Normalizing Flow-Based Distribution Estimation of Pharmacokinetic Parameters in Dynamic Contrast-Enhanced Magnetic Resonance Imaging.

OBJECTIVE: The pharmacokinetic (PK) parameters estimated from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provide valuable information for clinical research and diagnosis. However, these estimated PK parameters suffer from many sources of variability. Thus, the estimation of the posterior distributions of these PK parameters could provide a way to simultaneously quantify the values and uncertainties of the PK parameters. Our objective is to develop an efficient and flexible method to more closely approximate and estimate the underlying posterior distributions of the PK parameters. METHODS: The normalizing flow model-based parameters distribution estimation neural network (FPDEN) is proposed to adaptively learn and estimate the posterior distributions of the PK parameters. The maximum likelihood estimation (MLE) loss is directly constructed based on the parameter distributions learned by the normalizing flow model, rather than pre-defined distributions. RESULTS: Experimental analysis shows that the proposed method can improve parameter estimation accuracy. Moreover, the uncertainty derived from the parameter distribution constitutes an effective indicator to exclude unreliable parametric results. A successful demonstration is the improved classification performance of the glioma World Health Organization (WHO) grading task, specifically in terms of distinguishing between low and high grades, as well as between Grade III and Grade IV. CONCLUSION: The FPDEN method offers improved accuracy for estimation of PK parameters and boosts the performance of the glioma grading task. SIGNIFICANCE: By enhancing the precision and reliability of DCE-MRI, the proposed method promotes its further applications in clinical practice.

Using deep learning to accelerate magnetic resonance measurements of molecular exchange.

Real-time monitoring and quantitative measurement of molecular exchange between different microdomains are useful to characterize the local dynamics in porous media and biomedical applications of magnetic resonance. Diffusion exchange spectroscopy (DEXSY) is a noninvasive technique for such measurements. However, its application is largely limited by the involved long acquisition time and complex parameter estimation. In this study, we introduce a physics-guided deep neural network that accelerates DEXSY acquisition in a data-driven manner. The proposed method combines sampling pattern optimization and physical parameter estimation into a unified framework. Comprehensive simulations and experiments based on a two-site exchange system are conducted to demonstrate this new sampling optimization method in terms of accuracy, repeatability, and efficiency. This general framework can be adapted for other molecular exchange magnetic resonance measurements.

2D probabilistic undersampling pattern optimization for MR image reconstruction.

With 3D magnetic resonance imaging (MRI), a tradeoff exists between higher image quality and shorter scan time. One way to solve this problem is to reconstruct high-quality MRI images from undersampled k-space. There have been many recent studies exploring effective k-space undersampling patterns and designing MRI reconstruction methods from undersampled k-space, which are two necessary steps. Most studies separately considered these two steps, although in theory, their performance is dependent on each other. In this study, we propose a joint optimization model, trained end-to-end, to simultaneously optimize the undersampling pattern in the Fourier domain and the reconstruction model in the image domain. A 2D probabilistic undersampling layer was designed to optimize the undersampling pattern and probability distribution in a differentiable manner. A 2D inverse Fourier transform layer was implemented to connect the Fourier domain and the image domain during the forward and back propagation. Finally, we discovered an optimized relationship between the probability distribution of the undersampling pattern and its corresponding sampling rate. Further testing was performed using 3D T1-weighted MR images of the brain from the MICCAI 2013 Grand Challenge on Multi-Atlas Labeling dataset and locally acquired brain 3D T1-weighted MR images of healthy volunteers and contrast-enhanced 3D T1-weighted MR images of high-grade glioma patients. The results showed that the recovered MR images using our 2D probabilistic undersampling pattern (with or without the reconstruction network) significantly outperformed those using the existing start-of-the-art undersampling strategies for both qualitative and quantitative comparison, suggesting the advantages and some extent of the generalization of our proposed method.

Convolutional neural network for accelerating the computation of the extended Tofts model in dynamic contrast-enhanced magnetic resonance imaging.

Quantitative physiological parameters can be obtained from nonlinear pharmacokinetic models, such as the extended Tofts (eTofts) model, applied to dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). However, the computation of such nonlinear models is time consuming. The aim of this study was to develop a convolutional neural network (CNN) for accelerating the computation of fitting eTofts model without sacrificing agreement with conventional nonlinear-least-square (NLLS) fitting. This was a retrospective study, which included 13 patients with brain glioma for training (75%) and validation (25%), and 11 patients (three glioma, four brain metastases, and four lymphoma) for testing. CAIPIRINHA-Dixon-TWIST DCE-MRI and double flip angle T1 map acquired at 3 T were used. A CNN with both local pathway and global pathway modules was designed to estimate the eTofts model parameters, the volume transfer constant (Ktrans ), blood volume fraction (vp ), and volume fraction of extracellular extravascular space (ve ), from DCE-MRI data of tumor and normal-appearing voxels. The CNN was trained on mixed dataset consisting of synthetic and patient data. The CNN result and computation speed were compared with NLLS fitting. The robustness to noise variations and generalization to brain metastases and lymphoma data were also evaluated. Statistical tests used were Student's t test on mean absolute error, concordance correlation coefficient (CCC), and normalized root mean squared error. Including global pathway modules in the CNN and training the network with mixed data significantly (p < 0.05) improved the CNN performance. Compared with NLLS fitting, CNN yields an average CCC greater than 0.986 for Ktrans , greater than 0.965 for vp , and greater than 0.948 for ve . The CNN accelerated computation speed approximately 2000 times compared to NLLS, showed robustness to noise (signal-to-noise ratio >34.42 dB), and had no significant (p > 0.21) difference applied to brain metastases and lymphoma data. In conclusion, the proposed CNN to estimate eTofts parameters showed comparable result as NLLS fitting while significantly reducing the computation time. LEVEL OF EVIDENCE: 3 TECHNICAL EFFICACY STAGE: 1.