprolactone) films using L929 mouse fibroblasts[END_REF] but without considering an identified final application. A very limited number of studies have been conducted to produce 3D scaffolds with an architecture mimicking the extracellular matrix of blood vessels. A sequential multilayering electrospinning has been described to form a bi-layered tubular scaffold, which is composed of an outer fibrous layer of stiff and oriented PLA and a fibrous inner layer of pliable and randomly oriented PCL. [START_REF] Vaz | Design of scaffolds for blood vessel tissue engineering using a multilayering electrospinning technique[END_REF] The same approach has been used for scaffolds made of an inner layer PCL microfibers and an outer layer of PCL nanofibers. [START_REF] Pham | Electrospun poly(epsiloncaprolactone) microfiber and multilayer nanofiber/microfiber scaffolds: Characterization of scaffolds and measurement of cellular infiltration[END_REF] Nevertheless, all these studies focused and reported on in vitro studies only.

In this article we present the preparation of PCLbased small-diameter electrospun vascular grafts, optimized by a factorial design approach in regard to their final application being suitable for in vivo implantation in rats. Furthermore, we report the initial in vivo results of an optimize graft in the rat arterial circulation, with a follow-up of 12 weeks after implantation.

MATERIALS AND METHODS

Materials

Poly(e-caprolactone) (PCL, M n 5 80,000 g/mol) was purchased from Sigma/Aldrich (Buchs, Switzerland), acetone and ethanol 96% of pharmaceutical grades from Ha ¨nseler (Herisau, Switzerland), and chloroform from Riedel-de Ha ¨en (Seelze, Germany). All products were used as received. The electrospinning system used in this study is a homemade system (Custom Design & Fabrication, Virginia Commonwealth University: under the guidance of Prof. G. Bowlin) composed of a variable high voltage power supply (Spellman High Voltage Electronics, Ltd. Pulborough, West Sussex, UK); a syringe pump (Fresenius Vial SA, Brezins, France) suitable for different controlled flow rates; stainless steel mandrels used as collectors with diameters of 2 or 4 mm; and a stainless steel plate used as a second negative pole to stabilize the electric field. Pump compatible Omnifix 1 syringes of 20 and 50 mL were received from Braun (Melsungen, Germany) and used with a 21G, Sterican 1 stainless steel needle with an inner diameter (I.D.) of 1.27 mm.

Electrospinning and optimization of vascular grafts

At first nonwoven PCL vascular grafts were electrospun from different PCL solutions. The solvents used for the preparation were acetone (Ac), chloroform/acetone (CHCl 3 /Ac) (7:3; v:v), and chloroform/ethanol (CHCl 3 / EtOH) (7:3; v:v). PCL solutions of various concentrations were prepared by dissolving the desired amount in the solvent of choice. In a typical experiment, the prepared PCL solution was ejected with a controlled flow by the syringe pump, while the positive pole of the high voltage power supply was connected to the needle, whereas the collector and the metal plate were both connected to the negative pole. A constant electric field was applied during the electrospinning process. The generated fibers were collected on a rotating (4500 rpm) and translating (200 movements/min, 4 cm amplitude) mandrel to form a nonwoven tubular PCL graft. The time of the graft preparation was adjusted to the PCL concentration to spin 360 mg of PCL. Vascular grafts having a length of 2 or 4 cm and an I.D. of 2 or 4 mm, respectively, were cut-off from the collector using a surgical scalpel before drying under reduced pressure at 378C for 24 h. In addition, all 2-mm I.D. vascular grafts were sterilized by g-radiation (2.5 MRad).

In the factorial design the following parameters solvents and solvents compositions (Ac, CHCl 3 /Ac, CHCl 3 /EtOH), PCL concentrations (5-15%; w:v), tip-collector distances (15-25 cm), applied voltages (15-25 kV), and flow-rates at which the PCL solution was ejected (12 or 24 mL/h), were studied for their influence on fiber size, bead and sheet occurrence, surface and 3D morphologies, and mechanical properties before and after g-sterilization. Statgraphic Plus 5.1 software (Statistical Graphics Corp, Herndon, VA) was used for the factorial design supported optimization.

