Direct parametric reconstruction from undersampled (k, t)-space data in dynamic contrast enhanced MRI

A Deep Learning-Based Framework for Highly Accelerated Prostate MR Dispersion Imaging

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) measures microvascular perfusion by capturing the temporal changes of an MRI contrast agent in a target tissue, and it provides valuable information for the diagnosis and prognosis of a wide range of tumors. Quantitative DCE-MRI analysis commonly relies on the nonlinear least square (NLLS) fitting of a pharmacokinetic (PK) model to concentration curves. However, the voxel-wise application of such nonlinear curve fitting is highly time-consuming. The arterial input function (AIF) needs to be utilized in quantitative DCE-MRI analysis. and in practice, a population-based arterial AIF is often used in PK modeling. The contribution of intravascular dispersion to the measured signal enhancement is assumed to be negligible. The MR dispersion imaging (MRDI) model was recently proposed to account for intravascular dispersion, enabling more accurate PK modeling. However, the complexity of the MRDI hinders its practical usability and makes quantitative PK modeling even more time-consuming. In this paper, we propose fast MR dispersion imaging (fMRDI) to effectively represent the intravascular dispersion and highly accelerated PK parameter estimation. We also propose a deep learning-based, two-stage framework to accelerate PK parameter estimation. We used a deep neural network (NN) to estimate PK parameters directly from enhancement curves. The estimation from NN was further refined using several steps of NLLS, which is significantly faster than performing NLLS from random initializations. A data synthesis module is proposed to generate synthetic training data for the NN. Two data-processing modules were introduced to improve the model's stability against noise and variations. Experiments on our in-house clinical prostate MRI dataset demonstrated that our method significantly reduces the processing time, produces a better distinction between normal and clinically significant prostate cancer (csPCa) lesions, and is more robust against noise than conventional DCE-MRI analysis methods.

Greybox: A hybrid algorithm for direct estimation of tracer kinetic parameters from undersampled DCE-MRI data

BACKGROUND

A variety of deep learning-based and iterative approaches are available to predict Tracer Kinetic (TK) parameters from fully sampled or undersampled dynamic contrast-enhanced (DCE) MRI data. However, both the methods offer distinct benefits and drawbacks.

PURPOSE

To propose a hybrid algorithm (named as 'Greybox'), using both model- as well as DL-based, for solving a multi-parametric non-linear inverse problem of directly estimating TK parameters from undersampled DCE MRI data, which is invariant to undersampling rate.

METHODS

The proposed algorithm was inspired by plug-and-play algorithms used for solving linear inverse imaging problems. This technique was tested for its effectiveness in solving the nonlinear ill-posed inverse problem of generating 3D TK parameter maps from four-dimensional (4D; Spatial + Temporal) retrospectively undersampled k-space data. The algorithm learns a deep learning-based prior using UNET to estimate theK trans $\mathbf {K_{trans}}$ andV p $\mathbf {V_{p}}$ parameters based on the Patlak pharmacokinetic model, and this trained prior was utilized to estimate the TK parameter maps using an iterative gradient-based optimization scheme. Unlike the existing DL models, this network is invariant to the undersampling rate of the input data. The proposed method was compared with the total variation-based direct reconstruction technique on brain, breast, and prostate DCE-MRI datasets for various undersampling rates using the Radial Golden Angle (RGA) scheme. For the breast dataset, an indirect estimation using the Fast Composite Splitting algorithm was utilized for comparison. Undersampling rates of 8 × $\times$ , 12 × $\times$ and 20 × $\times$ were used for the experiments, and the results were compared using the PSNR and SSIM as metrics. For the breast dataset of 10 patients, data from four patients were utilized for training (1032 samples), two for validation (752 samples), and the entire volume of four patients for testing. Similarly, for the prostate dataset of 18 patients, 10 patients were utilized for training (720 samples), five for validation (216 samples), and the whole volume of three patients for testing. For the brain dataset of nineteen patients, ten patients were used for training (3152 samples), five for validation (1168 samples), and the whole volume of four patients for testing. Statistical tests were also conducted to assess the significance of the improvement in performance.

