An algorithmic and software framework to incorporate orientation distribution functions in finite element simulations for biomechanics and biophysics

Biological tissues and biomaterials routinely feature a fibrous microstructure that contributes to physical and mechanical properties while influencing cellular guidance, organization and extracellular matrix (ECM) production. Specialized three-dimensional (3D) imaging techniques can visualize fibrillar structure and orientation, and previously we developed a nonparametric approach to extract orientation distribution functions (ODFs) directly from 3D image data [1]. In this work, we expanded our previous approach to provide a complete algorithmic and software framework to characterize inhomogeneous ODFs in image data and use ODFs to model the physics of materials with the finite element method. We characterized inhomogeneity using image subdomains and specialized interpolation methods, and we developed methods to incorporate ODFs directly into constitutive models. To facilitate its adoption by the biomechanics and biophysics communities, we developed a unified software framework in FEBio Studio (www.febio.org). This included new interpolation methods to spatially map the ODFs onto finite element meshes and an approach to downsample ODFs for efficient numerical calculations. The software provides the option to fit ODFs to parametric distributions, and scalar metrics provide means to assess goodness of fit. We evaluated the utility and accuracy of the algorithms and implementation using representative 3D image datasets. Our results demonstrated that utilizing the true measured ODFs provide a more accurate and spatially resolved representation of fiber ODFs and the resulting predicted mechanical response when compared with parametric approaches to approximating the true ODFs. This research provides a powerful, interactive software framework to extract and represent the inhomogeneous anisotropic characteristics of fibrous tissues directly from image data, and to incorporate them into biomechanics and biophysics simulations using the finite element method. STATEMENT OF SIGNIFICANCE: Biological tissues and biomaterials routinely feature a fibrous microstructure that contributes to physical and mechanical properties while influencing cellular guidance, organization and extracellular matrix (ECM) production. In this study, we developed a complete algorithmic and software framework to characterize inhomogeneous orientation distribution functions (ODFs) directly from biomedical image data and apply the ODFs to model the physics of biological materials. We characterized inhomogeneity using image subdomains and specialized interpolation methods, and we developed methods to incorporate ODFs directly into constitutive models. We developed a unified software framework in FEBio Studio (www.febio.org) to accommodate its adoption by the biomechanics and biophysics communities. The result is a powerful, interactive software framework to extract and represent inhomogeneous, anisotropic characteristics directly from image data, and incorporate them into biomechanics and biophysics simulations.