Differentiating small (= 1 cm) focal liver lesions as metastases or cysts by means of computed tomography: a case study to illustrate a fuzzy logicbased method to quantify uncertainty in radiological diagnosis

Purpose: To illustrate a fuzzy logic-based method to quantify uncertainty in radiological diagnosis. Material and Methods: We enrolled 22 oncologic patients with 50 focal liver lesions ≤1 cm detected at 64-row computed tomography (CT), proven to be cysts (n = 20) or metastases (n = 30). Two readers with 15 (R1) and 5 (R2) years of experience independently reviewed CT images. For each lesion, they expressed the diagnosis of metastasis as a certainty level (C) within the interval [0,1] (certainty in the alternative diagnosis of cyst was assumed to be 1-C). After cross-tabulating data according to the gold standard, table cells were considered as fuzzy subsets and complementary certainty values as their degrees of memberships. Accordingly, we estimated per-lesion diagnostic performance of readers both on usual crisp (C ≥ 0.51) and fuzzy basis. Results: Uncertainty mainly increased the crisp subset of false-positive cases: from 0 to 0.8 (R1) and from 1 to 2.4 (R2). The difference between crisp and fuzzy diagnostic performance was larger for the less experienced reader: sensitivity, specificity, PPV, NPV and accuracy were 90.0, 100, 100, 87.0 and 94.0% versus 90.0, 96.0, 97.1, 86.5 and 92.4% for R1 and 93.3, 95.0, 96.6, 90.5 and 94% versus 94.0, 88.0, 92.1, 90.7 and 91.6% for R2, respectively. Conclusion: Radiological diagnosis can be expressed as a fuzzy degree membership to weight the impact of readers’ uncertainty on crisp diagnostic performance. One potential application is to test the readers’ competency.