RESULTS

The experiments showed that the proposed Greybox performs significantly better than other direct reconstruction methods. The proposed algorithm improved the estimatedK trans $\mathbf {K_{trans}}$ andV p $\mathbf {V_{p}}$ in terms of the peak signal-to-noise ratio by up to 3 dB compared to other standard reconstruction methods.

CONCLUSION

The proposed hybrid reconstruction algorithm, Greybox, can provide state-of-the-art performance in solving the nonlinear inverse problem of DCE-MRI. This is also the first of its kind to utilize convolutional neural network-based encodings as part of the plug-and-play priors to improve the performance of the reconstruction algorithm.

1H magnetic resonance spectroscopic imaging of deuterated glucose and of neurotransmitter metabolism at 7 T in the human brain

Impaired glucose metabolism in the brain has been linked to several neurological disorders. Positron emission tomography and carbon-13 magnetic resonance spectroscopic imaging (MRSI) can be used to quantify the metabolism of glucose, but these methods involve exposure to radiation, cannot quantify downstream metabolism, or have poor spatial resolution. Deuterium MRSI (2H-MRSI) is a non-invasive and safe alternative for the quantification of the metabolism of 2H-labelled substrates such as glucose and their downstream metabolic products, yet it can only measure a limited number of deuterated compounds and requires specialized hardware. Here we show that proton MRSI (1H-MRSI) at 7 T has higher sensitivity, chemical specificity and spatiotemporal resolution than 2H-MRSI. We used 1H-MRSI in five volunteers to differentiate glutamate, glutamine, γ-aminobutyric acid and glucose deuterated at specific molecular positions, and to simultaneously map deuterated and non-deuterated metabolites. 1H-MRSI, which is amenable to clinically available magnetic-resonance hardware, may facilitate the study of glucose metabolism in the brain and its potential roles in neurological disorders.

VTDCE-Net: A time invariant deep neural network for direct estimation of pharmacokinetic parameters from undersampled DCE MRI data

PURPOSE

To propose a robust time and space invariant deep learning (DL) method to directly estimate the pharmacokinetic/tracer kinetic (PK/TK) parameters from undersampled dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) data.

METHODS

DCE-MRI consists of 4D (3D-spatial + temporal) data and has been utilized to estimate 3D (spatial) tracer kinetic maps. Existing DL architecture for this task needs retraining for variation in temporal and/or spatial dimensions. This work proposes a DL algorithm that is invariant to training and testing in both temporal and spatial dimensions. The proposed network was based on a 2.5-dimensional Unet architecture, where the encoder consists of a 3D convolutional layer and the decoder consists of a 2D convolutional layer. The proposed VTDCE-Net was evaluated for solving the ill-posed inverse problem of directly estimating TK parameters from undersampled k - t $k-t$ space data of breast cancer patients, and the results were systematically compared with a total variation (TV) regularization based direct parameter estimation scheme. In the breast dataset, the training was performed on patients with 32 time samples, and testing was carried out on patients with 26 and 32 time samples. Translation of the proposed VTDCE-Net for brain dataset to show the generalizability was also carried out. Undersampling rates (R) of 8× , 12× , and 20× were utilized with PSNR and SSIM as the figures of merit in this evaluation. TK parameter maps estimated from fully sampled data were utilized as ground truth.

RESULTS

Experiments carried out in this work demonstrate that the proposed VTDCE-Net outperforms the TV scheme on both breast and brain datasets across all undersampling rates. For K trans $\mathbf {K_{trans}}$ and V p $\mathbf {V_{p}}$ maps, the improvement over TV is as high as 2 and 5 dB, respectively, using the proposed VTDCE-Net.

CONCLUSION

Temporal points invariant DL network that was proposed in this work to estimate the TK-parameters using DCE-MRI data has provided state-of-the-art performance compared to standard image reconstruction methods and is shown to work across all undersampling rates.

