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

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.

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.

Joint Optimization of k-t Sampling Pattern and Reconstruction of DCE MRI for Pharmacokinetic Parameter Estimation

This work proposes to develop and evaluate a deep learning framework that jointly optimizes k-t sampling patterns and reconstruction for head and neck dynamic contrast-enhanced (DCE) MRI aiming to reduce bias and uncertainty of pharmacokinetic (PK) parameter estimation. 2D Cartesian phase encoding k-space subsampling patterns for a 3D spoiled gradient recalled echo (SPGR) sequence along a time course of DCE MRI were jointly optimized in a deep learning-based dynamic MRI reconstruction network by a loss function concerning both reconstruction image quality and PK parameter estimation accuracy. During training, temporal k-space data sharing scheme was optimized as well. The proposed method was trained and tested by multi-coil complex digital reference objects of DCE images (mcDROs). The PK parameters estimated by the proposed method were compared with two published iterative DCE MRI reconstruction schemes using normalized root mean squared errors (NRMSEs) and Bland-Altman analysis at temporal resolutions of [Formula: see text] = 2s, 3s, 4s, and 5s, which correspond to undersampling rates of R = 50, 34, 25, and 20. The proposed method achieved low PK parameter NRMSEs at all four temporal resolutions compared with the benchmark methods on testing mcDROs. The Bland-Altman plots demonstrated that the proposed method reduced PK parameter estimation bias and uncertainty in tumor regions at temporal resolution of 2s. The proposed method also showed robustness to contrast arrival timing variations across patients. This work provides a potential way to increase PK parameter estimation accuracy and precision, and thus facilitate the clinical translation of DCE MRI.

Dynamic contrast-enhanced MRI parametric mapping using high spatiotemporal resolution Golden-angle RAdial Sparse Parallel MRI and iterative joint estimation of the arterial input function and pharmacokinetic parameters

The aim of this work is to develop a data-driven quantitative dynamic contrast-enhanced (DCE) MRI technique using Golden-angle RAdial Sparse Parallel (GRASP) MRI with high spatial resolution and high flexible temporal resolution and pharmacokinetic (PK) analysis with an arterial input function (AIF) estimated directly from the data obtained from each patient. DCE-MRI was performed on 13 patients with gynecological malignancy using a 3-T MRI scanner with a single continuous golden-angle stack-of-stars acquisition and image reconstruction with two temporal resolutions, by exploiting a unique feature in GRASP that reconstructs acquired data with user-defined temporal resolution. Joint estimation of the AIF (both AIF shape and delay) and PK parameters was performed with an iterative algorithm that alternates between AIF and PK estimation. Computer simulations were performed to determine the accuracy (expressed as percentage error [PE]) and precision of the estimated parameters. PK parameters (volume transfer constant [K^trans ], fractional volume of the extravascular extracellular space [v_e ], and blood plasma volume fraction [v_p ]) and normalized root-mean-square error [nRMSE] (%) of the fitting errors for the tumor contrast kinetic data were measured both with population-averaged and data-driven AIFs. On patient data, the Wilcoxon signed-rank test was performed to compare nRMSE. Simulations demonstrated that GRASP image reconstruction with a temporal resolution of 1 s/frame for AIF estimation and 5 s/frame for PK analysis resulted in an absolute PE of less than 5% in the estimation of K^trans and v_e , and less than 11% in the estimation of v_p . The nRMSE (mean ± SD) for the dual temporal resolution image reconstruction and data-driven AIF was 0.16 ± 0.04 compared with 0.27 ± 0.10 (p < 0.001) with 1 s/frame using population-averaged AIF, and 0.23 ± 0.07 with 5 s/frame using population-averaged AIF (p < 0.001). We conclude that DCE-MRI data acquired and reconstructed with the GRASP technique at dual temporal resolution can successfully be applied to jointly estimate the AIF and PK parameters from a single acquisition resulting in data-driven AIFs and voxelwise PK parametric maps.

Optimizing constrained reconstruction in magnetic resonance imaging for signal detection

Constrained reconstruction in magnetic resonance imaging (MRI) allows the use of prior information through constraints to improve reconstructed images. These constraints often take the form of regularization terms in the objective function used for reconstruction. Constrained reconstruction leads to images which appear to have fewer artifacts than reconstructions without constraints but because the methods are typically nonlinear, the reconstructed images have artifacts whose structure is hard to predict. In this work, we compared different methods of optimizing the regularization parameter using a total variation (TV) constraint in the spatial domain and sparsity in the wavelet domain for one-dimensional (2.56×) undersampling using variable density undersampling. We compared the mean squared error (MSE), structural similarity (SSIM), L-curve and the area under the receiver operating characteristic (AUC) using a linear discriminant for detecting a small and a large signal. We used a signal-known-exactly task with varying backgrounds in a simulation where the anatomical variation was the major source of clutter for the detection task. Our results show that the AUC dependence on regularization parameters varies with the imaging task (i.e. the signal being detected). The choice of regularization parameters for MSE, SSIM, L-curve and AUC were similar. We also found that a model-based reconstruction including TV and wavelet sparsity did slightly better in terms of AUC than just enforcing data consistency but using these constraints resulted in much better MSE and SSIM. These results suggest that the increased performance in MSE and SSIM over-estimate the improvement in detection performance for the tasks in this paper. The MSE and SSIM metrics show a big difference in performance where the difference in AUC is small. To our knowledge, this is the first time that signal detection with varying backgrounds has been used to optimize constrained reconstruction in MRI.

