A NEW PHENOMENOLOGICAL MODEL TO DESCRIBE THE MECHANICAL BEHAVIOUR OF ALGINATE STRUCTURES FOR TISSUE ENGINEERING.

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1 A NEW PHENOMENOLOGICAL MODEL TO DESCRIBE THE MECHANICAL BEHAVIOUR OF ALGINATE STRUCTURES FOR TISSUE ENGINEERING. R.A. Rezende 1,2, P.J. Bártolo 1*, A. Mendes 1, H. Almeida 1 and R. Maciel Filho 2 1* Centre for Rapid and Sustainable Product Development, School of Technology and Management, Leiria Polytechnic Institute, Campus 2, Morro do Lena, Alto do Vieiro, Leiria, Portugal, pbartolo@estg.ipleiria.pt; 2 Laboratory of Optimization, Design and Advanced Control, School of Chemical Engineering, State University of Campinas, Cidade Universitária Zeferino Vaz, CP 666, Campinas, São Paulo, Brazil. Abstract - Alginates are linear unbranched polysaccharides containing -(1-4) linked D-mannuronic acid and -(1-4) linked L-guluronic acid. The alginate hydrogels are produced by mixing the alginate with a proper cross-linking agent. During the gel formation, cross-links between the alginate chains and the cationic species are formed, changing the elastic behaviour of the material controling the volume change phenomena of gels. This research study focuses on a new route to produce three-dimensional patterns (or scaffolds) in alginate hydrogels for tissue engineering applications, using a biomimetic rapid prototyping system. These patterns or scaffolds must have sufficient strength and stiffness to withstand stresses within the host tissue environment. This paper proposes a phenomenological model describing the viscoelastic behaviour of alginate scaffolds. This model, describing the effect of the alginate composition on the mechanical behaviour of these structures, is based on an extensive experimental work showing a good correlation between experimental and predicted values. A Finite Element Code using the software Abaqus, that has been developed to implement the phenomenological model, which will enable to predict the behaviour of alginate scaffolds for different values of porosity and pore configuration. Introduction In 23, patients were waiting for organ transplantation in USA alone [1]. This number has increased by May 25, while transplants were performed between January and February 25 [2]. Although clinics have tried to replace the function of failing organs mechanically or through implantation of synthetic replacements, these are often temporary solutions, not allowing the patient to completely resume normal activities. Moreover, infection and device rejection are also serious concerns in such procedures. As of the end of 24 there were 153,245 persons living with a functioning organ transplant in the United States. This number reflects an increase by about 1.8% over the prior year and a 1.7-fold increase since Some data reported by United Network for Organ Sharing (UNOS) are shown in Figures 1 and 2. Number of Candidates per year in the waiting list for organs transplants in US Number of Candidates for organs transplantations by 27 March in US Intestine 1996 / / / / / / / / / / Figure 1 Number of candidates per year waiting for transplants in US. Organs Heart/Lung Lung Heart Kidney/Pancreas Pancreas Liver Kidney Number of Candidates Figure 2 Number of candidates for organ transplantations by 27 March. Tissue Engineering (TE) typically involves the assembly of tissue structures by combining cells and biomaterials with the ultimate goal of replacing or restoring physiological functions lost in diseased or damaged organs [3].

2 Hydrogels have been receiving much attention due to their potential use in a wide variety of biomedical applications, including tissue engineering scaffolds, drug delivery, contact lenses, corneal implants and wound dressing [4-6]. They usually exhibit excellent biocompatibility and high permeability for oxygen nutrients [7-9]. Because the mechanical properties of many hydrogels can be tailored to match those of soft tissues, these materials may be attractive scaffolds for development or regeneration of soft tissues by acting as tissue barriers or local drug delivery system, and as cell carrier materials for tissue replacement [1]. A variety of biodegradable and biocompatible hydrogels have already been used for tissue engineering. Among them alginate is one of the most popular material due to its relatively low cost, natural origin and easy handling. Alginate gels are currently being explored for cell encapsulation and drug delivery [11,12]. Examples are the encapsulation of islets of Langerhans and parathyroid tissue for the treatment of diabetes mellitus and hypoparathyroidism [13,14] and the encapsulation of human chondrocytes and mesenchymal stem cells for cartilage repair [15]. Additionally, alginate materials are important for wound healing, as they are converted into a hydrophilic gel by an ion exchange interaction between calcium in alginate and sodium in the blood and wound fluid [16] A large number of processes have been developed for obtaining calcium alginate in the form of micro and macroscopic spherical objects for cell encapsulation [17]: dripping, air jet, electrostatic dripping, mechanical cutting and jet breakup. These technologies enable cell immobilisation in monodisperse beads of small sizes and at high production rate. Depending on the nozzle geometry, different capsule morphologies can be obtained (Figure 3). Figure 3 Different capsule cells morphologies as a function of nozzle geometry. This paper focuses on a new concept of biomanufacturing, investigating a new route to produce three-dimensional structures in alginate hydrogels, through a biomimetic rapid prototyping system. This system replicates natural procedures used by some marine brown algae to produce alginate, a structural component of the algae. The intercellular alginate gel matrix gives the plants both mechanical strength and flexibility. The alginate-based rapid prototyping system produces alginate scaffolds by extruding, layer-by-layer, a solution of sodium alginate into a calcium chloride solution (Figure 4). The system comprises two nozzles, one for the sodium alginate and the other for the calcium chloride deposition [18]. The polymer solution in water is pushed by a piston pump through a capillary down to a nozzle. The polymer solution gelled immediately in a hardening bath. An example of an alginate structure is shown is Figure 5. This paper investigates the effect of the gel composition in terms of both viscoelastic behaviour and surface morphology. Figure 4 Alginate-based rapid prototyping system.