Maximum Entropy Technique and Regularization Functional for Determining the Pharmacokinetic Parameters in DCE-MRI

This paper aims to solve the arterial input function (AIF) determination in dynamic contrast-enhanced MRI (DCE-MRI), an important linear ill-posed inverse problem, using the maximum entropy technique (MET) and regularization functionals. In addition, estimating the pharmacokinetic parameters from a DCE-MR image investigations is an urgent need to obtain the precise information about the AIF-the concentration of the contrast agent on the left ventricular blood pool measured over time. For this reason, the main idea is to show how to find a unique solution of linear system of equations generally in the form of [Formula: see text] named an ill-conditioned linear system of equations after discretization of the integral equations, which appear in different tomographic image restoration and reconstruction issues. Here, a new algorithm is described to estimate an appropriate probability distribution function for AIF according to the MET and regularization functionals for the contrast agent concentration when applying Bayesian estimation approach to estimate two different pharmacokinetic parameters. Moreover, by using the proposed approach when analyzing simulated and real datasets of the breast tumors according to pharmacokinetic factors, it indicates that using Bayesian inference-that infer the uncertainties of the computed solutions, and specific knowledge of the noise and errors-combined with the regularization functional of the maximum entropy problem, improved the convergence behavior and led to more consistent morphological and functional statistics and results. Finally, in comparison to the proposed exponential distribution based on MET and Newton's method, or Weibull distribution via the MET and teaching-learning-based optimization (MET/TLBO) in the previous studies, the family of Gamma and Erlang distributions estimated by the new algorithm are more appropriate and robust AIFs.

An Anthropomorphic Digital Reference Object (DRO) for Simulation and Analysis of Breast DCE MRI Techniques

Advances in accelerated magnetic resonance imaging (MRI) continue to push the bounds on achievable spatial and temporal resolution while maintaining a clinically acceptable image quality. Validation tools, including numerical simulations, are needed to characterize the repeatability and reproducibility of such methods for use in quantitative imaging applications. We describe the development of a simulation framework for analyzing and optimizing accelerated MRI acquisition and reconstruction techniques used in dynamic contrast enhanced (DCE) breast imaging. The simulation framework, in the form of a digital reference object (DRO), consists of four modules that control different aspects of the simulation, including the appearance and physiological behavior of the breast tissue as well as the MRI acquisition settings, to produce simulated k-space data for a DCE breast exam. The DRO design and functionality are described along with simulation examples provided to show potential applications of the DRO. The included simulation results demonstrate the ability of the DRO to simulate a variety of effects including the creation of simulated lesions, tissue enhancement modeled by the generalized kinetic model, T1-relaxation, fat signal precession and saturation, acquisition SNR, and changes in temporal resolution.

Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data

The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by L+S. The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. L+S decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a L+S decomposition for undersampled MR data.

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated—in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching (“method of moments”), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters.

Joint Reconstruction of Vascular Structure and Function Maps in Dynamic Contrast Enhanced MRI Using Vascular Heterogeneity Priors

This work introduces a novel, joint reconstruction of vascular structure and microvascular function maps directly from highly undersampled data in k - t space using vascular heterogeneity priors for high-definition, dynamic contrast-enhanced (DCE) MRI. In DCE MRI, arteries and veins are characterized by rapid, high uptake and wash-out of contrast agents (CA). On the other hand, depending on CA uptake and wash-out signal patterns, capillary tissues can be categorized into highly perfused, moderately perfused, and necrotic regions. Given the above considerations, macrovascular maps are generated as a prior to differentiate penalties on arteries relative to capillary tissues during image reconstruction. Furthermore, as a microvascular prior, contrast dynamics in capillary regions are represented in a low dimensional space using a finite number of basic vectors that reflect actual tissue-specific signal patterns. Both vascular structure and microvascular function maps are jointly estimated by solving a constrained optimization problem in which the above vascular heterogeneity priors are represented by spatially weighted nonnegative matrix factorization. Retrospective and prospective experiments are performed to validate the effectiveness of the proposed method in generating well-defined vascular structure and microvascular function maps for patients with brain tumor at high reduction factors.

Inferring CT perfusion parameters and uncertainties using a Bayesian approach

BACKGROUND

Computed tomography perfusion imaging is commonly used for the rapid assessment of patients presenting with symptoms of acute stroke. Maps of perfusion parameters, such as cerebral blood volume (CBV), cerebral blood flow (CBF), and mean transit time (MTT) derived from the perfusion scan data, provide crucial information for stroke diagnosis and treatment decisions. Most CT scanners use singular value decomposition (SVD)-based methods to calculate these parameters. However, some known problems are associated with conventional methods.

