Distribution of wall shear rate throughout the arterial tree: a case study

The generally accepted assumption that the arterial system remodels itself to maintain constant wall shear stress throughout is based on Murray's law, utilising the principle of minimum work for steady flow. However, blood flow in the human arterial system is pulsatile. In this work we outline a method allowing for estimation of wall shear rate in arteries using the flow waveforms as the input signal and estimate wall shear rates in the common carotid, brachial, and femoral arteries to determine the uniformity of distribution of wall shear rates throughout the arterial system. Time-dependent wall shear rates occurring in fully developed pulsatile flow were obtained using Womersley's theory. Flow waveforms and radii of the arteries measured in a young healthy male subject without any known cardiac disease using magnetic resonance taken from the literature were used as the input to the model. Peak/mean wall shear rates were found to be (1640/403.2 s(-1)) in common carotid, (908.8/84.95 s(-1)) in brachial, and (1251/134.2 s(-1)) in femoral arteries. Our findings suggest a non-uniform distribution of wall shear rates throughout the arterial system. The advantage of using this method is that such input data are being routinely recorded during diagnostic ultrasonography.