A continuum mechanics based quantification of microscale kinematics of nanofibrous membranes

Introduction: There is an urgent need for new implant materials for soft tissue and, in particular, pelvic organ prolapse repair [1]. Recent trends are moving toward nanostructured materials, e.g. derived by electrospinning [2]. While there has been research on the clinical, biological and chemical biocompatibility of these new materials, a detailed evaluation of their mechanical biocompatibility is still missing [2]. This study proposes a novel continuum mechanics-based procedure to quantify the inherently inhomogeneous microscale kinematics at the surface of electrospun networks (ESNs). Developed from a numerical model, this method can be directly transferred to experimental observations using SEMDIC (scanning electron microscopy with digital image correlation). By addressing the cellular length scale, this study shall serve future quantitative mechanobiology investigations. Material and Methods: A numerical discrete fiber model inspired by the work of Zündel et al. [3] was used to simulate the inhomogeneous deformation patterns of ESNs (Figure 1). The FEM model was used to determine the actual representative volume element (RVE) and representative area element (RAE) sizes. The size of the RAE allows for the definition of a minimum image section that guarantees a representative image of the surface deformations. To this end, a kinematic fingerprint was introduced, which is constituted by the distributions of the relative frequencies of the local Green-Lagrange strains, local deformation types (uniaxial, shear and equibiaxial) and local rotations (Figure 1C, 2). These local kinematic quantities are calculated by subdividing the RAE into small (5–10 um) facets and by homogenizing local fiber deformations over the facet areas. Lastly, deformation tensors from classical continuum mechanics are used, assuming local affine deformations. The standard deviation and mean of the distributions of the local kinematic quantities provide a quantitative fingerprint of the ESN. Results: The fingerprint displays a clear characteristic of the ESNs and their non-affine deformations (Figure 2). The results obtained from the FEM model determined a RVE size of 29 ∙ 103 μm3 and a RAE size of 160 × 160 μm2 (depth: 6 μm). The size of the facets turned out to be another crucial parameter. In this study, the minimum facet size was identified to be 5 × 5 μm. It is hypothesized that below this threshold, the assumption of locally affine deformations is no longer valid. This is in accordance with our SEM-DIC investigations. Discussion: This study presents a methodology for quantifying inhomogeneous deformations in ESNs. The numerical model can be directly applied to develop and validate experimental methods using SEM-DIC. It enables a comprehensive understanding of the deformation behavior at the length scales, which are relevant for biological tissue components. Thus, this study provides a tool for future research in mechanobiology.