A Nonparametric Approach for Estimating Three-Dimensional Fiber Orientation Distribution Functions (ODFs) in Fibrous Materials

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.

Dynamic Biophysical Cues Near the Tip Cell Microenvironment Provide Distinct Guidance Signals to Angiogenic Neovessels

The formation of new vascular networks via angiogenesis is a crucial biological mechanism to balance tissue metabolic needs, yet the coordination of factors that influence the guidance of growing neovessels remain unclear. This study investigated the influence of extracellular cues within the immediate environment of sprouting tips over multiple hours and obtained quantitative relationships describing their effects on the growth trajectories of angiogenic neovessels. Three distinct microenvironmental cues-fibril tracks, ECM density, and the presence of nearby cell bodies-were extracted from 3D time series image data. The prominence of each cue was quantified along potential sprout trajectories to predict the response to multiple microenvironmental factors simultaneously. Sprout trajectories significantly correlated with the identified microenvironmental cues. Specifically, ECM density and nearby cellular bodies were the strongest predictors of the trajectories taken by neovessels (p < 0.001 and p = 0.016). Notwithstanding, direction changing trajectories, deviating from the initial neovessel orientation, were significantly correlated with fibril tracks (p = 0.003). Direction changes also occurred more frequently with strong microenvironmental cues. This provides evidence for the first time that local matrix fibril alignment influences changes in sprout trajectories but does not materially contribute to persistent sprouting. Together, our results suggest the microenvironmental cues significantly contribute to guidance of sprouting trajectories. Further, the presented methods quantitatively distinguish the influence of individual microenvironmental stimuli during guidance.

Matrix anisotropy promotes angiogenesis in a density-dependent manner

Angiogenesis is necessary for wound healing, tumorigenesis, implant inosculation, and homeostasis. In each situation, matrix structure and mechanics play a role in determining whether new vasculatures can establish transport to new or hypoxic tissues. Neovessel growth and directional guidance are sensitive to three-dimensional (3-D) matrix anisotropy and density, although the individual and integrated roles of these matrix features have not been fully recapitulated in vitro. We developed a tension-based method to align 3-D collagen constructs seeded with microvessel fragments in matrices of three levels of collagen fibril anisotropy and two levels of collagen density. The extent and direction of neovessel growth from the parent microvessel fragments increased with matrix anisotropy and decreased with density. The proangiogenic effects of anisotropy were attenuated at higher matrix densities. We also examined the impact of matrix anisotropy in an experimental model of neovessel invasion across a tissue interface. Matrix density was found to dictate the success of interface crossing, whereas interface curvature and fibril alignment were found to control directional guidance. Our findings indicate that complex configurations of matrix density and alignment can facilitate or complicate the establishment or maintenance of vascular networks in pathological and homeostatic angiogenesis. Furthermore, we extend preexisting methods for tuning collagen anisotropy in thick constructs. This approach addresses gaps in tissue engineering and cell culture by supporting the inclusion of large multicellular structures in prealigned constructs.NEW & NOTEWORTHY Matrix anisotropy and density have a considerable effect on angiogenic vessel growth and directional guidance. However, the current literature relies on 2-D and simplified models of angiogenesis (e.g., tubulogenesis and vasculogenesis). We present a method to align 3-D collagen scaffolds embedded with microvessel fragments to different levels of anisotropy. Neovessel growth increases with anisotropy and decreases with density, which may guide angiogenic neovessels across tissue interfaces such as during implant inosculation and tumorigenesis.