Aurore Van De Walle

Jose Efrain Perez

Claire Wilhelm
email: claire.wilhelm@curie.fr

Jose Efrain Perez

Co

Magnetic bioprinting of stem cell-based tissues

come

Introduction

Recent developments in tissue engineering have focused on techniques yielding spatial organization of cells. Tissues are hierarchical structures whose proper functioning depends on their precise, complex architecture. This framework needs first to be reproduced in vitro if we are to succeed in modeling tissues with the same functions as their in vivo equivalents. Initial tissue engineering approaches through cell seeding of scaffolds generally lacked control of cell organization [START_REF] Bueno | Enhancing cell seeding of scaffolds in tissue engineering through manipulation of hydrodynamic parameters[END_REF]. To elicit spatial control, cell adhesion guidance has been tested by different strategies [START_REF] Falconnet | Surface engineering approaches to micropattern surfaces for cell-based assays[END_REF]. For example, cells can be (i) passively patterned on engineered substrates (e.g. nano-structuration [START_REF] Curtis | Topographical control of cells[END_REF] or biochemical modifications [START_REF] Zhang | Biological surface engineering: a simple system for cell pattern formation[END_REF][START_REF] Veiseh | Guided cell patterning on goldsilicon dioxide substrates by surface molecular engineering[END_REF][START_REF] Dillmore | A photochemical method for patterning the immobilization of ligands and cells to self-assembled monolayers[END_REF][START_REF] Tan | Simple approach to micropattern cells on common culture substrates by tuning substrate wettability[END_REF][START_REF] Yamazoe | Facile cell patterning on an albumin-coated surface[END_REF]), with the risk of irreversibly affecting the cell adhesion properties, or (ii) actively patterned by the remote application of a force (e.g. electric [START_REF] Sebastian | Tissue engineering with electric fields: immobilization of mammalian cells in multilayer aggregates using dielectrophoresis[END_REF][START_REF] Venkatesh | On the height of cell aggregates formed with positive dielectrophoresis[END_REF] or optic [START_REF] Nahmias | Laser-guided direct writing for three-dimensional tissue engineering[END_REF][START_REF] Zhang | Optical tweezers for single cells[END_REF]). To avoid permanent cell adhesion, reversible substrates were proposed [START_REF] Yeo | Dynamic interfaces between cells and surfaces: electroactive substrates that sequentially release and attach cells[END_REF], yet they are expensive and timeconsuming.

Active patterning of cells to build structural tissues can be achieved by 3D bioprinting. It traditionally refers to the use of a printer with a three-axis mechanical platform moving accordingly to defined coordinates that controls the deposition of biomaterials, either encapsulating cells or loaded with them afterwards. Bioprinting methodologies are still evolving, with new bioinks tailored to the tissue specificities or made of cells only [START_REF] Jeon | Individual cell-only bioink and photocurable supporting medium for 3D printing and generation of engineered tissues with complex geometries[END_REF][START_REF] Zhu | Gold Nanocomposite Bioink for Printing 3D Cardiac Constructs[END_REF], and with higher resolution printers that allow multi-material deposition for the assembly of more complex structures [START_REF] Derakhshanfar | 3D bioprinting for biomedical devices and tissue engineering: A review of recent trends and advances[END_REF][START_REF] Rutz | A Multimaterial Bioink Method for 3D Printing Tunable, Cell-Compatible Hydrogels[END_REF][START_REF] Hardin | Microfluidic Printheads for Multimaterial 3D Printing of Viscoelastic Inks[END_REF] while becoming cost-effective [START_REF] Tong | Review of Low-Cost 3D Bioprinters: State of the Market and Observed Future Trends[END_REF]. Following these approaches, teams have succeeded in reproducing human scale skin, bone, cartilage, and skeletal muscle [START_REF] Kang | A 3D bioprinting system to produce human-scale tissue constructs with structural integrity[END_REF][START_REF] Albanna | In Situ Bioprinting of Autologous Skin Cells Accelerates Wound Healing of Extensive Excisional Full-Thickness Wounds[END_REF][START_REF] Markstedt | 3D Bioprinting Human Chondrocytes with Nanocellulose-Alginate Bioink for Cartilage Tissue Engineering Applications[END_REF]. Some studies even moved to 4D, with materials able to change shape [START_REF] Tibbits | 4D Printing: Multi-Material Shape Change[END_REF], and combined such materials with anisotropic particles that can be controlled magnetically to generate unprecedented microstructural features [START_REF] Kokkinis | Multimaterial magnetically assisted 3D printing of composite materials[END_REF].

The 3D bioprinting of tissues can also be performed magnetically. In this case, cells are organized into specific 3D patterns using external magnetic forces. A pre-requirement to this remote organization of cells is their labeling with magnetic nanoparticles to render them magnetic. It should be noted that the biocompatibility of magnetic nanoparticles has already been validated, and they are utilized in medical applications such as magnetic resonance imaging (MRI) and iron replacement therapy [START_REF] Ventola | Progress in Nanomedicine: Approved and Investigational Nanodrugs[END_REF]. Their use has also been assessed for thermal cancer therapy such as hyperthermia [START_REF] Hemery | multicore magnetic iron oxide nanoparticles: uptake by glioblastoma cells and efficiency for magnetic hyperthermia[END_REF][START_REF] Espinosa | Magnetic (Hyper)Thermia or Photothermia? Progressive Comparison of Iron Oxide and Gold Nanoparticles Heating in Water, in Cells, and In Vivo[END_REF] or targeting and drug delivery [START_REF] Martina | The in vitro kinetics of the interactions between PEG-ylated magnetic-fluid-loaded liposomes and macrophages[END_REF][START_REF] Martina | The effect of magnetic targeting on the uptake of magnetic-fluid-loaded liposomes by human prostatic adenocarcinoma cells[END_REF]. Lastly, magnetic nanoparticles are good candidates in applications with stem cells, provided the control of their design and internalization dose [START_REF] Van De Walle | Magnetic nanoparticles in regenerative medicine: what of their fate and impact in stem cells?[END_REF].

