Articular hyaline cartilage covers articulating bone surfaces in diarthroidal joints of the human body. The self-repair capability of articular cartilage is limited because of non-vascularisation and low turnover of its extracellular matrix. Despite tremendous advancements in regenerative medicine, it remains challenging to repair articular cartilage defects. Since articular cartilage is a natural polyelectrolyte hydrogel, electroactive hydrogel scaffolds are specifically significant in tissue engineering approaches. The chondrogenic phenotype of these hydrogels may be enhanced by settling them with cartilaginous cells and applying suitable biophysical stimuli, e.g. electrical stimulation [1]. These scaffolds can then be implanted at the defect site, as illustrated in Figure 1. The application of electric stimulation causes the movement of ions and the opening of the voltage-gated calcium channels of the cells. The increased activity of the intracellular calcium concentration activates the underlying mechanisms to facilitate cell growth, proliferation, and differentiation at the defect site. Employing numerical simulations, these mechanisms can be studied at different length scales. The current study aims to analyse the ions and electric potential distributions in a hydrogel scaffold and the surrounding medium. For this purpose, the model consisting of nonlinear Poisson-Nernst-Planck (PNP) equations is solved numerically using the open-source numerical software NGSolve [2] for electroactive hydrogels to be used in cartilage tissue engineering. Previously, we have presented a numerical simulation model of electroactive hydrogels for cartilage tissue engineering [3] employing the open-source finite element software FEniCS [4]. Compared to FEniCS, NGSolve is preferred due to its integrated CAD kernel and Netgen mesh generator, reduced dependencies, and increased user-friendliness.

Acknowledgement: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB 1270/2 - 299150580. 

References 

[1] R. Vaiciuleviciute; I. Uzieliene; P. Bernotas; V. Novickij; A. Alaburda Bioengineering, 2023, 10, 454.
[2] J. Schöberl; Computing and visualization in science, 1997, 1, 41–52.
[3] A.R. Farooqi; J. Zimmermann; R. Bader; U. van Rienen Computer Methods and Programs in Biomedicine, 2020, 197, 105739.
[4] A. Logg; K.A. Mardal; G. Wells Automated solution of differential equations by the finite element method: The FEniCS book, 2012.