Convex-Optimization-Based Compartmental Pharmacokinetic Analysis for Prostate Tumor Characterization Using DCE-MRI

A weakly supervised NMF method to decipher molecular subtype-related dynamic patterns in breast DCE-MR images

Objective. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important imaging modality for breast cancer diagnosis. Intratumoral heterogeneity causes a major challenge in the interpretation of breast DCE-MRI. Previous studies have introduced decomposition methods on DCE-MRI to reveal intratumoral heterogeneity by analyzing distinct dynamic patterns within each tumor. However, these methods estimated the dynamic patterns and their corresponding component coefficients in an unsupervised manner, without considering any clinically relevant information.Approach. To decipher molecular subtype-related dynamic patterns, we propose a weakly supervised nonnegative matrix factorization method (WSNMF), which is able to decompose the pixel kinetics of DCE-MRI with image-level subtype labels. The WSNMF is developed based on a discriminant nonnegative matrix factorization (NMF) to utilize coarse-grained subtype information, in which between- and within-class scatters are defined on the mean vector of component coefficients over all pixels in each tumor, rather than directly on the vector of component coefficients of each pixel.Main results. Experiments demonstrated that the dynamic patterns identified by WSNMF had superior performance in distinguishing between luminal A and the other subtype tumors. The classification performance was evaluated using the area under the receiver operating characteristic curve (AUC). WSNMF yielded better classification performance (AUC = 0.822) than other heterogeneity analysis methods, including two partitioning-based methods (KPC with AUC = 0.697 and TTP with AUC = 0.760) and two unsupervised decomposition-based methods (PCA with AUC = 0.774 and NMF with AUC = 0.797).Significance. Our method adds a valuable new perspective into DCE-MRI decomposition-based heterogeneity analysis by taking advantage of intrinsic tumor characteristics to improve the diagnosis of breast cancer.

A deep matrix factorization framework for identifying underlying tissue-specific patterns of DCE-MRI: applications for molecular subtype classification in breast cancer

Objective.Breast cancer is heterogeneous in that different angiogenesis and blood flow characteristics could be present within a tumor. The pixel kinetics of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can assume several distinct signal patterns related to specific tissue characteristics. Identification of the latent, tissue-specific dynamic patterns of intratumor heterogeneity can shed light on the biological mechanisms underlying the heterogeneity of tumors.Approach.To mine this information, we propose a deep matrix factorization-based dynamic decomposition (DMFDE) model specifically designed according to DCE-MRI characteristics. The time-series imaging data were decomposed into tissue-specific dynamic patterns and their corresponding proportion maps. The image pixel matrix and the reference matrix of population-level kinetics obtained by clustering the dynamic signals were used as the inputs. Two multilayer neural network branches were designed to collaboratively project the input matrix into a latent dynamic pattern and a dynamic proportion matrix, which was justified using simulated data. Clinical implications of DMFDE were assessed by radiomics analysis of proportion maps obtained from the tumor/parenchyma region for classifying the luminal A subtype.Main results.The decomposition performance of DMFDE was evaluated by the root mean square error and was shown to be better than that of the conventional convex analysis of mixtures (CAM) method. The predictive model withK = 3, 4, and 5 dynamic proportion maps generated AUC values of 0.780, 0.786 and 0.790, respectively, in distinguishing between luminal A and nonluminal A tumors, which are better than the CAM method (AUC = 0.726). The combination of statistical features from images with different proportion maps has the highest prediction value (AUC = 0.813), which is significantly higher than that based on CAM.Conclusion.This proposed method identified the latent dynamic patterns associated with different molecular subtypes, and radiomics analysis based on the pixel compositions of the uncovered dynamic patterns was able to determine molecular subtypes of breast cancer.

Spatiotemporal Flexible Sparse Reconstruction for Rapid Dynamic Contrast-enhanced MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a tissue perfusion imaging technique. Some versatile free-breathing DCE-MRI techniques combining compressed sensing (CS) and parallel imaging with golden-angle radial sampling have been developed to improve motion robustness with high spatial and temporal resolution. These methods have demonstrated good diagnostic performance in clinical setting, but the reconstruction quality will degrade at high acceleration rates and overall reconstruction time remains long. In this paper, we proposed a new parallel CS reconstruction model for DCE-MRI that enforces flexible weighted sparse constraint along both spatial and temporal dimensions. Weights were introduced to flexibly adjust the importance of time and space sparsity, and we derived a fast-thresholding algorithm which was proven to be simple and efficient for solving the proposed reconstruction model. Results on both the brain tumor DCE and liver DCE show that, at relatively high acceleration factor of fast sampling, lowest reconstruction error and highest image structural similarity are obtained by the proposed method. Besides, the proposed method achieves faster reconstruction for liver datasets and better physiological measures are also obtained on tumor images.