Relative to other patterning techniques, magnetic forces provide access to the third dimension thanks to the long range of magnetic interactions. In addition, they are totally nonspecific to cell functions and the forces applied can be precisely controlled. The magnetic bioprinting strategy has been initially explored to engineer cell sheets [START_REF] Gonçalves | Tissue-engineered magnetic cell sheet patches for advanced strategies in tendon regeneration[END_REF][START_REF] Ito | Construction and Delivery of Tissue-Engineered Human Retinal Pigment Epithelial Cell Sheets, Using Magnetite Nanoparticles and Magnetic Force[END_REF][START_REF] Akiyama | Genetically engineered angiogenic cell sheets using magnetic force-based gene delivery and tissue fabrication techniques[END_REF], taking advantage of cell magnetization to form and organize tissue constructs in the presence of a magnetic field gradient that resulted in successive cell layering. The magnetic formation of cell spheroids has also been achieved. For instance, it has been performed through the application of an external magnetic to "levitate" cells at the air-medium interface of a culture, resulting in cohesive 3D cell assembly [START_REF] Haisler | Threedimensional cell culturing by magnetic levitation[END_REF][START_REF] Souza | Three-dimensional Tissue Culture Based on Magnetic Cell Levitation[END_REF]. Another strategy is to use magnetic forces to fuse cell-spheroids and this way create thick 3D tissue-like structures [START_REF] Fayol | Use of magnetic forces to promote stem cell aggregation during differentiation, and cartilage tissue modeling[END_REF][START_REF] Van De Walle | 3D Magnetic Stem Cell Aggregation and Bioreactor Maturation for Cartilage Regeneration[END_REF]. Magnetic patterning of cells has been successful in building submillimetric scale-tissues, as well as to promote cell assembly with tuneable size, controlled geometry, and without the need of a supporting matrix [START_REF] Frasca | Formation of a three-dimensional multicellular assembly using magnetic patterning[END_REF][START_REF] Frasca | Magnetically shaped cell aggregates: from granular to contractile materials[END_REF][START_REF] Kimura | Micropatterning of cells using modulated magnetic fields[END_REF][START_REF] Ino | Cell patterning using magnetite nanoparticles and magnetic force[END_REF][START_REF] Ino | Cell culture arrays using magnetic force-based cell patterning for dynamic single cell analysis[END_REF]. More recently, magnetic bioprinting approaches have moved to 4D, with the rationale of magnetically arranging millions of cells into a 3D construct and to exploit the magnetic properties of the construct to stimulate it by remote physical forces [START_REF] Du | A 3D magnetic tissue stretcher for remote mechanical control of 20/24 embryonic stem cell differentiation[END_REF]. Tissue engineering strategies are generally grounded on stem cells as a source due to their vast proliferation and differentiation potentials. They can generate one or several specialized cell types depending on their level of potency. Embryonic stem cells (ESCs) are pluripotent and can develop into any cell type, except those of the placenta [START_REF] Wobus | Embryonic Stem Cells: Prospects for Developmental Biology and Cell Therapy[END_REF]. They are found at an early embryonic stage and give rise to the different organs during ontogenesis. Although less numerous than in embryos, stem cells are also present in adults, where they ensure maintenance and in some cases the regeneration of tissue. Among them, the multipotent mesenchymal stem cells (MSCs) have the capacity to differentiate into cell types derived from the mesenchyme, including osteoblasts, chondrocytes, adipocytes, and myocytes [START_REF] Pittenger | Mesenchymal stem cell perspective: cell biology to clinical progress[END_REF]. Endothelial progenitor cells (EPCs) are even more specialized, being integrated in the formation of new vessels and able to differentiate into mature endothelial cells [START_REF] Yoder | Human Endothelial Progenitor Cells, Cold Spring Harb[END_REF]. Naturally, this differentiation potential of stem cells can be exploited through tissue engineering approaches. While the molecular determinants of stem cell differentiation have now been characterized, they are not the sole factors involved in this processes, some physical features of the cellular microenvironment and its dynamic behavior also play a determining role [START_REF] Han | Mechanical Properties of Materials for Stem Cell Differentiation[END_REF][START_REF] Benayahu | How is mechanobiology involved in mesenchymal stem cell differentiation toward the osteoblastic or adipogenic fate?[END_REF][START_REF] Xing | Regulation and Directing Stem Cell Fate by Tissue Engineering Functional Microenvironments: Scaffold Physical and Chemical Cues[END_REF]. For instance, the relative rigidity of a substrate can orient the differentiation of mesenchymal stem cells without the need for specific growth factors [START_REF] Engler | Matrix elasticity directs stem cell lineage specification[END_REF]. A soft substrate with a rigidity similar to that of the brain (1 kPa) orients MSC differentiation into neuronal cells, while a hard substrate comparable to bone tissue (100 kPa) gives rise to bone cells. In addition to matrix stiffness, the spatial organization of substrate molecules and cells can affect differentiation. For instance, the nanoscale patterning of cell-adhesion ligands on a substrate affects the spreading area of MSCs and their differentiation [START_REF] Ye | Matrix Stiffness and Nanoscale Spatial Organization of Cell-Adhesive Ligands Direct Stem Cell Fate[END_REF], and has been heavily investigated in the promotion of osteogenesis [START_REF] Dobbenga | Nanopattern-induced osteogenic differentiation of stem cells -A systematic review[END_REF]. Another example is the necessity of cell-cell interactions for the initiation of chondrogenesis, which can be promoted by the confinement of MSCs in a 3D aggregate composed of several thousand cells [START_REF] Yu | Stimulation of Chondrogenic Differentiation of Mesenchymal Stem Cells[END_REF]. The influence of dynamic external constraints such as fluid flow (shear stress) or compression has also been demonstrated, and the importance of specific and precise mechanical microstimulations is still being revealed. Indeed, it was shown that the capacity of EPCs to build new functional vessels is influenced by the shear stress generated by blood flow [START_REF] Kutikhin | Shear stress: An essential driver of endothelial progenitor cells[END_REF]. Flow conditions also encourage MSCs to differentiate into endothelial cells [START_REF] Wang | Shear stress induces endothelial differentiation from a murine embryonic mesenchymal progenitor cell line[END_REF] and osteoblasts [START_REF] Datta | In vitro generated extracellular matrix and fluid shear stress synergistically enhance 3D osteoblastic differentiation[END_REF]. Mechanical loading, such as compression of 3D gels incorporating stem cells (generally MSCs), induces differentiation and strongly enhances the regeneration of bone and cartilage tissues by activation of specific mechanotransduction pathways [START_REF] Choi | Effects of mechanical loading on human mesenchymal stem cells for cartilage tissue engineering[END_REF][START_REF] Hao | Mechanobiology of mesenchymal stem cells: Perspective into mechanical induction of MSC fate[END_REF][START_REF] Yanagisawa | Effects of compressive force on the differentiation of pluripotent mesenchymal cells[END_REF][START_REF] Huang | Effects of cyclic compressive loading on chondrogenesis of rabbit bone-marrow derived mesenchymal stem cells[END_REF][START_REF] Park | An electromagnetic compressive force by cell exciter stimulates chondrogenic differentiation of bone marrow-derived mesenchymal stem cells[END_REF]. Multiple biomaterial-based niches have been proposed in order to better understand the role of mechanical transduction in stem cell differentiation and to further develop the field of tissue engineering and regenerative medicine [START_REF] Vining | Mechanical forces direct stem cell behaviour in development and regeneration[END_REF]. Matrix stiffness has for example been coupled with molecular factors to induce smooth muscle cell differentiation [START_REF] Park | The effect of matrix stiffness on the differentiation of mesenchymal stem cells in response to TGF-β[END_REF][START_REF] Floren | Human mesenchymal stem cells cultured on silk hydrogels with variable stiffness and growth factor differentiate into mature smooth muscle cell phenotype[END_REF], and focus has been placed on trying to understand the molecular mechanisms [START_REF] Cosgrove | N-cadherin adhesive interactions modulate matrix mechanosensing and fate commitment of mesenchymal stem cells[END_REF] and subsequent gene response [START_REF] Darnell | RNA-seq reveals diverse effects of substrate stiffness on mesenchymal stem cells[END_REF]. However, in these studies the constraint was applied globally, meaning that the cells could not be assembled into a particular architecture. A particular advantage of the magnetic bioprinting strategy is that it permits, in addition to 3D cell assembly, to stimulate the tissue construct remotely through the use of magnetic forces, thereby providing an all integrating approach for tissue formation and potential stem cell differentiation.

This review reports different works of magnetically engineered stem cell tissues whose differentiation is directed. Fabrication of vessels de novo can for example be achieved by organizing two different stem cell types (endothelial progenitors EPCs and MSCs) [START_REF] Fayol | Design of biomimetic vascular grafts with magnetic endothelial patterning[END_REF]. The formation of cartilaginous tissue can be accomplished via an initial magnetic aggregation of human MSCs followed by their differentiation along the chondrogenic pathway and further tissue building [START_REF] Fayol | Use of magnetic forces to promote stem cell aggregation during differentiation, and cartilage tissue modeling[END_REF]. Magnetically induced cyclic stretching and compression of mouse ESCs can be performed to induce cardiomyogenesis [START_REF] Du | A 3D magnetic tissue stretcher for remote mechanical control of 20/24 embryonic stem cell differentiation[END_REF]. The magnetic labeling of stem cells with magnetic nanoparticles will first be discussed, followed by the presentation of the principles of magnetic cell assembling and the dynamic behavior of the MSC magnetic aggregates.

Stem cells magnetization upon internalization of magnetic nanoparticles

Cell uptake of nanoparticles: quantification by single-cell magnetophoresis

As for most nanomaterials, magnetic nanoparticles are generally captured by the cells through the endocytosis pathway and concentrated within lysosomes (Figure 1A). One of the most used magnetic nanoparticles in the biomedical field are synthesized by co-precipitation of iron salts and stabilized by citrate adsorption on their surface to ensure colloidal stability via negative electrostatic repulsions. Figure 1B and 1C show transmission electron microscopy (TEM) images of MSCs and endothelial progenitor cells upon internalization of these types of nanoparticles, which appear densely confined within endosomes. Cells having incorporated the nanoparticles become magnetic: they can be attracted by any magnet creating a magnetic field gradient. Single-cell magnetophoresis relies precisely on this concept of magnetic migration to measure the magnetic moment of cells, or equivalently the amount of nanoparticles per cell (expressed usually in pg of iron) [START_REF] Wilhelm | Magnetophoresis and ferromagnetic resonance of magnetically labeled cells[END_REF][START_REF] Van De Walle | Biosynthesis of magnetic nanoparticles from nano-degradation products revealed in human stem cells[END_REF]. Figure 1D shows a sequence of magnetophoresis of MSCs. It also clearly demonstrates that the labeling with nanoparticles provides the cells with sufficient magnetization to be manipulated by external magnets, and analysis of this magnetic migration provides the nanoparticle uptake in mass of iron per cell. Figure 1E shows this uptake as a function of the dose of nanoparticles for MSCs, EPCs, and ESCs upon incubation with the nanoparticles for only 30 min. The nanoparticles presence within the cells can then be confirmed via direct observation after histological iron staining (Figure 1F). Each cell is exposed to a magnetic force mcell x gradB, where mcell is the magnetic moment of the cell and gradB = 17 T/m for the magnet used. The cell migrates towards the magnet at a constant velocity vcell depending on the equilibrium between the magnetic force and the Stokes viscous force (6πηRcellvcell, with η being the water viscosity and Rcell being the cell radius). Here, the cells (MSCs) have a mean diameter of 24 ± 2 µm and a velocity of 46 ± 11 µm/s, meaning a calculated moment of 6 ± 2 x 10 -13 A.m², corresponding to a mass of iron per cell of 10 ± 3 pg, or about 10 million nanoparticless per cell. E. Uptake curves of human MSCs (hMSC) and EPCs (hEPC), and mouse ESCs (mESC). The variations in internalization mass are essentially due to the cell diameter, which can be noted between the human cells, having a diameter of 24 µm for the hMSCs and 14 µm for the hEPCs (diameters when in suspension). F. Prussian blue staining of labeled MSCs showing the iron internalized into the intracellular compartments in blue and the viable cells in pink (counterstained with nuclear fast red).

