https://doi.org/10.1177/0391398819856024 The International Journal of Artificial Organs 1–10 © The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0391398819856024 journals.sagepub.com/home/jao IJAO e International Journal of Artificial Organs Introduction Alginate is an anionic copolymer composed by mannu- ronic (M) blocks and guluronic acid (G) blocks. Only the G-blocks of the alginate participate in the intermolecular cross-linking with divalent or trivalent cations, for exam- ple, Ca 2+ , forming intersections in which calcium ions are placed. Such binding zones between the G-blocks are referred to as “egg-boxes.” 1 Usually, sodium alginate (SA) is combined with copolymers, for example, gelatin (Gel), to improve both printability and cell viability. 2 In order to confer suitable mechanical properties to the printed construct, the hydrogel is stabilized using post- printing chemical treatments, generally referred to as gela- tion processes. 3,4 Among different techniques, chemical gelation promotes the formation of G-blocks thanks to the diffusion of reactive ions through the gel. Calcium chloride (CaCl 2 ) is one of the most used alginate cross-linking agents, since it allows for a simple and rapid gelation thanks to the release of Ca 2+ cations. At the same time, cross-link- ing via CaCl 2 is not a controlled process due to its high solubility in aqueous solutions. 5–7 The cross-linking degree highly depends on alginate and CaCl 2 concentration and is a critical factor for controlling hydrogel uniformity and strength: a faster gelation rate is better for cell encapsula- tion, while slower gelation rate produces more uniform structures with higher mechanical properties. 1,8,9 Moreover, cross-linking processes alter the topology of the polymeric network, obstructing diffusive processes. 5,10,11 Therefore, Experimental characterization and computational modeling of hydrogel cross-linking for bioprinting applications Aidin Hajikhani 1 , Franca Scocozza 2 , Michele Conti 2 , Michele Marino 1 , Ferdinando Auricchio 2 and Peter Wriggers 1 Abstract Alginate-based hydrogels are extensively used to create bioinks for bioprinting, due to their biocompatibility, low toxicity, low costs, and slight gelling. Modeling of bioprinting process can boost experimental design reducing trial-and-error tests. To this aim, the cross-linking kinetics for the chemical gelation of sodium alginate hydrogels via calcium chloride diffusion is analyzed. Experimental measurements on the absorbed volume of calcium chloride in the hydrogel are obtained at different times. Moreover, a reaction-diffusion model is developed, accounting for the dependence of diffusive properties on the gelation degree. The coupled chemical system is solved using finite element discretizations which include the inhomogeneous evolution of hydrogel state in time and space. Experimental results are fitted within the proposed modeling framework, which is thereby calibrated and validated. Moreover, the importance of accounting for cross-linking- dependent diffusive properties is highlighted, showing that, if a constant diffusivity property is employed, the model does not properly capture the experimental evidence. Since the analyzed mechanisms highly affect the evolution of the front of the solidified gel in the final bioprinted structure, the present study is a step towards the development of reliable computational tools for the in silico optimization of protocols and post-printing treatments for bioprinting applications. Keywords Sodium alginate, gelation, chemical cross-linking, diffusive properties, bioprinting Date received: 30 January 2019; accepted: 20 May 2019 1 Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany 2 Dipartimento di Ingegneria Civile ed Architettura, Università degli Studi di Pavia, Pavia, Italy Corresponding author: Aidin Hajikhani, Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstr. 11, 30167 Hannover, Germany. Email: hajikhani@ikm.uni-hannover.de 856024JAO 0 0 10.1177/0391398819856024The International Journal of Artificial OrgansHajikhani et al. research-article 2019 Original research article