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Morphological changes in brain tumors may be related to their malignancy. The objective of this work is to be able to detect and quantify these changes in a magnetic resonance imaging, since it can represent an important advantage for the noninvasive diagnosis in patients. One way to identify such morphological changes can be through the measurement of their tortuosity. The discrete tortuosity is a descriptor that characterizes bi-dimensional curves, as the contour of a region. In this work an alternative procedure for calculating the volumetric tortuosity of a surface is proposed. This technique is based in the slope chain code of the surface contour of a volume, and here we call it tridimensional discrete tortuosity. This descriptor is used as a morphometric index to study the tortuosity of brain tumors. For this, magnetic resonance images from 20 patients with low and high malignancy levels were analyzed, considering four regions: edema, whole tumor, enhancing region, and necrotic region. As a result, the tortuosities of the different regions are presented, with significant differences only in some of them. It should be noted that a disadvantage that is present, is the dependence of the measurement to the use of a robust method of segmentation, nevertheless the proposal of the discrete tortuosity for volumetric surfaces is satisfactory. [ABSTRACT FROM AUTHOR]