—
Pascal (Pa)
Wall Shear Stress
Adjust Parameters
Flow Rate (Q)
200 mL/hr
Slow drip → rapid bolus → pressure-bag infusion
Vessel Radius (r)
2.0 mm
Small peripheral vein → basilic → subclavian
Viscosity (η)
1.0 cP
NS ≈ 1 · Blood ≈ 3.5 · Contrast ≈ 5–8 cP
Vessel Cross-Section
Endothelial Shear Forces
Velocity Profile
Wall Gradient (∂v/∂r)
Medication Compatibility — Vessel Injury Risk
Normal Saline
pH 5.0–7.0
290 mOsm/L
Low Risk
Amiodarone (IV)
pH 3.5–4.5
700 mOsm/L
High Risk
Vancomycin (IV)
pH 2.5–4.5
5000 mOsm/L
High Risk
D5W
pH 4.0–5.0
252 mOsm/L
Moderate
Potassium Chloride
pH 4.0–8.0
Variable
Moderate
TPN (full formula)
pH 5.5–6.5
>900 mOsm/L
Central Only
The Cube Relationship
Shear stress scales with 1/r³ — much more sensitive than flow rate's 1/r⁴ in the HP equation. A small vein (r=1mm) sees 8× the shear stress of a moderate vein (r=2mm) at the same flow rate.
Endothelial Response
Endothelial cells sense shear stress via mechanoreceptors. Physiologic shear (0.1–1 Pa) upregulates protective factors (eNOS, t-PA). High shear (>40 Pa) causes cell detachment. Very low shear promotes von Willebrand factor and VCAM-1 — thrombogenesis.
Chemical + Mechanical Injury
Phlebitis from peripheral IVs combines mechanical shear injury with chemical injury from osmolarity and pH extremes. Amiodarone in a small vein is a double insult — high osmolarity AND high shear stress from the narrow radius.
Dilution as Protection
Diluting irritant medications reduces concentration injury but also reduces viscosity, which can lower shear stress slightly. More importantly, infusing into a larger vessel (central) dramatically reduces shear stress via the r³ factor.