Task 2: 3D tissue complication probability (NTCP) models
Medical context : Prostate Cancer RadioTherapy (PCRT)
Radiotherapy is one of the standard treatment of localized prostate cancer. The main challenge in Prostate Cancer RadioTherapy (PCRT) is to deliver the prescribed dose to the clinical target (prostate and seminal vesicles) while minimizing the dose to the Organs At Risk (OAR) of toxicity -related events. Intensity Modulated RadioTherapy (IMRT)  is the reference conformal radiotherapy technique which has improved the dose delivery reaching complex tumor shapes. However, the underlying toxicity dose-volume-effect relationships are still to be unraveled in order to adapt specifically the treatment to each patient and therefore decrease toxicity . Several issues are still to be tackled especially regarding the customization of the treatment by introducing individual specificities with the goal of improving local tumor control and decreasing toxicity.
Prediction of rectal bleeding in prostate cancer radiotherapy
Rectal bleeding is one of the most important sequelae after prostate cancer radiotherapy and impacts the patient's quality of life . The potential secondary effects due to the delivered dose to the OAR are far from being completely explained . Therefore, unraveling the underlying local dose–volume effect toxicity relationships and identifying patients at higher risk, appears as a cornerstone in further definitions of constraints for personalized IMRT planning.
State of the Art
In case of rectal toxicity, different studies have shown a correlation between dose, volume, and secondary effects [5-6]. However, most of the proposed models have been solely based on the dose–volume histograms (DVH) such as the Normal Tissue Complication Probability (NTCP) model , thereby loosing spatial information. Other approaches have been used. With principal component analysis the most relevant DVH bins are extracted and used to predict late toxicity . These methods do not perform a formal classification exploiting the spatial characteristics of the dose distributions since they considered the organs as having homogeneous radio-sensitivity. Buettner et al. [9-10] addressed the issue of spatial information loss. In , a classification approach based on locally connected neural network using a two-dimensional dose-surface maps was performed. In , they proposed a parameterized representation of the dose to describe its geometrical properties, such as the eccentricity, and its lateral and longitudinal extent which still remains approximative in terms of spatial location. New methods aimed at jointly taking advantage of the Three-Dimensional (3D) dose distributions, unraveling the subtle correlation between local dose and toxicity at a voxel level to classify patients at risk, are still to be devised.
Performing classification by simultaneously exploiting the 3D signal across a population is challenging because the inter-individual anatomical variability leading to a misalignment of information. To cope with this issue, non-rigid registration methods have been employed in order to map all the data to a common coordinate system where voxel analysis may be meaningful in terms of spatial localization . Following this idea, previous classification approaches exploiting the 3D signal across a given population have been proposed. For instance, Principal Component Analysis (PCA) was used by Fripp et al.  to discriminate Alzheimer’s disease and normal elderly control participants based on non-rigidly registered 3D Positron Emission Tomography (PET) images.
Our first objective is to propose a new variable computed with independent component analysis to predict late rectal toxicity following prostate cancer radiotherapy and to compare its performance to classic models (logistic regression).
Our second objective is to propose new methods able to predict late rectal bleeding following high-dose prostate cancer radiotherapy by fully exploit the tri-dimensional planned Dose Distribution (3DpDD) to study the correlation with rectal toxicity.
Independent Component analysis to predict rectal toxicity
Clinical data and dose-volume histograms were prospectively collected from 544 patients having received 3DCRT for prostate cancer with at least two years of follow-up. The serie was split into training and validation cohort.
Independent component analysis (ICA) was trained to predict the risk of 4-years G>= 2 rectal bleeding. The performance of all the models was assessed by computing the area under the receiving operating characteristic curve (AUC). The database was randomly split into a training cohort (65% of patients) and a validation cohort (35%).
Firstly, ICA was trained on the training cohort using DVH. The resulting ICA variables were computed according to the entired DVH. Then, ICA variables and additional clinical parameters that contribute to improve prediction (age, history of diabetes, anticoagulant treatment and abdominal surgery) were added in a logistic regression.
Clinical parameters were found to be predictive of rectal bleeding. The mean area under the receiving operating curve for our proposed approach was 0.71. The mean AUC values for the logistic regression based solely on DVH was 0.64.
Wilcoxon test was performed to compare the different predictive capabilities of each model. It appears that our new variable improved significatively (pvalue=0.044) the well-known logistic regression based solely on DVH and clinical variables.
Our proposed new variable may be a useful new predictive variable to improve prediction of late rectal toxicity.
Feature extraction and classification using 3D planned dose distributions
1. Data and registration
A total of 63 patients having received a dose of 80 Gy in the prostate by IMRT have been included in the study. Twelve of them presented rectal bleeding (Grade>1) at two years. Only the 3D pDD within the rectum was analyzed. Patient's planned CT and dose distributions were elastically registered with the demons algorithm , on a single coordinate system by combining the CTs and organs delineations as explained in .
