Theoretical hydraulic consequences of vein graft taper

Sang Wook Lee, Michael A. Curi, Zachary K. Baldwin, Viji Balasubramanian, Francis Loth, Lewis B. Schwartz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Objective: 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 (ZL), a conduit-specific measure of pulsatile resistance along straight rigid tubes. Methods: 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 x [proximal diameter - distal diameter]/proximal diameter). For each set of ΔP and Q, ZL was calculated as ΔP/Q, plotted over a range of 8 Hz, and integrated over 4 Hz to yield ∫ZL. Results: The architecture of the calculated ΔP and ZL waveforms closely approximated their measured counterparts, validating the method. As expected, ZL was highly diameter-dependent in a nonlinear fashion. With a clinically relevant boundary of less than 50 × 103 dyne/cm5 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 ∫ZL (from 32 to 35 × 103 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 ∫ZL of 70 × 103 dyne/cm5, well above the acceptable limit. The relationship between ZL and percent taper was nonlinear and strongly dependent on mean diameter. Conclusions: The relationship between ZL and diameter in vein grafts is nonlinear; thus ZL 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 degree of taper is less than 40%. Tapered veins are satisfactory conduits for long-segment bypass grafts, provided their mean diameter is acceptable.

Original languageEnglish (US)
Pages (from-to)785-792
Number of pages8
JournalJournal of Vascular Surgery
Issue number4
StatePublished - Oct 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Surgery
  • Cardiology and Cardiovascular Medicine

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