Cramér-Rao bound-informed training of neural networks for quantitative MRI

Bias-reduced neural networks for parameter estimation in quantitative MRI

PURPOSE

To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound.

THEORY AND METHODS

We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications.

RESULTS

In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations.

CONCLUSION

The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Optimisation of quantitative brain diffusion-relaxation MRI acquisition protocols with physics-informed machine learning

Diffusion-relaxation MRI aims to extract quantitative measures that characterise microstructural tissue properties such as orientation, size, and shape, but long acquisition times are typically required. This work proposes a physics-informed learning framework to extract an optimal subset of diffusion-relaxation MRI measurements for enabling shorter acquisition times, predict non-measured signals, and estimate quantitative parameters. In vivo and synthetic brain 5D-Diffusion-T1-T2∗-weighted MRI data obtained from five healthy subjects were used for training and validation, and from a sixth participant for testing. One fully data-driven and two physics-informed machine learning methods were implemented and compared to two manual selection procedures and Cramér-Rao lower bound optimisation. The physics-informed approaches could identify measurement-subsets that yielded more consistently accurate parameter estimates in simulations than other approaches, with similar signal prediction error. Five-fold shorter protocols yielded error distributions of estimated quantitative parameters with very small effect sizes compared to estimates from the full protocol. Selected subsets commonly included a denser sampling of the shortest and longest inversion time, lowest echo time, and high b-value. The proposed framework combining machine learning and MRI physics offers a promising approach to develop shorter imaging protocols without compromising the quality of parameter estimates and signal predictions.

Bias-Reduced Neural Networks for Parameter Estimation in Quantitative MRI

Purpose

To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound.

Theory and Methods

We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications.

Results

In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as non-linear least-squares fitting, while state-of-the-art NNs show larger deviations.

Conclusion

The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Rapid quantitative magnetization transfer imaging: Utilizing the hybrid state and the generalized Bloch model

PURPOSE

To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters.

THEORY AND METHODS

We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency.

RESULTS

We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, consistent with previous reports.

CONCLUSION

The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters.

Unconstrained quantitative magnetization transfer imaging: disentangling T1 of the free and semi-solid spin pools

Since the inception of magnetization transfer (MT) imaging, it has been widely assumed that Henkelman's two spin pools have similar longitudinal relaxation times, which motivated many researchers to constrain them to each other. However, several recent publications reported a T 1 s of the semi-solid spin pool that is much shorter than T 1 f of the free pool. While these studies tailored experiments for robust proofs-of-concept, we here aim to quantify the disentangled relaxation processes on a voxel-by-voxel basis in a clinical imaging setting, i.e., with an effective resolution of 1.24mm isotropic and full brain coverage in 12min. To this end, we optimized a hybrid-state pulse sequence for mapping the parameters of an unconstrained MT model. We scanned four people with relapsing-remitting multiple sclerosis (MS) and four healthy controls with this pulse sequence and estimated T 1 f ≈ 1.84 s and T 1 s ≈ 0.34 s in healthy white matter. Our results confirm the reports that T 1 s ≪ T 1 f and we argue that this finding identifies MT as an inherent driver of longitudinal relaxation in brain tissue. Moreover, we estimated a fractional size of the semi-solid spin pool of m 0 s ≈ 0.212 , which is larger than previously assumed. An analysis of T 1 f in normal-appearing white matter revealed statistically significant differences between individuals with MS and controls.

Minimization of eddy current artifacts in sequences with periodic dynamics

PURPOSE

To minimize eddy current artifacts in periodic pulse sequences with balanced gradient moments as, for example, used for quantitative MRI.

THEORY AND METHODS

Eddy current artifacts in balanced sequences result from large jumps in k-space. In quantitative MRI, one often samples some spin dynamics repeatedly while acquiring different parts of k-space. We swap individual k-space lines between different repetitions in order to minimize jumps in temporal succession without changing the overall trajectory. This reordering can be formulated as a traveling salesman problem and we tackle the discrete optimization with a simulated annealing algorithm.

RESULTS

Compared to the default ordering, we observe a substantial reduction of artifacts in the reconstructed images and the derived quantitative parameter maps. Comparing two variants of our algorithm, one that resembles the pairing approach originally proposed by Bieri et al., and one that minimizes all k-space jumps equally, we observe slightly lower artifact levels in the latter.

CONCLUSION

The proposed reordering scheme effectively reduces eddy current artifacts in sequences with balanced gradient moments. In contrast to previous approaches, we capitalize on the periodicity of the sampled signal dynamics, enabling both efficient k-space sampling and minimizing artifacts caused by eddy currents.

