Numerical Simulations as Means for Tailoring Electrically Conductive Hydrogels towards Cartilage Tissue Engineering by Electrical Stimulation

Abstract

Cartilage regeneration is a clinical challenge. In recent years, hydrogels have emerged as implantable scaffolds in cartilage tissue engineering. Similarly, electrical stimulation has been employed to improve matrix synthesis of cartilage cells, and thus to foster engineering and regeneration of cartilage tissue. The combination of hydrogels and electrical stimulation may pave the way for new clinical treatment of cartilage lesions. To find the optimal electric properties of hydrogels, theoretical considerations and corresponding numerical simulations are needed to identify well-suited initial parameters for experimental studies. We present the theoretical analysis of a hydrogel in a frequently used electrical stimulation device for cartilage regeneration and tissue engineering. By means of equivalent circuits, finite element analysis, and uncertainty quantification, we elucidate the influence of the geometric and dielectric properties of cell-seeded hydrogels on the capacitive-coupling electrical field stimulation. Moreover, we discuss the possibility of cellular organisation inside the hydrogel due to forces generated by the external electric field. The introduced methodology is easily reusable by other researchers and allows to directly develop novel electrical stimulation study designs. Thus, this study paves the way for the design of future experimental studies using electrically conductive hydrogels and electrical stimulation for tissue engineering.

Electrically Conductive Hydrogels for Articular Cartilage Tissue Engineering

“…Additionally, the conductivities of the produced scaffolds should attempt to match the physiological values of the target tissue. Despite the high electrical conductivities described for metallic nanoparticles (e.g., gold—41 × 10 6 S m −1 ; silver—62.9 × 10 6 S m −1 ; platinum—9.1 × 10 6 S m −1 ) [ 79 ], as such nanoparticles will be incorporated in low conductivity or non-conductive hydrogel materials, the overall conductivity of the composite will be much lower and closer to the values reported for articular cartilage (≈1.2 S m −1 ) [ 84 , 85 ]. Accordingly, Baei and co-workers have developed a gold nanoparticle–chitosan hydrogel with an electrical conductivity of approximately 0.13 S m −1 [ 80 ].…”

Bizonal cardiac engineered tissues with differential maturation features in a mid-throughput multimodal bioreactor

“…The values of electrical conductivity (σ) and relative electric permittivity (ε r ) for the components are summarized in Table 1 . Characterization of the electrical module ( Qi et al., 2011 ; Pavesi et al., 2014 ; Tsai et al., 2017 ; Hogenes et al., 2020 ; Zimmermann et al., 2020 , onlinelibrary.wiley.com , www.engineeringtoolbox.com ).…”

Addressing Model Uncertainties in Finite Element Simulation of Electrically Stimulated Implants for Critical-Size Mandibular Defects

“…Research in the field of computational bioelectric engineering has explored the use of UQ in a range of areas, including electrostimulating hip revision systems [61], cartilage tissue engineering [62], [63], deep brain stimulation [64]- [67], and cochlear implants [68]. For the UQ studies in this work, a modified version (https://github.com/jzimmermann/uncertainpy/tree/1.2.0.1) of the open source Python toolbox Uncertainpy (version 1.2.3) [69] was used to compute the statistical measures and perform sensitivity analysis based on Sobol' indices.…”

“…Originally designed for computational neuroscience, Uncertainpy is also broadly applicable to other areas of study. For instance, it has been used to characterize uncertainties in the numerical modeling of electrically stimulated cells [62], [63], [70] or deep brain stimulation in a rodent model [64]. Uncertainpy is based on Chaospy [71], [72], an established open-source Python toolkit with UQ functionalities, in particular PC and advanced MC methods.…”