White matter standard model estimates in synthetic voxels with varying complexity
Poster No:
1277
Submission Type:
Abstract Submission
Authors:
Jasmine Nguyen-Duc1, Inès de Riedmatten2, Quentin Uhl1, Rémy Gardier3, Jonathan Rafael-Patino3, Ileana Jelescu4
Institutions:
1CHUV, Lausanne, Vaud, 2Université de Lausanne, Lausanne, Switzerland, 3EPFL, Lausanne, Vaud, 4Department of Radiology, Lausanne University Hospital (CHUV) and University of Lausanne (UNIL), Lausanne, Vaud
First Author:
Co-Author(s):
Ileana Jelescu
Department of Radiology, Lausanne University Hospital (CHUV) and University of Lausanne (UNIL)
Lausanne, Vaud
Department of Radiology, Lausanne University Hospital (CHUV) and University of Lausanne (UNIL)
Lausanne, Vaud
Introduction:
Diffusion MRI (dMRI) quantifies the main features of tissue microstructure using biophysical models that simplify the tissue's complex microgeometry.
The Standard Model Imaging (SMI) model (Coelho, 2022; Novikov, 2018), widely used for white matter (WM), disentangles contributions from the intra-axonal (IAS) and extra-axonal (EAS) spaces. It models IAS as a collection of impermeable sticks with unidimensional diffusion Da, while EAS diffusion is anisotropic, Gaussian, and locally represented by an axially symmetric tensor. The axonal orientation distribution function is parametrized by its second order spherical harmonic p2 (Fig1A). The true complexity of brain tissue microstructure exceeds these simplifying assumptions. For example, axon morphology displays undulation and caliber variations (Lee, 2020), while unmyelinated axons are permeable to water, and their prevalence increases in conditions like multiple sclerosis. Consequently, a bias may be introduced in SMI estimates when applied to real tissue.
This study assesses the performance of the SMI model in estimating microstructural parameters using numerical phantoms, including those with complex axonal morphologies and varying permeability (κ). We hypothesize that deviations from the model's assumptions will progressively challenge its predictions.
The Standard Model Imaging (SMI) model (Coelho, 2022; Novikov, 2018), widely used for white matter (WM), disentangles contributions from the intra-axonal (IAS) and extra-axonal (EAS) spaces. It models IAS as a collection of impermeable sticks with unidimensional diffusion Da, while EAS diffusion is anisotropic, Gaussian, and locally represented by an axially symmetric tensor. The axonal orientation distribution function is parametrized by its second order spherical harmonic p2 (Fig1A). The true complexity of brain tissue microstructure exceeds these simplifying assumptions. For example, axon morphology displays undulation and caliber variations (Lee, 2020), while unmyelinated axons are permeable to water, and their prevalence increases in conditions like multiple sclerosis. Consequently, a bias may be introduced in SMI estimates when applied to real tissue.
This study assesses the performance of the SMI model in estimating microstructural parameters using numerical phantoms, including those with complex axonal morphologies and varying permeability (κ). We hypothesize that deviations from the model's assumptions will progressively challenge its predictions.
Methods:
Numerical Phantom Generation: A novel CATERPillar tool (Nguyen-Duc, 2024) is used to generate numerical phantoms (150-μm cubes). Axons are grown to match a given volume fraction (f), Gamma-distributed radii (1 μm), specified beading amplitudes (0.3 × mean radius) and tortuosity levels (1.2). Phantoms are separated into 3 different sets : (1) straight, parallel axons with varying f, (2) tortuous and beaded axons with varying f, and (3) tortuous and beaded axons at f=0.6 with varying permeability κ (Fig1B), up to 4 x 10⁻³ cm/s (Boss, 2013).
Monte Carlo Simulations: Using the MCDC Simulator (Rafael-Patino, 2020), diffusion trajectories of 10⁵ random walkers are simulated with a step length of 0.1 μm. IAS and EAS free diffusivities are set to 2.5 × 10⁻⁹ m²/s and 1.5 × 10⁻⁹ m²/s, respectively. Synthetic DWI data is generated using a PGSE sequence with ∆=55.5 ms and δ=16.5 ms, acquired along 60 directions for b-values [0, 500, 1000, 2000, 3000, 5000] s/mm².
Biophysical Models : SMI was estimated using the TMI tool (Ades-Aron, 2018). In addition to ground truth (GT) values, diffusion kurtosis (DKI) was estimated on the IAS and EAS signals separately in impermeable phantom sets 1 and 2 to yield ^Da, ^De||, ^De.
Monte Carlo Simulations: Using the MCDC Simulator (Rafael-Patino, 2020), diffusion trajectories of 10⁵ random walkers are simulated with a step length of 0.1 μm. IAS and EAS free diffusivities are set to 2.5 × 10⁻⁹ m²/s and 1.5 × 10⁻⁹ m²/s, respectively. Synthetic DWI data is generated using a PGSE sequence with ∆=55.5 ms and δ=16.5 ms, acquired along 60 directions for b-values [0, 500, 1000, 2000, 3000, 5000] s/mm².
Biophysical Models : SMI was estimated using the TMI tool (Ades-Aron, 2018). In addition to ground truth (GT) values, diffusion kurtosis (DKI) was estimated on the IAS and EAS signals separately in impermeable phantom sets 1 and 2 to yield ^Da, ^De||, ^De.
