Estimating kinetic parameter maps from dynamic contrast-enhanced MRI using spatial prior knowledge

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.

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.

Efficient estimation of pharmacokinetic parameters from breast dynamic contrast-enhanced MRI based on a convolutional neural network for predicting molecular subtypes

Objective. Tracer kinetic models allow for estimating pharmacokinetic (PK) parameters, which are related to pathological characteristics, from breast dynamic contrast-enhanced magnetic resonance imaging. However, existing tracer kinetic models subject to inaccuracy are time-consuming for PK parameters estimation. This study aimed to accurately and efficiently estimate PK parameters for predicting molecular subtypes based on convolutional neural network (CNN).Approach. A CNN integrating global and local features (GL-CNN) was trained using synthetic data where known PK parameters map was used as the ground truth, and subsequently used to directly estimate PK parameters (volume transfer constantKtransand flux rate constantKep) map. The accuracy assessed by the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and concordance correlation coefficient (CCC) was compared between the GL-CNN and Tofts-based PK parameters in synthetic data. Radiomic features were calculated from the PK parameters map in 208 breast tumors. A random forest classifier was constructed to predict molecular subtypes using a discovery cohort (n= 144). The diagnostic performance evaluated on a validation cohort (n= 64) using the area under the receiver operating characteristic curve (AUC) was compared between the GL-CNN and Tofts-based PK parameters.Main results. The average PSNR (48.8884), SSIM (0.9995), and CCC (0.9995) between the GL-CNN-basedKtransmap and ground truth were significantly higher than those between the Tofts-basedKtransmap and ground truth. The GL-CNN-basedKtransobtained significantly better diagnostic performance (AUCs = 0.7658 and 0.8528) than the Tofts-basedKtransfor luminal B and HER2 tumors. The GL-CNN method accelerated the computation by speed approximately 79 times compared to the Tofts method for the whole breast of all patients.Significance. Our results indicate that the GL-CNN method can be used to accurately and efficiently estimate PK parameters for predicting molecular subtypes.

Denoising and uncertainty estimation in parameter mapping with approximate Bayesian deep image priors

PURPOSE

To mitigate the problem of noisy parameter maps with high uncertainties by casting parameter mapping as a denoising task based on Deep Image Priors.

METHODS

We extend the concept of denoising with Deep Image Prior (DIP) into parameter mapping by treating the output of an image-generating network as a parametrization of tissue parameter maps. The method implicitly denoises the parameter mapping process by filtering low-level image features with an untrained convolutional neural network (CNN). Our implementation includes uncertainty estimation from Bernoulli approximate variational inference, implemented with MC dropout, which provides model uncertainty in each voxel of the denoised parameter maps. The method is modular, so the specifics of different applications (e.g., T1 mapping) separate into application-specific signal equation blocks. We evaluate the method on variable flip angle T1 mapping, multi-echo T2 mapping, and apparent diffusion coefficient mapping.

RESULTS

We found that deep image prior adapts successfully to several applications in parameter mapping. In all evaluations, the method produces noise-reduced parameter maps with decreased uncertainty compared to conventional methods. The downsides of the proposed method are the long computational time and the introduction of some bias from the denoising prior.

CONCLUSION

DIP successfully denoise the parameter mapping process and applies to several applications with limited hyperparameter tuning. Further, it is easy to implement since DIP methods do not use network training data. Although time-consuming, uncertainty information from MC dropout makes the method more robust and provides useful information when properly calibrated.

Physics-informed neural networks for myocardial perfusion MRI quantification

Tracer-kinetic models allow for the quantification of kinetic parameters such as blood flow from dynamic contrast-enhanced magnetic resonance (MR) images. Fitting the observed data with multi-compartment exchange models is desirable, as they are physiologically plausible and resolve directly for blood flow and microvascular function. However, the reliability of model fitting is limited by the low signal-to-noise ratio, temporal resolution, and acquisition length. This may result in inaccurate parameter estimates. This study introduces physics-informed neural networks (PINNs) as a means to perform myocardial perfusion MR quantification, which provides a versatile scheme for the inference of kinetic parameters. These neural networks can be trained to fit the observed perfusion MR data while respecting the underlying physical conservation laws described by a multi-compartment exchange model. Here, we provide a framework for the implementation of PINNs in myocardial perfusion MR. The approach is validated both in silico and in vivo. In the in silico study, an overall decrease in mean-squared error with the ground-truth parameters was observed compared to a standard non-linear least squares fitting approach. The in vivo study demonstrates that the method produces parameter values comparable to those previously found in literature, as well as providing parameter maps which match the clinical diagnosis of patients.