METHODS

In this work, we propose a Bayesian inference algorithm, which can derive both the perfusion parameters and their uncertainties. We apply the variational technique to the inference, which then becomes an expectation-maximization problem. The probability distribution (with Gaussian mean and variance) of each estimated parameter can be obtained, and the coefficient of variation is used to indicate the uncertainty. We perform evaluations using both simulations and patient studies.

RESULTS

In a simulation, we show that the proposed method has much less bias than conventional methods. Then, in separate simulations, we apply the proposed method to evaluate the impacts of various scan conditions, i.e., with different frame intervals, truncated measurement, or motion, on the parameter estimate. In one patient study, the method produced CBF and MTT maps indicating an ischemic lesion consistent with the radiologist's report. In a second patient study affected by patient movement, we showed the feasibility of applying the proposed method to motion corrected data.

CONCLUSIONS

The proposed method can be used to evaluate confidence in parameter estimation and the scan protocol design. More clinical evaluation is required to fully test the proposed method.

Motion correction of free-breathing magnetic resonance renography using model-driven registration

INTRODUCTION

Model-driven registration (MDR) is a general approach to remove patient motion in quantitative imaging. In this study, we investigate whether MDR can effectively correct the motion in free-breathing MR renography (MRR).

MATERIALS AND METHODS

MDR was generalised to linear tracer-kinetic models and implemented using 2D or 3D free-form deformations (FFD) with multi-resolution and gradient descent optimization. MDR was evaluated using a kidney-mimicking digital reference object (DRO) and free-breathing patient data acquired at high temporal resolution in multi-slice 2D (5 patients) and 3D acquisitions (8 patients). Registration accuracy was assessed using comparison to ground truth DRO, calculating the Hausdorff distance (HD) between ground truth masks with segmentations and visual evaluation of dynamic images, signal-time courses and parametric maps (all data).

RESULTS

DRO data showed that the bias and precision of parameter maps after MDR are indistinguishable from motion-free data. MDR led to reduction in HD (HDunregistered = 9.98 ± 9.76, HDregistered = 1.63 ± 0.49). Visual inspection showed that MDR effectively removed motion effects in the dynamic data, leading to a clear improvement in anatomical delineation on parametric maps and a reduction in motion-induced oscillations on signal-time courses.

DISCUSSION

MDR provides effective motion correction of MRR in synthetic and patient data. Future work is needed to compare the performance against other more established methods.

Pseudo Test-Retest Evaluation of Millimeter-Resolution Whole-Brain Dynamic Contrast-enhanced MRI in Patients with High-Grade Glioma

Background

Advances in sub-Nyquist–sampled dynamic contrast-enhanced (DCE) MRI enable monitoring of brain tumors with millimeter resolution and whole-brain coverage. Such undersampled quantitative methods need careful characterization regarding achievable test-retest reproducibility.

Purpose

To demonstrate a fully automated high-resolution whole-brain DCE MRI pipeline with 30-fold sparse undersampling and estimate its reproducibility on the basis of reference regions of stable tissue types during multiple posttreatment time points by using longitudinal clinical images of high-grade glioma.

Materials and Methods

Two methods for sub-Nyquist–sampled DCE MRI were extended with automatic estimation of vascular input functions. Continuously acquired three-dimensional k-space data with ramped-up flip angles were partitioned to yield high-resolution, whole-brain tracer kinetic parameter maps with matched precontrast-agent T1 and M₀ maps. Reproducibility was estimated in a retrospective study in participants with high-grade glioma, who underwent three consecutive standard-of-care examinations between December 2016 and April 2019. Coefficients of variation and reproducibility coefficients were reported for histogram statistics of the tracer kinetic parameters plasma volume fraction and volume transfer constant (K^trans) on five healthy tissue types.

Results

The images from 13 participants (mean age ± standard deviation, 61 years ± 10; nine women) with high-grade glioma were evaluated. In healthy tissues, the protocol achieved a coefficient of variation less than 57% for median K^trans, if K^trans was estimated consecutively. The maximum reproducibility coefficient for median K^trans was estimated to be at 0.06 min^–1 for large or low-enhancing tissues and to be as high as 0.48 min^–1 in smaller or strongly enhancing tissues.

