Some contributions to the mathematical biology of blood circulation. Reflections of pressure waves in the arterial system

If, along the length of a blood vessel, there is a discontinuous change of diameter, the pressure waves will be reflected at the discontinuity. The transmission and reflection coefficients of the waves are calculated in terms of the ratio of the diameters and the ratio of the propagation velocities of the waves in the parts of the blood vessel. We obtain also the reflection coefficient in terms of the ratios of the diameters, of the elasticity moduli, and of the wall thicknesses. The possible clinical importance of the results is pointed out for cases of coarctation, arteriosclerosis, and other pathological conditions which might effect local changes in the structure of the blood vessel wall.