AI-Enhanced Diagnosis of Challenging Lesions in Breast MRI: A Methodology and Application Primer

Computer-aided diagnosis (CAD) systems have become an important tool in the assessment of breast tumors with magnetic resonance imaging (MRI). CAD systems can be used for the detection and diagnosis of breast tumors as a "second opinion" review complementing the radiologist's review. CAD systems have many common parts, such as image preprocessing, tumor feature extraction, and data classification that are mostly based on machine-learning (ML) techniques. In this review article, we describe applications of ML-based CAD systems in MRI covering the detection of diagnostically challenging lesions of the breast such as nonmass enhancing (NME) lesions, and furthermore discuss how multiparametric MRI and radiomics can be applied to the study of NME, including prediction of response to neoadjuvant chemotherapy (NAC). Since ML has been widely used in the medical imaging community, we provide an overview about the state-of-the-art and novel techniques applied as classifiers to CAD systems. The differences in the CAD systems in MRI of the breast for several standard and novel applications for NME are explained in detail to provide important examples, illustrating: 1) CAD for detection and diagnosis, 2) CAD in multiparametric imaging, 3) CAD in NAC, and 4) breast cancer radiomics. We aim to provide a comparison between these CAD applications and to illustrate a global view on intelligent CAD systems based on machine and deep learning in MRI of the breast. LEVEL OF EVIDENCE: 2 TECHNICAL EFFICACY STAGE: 2.

Diffusion-weighted and dynamic contrast-enhanced magnetic resonance imaging after radiation therapy for bone metastases in patients with hepatocellular carcinoma

The objectives of this study were to assess changes in apparent diffusion coefficient (ADC) and dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) parameters after radiation therapy (RT) for bone metastases from hepatocellular carcinoma (HCC) and to evaluate their prognostic value. This prospective study was approved by the Institutional Review Board. Fourteen patients with HCC underwent RT (30 Gy in 10 fractions once daily) for bone metastases. The ADC and DCE-MRI parameters and the volume of the target lesions were measured before (baseline) and one month after RT (post-RT). The Wilcoxon signed-rank test was used to compare the parameters between the baseline and post-RT MRI. The parameters were compared between patients with or without disease progression in RT fields using the Mann–Whitney test. Intraclass correlation coefficients were used to evaluate the interobserver agreement. The medians of the ADC, rate constant [k_ep], and volume fraction of the extravascular extracellular matrix [v_e] in the baseline and post-RT MRI were 0.67 (range 0.61–0.72) and 0.75 (range 0.63–1.43) (× 10^–3 mm²/s) (P = 0.027), 836.33 (range 301.41–1082.32) and 335.80 (range 21.86–741.87) (× 10^–3/min) (P = 0.002), and 161.54 (range 128.38–410.13) and 273.99 (range 181.39–1216.95) (× 10^–3) (P = 0.027), respectively. The medians of the percent change in the ADC of post-RT MRI in patients with progressive disease and patients without progressive disease were − 1.35 (range − 6.16 to 6.79) and + 46.71 (range 7.71–112.81) (%) (P = 0.011), respectively. The interobserver agreements for all MRI parameters were excellent (intraclass correlation coefficients > 0.8). In conclusion, the ADC, k_ep, and v_e of bone metastases changed significantly after RT. The percentage change in the ADC was closely related to local tumor progression.

Direct Comparison of Bayesian and Fermi Deconvolution Approaches for Myocardial Blood Flow Quantification: In silico and Clinical Validations

Cardiac magnetic resonance myocardial perfusion imaging can detect coronary artery disease and is an alternative to single-photon emission computed tomography or positron emission tomography. However, the complex, non-linear MR signal and the lack of robust quantification of myocardial blood flow have hindered its widespread clinical application thus far. Recently, a new Bayesian approach was developed for brain imaging and evaluation of perfusion indexes (Kudo et al., 2014). In addition to providing accurate perfusion measurements, this probabilistic approach appears more robust than previous approaches, particularly due to its insensitivity to bolus arrival delays. We assessed the performance of this approach against a well-known and commonly deployed model-independent method based on the Fermi function for cardiac magnetic resonance myocardial perfusion imaging. The methods were first evaluated for accuracy and precision using a digital phantom to test them against the ground truth; next, they were applied in a group of coronary artery disease patients. The Bayesian method can be considered an appropriate model-independent method with which to estimate myocardial blood flow and delays. The digital phantom comprised a set of synthetic time-concentration curve combinations generated with a 2-compartment exchange model and a realistic combination of perfusion indexes, arterial input dynamics, noise and delays collected from the clinical dataset. The myocardial blood flow values estimated with the two methods showed an excellent correlation coefficient (r² > 0.9) under all noise and delay conditions. The Bayesian approach showed excellent robustness to bolus arrival delays, with a similar performance to Fermi modeling when delays were considered. Delays were better estimated with the Bayesian approach than with Fermi modeling. An in vivo analysis of coronary artery disease patients revealed that the Bayesian approach had an excellent ability to distinguish between abnormal and normal myocardium. The Bayesian approach was able to discriminate not only flows but also delays with increased sensitivity by offering a clearly enlarged range of distribution for the physiologic parameters.

