Constitutive modeling of mouse carotid arteries using experimentally measured microstructural parameters

Changes in the local mechanical environment and tissue mechanical properties affect the biological activity of cells and play a key role in a variety of diseases, such as cancer, arthritis, nephropathy, and cardiovascular disease. Constitutive relations have long been used to predict the local mechanical environment within biological tissues and to investigate the relationship between biological responses and mechanical stimuli. Recent constitutive relations for soft tissues consider both material and structural properties by incorporating parameters that describe microstructural organization, such as fiber distributions, fiber angles, fiber crimping, and constituent volume fractions. The recently developed technique of imaging the microstructure of a single artery as it undergoes multiple deformations provides quantitative structural data that can reduce the number of estimated parameters by using parameters that are truly experimentally intractable. Here, we employed nonlinear multiphoton microscopy to quantify collagen fiber organization in mouse carotid arteries and incorporated measured fiber distribution data into structurally motivated constitutive relations. Microscopy results demonstrate that collagen fibers deform in an affine manner over physiologically relevant deformations. The incorporation of measured fiber angle distributions into constitutive relations improves the model's predictive accuracy and does not significantly reduce the goodness of fit. The use of measured structural parameters rather than estimated structural parameters promises to improve the predictive capabilities of the local mechanical environment, and to extend the utility of intravital imaging methods for estimating the mechanical behavior of tissues using in situ structural information.