Method Inform Med 1999; 38: 207–13 Methods of Information in Medicine © F. K. Schattauer Verlagsgesellschaft mbH (1999) 207 1. Introduction Digital subtraction angiography pro- vides images of a vascular network that are obtained by subtraction of precon- trast from postcontrast X-ray images. Such images are valuable for the physi- cian in evaluating the severity of visible lesions and in proposing the best thera- py. The traditional evaluation method is the visual estimation of the geometry of the artery as observed in an angiogram. In practice, this qualitative interpreta- tion of a lesion geometry is associated with substantial inter- and intra-observ- er variability [1]. Automated lesion quantification methods are needed to standardize artery lesion description and to reduce the variability [2]. Over the last decade, many efforts have been made to develop computer imaging systems capable of providing accurate and reproducible quantitative data from two-dimensional (2D) arterio- grams. Many studies have focused on the quality of the segmentation process that describes the geometry of the arter- ies, in particular the coronary arteries [3]. The systems that are used yield pre- cise quantities to describe the lesions and, in particular, the degree of steno- sis. The usefulness of such systems is limited by two factors. On the one hand, the procedure that provides the degree of stenosis is not fully automatic. User intervention is of- ten needed to delineate the regions of interest. Moreover, the quality of the image and preliminary post-processing introduce a degree of uncertainty in the image analysis. On the other hand, the major problem that remains is the eval- uation of the reliability of the computed degree of the stenosis. A correct evalu- ation of the systems should rely on a gold standard corresponding to the real degree of stenosis which is unknown a priori and can only be estimated from imperfect images. In clinical studies, the degree of stenosis is usually assessed by several experts. Our objective was to develop a meth- od, based on fuzzy set theory, that pro- vides fuzzy quantities rather than pre- cise values to characterize stenotic fea- tures. The study is limited to lesions seen in renal arteriograms. Our hypoth- esis is that a fuzzy estimation of a steno- sis should allow to take into account the uncertainty introduced by initial post- processing. One should also be able to compare it with a gold standard based on estimates from experts. In this study, we present the first step concerning the computation of a fuzzy degree of a sten- osis, using a fuzzy syntactic approach and the comparison with a non-fuzzy quantity obtained from a non-fuzzy ap- proach. The two methods, one precise and the other one fuzzy, implement a syntactic analysis of the arterial outline and provide a quantification of the sten- osis. In the next section we present the two methods, which are based on the same methodology for the quantifica- tion of arterial lesions. A general syn- tactic analysis approach is presented and the non-fuzzy and fuzzy approaches are described in detail. The approaches have been tested and compared on the basis of several images. A. Lalande 1 , M. C. Jaulent 2 , I. Cherrak 2 , F. Brunotte 1 , P. Degoulet 2 Quantifying Stenosis in Renal Arteriograms: A Fuzzy Syntactic Analysis 1 Laboratoire de Biophysique, Faculté de Médecine, Université de Bourgogne, Dijon, 2 Service d’Informatique Médicale, Hôpital Broussais, Paris, France Abstract: The introduction of fuzzy logic improves a system for the automatic quantification of renal artery lesions seen in digital subtraction angiograms. A two-step approach has been followed. An earlier system based on non- fuzzy syntactic analysis provided a clear symbolic description of the stenot- ic lesions. Although this system worked correctly, it did not take into account the variability and uncertainty inherent to image processing and to knowl- edge on the reference diameter. This system has been improved by the introduction of fuzzy logic in the representation of the reference diameter. It provides a description of the stenosis in terms of fuzzy quantities. To illus- trate the benefits of the fuzzy approach, the results of the two systems have been compared by plotting the differences of an index of variability. It ap- pears that the differences are statistically different when using a two-tailed paired t-test (t = 2.37; p = 0.025). The result shows that the fuzzy approach is better than a non-fuzzy approach in the sense that the index of variability is reduced significantly. Keywords: Fuzzy Logic, Syntactic Analysis, Renal Arteriogram Quantifica- tion, Stenosis Downloaded by: Thieme E-Books & E-Journals. Copyrighted material.