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Revolutionizing Diffusion MRI Microstructure Mapping via Global Inversion
Yuxiang Wan, Hamza Farooq, Wenjie Zhang, Qiaozhi Huang, Lingjie Su, Christophe Lenglet, Ju Sun
TL;DR
Diffusion MRI microstructure mapping is framed as a nonlinear inverse problem whose voxel-wise treatment misses potential global structure. The paper proposes joint whole-volume inversion with untrained neural and T1-based priors; its synthetic and in-vivo results compare favorably with established methods.
Problem
Voxel-wise MM simplifies a nonlinear inverse problem but ignores potential global tissue structures that could provide useful priors.
Source: §1 · p. 1Method
The method jointly estimates microstructures across the tissue volume, using untrained neural priors and T1-weighted MRI structural guidance.
Source: §1 · p. 1, §3.4 · p. 3Results
On synthetic data, Ada-WIRE has the lowest ODI MSRE and improves all three parameter errors over AMICO–NODDI and MIX; in-vivo Ada-WIRE Anatomy has the lowest mean MAE and MSRE.
Source: §4.2 · p. 4Takeaways & Limitations
Global inversion offers a whole-volume optimization-based alternative to predominantly local or semi-local MM methods.
Source: §1 · pp. 1–2The global forward model aggregates voxel-level biophysical models; more faithful global models are left to future work.
Source: §1 · p. 1
Abstract
from arXiv · showhide
Diffusion MRI microstructure mapping (MM) is conventionally solved voxel by voxel, ignoring the fact that tissue microstructure forms a spatially organized field. This isolation leaves each estimation problem ill-posed and nonconvex. We instead cast MM as a single global inverse problem, reconstructing the entire parameter field jointly from all measurements of a subject. An untrained neural representation supplies implicit spatial priors and eases the nonconvex optimization, requiring no training data, while coregistered T1-weighted anatomy contributes structural guidance that is freely available in standard protocols. On both synthetic and in-vivo data, our method compares favorably with established voxel-wise and learning-based baselines, suggesting global inversion is a promising alternative.
1. INTRODUCTION
The introduction argues that voxel-wise simplification neglects useful global tissue structure and proposes jointly estimating the entire microstructure field, using untrained neural and T1-based priors to address nonconvexity.
1. INTRODUCTION
- Microstructure mapping is a highly nonlinear inverse problem because diffusion measurements depend on tissue microstructures through a nonlinear process.The forward relation also allows for modeling errors and measurement noise.Source: §1 · p. 1
- Current methods simplify the problem through voxel isolation and by estimating image-derived features rather than microstructures directly.They then perform independent voxel-wise inversion.Source: §1 · p. 1
- Local isolation discards potential global spatial priors and leaves highly nonconvex voxel-level optimization problems that may benefit from joint optimization.The cited priors include spatial smoothness, symmetries, and spatial recurrence.Source: §1 · p. 1
- The proposed global inversion jointly estimates the entire tissue volume from its measurements, contrasting with predominantly local or semi-local methods.Its global forward model aggregates voxel-level biophysical models, leaving more faithful global models to future work.Source: §1 · p. 1
- The method uses untrained neural priors for implicit global structure and nonconvex optimization, alongside structural guidance from T1-weighted MRI.The authors present it as the first optimization-based global-inversion MM method.Source: §1 · pp. 1–2
2. RELATED WORK AND BACKGROUND
The background describes untrained neural priors as data-free representations with implicit structural biases, then contrasts local MM approaches with global inversion and its related work.
2.1. Untrained Neural Priors (UNPs)
- Untrained neural priors reparameterize the target with a deep network whose architecture and optimization can favor simple spatial solutions without training data.Examples include deep image prior and implicit neural representation; the authors choose UNPs for global optimization and implicit structural biases.Source: §2.1 · p. 2
2.2. Microstructure Mapping (MM) for dMRI
- Optimization-based MM methods solve voxel-level nonconvex problems, while most supervised learning-based methods learn voxel-level inverse mappings from paired data.The described optimization examples include MIX and AMICO; supervised methods vary from multilayer perceptrons to unrolling and cascades.Source: §2.2 · p. 2
- The authors distinguish their approach from, a related global method using a standard white-matter model, by targeting NODDI and adding wavelet-inspired INR modification and T1-weighted MRI guidance.Source: §2.2 · p. 2
3. OUR GLOBAL INVERSION METHOD
The method jointly estimates brain microstructure fields from diffusion MRI measurements using an INR-based global inversion formulation. It combines a NODDI forward model, Ada-WIRE, and T1-informed modulation of the representation.
3.1. NODDI Forward Model
- The global forward model aggregates voxel-level NODDI signals, modeled as mixtures of intracellular, extracellular, and isotropic compartments.The parameter field includes intracellular and isotropic fractions, Watson concentration, and mean neurite orientation.Source: §3.1 · p. 2
3.2. Our Global-Inversion Formulation
- The coordinate-based INR predicts constrained NODDI parameter fields as part of the global-inversion formulation.Its prediction heads use final activations to enforce the parameters’ respective constraints.Source: §3.2 · pp. 2–3, §3 · p. 2
3.3. The Details of Our INR Model
- Ada-WIRE adapts WIRE by learning each neuron’s frequency and magnitude scales alongside the standard MLP weights.The scales begin from WIRE’s default initialization.Source: §3.3 · p. 3
3.4. MRI-Based Regularization
- T1-informed modulation supplies WIRE with resampled MRI intensity and gradient cues, emphasizing tissue boundaries while limiting modulation to roughly ±10%.T1-weighted scans are routinely acquired alongside dMRI in standard protocols, typically at no additional acquisition cost.Source: §3.4 · p. 3
4. EXPERIMENT
Experiments evaluate synthetic NODDI volumes with parameter ground truth and HCP data without in-vivo parameter ground truth. Ada-WIRE leads on synthetic ODI error, while anatomy-modulated Ada-WIRE produces coherent HCP maps and the lowest reported mean signal-fit errors.
4.2. Results
- Ada-WIRE achieves the lowest ODI MSRE and improves all three parameter errors over AMICO–NODDI and MIX; DIMOND has the lowest vic and viso errors but less consistent ODI recovery.DIMOND’s larger ODI standard deviation indicates less consistent recovery across samples.Source: Table 1 · p. 3, §4.2 · p. 4
4.1. Setup
- Evaluation compares estimated synthetic parameters with ground truth using three voxel-level MSRE variants, while HCP data from 10 subjects are assessed by MSRE/MAE signal fit and visual spatial organization.Each HCP subject has 288 measurements per voxel and an accompanying T1-weighted MRI scan.Source: §4.1 · p. 4
- The authors characterize the subject count as small but comparable to dMRI practice focused on voxel-level performance, and plan to scale up the number of subjects.Source: §4.1 · p. 4
4.2. Results
- On HCP subject 100408, anatomy-modulated Ada-WIRE shows clearer tract-like boundaries, and Ada-WIRE Anatomy achieves the lowest mean MAE and MSRE for diffusion-signal reconstruction.AMICO–NODDI and MIX show speckled variations, while DIMOND maps are smoother but some narrow bands are less distinct; in-vivo parameter ground truth is unavailable.Source: Figure 1 · p. 4, §4.2 · p. 4, Table 2 · p. 4