Continuum Growth Mechanics: Reconciling Two Common Frameworks.

The objective of this study was to investigate whether the two most common growth mechanics modeling frameworks, the constrained-mixture growth model and the kinematic growth model, could be reconciled mathematically. The purpose of this effort was to provide practical guidelines for potential users of these modeling frameworks. Results showed that the kinematic growth model is mathematically consistent with a special form of the constrained-mixture growth model, where only one generation of a growing solid exists at any given time, overturning its entire solid mass at each instant of growth in order to adopt the reference configuration dictated by the growth deformation. The thermodynamics of the kinematic growth model, along with the specialized constrained-mixture growth model, requires a cellular supply of chemical energy to allow deposition of solid mass under a stressed state. A back-of-the-envelope calculation shows that the amount of chemical energy required to sustain biological growth under these models is negligibly small, when compared to the amount of energy normally consumed daily by the human body. In conclusion, this study successfully reconciled the two most popular growth theories for biological growth and explained the special circumstances under which the constrained-mixture growth model reduces to the kinematic growth model.

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis.

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

Early Resistance Rehabilitation Improves Functional Regeneration Following Segmental Bone Defect Injury.

Mechanical loading is integral to bone development and repair. The application of mechanical loads through rehabilitation are regularly prescribed as a clinical aide following severe bone injuries. However, current rehabilitation regimens typically involve long periods of non-loading and rely on subjective patient feedback, leading to muscle atrophy and soft tissue fibrosis. While many pre-clinical studies have focused on unloading, ambulatory loading, or direct mechanical compression, rehabilitation intensity and its impact on the local strain environment and subsequent bone healing have largely not been investigated. This study combines implantable strain sensors and subject-specific finite element models in a pre-clinical rodent model with a defect size on the cusp of critically-sized. Animals were enrolled in either high or low intensity rehabilitation one week post injury to investigate how rehabilitation intensity affects the local mechanical environment and subsequent functional bone regeneration. The high intensity rehabilitation animals were given free access to running wheels with resistance, which increased local strains within the regenerative niche by an average of 44% compared to the low intensity (no-resistance) group. Finite element modeling demonstrated that resistance rehabilitation significantly increased compressive strain by a factor of 2.0 at week 1 and 4.45 after 4 weeks of rehabilitation. The resistance rehabilitation group had significantly increased regenerated bone volume and higher bone bridging rates than its sedentary counterpart (bone volume: 22.00 mm3 ± 4.26 resistance rehabilitation vs 8.00 mm3 ± 2.27 sedentary; bridging rates: 90% resistance rehabilitation vs 50% sedentary). In addition, animals that underwent resistance running had femurs with improved mechanical properties compared to those left in sedentary conditions, with failure torque and torsional stiffness values matching their contralateral, intact femurs (stiffness: 0.036 Nm/deg ± 0.006 resistance rehabilitation vs 0.008 Nm/deg ± 0.006 sedentary). Running on a wheel with no resistance rehabilitation also increased bridging rates (100% no resistance rehabilitation vs 50% sedentary). Analysis of bone volume and von Frey suggest no-resistance rehabilitation may improve bone regeneration and hindlimb functionality. These results demonstrate the potential for early resistance rehabilitation as a rehabilitation regimen to improve bone regeneration and functional recovery.

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.

Stromal Cells Promote Neovascular Invasion Across Tissue Interfaces.

Vascular connectivity between adjacent vessel beds within and between tissue compartments is essential to any successful neovascularization process. To establish new connections, growing neovessels must locate other vascular elements during angiogenesis, often crossing matrix and other tissue-associated boundaries and interfaces. How growing neovessels traverse any tissue interface, whether part of the native tissue structure or secondary to a regenerative procedure (e.g., an implant), is not known. In this study, we developed an experimental model of angiogenesis wherein growing neovessels must interact with a 3D interstitial collagen matrix interface that separates two distinct tissue compartments. Using this model, we determined that matrix interfaces act as a barrier to neovessel growth, deflecting growing neovessels parallel to the interface. Computational modeling of the neovessel/matrix biomechanical interactions at the interface demonstrated that differences in collagen fibril density near and at the interface are the likely mechanism of deflection, while fibril alignment guides deflected neovessels along the interface. Interestingly, stromal cells facilitated neovessel interface crossing during angiogenesis via a vascular endothelial growth factor (VEGF)-A dependent process. However, ubiquitous addition of VEGF-A in the absence of stromal cells did not promote interface invasion. Therefore, our findings demonstrate that vascularization of a tissue via angiogenesis involves stromal cells providing positional cues to the growing neovasculature and provides insight into how a microvasculature is organized within a tissue.

