Kawanaka, H.;Miura, T.

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.