Biomedical Engineering Reference
In-Depth Information
at
t/tp
0.05) significant flow separation and reversed flow appear in the sinus. The
reversed flow occupies around 50% of the sinus diameter in the branching plane.
The numerical findings on flow separation near the outer sinus wall agree with
previously published results. In further studies the carotid bifurcation flow field will
be investigated using parameters obtained from clinical observations.
D
4
Optimization of an Artificial Bypass Graft
Numerical simulations of blood flow in arteries can be used to improve the
understanding of vascular diseases searching efficient treatments and medical
devices. A framework for graft design optimization used in a bypass surgery,
which is performed to restore blood flow in stenosed arteries is described here.
Coupling shape optimization to three-dimensional unsteady blood flow simulations
poses several key challenges, including high computational cost, a need to handle
constraints, and a need for automatic generation of parameterized vessel geometry.
Instead, the applicability of the optimization framework is demonstrated considering
a two-dimensional steady flow simulation. An idealized graft/artery model is
parameterized with a geometry allowing the analysis of the influence of graft-to-
artery angle and diameter. Search for optimized arterial bypass grafts has been
presented in the literature [
12
,
14
] always restricted to one objective function.
This work represents the use of formal multi-objective optimization algorithms for
surgery design.
4.1
Multi-Objective Optimization Strategy
In shape optimization, the goal is to minimize an objective function that typically
depends on a state vector
u,
over a domain of design vector
b
. The state vector
and the design parameters are coupled by a partial differential equation that can be
written in a generic form as
s.
u
;
b
/
D
0
(19)
This so-called state equation forms the constraint of the minimization problem
Minimize ˆ.
u
;
b
/
subject to s.
u
;
b
/
D
0
(20)
Furthermore, the problem can be recast using the reduced form of the objective
function
Minimize ˆ
.
u
.
b
/;
b
/
(21)