Nonnegative Blind Source Separation for Ill-Conditioned Mixtures via John Ellipsoid

Nonnegative blind source separation (nBSS) is often a challenging inverse problem, namely, when the mixing system is ill-conditioned. In this work, we focus on an important nBSS instance, known as hyperspectral unmixing (HU) in remote sensing. HU is a matrix factorization problem aimed at factoring the so-called endmember matrix, holding the material hyperspectral signatures, and the abundance matrix, holding the material fractions at each image pixel. The hyperspectral signatures are usually highly correlated, leading to a fast decay of the singular values (and, hence, high condition number) of the endmember matrix, so HU often introduces an ill-conditioned nBSS scenario. We introduce a new theoretical framework to attack such tough scenarios via the John ellipsoid (JE) in functional analysis. The idea is to identify the maximum volume ellipsoid inscribed in the data convex hull, followed by affinely mapping such ellipsoid into a Euclidean ball. By applying the same affine mapping to the data mixtures, we prove that the endmember matrix associated with the mapped data has condition number 1, the lowest possible, and that these (preconditioned) endmembers form a regular simplex. Exploiting this regular structure, we design a novel nBSS criterion with a provable identifiability guarantee and devise an algorithm to realize the criterion. Moreover, for the first time, the optimization problem for computing JE is exactly solved for a large-scale instance; our solver employs a split augmented Lagrangian shrinkage algorithm with all proximal operators solved by closed-form solutions. The competitiveness of the proposed method is illustrated by numerical simulations and real data experiments.

The Application of Radiomics in Breast MRI: A Review

Breast cancer has been a worldwide burden of women's health. Although concerns have been raised for early diagnosis and timely treatment, the efforts are still needed for precision medicine and individualized treatment. Radiomics is a new technology with immense potential to obtain mineable data to provide rich information about the diagnosis and prognosis of breast cancer. In our study, we introduced the workflow and application of radiomics as well as its outlook and challenges based on published studies. Radiomics has the potential ability to differentiate between malignant and benign breast lesions, predict axillary lymph node status, molecular subtypes of breast cancer, tumor response to chemotherapy, and survival outcomes. Our study aimed to help clinicians and radiologists to know the basic information of radiomics and encourage cooperation with scientists to mine data for better application in clinical practice.

Radiomic analysis of imaging heterogeneity in tumours and the surrounding parenchyma based on unsupervised decomposition of DCE-MRI for predicting molecular subtypes of breast cancer

OBJECTIVES

This study aimed to predict the molecular subtypes of breast cancer via intratumoural and peritumoural radiomic analysis with subregion identification based on the decomposition of contrast-enhanced magnetic resonance imaging (DCE-MRI).

METHODS

The study included 211 women with histopathologically confirmed breast cancer. We utilised a completely unsupervised convex analysis of mixtures (CAM) method by unmixing dynamic imaging series from heterogeneous tissues. Each tumour and the surrounding parenchyma were thus decomposed into multiple subregions, representing different vascular characterisations, from which radiomic features were extracted. A random forest model was trained and tested using a leave-one-out cross-validation (LOOCV) method to predict breast cancer subtypes. The predictive models from tumoural and peritumoural subregions were fused for classification.

RESULTS

Tumour and peritumour DCE-MR images were decomposed into three compartments, representing plasma input, fast-flow kinetics, and slow-flow kinetics. The tumour subregion related to fast-flow kinetics showed the best performance among the subregions for differentiating between patients with four molecular subtypes (area under the receiver operating characteristic curve (AUC) = 0.832), exhibiting an AUC value significantly (p < 0.0001) higher than that obtained with the entire tumour (AUC = 0.719). When the tumour- and parenchyma-based predictive models were fused, the performance, measured as the AUC, increased to 0.897; this value was significantly higher than that obtained with other tumour partition methods.

CONCLUSIONS

Radiomic analysis of intratumoural and peritumoural heterogeneity based on the decomposition of image time-series signals has the potential to more accurately identify tumour kinetic features and serve as a valuable clinical marker to enhance the prediction of breast cancer subtypes.

KEY POINTS

• Decomposition of image time-series signals has the potential to more accurately identify tumour kinetic features. • Fusion of intratumoural- and peritumoural-based predictive models improves the prediction of breast cancer subtypes.

Detection of Sources in Non-Negative Blind Source Separation by Minimum Description Length Criterion

While non-negative blind source separation (nBSS) has found many successful applications in science and engineering, model order selection, determining the number of sources, remains a critical yet unresolved problem. Various model order selection methods have been proposed and applied to real-world data sets but with limited success, with both order over- and under-estimation reported. By studying existing schemes, we have found that the unsatisfactory results are mainly due to invalid assumptions, model oversimplification, subjective thresholding, and/or to assumptions made solely for mathematical convenience. Building on our earlier work that reformulated model order selection for nBSS with more realistic assumptions and models, we report a newly and formally revised model order selection criterion rooted in the minimum description length (MDL) principle. Adopting widely invoked assumptions for achieving a unique nBSS solution, we consider the mixing matrix as consisting of deterministic unknowns, with the source signals following a multivariate Dirichlet distribution. We derive a computationally efficient, stochastic algorithm to obtain approximate maximum-likelihood estimates of model parameters and apply Monte Carlo integration to determine the description length. Our modeling and estimation strategy exploits the characteristic geometry of the data simplex in nBSS. We validate our nBSS-MDL criterion through extensive simulation studies and on four real-world data sets, demonstrating its strong performance and general applicability to nBSS. The proposed nBSS-MDL criterion consistently detects the true number of sources, in all of our case studies.