Pulsatile blood flow in arteries is described by Womersley flow — the oscillatory solution to Navier-Stokes in a cylindrical pipe. The standard treatment decomposes the cardiac pulse into Fourier harmonics, solves each independently, and sums. The artery is a passive pipe; the geometry attenuates harmonics but doesn't create new ones.
Amiri, Guimond, Bhatt, and Bhatt show the artery is not passive. In tapered, curved, and branching vessels, the nonlinear convective acceleration couples Fourier harmonics. A pulse entering at frequency ω exits with energy at 2ω, 3ω, and higher harmonics — energy that wasn't in the input. The geometry actively generates spectral complexity.
The mechanism is resonant spectral cascade. At specific Womersley numbers (the dimensionless frequency parameter), the coupling between harmonics is maximized. The geometry acts as a nonlinear filter that amplifies certain harmonic combinations while suppressing others. The output spectrum depends not just on the input pulse shape but on the geometric details of the vessel: taper angle, curvature radius, branch angle.
The clinical implication: the spectral content of the pulse waveform measured downstream of a stenosis or bifurcation carries geometric information about the vessel. The harmonics that appear (or don't appear) in the measured waveform encode the shape of the artery that generated them. The spectral signature is a geometric fingerprint.
The artery as instrument. The cardiac pulse is the input; the vessel geometry modulates it; the output waveform carries the shape of the channel it passed through.