Spectral fingerprints distinguish buckling from angiogenesis in tortuous blood vessels

Physiological blood vessels are generally straight, but tortuous curvature is observed under pathological conditions across spatial scales, from large arteries to retinal microvasculature and tumor-associated vessels. Here, we compare two theoretical mechanisms of curved vessel formation--mechanical buckling and angiogenic biased random walk--within a common spectral framework. We simplify the Chaplain-Anderson angiogenesis model and an Euler-Bernoulli buckling model with surrounding-tissue support, reproduce curvature numerically, and analyze the power spectra of the resulting patterns. Buckling yields a single characteristic peak in the power spectrum, whereas angiogenesis yields k-2 scaling in the low-frequency range. Mathematical analysis explains the selective growth of a dominant buckling wavelength and scaling characteristics in the Chaplain-Anderson model. We further test these predictions using morphological descriptors (power spectrum, autocorrelation, and mean squared displacement) applied to a public retinal vessel dataset and propose a two-phase model combining angiogenic structure generation with subsequent mechanical remodeling. These results suggest that spectral fingerprints may help distinguish mechanically driven tortuosity from angiogenesis-driven tortuosity in vascular images.