Conclusion

A fully automated, sparsely sampled DCE MRI reconstruction with patient-specific vascular input function offered high spatial and temporal resolution and whole-brain coverage; in healthy tissues, the protocol estimated median volume transfer constant with maximum reproducibility coefficient of 0.06 min^–1 in large, low-enhancing tissue regions and maximum reproducibility coefficient of less than 0.48 min^–1 in smaller or more strongly enhancing tissue regions.

Published under a CC BY 4.0 license.

Online supplemental material is available for this article.

See also the editorial by Lenkinski in this issue.

Quantification of T1, T2 relaxation times from Magnetic Resonance Fingerprinting radially undersampled data using analytical transformations

Quantitative magnetic resonance imaging (MRI) estimates magnetic parameters related to tissue, such as T1, T2 relaxation times and proton density. MR fingerprinting (MRF) is a new concept that uses pseudo-random, incoherent measurements to create a unique fingerprint for each tissue type to quantify magnet parameters. This paper aims to enhance MRF performance by investigating (i) the most suitable acquisition trajectory, and (ii) analytical transformations, suitable for radial acquisitions. Highly undersampled MRF brain (k, t)-space data have been simulated and non-linearly reconstructed to exploit the low-rank property of dynamic imaging. Based on our findings, the radial trajectory is the most suitable for MRF compared to Cartesian and spiral acquisitions. Perhaps this is due to the fact that its aliasing artifacts are more noise-like, and that unlike spiral trajectories, it can use analytical transformations that do not require re-gridding. One such analytical algorithm is the spline reconstruction technique (SRT) that is based on a novel numerical implementation of an analytic representation of the inverse Radon transform. Here, for the first time, this algorithm is applied to MR radial data. Reconstructions using SRT were compared to the ones using filtered back-projection. SRT provided images of higher contrast, lower bias, which resulted in more accurate T1, T2 values.

Three Dimensional Reconstruction Models for Medical Modalities: A Comprehensive Investigation and Analysis

BACKGROUND

Image reconstruction is the mathematical process which converts the signals obtained from the scanning machine into an image. The reconstructed image plays a fundamental role in the planning of surgery and research in the medical field.

DISCUSSION

This paper introduces the first comprehensive survey of the literature about medical image reconstruction related to diseases, presenting a categorical study about the techniques and analyzing advantages and disadvantages of each technique. The images obtained by various imaging modalities like MRI, CT, CTA, Stereo radiography and Light field microscopy are included. A comparison on the basis of the reconstruction technique, Imaging Modality and Visualization, Disease, Metrics for 3D reconstruction accuracy, Dataset and Execution time, Evaluation of the technique is also performed.

CONCLUSION

The survey makes an assessment of the suitable reconstruction technique for an organ, draws general conclusions and discusses the future directions.

Efficient DCE-MRI Parameter and Uncertainty Estimation Using a Neural Network

Quantitative DCE-MRI provides voxel-wise estimates of tracer-kinetic parameters that are valuable in the assessment of health and disease. These maps suffer from many known sources of variability. This variability is expensive to compute using current methods, and is typically not reported. Here, we demonstrate a novel approach for simultaneous estimation of tracer-kinetic parameters and their uncertainty due to intrinsic characteristics of the tracer-kinetic model, with very low computation time. We train and use a neural network to estimate the approximate joint posterior distribution of tracer-kinetic parameters. Uncertainties are estimated for each voxel and are specific to the patient, exam, and lesion. We demonstrate the methods' ability to produce accurate tracer-kinetic maps. We compare predicted parameter ranges with uncertainties introduced by noise and by differences in post-processing in a digital reference object. The predicted parameter ranges correlate well with tracer-kinetic parameter ranges observed across different noise realizations and regression algorithms. We also demonstrate the value of this approach to differentiate significant from insignificant changes in brain tumor pharmacokinetics over time. This is achieved by enforcing consistency in resolving model singularities in the applied tracer-kinetic model.