3 Figure 5 Alginate scaffold structure. Alginate Alginate represents a family of polysaccharides derived from brown algae and bacteria. Chemically they are linear binary copolymers of β-d-mannuronic acid (M blocks) and α-l-guluronic acid (G blocks) (Figure 6). The alginate composition and sequential arrangement of the two residues vary with the species or the tissue from which they are isolated (Table 1). This is also a biocompatible material approved by both the European Pharmacopoeia (Ph. Eur) and the Food and Drug Administration (FDA). Figure 6 Mixed Mannuronic and Guluronic Alginate blocks [19]. Table 1.Typical M/G composition of various species of brown algae [19]. Type of seaweed %M %G Laminaria hyperborean(stem) 3 7 Laminaria hyperborean(leaf) Laminaria japonica Lessonia nigrescens 6 4 Durvillaea antarctica Durvillaea potarum Macrocystis pyrifera 6 4 Ascophyllum nodosum Alginate is soluble in aqueous solutions and forms stable gels at room temperature in the presence of non-cytotoxic concentrations of certain divalent cations (Ca 2+, Ba 2+, Fe 2+, Sr 2+, etc.) or trivalent ones (Al 3+ ) through the ionic interaction between guluronic acid group. Such binding zones between the G-blocks are often referred to as egg boxes This cross-linking mechanism enables 3D shapes to be formed, often with viable cells embedded in the gel. Gels made of M-rich alginate are softer and more fragile, and may also have lower porosity. This is due to the lower binding strength between the polymer chains and to the higher flexibilities of the molecules. Material Sodium alginate was purchased at Panreac (Barcelona, Spain). Calcium chloride was supplied by Carlo Erba (Milano, Italy). All solutions were prepared with pure water, with conductivity of.54 S/cm. Alginate solutions were prepared by addition of weighted portions of sodium alginate to measured volumes of water. Due to their high viscosity, these solutions were agitated by orbital shaking for three hours at 5 ºC to ensure good homogeneity. Calcium chloride

4 solution 5% (w/v) was obtained dissolving the salt in water. This solution was diluted to obtain solutions containing different concentrations of calcium chloride. Results Materials are classified into various classes based on their rheological properties (Figure 7). An idealised elastic solid responds to an instantaneous stress at t = by an instantaneous strain (Figure 8). Strain then remains constant until the removal of stress. An idealised viscous fluid responds to a constant imposed stress by a linear in time strain, while an idealised viscoelastic material exhibits a complex time-dependent behaviour that lies between purely elastic and purely viscous behaviours. Inviscid fluid Materials Liquids Linear viscous fluid Non-linear viscous fluid. Non-linear elastic solid Viscoelastic materials Solids Linear elastic solid Rigid solid Figure 7 Classification of materials based on rheology. Three time-dependent situations, known as creep, stress relaxation and oscillatory response, are widely used to study the viscoelastic properties of a material. In the creep analysis, steady stress is applied for an interval of time and then released, at which time the material recoils to a certain extent. In the stress relaxation case, a constant strain is applied and maintained during a period of time. Finally, in the oscillatory response, the material undergoes a sinusoidal timevarying stress/strain. Figure 8 Solid, viscous and viscoelastic behaviours. Sinusoidal time-varying stress/strain tests provide a basis for clear differentiation of the elastic and viscous properties of the material, and for understanding the viscoelastic behaviour. In this case stress and strains are given by: 2 f t sin (1) T 2 f t sin (2) T Equation (1) may be expanded to: sin 2 f t T cos( ) cos 2 f t sin( ) (3) where f is the frequency in hertz (Hz), T is the period of the sinusoidal oscillations and δ the phase lag. T

