A Microvascular Wall Shear Rate Function Derived From In Vivo Hemodynamic and Geometric Parameters in Continuously Branching Arterioles

OBJECTIVES: Conventional approaches to WSR estimation in the microcirculation involve assumptions that may result in under-/over-estimation of WSR. Therefore, our objectives were: (i) calculate WSR from RBC velocity profiles for a wide range of arteriolar diameters, (ii) provide an experimentally derived and straightforward WSR estimation function, and (iii) compare calculated to conventional WSR estimations. METHODS: We characterized RBC velocity profiles in arterioles (n = 39) of branching networks (21-115 μm) in the rat gluteus maximus muscle (n = 6). Measures included mean and maximum velocities, CFL thickness, and RBC column edge velocity, and an experiment-based WSR function was derived. RESULTS: CFL thickness (1-4.3 μm) positively correlated with arteriolar diameter (r(2)  = 0.64). Results from the WSR equation were similar to values from edge RBC velocities/CFL. Experimental WSRs (1317-4334/sec) were independent of arteriolar diameter, and were greater than pseudoshear rates (for VRatio of 1.6, 2, or diameter-dependent VRatio function) (p < 0.05). CONCLUSION: A WSR equation was derived from experimental hemodynamic parameters, and is adaptable to other velocity measurement techniques in order to obtain WSR and stress (when plasma viscosity is known). These findings provide insight on the nature of conventional WSR calculation methods in underestimating microvascular WSR values.