Effect of length on the fundamental resonance frequency of arterial modelshaving radial dilatation

The pressure wave moving along an elastic artery filled with blood was exam ined as a moving Windkessel having a natural oscillation angular frequency v(0) and a damping coefficient b. The radial directional motion for an elem ent of the wall segment and the adherent fluid was considered. This equatio n was solved with conditions at both ends of an artery of length L, An exte rnal impulse force was applied at one end and a static pressure P-0 at the other. Analytic solution allowed only certain oscillation modes of resonanc e frequencies f(n), where f(n)(2) = a + c(n)L(-2) with a = v(0)(2)/4 pi(2) - b(2)/16 pi(2), c(n) = (n + 1/2)(2) V-infinity(2)/4, n = 0, 1, 2, 3, ... and V-infinity is the high frequency phase velocity, The relationship between f(0) and L was examined experimentally for tubes c onstructed of latex, rubber, or dissected aorta. The effect of raising the static pressure P-0 or increasing the tension in the tube was consistent wi th the prediction. The hypertension that accompanies an augmentation in art erial wall and the association between the heart rate and the mean blood pr essure were discussed.