Biomedical Engineering Reference
In-Depth Information
Initialization
Model Construction:
1. Create centerline of graft
2. Take lines perpendicularly to
the centerline
3. Mesh generation
Design parameters for
every new memeber of
the population
GA Operators:
Selection, Crossover,
Mutation, Deletion
Flow Simulation and
Objective Function
Computation
Fig. 4
Shape optimization algorithm
from the elite group making possible the exploitation of previously unmapped space
design regions and guaranteeing the diversity of the generated population.
Deletion: After mutation, new ranking of the enlarged population according to their
fitness. Then, it follows the deletion of the worst solutions with low fitness simu-
lating the natural death of weak and old individuals. The original size population
is recovered and the new population P
t
C
1
is obtained; the evolutionary process will
continue until the stopping criterion is reached.
Termination: checking the termination condition. If it is satisfied, the GA is
terminated. Otherwise, the process returns to step Selection.
To fully automate the shape optimization procedure, the following sub-steps
are linked in our framework: model generation, meshing, multi-objective function
evaluation (flow simulation and post processing) and data transfer into the GA so
that the optimization procedure does not require any user intervention. Figure
4
shows the sub-steps of the optimization procedure. The boxes and arrows in Fig.
4
form a loop that repeats until stopping criteria are satisfied.
4.3
Optimized Graft Example
Search for an optimized geometry of an idealized arterial bypass system with
fully occluded host artery is addressed here. This shape optimization problem
requires an efficient and accurate solver for steady flow simulation. The Navier-
Stokes equations are solved using the previously described penalty finite element
model. The non-Newtonian behaviour of the blood is described using Casson law
given by (
18
).