Imaging the Dynamic Interaction Between Sprouting Microvessels and the Extracellular Matrix.

Thorough understanding of growth and evolution of tissue vasculature is fundamental to many fields of medicine including cancer therapy, wound healing, and tissue engineering. Angiogenesis, the growth of new vessels from existing ones, is dynamically influenced by a variety of environmental factors, including mechanical and biophysical factors, chemotactic factors, proteolysis, and interaction with stromal cells. Yet, dynamic interactions between neovessels and their environment are difficult to study with traditional fixed time imaging techniques. Advancements in imaging technologies permit time-series and volumetric imaging, affording the ability to visualize microvessel growth over 3D space and time. Time-lapse imaging has led to more informative investigations of angiogenesis. The environmental factors implicated in angiogenesis span a wide range of signals. Neovessels advance through stromal matrices by forming attachments and pulling and pushing on their microenvironment, reorganizing matrix fibers, and inducing large deformations of the surrounding stroma. Concurrently, neovessels secrete proteolytic enzymes to degrade their basement membrane, create space for new vessels to grow, and release matrix-bound cytokines. Growing neovessels also respond to a host of soluble and matrix-bound growth factors, and display preferential growth along a cytokine gradient. Lastly, stromal cells such as macrophages and mesenchymal stem cells (MSCs) interact directly with neovessels and their surrounding matrix to facilitate sprouting, vessel fusion, and tissue remodeling. This review highlights how time-lapse imaging techniques advanced our understanding of the interaction of blood vessels with their environment during sprouting angiogenesis. The technology provides means to characterize the evolution of microvessel behavior, providing new insights and holding great promise for further research on the process of angiogenesis.

A Plugin Framework for Extending the Simulation Capabilities of FEBio.

The FEBio software suite is a set of software tools for nonlinear finite element analysis in biomechanics and biophysics. FEBio employs mixture theory to account for the multiconstituent nature of biological materials, integrating the field equations for irreversible thermodynamics, solid mechanics, fluid mechanics, mass transport with reactive species, and electrokinetics. This communication describes the development and application of a new "plugin" framework for FEBio. Plugins are dynamically linked libraries that allow users to add new features and to couple FEBio with other domain-specific software applications without modifying the source code directly. The governing equations and simulation capabilities of FEBio are reviewed. The implementation, structure, use, and application of the plugin framework are detailed. Several example plugins are described in detail to illustrate how plugins enrich, extend, and leverage existing capabilities in FEBio, including applications to deformable image registration, constitutive modeling of biological tissues, coupling to an external software package that simulates angiogenesis using a discrete computational model, and a nonlinear reaction-diffusion solver. The plugin feature facilitates dissemination of new simulation methods, reproduction of published results, and coupling of FEBio with other domain-specific simulation approaches such as compartmental modeling, agent-based modeling, and rigid-body dynamics. We anticipate that the new plugin framework will greatly expand the range of applications for the FEBio software suite and thus its impact.

Decorin-containing collagen hydrogels as dimensionally stable scaffolds to study the effects of compressive mechanical loading on angiogenesis.

Angiogenesis is a critical component during wound healing, and the process is sensitive to mechanical stimuli. Current in vitro culture environments used to investigate three-dimensional microvascular growth often lack dimensional stability and the ability to withstand compression. We investigated the ability of decorin, a proteoglycan known to modulate collagen fibrillogenesis, incorporated into a collagen hydrogel to increase construct dimensional stability while maintaining vascular growth. Decorin did not affect microvascular growth parameters, while increasing the compressive modulus of collagen gels and significantly reducing the contraction of 3% collagen gels after 16 days in culture.