Bayesian non-linear regression with spatial priors for noise reduction and error estimation in quantitative MRI with an application in T1 estimation

PURPOSE

To develop a method that can reduce and estimate uncertainty in quantitative MR parameter maps without the need for hand-tuning of any hyperparameters.

METHODS

We present an estimation method where uncertainties are reduced by incorporating information on spatial correlations between neighbouring voxels. The method is based on a Bayesian hierarchical non-linear regression model, where the parameters of interest are sampled, using Markov chain Monte Carlo (MCMC), from a high-dimensional posterior distribution with a spatial prior. The degree to which the prior affects the model is determined by an automatic hyperparameter search using an information criterion and is, therefore, free from manual user-dependent tuning. The samples obtained further provide a convenient means to obtain uncertainties in both voxels and regions. The developed method was evaluated on T ₁ estimations based on the variable flip angle method.

RESULTS

The proposed method delivers noise-reduced T ₁ parameter maps with associated error estimates by combining MCMC sampling, the widely applicable information criterion, and total variation-based denoising. The proposed method results in an overall decrease in estimation error when compared to conventional voxel-wise maximum likelihood estimation. However, this comes with an increased bias in some regions, predominately at tissue interfaces, as well as an increase in computational time.

CONCLUSIONS

This study provides a method that generates more precise estimates compared to the conventional method, without incorporating user subjectivity, and with the added benefit of uncertainty estimation.

Quantifying Perfusion Properties with DCE-MRI Using a Dictionary Matching Approach

Perfusion properties can be estimated from pharmacokinetic models applied to DCE-MRI data using curve fitting algorithms; however, these suffer from drawbacks including the local minimum problem and substantial computational time. Here, a dictionary matching approach is proposed as an alternative. Curve fitting and dictionary matching were applied to simulated data using the dual-input single-compartment model with known perfusion property values and 5 in vivo DCE-MRI datasets. In simulation at SNR 60 dB, the dictionary estimate had a mean percent error of 0.4-1.0% for arterial fraction, 0.5-1.4% for distribution volume, and 0.0% for mean transit time. The curve fitting estimate had a mean percent error of 1.1-2.1% for arterial fraction, 0.5-1.3% for distribution volume, and 0.2-1.8% for mean transit time. In vivo, dictionary matching and curve fitting showed no statistically significant differences in any of the perfusion property measurements in any of the 10 ROIs between the methods. In vivo, the dictionary method performed over 140-fold faster than curve fitting, obtaining whole volume perfusion maps in just over 10 s. This study establishes the feasibility of using a dictionary matching approach as a new and faster way of estimating perfusion properties from pharmacokinetic models in DCE-MRI.

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.

Hierarchical Bayesian myocardial perfusion quantification

Myocardial blood flow can be quantified from dynamic contrast-enhanced magnetic resonance (MR) images through the fitting of tracer-kinetic models to the observed imaging data. The use of multi-compartment exchange models is desirable as they are physiologically motivated and resolve directly for both blood flow and microvascular function. However, the parameter estimates obtained with such models can be unreliable. This is due to the complexity of the models relative to the observed data which is limited by the low signal-to-noise ratio, the temporal resolution, the length of the acquisitions and other complex imaging artefacts. In this work, a Bayesian inference scheme is proposed which allows the reliable estimation of the parameters of the two-compartment exchange model from myocardial perfusion MR data. The Bayesian scheme allows the incorporation of prior knowledge on the physiological ranges of the model parameters and facilitates the use of the additional information that neighbouring voxels are likely to have similar kinetic parameter values. Hierarchical priors are used to avoid making a priori assumptions on the health of the patients. We provide both a theoretical introduction to Bayesian inference for tracer-kinetic modelling and specific implementation details for this application. This approach is validated in both in silico and in vivo settings. In silico, there was a significant reduction in mean-squared error with the ground-truth parameters using Bayesian inference as compared to using the standard non-linear least squares fitting. When applied to patient data the Bayesian inference scheme returns parameter values that are in-line with those previously reported in the literature, as well as giving parameter maps that match the independant clinical diagnosis of those patients.