Impact of nanoparticles internalization on stem cell function

For therapeutic and diagnostic applications of magnetically labeled cells, it is crucial to first verify the biological safety of intracellular magnetic nanoparticles. The labeling method (with nanoparticles made by co-precipitation, in aqueous medium, with or without polymer coating) has already been tested on many cell types from different species, in primary and secondary cultured cells, immune cells, malignant cells and muscle cells, among others. The labeling did not affect cell viability, proliferation or the therapeutic and functional properties of the tested cell types, neither in vitro or in vivo [START_REF] Chamorro | Safety assessment of chronic oral exposure to iron oxide nanoparticles[END_REF][START_REF] Calero | Efficient and safe internalization of magnetic iron oxide nanoparticles: Two fundamental requirements for biomedical applications[END_REF][START_REF] Mejías | Long term biotransformation and toxicity of dimercaptosuccinic acidcoated magnetic nanoparticles support their use in biomedical applications[END_REF]. These magnetic nanoparticles are thus generally considered biocompatible.

By contrast, the question of differentiation capacity after magnetic labeling has been debated in the context of MSC differentiation. Using a variety of magnetic nanoparticles with an iron oxide core, no alteration but rather a positive effect in the adipogenic and osteogenic differentiation capacity of human MSCs was demonstrated [START_REF] Van De Walle | Magnetic nanoparticles in regenerative medicine: what of their fate and impact in stem cells?[END_REF][START_REF] Van De Walle | Biosynthesis of magnetic nanoparticles from nano-degradation products revealed in human stem cells[END_REF][START_REF] Arbab | Efficient magnetic cell labeling with protamine sulfate complexed to ferumoxides for cellular MRI[END_REF][START_REF] Arbab | Labeling of cells with ferumoxides-protamine sulfate complexes does not inhibit function or differentiation capacity of hematopoietic or mesenchymal stem cells[END_REF][START_REF] Heymer | Iron oxide labelling of human mesenchymal stem cells in collagen hydrogels for articular cartilage repair[END_REF][START_REF] Harrison | Autonomous magnetic labelling of functional mesenchymal stem cells for improved traceability and spatial control in cell therapy applications[END_REF][START_REF] Bulte | Chondrogenic differentiation of mesenchymal stem cells is inhibited after magnetic labeling with ferumoxides[END_REF][START_REF] Kostura | Feridex labeling of mesenchymal stem cells inhibits chondrogenesis but not adipogenesis or osteogenesis[END_REF][START_REF] Farrell | Effects of iron oxide incorporation for long term cell tracking on MSC differentiation in vitro and in vivo[END_REF][START_REF] Jiang | Fe3O4/BSA particles induce osteogenic differentiation of mesenchymal stem cells under static magnetic field[END_REF][START_REF] Li | Iron oxide nanoparticles promote the migration of mesenchymal stem cells to injury sites[END_REF][START_REF] Wei | Nanomaterials modulate stem cell differentiation: biological interaction and underlying mechanisms[END_REF][START_REF] Jia | Regeneration of large bone defects using mesoporous silica coated magnetic nanoparticles during distraction osteogenesis[END_REF]. Oppositely, the chondrogenic differentiation has been discussed controversially, with some studies showing no effects [START_REF] Arbab | Efficient magnetic cell labeling with protamine sulfate complexed to ferumoxides for cellular MRI[END_REF][START_REF] Arbab | Labeling of cells with ferumoxides-protamine sulfate complexes does not inhibit function or differentiation capacity of hematopoietic or mesenchymal stem cells[END_REF][START_REF] Heymer | Iron oxide labelling of human mesenchymal stem cells in collagen hydrogels for articular cartilage repair[END_REF][START_REF] Harrison | Autonomous magnetic labelling of functional mesenchymal stem cells for improved traceability and spatial control in cell therapy applications[END_REF][START_REF] Son | Physical Stimuli-Induced Chondrogenic Differentiation of Mesenchymal Stem Cells Using Magnetic Nanoparticles[END_REF], whereas others indicated the inhibition and even failure of chondrogenesis [START_REF] Bulte | Chondrogenic differentiation of mesenchymal stem cells is inhibited after magnetic labeling with ferumoxides[END_REF][START_REF] Kostura | Feridex labeling of mesenchymal stem cells inhibits chondrogenesis but not adipogenesis or osteogenesis[END_REF][START_REF] Negi | Safety and Quality of Magnetically Labeled Human Mesenchymal Stem Cells for Cartilage Repair[END_REF].

Further, it was demonstrated that the differentiation of MSCs was influenced by magnetic nanoparticle aggregation and by the amount of intracellular iron, with this iron "dose" likely being an important determinant of nanoparticle toxicity [START_REF] Van De Walle | Magnetic nanoparticles in regenerative medicine: what of their fate and impact in stem cells?[END_REF][START_REF] Roeder | Dose-response of superparamagnetic iron oxide labeling on mesenchymal stem cells chondrogenic differentiation: a multi-scale in vitro study[END_REF]. The amount of iron internalized by each cell mainly depends on the external iron concentration (nanoparticle dose) and on the incubation time. For MSCs, the iron uptake saturates at about 30 pg, with higher iron values obtained being explained by nanoparticle aggregation on the outer surface of the cells [START_REF] Fayol | Managing magnetic nanoparticle aggregation and cellular uptake: a precondition for efficient stem-cell differentiation and MRI tracking[END_REF]. Regardless of the intracellular amount and aggregation configuration of iron oxide nanoparticles, magnetic labeling did not affect the survival or proliferation of MSCs. Moreover, the osteogenic and adipogenic differentiation pathways were neither modified, regardless of the magnetic labeling conditions. In contrast, chondrogenesis was inhibited by high intracellular iron content and by nanoparticle aggregation on the outer cell surface [START_REF] Fayol | Managing magnetic nanoparticle aggregation and cellular uptake: a precondition for efficient stem-cell differentiation and MRI tracking[END_REF].

The differentiation capacities of ESCs after magnetic labeling are not fully documented. Au et al. [START_REF] Au | Effects of iron oxide nanoparticles on cardiac differentiation of embryonic stem cells[END_REF] demonstrated that magnetic nanoparticles associated with polylysine do not impact cardiac differentiation. Similarly, labeling of ESCs with magnetic nanoparticles wrapped with stearic acid-grafted PEI600 did not impact the expression of ectoderm, endoderm, and mesoderm markers [START_REF] Liu | Functional investigations on embryonic stem cells labeled with clinically translatable iron oxide nanoparticles[END_REF]. In our work [START_REF] Du | A 3D magnetic tissue stretcher for remote mechanical control of 20/24 embryonic stem cell differentiation[END_REF], magnetic labeling of mouse ESCs was achieved with anionic magnetic nanoparticles and the absence of a negative impact on their differentiation towards the mesoderm pathway was demonstrated.

Concerning EPCs, the magnetic labeling had no negative impact on the cell phenotype, in particular their viability, proliferation and migration capacities, as well as vascular tube formation in Matrigel [START_REF] Wilhelm | Magnetic control of vascular network formation with magnetically labeled endothelial progenitor cells[END_REF].

3D magnetic patterning with magnetically labeled stem cells: an alternative to bioprinting

Stem cells, via a simple incubation with magnetic nanoparticles, can be labeled with magnetic nanoparticles and guided at a distance using magnetic forces. Magnetic cells can then be patterned within a supporting matrix. Also, they can be organized without a matrix, by the formation of cellular aggregates compacting as spheroids that can be fused to form larger tissues. This magnetic fusion of spheroids to form large structures is quite similar to bioprinting techniques that rely on spheroids as building blocks for tissue modeling [START_REF] Zhuang | Using Spheroids as Building Blocks Towards 3D Bioprinting of Tumor Microenvironment[END_REF].

Development of local micro-magnetic devices for controlling cellular organization

The aim is therefore to modulate, in space and time, the way in which cells assemble by applying a local magnetic constraint. This 3D "magnetic patterning" allows controlling the geometric arrangement of cells, as well as the cell-cell compactness once aggregated [START_REF] Frasca | Formation of a three-dimensional multicellular assembly using magnetic patterning[END_REF].

This can be achieved with cylindrical iron tips or rectangular iron plates in the submillimeter scale, magnetized at saturation by applying an external permanent magnet, in order to generate localized magnetic spots (Figure 2A-C). Hollow cylindrical magnets can also be used to create tubular patterns (Figure 2D). Magnetized cells are seeded in cell culture plates placed on top of these magnetized tips or magnets, and they are directly attracted to the tips/magnets. Cells are this way magnetically "trapped" at localized spots; they aggregate and adopt a shape that is dictated by the given configuration of the applied magnetic field and the area of confinement. The variety of configurations permits the assembly of cells into a myriad of shapes and sizes.

The field gradients are in the range 2-100 mT/mm, which is sufficient to attract suspended cells on millimetric scales (force exerted on a cell labeled with 10 pg of iron: 1-60 pN). It is then possible to form spherical or linear aggregates of thousands or hundreds of thousands of cells.

It has to be noted that, within the intracellular environment, magnetic nanoparticles have been shown to progressively degrade [START_REF] Mazuel | Massive Intracellular Biodegradation of Iron Oxide Nanoparticles Evidenced Magnetically at Single-Endosome and Tissue Levels[END_REF]. Even though this degradation can be massive in the first month after internalization, it has not been an issue for the introduced applications. Indeed, the magnetic forces used for cell arrangement and tissue formation are usually applied rather rapidly after nanoparticle internalization, within the first one to two weeks of culture, when the cell magnetism is still strong enough. In case of longer use needed, new nanoparticle designs could be considered. Works have for instance demonstrated that the degradation of magnetic nanoparticles can be prevented by adding a gold shell [START_REF] Mazuel | Magneto-Thermal Metrics Can Mirror the Long-Term Intracellular Fate of Magneto-Plasmonic Nanohybrids and Reveal the Remarkable Shielding Effect of Gold[END_REF]. [START_REF] Frasca | Formation of a three-dimensional multicellular assembly using magnetic patterning[END_REF] for A&B and from [START_REF] Fayol | Design of biomimetic vascular grafts with magnetic endothelial patterning[END_REF] for D).