Model-Based High-Definition Dynamic Contrast Enhanced MRI for Concurrent Estimation of Perfusion and Microvascular Permeability

This work introduces a model-based, high-definition dynamic contrast enhanced (DCE) MRI for concurrent estimation of perfusion and microvascular permeability over the whole brain. A time series of reference-subtracted signals is decomposed into one component that reflects main contrast dynamics and the other one that includes residual contrast agents (CA) and background signals. The former is described by linear superposition of a finite number of basic vectors trained from an augmented set of data that consists of tracer-kinetic model driven signal vectors and patient-specific measured ones. Contrast dynamics is estimated by solving a constrained optimization problem that incorporates the linearized signal decomposition into the measurement model of DCE MRI and then combining the main component with the background-suppressed, residual CA signals. To the best of our knowledge, this is the first work that prospectively enables rapid temporal sampling with 1.5 s (3 ∼ 4 times higher than clinical routines) while simultaneously achieving high isotropic spatial resolution with 1.0 mm³ (4 ∼ 6 times higher than routines), enhancing estimation of both patient-specific inputs and outputs for quantification of microvascular functions. Simulations and experiments are performed to demonstrate the effectiveness of the proposed method in patients with brain cancer.

Robust estimation of hemo-dynamic parameters in traditional DCE-MRI models

PURPOSE

In dynamic contrast enhanced (DCE) MRI, separation of signal contributions from perfusion and leakage requires robust estimation of parameters in a pharmacokinetic model. We present and quantify the performance of a method to compute tissue hemodynamic parameters from DCE data using established pharmacokinetic models.

METHODS

We propose a Bayesian scheme to obtain perfusion metrics from DCE MRI data. Initial performance is assessed through digital phantoms of the extended Tofts model (ETM) and the two-compartment exchange model (2CXM), comparing the Bayesian scheme to the standard Levenberg-Marquardt (LM) algorithm. Digital phantoms are also invoked to identify limitations in the pharmacokinetic models related to measurement conditions. Using computed maps of the extra vascular volume (ve) from 19 glioma patients, we analyze differences in the number of un-physiological high-intensity ve values for both ETM and 2CXM, using a one-tailed paired t-test assuming un-equal variance.

RESULTS

The Bayesian parameter estimation scheme demonstrated superior performance over the LM technique in the digital phantom simulations. In addition, we identified limitations in parameter reliability in relation to scan duration for the 2CXM. DCE data for glioma and cervical cancer patients was analyzed with both algorithms and demonstrated improvement in image readability for the Bayesian method. The Bayesian method demonstrated significantly fewer non-physiological high-intensity ve values for the ETM (p<0.0001) and the 2CXM (p<0.0001).

CONCLUSION

We have demonstrated substantial improvement of the perceptive quality of pharmacokinetic parameters from advanced compartment models using the Bayesian parameter estimation scheme as compared to the LM technique.

An overview of deep learning in medical imaging focusing on MRI

What has happened in machine learning lately, and what does it mean for the future of medical image analysis? Machine learning has witnessed a tremendous amount of attention over the last few years. The current boom started around 2009 when so-called deep artificial neural networks began outperforming other established models on a number of important benchmarks. Deep neural networks are now the state-of-the-art machine learning models across a variety of areas, from image analysis to natural language processing, and widely deployed in academia and industry. These developments have a huge potential for medical imaging technology, medical data analysis, medical diagnostics and healthcare in general, slowly being realized. We provide a short overview of recent advances and some associated challenges in machine learning applied to medical image processing and image analysis. As this has become a very broad and fast expanding field we will not survey the entire landscape of applications, but put particular focus on deep learning in MRI. Our aim is threefold: (i) give a brief introduction to deep learning with pointers to core references; (ii) indicate how deep learning has been applied to the entire MRI processing chain, from acquisition to image retrieval, from segmentation to disease prediction; (iii) provide a starting point for people interested in experimenting and perhaps contributing to the field of deep learning for medical imaging by pointing out good educational resources, state-of-the-art open-source code, and interesting sources of data and problems related medical imaging.