Spatially regularized estimation of the tissue homogeneity model parameters in DCE-MRI using proximal minimization

PURPOSE

The Tofts and the extended Tofts models are the pharmacokinetic models commonly used in dynamic contrast-enhanced MRI (DCE-MRI) perfusion analysis, although they do not provide two important biological markers, namely, the plasma flow and the permeability-surface area product. Estimates of such markers are possible using advanced pharmacokinetic models describing the vascular distribution phase, such as the tissue homogeneity model. However, the disadvantage of the advanced models lies in biased and uncertain estimates, especially when the estimates are computed voxelwise. The goal of this work is to improve the reliability of the estimates by including information from neighboring voxels.

THEORY AND METHODS

Information from the neighboring voxels is incorporated in the estimation process through spatial regularization in the form of total variation. The spatial regularization is applied on five maps of perfusion parameters estimated using the tissue homogeneity model. Since the total variation is not differentiable, two proximal techniques of convex optimization are used to solve the problem numerically.

RESULTS

The proposed algorithm helps to reduce noise in the estimated perfusion-parameter maps together with improving accuracy of the estimates. These conclusions are proved using a numerical phantom. In addition, experiments on real data show improved spatial consistency and readability of perfusion maps without considerable lowering of the quality of fit.

CONCLUSION

The reliability of the DCE-MRI perfusion analysis using the tissue homogeneity model can be improved by employing spatial regularization. The proposed utilization of modern optimization techniques implies only slightly higher computational costs compared to the standard approach without spatial regularization.

Convolutional Neural Networks for Direct Inference of Pharmacokinetic Parameters: Application to Stroke Dynamic Contrast-Enhanced MRI

Background and Purpose: The T1-weighted dynamic contrast enhanced (DCE)-MRI is an imaging technique that provides a quantitative measure of pharmacokinetic (PK) parameters characterizing microvasculature of tissues. For the present study, we propose a new machine learning (ML) based approach to directly estimate the PK parameters from the acquired DCE-MRI image-time series that is both more robust and faster than conventional model fitting.

Materials and Methods: We specifically utilize deep convolutional neural networks (CNNs) to learn the mapping between the image-time series and corresponding PK parameters. DCE-MRI datasets acquired from 15 patients with clinically evident mild ischaemic stroke were used in the experiments. Training and testing were carried out based on leave-one-patient-out cross- validation. The parameter estimates obtained by the proposed CNN model were compared against the two tracer kinetic models: (1) Patlak model, (2) Extended Tofts model, where the estimation of model parameters is done via voxelwise linear and nonlinear least squares fitting respectively.

Results: The trained CNN model is able to yield PK parameters which can better discriminate different brain tissues, including stroke regions. The results also demonstrate that the model generalizes well to new cases even if a subject specific arterial input function (AIF) is not available for the new data.

Conclusion: A ML-based model can be used for direct inference of the PK parameters from DCE image series. This method may allow fast and robust parameter inference in population DCE studies. Parameter inference on a 3D volume-time series takes only a few seconds on a GPU machine, which is significantly faster compared to conventional non-linear least squares fitting.

Application of whole-lesion histogram analysis of pharmacokinetic parameters in dynamic contrast-enhanced MRI of breast lesions with the CAIPIRINHA-Dixon-TWIST-VIBE technique

PURPOSE

To investigate the application of whole-lesion histogram analysis of pharmacokinetic parameters for differentiating malignant from benign breast lesions on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).

MATERIALS AND METHODS

In all, 92 women with 97 breast lesions (26 benign and 71 malignant lesions) were enrolled in this study. Patients underwent dynamic breast MRI at 3T using a prototypical CAIPIRINHA-Dixon-TWIST-VIBE (CDT-VIBE) sequence and a subsequent surgery or biopsy. Inflow rate of the agent between plasma and interstitium (K^trans ), outflow rate of agent between interstitium and plasma (K_ep ), extravascular space volume per unit volume of tissue (v_e ) including mean value, 25th/50th/75th/90th percentiles, skewness, and kurtosis were then calculated based on the whole lesion. A single-sample Kolmogorov-Smirnov test, paired t-test, and receiver operating characteristic curve (ROC) analysis were used for statistical analysis.

