Spectral fingerprints distinguish buckling from angiogenesis in tortuous blood vessels

HighlightsO_LIBuckling and angiogenesis yield distinct vessel power spectra C_LIO_LIDominant buckling wavelength vs k-2 angiogenic scaling C_LIO_LITwo-phase CA+EB model matches real retinal vessel morphology C_LIO_LIOCTA500 segments show morphology beyond single-mechanism models C_LI 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--by analyzing the vessel centerline height function in Fourier space. 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 in the buckling model and the origin of the scaling in the Chaplain-Anderson model. We further analyze OCTA500 segments using morphological descriptors (power spectrum, autocorrelation, and mean squared displacement); neither single-mechanism prediction alone accounts for the observed morphology, motivating a two-phase model in which angiogenic structure generation is followed by mechanical remodeling. Based on this two-phase hypothesis (a Chaplain-Anderson (CA)-like scaling background plus mechanical remodeling), we introduce quantitative indices--residual low-to-high wavenumber power ratio (rLHP) and slope reversal density (SRD)--to quantify Euler-Bernoulli-like buckling contributions in vessel segments. These results suggest that spectral fingerprints and complementary metrics may help distinguish mechanically driven tortuosity from angiogenesis-driven tortuosity in vascular images.