Coronary bridgings
 Numerical method
 
The model of bridging used is shown on fig. 19. Dimensions are anatomical : the diameter D (3mm) of the graft was chosen the same as the one of the receiving coronary artery. For an angle of insertion of bridging (beta=45°) and a fixed degree of stenosis severity (75%), the characteristics of the flow are studied for various distances of bridging and of flows distributions.
 
 
Geometry and netting of the anastomosis.

The numerical simulations are based on models of the finite elements (N3S) type. The flow, three-dimensional and physiological, is considered as laminar, and the fluid, of same viscosity as blood, as uncompressible, Newtonian and isothermal. The intake flows, simulated both numerically and experimentally come from in vivo recordings done by Dr Dupouy on patients who had a coronary bridging during the week before the measure. The eventual phase-shift of the two intake flows was put into light : RCA systolic coronary debt and diastolic flow in the IMA graft. A typical coronary flow (Berne and Levy, 1967) was also modeled for various coronary/graft flow distributions and total occlusion.
Intravascular Doppler probe and in vivo velocities recordings.

In any case, the frequency parameter is ?=4.9, and the maximum Reynolds number ReMAX ranges from 24.7 to 162.7, for the receiving artery, and between 97.4 and 295, for the graft.
Human physiological flows : LAD (former interventricular coronary), RCA (right coronary), IMA (mammary intern artery).

Using a decomposition in Fourier Series of the flow and an analytical solution of Navier-Stokes equations for a periodic flow in a straight duct of constant section, the intake conditions are implemented as a velocities profile. The rigid and non-porous linings are submitted to grip conditions. On exhaust, a condition of zero traction is applied. The period (T=0.8s) is divided in 3200 instants, ie Dt=2.5e-4 s.