Image-based multiscale modeling predicts tissue-level and network-level fiber reorganization in stretched cell-compacted collagen gels

Abstract

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 off-axis 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.

Fig. 1.

Cruciform mechanical response to off-axis hold and equibiaxial stretch. (A) Inset shows a representative cruciform in mold with horizontal and vertical arm widths of 8 and 4 mm, respectively. Parameters A and B, which define the mechanical response of a network fiber, were selected so that the model predictions (red lines) matched the off-axis hold experiment (circular markers) and were used to predict the model response to equibiaxial stretch. In the off-axis hold test (A), the vertical arms of the cruciform were each displaced 2 mm (λ_y = 1.29) in 15 sec while the horizontal arms remained stationary. The average loading response of both axes is plotted as a function of vertical axis extension. (B) For equibiaxial stretch, both arms were extended 1.5 mm (λ_y = 1.21) in 15 sec. The model reasonably predicted the cruciform response but underpredicted nonlinearity in the vertical arm.

Fig. 2.

Cruciform domain changes and microstructural reorganization for off-axis and equibiaxial stretch. The bottom left quadrant of the cruciform is shown with the model domain and network alignment properties (red) overlaid on PFAI measurements of fiber orientation and strength of alignment (white). The areas of black on the horizontal and vertical are the compression grips, which are spanned by the free surface of the cruciform. The difference in principal direction between the model and experiment is depicted in the Inset. Also shown is the network angle distribution in the model (red) and the experiment (blue). (A) For the off-axis hold test, the model predicts the measured rotation and alignment of the fiber networks with extension of the vertical axis. (B) The same model subjected to equibiaxial stretch predicts that local network direction rotates some toward the horizontal and reasonably matches the experiment.

Fig. 3.

Network reorganization in response to off-axis and equibiaxial stretch. Depicted are networks from three different regions in the cruciform before stretch (Center) and their response to increasing stretch via off-axis stretch (Center to Left) and equibiaxial stretch (Center to Right). Network reorganization occurs in a location-dependent manner and a range of intranetwork forces develops. A histogram of the fiber stretch ratios in the deformed networks reveals that some fibers are in compression, even though a macroscopic tensile load is applied to the sample. Solid red lines show the macroscopic, tissue-level stretch ratio (λ_y) in the y-direction (vertical axis). λ_y = 1.15 at d = 1.00 mm, λ_y = 1.21 at d = 1.50 mm, and λ_y = 1.29 at d = 2.0 mm.