title: Theoretical hydraulic consequences of vein graft taper.
abstract: 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 (Z(L)), a conduit-specific measure of pulsatile resistance along straight rigid tubes.
  
  
  METHODS
  Proximal and distal graft pressure, pressure gradient (DeltaP), 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 DeltaP 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 DeltaP 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 DeltaP and Q, Z(L) was calculated as DeltaP/Q, plotted over a range of 8 Hz, and integrated over 4 Hz to yield integral Z(L).
  
  
  RESULTS
  The architecture of the calculated DeltaP 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 x 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 integral Z(L) (from 32 to 35 x 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 integral Z(L) of 70 x 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.
  
  
  CONCLUSIONS
  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 degree of taper is less than 40%. Tapered veins are satisfactory conduits for long-segment bypass grafts, provided their mean diameter is acceptable.
authors.affiliation: Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, USA.
authors.forename: Sang-Wook
authors.initials: SW
authors.lastname: Lee
authors.forename: Michael A
authors.initials: MA
authors.lastname: Curi
authors.forename: Zachary K
authors.initials: ZK
authors.lastname: Baldwin
authors.forename: Viji
authors.initials: V
authors.lastname: Balasubramanian
authors.forename: Francis
authors.initials: F
authors.lastname: Loth
authors.forename: Lewis B
authors.initials: LB
authors.lastname: Schwartz
mesh_terms: D006439:Hemodynamics; D018056:Hemorheology; D006801:Humans; D066298:In Vitro Techniques; D008955:Models, Cardiovascular; D014654:Vascular Patency; D014680:Veins / Q000033:anatomy & histology / Q000637:transplantation*