RESULTS

Malignant breast lesions had significantly higher K^trans , K_ep , and lower v_e in mean values, 25th/50th/75th/90th percentiles, and significantly higher skewness of v_e than benign breast lesions (all P < 0.05). There was no significant difference in kurtosis values between malignant and benign breast lesions (all P > 0.05). The 90th percentile of K^trans , the 90th percentile of K_ep , and the 50th percentile of v_e showed the greatest areas under the ROC curve (AUC) for each pharmacokinetic parameter derived from DCE-MRI. The 90th percentile of K_ep achieved the highest AUC value (0.927) among all histogram-derived values.

CONCLUSION

The whole-lesion histogram analysis of pharmacokinetic parameters can improve the diagnostic accuracy of breast DCE-MRI with the CDT-VIBE technique. The 90th percentile of K_ep may be the best indicator in differentiation between malignant and benign breast lesions.

LEVEL OF EVIDENCE

4 Technical Efficacy Stage: 2 J. Magn. Reson. Imaging 2018;47:91-96.

Partial Discreteness: A Novel Prior for Magnetic Resonance Image Reconstruction

An important factor influencing the quality of magnetic resonance (MR) images is the reconstruction method that is employed, and specifically, the type of prior knowledge that is exploited during reconstruction. In this work, we introduce a new type of prior knowledge, partial discreteness (PD), where a small number of regions in the image are assumed to be homogeneous and can be well represented by a constant magnitude. In particular, we mathematically formalize the partial discreteness property based on a Gaussian Mixture Model (GMM) and derive a partial discreteness image representation that characterizes the salient features of partially discrete images: a constant intensity in homogeneous areas and texture in heterogeneous areas. The partial discreteness representation is then used to construct a novel prior dedicated to the reconstruction of partially discrete MR images. The strength of the proposed prior is demonstrated on various simulated and real k-space data-based experiments with partially discrete images. Results demonstrate that the PD algorithm performs competitively with state-of-the-art reconstruction methods, being flexible and easy to implement.

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.

Bayesian Framework Based Direct Reconstruction of Fluorescence Parametric Images

Fluorescence imaging has been successfully used in the study of pharmacokinetic analysis, while dynamic fluorescence molecular tomography (FMT) is an attractive imaging technique for three-dimensionally resolving the metabolic process of fluorescent biomarkers in small animals in vivo. Parametric images obtained by combining dynamic FMT with compartmental modeling can provide quantitative physiological information for biological studies and drug development. However, images obtained with conventional indirect methods suffer from poor image quality because of failure in utilizing the temporal correlations of boundary measurements. Besides, FMT suffers from low spatial resolution due to its ill-posed nature, which further reduces the image quality. In this paper, we propose a novel method to directly reconstruct parametric images from boundary measurements based on maximum a posteriori (MAP) estimation with structural priors in a Bayesian framework. The proposed method can utilize structural priors obtained from an X-ray computed tomography system to mitigate the ill-posedness of dynamic FMT inverse problem, and use direct reconstruction strategy to make full use of temporal correlations of boundary measurements. The results of numerical simulations and in vivo mouse experiments demonstrate that the proposed method leads to significant improvements in the reconstruction quality of parametric images as compared with the conventional indirect method and a previously developed direct method.

Acceleration of dynamic fluorescence molecular tomography with principal component analysis

Dynamic fluorescence molecular tomography (FMT) is an attractive imaging technique for three-dimensionally resolving the metabolic process of fluorescent biomarkers in small animal. When combined with compartmental modeling, dynamic FMT can be used to obtain parametric images which can provide quantitative pharmacokinetic information for drug development and metabolic research. However, the computational burden of dynamic FMT is extremely huge due to its large data sets arising from the long measurement process and the densely sampling device. In this work, we propose to accelerate the reconstruction process of dynamic FMT based on principal component analysis (PCA). Taking advantage of the compression property of PCA, the dimension of the sub weight matrix used for solving the inverse problem is reduced by retaining only a few principal components which can retain most of the effective information of the sub weight matrix. Therefore, the reconstruction process of dynamic FMT can be accelerated by solving the smaller scale inverse problem. Numerical simulation and mouse experiment are performed to validate the performance of the proposed method. Results show that the proposed method can greatly accelerate the reconstruction of parametric images in dynamic FMT almost without degradation in image quality.

