Physiological interpretation of doppler-shift waveforms—I theoretical considerations

A method is presented for describing the shape of the blood-velocity/time waveforms recorded at the posterior tibial artery, using Doppler-shift flowmeters. A third order mathematical model is developed which describes these waveforms in patients with occlusive arterial disease and in normal volunteers. In normals, the model has two complex and one real pole, and in occluded arteries with collateral circulation all the poles are real. The complex poles are shown to be related to the elastic modulus of the artery and also to the lumen size. The third pole is shown to be related to the degree of vasoconstriction of the peripheral circulation.