title: Analytical modeling and numerical simulation of forces in an endoluminal graft.
abstract: OBJECTIVE
  To utilize mathematical analysis and computational fluid dynamics (CFD) to investigate the forces acting within the pressurized aorta and upon a stent-graft and how these forces may affect the ongoing performance of the stent-graft.
  
  
  METHODS
  Analytical force balance analysis and CFD simulations using the Fluent code were used to mimic blood flow through a bifurcated stent-graft in a person at rest. Steady-state blood flow was assumed in which the inlet pressure approximated the mean blood pressure (100 mm Hg) and the blood flow velocity was an approximation of the peak systolic flow rate (0.6 m/s). Two sizes of endoluminal grafts were analyzed: the larger graft had an inlet diameter of 3 cm and outlet diameters of 1 cm; the smaller graft diameters measured 2.4 cm proximally and 1.2 cm distally. The endografts were studied in 2 configurations: with the limbs straight and with one bent.
  
  
  RESULTS
  For the larger graft model, the normal peak blood flow induced a downward force of 7 to 9 N on the bifurcated grafts. Bending one of the limbs of the graft produced a sideways force of 1.3 N. For the smaller endograft, the downward force was in the range of 3.1 to 5.1 N and the sideways force on a curved limb was approximately 1.5 N. The magnitude of the forces given by the analytical formulae and the CFD results agreed to within 2 significant figures.
  
  
  CONCLUSIONS
  These results suggest that the downward force on a bifurcated stent-graft, which may exceed the force required to dislodge it when relying on radial attachment alone, is determined mostly by the proximal graft diameter. Curvature of the graft limbs creates an additional sideways force that works to displace the distal limbs of the graft from the iliac arteries.
authors.affiliation: Thermal and Fluids Engineering, CSIRO/BCE, Highett, Victoria, Australia.
authors.forename: K
authors.initials: K
authors.lastname: Liffman
authors.forename: M M
authors.initials: MM
authors.lastname: Lawrence-Brown
authors.forename: J B
authors.initials: JB
authors.lastname: Semmens
authors.forename: A
authors.initials: A
authors.lastname: Bui
authors.forename: M
authors.initials: M
authors.lastname: Rudman
authors.forename: D E
authors.initials: DE
authors.lastname: Hartley
mesh_terms: D017130:Angioplasty / Q000295:instrumentation; D017544:Aortic Aneurysm, Abdominal / Q000503:physiopathology / Q000601:surgery; D001783:Blood Flow Velocity / Q000502:physiology; D001794:Blood Pressure / Q000502:physiology; D019917:Blood Vessel Prosthesis Implantation / Q000295:instrumentation; D003430:Cross-Sectional Studies; D005121:Extremities / Q000098:blood supply; D006801:Humans; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D015607:Stents; D014654:Vascular Patency / Q000502:physiology