Rapid look-up table method for noise-corrected curve fitting in the R2* mapping of iron loaded liver

Effect of particle size on liver MRI R 2 * relaxometry: Monte Carlo simulation and phantom studies

PURPOSE

To investigate the effect of particle size on liverR 2 * $$ {\mathrm{R}}_2^{\ast } $$ by Monte Carlo simulation and phantom studies at both 1.5 T and 3.0 T.

METHODS

Two kinds of particles (i.e., iron sphere and fat droplet) with varying sizes were considered separately in simulation and phantom studies. MRI signals were synthesized and analyzed for predictingR 2 * $$ {\mathrm{R}}_2^{\ast } $$ , based on simulations by incorporating virtual liver model, particle distribution, magnetic field generation, and proton movement into phase accrual. In the phantom study, iron-water and fat-water phantoms were constructed, and each phantom contained 15 separate vials with combinations of five particle concentrations and three particle sizes.R 2 * $$ {\mathrm{R}}_2^{\ast } $$ measurements in the phantom were made at both 1.5 T and 3.0 T. Finally, differences inR 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions or measurements were evaluated across varying particle sizes.

RESULTS

In the simulation study, strong linear and positively correlated relationships were observed betweenR 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions and particle concentrations across varying particle sizes and magnetic field strengths (r ≥ 0.988 $$ r\ge 0.988 $$ ). The relationships were affected by iron sphere size (p < 0.001 $$ p<0.001 $$ ), where smaller iron sphere size yielded higher predictedR 2 * $$ {\mathrm{R}}_2^{\ast } $$ , whereas fat droplet size had no effect onR 2 * $$ {\mathrm{R}}_2^{\ast } $$ predictions (p ≥ 0.617 $$ p\ge 0.617 $$ ) for constant total fat concentration. Similarly, the phantom study showed thatR 2 * $$ {\mathrm{R}}_2^{\ast } $$ measurements were relatively sensitive to iron sphere size (p ≤ 0.004 $$ p\le 0.004 $$ ) unlike fat droplet size (p ≥ 0.223 $$ p\ge 0.223 $$ ).

CONCLUSION

LiverR 2 * $$ {\mathrm{R}}_2^{\ast } $$ is affected by iron sphere size, but is relatively unaffected by fat droplet size. These findings may lead to an improved understanding of the underlying mechanisms ofR 2 * $$ {\mathrm{R}}_2^{\ast } $$ relaxometry in vivo, and enable improved quantitative MRI phantom design.

Cascade of Denoising and Mapping Neural Networks for MRI R2* Relaxometry of Iron-Loaded Liver

MRI of effective transverse relaxation rate (R2*) measurement is a reliable method for liver iron concentration quantification. However, R2* mapping can be degraded by noise, especially in the case of iron overload. This study aimed to develop a deep learning method for MRI R2* relaxometry of an iron-loaded liver using a two-stage cascaded neural network. The proposed method, named CadamNet, combines two convolutional neural networks separately designed for image denoising and parameter mapping into a cascade framework, and the physics-based R2* decay model was incorporated in training the mapping network to enforce data consistency further. CadamNet was trained using simulated liver data with Rician noise, which was constructed from clinical liver data. The performance of CadamNet was quantitatively evaluated on simulated data with varying noise levels as well as clinical liver data and compared with the single-stage parameter mapping network (MappingNet) and two conventional model-based R2* mapping methods. CadamNet consistently achieved high-quality R2* maps and outperformed MappingNet at varying noise levels. Compared with conventional R2* mapping methods, CadamNet yielded R2* maps with lower errors, higher quality, and substantially increased efficiency. In conclusion, the proposed CadamNet enables accurate and efficient iron-loaded liver R2* mapping, especially in the presence of severe noise.

A Joint Framework for Denoising and Estimating Diffusion Kurtosis Tensors Using Multiple Prior Information

Diffusion kurtosis imaging (DKI) has been shown to be valuable in a wide range of neuroscientific and clinical applications. However, reliable estimation of DKI tensors is often compromised by noise, especially for the kurtosis tensor (KT). Here, we propose a joint denoising and estimating framework that integrates multiple sources of prior information, including nonlocal structural self-similarity (NSS), local spatial smoothness (LSS), physical relevance (PR) of the DKI model, and noise characteristics of magnitude diffusion MRI (dMRI) images for improved estimation of DKI tensors. The local and nonlocal spatial smoothing constraints are complementary to each other, making the proposed framework highly effective in reducing the noise fluctuations on DKI tensors, especially KT. As an additional refinement, we propose to impose a physically relevant constraint within our joint denoising and estimation framework. We further adopt the first-moment noise-corrected fitting model (M¹NCM) to remove the noncentral χ -distribution noise bias. The effectiveness of integrating multiple sources of priors into the joint framework is verified by comparing the proposed M¹NCM-NSS-LSS-PR method with various versions of M¹NCM-based estimators and two state-of-the-art methods. Results show that the proposed method outperformed the compared methods in simulations and in-vivo dMRI datasets of both spatially stationary and nonstationary noise distributions. The in-vivo experiments also show that the proposed M¹NCM-NSS-LSS-PR method was robust to the number of diffusion directions.

Multicenter validation of the magnetic resonance T2* technique for quantification of pancreatic iron

OBJECTIVES

To assess the transferability of the magnetic resonance imaging (MRI) multislice multiecho T2* technique for pancreatic iron overload assessment.