Magnetic formation of cellular aggregates: a rapid way to probe cell-to-cell interactions

Cellular spheroids have emerged as alternative in vitro models to 2D cultures as they integrate the 3D geometry of the physiological environment. The immediate application of the 3D magnetic patterning is to maintain, for several hours or days, a large number of cells in a well-defined region of space by transient application of an external magnetic field, thereby facilitating the required cell-cell contact for spheroid formation. The magnetic field gradients generated by the magnetic tips shown in Figure 2A & 2B are sufficiently powerful to entrap labeled cells. The advantages of this type of magnetic confinement are that it does not require prior chemical surface treatment and it can yield 3D cell aggregation almost instantaneously. Magnetic molding can lead to the obtention of cohesive tumor spheroids with defined diameter within 24h, allowing for the exploration of the establishment of cellto-cell liaisons during the early stages of tissue formation in a unique way [START_REF] Perez | Magnetic molding of tumor spheroids: emerging model for cancer screening[END_REF]. Figure 3 shows the magnetic assemblies obtained over a magnetic tip for multiple cell lines, including human MSCs. The tip is maintained for 10 min, then removed, with the spontaneous dynamic behavior of the cell aggregates upon the release of the magnetic force directly reflecting tissue cohesion and cell-to-cell adhesion properties.

Understanding how cells interact to form functional structures is a major challenge. Besides, a precise knowledge of cellular behavior within tissues is necessary to meet the goals of tissue engineering and regenerative medicine. In recent decades, significant progress has been made in the description and modeling of tissue morphogenesis, driven by the differential adhesion hypothesis (DAH) advanced by Steinberg in the 1960s [START_REF] Steinberg | On the mechanism of tissue reconstruction by dissociated cells. I. Population kinetics, differential adhesiveness. and the absence of directed migration[END_REF]. This one proposed that cell populations follow the behavior of immiscible liquids, such as oil and water. A tissue aggregate is now described most of the time as a liquid droplet, defined by a surface tension that reflects the intercellular adhesiveness. The spatial organization of two cell populations thus depends on surface tension, and the tissue of lower surface tension always tends to envelop its partner [START_REF] Foty | The differential adhesion hypothesis: a direct evaluation[END_REF]. However, existing experiments apply to aggregates already formed and made of cells exhibiting strong intercellular interactions (embryonic, heart, liver, retina cells, etc.). In contrast, the initial steps leading to the formation of a tissue structure, through cell-cell adhesion, have so far been described mainly for small numbers of interacting cells. Methods such as atomic force microscopy (AFM)-based single-cell force spectroscopy or again dual micropipette aspiration have been applied for studying adhesion between cell doublets (two cells) [START_REF] Kashef | Quantitative methods for analyzing cell-cell adhesion in development[END_REF].

Thanks to the magnetic cell aggregation technique allowing the assembly of millions of cells instantaneously, it has become possible to probe the establishment of 3D cell-cell adhesion at early stages within cell aggregates. By testing a large number of cell types, it was clearly evidenced that cell aggregates behave like complex materials, with a transition from wet granules to contractile structures, controlled by cell-cell interactions [START_REF] Frasca | Magnetically shaped cell aggregates: from granular to contractile materials[END_REF]. Importantly, such magnetic experiments provided access to an estimate of both the cell elasticity and of the adhesion energy of cell-cell interaction. This relationship between the macroscopic behavior of a cellular aggregate and the microscopic properties of cell components sheds light on the material properties of cell assemblies and has important implications on the attempts to create functional tissue structures in vitro.

Figure 3: Formation of cell aggregates by the application of field gradients generated by magnetic tips. The latter is maintained in place for 10 minutes before being removed. The second and fourth rows of images show aggregate evolution after 2 hours of tissue relaxation, which provides insight of the cellular dynamics during the first moments of tissue development. We observe a behavior that varies from granular (similar to a heap of sand that flows when the constraint is removed) to viscoelastic, with the most cohesive aggregates being composed of cancerous and stem cells. (Images derived, with permission, from [START_REF] Frasca | Magnetically shaped cell aggregates: from granular to contractile materials[END_REF]).

Magnetic endothelialization of tubular scaffolds with EPCs: towards vessel substitutes

The organization of two or more cell types in 3D, within a scaffold, remains a challenge to the engineering of functional tissues, which can partly be answered to by magnetic patterning. A magnetic force has for instance been used to generate, within a porous tube scaffold, a cellular organization approaching that of native blood vessels. The goal was to obtain a geometry in which EPCs are located on the tube lumen, and smooth muscle cell precursors (MSCs) are located within the tube [START_REF] Fayol | Design of biomimetic vascular grafts with magnetic endothelial patterning[END_REF]. For this purpose, a circular permanent magnet with a radial field gradient was used to magnetically attract the EPCs on the lumen, as described in Figure 2D. The tube was first seeded with non-magnetic MSCs, then placed at the center of the magnet before injection of magnetic EPCs into the lumen (Figure 4A). It has to be noted that the full biocompatibility of the magnetic labeling for EPCs was demonstrated, and particularly the preservation of endothelial capillary formation with the magnetic cells [START_REF] Wilhelm | Magnetic control of vascular network formation with magnetically labeled endothelial progenitor cells[END_REF][START_REF] Gazeau | Magnetic labeling, imaging and manipulation of endothelial progenitor cells using iron oxide nanoparticles[END_REF]. Here, the combination of polysaccharide scaffolds with tubular geometry and a magnetic endothelial patterning allowed creating pluricellular and organized vascular grafts of 2 mm of diameter (Figure 4B). The co-culture of two cell types for the development of small diameter vascular grafts has been achieved by other means, such as the progressive migration of smooth muscle cells throughout the vascular wall to fully repopulate it, followed by the seeding of an endothelial layer [START_REF] Van De Walle | Flow with variable pulse frequencies accelerates vascular recellularization and remodeling of a human bioscaffold[END_REF]. These developments require extended culture time, while it was achieved within few hours only with the magnetic patterning of EPCs. It marks a significant advancement in vascular tissue engineering, where the development of small diameter vascular grafts that recapitulate the native structure and cell composition of vessels are still lacking.

An additional advantage was the ability to detect the two cell types simultaneously, by MRI. Down the road in the development of tissue engineered products, imaging methods to control the precise fate of these cell therapy products after their implantation in the body must be developed. Combining cellular-scale resolution with MRI is one of the most interesting biomedical imaging methods, as it provides both morphological and functional information while avoiding the use of ionizing radiation. It was possible to visualize the two types of stem cell within the fabricated vessel by high-resolution MRI using distinct nanoparticles. MSCs were labelled with gadolinium and EPCs with iron oxides nanoparticles [START_REF] Di Corato | High-resolution cellular MRI: gadolinium and iron oxide nanoparticles for in-depth dual-cell imaging of engineered tissue constructs[END_REF]. The two cell types remained visible, one in black and the other in white, when embedded in the polysaccharide tubular scaffolds (Figure 4C). This method provides cellular-level resolution, deep within the body, along with the corresponding anatomical image. Having no depth limit, this approach has a key advantage over the few techniques currently available for imaging multicellular tissue, most of which are based on multiphoton microscopy.

Magnetic confinement of MSCs and magnetic spheroids fusion: towards cartilage tissue engineering

As already stated, and in addition to biochemical triggers, MSCs need to be densely compacted (i.e. such as in spheroids) for chondrocyte differentiation. The classical method to achieve this consists in centrifuging a cell suspension, followed by the addition of differentiation medium containing growth factors after pellet formation (Figure 5A). Using magnetic cell aggregation to pack the MSCs in 3D could help reproduce and improve this process [START_REF] Fayol | Use of magnetic forces to promote stem cell aggregation during differentiation, and cartilage tissue modeling[END_REF]. In particular, a current limitation in cartilage tissue engineering is that only small (submillimetric) spherical spheroids of around 200 000 cells remain viable and effectively differentiate, to the opposite of spheroids made of one million cells (Figure 5A). It indicates that the number of cells leading to successful chondrogenesis after centrifugation compaction lies in a very narrow window. The first challenge was to determine whether the magnetic compaction could help to overcome this size limitation, yet this was proven to not be the case due to limited diffusion of nutrients and growth factors towards the core of largesized spheroids (Figure 5B). Next, the shape control elicited by the magnetic patterning was taken advantage of by creating rod shaped tissues (Figure 5C) containing much more cells, but with small lateral diameter, which still allows for nutriment diffusion [START_REF] Du | Magnetic engineering of stable rod-shaped stem cell aggregates: circumventing the pitfall of selfbending[END_REF]. Such rod-shaping is clearly impossible for cell pellets prepared by centrifugation. What occurred however was quite unexpected, as a spontaneous shape transition from tissue rods to sphere-like structures happened. However, the final size of the sphere formed overcame the existing spheroid-only configuration size threshold by four times, presenting viable cells that successfully differentiated as chondrocytes with the production of both collagen II and proteoglycans, probably due to increased nutrients and growth factors access.

