A theory of aneurysm sounds

Narrow-band sounds are known to be associated with some intracranial aneurysms. Previously proposed theories for the mechanism of aneurysm sounds do not satisfactorily explain the small spectral widths of the sounds. A simple theory is proposed here which gives quantitatively correct predictions of the spectral widths and which also explains other salient features of aneurysm sounds. The physical features of the aneurysm are described in terms of lumped mechanical elements, and the interaction between the aneurysm vibration and the blood flow is recognized as having the characteristic features of a nonlinear feedback system. The resulting model, with the application of the method of describing function analysis commonly used in nonlinear control theory, yields predictions of steady oscillation frequencies and predictions of the ranges of arterial flow velocities for which substantial oscillations can be excited. An analysis of radiation losses associated with peristaltic waves indicates that aneurysms, in the absence of any nonlinearity, behave as low-quality factor resonators with resonator quality factors on the order of 1–10, much lower than those that would be inferred from the observed spectral widths of aneurysm sounds. Aneurysm sounds are predicted by the present nonlinear theory to have center frequencies on the order of 400 Hz and bandwidths corresponding to quality factors on the order of 40, in good agreement with in vivo observations. It is concluded that linear resonance theories are incapable of fully describing aneurysm sounds. Instead, narrow-band aneurysm sounds are a result of a self-excited nonlinear oscillation that involves the disturbed arterial flow, the flow into and out of the aneurysm, and the expansion and contraction of the aneurysm volume. The finite magnitude of the spectral peaks arises because of the time variation of the arterial flow during the cycle associated with the heartbeat.