On feature extraction and classification in prostate cancer radiotherapy using tensor decompositions

External beam radiotherapy is commonly prescribed for prostate cancer. Although new radiation techniques allow high doses to be delivered to the target, the surrounding healthy organs (rectum and bladder) may suffer from irradiation, which might produce undesirable side-effects. Hence, the understanding of the complex toxicity dose-volume effect relationships is crucial to adapt the treatment, thereby decreasing the risk of toxicity. In this paper, we introduce a novel method to classify patients at risk of presenting rectal bleeding based on a Deterministic Multi-way Analysis (DMA) of three-dimensional planned dose distributions across a population. After a non-rigid spatial alignment of the anatomies applied to the dose distributions, the proposed method seeks for two bases of vectors representing bleeding and non bleeding patients by using the Canonical Polyadic (CP) decomposition of two fourth order arrays of the planned doses. A patient is then classified according to its distance to the subspaces spanned by both bases. A total of 99 patients treated for prostate cancer were used to analyze and test the performance of the proposed approach, named CP-DMA, in a leave-one-out cross validation scheme. Results were compared with supervised (linear discriminant analysis, support vector machine, K-means, K-nearest neighbor) and unsupervised (recent principal component analysis-based algorithm, and multidimensional classification method) approaches based on the registered dose distribution. Moreover, CP-DMA was also compared with the Normal Tissue Complication Probability (NTCP) model. The CP-DMA method allowed rectal bleeding patients to be classified with good specificity and sensitivity values, outperforming the classical approaches.