Finally, the MSCs magnetic spheroid patterning were used to create large tissue substitutes of variable geometry [START_REF] Fayol | Use of magnetic forces to promote stem cell aggregation during differentiation, and cartilage tissue modeling[END_REF]. In this case, MSCs spheroids were formed and then fused using magnetic forces. It resulted in the merging of single spheroid units into a bigger tissue structure, of which the final size and shape were magnetically controlled by micromagnets of different geometries (Figure 5D). Thick tissue sheets of functional cartilage tissue were produced with this method. Moreover, spheroids made of magnetic MSCs can be remotely stimulated using a magnetic field. For instance, spheroids composed of magnetic nanoparticles-loaded adipose-derived MSCs showed an increase in their chondrogenic differentiation profile after brief, 10 minute pulses of a magnetic field every 2 hours during the initial 7 days of chondrogenic induction [START_REF] Labusca | Magnetic Nanoparticles and Magnetic Field Exposure Enhances Chondrogenesis of Human Adipose Derived Mesenchymal Stem Cells But Not of Wharton Jelly Mesenchymal Stem Cells[END_REF].

Several approaches are being attempted for tissue regeneration, which include the direct injection of cells or again the production of tissue substitutes consisting of cells seeded in scaffolds [START_REF] De Pieri | Scaffold-free cell-based tissue engineering therapies: advances, shortfalls and forecast[END_REF]. Although promising, cell transplantation often results in poor retention and survival at the site of injury. In turn, scaffold-based strategies can overcome the limitations of cell transplantation; however, providing a cytocompatible, biodegradable, mechanically stable scaffold that supports the cell repopulation and extracellular matrix (ECM) remodeling is complex. The successful developments of scaffold-free tissues reproducing the cell ECM composition of cartilage obtained by magnetic printing could answer to some of the drawbacks brought by these cell injection or scaffold-based tissue engineering approaches.

Figure 5: A: Spheroids of 250 000 and 1 million MSCs were formed by centrifugation and then differentiated as cartilage. The 250 000 cells spheroids obtained expressed gycosaminoglycans (typically synthesized in cartilage) after 28 days of chondrogenic differentiation, as demonstrated by the positive toluidine blue (top) and safranin O (bottom) stainings. B: Spheroid formation was also performed magnetically, by attracting a given number stem cells (here 250 000 and 1 million) to a magnetic tip. The cell pellets obtained are more compact when formed magnetically than by centrifugation. Toluidine blue (top row) and safranin O (bottom row) stainings for glycosaminoglycans detection indicate a more abundant production when the spheroids are composed of 250 000 cells. C: Magnetic cell patterning can also be used to create rod-shaped aggregates. In this case, 1 million MSCs are seeded on top of a magnetic line. The linear cell aggregate curves within 12 hours and evolves into a fully formed sphere at day 4-5, which contains glycosaminoglycans after 28 days of chondrogenic differentiation, observed by positive toluidine blue (top row) and safranin O (bottom row) stainings. D: Spheroids of MSCs formed magnetically can be used to create scaffold-free tissues. Independent spheroid units are first created as described previously. These spheroids can be fused two-by-two, then four-by-four up to creating a mm-scale tissue. Cell-cell contact combined with chemical factors allowed to drive the differentiation of the MSCs into chondrocytes and develop a large cartilage tissue containing glycosaminoglycans (toluidine blue staining, far right image). Reproduced with permission from [START_REF] Fayol | Use of magnetic forces to promote stem cell aggregation during differentiation, and cartilage tissue modeling[END_REF].

The magnetic fingerprint of tissue as a driver of external stimulation

Compression of magnetic spheroids to retrieve their surface tension

The magnetic fingerprint of the magnetically formed spherical aggregates, or spheroids, conferred by the magnetized cells prior to formation, can be used to measure their surface tension, in itself an important marker of tissue cohesion [START_REF] Foty | The differential adhesion hypothesis: a direct evaluation[END_REF], and in the case of cancer spheroids, a marker of cell invasion [START_REF] Winters | Biophysical measurement of brain tumor cohesion[END_REF]. In this case, the stimulation can be performed within 24-72 hours of tissue maturation by subjecting the spheroid to a magnetic field in order to induce a deformation when on a flat surface. The magnetic force required to induce this deformation is equivalent to a "magnetic super-gravity" of around 100 g, quite similar to a centrifugal force. This stimulation forces the spheroid to adopt a compressed shape which reaches equilibrium within minutes. This deformation in magnetic super-gravity provides the surface tension parameter of the whole spheroid, mirroring the cells intra-spheroid interactions. Such measurement has been performed not only on stem cells spheroids [106] but also on cancer cells spheroids, with a direct implication to measurement of cancer cells invasiveness [START_REF] Perez | Magnetic molding of tumor spheroids: emerging model for cancer screening[END_REF]. Results obtained on spheroids made of stem cells indicated these have two deformation regimes before reaching their capillarity-driven equilibrium shape [106]. First, individual cells in the aggregate undergo rapid elastic deformation. A more viscous-like deformation with cell rearrangement then occurs.

Magneto-mechanical induction of ESCs mesoderm differentiation: towards cardiac tissue engineering 14/24

A major challenge in tissue engineering remains to manage, after tissue building, to stimulate mechanically the 3D tissue-like structure at will. It is of relevance for cardiac development, where tissues are continuously subject to pulse contractions.

Cell spheroids composed of ESCs can be formed magnetically following a similar protocol to the one described in the previous section and can serve as initial units for cardiac tissue formation. Their further magneto-mechanical stimulation remarkably improved the mesodermal differentiation. In this case, the magnetic micro-attractor used for 3D cell assembly also functions as a micro-controlled attractor network to manipulate the model tissue without direct contact [START_REF] Du | A 3D magnetic tissue stretcher for remote mechanical control of 20/24 embryonic stem cell differentiation[END_REF]. This approach provides an "all-in-one" solution: the same device is used to create the model tissue and to stimulate it throughout its maturation, for example in a cyclical manner that mimics cardiac muscle contraction. The principle was to form a spheroid of ESCs on one micro-magnet (Figure 6A), then to trap the spheroid by approaching a second similar micro-magnet and stretch at will the maturing embryoid body (Figure 6B) in between. When imposing a cyclic stimulation, magnetic ESCs differentiation was driven towards the cardiac pathway (Figure 6D &6C). This constitutes the first tried and tested approach allowing the creation of an embryoid body with no direct contact and no supporting matrix, followed by its maturation and stimulation in situ.

A higher-throughput magnetic micro-array containing 900 micro-magnets served a similar purpose by providing the advantage of creating 900 embryoid bodies (EBs) in one single pipetting step. These EBs could then be compacted cyclically by placing an electromagnet underneath. The cyclic magnetic compaction applied during the first fundamental stages of differentiation enhanced the process toward the cardiac mesoderm pathway, similarly to the differentiation obtained with single EBs, but in a high-throughput manner in this case [START_REF] Mary | High-Throughput Differentiation of Embryonic Stem Cells into Cardiomyocytes with a Microfabricated Magnetic Pattern and Cyclic Stimulation[END_REF]. When compared with previous studies that used growth factors (e.g. TGF and BMP2) to increase cardiomyogenesis, the enhancement obtained by the cyclic compaction seems even more effective. The positive differentiation obtained by applying cyclic forces to EBs reinforces the role of mechanical stimuli during tissue development, which is often overlooked in comparison to chemical factors. (such as the one described in Figure 2A) aggregates the magnetic ESCs together as an embryoid body before a second magnet is used to stretch and stimulate the created tissue in a cyclical manner. B. Typical bright field images of embryoid body formation, stretching in between the two micro-magnets after a second one is approached, and cyclic stimulation. C. Mesoderm gene expression was assessed after 5 days of differentiation for embryoid bodies formed magnetically and then subjected to cyclic stimulation and compared to embryoids created via the hanging drop method. D. Immunofluorescent imaging was performed on both of these samples and stained with NKX 2.5 (marker of differentiation, in green) and DAPI (cell nuclei, in blue).

Conclusion

Overall, magnetic forces can be powerful tools to organize and differentiate cells, particularly stem cells in different mechanical microenvironments.

Stem cells were easily confined in controlled configurations (spheroidal, tubular) thanks to magnetic substrates of variable architecture, at sub-millimetric and millimetric scales. Magnetic forces are applied to the cells remotely and can be modulated at will, in space and/or time. They can also create a specific mechanical environment (such as a cyclic contraction) sufficient to improve in vitro tissue functionality.