Characterizations of the vascular grafts

Fiber diameter and morphology of electrospun material were investigated using a scanning-electron microscope (JEOL JSM-6400, Jeol Ltd, Tokyo, Japan). SEM images were taken after depositing a conductive coating of gold on the graft sample with a sputter coater (Balzers SCD004, Oerlikon AG, Pfa ¨ffikon, Switzerland). ImageJ software (National Institutes of Health, USA) was used to measure the fiber size and to count the number of bead defects in the grafts. Fiber diameter mean values were calculated from 100 measurements.

Tensile stress and tensile strain were measured on complete vascular grafts using a mechanical testing bench from Schenck AG (Na ¨nikon, Switzerland) using a cross-head speed of 10 mm/min at room temperature. The vascular grafts were fixed by clamps using 5 mm of each end of the graft, so that either a 1 or 3 cm length was used for the measurements corresponding for the 2 and 4 mm, respectively I.D. grafts.

Residual solvents were analyzed with a Headspace Sampler (HP7694, Hewlett-Packard, Palo Alto, CA) coupled to a gas-chromatography system (GC System, 6850 Series, Agilent Technologies, Santa Clara, CA) equipped with an HP-1 capillary column (Agilent Technologies, Santa Clara, CA). A 20 mg sample of the vascular graft was dissolved in benzyl alcohol containing a fixed amount of dioxane as an internal standard. The results were evaluated with the Agilent Chemstation software.

Feasibility of in vivo implantations using a dynamic model

The in vivo studies on rats were carried out in conformity with protocols approved by the local ethical commit-tee (Protocol N o . 1081-3232-11 from the Veterinary Office of the Canton of Geneva, Experimental Ethics Committee Approval N o . 06/52 from the University of Geneva). Nine PCL-based vascular grafts having a 2-mm I.D. and a length of 1.3 cm were randomly selected out of a batch of 30 g-sterilized, identical grafts. They were implanted in nine male Sprague-Dawley rats (350-400 g) under Isoflurane 2% mask anaesthesia after induction with Isoflurane 5%. The abdominal cavity was entered, and the infrarenal abdominal aorta was dissected by blunt and sharp dissection. PCL-based vascular grafts were implanted by simple sutures of 10/0 Nylon and standard microsurgical techniques under sterile conditions. Rats were followed up for 3, 6, and 12 weeks (n 5 3 for each time point), and were sacrificed after digital subtraction angiography (DSA). For histological investigations, the whole graft was fixed in 4% formaldehyde for 24 h, embedded in paraffin, and 4-lm sections were stained with hematoxylin-eosin.

RESULTS AND DISCUSSION

This study focused on the preparation of a functional vascular graft based on poly(e-caprolactone) nanofibers by electrospinning. PCL was chosen due to its well known good mechanical properties as well as its slower degradation rate compared to the often proposed PLA, PLGA or PDS, which fail to maintain sufficient mechanical properties over the time period necessary for tissue reconstruction. [START_REF] Zong | Control of structure, morphology and property in electrospun poly (glyclodide-co-lactide) non-woven membranes via post-draw treatments[END_REF][START_REF] Im | In vitro and in vivo degradation of synthetic absorbable bicomponent monofilament suture prepared with poly(p-dioxanone) and its copolymer[END_REF] The main aim was to optimize the mechanical and morphological properties of a PCL biodegradable prosthesis candidate to prepare a ''reproducible'', ''shelf-ready'', and ''simple'' alternative to biostable PTFE-or in vitro bio-engineered grafts. To achieve this goal, a factorial design for the process parameters optimization was set up, and the influence of the chosen parameters was evaluated in terms of mechanical and morphological properties on two different types of small-sized vascular grafts (2 and 4mm I.D.) For the assessment of the applicability of the obtained optimized vascular prosthesis, in vivo implantations in rats were followed up for 12 weeks.

