Imagine a kinked garden hose: water meets resistance, and pressure drops. A similar process occurs in arteries when they lose their straight geometry. Vascular tortuosity is not just a cosmetic defect but a factor that disrupts hemodynamics and poses a threat of ischemic stroke. For a long time, doctors relied on visual assessment of such bends, but the human eye and experience are subjective and poorly reproducible tools.

A new approach turns vessel morphology into a digital code. A specialized program extracts six geometric parameters from a three-dimensional model of the artery: total bend angle, local curvature, degree of twisting (torsion), and their mutual relationships. This is not just a set of numbers — behind them lies differential geometry, the same mathematical apparatus that describes the shape of curves in space. Then an algorithm steps in, using entropy — a measure of uncertainty that here serves as a criterion for selecting the most informative features. Based on these calculations, arteries are classified into three groups: from nearly straight to severely deformed. The result is the Morphological Risk Index (MRI)—a single number that concentrates the danger assessment. No intuition — only rigorous measurement.

Remarkably, the mathematical language of vascular bends turns out to be surprisingly close to the description of curved spacetime in general relativity. The very equations that predict planetary orbits and the deflection of light in a gravitational field now help predict stroke risk. Of course, the analogy is not literal: an artery does not curve space, and its geometry obeys the laws of hydrodynamics, not gravity. But the commonality of mathematical structures allows transferring powerful tools from one field to another, opening the way to more accurate and personalized diagnostics.