Keywords: blood flow simulation, multi-objective optimization, genetic algorithms.

Nowadays, the available arterial prostheses present uniform homogeneous physical properties fully along their length which closely match those for normal human arteries. Nevertheless vascular interventions for the treatment of symptomatic stenosis fail in many cases during the first years due to restenosis. Geometry configuration has a profound influence on flow patterns, pressure distribution and shear stress which are correlated with postoperative occlusion pathogenesis of bypass grafts. Improvement of the hemodynamics conditions are considered for the optimization of the geometry of grafts [1,2,3].

The purpose of the research described in this paper is to contribute towards the improvement of arterial bypass surgeries based on simulated models. Simulation of blood flow is of great importance for designing vascular devices and a finite element model developed for blood flow simulation is considered in this work [4]. Shape optimization will be accomplished by simultaneously minimizing stagnation and recirculation zones. In particular, a specific graft shape and three design variables are considered. A multi-objective shape optimization algorithm using a genetic algorithm iterating over a population of simulated bypass grafts with blood flow determined using the finite element model developed is presented.

Pareto optimality is a concept that formalizes the trade-off between a given set of possible contradicting objectives. The present work considers an iterative procedure that evaluates all individuals using the objective functions until all individuals have their own Pareto ranking. Using an only one time global search procedure all the Pareto optimal solutions will be found managing the drawing of the Pareto front and then extracting optimal solutions according to selected preferences. The study reported herein establishes the methodology as a viable means of achieving optimal artificial graft shapes.

1

M. Probst, M. Lülfesmann, H.M. Bücker, M. Behr, C.H. Bischof, "Sensitivity of shear rate in artificial grafts using automatic differentiation", Int. J. Numer. Meth. Fluids, 62, 1047-1062, 2010.

2

Z. El Zahab, E. Divo, A.J. Kassab, "Minimisation of the wall shear stress gradients in bypass grafts anastomoses using meshless CFD and genetic algorithms optimisation", Computer Methods in Biomechanics and Biomedical Engineering, 13(1), 35-47, 2010.

3

C.F. Castro, C.C. António, L.C. Sousa, "Multi-objective optimization of bypass grafts in arteries", TMSi - Sixth International Conference on Technology and Medical Sciences, Porto, Portugal, 191-196, 21-23 October 2010.

4

L. Sousa, C. Castro, C. Antonio, R. Chaves, "Computational Techniques and Validation of Blood Flow Simulation", WEAS Transactions on Biology and Biomedicine, 4-8, 145-155, 2011.

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