Nonlinear Dynamics in the Progression of Atherosclerotic Fatty Streaks: Morphometric Analysis

Abstract

Atherosclerotic lesions are heterogeneous in terms of their cellular and lipid composition. While heterogeneity can be the result of stochastic noise, an alternate hypothesis is that the differences observed among individual lesions arise from deterministic chaos. Five New Zealand white rabbits were fed a diet containing 0.15% cholesterol for 6 months. Segments of the aorta were fixed in formalin, stained en bloc with Nile red (NR) and filipin (F), and en face fluorescence microscopy was used to map the distribution of lipids in fatty streaks (FS). The smallest lesions detected stained only with filipin. Larger lesions stained with both Nile red and filipin and two distinct regions of Nile red staining, NR-orange (rich in polar lipids) and NR-yellow (rich in neutral lipids) were observed. Digital overlays revealed a “nested” arrangement of F, NR-orange, and NR-yellow. The lesions also showed marked heterogeneity in their lipid composition. Thus, although initially similar, as FS increased in size, their composition became divergent, suggesting that the ultimate composition of a FS was highly sensitive to its initial composition. Sensitivity to initial condition is one of the hallmarks of deterministic systems. To determine if FS were self-similar, another hallmark of deterministic chaos, the borders of the different regions defined by NR and F staining were subjected to fractal analysis. For each lesion, the borders of the F, NR-orange, and NR-yellow regions were found to be fractal. Return maps were constructed for the differently stained regions. Analysis of the entire 104-lesion data set showed that although the data could be described by a four-parameter logistic model, the population was not chaotic. However, return maps drawn for the maxima of the NR-orange stained regions demonstrated chaos. Taken together, the data suggest that deterministic chaos plays a role in the evolution of atheromatous disease but, in common with most biologic systems, as the lesions progress, chaotic behavior is dampened.