An Experimentally‐Derived Wall Shear Rate Equation for Use in Microvascular Preparations
Authors: Goldman Daniel , Al‐Khazraji Baraa K. , Jackson Dwayne N. 
Published: November 2023

Background

Obtaining the experimental data needed to accurately calculate wall shear rates is challenging and time consuming. Thus, many have quantified shear rate from experimentally‐derived mean blood velocity (Vmean) and arteriolar diameter (D). These pseudoshear rate (Vmean/D) data pose two problems: 1) they imply a fixed shape for the velocity profile with a velocity ratio (Vratio = Vmax/Vmean) of 1.6 or 2, and 2) they are not specific to local shear rate changes at the cell‐free layer (CFL)‐wall interface. To date, wall shear rates from experimentally‐derived velocity profiles for branching arteriolar networks in skeletal muscle have not been calculated.

Methods

Using intravital video microscopy, we imaged branching arteriolar networks in the in situ rat gluteus maximus (GM) preparation (N=6) and characterized in vivo red blood cell velocity (RBC) profiles at each arteriolar segment (n=39) using our previously described “streak length” method. Our objectives were to: 1) calculate wall shear rate from in vivo RBC velocity profiles in GM arterioles for a wide range of diameters, 2) provide an experimentally‐derived and straightforward wall shear rate estimation function for use in skeletal muscle microvascular studies (and possibly in other tissues), and 3) compare our calculated wall shear rates to conventional wall shear rate estimations. From the velocity profiles, we measured: mean velocities, thickness of the CFL, axial flow velocity at the outer edge of the RBC column, and centerline RBC velocity and its relation to mean blood velocity. We used these data to derive an experiment‐based wall shear rate function.

Results

Arteriolar diameters ranged from 0.021 to 0.115 mm. CFL data ranged from 0.001 to 0.0043 mm and were positively correlated with arteriolar diameter (r2=0.64). Our novel wall shear rate equation was similar to experimental wall shear rates (using edge RBC velocities/CFL). Calculated experimental wall shear rates ranged from 1317 to 3684 sec−1, did not correlate with arteriolar diameter, and in all cases were greater than pseudoshear rates calculated using either a fixed Vratio of 1.6 or 2, or our previously characterized diameter‐dependent Vratio function.

Conclusion

In this study, we provided a straightforward wall shear rate equation, derived from the relationship of experimental hemodynamic parameters with arteriolar diameter, that yields values similar to our experiment‐based values. This equation does not assume a velocity ratio, is calculated at the CFL‐wall interface, and can easily be adapted for use in studies investigating wall shear rate. The equations provided in this study are adaptable for use with other velocity measurement techniques in order to obtain wall shear rate and stress (when plasma viscosity is known) in skeletal muscle preparations for a wide range of arterioles.

Support or Funding Information

Funding: Natural Sciences and Engineering Research Council (NSERC) CGS‐D Scholarship awarded to BKA, NSERC grant #R4218A03 awarded to DNJ, and NSERC grant #R4081A03 awarded to DG.