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Minkowski functionals: An MRI texture analysis tool for determination of the aggressiveness of breast cancer

Fox, Michael J.; Gibbs, Peter; Pickles, Martin D.


Michael J. Fox

Peter Gibbs

Martin D. Pickles


Purpose: This work aims to see whether Minkowski Functionals can be used to distinguish between cancer types before chemotherapy treatment has begun, and whether a response to treatment can be predicted by an initial scan alone. Methods: Fat-nulled T1w 3T DCE-MRI scans were taken of 100 cases of biopsy confirmed breast cancer and a series of binary images created on lesion containing slices. Minkowski Functionals were calculated for each binary image and the change in these values as the binary threshold was raised was described using 6th order polynomials. These polynomials were used to compare between patient sub-groups, for triple negative breast cancer (TNBC) status, chemotherapy response, biopsy grade, nodal status, and lymphovascular invasion status. Results: When using Minkowski Functionals statistically significant (p<0.05) differences were found between TNBC status, biopsy grade, and lymphovascular invasion status sub-groups for all methodologies. The analysis performance did not appear to be affected by the number of threshold steps used. Most notably, very strong differences (p≤0.01) were found between TNBC and other intrinsic subtype patients. When analysed with a binary logistic regression model, an AUC value of 0.917 (0.846 – 0.987, 95% CI) for TNBC classification was found. Conclusion: The method of texture analysis presented here provides a novel way to characterise tumours, and demonstrates clear differences between cancer groups which are detectable before treatment begins, and can help with treatment planning as a valuable prognosis tool.


Fox, M. J., Gibbs, P., & Pickles, M. D. (2016). Minkowski functionals: An MRI texture analysis tool for determination of the aggressiveness of breast cancer. Journal of magnetic resonance imaging : JMRI, 43(4), 903-910.

Acceptance Date Sep 15, 2015
Online Publication Date Oct 10, 2015
Publication Date Apr 1, 2016
Deposit Date Oct 21, 2015
Publicly Available Date Oct 27, 2022
Journal Journal of magnetic resonance imaging
Print ISSN 1053-1807
Electronic ISSN 1522-2586
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 43
Issue 4
Pages 903-910
Keywords Texture analysis; Breast cancer; Minkowski functionals; Contrast enhanced MRI; Image processing
Public URL
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Additional Information Authors' accepted manuscript of article published in: Journal of magnetic resonance imaging, 2016, v.43, issue 4.