Paquet R pour l'estimation d'un mélange de lois de Student multivariées à échelles multiples

National audienceL'utilisation d'un modèle de mélange de lois est une approche statistique classique en classification non-supervisée. Un mélange fréquemment utilisé pour sa simplicité est le mélange gaussien. Cependant, un tel modèle est sensible aux données atypiques. Pour remédier à cela, nous présentons ici le mélange de lois de Student multivariées à échelles multiples, que nous sommes en train d'incorporer au sein d'un paquet R. Ces lois peuvent gérer des queues de lourdeurs différentes selon les directions alors que les lois gaussiennes et les lois de Student multivariées standards sont contraintes à être symétriques

Multivariate Multi-scaled Student Distributions : brain tumor characterization from multiparametric MRI

International audienceBrain tumor characterization is very useful for patients treatment, but it can be time-consuming for medical experts. Furthermore, the reference method to characterize tissues is biopsy which is a local and invasive technique. Because of this, there is a huge interest for automatic and non-invasive approaches in order to characterize tumor. In this study we use a statistical model-based method to classify multiparametric MRI of brain rat tumors, which allows data quality control with atypical observations detection, and may provide a dictionary of tumor signatures. A previous study, [1], used a Gaussian mixture model to characterize pixels inside tumors. With this model, the observations are gathered into classes resulting from Gaussian distributions. However, this model is sensitive to outliers which degrade the relevance of the obtained groups. And inside a tumor, there could be a huge variability and so a lot of outliers. To account for this biological variability, we propose to use generalized Student distributions : the multivariate multi-scaled Student distributions (MMSD, [2]). The MMSD distribution extends the standard multivariate Student distribution by using the Gaussian scale mixture representation of Student distributions. This representation allows us to introduce multi-dimensional weights, which control different tail thickness of the distribution for each dimension, and provide a way to detect outlier data. In this way, we obtain a finer regulation of the influence of atypical data on the groups shapes, and so a greater flexibility of the clustering model. We use an Expectation-Maximization algorithm (EM) to adjust a MMSD mixture on brain tumor MRI. The number of classes inside the mixture is selected by minimizing the Bayesian information criterion (BIC). Our sample consists of healthy rats (n=8) and 4 groups of rats bearing a brain tumor model (n=8 per group), and 5 quantitative MRI parameter maps for each rat. We adjust a MMSD mixture on the healthy sample to detect tumor area in the tumor sample through the multi-dimensional weights. Then we characterize the tumor areas with another MMSD mixture and build a tumor dictionary which discriminates the 4 tumor

Multivariate Multi-scaled Student Distributions : brain tumor characterization from multiparametric MRI

International audienceBrain tumor characterization is very useful for patients treatment, but it can be time-consuming for medical experts. Furthermore, the reference method to characterize tissues is biopsy which is a local and invasive technique. Because of this, there is a huge interest for automatic and non-invasive approaches in order to characterize tumor. In this study we use a statistical model-based method to classify multiparametric MRI of brain rat tumors, which allows data quality control with atypical observations detection, and may provide a dictionary of tumor signatures. A previous study, [1], used a Gaussian mixture model to characterize pixels inside tumors. With this model, the observations are gathered into classes resulting from Gaussian distributions. However, this model is sensitive to outliers which degrade the relevance of the obtained groups. And inside a tumor, there could be a huge variability and so a lot of outliers. To account for this biological variability, we propose to use generalized Student distributions : the multivariate multi-scaled Student distributions (MMSD, [2]). The MMSD distribution extends the standard multivariate Student distribution by using the Gaussian scale mixture representation of Student distributions. This representation allows us to introduce multi-dimensional weights, which control different tail thickness of the distribution for each dimension, and provide a way to detect outlier data. In this way, we obtain a finer regulation of the influence of atypical data on the groups shapes, and so a greater flexibility of the clustering model. We use an Expectation-Maximization algorithm (EM) to adjust a MMSD mixture on brain tumor MRI. The number of classes inside the mixture is selected by minimizing the Bayesian information criterion (BIC). Our sample consists of healthy rats (n=8) and 4 groups of rats bearing a brain tumor model (n=8 per group), and 5 quantitative MRI parameter maps for each rat. We adjust a MMSD mixture on the healthy sample to detect tumor area in the tumor sample through the multi-dimensional weights. Then we characterize the tumor areas with another MMSD mixture and build a tumor dictionary which discriminates the 4 tumor