5 For dynamic analysis it is assumed that the stress strain curve within a given cycle has a linear, but not necessarily elastic, region from which storage modulus can be calculated. Storage (elastic) modulus is calculated at each cycle from the force required to produce the selected amplitude and loss (viscous) modulus is derived from the lag or phase angle: E 2 tan (4) E 1 where E 1 is the storage modulus and E 2 the loss modulus In order to characterise the viscoelastic behaviour of alginate structures it was used a dynamic mechanical analysis (DMA) system Tritec 2 (Triton Technology, UK). The experiences were performed using a proof-body with a parallelepiped shape. Table 2 illustrates the variation of the storage modulus, loss modulus and the phase angle δ as function of both temperature and alginate composition. Results reveal that both loss and storage modulus decrease by increasing temperature and alginate content. The tests were carried out considering a single cantilever bending at 1 Hz imposing a strain of 1%. Table 2: Viscoelastic properties as a function of temperature and alginate composition. Material Temperature E1 E2 tan δ composition (ºC) (KPa) (KPa) Alginate 3% CaCl 2 3% Alginate 2% CaCl 2 3% The effect of frequency on alginate was also analysed through the same experiment but using different oscillations as is shown Table 3. Table 3: Investigation of alginate elastic modulus under different frequencies, at 3ºC. Material Frequency E1 E2 tan δ composition (Hz) (KPa) (KPa) Alginate 2% CaCl 2 3% Alginate 5% CaCl 2 3% Figure 9 shows the creep behaviour of an alginate structure (2% (w/v) of alginate and 3% of CaCl 2 ) under different load conditions. Tests were performed at 23º C. As expected the increase of load increases the maximum strain achieved. The creep behaviour was fitted using the viscoelastic model illustrated in Figure 1. A good correlation was obtained. According to this model the deformation is described by: ( ) t E 1 1 e E 2 te2 (5) Figure 11 shows the variation of the viscosity as a function of load for the selected rheological model. The concentration of both sodium alginate and CaCl 2 determines not only the kinetics of the gelation process, but also the internal and surface morphology of alginate gels as indicated (not shown in this paper). Gels obtained from solutions containing higher sodium alginate and low CaCl 2 contents have smooth surfaces.

6 4 Alginate 2% 3 Strain (%) Loading time (min) Figure 9 Strain profile for different loads on an alginate proof-body. where: σ : load applied E1: elasticity of the 1 st element E2: elasticity of the 2 nd element η: viscosity Figure 1 The viscoelastic scheme. 2,3 2,2 Viscosidade (MPa.min) 2,1 2, 1,9 1,8 1,7 1,6 1,5,5,1,15,2,25,3,35 Tensão aplicada (MPa) Figure 11 Pure viscosity behaviour in alginate composition. Finite Element Code The existence of software able to define the elementary unities constitutive of scaffolds, through the definition of attributes as porosity, pore geometry and the mechanical properties (Longitudinal and Transversal Elasticity Modulus) figures as an important tool for developing the tissue engineering. The designed software associated with this work, named CADS (Computer Aided Design of Scaffolds), is a computational tool that links some other informatics applications since a bridge is established to relation 3D modelling system, data base and numerical simulations. The

7 integrated software managed by CADS are: Solidworks to the 3D modelling, Abaqus to numerical simulations, Ansys to the topological optimization and Access to the data base construction about the materials and previous results through the own CADS. The software CADS was developed by Delphi computational language. With the creation of CADS, simulations can possibility analyses in order to get optimized scaffolds with the appropriate characteristics and structure for each type of application. Figure 12 depicts the main windows of CADS. Figure 13 presents a graph illustrating hyperelastic behaviour of one scaffold at which can be observed the influence of the porosity into the final modulus. This picture is only to give an idea of which results can be obtained by CADS. Figure 12 Presentation window of CADS. Figure 13 Hyperelastic Behaviour. Conclusions Alginate is a natural biopolymer very indicated to fabrication of scaffolds to promote wound healing in the tissue engineering science since it is a biodegradable and biocompatible material. This work introduces a new rapid prototyping approach to produce three-dimensional alginate scaffolds and analysis the viscoelastic behaviour of alginate structures. The results reveal that alginate composition, temperature and frequency determine both storage and loss modulus. Through Finite Element Analysis a computational method has been adapted and can help on the determination of optimum characteristics of scaffolds. Acknowledgements The Portuguese Foundation for Science and Technology has been sponsoring this research through the projects POCI/SAU-BMA/6287/24 and POCTI/EME/665/24. References 1. Mendes, A., Lagoa, R. and Bartolo, P.J., Rapid prototyping system for tissue engineering, Proceedings of the International Conference on Advanced Research in Virtual and Physical Prototyping, pp , Network for Organ Sharing website: 27 March. 3. Tsang, V. L., Bhatia, S. N. Three-dimensional tissue fabrication. Advanced Drug Delivery Reviews, 56, , L.G. Griffith and G. Naughton, Science, 295, , A.M. Garcia and E.S. Ghaly, J. Control Rel., 4, , S.S. Kim, H. Utsunomiya, J.A. Koski, B.M. Wu, M.J. Cima, J. Sohn, K. Mukai, L.G. Griffith and J.P. Vacanti, Ann. Surg., 228, 8-13, N.B. Graham, Med Device Technol, 9, 18-22, N.B. Graham, Med Device Technol, 9, 22-25, A.S. Hoffman, Adv Drug Deliv Rev, 43, 3-12, 22.

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