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Planar biaxial testing offers a physiologically relevant approach for mechanically characterizing thin deformable soft tissues, but often relies on erroneous assumptions of uniform strain fields and negligible shear strains and forces. In addition to the complex mechanical behavior exhibited by soft tissues, constraints on sample size, geometry, and aspect ratio often restrict sample shape and symmetry. Using simple PDMS gels, we explored the unknown and unquantified effects of sample shape asymmetry on planar biaxial testing results, including shear strain magnitudes, shear forces measured at the sample’s boundary, and the homogeneity of strains experienced at the center of each sample. We used a combination of finite element modeling and experimental validation to examine PDMS gels of varying levels of asymmetry, allowing us to identify effects of sample shape without confounding factors introduced by the nonlinear, spatially variable, and anisotropic properties of soft tissues. Both biaxial simulations and experiments, which showed strong agreement, revealed that sample shape asymmetry led to significantly larger shear strains, shear forces, and overestimation of principal stresses. Excluding these shear forces resulted in an underestimation of shear moduli during inverse mechanical characterizations. Even in the simplest of deformable biomaterials, sample shape asymmetry should be avoided as it can induce drastic increases in shear strains and shear forces, invalidating traditional planar biaxial testing analyses. Alternatively, sample shape asymmetry may be exploited to generate more robust estimates of constitutive parameters in more complex materials, which could lead to a refined understanding and inference of mechanical behavior. 

Abstract Soft biological tissues often function as highly deformable membranes in vivo and exhibit impressive mechanical behavior effectively characterized by planar biaxial testing. The Generalized Anisotropic Inverse Mechanics (GAIM) method links full-field deformations and boundary forces from mechanical testing to quantify material properties of soft, anisotropic, heterogeneous tissues. In this study, we introduced an orthotropic constraint to GAIM to improve the quality and physical significance of its mechanical characterizations. We evaluated the updated GAIM method using simulated and experimental biaxial testing datasets obtained from soft tissue analogs (PDMS and TissueMend) with well-defined mechanical properties. GAIM produced stiffnesses (first Kelvin moduli, K1) that agreed well with previously published Young's moduli of PDMS samples. It also matched the stiffness moduli determined via uniaxial testing for TissueMend, a collagen-rich patch intended for tendon repair. We then conducted the first biaxial testing of TissueMend and confirmed that the sample was mechanically anisotropic via a relative anisotropy metric produced by GAIM. Next, we demonstrated the benefits of full-field laser micrometry in distinguishing between spatial variations in thickness and stiffness. Finally, we conducted an analysis to verify that results were independent of partitioning scheme. The success of the newly implemented constraints on GAIM suggests notable potential for applying this tool to soft tissues, particularly following the onset of pathologies that induce mechanical and structural heterogeneities. 

Myocardial infarctions (MIs) kickstart an intense inflammatory response resulting in extracellular matrix (ECM) degradation, wall thinning, and chamber dilation that leaves the heart susceptible to rupture. Reperfusion therapy is one of the most effective strategies for limiting adverse effects of MIs, but is a challenge to administer in a timely manner. Late reperfusion therapy (LRT; 3 + hours post-MI) does not limit infarct size, but does reduce incidences of post-MI rupture and improves long-term patient outcomes. Foundational studies employing LRT in the mid-twentieth century revealed beneficial reductions in infarct expansion, aneurysm formation, and left ventricle dysfunction. The mechanism by which LRT acts, however, is undefined. Structural analyses, relying largely on one-dimensional estimates of ECM composition, have found few differences in collagen content between LRT and permanently occluded animal models when using homogeneous samples from infarct cores. Uniaxial testing, on the other hand, revealed slight reductions in stiffness early in inflammation, followed soon after by an enhanced resistance to failure for cases of LRT. The use of one-dimensional estimates of ECM organization and gross mechanical function have resulted in a poor understanding of the infarct’s spatially variable mechanical and structural anisotropy. To resolve these gaps in literature, future work employing full-field mechanical, structural, and cellular analyses is needed to better define the spatiotemporal post-MI alterations occurring during the inflammatory phase of healing and how they are impacted following reperfusion therapy. In turn, these studies may reveal how LRT affects the likelihood of rupture and inspire novel approaches to guide scar formation.