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.

Sparse precontrast T1 mapping for high-resolution whole-brain DCE-MRI

PURPOSE

To develop and evaluate an efficient precontrast T₁ mapping technique suitable for quantitative high-resolution whole-brain dynamic contrast-enhanced-magnetic resonance imaging (DCE-MRI).

METHODS

Variable flip angle (VFA) T₁ mapping was considered that provides 1 × 1 × 2 mm³ resolution to match a recent high-resolution whole-brain DCE-MRI protocol. Seven FAs were logarithmically spaced from 1.5° to 15°. T₁ and M₀ maps were estimated using model-based reconstruction. This approach was evaluated using an anatomically realistic brain tumor digital reference object (DRO) with noise-mimicking 3T neuroimaging and fully sampled data acquired from one healthy volunteer. Methods were also applied on fourfold prospectively undersampled VFA data from 13 patients with high-grade gliomas.

RESULTS

T₁ -mapping precision decreased with undersampling factor R, althoughwhereas bias remained small before a critical R. In the noiseless DRO, T₁ bias was <25 ms in white matter (WM) and <11 ms in brain tumor (BT). T₁ standard deviation (SD) was <119.5 ms in WM (coefficient of variation [COV] ~11.0%) and <253.2 ms in BT (COV ~12.7%). In the noisy DRO, T₁ bias was <50 ms in WM and <30 ms in BT. For R ≤ 10, T₁ SD was <107.1 ms in WM (COV ~9.9%) and <240.9 ms in BT (COV ~12.1%). In the healthy subject, T₁ bias was <30 ms for R ≤ 16. At R = 4, T₁ SD was 171.4 ms (COV ~13.0%). In the prospective brain tumor study, T₁ values were consistent with literature values in WM and BT.

CONCLUSION

High-resolution whole-brain VFA T₁ mapping is feasible with sparse sampling, supporting its use for quantitative DCE-MRI.

The LEGATOS technique: A new tissue-validated dynamic contrast-enhanced MRI method for whole-brain, high-spatial resolution parametric mapping

PURPOSE

A DCE-MRI technique that can provide both high spatiotemporal resolution and whole-brain coverage for quantitative microvascular analysis is highly desirable but currently challenging to achieve. In this study, we sought to develop and validate a novel dual-temporal resolution (DTR) DCE-MRI-based methodology for deriving accurate, whole-brain high-spatial resolution microvascular parameters.

METHODS

Dual injection DTR DCE-MRI was performed and composite high-temporal and high-spatial resolution tissue gadolinium-based-contrast agent (GBCA) concentration curves were constructed. The high-temporal but low-spatial resolution first-pass GBCA concentration curves were then reconstructed pixel-by-pixel to higher spatial resolution using a process we call LEGATOS. The accuracy of kinetic parameters (K^trans , v_p , and v_e ) derived using LEGATOS was evaluated through simulations and in vivo studies in 17 patients with vestibular schwannoma (VS) and 13 patients with glioblastoma (GBM). Tissue from 15 tumors (VS) was examined with markers for microvessels (CD31) and cell density (hematoxylin and eosin [H&E]).

RESULTS

LEGATOS derived parameter maps offered superior spatial resolution and improved parameter accuracy compared to the use of high-temporal resolution data alone, provided superior discrimination of plasma volume and vascular leakage effects compared to other high-spatial resolution approaches, and correlated with tissue markers of vascularity (P ≤ 0.003) and cell density (P ≤ 0.006).

CONCLUSION

The LEGATOS method can be used to generate accurate, high-spatial resolution microvascular parameter estimates from DCE-MRI.

Bulk motion-compensated DCE-MRI for functional imaging of kidneys in newborns

BACKGROUND

Evaluation of kidney function in newborns with hydronephrosis is important for clinical decisions. Dynamic contrast-enhanced (DCE) MRI can provide the necessary anatomical and functional information. Golden angle dynamic radial acquisition and compressed sensing reconstruction provides sufficient spatiotemporal resolution to achieve accurate parameter estimation for functional imaging of kidneys. However, bulk motion during imaging (rigid or nonrigid movement of the subject resulting in signal dropout) remains an unresolved challenge.

PURPOSE

To evaluate a motion-compensated (MoCo) DCE-MRI technique for robust evaluation of kidney function in newborns. Our method includes: 1) motion detection, 2) motion-robust image reconstruction, 3) joint realignment of the volumes, and 4) tracer-kinetic (TK) model fitting to evaluate kidney function parameters.

STUDY TYPE

Retrospective.

SUBJECTS

Eleven newborn patients (ages <6 months, 6 female).