Spatio-Temporally Constrained Reconstruction for Hyperpolarized Carbon-13 MRI Using Kinetic Models

We present a method of generating spatial maps of kinetic parameters from dynamic sequences of images collected in hyperpolarized carbon-13 magnetic resonance imaging (MRI) experiments. The technique exploits spatial correlations in the dynamic traces via regularization in the space of parameter maps. Similar techniques have proven successful in other dynamic imaging problems, such as dynamic contrast enhanced MRI. In this paper, we apply these techniques for the first time to hyperpolarized MRI problems, which are particularly challenging due to limited signal-to-noise ratio (SNR). We formulate the reconstruction as an optimization problem and present an efficient iterative algorithm for solving it based on the alternation direction method of multipliers. We demonstrate that this technique improves the qualitative appearance of parameter maps estimated from low SNR dynamic image sequences, first in simulation then on a number of data sets collected in vivo. The improvement this method provides is particularly pronounced at low SNR levels.

Joint arterial input function and tracer kinetic parameter estimation from undersampled dynamic contrast-enhanced MRI using a model consistency constraint

PURPOSE

To develop and evaluate a model-based reconstruction framework for joint arterial input function (AIF) and kinetic parameter estimation from undersampled brain tumor dynamic contrast-enhanced MRI (DCE-MRI) data.

METHODS

The proposed method poses the tracer-kinetic (TK) model as a model consistency constraint, enabling the flexible inclusion of different TK models and TK solvers, and the joint estimation of the AIF. The proposed method is evaluated using an anatomic realistic digital reference object (DRO), and nine retrospectively down-sampled brain tumor DCE-MRI datasets. We also demonstrate application to 30-fold prospectively undersampled brain tumor DCE-MRI.

RESULTS

In DRO studies with up to 60-fold undersampling, the proposed method provided TK maps with low error that were comparable to fully sampled data and were demonstrated to be compatible with a third-party TK solver. In retrospective undersampling studies, this method provided patient-specific AIF with normalized root mean-squared-error (normalized by the 90th percentile value) less than 8% at up to 100-fold undersampling. In the 30-fold undersampled prospective study, the proposed method provided high-resolution whole-brain TK maps and patient-specific AIF.

CONCLUSION

The proposed model-based DCE-MRI reconstruction enables the use of different TK solvers with a model consistency constraint and enables joint estimation of patient-specific AIF. TK maps and patient-specific AIF with high fidelity can be reconstructed at up to 100-fold undersampling in k,t-space. Magn Reson Med 79:2804-2815, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

A comparison of Bayesian and non-linear regression methods for robust estimation of pharmacokinetics in DCE-MRI and how it affects cancer diagnosis

The aim of this work is to compare Bayesian Inference for nonlinear models with commonly used traditional non-linear regression (NR) algorithms for estimating tracer kinetics in Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI). The algorithms are compared in terms of accuracy, and reproducibility under different initialization settings. Further it is investigated how a more robust estimation of tracer kinetics affects cancer diagnosis. The derived tracer kinetics from the Bayesian algorithm were validated against traditional NR algorithms (i.e. Levenberg-Marquardt, simplex) in terms of accuracy on a digital DCE phantom and in terms of goodness-of-fit (Kolmogorov-Smirnov test) on ROI-based concentration time courses from two different patient cohorts. The first cohort consisted of 76 men, 20 of whom had significant peripheral zone prostate cancer (any cancer-core-length (CCL) with Gleason>3+3 or any-grade with CCL>=4mm) following transperineal template prostate mapping biopsy. The second cohort consisted of 9 healthy volunteers and 24 patients with head and neck squamous cell carcinoma. The diagnostic ability of the derived tracer kinetics was assessed with receiver operating characteristic area under curve (ROC AUC) analysis. The Bayesian algorithm accurately recovered the ground-truth tracer kinetics for the digital DCE phantom consistently improving the Structural Similarity Index (SSIM) across the 50 different initializations compared to NR. For optimized initialization, Bayesian did not improve significantly the fitting accuracy on both patient cohorts, and it only significantly improved the ve ROC AUC on the HN population from ROC AUC=0.56 for the simplex to ROC AUC=0.76. For both cohorts, the values and the diagnostic ability of tracer kinetic parameters estimated with the Bayesian algorithm weren't affected by their initialization. To conclude, the Bayesian algorithm led to a more accurate and reproducible quantification of tracer kinetic parameters in DCE-MRI, improving their ROC-AUC and decreasing their dependence on initialization settings.

