Modeling calcium diffusion and crosslinking dynamics in a thermogelling Alginate-Gelatin-Hyaluronic acid ink: 3D bioprinting applications

Abstract

Alginate-based inks are widely used in 3D bioprinting. Its crosslinking by Ca²⁺ ions is extremely important to achieve scaffolds with optimal mechanical properties. Notably, despite previous studies on calcium diffusion in alginate systems, there have been no reported data regarding the effect of temperature on the diffusion and crosslinking dynamics of thermogelling alginate-based hydrogels. This study focuses on investigating the kinetics of the crosslinking front and Ca²⁺ diffusion within a matrix of Alginate-Gelatin-Hyaluronic acid ink, exploring the impact of temperature and Ca²⁺ concentration. The Ca²⁺ diffusion rate or ink crosslinking rate increase as the crosslinker concentration and ink temperature increase. Additionally, the mechanical properties of the scaffolds, assessed through compression, tension, and dynamic tests, were correlated with the crosslinking time.

The innovative aspect of this study lies in the development of a code that simulates the diffusion of Ca²⁺ ions from the exterior to the interior of a hydrogel structure. Specifically, the code facilitates the calculation of the crosslinking time for a cylindrical structure up to a specified thickness, providing valuable insights for the production of airways or blood vessels. Furthermore, the Python script, incorporating the numerical model, manages to simulate the crosslinking dynamics of scaffolds of any shape, and properly fits the rheological measurements of dynamic moduli during the crosslinking process. This represents a significant advance for the precise and controlled scaffold fabrication process using 3D bioprinting.