Paquet R pour l'estimation d'un mélange de lois de Student multivariées à échelles multiples

National audienceL'utilisation d'un modèle de mélange de lois est une approche statistique classique en classification non-supervisée. Un mélange fréquemment utilisé pour sa simplicité est le mélange gaussien. Cependant, un tel modèle est sensible aux données atypiques. Pour remédier à cela, nous présentons ici le mélange de lois de Student multivariées à échelles multiples, que nous sommes en train d'incorporer au sein d'un paquet R. Ces lois peuvent gérer des queues de lourdeurs différentes selon les directions alors que les lois gaussiennes et les lois de Student multivariées standards sont contraintes à être symétriques

Development of a multiparametric voxel-based magnetic resonance imaging biomarker for early cancer therapeutic response assessment

Quantitative magnetic resonance imaging (MRI)-based biomarkers, which capture physiological and functional tumor processes, were evaluated as imaging surrogates of early tumor response following chemoradiotherapy in glioma patients. A multiparametric extension of a voxel-based analysis, referred as the parametric response map (PRM), was applied to quantitative MRI maps to test the predictive potential of this metric for detecting response. Fifty-six subjects with newly diagnosed high-grade gliomas treated with radiation and concurrent temozolomide were enrolled in a single-site prospective institutional review board-approved MRI study. Apparent diffusion coefficient (ADC) and relative cerebral blood volume (rCBV) maps were acquired before therapy and 3 weeks after therapy was initiated. Multiparametric PRM (mPRM) was applied to both physiological MRI maps and evaluated as an imaging biomarker of patient survival. For comparison, single-biomarker PRMs were also evaluated in this study. The simultaneous analysis of ADC and rCBV by the mPRM approach was found to improve the predictive potential for patient survival over single PRM measures. With an array of quantitative imaging parameters being evaluated as biomarkers of therapeutic response, mPRM shows promise as a new methodology for consolidating physiologically distinct imaging parameters into a single interpretable and quantitative metric

Structured Mixture of Linear Mappings in High Dimension

When analyzing data with complex structures such as high dimensionality and non-linearity, one often needs sophisticated models to capture the intrinsic complexity. However, practical implementation using these models could be difficult. Striking a balance between parsimony and model flexibility is essential to tackle data complexity while maintaining feasibility and satisfactory prediction performances. In this work, we proposed the use of Structured Mixture of Gaussian Locally Linear Mapping (SMoGLLiM) when there is a need to use high-dimensional predictors to predict low-dimensional responses and there is a possibility that the underlying associations could be heterogeneous or non-linear. Besides using mixtures of linear associations to approximate non-linear patterns locally and using inverse regression to mitigate the complications due to high-dimensional predictors, SMoGLLiM also aims at achieving robustness by adopting cluster-size constraints and trimming abnormal samples. Its hierarchical structure enables covariance matrices and latent factors being shared across smaller clusters, which effectively reduce the number of parameters. An Expectation-Maximization (EM) algorithm is devised for parameter estimation and, with analytical solutions; the estimation process is computa-tionally efficient. Numerical results obtained from three real-world datasets demonstrate the flexibility and ability of SMoGLLiM in accommodating complex data structure. They include using high-dimensional face images to predict the parameters under which the images were taken, predicting the sucrose levels by the high-dimensional hyperspectral measurements obtained from different types of orange juice and a magnetic resonance vascular fingerprinting (MRvF) study in which researchers are interested at using the so-called MRv fingerprints at voxel level to predict the microvascular properties in brain. The three datasets bear different features and presents different types of challenges. For example , the size of the MRv fingerprint dataset demands special consideration to reduce computational burden. With the hierarchical structure of SMoGLLiM, we are able to adopt parallel computing techniques to reduce the model building time by 97%. These examples illustrate the wide range of applicability of SMoGLLiM on handling different kinds of complex data structure