We introduce different approaches which jointly taking advantage of the tri-dimensional pDD to classify patients at high risks of presenting rectal bleeding.
First approach: Feature extraction using blind source separation approaches
We studied the efficiency of principal component analysis (PCA) for feature extraction and classification. We compared different possibilities for selecting the most relevant features (sequential and combinatory). An inherent problem of outcome modeling is that the analysis with a large number of variables is computationally expensive. Many features may be extracted from data to provide new representations of the population's anatomy. The main goal of features selection is to find an optimal subset from a full set of features which provide relevant information to match or improve the performances of classifiers. The performance of the proposed methods is evaluated by computing the sensitivity (Se) and the specificity (Sp).The Se, represents the percentage of patients with rectal bleeding who are correctly identified as having toxicity, and the Sp defines the percentage of patients without rectal bleeding who are correctly identified as not having toxicity. Figure 1 displays the performance of the classier as a function of the number, n, of exploited features when using (a) the sequential approach and (b) the combinatory approach. When using just the best feature (namely the 16th), 92% of rectal bleeding and 80% of non-rectal bleeding patients have been well classified (Se=0.92 and Sp=0.8). The results of accuracy compared to the number of exploited features are represented in figure 2. This work was presented at RITS (Recherche en Imagerie et Technologies pour la Santé) conference, 2013 and published in IRBM, 2013.
Figure 2. Accuracy, sensitivity and specificity as function of the number of exploited features using: (a) sequential approach, and (b) combinatory approach.
Second approach: subspaces representation of both rectal and non rectal bleeding patients
We seek for two bases of vectors built with the tri-dimensional pDD from a population of bleeding and non-bleeding patients,respectively. Then, a patient could be classified according to its distance to the subspaces spanned by both bases.
To obtain these two subspaces, we firstly used Multiway Deterministic Analysis (DMA) technique which aims at finding two bases of vectors from 3D dose distributions of bleeders and non-bleeders patients, respectively, from a Canonical Polyadic (CP) decomposition. Tests on real clinical data demonstrated a 0.76 Se and a 0,89 Sp. It opens the way for potential applications to plan the dose distribution. For a thorough evaluation, we also compared CP-DMA with the Lyman-Kurcher-Burman (LKB) NTCP model. Indeed, it is important to compare our approach to current standard techniques. The Receiver operating characteristic curve (ROC) and the area under the curve(AUC) at the output of the CP-DMA algorithm and the NTCP model are given in figure 3. This work was published to Medical Engineering Physics, 2015.
Secondly, we tried to use blind source approaches technique like PCA or ICA instead of DMA technique to perform the two bases of vectors. This work was presented at the European SocieTy for Radiotherapy and Oncology (ESTRO) conference, 2013. We are writing a paper about this work.
Figure 3. ROC and AUC to predict 2-year grade>1 rectal bleeding for LKB-NTCP model and CP-DMA
Third, we proposed a new classification method for three-dimensional individuals' doses, based on a new semi-nonnegative ICA algorithmaimed at classifying rectal bleeding and non rectal bleeding patients from a population treated for prostate cancer. In order to improve the extraction quality, we exploited this nonnegativity property, giving rise to what we call hereafter the Semi-Nonnegative ICA (SN-ICA). In our context, the components of the mixing matrixcorrespond also to the positive character of dose (which means delivered energy per mass unit at each voxel). This work was published to Journal of Biomedical and Health Informatics 2014.
We also proposed a new method named Discriminant Nonnegative Matrix Factorization (DNMF). This method is based on Non-negative Matrix Factorization and Fisher’s linear discriminant criterion. The proposed method differs from the classical NMF by choosing two subspaces that maximize the distance between the means of the two classes (3DpDD of rectal bleeding versus 3DpDD non rectal bleeding) while minimizing the variance within each class. The classification results were 0.77 sensitivity and 0.82 specificity. This work will be presented at RITS (Recherche en Imagerie et Technologies pour la Santé) conference, in march 2015 and will be publish in IRBM, 2015.
Representative features are extracted and used as inputs of a simple classifier with low computational cost comparing two distances. Promising very high performance values were obtained. Forthcoming works include the use of a larger database of patients in order to confirm the efficiency of the method.
Finally, these preliminary studies focused on the tri-dimensional pDD in the rectum in order to produce a new efficient predictive models of rectal bleeding after prostate radiotherapy. The proposed approaches jointly uses 3D spatial patterns of dose of several patients sharing the same characteristics. pDD and late rectal bleeding appear to be correlated.
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