Importantly, stem cells needed first to be magnetized by allowing them to internalize magnetic nanoparticles. The biocompatibility of these nanoparticles is excellent, and the magnetic labeling generally does not affect cell function. However, before considering their use for regenerative medicine applications, it is crucial to study their long-term intracellular fate within tissues. Stem cell spheroids appear as a well-designed tool to monitor intracellular nanoparticle processing, degradation, and subsequent iron release. Indeed, each single spheroid's magnetism is a fingerprint of nanoparticle integrity, and therefore of their physical state and potential degradation. Remarkably, it was found that magnetic nanoparticles can be more than 90% purged inside the stem cells spheroids in the first ten days of tissue maturation [START_REF] Mazuel | Massive Intracellular Biodegradation of Iron Oxide Nanoparticles Evidenced Magnetically at Single-Endosome and Tissue Levels[END_REF]. This near-total nanoparticle degradation yet barely affected cellular iron homeostasis, which bodes well for their safety in regenerative medicine applications. Also worth mentioning, the massive biodegradation of the nanoparticles' magnetic core can be prevented by fine-tuning an inert gold shell [START_REF] Mazuel | Magneto-Thermal Metrics Can Mirror the Long-Term Intracellular Fate of Magneto-Plasmonic Nanohybrids and Reveal the Remarkable Shielding Effect of Gold[END_REF]. This can be important for long-term use of the nano-functionality, for instance for monitoring the outcome of cell therapy by MRI, or for applying multiple stimulations on an engineered tissue. It was recently demonstrated that MSCs are capable of biosynthesizing magnetic nanoparticles upon transformation of previously internalized synthetic nanoparticles [START_REF] Van De Walle | Biosynthesis of magnetic nanoparticles from nano-degradation products revealed in human stem cells[END_REF][START_REF] Curcio | Transformation Cycle of Magnetosomes in Human Stem Cells: from Degradation to Biosynthesis of Magnetic Nanoparticles Anew[END_REF]. This process opens to the potential of producing stable and fully biogenic nanoparticles that can be 100% biocompatible.

The development of magnetic tools to improve tissue engineering and understand cell differentiation involves cross-disciplinary scientific and technological approaches in microfabrication, physics, and life sciences. The multidisciplinary nature of the research achieved combines nanoparticles, magnetic field miniaturization, cellular biology, and tissue engineering. This latter field relates to the study of stem cells and is receiving input from the fields of cell biology, chemistry, biomechanics, and medicine. With magnetism, it adds a physical approach to cell differentiation and tissue regeneration, placing the focus on the influence of mechanical constraints.

Figure 1 :

 1 Figure 1: A. Schematic representation of magnetic nanoparticle endocytosis. B,C. Representative TEM images of EPCs (B) and MSCs (C) showing the nanoparticles in the endocytic compartments. D. Magnetophoresis sequence showing that labeled cells are attracted towards a magnet. Each cell is exposed to a magnetic force mcell x gradB, where mcell is the magnetic moment of the cell and gradB = 17 T/m for the magnet used. The cell migrates towards the magnet at a constant velocity vcell depending on the equilibrium between the magnetic force and the Stokes viscous force (6πηRcellvcell, with η being the water viscosity and Rcell being the cell radius). Here, the cells (MSCs) have a mean diameter of 24 ± 2 µm and a velocity of 46 ± 11 µm/s, meaning a calculated moment of 6 ± 2 x 10 -13 A.m², corresponding to a mass of iron per cell of 10 ± 3 pg, or about 10 million nanoparticless per cell. E. Uptake curves of human MSCs (hMSC) and EPCs (hEPC), and mouse ESCs (mESC). The variations in internalization mass are essentially due to the cell diameter, which can be noted between

Figure 2 :

 2 Figure 2: Map of the field gradients generated by a cylindrical tip (A), a truncated tip (B), a line (C), all made of iron, and (D) map in the center of a hollow disk magnet (extracted from[START_REF] Frasca | Formation of a three-dimensional multicellular assembly using magnetic patterning[END_REF] for A&B and from[START_REF] Fayol | Design of biomimetic vascular grafts with magnetic endothelial patterning[END_REF] for D).

Figure 4 :

 4 Figure 4: A. To fashion vessel substitutes, tubular gels were seeded with MSCs (labeled for instance with a green PKH67 fluorescent marker) and a circular empty magnet was used to attract magnetically labeled EPCs (labeled with a red PKH26 fluorescent marker) towards the tube lumen. B. The final vessel-like construct is observed by fluorescence microscopy, in green for the MSCs seeded within the core of the tube, in red for the EPCs attached to the lumen by magnetic patterning. C. Non-invasive imaging by MRI of the tube, with MSCs appearing in white due to a gadolinium labeling (T1 agent), and EPCs being detected in black due to the presence of the magnetic nanoparticles (T2 agent). Adapted with permission from Di Corato et al. [100]. Copyright 2013 American Chemical Society.

Figure 6 :

 6 Figure 6: A. Principle of the magnetic tissue builder and stretcher: A first micro-magnet(such as the one described in Figure2A) aggregates the magnetic ESCs together as an embryoid body before a second magnet is used to stretch and stimulate the created tissue in a cyclical manner. B. Typical bright field images of embryoid body formation, stretching in between the two micro-magnets after a second one is approached, and cyclic stimulation. C. Mesoderm gene expression was assessed after 5 days of differentiation for embryoid bodies formed magnetically and then subjected to cyclic stimulation and compared to embryoids created via the hanging drop method. D. Immunofluorescent imaging was performed on

Acknowledgments

The writing of this review article was supported by the European Union (ERC-2019-CoG project NanoBioMade #865629).


Matthias Roth

Jean-Jacques Lesage

Lothar Litz

Distributed identification of concurrent discrete event systems for fault detection purposes

An identification method for concurrent discrete event systems (DES) is presented. The purpose of the identified model is model-based fault detection in closed loop industrial DES such as production or manufacturing systems. The method consists of identifying an automata network with a scalable restriction of the network behavior. We especially deal with incomplete observation of the system language within a finite time horizon which is a typical result of a high degree of concurrency. It is shown how models identified on the basis of an incompletely observed language can be used for fault detection.

I. INTRODUCTION

Fault Detection and Isolation (FDI) in Discrete Event Systems (DES) has been an active research area in the last 10 to 15 years. Since the introduction of the diagnoser approach in [START_REF] Sampath | Failure Diagnosis using Discrete-Event Models[END_REF] various modifications and improvements of this model-based diagnosis technique have been developed. The core of this method is to build component models of a system that reflect the normal, fault-free behavior as well as the behavior in the case of given faults. The goal is to detect and diagnose a fault in the system by only considering so called "observable events" using a special observer (diagnoser). Although the method has successfully been applied to small and medium sized systems, the manual model-building is a laborious task if large industrial production systems are considered. Using identification techniques to get the necessary models for fault detection and isolation (FDI) allows minimizing the modeling effort. In contrast to the classical diagnoser approach an identified model is usually based on the fault-free observed system behavior. Thus, the identified model contains only the faultfree behavior. If the identified model is used as an observer it must be analyzed if an observed behavior cannot be reproduced by the fault-free model. In this case a fault is detected.

Since industrial production systems often consist of concurrent parts an identification method should be able to handle this concurrency. The identification of concurrent discrete event systems has been examined by several research groups in the last years. Usually, the methods are Matthias Roth is with the Institute of Automatic Control at the University of Kaiserslautern, Germany, and the LURPA, Ecole Normale Supérieure de Cachan, France. (mroth@eit.uni-kl.de)

J.-J. Lesage is the head of the LURPA at the Ecole Normale Supérieure de Cachan, F -94235 Cachan Cedex, France (lesage@lurpa.ens-cachan.fr) L. Litz is the head of the Institute of Automatic Control at the University of Kaiserslautern, D -67653 Kaiserslautern, Germany (litz@eit.uni-kl.de) based on Petri Nets. In [START_REF] Meda-Campaña | Identification of Concurrent Discrete Event Systems using Petri Nets[END_REF] an identification algorithm for Interpreted Petri Nets is given that detects concurrent transitions by the analysis of the order of their occurrence. The algorithm uses some rules when to add non-measurable places to the identified net such that the observed sequence of transitions and measurable net places can be produced by the identified model.

In [START_REF] Giua | Identification of Petri nets via integer programming[END_REF] an identification method for Petri nets based on the formulation of algebraic constraints for an integer programming problem is given. The method allows considering additional information such as structural constraints if available. Since like shown in [START_REF] Giua | Identification of Petri nets via integer programming[END_REF], solving the integer programming problem has exponential complexity with respect to the longest string in the observed language, finding a solution for large scale systems with long cycles may be impossible within a reasonable time.

Dealing with the identification of concurrent systems one key problem arises that has not been addressed in literature so far: the concurrency can lead to a very large possible behavior of the system that cannot be completely observed within a given time. In order to deal with incomplete observation of the system behavior a new distributed identification approach is presented in this paper. It is an extension of an identification method given in [START_REF] Klein | Fault detection of Discrete Event Systems using an identification approach[END_REF] that yields a monolithic automaton that is especially suitable for fault detection.

II. MONOLITHIC IDENTIFICATION OF A DES

The identification approach in [START_REF] Klein | Fault detection of Discrete Event Systems using an identification approach[END_REF] considers closed loop DES. The closed loop consists of controller and plant, which is a typical configuration for industrial production systems. The identification works on the basis of the I/O (input/output) vectors of the controller collected during p different production cycles.

Definition 1: The j-th I/O vector in the h-th of p production cycles is defined as

h h h h h u u u l = .
If each observed I/O vector is considered as a letter of an alphabet it is possible to define the set of observed words with length q observed during p different production cycles. A word represents an observed I/O vector sequence.

Distributed identification of concurrent discrete event systems for fault detection purposes

Matthias Roth, Jean-Jacques Lesage Member, IEEE, Lothar Litz Member, IEEE Definition 3: The observed words of length q are denoted as

( ) ( ) ( ) ( ) 1 Obs 1 1 , 1 , ..., 1 i l q p q i i i i j W u j u j u j q -+ = = =   + + -    

∪ ∪

With this definition it is possible to describe the behavior of a system by the language built on the basis of the observed words.

