## 1 Introduction  
One aim of tissue engineering is to develop tissue/organ substitutes or scaffolds, based on the principles of biology and engineering, for the repair or replacement of damaged tissues and organs [1; 2]. For this, scaffolds, typically of a three-dimensional (3D) porous structure made from biomaterials, play an important role in supporting and/or promoting cell growth, tissue regeneration, and transport of nutrients and wastes. Design and fabrication of scaffolds have proven to be a challenging task [3]. One important issue in the design and fabrication of scaffolds is achieving the desired mechanical properties to match those of tissue at the site of implantation. More specifically, the scaffold must be strong enough to resist structural collapse upon implantation, yet sufficiently compliant so as not to damage the surrounding tissues. Tissue scaffolds can be fabricated by either conventional or modern techniques. Conventional methods, like electrospinningning, are limited for the fabrication of 3D scaffolds with interconnected pores [4; 5] and in some cases, organic solvents have to be used, thus being detrimental for cellular proliferation/differentiation [6]. Nowadays, additive manufacturing (AM) techniques have drawn considerable attention since they allow fabrication of scaffolds layer-by-layer [7], and thus open a new door to create scaffolds with a complex 3D microstructure and a controllable pore shape and size [8]. Among various AM techniques, extrusion-based 3D biopltting shows promise, where bioinks are extruded from either one or multiple needles and thus form 3D scaffolds [9; 10; 11; 12], as shown in Figure 1 (a pneumatic-based 3D biopltter extruding biomaterials from one needle). Notably, the bioink for biopltting can be prepared from the biomaterials favorable for cells, thus being capable of incorporating cells and proteins in the scaffold fabrication process [13; 14]. For this, hydrogels have been widely utilized as they are able to provide an appropriate environment for encapsulating cells and growth factors [15]. This is mainly due to the fact the hydrogels involve a large amount of water in their polymeric 3D network, which is favorable to cell growth and tissue regeneration [16; 17]. Alginate is one of the widely-used natural polymers with properties of good biocompatibility and ease of gelation and has found many applications in tissue engineering, such as wound healing and drug delivery [18]. As inspired, we selected alginate in the present study for the scaffold fabrication. As noted previously, scaffolds should have the mechanical properties similar to those of targeted tissue. To this end, research has been performed to fabricate scaffolds with desired mechanical properties by taking the aforementioned advantages of 3D biopltting [19; 20]. The experimental results illustrate the mechanical properties of 3D-biopltted scaffolds can be affected by the scaffold-material properties and the geometrical features of scaffolds (including pore size, strand diameter, and orientation of strands) [19; 21]. Notably, experimental measurements and characterization of the mechanical properties of scaffolds are time-consuming, even impractical once implanted in vivo. Therefore, there is a need to develop alternative methods, like numerical modeling, to represent or predict the mechanical properties of scaffolds instead of the use of experimental tests. Recently, finite element modeling (FEM) has been introduced as a method to represent the mechanical properties of scaffolds fabricated by means of 3D extrusion-based printing. In our previous studies [8; 22], models based on FEM have been developed to predict the elastic modulus of printed scaffolds. By these models, the elastic modulus of scaffolds was predicted with a good agreement with the measured ones [8; 22]. FEM-based models can also be used to represent the change of mechanical properties of scaffolds with time due to the scaffold degradation [23] and the mechanical  
Figure 1: Schematic of 3D biopltting.