Solvent, PCL concentration, and flow rate optimization

Commonly used PTFE vascular grafts with an inner diameter less than 6 mm carry severe risks of early thrombosis and late intimal hyperplasia. Vascular grafts based on biocompatible and -degradable polymeric nanofibers with suitable properties may overcome these problems. For this reason, 4-mm I.D. PCL-based vascular grafts were prepared by the electrospinning process in order to evaluate this preparation method and their in vivo application feasibility. In a first series of experiments, the suitability of different solvents was evaluated. The use of acetone, [START_REF] Williamson | PCL-PU composite vascular scaffold production for vascular tissue engineering: Attachment, proliferation and bioactivity of human vascular endothelial cells[END_REF][START_REF] Yarin | Branching in electrospinning of nanofibers[END_REF] CHCl 3 /acetone, [START_REF] Hsu | Nano-sized beads and porous fiber constructs of poly(e-caprolactone) produced by electrospinning[END_REF] and CHCl 3 /EtOH 42 to electrospin PCL fibers has been reported in the literature, and these solvents were chosen here for their relative ease of removal, their weak or absence of toxicity, and their low price compared to more frequently used fluoro-compounds. [START_REF] Cikirikciouglu | Biodegradable poly-dioxanone grafts for replacement of the abdominal aorta in the rat model[END_REF][START_REF] Mcmanus | Mechanical properties of electrospun fibrinogen structures[END_REF] Vascular grafts having an inner diameter of 4 mm and a length of 4 cm were prepared using each of the above mentioned solvent and solvent mixtures and studied in terms of their mechanical and morphological properties.

Considering the in vivo application of vascular grafts, the properties of the prepared prosthesis should be ideally of equal value to the ones found in human, or accordingly higher to account for loss of mechanical properties with the in vivo degradation. In native human arteries, tensile stress and strain were found to be 1.4 MPa 59 and around 100%, [START_REF] Evans | Strength of Biological Materials[END_REF] respectively. In this study, the highest tensile stress and tensile strain were achieved with the CHCl 3 / EtOH (7:3; v:v) solvent mixture followed by CHCl 3 / acetone (7:3; v:v) and pure acetone (Fig. 1). The desired value was hardly reached with pure acetone, while almost all grafts prepared with CHCl 3 /EtOH had maximum tensile stress above 1.5 MPa, independent of the flow rate or PCL concentration. From the morphological point of view, SEM pictures of the grafts showed that these solvents did not appear to have great influence on the fiber sizes, or number and size of beads, which are considered to be a defect structure in the fibers. In fact, the dominant factor was the PCL concentration. Because of these observations, the solvent mixture CHCl 3 /EtOH (7:3; v:v) was chosen for all the following experiments.

For the factorial design supported optimization of vascular grafts, a randomized rotatable central composite design with three repetitions at the center of the domain was carried out. The flow rate (12 and 24 mL/h) and PCL concentration (5-15% (w:v)) were the variables, while the tip-collector distance (20 cm) and the voltage (20 kV) were fixed. The obtained surface response diagrams, as well as the interdependence between the two variables, PCL concentration and flow rate, are presented in Table I and Figure 2. From the R 2 adjusted to the degree of freedom, it can be concluded that in all cases the proposed mathematical treatment of the data is in good agreement with the observed experimental results, except for the size of the beads, which can occur as defects in the fibers.

Regarding the mechanical properties, the tensile strain values increased with the PCL concentration from about 100 to 700% [Fig. 2(a)]. A slight interdependence was found for the flow rate and PCL concentration on strain values. High flow rates and high PCL concentration lead to the highest strain values, whereas high flow rates and low PCL concentration lead to the lowest strain values. The maximum tensile stress should theoretically be obtained with a PCL concentration around 11% (w:v). Higher values of tensile stress were also obtained with lower flow rates [Fig. 2(b)]. These results confirm that the good inherent mechanical properties of PCL ensure suffi- Summary of the central composite design carried out with PCL concentration in the range 5-15% (w:v) and a flow rate in the range 12-24 mL/h. cient strength to the prosthesis despite the nanosize of the fibers. In terms of morphology, the fiber diameter increased from 200 to 1800 nm with an increasing PCL concentration from 5 to 15% (w:v), but was independent of the flow rate [Fig. 2(c)]. Both the number and the size of beads (starting from ca. 10 lm) decreased with increasing PCL concentration up to 11% (w:v); for higher concentrations no more fiber defects could be detected. Again this was independent from the flow rate [Fig. 2(d)], which is in agreement with data from the literature for PCL nanofibers. [START_REF] Bolgen | In vitro and in vivo degradation of non-woven materials made of poly(e-caprolactone) nanofibers prepared by electrospinning under different conditions[END_REF][START_REF] Jeun | Study on morphology of electrospun poly(caprolactone) nanofiber[END_REF][START_REF] Pham | Electrospun poly(epsiloncaprolactone) microfiber and multilayer nanofiber/microfiber scaffolds: Characterization of scaffolds and measurement of cellular infiltration[END_REF] In summary, the results obtained with this randomized rotatable central composite design applied for 4-mm I.D. vascular grafts showed that the fiber sizes are controllable and depend mainly on the used PCL solution and proved the feasibility of electrospinning vascular grafts with defined properties. In a next step, smaller 2-mm I.D. vascular grafts were investigated for in vivo studies in rats.