Tumor classification and prediction using robust multivariate clustering of multiparametric MRI

International audienceIn neuro-oncology, the use of multiparametric MRI may better characterize brain tumor heterogeneity. To fully exploit multiparametric MRI (e.g. tumor classification), appropriate analysis methods are yet to be developed. In this work, we show on small animals data that advanced statistical learning approaches can help 1) in organizing existing data by detecting and excluding outliers and 2) in building a dictionary of tumor fingerprints from a clustering analysis of their microvascular features

Monitoring glioma heterogeneity during tumor growth using clustering analysis of multiparametric MRI data

International audienceSynopsis Brain tumor heterogeneity plays a major role during gliomas growth and for the tumors resistance to therapies. The goal of this study was to demonstrate the ability of clustering analysis applied to multiparametric MRI (mpMRI) data to summarize and quantify intralesional heterogeneity during tumor growth. A mpMRI dataset of rats bearing glioma was acquired during the tumor growth (5 maps, 8 animals and 6 time points). After co-registration of every MR data over time, a clustering analysis was performed using a Gaussian mixture distribution model. Although preliminary, our results show that clustering analysis of mpMRI has a great potential to monitor quantitatively intralesional heterogeneity during the growth of tumors. Introduction For tumor diagnosis, histology often remains the reference, but due to tumor heterogeneity, it is widely acknowledged that biopsies are not reliable. There is thus a strong interest in monitoring quantitatively intralesional brain tumor heterogeneity. MRI has demonstrated its ability to quantitatively map structural information like diiusion (ADC) as well as functional characteristics such as the blood volume (BVf), vessel size (VSI), the oxygen saturation of the tissue (StO), or the blood brain barrier permeability. In a recent study (1), these MR parameters were analyzed independently from each other to demonstrate the great potential of a multiparametric MR (mpMRI) protocol to monitor combined radio-and chemo-therapies. However, to summarize and quantify all the information contained in an mpMRI protocol while preserving information about tumor heterogeneity, new methods to extract information need to be developed. The goal of this study is to demonstrate the ability of clustering analysis (2) applied to longitudinal mpMRI to summarize and quantify intralesional heterogeneity during tumor growth. Methods Animal model: The local IRB committee approved all studies. 9L tumors were implanted in 8 rats and imaging was performed every 2 days between day 7 and day 17 post tumor implantation on a 4.7T Bruker system (D7, D9, D11, D13, D15 and D17; respectively). The following mpMRI protocol was acquired at each MR session: a T2-weighted spin echo sequence to obtain structural information over the whole brain, a diiusion weighted EPI sequence to map the Apparent Diiusion Coeecient (ADC) and multiple spin/gradient echo sequences to map T2 and T2*. A Gradient Echo Sampling of the FID and Spin Echo (GESFIDE) sequence was acquired pre-and post-injection of USPIO (133 µmol/kg). A dynamic contrast enhancing sequence was acquired using a RARE sequence (T1w images; n=15, 15.6 sec per image). After the acquisition of 4 images, a bolus of gadolinium-chelate was administered (100µmol/kg). Parametric maps: for each MR session, BVf and VSI maps were computed using the approach described in (3), StO using the method described in (4) and the vessel permeability maps (Perm) was calculated as the percentage of enhancement (voxel-wise) within 3 min post injection of gadolinium (cf. g1-a). Co-registration: each parametric map of each MR session was co-registered to that acquired at the previous time point using rigid registration (SPM toolbox and Matlab). ROI: tumor was manually delineated using the T2w images (Tumor-ROI; Red line in g1-a). Cluster analysis: parameter values were centered and normalized. Then, a Gaussian mixture distribution (Matlab function called: tgmdist) was use to performed the clustering analysis of all voxels included in the tumor-ROI. The number of classes inside the mixture was selected by minimizing the Bayesian information criterion (BIC). Results Firstly, we performed the clustering analysis 9 times using 1 to 9 classes. The optimal classes number, deened by the BIC was 5. Each cluster may be seen as a tissue type, as described Fig.1-E. The result of the clustering analysis is illustrated Fig1-A for one animal. For each of the ve clusters (labeled K1 to K5), the evolution of the mean cluster volume over the entire population of tumor is presented Fig 1-B. Note that the sum of the ve cluster volumes represents the whole tumor volume. Fig.1-C illustrates the longitudinal evolution of the 5 clusters in 2 animals with diierent tumor growth rate (slow on the top and high on the bottom). Although the cluster analysis analyzed every voxel independently from each other, one can see that the clustering results are spatially consistent at 1 time point but also over time. Indeed, clusters are spatially grouped: for example, the green cluster is mostly located in the center of the tumor (Fig1-C). Our result shows a diierence in cluster composition between the slow and the high growth rate tumors (Fig.1-C,D). For example, in the slow growth rate tumor, the yellow cluster takes more and more space in the tumor overtime (up to 49% at D17) whereas, in the high growth rate tumor, it is the green one. The main diierence between the yellow and the green cluster is the strong reduction in StO in the green cluster versus the yellow cluster (cf. Fig.1-E). Conclusions To our knowledge, it is a rst study demonstrating the feasibility of performing a clustering analysis on mpMRI data to monitor the evolution of brain tumor heterogeneity in vivo. This approach highlights the type of tissue, which mostly contributes to the development of the tumor. The composition in tissue type could be used to reene the evaluation of chemo and radiotherapies and could contribute to improve tumor prognosis