Maximum Entropy Approach in Dynamic Contrast-Enhanced Magnetic Resonance Imaging

BACKGROUND

In the estimation of physiological kinetic parameters from Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) data, the determination of the arterial input function (AIF) plays a key role.

OBJECTIVES

This paper proposes a Bayesian method to estimate the physiological parameters of DCE-MRI along with the AIF in situations, where no measurement of the AIF is available.

METHODS

In the proposed algorithm, the maximum entropy method (MEM) is combined with the maximum a posterior approach (MAP). To this end, MEM is used to specify a prior probability distribution of the unknown AIF. The ability of this method to estimate the AIF is validated using the Kullback-Leibler divergence. Subsequently, the kinetic parameters can be estimated with MAP. The proposed algorithm is evaluated with a data set from a breast cancer MRI study.

RESULTS

The application shows that the AIF can reliably be determined from the DCE-MRI data using MEM. Kinetic parameters can be estimated subsequently.

CONCLUSIONS

The maximum entropy method is a powerful tool to reconstructing images from many types of data. This method is useful for generating the probability distribution based on given information. The proposed method gives an alternative way to assess the input function from the existing data. The proposed method allows a good fit of the data and therefore a better estimation of the kinetic parameters. In the end, this allows for a more reliable use of DCE-MRI.

Direct estimation of tracer-kinetic parameter maps from highly undersampled brain dynamic contrast enhanced MRI

PURPOSE

The purpose of this work was to develop and evaluate a T₁ -weighted dynamic contrast enhanced (DCE) MRI methodology where tracer-kinetic (TK) parameter maps are directly estimated from undersampled (k,t)-space data.

THEORY AND METHODS

The proposed reconstruction involves solving a nonlinear least squares optimization problem that includes explicit use of a full forward model to convert parameter maps to (k,t)-space, utilizing the Patlak TK model. The proposed scheme is compared against an indirect method that creates intermediate images by parallel imaging and compressed sensing before to TK modeling. Thirteen fully sampled brain tumor DCE-MRI scans with 5-second temporal resolution are retrospectively undersampled at rates R = 20, 40, 60, 80, and 100 for each dynamic frame. TK maps are quantitatively compared based on root mean-squared-error (rMSE) and Bland-Altman analysis. The approach is also applied to four prospectively R = 30 undersampled whole-brain DCE-MRI data sets.

RESULTS

In the retrospective study, the proposed method performed statistically better than indirect method at R ≥ 80 for all 13 cases. This approach provided restoration of TK parameter values with less errors in tumor regions of interest, an improvement compared to a state-of-the-art indirect method. Applied prospectively, the proposed method provided whole-brain, high-resolution TK maps with good image quality.

CONCLUSION

Model-based direct estimation of TK maps from k,t-space DCE-MRI data is feasible and is compatible up to 100-fold undersampling. Magn Reson Med 78:1566-1578, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Joint Reconstruction of Multiple Images and Motion in MRI: Application to Free-Breathing Myocardial T₂Quantification

Exploiting redundancies between multiple images of an MRI examination can be formalized as the joint reconstruction of these images. The anatomy is preserved indeed so that specific constraints can be implemented (e.g. most of the features or spatial gradients should be in the same place in all these images) and only the contrast changes from one image to another need to be encoded. The application of this concept is particularly challenging in cardiovascular and body imaging due to the complex organ deformations, especially with the patient breathing. In this study a joint optimization framework is proposed for reconstructing multiple MR images together with a nonrigid motion model. The motion model takes into account both intra-image and inter-image motion and therefore can correct for most ghosting/blurring artifacts and misregistration between images. The framework was validated with free-breathing myocardial T2 mapping experiments from nine heart transplant patients at 1.5 T. Results showed improved image quality and excellent image alignment with the multi-image reconstruction compared to the independent reconstruction of each image. Segment-wise myocardial T2 values were in good agreement with the reference values obtained from multiple breath-holds (62.5 ± 11.1 ms against 62.2 ± 11.2 ms which was not significant with p=0.49).