Definition 4: The observed language of length n is

1 n n i Obs Obs i L W = = ∪
The identification algorithm given in [START_REF] Klein | Fault detection of Discrete Event Systems using an identification approach[END_REF] consists of building an automaton that generates the observed language of length n of the identified DES. Since a system with interaction of controller (deterministic behavior) and physical process (non-deterministic behavior) has to be identified, the identified model is a non-deterministic autonomous automaton with output (NDAAO):

Definition 5:

0 ( NDAAO , , , , x ) X r λ = Ω X finite set of states, Ω output alphabet, : 2 X r → X non-deterministic transition relation, : λ → X Ω output function, 0 x X ∈ initial state.
The output alphabet Ω consists of the observed I/O vectors such that in the case of an identified NDAAO

1 Obs W = Ω
. λ assigns a word and thus an I/O vector from the output alphabet to each state. The NDAAO generates a set of words of length n from each state ( ) x i X ∈ that is defined as:

Definition 6:

) : ( 1) ( ( )) 2} n n x i W w w x i x i x i n x j r x j i j i n λ λ λ > = ∈ = + + - + ∈ ∀ ≤ ≤ + - Ω ( 1))
The definition of the language of length n generated by an NDAAO follows definition 4:

Definition 7: The language of length n generated by an NDAAO is

1 n n i Ident x i x X L W = ∈ = ∪ ∪
Thus, the language consists of all the words up to length n that can be produced starting from each state x X ∈ .

The algorithm in [START_REF] Klein | Fault detection of Discrete Event Systems using an identification approach[END_REF] allows to construct an NDAAO on the basis of observed words of the parametric length k, the identified automaton is able to produce the observed language of the system and is k+1-complete ( 1

1 k k Obs Ident L L + + = ) [5].
If the language (and thus the cardinality of the word set) of the system has not been completely observed like in the case of the dashed line in Fig 1, the identified NDAAO will not be able to produce each fault-free I/O vector sequence of length n=k+1 of the system. Not yet observed regular sequences are not part of the model and can thus not be produced which leads to false alerts when monitoring the system with the identified model. For large scale systems with a high degree of concurrency it is by experience not possible to observe all fault-free words (I/O vectors) within a reasonable time. It is only possible to determine an upper bound of new words that are expected in each new system cycle (see as an example Fig 7). To handle concurrent systems which make a complete observation impossible, a new distributed approach is presented.

III. PROPOSED DISTRIBUTED APPROACH

A. Automata Network Behavior

The main goal of the presented approach is to handle incomplete observation due to a high degree of concurrency of a closed loop DES when identifying a model. To handle the concurrent parts of a system it is advantageous to divide the system into concurrent subsystems for the identification and online observation. Even if the combined behavior of the concurrent subsystems can not be completely observed within a reasonable time, a complete (or almost complete) observation is much more likely for each single subsystem. For the considered class of closed loop industrial production systems this division can be made by considering well-defined parts of the I/O vectors of the controller for each subsystem.

Definition 8: The j-th partial I/O vector in the h-th of p-th production cycle is defined as

1 1
( ) ( ( ), ..., ( ), ( ), ..., ( ))

h s m h u j I j I j O j O j = with I 1 , .., I s and O 1 , .., O m {0,1, } ∈ -.
The I/Os get a "-" if they are not considered in the partial vector, else they have values "1" or "0" according to the observed values. In this paper we suppose that the division of the system into subsystems and thus the allocation of I/Os to the subsystems is performed using a-priori knowledge. Other approaches to automatically divide the system based on an analysis of the observed language are part of current research.

1 0 1 1 0                 1 1 1     -           -   0 1 0 -           -       Global I/O vector partial automaton 2 partial automaton 1 1 0 1 1 0                 1 1 1     -           -   0 1 0 -           -       Global I/O vector partial automaton 2 partial automaton 1
For each subsystem a partial automaton is identified according to the procedure given in [START_REF] Klein | Fault detection of Discrete Event Systems using an identification approach[END_REF]. Each partial automaton contains only parts of the entire I/O vector like in Fig 2.

The combined output of two or more partial NDAAOs is defined by a join operation on the outputs of the active states:

Definition 9: The join of two partial I/O vectors (v 1 ,v 2 ) is defined as

1 2 1 2 1 2 1 2 1 2 2 1 1 1 2 if | | | | if ( ) ( ) ( ) ( ) ( , )( ) ( ) if ( ) ( ) if ( ) ( ) if ( ) ( ) c v v c v i v i v i v i J v v i v i v i v i v i v i v i v i ≠   ≠ -∧ ≠ -∧ ≠   = = -   = -   =  1 2 1,.., max(| |,| |) i v v ∀ =
The I/Os at each position of the two partial I/O vectors are compared. If one of them is "-" (it is not considered in the subsystem represented by the partial automaton) the value of the other vector is taken. If one of them is "1" and the other "0" c for contradiction is taken.

From this definition follows directly that a valid state combination 1 ( ,.., ) n x x of partial automata for modeling of a system state must fulfill the condition 1 ( ( ),.., ( ))

n c J x x λ λ ∉ .
If the identified automata are used to monitor the system they can evolve independently as long as their state combination produces a valid system output. The language of the automata network is the language of the cross product of the partial automata given as: Definition 10: Cross product of two partial NDAAO: State space:

|| 1 2 1 2 1 2 1 2 | ( , ) : ( ( ), ( )) X X X x x X X c J x x λ λ = × ∀ ∈ × ∉ State output 1 2 || 1 2 1 2 ( , ) : (( , )) ( ( ), ( )) x x X x x J x x λ λ λ ∀ ∈ = Transition relation 1 2 || 1 2 1 2 1 2 1 1 2 2 1 2 1 2 1 2 ( , ) : (( , )) {( , ) | ( , ) ( ( )) ( ( )) : ( ( ), ( ))
and ( , ) ( , )}

p p p p p p p p x x X r x x x x x x x r x x r x c J x x x x x x λ λ ∀ ∈ = ∈ ∪ × ∪ ∉ ≠ Initial state: 0 1_ 0 2 _ 0 ( , ) x x x =
From this definition it follows directly that the cross product contains only states with a valid output

( || : ( ) x X c x λ ∀ ∈ ∉ ).
Let S B denote the complete fault-free system behavior and The observed cross product is derived from the cross product of the partial automata and data of the observed production cycles:

0 0 0 0 , , , ... 1 0 1 1 1 1 0 1                                                 p production cycles I/O vector sequences

Cross product

Observed cross product The automata network and the observed cross product can now be combined according to the following definition:

1 1 1 1 0 0 0 0 , , , ... 1 0 1 1 1 1 0 1                                               
Definition

POCP POCP POCP X X Θ × { , } true false →
is the transition observation function.

The POCP is constructed starting from the observed cross product according to the following algorithm: ∪ where e x is a state with an empty output that is connected to each state in the state space.

Step 6: Enlarged transition relation

( ) : ( ) : \ e POCP POCP POCP x x X r x X x ∀ ≠ ∈ =
Step 7: Complete definition of the observation function: : if ( , ( )

) not yet defined:

( , ( )) : The dynamics of the combination of automata network and POCP is defined as follows:

EOCP POCP POCP POCP POCP x X x r x x r x false ∀ ∈ Θ Θ = End algorithm 2
Definition

j n j i n i x x x x ≠ if 1 : a n ∀ ≤ ≤ _ _ a i a j x x = or _ _ ( ) a j a a i x r x ∈
holds. The POCP evolutes according to the following rule: Following this definition, the network can produce observed and unobserved trajectories of state combinations. If two consecutive state combinations have already been observed, the POCP will take a transition with POCP true Θ = .

If 1_ _ | ( ( ) ( ,.., )) POCP POCP POCP j n j x X x x x λ ∃ ∈ = ∧ POCP x ∈ _ ( ) POCP POCP actual
If the consecutive state combinations are not yet known, a transition with POCP false Θ = will be taken. The state with the empty output aggregates all state combinations that have not been observed. Hence, if the automata network produces state combinations that are unknown they can be represented by this state. By analyzing the transition observation function POCP Θ it is now possible to distinguish observed and unobserved state trajectories of the network.

D. Tolerance specification

The information of POCP Θ during the combined evolution of network and POCP can be used to specify the length of yet unobserved network trajectories that is considered as a fault symptom. This specification is given by a tolerance specification automaton. Definition 15: The tolerance specification is a 6-tuple The tolerance specification is to be used in combination with the network and the POCP. The evolution of network and POCP is given in definition 14. The tolerance specification automaton monitors the POCP evolution via the transition observation function:

If the POCP moves from a state x A to a state x B the tolerance specification moves from its actual state 1

x to a

IV. APPLICATION

In order to evaluate the ability of the identified models to detect faults the method was not directly applied to an industrial production system. For an evaluation of the method it is necessary to do tests with faults in the system which is usually not possible in a production system in operation. The lab size plant which was treated has a significant degree of concurrency that can also be found in industrial manufacturing systems. The evolution of the observed language is also comparable with industrial systems that have been treated with the method from [START_REF] Klein | Fault detection of Discrete Event Systems using an identification approach[END_REF].

