Accurate diagnosis and therapeutic evaluation of coronary dysfunction is possible by tri-dimensional (3D) visualization of Coronary arteries. Reconstruction based on bi-dimensional (2D) images can be presented as a discrete optimization problem. A blind search cannot be applied, instead a Branch-and-Bound algorithm is used to explore the state space and give an intermediate result. The heuristic information used is based on 2D and 3D a priori knowledge. A sequential algorithm using suitable filters leads to implementations where the execution time is measured in days. In order to minimize the execution time we propose to apply parallel computing techniques. The critical issue in parallel search algorithms is the distribution of the search space among the processors. We propose a technique to compute the total amount of work units among the processors. The technique is based on the enlargement of segments (unitary threads) representing pieces of arteries. We achieve a good load balancing and the speedup obtained is nearly optimum.