Implantable 2-mm I.D. vascular grafts optimization

The 2-mm I.D. implantable grafts were prepared using conditions, which previously led to the best tensile stress values, namely, CHCl 3 /EtOH (7:3; v:v) as the solvent at a flow rate of 12 mL/h. A second factorial design was set up to study the additional parameters electric field density, needle-collector distance and spinning time (see Table II). All grafts were g-sterilized prior to any tensile stress and strain measurement to ensure that implanted grafts would have sufficient mechanical properties under real application conditions. It is well known that sterilization can influence the mechanical properties of polymer devices, which could have a dramatic impact in the case of vascular grafts in vivo. The mechanical properties of all tested sterilized grafts are summarized in Figure 3. As observed for the 4-mm I.D. grafts, only the PCL concentration influenced the tensile strain of the 2-mm I.D. grafts [Fig. 3(a)]. The tensile strain increased from about 200% for concentrations of 7.5 and 9% (w:v) to values between 750 and 1200% for the 12 and 15% (w:v) PCL solutions. Results were slightly different for the tensile stress, as shown in Figure 3(b). Many of the prepared grafts had tensile stress values of around 4 MPa after g-sterilization, which is far above the minimum desired value of 1.4 MPa. Only a few grafts prepared with the lowest PCL concentration of 7.5% and a longer spinning time showed lower tensile stress values. Secondly, and surprisingly, it appeared that increasing the spinning time, and thus the total amount of PCL, weakened the prostheses. Although it is not fully understood yet, this effect was mainly pronounced for the lower PCL concentrations, which underwent a 30-50% decrease. All other parameters did not show a significant influence in the studied parameter ranges, and thus the only relevant parameters for the tensile stress are the PCL solution concentration and the spinning time. Figure 4 shows the mean stress and strain values as a function of the mean fiber sizes for vascular grafts with a tensile stress superior to 2 MPa. The same tendencies were observed as found for the 4-mm I.D. grafts. The highest stress values are obtained from grafts with fibers having a diameter of about 2 lm, which are mainly obtained by electrospinning with a PCL concentration of 12% (w:v). For the strain values, a lower elongation before rupture is found for thin fibers, around 250%, while thicker fibers show elongations of around 900%.

Finally, the influence of the studied parameters on the morphological properties of the vascular grafts having tensile stress values above 2 MPa after sterilization was studied. Results are shown in Figures 5 and6. As expected, the PCL concentration was the main parameter influencing the fiber sizes, with mean diameters of 500 nm, 1 lm, 1.9 lm, and 2.5 lm for 7.5, 9, 12, and 15% (w:v) PCL solutions, respectively. No beads were observed by SEM-analysis for grafts prepared with the two highest concentrations. These results correspond to the reported behaviors for the electrospinning process. [START_REF] Fong | Beaded nanofibers formed during electrospinning[END_REF][START_REF] Deitzel | The effect of processing variables on the morphology of electrospun nanofibers and textiles[END_REF] Fiber sizes in the micrometer range seem to be quite thick for electrospun fibers, but could be of advantage for good cell adherence. The spinning time influenced the size of the fiber diameters, which increased with the spinning time when other parameters were kept constant (Fig. 6). It appeared, that in most cases, a higher electric field density led to thinner fibers, which is easily understood considering that the jets ejected out of the needle tip were subjected to higher stretching stress when the electric field increased.

As a result of this optimization process, the best PCL-based graft was selected for in vivo implantations. Thirty identical grafts were prepared by using a 15% (w:v) PCL solution in CHCl 3 /EtOH (7:3; v:v), a 6-min spinning time, a 12 mL/h flow rate, a 20-cm tip-collector distance, and a 20 kV voltage (see Table II, Figs. 3 and6, graft n826). They were free of beads, had a fiber diameter of 1.90 lm, a tensile stress of 4.8 MPa, and a tensile strain value of 600% after g-sterilization. Prior to implantation, three sterile grafts were tested for residual solvent traces using a headspace-coupled GC detection technique. None of these controls contained chloroform or ethanol traces.

