This article presents a novel computational model to study the selective filtering of biological hydrogels due to the surface charge and size of diffusing particles. It is the first model that includes the random three-dimensional fibre orientation and connectivity of the biopolymer network and that accounts for elastic deformations of the fibres by means of beam theory. As a key component of the model, novel formulations are proposed both for the electrostatic and repulsive steric interactions between a spherical particle and a beam. In addition to providing a thorough validation of the model, the presented computational studies yield new insights into the underlying mechanisms of hindered particle mobility, especially regarding the influence of the aforementioned aspects that are unique to this model. It is found that the precise distribution of fibre and thus charge agglomerations in the network have a crucial influence on the mobility of oppositely charged particles and gives rise to distinct motion patterns. Considering the high practical significance for instance with respect to targeted drug release or infection defence, the provided proof of concept motivates further advances of the model towards a truly predictive computational tool that allows a case- and patient-specific assessment for real (biological) systems.

本文提出了一种新型的计算模型，以研究由于表面电荷和扩散颗粒的大小而对生物水凝胶的选择性过滤。这是第一个模型，该模型包括随机的三维纤维取向和生物聚合物网络的连通性，并通过射束理论解释了纤维的弹性变形。作为模型的关键组成部分，提出了新颖的公式，用于球形粒子和射束之间的静电和排斥空间相互作用。除了提供对模型的全面验证之外，提出的计算研究还对受阻碍的颗粒迁移性的潜在机制产生了新的见解，尤其是关于该模型独有的上述方面的影响。已经发现，纤维的精确分布以及由此在网络中的电荷团聚对带相反电荷的粒子的迁移率具有至关重要的影响，并产生了不同的运动模式。考虑到例如在靶向药物释放或感染防御方面的高度实际意义，所提供的概念证明促使该模型进一步朝着真正的预测性计算工具发展，该工具可以针对实际（生物）系统进行针对病例和患者的评估。