Background and Objective

The self-repair capability of articular cartilage is limited because of non-vascularization and low turnover of its extracellular matrix. Regenerating hyaline cartilage remains a significant clinical challenge as most non-surgical and surgical treatments provide only mid-term relief. Eventually, further pain and mobility loss occur for many patients in the long run due to further joint deterioration. Repair of articular cartilage tissue using electroactive scaffolds and biophysical stimuli like electrical and osmotic stimulation may have the potential to heal cartilage defects occurring due to trauma, osteoarthritis, or sport-related injuries. Therefore, the focus of the current study is to present a computational model of electroactive hydrogels for the cartilage-tissue repair as a first step towards an optimized experimental design.

Methods

The multiphysics transport model that mainly includes the Poisson–Nernst–Planck equations and the mechanical equation is used to find the electrical stimulation response of the polyelectrolyte hydrogels. Based upon this, a numerical model on electromechanics of electroactive hydrogels seeded with chondrocytes is presented employing the open-source software FEniCS, which is a Python library for finite-element analysis.

Results

We analyzed the ionic concentrations and electric potential in a hydrogel sample and the cell culture medium, the osmotic pressure created due to ionic concentration variations and the resulting hydrogel displacement. The proposed mathematical model was validated with examples from literature.

Conclusions

The presented model for the electrical and osmotic stimulation of a hydrogel sample can serve as a useful tool for the development and analysis of a cartilaginous scaffold employing electrical stimulation. By analyzing various parameters, we pave the way for future research on a finer scale using open-source software.

中文翻译：

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用于软骨组织修复的电活性水凝胶的机电计算研究。

背景与目的

关节软骨的自我修复能力受到限制，原因是非血管形成及其细胞外基质的周转率低。透明软骨的再生仍然是一项重大的临床挑战，因为大多数非手术和手术疗法只能提供中期缓解。最终，由于关节的进一步恶化，从长远来看，许多患者还会出现进一步的疼痛和活动能力丧失。使用电活性支架和生物物理刺激（如电刺激和渗透刺激）修复关节软骨组织可能具有治愈因外伤，骨关节炎或运动相关损伤而发生的软骨缺损的潜力。因此，当前研究的重点是提出用于软骨组织修复的电活性水凝胶的计算模型，作为朝着优化实验设计的第一步。

方法

多物理场输运模型主要包括泊松－能斯特－普朗克方程和力学方程，用于寻找聚电解质水凝胶的电刺激响应。在此基础上，利用开源软件FEniCS（一种用于有限元分析的Python库），提出了用软骨细胞接种的电活性水凝胶的机电模型。

结果

我们分析了水凝胶样品和细胞培养基中的离子浓度和电势，由于离子浓度变化而产生的渗透压以及所产生的水凝胶位移。所提出的数学模型已通过文献验证。

结论

所提出的用于水凝胶样品的电和渗透刺激的模型可以用作开发和分析采用电刺激的软骨支架的有用工具。通过分析各种参数，我们为使用开放源代码软件的更大规模研究铺平了道路。