Pharmacokinetic Tumor Heterogeneity as a Prognostic Biomarker for Classifying Breast Cancer Recurrence Risk

GOAL

Heterogeneity in cancer can affect response to therapy and patient prognosis. Histologic measures have classically been used to measure heterogeneity, although a reliable noninvasive measurement is needed both to establish baseline risk of recurrence and monitor response to treatment. Here, we propose using spatiotemporal wavelet kinetic features from dynamic contrast-enhanced magnetic resonance imaging to quantify intratumor heterogeneity in breast cancer.

METHODS

Tumor pixels are first partitioned into homogeneous subregions using pharmacokinetic measures. Heterogeneity wavelet kinetic (HetWave) features are then extracted from these partitions to obtain spatiotemporal patterns of the wavelet coefficients and the contrast agent uptake. The HetWave features are evaluated in terms of their prognostic value using a logistic regression classifier with genetic algorithm wrapper-based feature selection to classify breast cancer recurrence risk as determined by a validated gene expression assay.

RESULTS

Receiver operating characteristic analysis and area under the curve (AUC) are computed to assess classifier performance using leave-one-out cross validation. The HetWave features outperform other commonly used features (AUC = 0.88 HetWave versus 0.70 standard features). The combination of HetWave and standard features further increases classifier performance (AUCs 0.94).

CONCLUSION

The rate of the spatial frequency pattern over the pharmacokinetic partitions can provide valuable prognostic information.

SIGNIFICANCE

HetWave could be a powerful feature extraction approach for characterizing tumor heterogeneity, providing valuable prognostic information.

Models and methods for analyzing DCE-MRI: a review

PURPOSE

To present a review of most commonly used techniques to analyze dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), discusses their strengths and weaknesses, and outlines recent clinical applications of findings from these approaches.

METHODS

DCE-MRI allows for noninvasive quantitative analysis of contrast agent (CA) transient in soft tissues. Thus, it is an important and well-established tool to reveal microvasculature and perfusion in various clinical applications. In the last three decades, a host of nonparametric and parametric models and methods have been developed in order to quantify the CA's perfusion into tissue and estimate perfusion-related parameters (indexes) from signal- or concentration-time curves. These indexes are widely used in various clinical applications for the detection, characterization, and therapy monitoring of different diseases.

RESULTS

Promising theoretical findings and experimental results for the reviewed models and techniques in a variety of clinical applications suggest that DCE-MRI is a clinically relevant imaging modality, which can be used for early diagnosis of different diseases, such as breast and prostate cancer, renal rejection, and liver tumors.

CONCLUSIONS

Both nonparametric and parametric approaches for DCE-MRI analysis possess the ability to quantify tissue perfusion.

A multi-task learning approach for compartmental model parameter estimation in DCE-CT sequences

Today's follow-up of patients presenting abdominal tumors is generally performed through acquisition of dynamic sequences of contrast-enhanced CT. Estimating parameters of appropriate models of contrast intake diffusion through tissues should help characterizing the tumor physiology, but is impeded by the high level of noise inherent to the acquisition conditions. To improve the quality of estimation, we consider parameter estimation in voxels as a multi-task learning problem (one task per voxel) that takes advantage from the similarity between two tasks. We introduce a temporal similarity between tasks based on a robust distance between observed contrast-intake profiles of intensity. Using synthetic images, we compare multi-task learning using this temporal similarity, a spatial similarity and a single-task learning. The similarities based on temporal profiles are shown to bring significant improvements compared to the spatial one. Results on real CT sequences also confirm the relevance of the approach.

Gaussian process inference for estimating pharmacokinetic parameters of dynamic contrast-enhanced MR images

In this paper, we propose a new pharmacokinetic model for parameter estimation of dynamic contrast-enhanced (DCE) MRI by using Gaussian process inference. Our model is based on the Tofts dual-compartment model for the description of tracer kinetics and the observed time series from DCE-MRI is treated as a Gaussian stochastic process. The parameter estimation is done through a maximum likelihood approach and we propose a variant of the coordinate descent method to solve this likelihood maximization problem. The new model was shown to outperform a baseline method on simulated data. Parametric maps generated on prostate DCE data with the new model also provided better enhancement of tumors, lower intensity on false positives, and better boundary delineation when compared with the baseline method. New statistical parameter maps from the process model were also found to be informative, particularly when paired with the PK parameter maps.

