Effect of length on the fundamental resonance frequency of arterial models having radial dilatation

The pressure wave moving along an elastic artery filled with blood was examined as a moving Windkessel having a natural oscillation angular frequency /spl nu//sub 0/ and a damping coefficient b. The radial directional motion for an element of the wall segment and the adherent fluid was considered. This equation was solved with conditions at both ends of an artery of length L. An external impulse force was applied at one end and a static pressure P/sub 0/ at the other. Analytic solution allowed only certain oscillation modes of resonance frequencies f/sub n/, where f/sub n//sup 2/=a+c/sub n/L/sup -2/ with a=/spl nu//sub 0//sup 2//4/spl pi//sup 2/-b/sup 2//16/spl pi//sup 2/, c/sub n/=(n+1/2)/sup 2/V/sup 2//sub /spl infin///4, n=0, 1, 2, 3, ..., and V/sub /spl infin// is the high frequency phase velocity. The relationship between f/sub 0/ and L was examined experimentally for tubes constructed of latex, rubber, or dissected aorta. The effect of raising the static pressure P/sub 0/ or increasing the tension in the tube was consistent with the prediction. The hypertension that accompanies an augmentation in arterial wall and the association between the heart rate and the mean blood pressure were discussed.