Pilot in vivo studies in rats

To evaluate the practical feasibility of the optimized graft in terms of surgical handling, functionality, and biocompatibility, identical grafts were implanted in rats following the experimental setup as described in the materials and methods part. The desired function of such a biodegradable graft requires the absence of blood leakage, of acute thrombogenicity, of inflammatory response, of intimal hyperplasia, and the colonization of the scaffolds by cells to regenerate natural tissues, and finally the degradation and disappearance of the graft at a rate compatible with the blood vessel reconstruction.

Out of the batch of the 30 identical grafts, nine grafts were picked randomly by the surgeon and implanted into the abdominal aortas of Sprague-Dawley rats. These grafts had good surgical handling and suture retention properties, and led to successful implantations. None of the nine vascular II. The black arrow identifies the graft, which was used for the in vivo pilot studies. grafts showed thrombosis or aneurysm formation at the three different time points. Figure 7 illustrates a typical DSA image of an implanted graft after 12 weeks of implantation, showing good patency, no anastomotic stenosis, and no aneurysmatic dilatation. Histological analyses of grafts revealed endothelial coverage limited to the endoluminal graft surface near the distal and proximal anastomoses after 3 weeks. Graft endothelialization was almost complete after 6 weeks with the exception of a small area in the middle of all three grafts. Full endothelialisation with some intima hyperplasia formation was observed in all grafts after 12 weeks (Fig. 8). Compared to previous studies, these PCL grafts showed faster endothelial coverage within 6 to 12 weeks than what has been reported in the literature for ePTFE grafts. Zhang et al. reported a slower endothelialization rate with 30 lm ePTFE grafts in a similar rat model, where only less than half of the graft surface was covered after 8 weeks. [START_REF] Zhang | Pore size, tissue ingrowth, and endothelialization of small-diameter microporous polyurethane vascular prostheses[END_REF] This might be a consequence of the fiber and pore size of the prosthesis, and the biocompatibility of the material. An increasing cellular infiltration of the graft from the adventitia through the graft body was observed for the three time points (Fig. 8). This infiltration is composed of macrophages and fibroblasts, and accompanied by new capillary formation. No chronic lymphocytic reaction was observed. A layer of multinucleated giant cells was present on the adventitial surface of the PCL grafts at all time points [Fig. 8(b)]. The adventitial part of the graft and then the middle part showed some degradation by macro- phages, as well as collagen deposition by fibroblasts, but without multinucleated giant cells [Fig. 8(c)].

These first promising results with in vivo cell colonization confirm the feasibility of electrospun biodegradable, porous, nano-and microfiber-based PCL vascular grafts. In future studies these PCL-based grafts need to be evaluated in comparison with conventional grafts over a whole clinical application time period.

CONCLUSION

In this article we present the successful preparation of biofunctional vascular grafts obtained by electrospinning of PCL solutions. Optimization of the electrospinning parameters led to small-diameter vascular grafts with reproducible mechanical and morphological properties. The control of the mean diameter of the fibers, ranging from 500 to 2500 nm, is mainly dependent on the PCL concentration of the electrospun solution. In addition, grafts could be prepared having tensile stress values higher than 2 MPa, and up to 7.4 MPa, and tensile strain values in the range of 200-1200% after g-sterilization. These values are above those for natural human blood vessels (1.4 MPa and 100%), which facilitate the in vivo use as vascular prostheses. In a pilot study on nine rats nine identical optimized PCL-based vascular grafts (fiber mean diameter 5 1.9 lm, tensile stress 5 4.8 MPa, tensile strain 5 600%) were implanted into the rats arterial circulation as an abdominal aortic substitute. In addition to easy surgical-handling of the grafts, this study showed, that all implanted grafts were fully patent up to 12 weeks after implantation, and none of the nine vascular grafts at the three different time points (3, 6, and 12 weeks) demonstrated thrombosis or aneurysmal dilatation. Histological analyses revealed a homogeneous cellular infiltration associated with polymer degradation and extracellular matrix deposition, and a complete endothelisation with little intimal hyperplasia. These results show that the combination of PCL and the optimized electrospinning procedure enables the preparation of biodegradable, shelf-ready vascular grafts. However, in vivo healing and degradation characteristics of the electrospun PCL grafts need to be studied more extensively and over a longer time period, in comparison with standard vascular prostheses as controls, before any clinical application.

