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International Journal of Bioprinting                               Shear-thinning and bioprinting parameters


            currently not mature enough to printing structures for use   These properties turn out to be very interesting for
            in humans. Some of the most sought after applications are   bioprinting. An ideal printable hydrogel should be highly
            the bioprinting of skin [5,6] , heart tissue , vascular grafts ,   thixotropic, meaning that the viscosity of the hydrogel
                                                        [4]
                                          [7]
            cartilage , and hard tissues such as bone [9,10] .  decreases rapidly when a shear force is applied, but recovers
                  [8]
              In bioprinting techniques, generating the desired geometry   rapidly after the shear force is removed. It is also important
            in 3D models using tissue engineering is as important as cell   to know how the viscosity behaves as the hydrogel dries
                                                                                            [31]
            proliferation in the subsequent step, both of which are the   before starting to print the next layer .
            key to the survival of the printed tissue and its functional   The viscoelastic behavior will favor the fluid’s
            success. The selected bioprinting technology also influences   maintaining the displacement properties typical of a fluid
            the strategy taken to approach the bioprinting process and the   while having the structural properties of an elastic solid. In
            selection of the materials to be used. Bioprinting techniques   this way, it will be capable of flowing when a deformation
            are classified into inkjet, microextrusion (μ-extrusion), and   force is applied, thus allowing the extrusion process to be
            laser-assisted techniques . The most widely used by the   achieved while also recovering part of the energy absorbed
                               [11]
            scientific community is microextrusion , which is one of   due to the characteristics of the elastic solid to form a
                                           [12]
            the reasons why this technology was chosen for simulation   consistent 3D structure.
            in the present study.
                                                                 Shear-thinning fluids become less viscous when a
              An important aspect of bioprinting process is to use   deforming force is applied. This implies that when the
            materials that allow the native extracellular matrix (ECM)   hydrogel is subjected to pressure in the bioprinter, these
            to be reproduced as a medium for cell development, that   forces lead to a deformation in the fluid, reducing its
            is, a medium that has the ideal biological, physical, and   viscosity,  and  thus  resulting  in  a  fluid  that  flows  more
            mechanical properties for a good bioprinting process to take   readily through the printing nozzle. Once the fluid has
            place and finally that emulate the development of the desired   been extruded, it is no longer subjected to the deformation
            system. Specifically, the definition of bioink is attributed to a   force and returns to its viscous consistency.
            biomaterial that contains a certain cellular load.
                                                                 Fluids with this shear-thinning property are governed
              The materials most used as bioinks to make 3D    by the mathematical model of the Ostwald–de Waele
            structures are polymers, ceramics, lipids, elastomers,   power law . The equation as represented in either linear
                                                                       [32]
            and hydrogels . Hydrogels stand out from the rest as   or logarithmic scales is shown in Equation I:
                       [13]
            being the materials that best simulate the ECM and have        or  log    log k        (I)
                                                                                                 n log
                                                                               n
                                                                              
                                                                          k
            become established as the practically universal option for
            bioprinting processes [14-16] .                      Where  τ and  γ are the shear stress and shear rate,
                                                               respectively. These variables are, in turn, related to the
              Biomaterials made of polymer chains do not usually
            have very good mechanical properties as they do not have   viscosity of the fluid, and  k and  n are the rheological
                                                               parameters of the model representing the flow consistency
            any well-formed 3D structures. This is often remedied by   and the flow behavior indices, respectively. The index, n,
            applying a cross-linking process. This involves a reaction,   serves to classify fluids according to their behavior so that
            in which a 3Dl network is formed by intertwining different   if n is equal to unity, the fluid is said to have a Newtonian
            linear or sparsely-branched polymer chains. One of   behavior, and when it is less than unity, the fluid will
            the most commonly used processes is based on ionic   present shear-thinning properties.
            cross-linking,  in  which the addition  of multivalent
                       [17]
            cations to the polymer solution leads to rapid gelation due   From the above, the rheological properties are directly
            to the cations’ high solubility in aqueous solutions . The   related to the bioprinting quality. However, the treatment
                                                    [18]
            cross-linking agent most widely used with alginate, for   and mathematical deduction of the bioprinting geometry
            example, is calcium chloride (CaCl ).              and the application conditions for each type of hydrogel
                                        2
              The resulting final composition of the hydrogels directly   constitute a long and tedious process. This has led to
            influences the quality of bioprinting and indicates the steps   increasing use of the resources provided by simulation,
            to achieve a certain 3D structure. Thorough rheological   with which complex calculations can be carried out at high
            characterization is therefore necessary. Thanks to rheology,   speeds, shortening the computation times and reducing or
            the behavior of fluids can be analyzed, and different   simplifying routine tests.
            parameters obtained allow the fluids to be classified,   Computer simulations use mathematical techniques
            their properties known, and their applications predicted.   that allow the behavior of practically any type of process
            Thus, a specific hydrogel, such as alginate, is considered   to be imitated. It also allows the behavior of various
            thixotropic [19-22] , viscoelastic [23-25] , and shear-thinning [26-30] .  real systems to be studied by constructing models that

            Volume 9 Issue 2 (2023)                        423                         https://doi.org/10.18063/ijb.687
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