Mechanical Interactions of Cells with Soft Synthetic Substrates: A Computational Analysis

Soft biological tissues are typically characterized by a combination of mechanical components leading to particular properties: They undergo large deformations and exhibit non-linear, anisotropic and time dependent responses. These properties mainly originate in the structural organization of soft tissues in the extracellular matrix (ECM), a bioactive scaffold composed of a protein fibre network embedded in a soft gel-like matrix. The exact composition and architecture of the ECM depends on the specific tissue function and defines the environment of the cells living within. Besides chemical signals, structural and mechanical characteristics of the ECM environment play an important role in the behaviour and fate of cells, due to their notable sensitivity to mechanical and topographical cues, originating in their mechanotransductive apparatus. While in native soft tissues the architecture of the ECM has been optimized by nature over the course of the evolutionary process, the design of equivalent synthetic materials represents nowadays a critical challenge in the development of tissue engineered implants. These implants aim to substitute damaged tissues so to restore the original functionality, and typically consist of a cell-populated ECM-mimicking synthetic scaffold, which defines the relevant mechanical characteristics of the implant at different lengthscales, such as the cellular micro-environment and the macroscopic response. Its design represents therefore a challenging interdisciplinary and multiscale engineering problem. Towards solving this problem, the present work focuses on the development of computational methods based on continuum and structural mechanics for the analysis of mechanical interaction of cells with synthetic substrates, both homogeneous and heterogeneous. Highly deformable homogeneous materials are widely used as cell culturing substrates in mechanobiological studies, and deformations induced in such substrates by contracting cells can be used to reconstruct the associated cellular forces by means of traction force microscopy (TFM). After considering the limitations of available methods, an improved TFM platform was developed in a collaborative work. This new approach accounts properly for geometric and material non-linearities inherent to large cell-induced substrate deformations and allows for a traction force acquisition in a single experimental step without the need to determine the reference configuration in a separate step. This feature is especially relevant for practical applications, since it reduces the experimental effort and allows the correlation of traction force fields with the spatial localization of proteins in cells for which no live-cell fluorescent reporter is available. This capability is unprecedented for TFM methods based on homogeneous flat substrates and enables the investigations of previously inaccessible mechanobiological problems. As a next step an extensive numerical study was performed to analyse different factors of experimental and computational origin that potentially affect TFM methods, allowing the quantification of related reconstruction errors and highlighting two critical issues associated with TFM on homogeneous flat substrates: First, a marked underestimation of integral focal adhesion forces occurs for insufficient displacement field measurement resolutions and leads to a general overestimation of traction stress peaks; Second, an excessive substrate compliance is associated with high cell-induced substrate deformations, leading to surface instabilities which cannot be properly accounted for during TFM, thus indicating the necessity for an adjustment of substrate stiffness to the expected cellular force magnitudes. While TFM methods based on flat substrates are suitable for the investigation of cellular interactions with topography-free substrates, corresponding studies on biomimetic scaffolds are significantly more complicated due to additional degrees of freedom introduced by the topology and heterogeneity. Out of the many microstructured materials considered for tissue engineering applications, this thesis focuses particularly on electrospun networks (ESNs), which are planar network-like scaffolds made out of thin (200nm-5um) and slender polymeric fibres. Accounting for the specific topology of these networks, an efficient computational model based on a discrete network approach and parametrized by physically meaningful and experimentally accessible parameters was developed. Compared to experimental data, the model demonstrated excellent predictive capabilities and matched both the macroscopic kinematics and elasto-plastic mechanical response to uniaxial cyclic loading. Furthermore, the analysis of loading induced fibre reorientation highlighted the models ability to capture relevant micromechanical phenomena in ESNs. Also, selected modelling assumptions inherent to the model were validated against a more complex and computationally intensive modelling approach. By comparing the generated network topography and predicted mechanical responses on different lengthscales, the validity of the used modelling assumptions for ESNs with porosities above 90% could be shown. The reasonable computational efficiency of the model, combined with its largely automated implementation, enables extensive parametric studies that relate topological and fibre material parameters to the multiscale mechanics of ESNs. Similarly, the model was used to assess the micro-mechanical environment provided by typical poly(epsilon-caprolactone)-based electrospun networks (with different fibre diameters) by analysing both the network kinematics at cellular lengthscale and the stiffness felt by the cells upon contraction, finally comparing the computational results to corresponding literature data for native and synthetic collagenous networks. While highlighting the potential of electrospun networks in mimicking micro-kinematics of native tissues, such as the long-range transmission of cell induced network deformations, the study indicates difficulties in matching tissue stiffnesses on both macroscopic and cellular lengthscales, especially for networks with thicker fibre diameters. The results also show that the peculiar micro-mechanical environment of these networks, characterized by a high spatial heterogeneity and marked sensitivity to the macroscopic loading state, is not predictable from their macroscopic mechanical behaviour. Thus the macroscopic characterization gives only very limited insight into the mechanical environment provided by such materials to cells, highlighting the importance of specific analyses at cellular lengthscale