Reliable estimation of incoherent motion parametric maps from diffusion-weighted MRI using fusion bootstrap moves

Diffusion-weighted MRI has the potential to provide important new insights into physiological and microstructural properties of the body. The Intra-Voxel Incoherent Motion (IVIM) model relates the observed DW-MRI signal decay to parameters that reflect blood flow in the capillaries (D*), capillaries volume fraction (f), and diffusivity (D). However, the commonly used, independent voxel-wise fitting of the IVIM model leads to imprecise parameter estimates, which has hampered their practical usage. In this work, we improve the precision of estimates by introducing a spatially-constrained Incoherent Motion (IM) model of DW-MRI signal decay. We also introduce an efficient iterative "fusion bootstrap moves" (FBM) solver that enables precise parameter estimates with this new IM model. This solver updates parameter estimates by applying a binary graph-cut solver to fuse the current estimate of parameter values with a new proposal of the parameter values into a new estimate of parameter values that better fits the observed DW-MRI data. The proposals of parameter values are sampled from the independent voxel-wise distributions of the parameter values with a model-based bootstrap resampling of the residuals. We assessed both the improvement in the precision of the incoherent motion parameter estimates and the characterization of heterogeneous tumor environments by analyzing simulated and in vivo abdominal DW-MRI data of 30 patients, and in vivo DW-MRI data of three patients with musculoskeletal lesions. We found our IM-FBM reduces the relative root mean square error of the D* parameter estimates by 80%, and of the f and D parameter estimates by 50% compared to the IVIM model with the simulated data. Similarly, we observed that our IM-FBM method significantly reduces the coefficient of variation of parameter estimates of the D* parameter by 43%, the f parameter by 37%, and the D parameter by 17% compared to the IVIM model (paired Student's t-test, p<0.0001). In addition, we found our IM-FBM method improved the characterization of heterogeneous musculoskeletal lesions by means of increased contrast-to-noise ratio of 19.3%. The IM model and FBM solver combined, provide more precise estimate of the physiological model parameter values that describing the DW-MRI signal decay and a better mechanism for characterizing heterogeneous lesions than does the independent voxel-wise IVIM model.

Spatially regularized T(1) estimation from variable flip angles MRI

PURPOSE

To develop efficient algorithms for fast voxel-by-voxel quantification of tissue longitudinal relaxation time (T(1)) from variable flip angles magnetic resonance images (MRI) to reduce voxel-level noise without blurring tissue edges.

METHODS

T(1) estimations regularized by total variation (TV) and quadratic penalty are developed to measure T(1) from fast variable flip angles MRI and to reduce voxel-level noise without decreasing the accuracy of the estimates. First, a quadratic surrogate for a log likelihood cost function of T(1) estimation is derived based upon the majorization principle, and then the TV-regularized surrogate function is optimized by the fast iterative shrinkage thresholding algorithm. A fast optimization algorithm for the quadratically regularized T(1) estimation is also presented. The proposed methods are evaluated by the simulated and experimental MR data.

RESULTS

The means of the T(1) values in the simulated brain data estimated by the conventional, TV-regularized, and quadratically regularized methods have less than 3% error from the true T(1) in both GM and WM tissues with image noise up to 9%. The relative standard deviations (SDs) of the T(1) values estimated by the conventional method are more than 12% and 15% when the images have 7% and 9% noise, respectively. In comparison, the TV-regularized and quadratically regularized methods are able to suppress the relative SDs of the estimated T(1) to be less than 2% and 3%, respectively, regardless of the image noise level. However, the quadratically regularized method tends to overblur the edges compared to the TV-regularized method.

CONCLUSIONS

The spatially regularized methods improve quality of T(1) estimation from multiflip angles MRI. Quantification of dynamic contrast-enhanced MRI can benefit from the high quality measurement of native T(1).

Reliable assessment of perfusivity and diffusivity from diffusion imaging of the body

Diffusion-weighted MRI of the body has the potential to provide important new insights into physiological and microstructural properties. The intra-voxel incoherent motion (IVIM) model relates the observed DW-MRI signal decay to parameters that reflect perfusivity (D*) and its volume fraction (f), and diffusivity (D). However, the commonly used voxel-wise fitting of the IVIM model leads to parameter estimates with poor precision, which has hampered their practical usage. In this work, we increase the estimates' precision by introducing a model of spatial homogeneity, through which we obtain estimates of model parameters for all of the voxels at once, instead of solving for each voxel independently. Furthermore, we introduce an efficient iterative solver which utilizes a model-based bootstrap estimate of the distribution of residuals and a binary graph cut to generate optimal model parameter updates. Simulation experiments show that our approach reduces the relative root mean square error of the estimated parameters by 80% for the D* parameter and by 50% for the f and D parameters. We demonstrated the clinical impact of our model in distinguishing between enhancing and nonenhancing ileum segments in 24 Crohn's disease patients. Our model detected the enhanced segments with 91%/92% sensitivity/specificity which is better than the 81%/85% obtained by the voxel-independent approach.