Factorial

  design optimization and in vivo feasibility of poly(ϵ-caprolactone)-micro-and nanofiber-based small diameter vascular grafts. Benjamin Nottelet, Erman Pektok, Delia Mandracchia, Jean-Christophe Tille, Beat H. Walpoth, Robert Gurny, Michael Moeller To cite this version: Benjamin Nottelet, Erman Pektok, Delia Mandracchia, Jean-Christophe Tille, Beat H. Walpoth, et al.. Factorial design optimization and in vivo feasibility of poly(ϵ-caprolactone)-micro-and nanofiberbased small diameter vascular grafts.. Journal of Biomedical Materials Research Part A, 2009, 89 (4), pp.865-75. 10.1002/jbm.a.32023. hal-00416778

Figure 1 .

 1 Figure 1. Influence of the solvent, PCL concentration and flow rate (dashed histograms 5 12 mL/h; plain histograms 5 24 mL/h) onto (a) tensile strain values and (b) tensile stress values of PCL electrospun vascular grafts (inner diameter 5 4 mm; length 5 3 cm).

Figure 2 .

 2 Figure 2. Response surfaces of (a) tensile strain, (b) tensile stress, (c) fiber diameter, and (d) number of beads, of PCL electrospun vascular grafts (inner diameter 5 4 mm; length 5 3 cm) as a function of the flow rate and the PCL concentration using a rotatable composite centered design.

  distance (cm) 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 15 20 Studied parameters using CHCl 3 /EtOH (7:3; v:v) as solvent at a 12 mL/h flow rate. a The spinning time was adjusted as a function of the PCL solution concentration. For each type of graft two spinning time have been tested. The first equals that of the 4 mm I.D. grafts and was the time necessary for the spinning of 360 mg of PCL. The second equalled half this time.

Figure 3 .

 3 Figure 3. (a) Tensile strain values and (b) tensile stress values of sterilized PCL electrospun vascular grafts (inner diameter 5 2 mm; length 5 1 cm) as a function of the PCL solution concentration, the spinning time (plain histogram 5 longer time, dashed histogram 5 shorter time), the electric field density, and the tip-collector distance. Parameters used for each graft are listed in TableII. The black arrow identifies the graft which was used for the in vivo studies.

Figure 4 .

 4 Figure 4. Mean tensile stress (^) and strain (l) values as a function of the fiber mean diameters of g-sterilized PCL electrospun vascular grafts (inner diameter 5 2 mm; length 5 1 cm).

Figure 5 .

 5 Figure 5. SEM pictures of g-sterilized PCL electrospun vascular grafts inner surface at a 3750 magnification showing the influence of the PCL solution concentration on the fiber sizes and the presence of beads.

Figure 6 .

 6 Figure 6. Fiber mean diameters of g-sterilized PCL electrospun vascular grafts (inner diameter 5 2 mm; length 5 1 cm and tensile stress value >2 MPa) as a function of the PCL solution concentration, the spinning time (plain histogram 5 longer time, dashed histogram 5 shorter time), the electric field density, and the tip-collector distance. Parameters used for each graft are listed in TableII. The black arrow identifies the graft, which was used for the in vivo pilot studies.

Figure 7 .

 7 Figure 7. Typical angiography of abdominal aortic PCL electrospun vascular graft in a rat after 12 weeks showing good patency, no stenosis, and no dilatation. White arrows point out the proximal and distal anastomoses on the abdominal aorta.

Figure 8 .

 8 Figure 8. Typical histological cut of an abdominal aortic PCL electrospun vascular graft in a rat, 12 weeks after implantation (hematoxylin-eosin staining, HE). (a) 320, (b) 3100, (c) and (d) 3200 magnification. A confluent layer of endothelium with some neo-intima formation can be observed on the luminal side of the graft (a, b, and c). Cellular infiltration was prominent from the adventitial side towards the graft matrix (a and b). Further magnification revealed that this infiltration was mainly composed of macrophages and fibroblasts, and was accompanied with new capillary formation in the matrix (d). The graft material was surrounded by a layer of multinucleated giant cells on the adventitial side (b). PA, Proximal anastomosis; L, Lumen; I, Intima, arrows in b: cellular infiltration; dotted arrows in c: endothelium, asterisk: capillary formation.

Journal of Biomedical Materials Research Part A15524965, 2009, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/jbm.a.32023 by Biu Montpellier, Wiley Online Library on [12/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

The authors thank Ste ´phanie Corboud for the help on some grafts electrospinning, Nathalie Boulens and Catherine Siegfried for the SEM pictures and Unn Lutzen for the preparation of the histological cuts.