Elastography, the imaging of soft tissues on the basis of elastic modulus has gained
popularity in the last few decades and holds promise for application in many medical
areas. Most of the attention has focused on heterogeneous materials that are
locally isotropic, the intent being to detect a stiff tumor within a compliant tissue.
Many tissues of mechanical interest, however, are anisotropic, so a method capable
of determining material anisotropy would be attractive. This work presents a
method, named GAIM (Generalized Anisotropic Inverse Mechanics), to determine
the mechanical anisotropy of heterogeneous, anisotropic tissues, by directly solving
the finite-element representation of the stress balance in the tissue. GAIM divides
the sample into subdomains assumed to have uniform properties and determines the
material constants in each subdomain. Use of a linear material model led to rapid
computation with statistical confidence levels as performance metrics. Multiple tests,
asymmetric loading and strain heterogeneity are needed to address the ill-posedness
of the inverse problem, and represent a paradigm shift in the testing of soft tissues.
Simulated experiments of fibrous soft-tissues demonstrated the ability of the method
to capture anisotropy qualitatively even though only a linear model is used. Results
from the tests on soft-tissue analogs demonstrated the success in identifying regional
differences in anisotropy based on full-field displacements and boundary forces obtained
from multiple biaxial extension tests. The method’s success in capturing
regional anisotropic changes associated with growth and remodelling in fibroblastpopulated
cruciforms is a significant achievement, and holds promise for determining
structural information of tissues from the mechanical response, since the structural
and mechanical anisotropy are correlated. The linear GAIM model can be extended
by a second step for nonlinearity with a fiber-based constitutive model. A closedform
solution for the latter was developed and provides rapid results for nonlinear
regression. In summary, this work has built a novel exploratory tool to extract regionspecific
anisotropic properties on intact tissue samples. GAIM can be applied to provide
information on the mechanical function of healthy tissue subjected to complex
physiologic loads, identify regions within a tissue that exhibit irregular mechanical
behavior (possibly due to disease or damage), and provide structural information
from the mechanical function of tissues that are not amenable to structural tests.
University of Minnesota Ph.D. dissertation. August 2011. Major: Mechanical Engineering. Advisor: Victor H Barocas. 1 computer file (PDF); xi, 103 pages, appendix A. + 1 Errata (PDF); 12 pages.
Form from function: generalized anisotropic inverse mechanics for soft tissues..
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