Assessment of wall shear stress in arteries, applied to the coronary circulation

Time dependent wall shear rates cannot be directly or accurately measured in arteries using presently available techniques. Here a simple method is presented for calculating them from a single measured velocity waveform (either centreline or cross-sectionally averaged velocity). The method involves only Fourier analysis and the application of given formulae, and it is expected to be approximately valid in any segment of artery which has no branches or sharp curves for a distance of several diameters. It is shown, however, that a frequency response of 30 Hz is required in the velocity measuring device if the resulting wall shear rate waveform is to be accurate throughout the cycle although 10 Hz is adequate if only the rms value is desired. This restriction on accuracy applies to this or any other method of estimating time-dependent wall shear. The method is applied to a prediction of wall shear in the left coronary arteries of the horse, based on measured velocities where they are available and calculated ones where they are not; the results show that in vivo the amplitude of wall shear fluctuations is much greater than the mean. The method is also applied to a scaled down model of the horse coronaries, thought to be representative of man; here the unsteadiness is still important but no longer dominant. The variation of wall shear with distance along the artery is discussed in the context of atherogenesis.