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Background  The expending and invasive features of tumor nests could reflect the malignant biological behaviors of breast invasive ductal carcinoma. Useful information on cancer invasiveness hidden within tumor nests could be extracted and analyzed by computer image processing and big data analysis.    Methods  Tissue microarrays from invasive ductal carcinoma (n = 202) were first stained with cytokeratin by immunohistochemical method to clearly demarcate the tumor nests. Then an expert-aided computer analysis system was developed to study the mathematical and geometrical features of the tumor nests. Computer recognition system and imaging analysis software extracted tumor nests information, and mathematical features of tumor nests were calculated. The relationship between tumor nests mathematical parameters and patients' 5-year disease free survival was studied.    Results  There were 8 mathematical parameters extracted by expert-aided computer analysis system. Three mathematical parameters (number, circularity and total perimeter) with area under curve >0.5 and 4 mathematical parameters (average area, average perimeter, total area/total perimeter, average (area/perimeter)) with area under curve <0.5 in ROC analysis were combined into integrated parameter 1 and integrated parameter 2, respectively. Multivariate analysis showed that integrated parameter 1 ( P  = 0.040) was independent prognostic factor of patients' 5-year disease free survival. The hazard risk ratio of integrated parameter 1 was 1.454 (HR 95% CI [1.017–2.078]), higher than that of N stage (HR 1.396, 95% CI [1.125–1.733]) and hormone receptor status (HR 0.575, 95% CI [0.353–0.936]), but lower than that of histological grading (HR 3.370, 95% CI [1.125–5.364]) and T stage (HR 1.610, 95% CI [1.026 –2.527]).    Conclusions  This study indicated integrated parameter 1 of mathematical features (number, circularity and total perimeter) of tumor nests could be a useful parameter to predict the prognosis of early stage breast invasive ductal carcinoma.

Computer-Based Image Studies on Tumor Nests Mathematical Features of Breast Cancer and Their Clinical Prognostic Value