“…42 Then the blood flow rate q ( t ) at the CCA could be calculated. Subsequently, the simplified Navier–Stokes equation 43,44 was used to establish a distributed parameter model of the circular tube similar to the CCA. Finally, the shear stress τ c ( t ) at the CCA endothelium under different pulsation frequency modes of the RBP could be expressed as follows:
where a n stands for the Womersley number corresponding to the n th harmonic component, expressed as follows:
where R is the inner diameter of the CCA, ρ is blood density, η is blood viscosity, Q ( ω n ) is the harmonic component of the macroscopic blood flow rate q ( t ) at the CCA, j is equal to the square root of −1, J 0 and J 1 represent the first class of zero-order and first-order Bessel functions, respectively, 45 and F 10 is expressed as follows:
…”