METHODS

Multiecho T2* sequences were installed on ten 1.5-T MRI scanners of the three main vendors. Five healthy subjects (n = 50) were scanned at each site. Five patients with thalassemia (n = 45) were scanned locally at each site and were rescanned at the reference site within 1 month. T2* images were analyzed using a previously validated software and the global pancreatic T2* value was calculated as the mean of T2* values over the head, body, and tail.

RESULTS

T2* values of healthy subjects were above 26 ms and showed inter-site homogeneity. The T2* values measured in the MRI sites were comparable to the correspondent values observed in the reference site (12.02 ± 10.20 ms vs 11.98 ± 10.47 ms; p = 0.808), and the correlation coefficient was 0.978 (p < 0.0001). Coefficients of variation (CoVs) ranged from 4.22 to 9.77%, and the CoV for all the T2* values independently from the sites was 8.55%. The intraclass correlation coefficient (ICC) for each MRI site was always excellent and the global ICC was 0.995, independently from the sites. The mean absolute difference in patients with pancreatic iron (n = 39) was -0.15 ± 1.38 ms.

CONCLUSION

The gradient-echo T2* MRI technique is an accurate and reproducible means for the quantification of pancreatic iron and may be transferred among MRI scanners by different vendors in several centers.

KEY POINTS

• The gradient-echo T2* MRI technique is an accurate and reproducible means for the quantification of pancreatic iron. • The gradient-echo T2* MRI technique for the quantification of pancreatic iron may be transferred among MRI scanners by different vendors in several centers. • Pancreatic iron might serve as an early predictor of cardiac siderosis and is the strongest overall predictor of glucose dysregulation.

Fisher information and Cramér-Rao lower bound for experimental design in parallel imaging

PURPOSE

The Cramér-Rao lower bound (CRLB) is widely used in the design of magnetic resonance (MR) experiments for parameter estimation. Previous work has considered only Gaussian or Rician noise distributions in this calculation. However, the noise distribution for multi-coil acquisitions, such as in parallel imaging, obeys the noncentral χ-distribution under many circumstances. The purpose of this paper is to present the CRLB calculation for parameter estimation from multi-coil acquisitions.

THEORY AND METHODS

We perform explicit calculations of Fisher matrix elements and the associated CRLB for noise distributions following the noncentral χ-distribution. The special case of diffusion kurtosis is examined as an important example. For comparison with analytic results, Monte Carlo (MC) simulations were conducted to evaluate experimental minimum standard deviations (SDs) in the estimation of diffusion kurtosis model parameters. Results were obtained for a range of signal-to-noise ratios (SNRs), and for both the conventional case of Gaussian noise distribution and noncentral χ-distribution with different numbers of coils, m.

RESULTS

At low-to-moderate SNR, the noncentral χ-distribution deviates substantially from the Gaussian distribution. Our results indicate that this departure is more pronounced for larger values of m. As expected, the minimum SDs (i.e., CRLB) in derived diffusion kurtosis model parameters assuming a noncentral χ-distribution provided a closer match to the MC simulations as compared to the Gaussian results.

CONCLUSION

Estimates of minimum variance for parameter estimation and experimental design provided by the CRLB must account for the noncentral χ-distribution of noise in multi-coil acquisitions, especially in the low-to-moderate SNR regime. Magn Reson Med 79:3249-3255, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Improved Liver R2* Mapping by Averaging Decay Curves

Liver R2* mapping is often degraded by the low signal-to-noise ratio (SNR) especially in the presence of severe iron. This study aims to improve liver R2* mapping at low SNRs by averaging decay curves before the process of curve-fitting. Independently filtering echo images by nonlocal means (NLM) demonstrated improved quality of R2* mapping, but may introduce new errors due to the nonlinear nature of the NLM filter, during which the averaging weights may vary with different image contents at multiple echo times. In addition, the image denoising effect of the NLM may decline when no sufficient similar patches are available. To overcome these drawbacks, we proposed to filter decay curves instead of images. In this novel scheme, decay curves were averaged in a local window, each with a weight assigned according to the curve-similarity measured by the distance between one of the neighboring curves and the targeted one. The proposed method was tested on simulated, phantom and patient data. The results demonstrate that the proposed method can provide more accurate R2* mapping compared with the NLM algorithm, and hence has the potential to improve diagnosis and therapy in patients with liver iron.

Bayesian analysis of transverse signal decay with application to human brain

PURPOSE

Transverse relaxation analysis with several signal models has been used extensively to determine tissue and material properties. However, the derivation of corresponding parameter values is notoriously unreliable. We evaluate improvements in the quality of parameter estimation using Bayesian analysis and incorporating the Rician noise model, as appropriate for magnitude MR images.

THEORY AND METHODS

Monoexponential, stretched exponential, and biexponential signal models were analyzed using nonlinear least squares (NLLS) and Bayesian approaches. Simulations and phantom and human brain data were analyzed using three different approaches to account for noise. Parameter estimation bias (reflecting accuracy) and dispersion (reflecting precision) were derived for a range of signal-to-noise ratios (SNR) and relaxation parameters.

RESULTS

All methods performed well at high SNR. At lower SNR, the Bayesian approach yielded parameter estimates of considerably greater precision, as well as greater accuracy, than did NLLS. Incorporation of the Rician noise model greatly improved accuracy and, to a somewhat lesser extent, precision, in derived transverse relaxation parameters. Analyses of data obtained from solution phantoms and from brain were consistent with simulations.

CONCLUSION

Overall, estimation of parameters characterizing several different transverse relaxation models was markedly improved through use of Bayesian analysis and through incorporation of the Rician noise model.