Quantification of the severity of the deterioration in bone tissue is an important diagnostic problem involving the assessment of connectedness of the tissue from its grey-level images. In this study a fuzzy parameter was introduced for quantifying the severity of discontinuities of network-like structures. For each two pixels of an analyzed image, the fuzzy parameter was derived from the grey-level intensity along the brightest path connecting them. The performance of this parameter was tested on images of continuous and discontinuous samples of vertebral trabecular bone, matched for mean gray-level intensity. It was shown that the values of the parameter were significantly different (P-value<10(-6)) in both groups and equal to 0.02+/-0.11 and 0.46+/-0.22 for discontinuous and continuous samples, respectively. The decrease in the fuzzy parameter could be interpreted as the result of either an increasing gap size in discontinuous structures or a decreasing thickness of structure elements in continuous structures. A possible application of the method for use in quantifying severity of discontinuities within the vertebral cortical rim was described.