A New Approach to Mechanical Testing and Modeling of Biological Tissues, With Application to Blood Vessels

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Abstract
The collection and processing of data from mechanical tests of biological tissues usually follow classical principles appropriate for studying engineering materials. However, difficulties specific to biological tissues have generally kept such methods from producing quantitative results for statistically-oriented studies. This paper demonstrates a different approach linking testing and data reduction with modern statistical tools. Experimental design theory is used to minimize the detrimental effects of collinearity on the stability of the parameters in constitutive equations. The numerical effects of time-dependent biasing factors such as viscoelasticity are reduced by randomizing the order of collection of data points. Some of the parameters of the model are allowed to vary from specimen to specimen while the others are computed once from a database of designed experiments on several specimens. Finally, a new self-modeling algorithm based on principal component analysis is used to generate uncorrelated parameters for a model that is linear in its specimen-dependent parameters. The method, associated with a recently published complementary energy formulation for vascular mechanics, is illustrated with biaxial canine saphenous vein data. Results show that three specimen-dependent linear parameters are enough to characterize the experimental data and that they can be repeatedly estimated from different data sets. Independently collected biaxial inflation data can also be predicted reasonably well with this model.