# Simulations of Extrusion 3D Printing of Chitosan Hydrogels
## 1 Introduction  
Three-dimensional (3D) printing, also referred to as additive manufacturing, is a type of rapid prototyping technology [1, 2, 3, 4]. Extrusion-based 3D printing has broad application prospects in the area of tissue engineering [5, 6, 7, 8], drug delivery [9, 10], and medical equipment [11, 12, 13, 14]. Hydrogel-based 3D printing combines additive manufacturing methods and hydrogel biomaterial [15, 16, 17, 18]. Degradability, biocompatibility, printability, mechanical strength, and chemical modification level affect the quality of 3D printing hydrogel-based ink [19, 20, 21]. The printability of hydrogel is one of the important factors in 3D printing [22, 23]. Among hydrogels, chitosan is a polysaccharide material from the deacetylation of chitin [24, 25, 26, 27]. The printed chitosan hydrogel requires some ability to construct a complex structure and high resolution devoid of structural defects [28]. Consequently, chitosan has more applications than the common materials in biological tissues due to its exceptional biocompatibility, biological activity, safety, and inexpensive printing production [29, 30]. Additionally, chitosan can be desirable for hydrogel fabrication in soft tissue regeneration [31]. Therefore, chitosan can be preferred for hydrogel fabrication in tissue engineering applications [32, 33, 34, 35]. Numerical simulation helps prevent wasting material and time in chitosan printing. In this way, some researchers have reported the simulation modeling of hydrogel-based 3D printing. For example, [PERSON] et al. [36] inferred that the modeling 3D bioprinting SAPHs and printing setups resulted in successful printing. [PERSON] et al. [37]investigated the impact of different printing parameters and examined the printing process using computational fluid dynamics simulation, which reduces the time and cost of bio-ink. This study examines the influence of cell viability on 3D bioprinting. [PERSON] et al. [38] compare the screw and syringe-based extrusion 3D printing techniques by employing a computational simulation model and printing experiment. [PERSON] et al. [39] reported mathematical simulations of cell scaffold fabrication. The glucose and TGF-82 with mass transfer in a wall vessel bioreactor (RWVB) and cell culture were simulated using the computational fluid dynamic (CFD) technique. The findings paved the way for fabricating tissue-engineered cartilage using chitosan/gelatin hydrogel. To simulate extrusion-based 3D printing, [PERSON] et al. [40] studied a numerical model of temperature-dependent non-Newtonian viscosity. A polylactic acid melt flow as a non-isothermal power-law fluid is used in the numerical simulation. The findings reveal that the nozzle's temperature can influence the shape strand and surface topography. Moreover, [PERSON] et al. [33,41] reported that 3D printing of chitosan hydrogel in the air causes shrinkage during printing and the formation of chitosan hydrogel. They immersed dry fabricated chitosan hydrogel in a sodium hydroxide (NaOH) solution for the neutralization process and attempted to reduce shrink-induced shape deformation. However, because the printing and incubation processes are independent, it is difficult to get the fabrication done in a short time. For this reason, the chitosan hydrogel is usually prepared via acid solvent and chemical crosslink. A novel chitosan hydrogel was used in this study. The new chitosan ink is dissolved in an alkaline aqueous solution called the green technique and rapid fabrication [42]. Therefore, the innovation of this study is a CFD simulation of the 3D printing of a novel chitosan ink. An experimental test supports this finding and paves the way for the optimization of the printing step and saving time and material in the 3D printing process. This simulation was conducted in COMSOL Multiphysics software version 5.2.a (Hangzhou, China).