The mechanical environment plays an important role in cell signaling and tissue homeostasis. Unraveling connections between externally applied loads and the cellular response is often confounded by extracellular matrix (ECM) heterogeneity. Image-based multiscale models provide a foundation for examining the fine details of tissue behavior, but they require validation at multiple scales. In this study, we developed a multiscale model that captured the anisotropy and heterogeneity of a cell-compacted collagen gel subjected to an offaxis hold mechanical test and subsequently to biaxial extension. In both the model and experiments, the ECM reorganized in a nonaffine and heterogeneous manner that depended on multiscale interactions between the fiber networks. Simulations predicted that tensile and compressive fiber forces were produced to accommodate macroscopic displacements. Fiber forces in the simulation ranged from ؊11.3 to 437.7 nN, with a significant fraction of fibers under compression (12.1% during off-axis stretch). The heterogeneous network restructuring predicted by the model serves as an example of how multiscale modeling techniques provide a theoretical framework for understanding relationships between ECM structure and tissue-level mechanical properties and how microscopic fiber rearrangements could lead to mechanotransductive cell signaling.mechanobiology ͉ tissue mechanics ͉ biomechanics ͉ cruciforms M any activities of anchorage-dependent cells, including proliferation (1, 2), migration (3-5), gene expression/protein synthesis (6, 7), chemical responsiveness (8, 9), and differentiation (10, 11), are mediated by mechanical interactions between the cells and their environment. Although it is often convenient for us to treat the cell's environment and interactions therewith as isotropic and homogeneous, the vast body of biology argues against that simplification. Tissues may appear homogeneous at the macroscopic scale, but they are, in fact, highly hierarchical, appearing as discrete structural entities (e.g., fibers) when viewed at the scale of a cell. Likewise, the cell does not interact smoothly with its surroundings, but rather forms cell-matrix adhesions, which are also distributed heterogeneously at discrete locations over the cell surface (12).It is thus imperative that we explore mechanobiology not just in terms of gross tissue mechanics, but also in terms of the constituents of the tissue, taking as detailed a view as possible. One must recognize that a nominally homogeneous loading environment on the tissue scale, such as uniaxial extension, in fact is highly heterogeneous at the fiber scale, with some fibers possibly even being in compression (i.e., buckled) because of the complex interactions of the network. Because the cell interrogates only a fraction of the total fiber population, a more detailed view of the extracellular matrix (ECM) is needed. Our group is developing multiscale modeling techniques to understand how the complex mechanical interactions that arise within the ECM microstruc...

Recent observations suggest that cells on fibrous extracellular matrix materials sense mechanical signals over much larger distances than they do on linearly elastic synthetic materials. In this work, we systematically investigate the distance fibroblasts can sense a rigid boundary through fibrous gels by quantifying the spread areas of human lung fibroblasts and 3T3 fibroblasts cultured on sloped collagen and fibrin gels. The cell areas gradually decrease as gel thickness increases from 0 to 150 μm, with characteristic sensing distances of >65 μm below fibrin and collagen gels, and spreading affected on gels as thick as 150 μm. These results demonstrate that fibroblasts sense deeper into collagen and fibrin gels than they do into polyacrylamide gels, with the latter exhibiting characteristic sensing distances of <5 μm. We apply finite-element analysis to explore the role of strain stiffening, a characteristic mechanical property of collagen and fibrin that is not observed in polyacrylamide, in facilitating mechanosensing over long distances. Our analysis shows that the effective stiffness of both linear and nonlinear materials sharply increases once the thickness is reduced below 5 μm, with only a slight enhancement in sensitivity to depth for the nonlinear material at very low thickness and high applied traction. Multiscale simulations with a simplified geometry predict changes in fiber alignment deep into the gel and a large increase in effective stiffness with a decrease in substrate thickness that is not predicted by nonlinear elasticity. These results suggest that the observed cell-spreading response to gel thickness is not explained by the nonlinear strain-stiffening behavior of the material alone and is likely due to the fibrous nature of the proteins.

The mechanical properties of tissues, tissue analogs, and biomaterials are dependent on their underlying microstructure. As such, many mechanical models incorporate some aspect of microstructure, but a robust protocol for characterizing fiber architecture remains a challenge. A number of image-based methods, including mean intercept length (MIL), line fraction deviation (LFD), and Fourier transform methods (FTM), have been applied to microstructural images to describe material heterogeneity and orientation, but a performance comparison, particularly for fiber networks, has not been conducted. In this study, we constructed 40 two-dimensional test images composed of simulated fiber networks varying in fiber number, orientation, and anisotropy index. We assessed the accuracy of each method in measuring principal direction (theta) and anisotropy index (alpha). FTM proved to be the superior method because it was more reliable in measurement accuracy (Deltatheta = 2.95 degrees +/- 6.72 degrees , Deltaalpha = 0.03 +/- 0.02), faster in execution time, and flexible in its application. MIL (Deltatheta = 6.23 degrees +/- 10.68 degrees , Deltaalpha = 0.08 +/- 0.06) was not significantly less accurate than FTM but was much slower. LFD (Deltatheta = 9.97 degrees +/- 11.82 degrees , Deltaalpha = 0.24 +/- 0.13) consistently underperformed. FTM results agreed qualitatively with fibrin gel SEM micrographs, suggesting that FTM can be used to obtain image-based statistical measurements of microstructure.

In many cases of traumatic bone injury, bone grafting is required. The primary source of graft material is either autograft or allograft. The use of both material sources are well established, however, both suffer limitations. In response, many grafting alternatives are being explored. This article specifically focuses on a porous tantalum metal grafting material (Trabecular Metaltrade mark) marketed by Zimmer. Twenty-one cylindrical scaffolds were manufactured (66% to 88% porous) and tested for porosity, intrinsic permeability, tangent elastic modulus, and for yield stress and strain behavior. Scaffold microstructural geometries were also measured. Tantalum scaffold intrinsic permeability ranged from 2.1 x 10(-10) to 4.8 x 10(-10) m(2) and tangent elastic modulus ranged from 373 MPa to 2.2 GPa. Both intrinsic permeability and tangent elastic modulus closely matched porosity-matched cancellous bone specimens from a variety of species and anatomic locations. Scaffold yield stress ranged from 4 to 12.7 MPa and was comparable to bovine and human cancellous bone. Yield strain was unaffected by scaffold porosity (average = 0.010 mm/mm). Understanding these structure-function relationships will help complete the basic physical characterization of this new material and will aid in the development of realistic mathematical models, ultimately enhancing future implant designs utilizing this material.