Abstract A numerical technique in the study of aorto-coronaric bypass anastomoses congurations using unsteady Stokes equations is presented. The theory of optimal control based on notations of the measure theory, functional analysis and linear programming (LP), is applied in order to optimize the shape of the zone of the incoming branch of the bypass (the toe) into the coronary. First the problem is expressed as a shape optimization problem by adding a suitable criteria, where the problem is governed by variational form on a xed domain. By using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. Then optimization problem in measure space is approximated by a LP problem. MSC 2000: 35Q30; 49J20; 76Z05; 62K05; 28A33.

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