Discussion: “Comparison of Statistical Methods for Assessing Spatial Correlations Between Maps of Different Arterial Properties” (Rowland, E. M., Mohamied, Y., Chooi, K. Y., Bailey, E. L., and Weinberg, P. D., 2015, ASME J. Biomech. Eng., 137(10), p. 101003): An Alternative Approach Using Segmentation Based on Local Hemodynamics

The biological response of living arteries to mechanical forces is an important component of the atherosclerotic process and is responsible, at least in part, for the well-recognized spatial variation in atherosusceptibility in man. Experiments to elucidate this response often generate maps of force and response variables over the arterial surface, from which the force–response relationship is sought. Rowland et al. discussed several statistical approaches to the spatial autocorrelation that confounds the analysis of such maps and applied them to maps of hemodynamic stress and vascular response obtained by averaging these variables in multiple animals. Here, we point out an alternative approach, in which discrete surface regions are defined by the hemodynamic stress levels they experience, and the stress and response in each animal are treated separately. This approach, applied properly, is insensitive to autocorrelation and less sensitive to the effect of confounding hemodynamic variables. The analysis suggests an inverse relation between permeability and shear that differs from that in Rowland et al. Possible sources of this difference are suggested

MODEL-BASED SHEAR STRESS GRADIENT IN REALISTIC VASCULAR FLOWS AND ITS RELATION TO ARTERIAL MACROMOLECULAR PERMEABILITY

ABSTRACT Evans blue dye (EBD) was injected into the carotid arteries of three anesthetized pigs and allowed to circulate for 90 minutes. At the conclusion of the 90-minute period, the animals were sacrificed and injection casts of the infrarenal aorta and iliac-femoral arteries were prepared. The casts with their surrounding arteries were removed and immersed in fixative. After fixation, the EBD-stained vessels were separated from the casts, which were used to construct computational meshes for simulation of the flow fields and wall shear stress distributions that had existed in the casted regions during the experiments. The inlet flow waves and flow partitions were based on flow measurements performed during each experiment. Based on a conceptual model of the relation between shear stress nonuniformity and permeability increase, the spatial and angular variation of the gradient of the time-average shear stress at the walls of the external iliac arteries was found from the computational fluid dynamic simulations for each experiment. Using affine transformations, the gradient and time-average shear stress results, and the EBD optical density distributions, were mapped to a common template, allowing pixel-by-pixel correlations of the hemodynamic stress parameters and local permeability. The results suggest that both shear stress gradient and time-average shear play a role in determining vascular permeability to macromolecules