A parallel algorithm for 3D reconstruction of angiographic images

Abstract

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.

Introduction

The detection, evaluation and therapeutic follow-up of dysfunctions affecting coronary arteries, the arteries responsible of oxygenating the cardiac muscle, are usually carried out by an imaging technique called angiography (see [4]).¹ Tri-dimensional (3D) visualization of coronary arteries can improve considerably diagnosis and maximizes patient protection by reducing exposure to radiation and contrast liquid infusion. Due to a variety of technical constrains, 3D reconstruction might be based on two orthogonal images taken simultaneously. Fig. 1 shows a pair of such images. These images have numerous structure superpositions as well as deformations caused by the projection process. The reconstruction based on two projections is a multiple solution problem.

The Applied Bioengineering and Biophysics Group (GBBA) at the Simón Bolívar University [3] has developed ANIA — a tool for angiographic image analysis and study. ANIA allows 2D and 3D image manipulation and it can generate the solution space for the problem of reconstruction from biplane images. From the solution space (see Fig. 2) generated by ANIA, a 3D reconstruction process can be done.

The reconstruction process involves a combinatorial generation of possible solutions (see Fig. 3), the identification of the correct solution can only be carried out using a priori knowledge (see [5]). This knowledge includes 3D aspects (object properties) and 2D aspects (object projection properties). None of the properties identified in [5] has enough discrimination capacity, but each one can help to eliminate a set of erroneous solutions. It is desirable to obtain only one solution — the right one — from the reconstruction process. This research is been carried out in order to have enough discrimination conditions [7]. At the moment, it is only possible to get a reduced set of valid solutions, those which satisfy a set of pre-establish conditions. The reconstruction process using a set of conditions and its algorithm is described in Section 2.

A prototype system to solve the reconstruction problem using a priori knowledge was developed in Prolog in an early work by Windyga [5], which proved the feasibility of the method. Nevertheless, the solution space of a real coronary tree is too large [6] to be managed efficiently by sequential Prolog, thus the performance of this prototype is poor. Running on a SUN Sparc Station the Prolog’s program is unable to find the set of valid solutions in 1 week. Based on this experience and using the set of conditions described in Section 2, a new sequential algorithm is implemented in C and then it is improved by including unitary threads. The key aspects used on this approach are given in Section 2.2.

The critical issue in parallel search algorithms is the distribution of the search space among the processors. There is a large amount of work in this subject [1], [2]. By increasing the length of artery segments with unitary threads, the search space is reduced. The reduced search space is partitioned in equal shares among the processors. Then we work with a simple load balancing technique — the static distribution of the search space (see Section 3). This approach normally leads to a severe load imbalance, but in our case the results are satisfactory (see Section 4) because the distribution does not cause high communication costs. Finally, the conclusions and future work are described in Section 5.