Fully Automatic Lesion Localization and Characterization: Application to Brain Tumors Using Multiparametric Quantitative MRI Data

International audienceWhen analyzing brain tumors, two tasks are intrinsically linked, spatial localization and physiological characterization of the lesioned tissues. Automated data-driven solutions exist, based on image segmentation techniques or physiological parameters analysis, but for each task separately, the other being performed manually or with user tuning operations. In this work, the availability of quantitative magnetic resonance (MR) parameters is combined with advanced multivariate statistical tools to design a fully automated method that jointly performs both localization and characterization. Non trivial interactions between relevant physiological parameters are captured thanks to recent generalized Student distributions that provide a larger variety of distributional shapes compared to the more standard Gaussian distributions. Probabilistic mixtures of the former distributions are then considered to account for the different tissue types and potential heterogeneity of lesions. Discriminative multivariate features are extracted from this mixture modelling and turned into individual lesion signatures. The signatures are subsequently pooled together to build a statistical fingerprint model of the different lesion types that captures lesion characteristics while accounting for inter-subject variability. The potential of this generic procedure is demonstrated on a data set of 53 rats, with 36 rats bearing 4 different brain tumors, for which 5 quantitative MR parameters were acquired

Image Registration for Quantitative Parametric Response Mapping of Cancer Treatment Response

AbstractImaging biomarkers capable of early quantification of tumor response to therapy would provide an opportunity to individualize patient care. Image registration of longitudinal scans provides a method of detecting treatment-associated changes within heterogeneous tumors by monitoring alterations in the quantitative value of individual voxels over time, which is unattainable by traditional volumetric-based histogram methods. The concepts involved in the use of image registration for tracking and quantifying breast cancer treatment response using parametric response mapping (PRM), a voxel-based analysis of diffusion-weighted magnetic resonance imaging (DW-MRI) scans, are presented. Application of PRM to breast tumor response detection is described, wherein robust registration solutions for tracking small changes in water diffusivity in breast tumors during therapy are required. Methodologies that employ simulations are presented for measuring expected statistical accuracy of PRM for response assessment. Test-retest clinical scans are used to yield estimates of system noise to indicate significant changes in voxel-based changes in water diffusivity. Overall, registration-based PRM image analysis provides significant opportunities for voxel-based image analysis to provide the required accuracy for early assessment of response to treatment in breast cancer patients receiving neoadjuvant chemotherapy