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The aim of this study is three fold: (1) to investigate the pulsatile blood flow in the brachial artery and its ulnar and radial tributaries in the attempt to understand aspects related to blood pressure measurements (BPM); (2) to assess the flow-vessel-muscle structural interactions that may occur normally and under occlusive constraints (the radial artery); (3) to investigate the BPM information for different rheological models of blood. Mathematical modeling and numerical simulations are used to solve these objectives.