The plant in W representing the set of I/O vector sequences up to length three does not reach a stable level and is thus not completely observed. A monolithic automaton identified according to section II with the parameter k=2 has 416 states. k=2 is chosen such that each physical system state can unambiguously be distinguished from each other physical system state by the analysis of k=2 consecutive I/O vectors. Hence, each automaton state represents only one physical system state which is advantageous for FDI. Since the set of words with length 3 is not completely observed the basic set of the identification is supposed to grow within the next production cycles. Consequently, monitoring the system with the monolithic model led to false alerts as soon as new words of length 3 have been observed. Fault-free words that are not observed within the given 62 fault-free production cycles are not included in the model and lead to fault detection since the model is not able to produce them.

To deal with this problem the system has been divided In Fig 6 it can be seen that in each new production cycle after the 53 th one at most two new words of length n=2 are observed in a new cycle (e.g. in the last one). This information can be interpreted as follows: in a fault-free production cycle we expect at most two consecutive unobserved transitions in the POCP since the partial automata are expected to produce at most two yet unobserved consecutive state combinations. The yet unobserved state combinations produce the new sequences of I/O vectors. Hence, an appropriate tolerance specification should accept two unobserved transitions as fault free but should lead to fault detection after the occurrence of the third unobserved transition in the POCP. Fig 7 shows the tolerance specification designed for the lab plant. As soon as the first unobserved transition is detected, the OK-state is left. If only one or two yet unobserved transitions are observed it is possible that the tolerance specification moves back to the "OK"-state. Here, the design is heuristically chosen such that each way back from a "-"-state to the OKstate takes one already observed transition more than it took unobserved transitions to get to the "-"-state. After the occurrence of three consecutive unobserved transitions in the POCP, the tolerance specification will be in the Fault-state. Using the automata network, the POCP and the tolerance specification allowed monitoring the whole system with an identified model without the occurrence of false alerts whereas built-in faults have been detected. Note that faults can be detected due to two situations: Firstly, a partial automaton can not produce the observed partial behavior. Secondly, the network behavior exceeds the accepted behavior and the tolerance specification moves to the Faultstate. The combination of POCP and tolerance specification realizes a scalable restriction of the automata network behavior.

The proposed framework is also able to handle inaccuracy during the I/O allocation to the subsystems which may not always be as obvious as in the presented case. Even if sensors of e.g. I/O-group 3 have been assigned to I/Ogroup 1, we were able to detect the built-in sensor-faults. Faults in cases like this are often not detectable by the partial automata but by the tolerance specification.

V. OUTLOOK

Current research is focused on building I/O groups of the concurrent subsystems based on the observed process behavior. The aim is to provide a method that divides a process like in

Fig 1 :

 1 Fig 1: Evolution of the number of observed words of length n over production cycles h

Fig. 2 :

 2 Fig. 2: Division of an I/O vector into two subsystems

Fig. 3 : 5 .

 35 Fig. 3: Proposed model schema B. Restriction of the Automata Network Behavior The first step to restrict the automata network behavior is the introduction of the observed network behavior: Definition 11: The Observed Cross Product of n partial NDAAO is a 5-tuple || || || || ||_ 0 ( , , , , ) obs obs obs obs obs r X x λ

Fig 4 :

 4 Fig 4: Construction of the observed cross product

Fig 3

 3 Fig 3 shows the result of the algorithm: the POCP includes the complete observed cross product plus one state e x (the black circle) containing the empty symbol as output. Each state is connected to the state e x and to each other state by a transition. If this transition has been observed -it was already part of the observed cross product -the transition observation function has the value "true" which is represented by a solid line in Fig 3. If the transition was

  rx the POCP moves to the according state else the POCP moves to the state with the empty output step 6 of the algorithm 2).

  13. The output alphabetTolerance Ω consists of the three elements { , , } OK Faultwhere OK represents a fault free situation, Fault represents a situation that leads to a fault detection and "-" represents an undecided situation.

  output of the following state x 2 it is possible to see if the network evolution that led to the PCOP trajectory is considered as a fault ( a design of the tolerance specification is given in Fig 7 in the next chapter. The combined evolution of tolerance specification and POCP works on the basis of observed (solid line) and unobserved (dashed line) transitions. If the POCP takes an already observed transition (solid line in Fig 3) the tolerance specification also takes an observed transition (solid line in Fig 7). If the transition in the POCP has not yet been observed (dashed line in Fig 3) the tolerance specification takes an unobserved transition (dashed line in Fig 7). In order to produce the observed and the unobserved behavior defined in the tolerance specification, the automata network, POCP and the tolerance specification (grey parts in Fig 3) evolve according to the rules given in this chapter.

  Fig 5 has 30 binary controller I/Os. During one production cycle the plant in Fig 5 treats three work pieces. Since there are three machine tools in the plant that work concurrently, a complete observation of the whole system language takes very long. In Fig 6 it can be seen that the evolution of | | n Obs

Fig 5 :Fig 6 :

 56 Fig 5: Identified lab system With the available data of 62 production cycles a partial NDAAO for each I/O group has been identified with k=2. The partial automata have 15, 15 and 17 states. Then, the observed cross product has been built. It consists of 327 states. Following the algorithm given in section III.C the POCP has been constructed.

Fig 7 :

 7 Fig 7: Tolerance specification for the lab plant

  Fig 5 automatically in concurrent parts and to allocate the according I/Os. Another research area is the development of fault localization algorithms for the proposed framework.

  Each I/O in the global I/O vector can be assigned to an own partial automaton containing only this I/O. The resulting network of partial automata can produce every combination of I/O values since the automata are not synchronized. Hence, no matter which I/O vector sequence will be the consequence of a fault, it is part of the identified network behavior and thus the fault can not be detected. Even if in real systems such an extreme choice of subsystems would not be made, it shows that the network behavior must be restrained in order to use the network for fault detection.To deal with this problem the framework in Fig 3 is proposed. In order to reduce the set The tolerance specification can be constructed using the gradient at the end of the curve in Fig 1.The gradient shows how many new words are usually expected in a new cycle. This information can be translated into an automaton defining the threshold of consecutive new words that are considered as a fault symptom.

										(	S B	,1	|| .. ||	, S n B	) \	S B
										containing non-detectable faults a permissive observed cross
										product is introduced that is built on the basis of the
										observed cross product of the partial automata. This
										automaton is used to detect if the combination of the
										identified partial behaviors	(	,1, S Ident B	|| .. ||	, , S n Ident B	)	is part of
										the already observed fault-free behavior	, S Obs B	of the entire
										system. Using a tolerance specification it is possible to adjust
										the amount of combined but not yet observed partial
										behavior	(	,1, S Ident B	|| .. ||	, , S n Ident B	)	∉	, S Obs B	that is accepted as
										fault-free.
	, S i B the fault-free partial behavior of the i-th subsystem. It is
	obvious that ,1 S B	|| .. ||	, S n B	S B ⊇ . Since there is usually a part
	(	S B	,1	|| .. ||	, S n B	) \	S B ≠	{}	the cross product is not suitable for
	use in FDI. Some faulty behaviors , S F B	∈	(	S B	,1	|| .. ||	, S n B	) \	S B
	cannot be distinguished from fault-free behaviors using the
	cross product even if for each identified partial behavior
	, , S i Ident B	=	, S i B	holds.

Instead of a proof consider the following (extreme) example:

  if they are part of the observed cross product. In order to deal with incomplete observation like the dashed line in Fig1, it is necessary to allow a certain number of not yet observed state combinations to reduce the number of false alerts. To do this the permissive observed cross product and the tolerance specification are introduced in the next two subsections.

														consecutive state combinations 1_ ( ,.., i x	_ n i x	)	, 1_ ( x	j	,..,	x	_ n j	)
														C. Permissive Observed Cross Product
														The aim of the permissive observed cross product (POCP)
														is to make it possible that the automata network can produce
														not yet observed trajectories of state combinations (and thus
														I/O vector sequences), but to recognize such a situation.
														Hence, a new function is introduced that determines if a
														transition of the POCP has already been observed during the
														model learning phase.
														Definition 13: The permissive observed cross product
														(POCP)	is	a	6-tuple	(	X	POCP	,	Ω	, POCP POCP r	,
														λ	POCP	,	x	POCP	_ 0	,	Θ	POCP	)	. The first five elements are defined
														according	to	definition 5.	:
										12: Combined evolution of n partial automata
	and observed cross product: Let	||_ obs actual x	be the actual state
	of					the				observed	cross	product	with
	obs λ	||	(	||_ obs actual x	1_ ) ( ,.., i x =	x	_ n i	)	. The n partial automata can
	move from state combination 1_ ( ,.., i x	_ n i x	)	to another state
	combination 1_ ( x	j	,..,	x	_ n j	1_ ) ( ,.., i x ≠	x	_ n i	)
		if 1 ∀ ≤ ≤ a n	:		x	_ a i	=	x	_ a j	or _ a j x	∈	( r x a	_ a i	)	holds (where
	a is the index of the a-th of n partial automata) and
		if							1 x X ∃ ∈	obs	|| |	obs λ	||	1 ( ) ( x =	1_ x	j	,..,	_ n j x	)	∧
	1 x r x || ( obs obs actual ||_ ∈	)	. If the condition is fulfilled the observed
	cross product moves to the new actual state 1 x and the
	automata network changes to the state combination
	(	1_ x	j	,..,	x	_ n j	)	.
		With this definition, the network can only produce two