Assessing apparent cell stiffness on fibrous substrates: A comparison of numerical-analytical and in silico models with a novel thermo-contraction approach

Understanding how cells sense mechanical properties of fibrous substrates is crucial for designing biomaterials that regulate cellular behaviour. Understanding how cells sense the mechanical properties of fibrous substrates is crucial for designing biomaterials that regulate cellular behaviour. This study aims to present an accessible initial model for calculating apparent cell stiffness (k_ap) while visualising the cell on a fibrous substrate. By comparing analytical-numerical methods and in silico simulations, we provide a comprehensive approach to exploring how these techniques can be employed to assess cellular mechanics in fibrous environments.

The model was initially validated on idealised fibre networks using three independent methods: full in silico contraction, analytical beam theory, and applied in silico force-displacement analysis. These approaches yielded consistent k_ap values. Subsequently, the methodology was applied to a real 3D scaffold geometry reconstructed from confocal laser scanning microscopy images of electrospun structures.

The evaluation of apparent stiffness shows that the closer the attachment point is to the intersection of the filaments, the higher the apparent stiffness. Additionally, on the same substrate, the greater the number of attachment points, the slight increase in apparent stiffness we observe. The analytical-numerical beam method represents the most cost-effective and efficient method for evaluating apparent stiffness. The equation incorporates a rotational correction factor (α = 0.85) to account for the semi-rigid behaviour of fibre intersections.

This method offers a predictive and scalable tool for evaluating the impact of fibrous architecture and the influence of the geometry of the cell-substrate mechanics. It can support the rational design of fibrous biomaterials for applications in tissue engineering, disease modelling, and regenerative medicine.