Using spatial prior knowledge in the spectral fitting of MRS images

We propose a Bayesian smoothness prior in the spectral fitting of MRS images which can be used in addition to commonly employed prior knowledge. By combining a frequency-domain model for the free induction decay with a Gaussian Markov random field prior, a new optimization objective is derived that encourages smooth parameter maps. Using a particular parameterization of the prior, smooth damping, frequency and phase maps can be obtained whilst preserving sharp spatial features in the amplitude map. A Monte Carlo study based on two sets of simulated data demonstrates that the variance of the estimated parameter maps can be reduced considerably, even below the Cramér-Rao lower bound, when using spatial prior knowledge. Long-TE (1)H MRSI at 1.5 T of a patient with a brain tumor shows that the use of the spatial prior resolves the overlapping peaks of choline and creatine when a single voxel method fails to do so. Improved and detailed metabolic maps can be derived from high-spatial-resolution, short-TE (1)H MRSI at 3 T. Finally, the evaluation of four series of long-TE brain MRSI data with various signal-to-noise ratios shows the general benefit of the proposed approach.

Tissue-specific compartmental analysis for dynamic contrast-enhanced MR imaging of complex tumors

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides a noninvasive method for evaluating tumor vasculature patterns based on contrast accumulation and washout. However, due to limited imaging resolution and tumor tissue heterogeneity, tracer concentrations at many pixels often represent a mixture of more than one distinct compartment. This pixel-wise partial volume effect (PVE) would have profound impact on the accuracy of pharmacokinetics studies using existing compartmental modeling (CM) methods. We, therefore, propose a convex analysis of mixtures (CAM) algorithm to explicitly mitigate PVE by expressing the kinetics in each pixel as a nonnegative combination of underlying compartments and subsequently identifying pure volume pixels at the corners of the clustered pixel time series scatter plot simplex. The algorithm is supported theoretically by a well-grounded mathematical framework and practically by plug-in noise filtering and normalization preprocessing. We demonstrate the principle and feasibility of the CAM-CM approach on realistic synthetic data involving two functional tissue compartments, and compare the accuracy of parameter estimates obtained with and without PVE elimination using CAM or other relevant techniques. Experimental results show that CAM-CM achieves a significant improvement in the accuracy of kinetic parameter estimation. We apply the algorithm to real DCE-MRI breast cancer data and observe improved pharmacokinetic parameter estimation, separating tumor tissue into regions with differential tracer kinetics on a pixel-by-pixel basis and revealing biologically plausible tumor tissue heterogeneity patterns. This method combines the advantages of multivariate clustering, convex geometry analysis, and compartmental modeling approaches. The open-source MATLAB software of CAM-CM is publicly available from the Web.

Permeability assessment of the focused ultrasound-induced blood-brain barrier opening using dynamic contrast-enhanced MRI

Focused ultrasound (FUS) in conjunction with microbubbles has been shown to successfully open the blood-brain barrier (BBB) in the mouse brain. In this study, we compute the BBB permeability after opening in vivo. The spatial permeability of the BBB-opened region was assessed using dynamic contrast-enhanced MRI (DCE-MRI). The DCE-MR images were post-processed using the general kinetic model (GKM) and the reference region model (RRM). Permeability maps were generated and the K(trans) values were calculated for a predefined volume of interest in the sonicated and the control area for each mouse. The results demonstrated that K(trans) in the BBB-opened region (0.02 +/- 0.0123 for GKM and 0.03 +/- 0.0167 min(-1) for RRM) was at least two orders of magnitude higher when compared to the contra-lateral (control) side (0 and 8.5 x 10(-4) +/- 12 x 10(-4) min(-1), respectively). The permeability values obtained with the two models showed statistically significant agreement and excellent correlation (R(2) = 0.97). At histological examination, it was concluded that no macroscopic damage was induced. This study thus constitutes the first permeability assessment of FUS-induced BBB opening using DCE-MRI, supporting the fact that the aforementioned technique may constitute a safe, non-invasive and efficacious drug delivery method.