FIELD STRENGTH/SEQUENCE

3T; dynamic "stack-of-stars" 3D fast low-angle shot (FLASH) sequence using a multichannel body-matrix coil.

ASSESSMENT

We evaluated the proposed technique in terms of the signal-to-noise ratio (SNR) of the reconstructed images, the presence of discontinuities in the contrast agent concentration time curves due to motion with a total variation (TV) metric and the goodness of fit of the TK model, and the standard variation of its parameters.

STATISTICAL TESTS

We used a paired t-test to compare the MoCo and no-MoCo results.

RESULTS

The proposed MoCo method successfully detected motion and improved the SNR by 3.3 (P = 0.012) and decreased TV by 0.374 (P = 0.017) across all subjects. Moreover, it decreased nRMSE of the TK model fit for the subjects with less than five isolated bulk motion events in 6 minutes (mean 1.53, P = 0.043), but not for the subjects with more frequent events or no motion (P = 0.745 and P = 0.683).

DATA CONCLUSION

Our results indicate that the proposed MoCo technique improves the image quality and accuracy of the TK model fit for subjects who present isolated bulk motion events.

LEVEL OF EVIDENCE

3 Technical Efficacy Stage: 1 J. Magn. Reson. Imaging 2020;52:207-216.

Tracer kinetic models as temporal constraints during brain tumor DCE-MRI reconstruction

Purpose

To apply tracer kinetic models as temporal constraints during reconstruction of under‐sampled brain tumor dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI).

Methods

A library of concentration vs time profiles is simulated for a range of physiological kinetic parameters. The library is reduced to a dictionary of temporal bases, where each profile is approximated by a sparse linear combination of the bases. Image reconstruction is formulated as estimation of concentration profiles and sparse model coefficients with a fixed sparsity level. Simulations are performed to evaluate modeling error, and error statistics in kinetic parameter estimation in presence of noise. Retrospective under‐sampling experiments are performed on a brain tumor DCE digital reference object (DRO), and 12 brain tumor in‐vivo 3T datasets. The performances of the proposed under‐sampled reconstruction scheme and an existing compressed sensing‐based temporal finite‐difference (tFD) under‐sampled reconstruction were compared against the fully sampled inverse Fourier Transform‐based reconstruction.

Results

Simulations demonstrate that sparsity levels of 2 and 3 model the library profiles from the Patlak and extended Tofts‐Kety (ETK) models, respectively. Noise sensitivity analysis showed equivalent kinetic parameter estimation error statistics from noisy concentration profiles, and model approximated profiles. DRO‐based experiments showed good fidelity in recovery of kinetic maps from 20‐fold under‐sampled data. In‐vivo experiments demonstrated reduced bias and uncertainty in kinetic mapping with the proposed approach compared to tFD at under‐sampled reduction factors >= 20.

Conclusions

Tracer kinetic models can be applied as temporal constraints during brain tumor DCE‐MRI reconstruction. The proposed under‐sampled scheme resulted in model parameter estimates less biased with respect to conventional fully sampled DCE MRI reconstructions and parameter estimation. The approach is flexible, can use nonlinear kinetic models, and does not require tuning of regularization parameters.

Impact of (k,t) sampling on DCE MRI tracer kinetic parameter estimation in digital reference objects

Purpose

To evaluate the impact of (k,t) data sampling on the variance of tracer‐kinetic parameter (TK) estimation in high‐resolution whole‐brain dynamic contrast enhanced magnetic resonance imaging (DCE‐MRI) using digital reference objects. We study this in the context of TK model constraints, and in the absence of other constraints.

Methods

Three anatomically and physiologically realistic brain‐tumor digital reference objects were generated. Data sampling strategies included uniform and variable density; zone‐based, lattice, pseudo‐random, and pseudo‐radial; with 50‐time frames and 4‐fold to 25‐fold undersampling. In all cases, we assume a fully sampled first time frame, and prior knowledge of the arterial input function. TK parameters were estimated by indirect estimation (i.e., image‐time‐series reconstruction followed by model fitting), and direct estimation from the under‐sampled data. We evaluated methods based on the Cramér‐Rao bound and Monte‐Carlo simulations, over the range of signal‐to‐noise ratio (SNR) seen in clinical brain DCE‐MRI.

Results

Lattice‐based sampling provided the lowest SDs, followed by pseudo‐random, pseudo‐radial, and zone‐based. This ranking was consistent for the Patlak and extended Tofts model. Pseudo‐random sampling resulted in 19% higher averaged SD compared to lattice‐based sampling. Zone‐based sampling resulted in substantially higher SD at undersampling factors above 10. CRB analysis showed only a small difference between uniform and variable density for both lattice‐based and pseudo‐random sampling up to undersampling factors of 25.

Conclusion

Lattice sampling provided the lowest SDs, although the differences between sampling schemes were not substantial at low undersampling factors. The differences between lattice‐based and pseudo‐random sampling strategies with both uniform and variable density were within the range of error induced by other sources, at up to 25‐fold undersampling.