Theoretical hydraulic consequences of vein graft taper

Internal diameter is a strong predictor of patency of infrainguinal vein grafts. However, most vein grafts are tapered, with variable diameter along their length. It is unknown which diameter is most important in determining graft resistive properties, that is, its mean diameter, minimum diameter, or some geometric combination thereof. The purpose of this analysis was to examine the hydraulic consequences of vein graft tapering, with longitudinal impedance (Z L), a conduit-specific measure of pulsatile resistance along straight rigid tubes. Proximal and distal graft pressure, pressure gradient (ΔP), and blood flow (Q) were measured intraoperatively in a 100 cm bypass graft and digitally recorded for 10 seconds at 200 Hz. With the Womersley solution for fully developed fluid flow in a rigid tube, a series of ΔP waveforms were generated for graft diameters ranging from 1.2 to 8.2 mm. With an axisymmetric form of the Navier-Stokes equations, a second series of ΔP waveforms were computed for grafts with long smooth symmetric tapers ranging from 0% to 90%, with geometric mean diameter of 3.2, 4.2, and 5.2 mm (%Taper = 100 × [proximal diameter − distal diameter]/proximal diameter). For each set of ΔP and Q, Z L was calculated as ΔP/Q, plotted over a range of 8 Hz, and integrated over 4 Hz to yield ∫Z L. The architecture of the calculated ΔP and Z L waveforms closely approximated their measured counterparts, validating the method. As expected, Z L was highly diameter-dependent in a nonlinear fashion. With a clinically relevant boundary of less than 50 × 10 3 dyne/cm 5 as “acceptable,” the minimum acceptable diameter of nontapered 100 cm bypass conduits was 4.3 mm. Analysis of graft taper revealed that small amounts of taper in large conduits were well-tolerated. For example, introduction of 32% taper in a 5.2 mm graft (6.2 mm → 4.2 mm) caused only an 8% increase in ∫Z L (from 32 to 35 × 10 3 dyne/cm 5). More pronounced taper in smaller conduits rendered them unacceptable. For example, 53% taper of a 4.2 mm graft (5.7 mm → 2.7 mm) created a conduit with ∫Z L of 70 × 10 3 dyne/cm 5, well above the acceptable limit. The relationship between Z L and percent taper was nonlinear and strongly dependent on mean diameter. The relationship between Z L and diameter in vein grafts is nonlinear; thus Z L increases rapidly in conduits smaller than 4 mm. Tapered vein grafts behave hydraulically like nontapered grafts, provided their geometric mean is greater than 4 mm and their