Genomic prediction and association mapping of maize grain yield in multi-environment trials based on reaction norm models

Genotype-by-environment interaction (GEI) is among the greatest challenges for maize breeding programs. Strong GEI limits both the prediction of genotype performance across variable environmental conditions and the identification of genomic regions associated with grain yield. Incorporating GEI into yield prediction models has been shown to improve prediction accuracy of yield; nevertheless, more work is needed to further understand this complex interaction across populations and environments. The main objectives of this study were to: 1) assess GEI in maize grain yield based on reaction norm models and predict hybrid performance across a gradient of environmental (EG) conditions and 2) perform a genome-wide association study (GWAS) and post-GWAS analyses for maize grain yield using data from 2014 to 2017 of the Genomes to Fields initiative hybrid trial. After quality control, 2,126 hybrids with genotypic and phenotypic data were assessed across 86 environments representing combinations of locations and years, although not all hybrids were evaluated in all environments. Heritability was greater in higher-yielding environments due to an increase in genetic variability in these environments in comparison to the low-yielding environments. GWAS was carried out for yield and five single nucleotide polymorphisms (SNPs) with the highest magnitude of effect were selected in each environment for follow-up analyses. Many candidate genes in proximity of selected SNPs have been previously reported with roles in stress response. Genomic prediction was performed to assess prediction accuracy of previously tested or untested hybrids in environments from a new growing season. Prediction accuracy was 0.34 for cross validation across years (CV0-Predicted EG) and 0.21 for cross validation across years with only untested hybrids (CV00-Predicted EG) when compared to Best Linear Unbiased Prediction (BLUPs) that did not utilize genotypic or environmental relationships. Prediction accuracy improved to 0.80 (CV0-Predicted EG) and 0.60 (CV00-Predicted EG) when compared to the whole-dataset model that used the genomic relationships and the environmental gradient of all environments in the study. These results identify regions of the genome for future selection to improve yield and a methodology to increase the number of hybrids evaluated across locations of a multi-environment trial through genomic prediction.

Emerging Trends in Fast MRI Using Deep-Learning Reconstruction on Undersampled k-Space Data: A Systematic Review

Magnetic Resonance Imaging (MRI) is an essential medical imaging modality that provides excellent soft-tissue contrast and high-resolution images of the human body, allowing us to understand detailed information on morphology, structural integrity, and physiologic processes. However, MRI exams usually require lengthy acquisition times. Methods such as parallel MRI and Compressive Sensing (CS) have significantly reduced the MRI acquisition time by acquiring less data through undersampling k-space. The state-of-the-art of fast MRI has recently been redefined by integrating Deep Learning (DL) models with these undersampled approaches. This Systematic Literature Review (SLR) comprehensively analyzes deep MRI reconstruction models, emphasizing the key elements of recently proposed methods and highlighting their strengths and weaknesses. This SLR involves searching and selecting relevant studies from various databases, including Web of Science and Scopus, followed by a rigorous screening and data extraction process using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. It focuses on various techniques, such as residual learning, image representation using encoders and decoders, data-consistency layers, unrolled networks, learned activations, attention modules, plug-and-play priors, diffusion models, and Bayesian methods. This SLR also discusses the use of loss functions and training with adversarial networks to enhance deep MRI reconstruction methods. Moreover, we explore various MRI reconstruction applications, including non-Cartesian reconstruction, super-resolution, dynamic MRI, joint learning of reconstruction with coil sensitivity and sampling, quantitative mapping, and MR fingerprinting. This paper also addresses research questions, provides insights for future directions, and emphasizes robust generalization and artifact handling. Therefore, this SLR serves as a valuable resource for advancing fast MRI, guiding research and development efforts of MRI reconstruction for better image quality and faster data acquisition.

Unravelling the genetic framework associated with grain quality and yield-related traits in maize (Zea mays L.)

Maize serves as a crucial nutrient reservoir for a significant portion of the global population. However, to effectively address the growing world population's hidden hunger, it is essential to focus on two key aspects: biofortification of maize and improving its yield potential through advanced breeding techniques. Moreover, the coordination of multiple targets within a single breeding program poses a complex challenge. This study compiled mapping studies conducted over the past decade, identifying quantitative trait loci associated with grain quality and yield related traits in maize. Meta-QTL analysis of 2,974 QTLs for 169 component traits (associated with quality and yield related traits) revealed 68 MQTLs across different genetic backgrounds and environments. Most of these MQTLs were further validated using the data from genome-wide association studies (GWAS). Further, ten MQTLs, referred to as breeding-friendly MQTLs (BF-MQTLs), with a significant phenotypic variation explained over 10% and confidence interval less than 2 Mb, were shortlisted. BF-MQTLs were further used to identify potential candidate genes, including 59 genes encoding important proteins/products involved in essential metabolic pathways. Five BF-MQTLs associated with both quality and yield traits were also recommended to be utilized in future breeding programs. Synteny analysis with wheat and rice genomes revealed conserved regions across the genomes, indicating these hotspot regions as validated targets for developing biofortified, high-yielding maize varieties in future breeding programs. After validation, the identified candidate genes can also be utilized to effectively model the plant architecture and enhance desirable quality traits through various approaches such as marker-assisted breeding, genetic engineering, and genome editing.