·(A) The SM estimates : f, Da, De∥, De⊥and p2. Image taken from (Liao, 2024). (B) 3 sets of numerical phantoms are generated using CATERPillar, with varying axonal morphologies and permeability values.
Results:
Figure 2 shows SMI estimates along with GT values and compartment tensor estimates. For both sets 1 and 2, f is accurately predicted, and De⊥ decreases with increasing f due to increased hindrance from additional axons. p2 is particularly in sets 2 and 3 where axonal morphology deviates from the model's assumptions.
In set 1, Da and De∥ deviate at f < 0.2 and f > 0.5. At high f, this is likely due to pockets between tightly packed axons being misinterpreted as axons, causing convergence between Da and De∥.
In set 2, the decrease observed in De⊥ now also affects the parallel direction ( Da and De∥) due restrictions caused by the axonal morphology. Da consistently shows higher values than ^Da, and is closer to GT values.
In set 3, increasing κ causes f to be progressively underestimated, consistent with grey matter and tumor studies showing the impact of exchange (Jelescu, 2022; Gardier, 2023). Similarly, predictions for Da and De|| increase with κ, consistent with reduced hindrance. De⊥ estimate on the other hand decreases as water entering the IAS experiences partially restricts diffusivity.
In set 1, Da and De∥ deviate at f < 0.2 and f > 0.5. At high f, this is likely due to pockets between tightly packed axons being misinterpreted as axons, causing convergence between Da and De∥.
In set 2, the decrease observed in De⊥ now also affects the parallel direction ( Da and De∥) due restrictions caused by the axonal morphology. Da consistently shows higher values than ^Da, and is closer to GT values.
In set 3, increasing κ causes f to be progressively underestimated, consistent with grey matter and tumor studies showing the impact of exchange (Jelescu, 2022; Gardier, 2023). Similarly, predictions for Da and De|| increase with κ, consistent with reduced hindrance. De⊥ estimate on the other hand decreases as water entering the IAS experiences partially restricts diffusivity.
·(A) SMI estimates as f increases in phantom set 1. (B) Same as (A) but for phantom set 2. (C) Phantom of set 3 has f ~ 0.6 and varying permeability values. All diffusivities are in um²/ms.
Conclusions:
In summary, our results demonstrate that SMI estimates are reasonably robust to realistic axonal morphology, but increasingly deviate from expected values as permeability increases.This reinforces the need to model inter-compartment exchange in tissues with limited myelination (e.g. gray matter or demyelinating diseases).
Modeling and Analysis Methods:
Diffusion MRI Modeling and Analysis 1
Novel Imaging Acquisition Methods:
Diffusion MRI 2
Keywords:
Computational Neuroscience
Informatics
White Matter
WHITE MATTER IMAGING - DTI, HARDI, DSI, ETC
Other - Simulations
1|2Indicates the priority used for review
Abstract Information
By submitting your proposal, you grant permission for the Organization for Human Brain Mapping (OHBM) to distribute your work in any format, including video, audio print and electronic text through OHBM OnDemand, social media channels, the OHBM website, or other electronic publications and media.
The Open Science Special Interest Group (OSSIG) is introducing a reproducibility challenge for OHBM 2025. This new initiative aims to enhance the reproducibility of scientific results and foster collaborations between labs. Teams will consist of a “source” party and a “reproducing” party, and will be evaluated on the success of their replication, the openness of the source work, and additional deliverables. Click here for more information. Propose your OHBM abstract(s) as source work for future OHBM meetings by selecting one of the following options:
Please indicate below if your study was a "resting state" or "task-activation” study.
Healthy subjects only or patients (note that patient studies may also involve healthy subjects):
Was this research conducted in the United States?
Were any human subjects research approved by the relevant Institutional Review Board or ethics panel? NOTE: Any human subjects studies without IRB approval will be automatically rejected.
Were any animal research approved by the relevant IACUC or other animal research panel? NOTE: Any animal studies without IACUC approval will be automatically rejected.
Please indicate which methods were used in your research:
Provide references using APA citation style.
- Boss, D. (2013). Measurement of absolute cell volume, osmotic membrane water permeability, and refractive index of transmembrane water and solute flux by digital holographic microscopy. Journal of Biomedical Optics, 18(3), 036007.
- Coelho, S. (2022). Reproducibility of the Standard Model of diffusion in white matter on clinical MRI systems. NeuroImage, 257, 119290.
- Gardier, R. (2023). Cellular Exchange Imaging (CEXI): Evaluation of a diffusion model including water exchange in cells using numerical phantoms of permeable spheres. Magnetic Resonance in Medicine, 90(4), 1625–1640.
- Jelescu, I. O. (2022). Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange. NeuroImage, 256, 119277.
- Lee, H.-H. (2020). The impact of realistic axonal shape on axon diameter estimation using diffusion MRI. NeuroImage, 223, 117228.
- Liao, Y. (2024). Mapping tissue microstructure of brain white matter in vivo in health and disease using diffusion MRI. Imaging Neuroscience, 2, 1–17.
- Nguyen-Duc, J. (2024). CATERPillar: A fast and flexible framework for generating synthetic white matter numerical phantoms. Proceedings of ISMRM 2024.
- Novikov, D. S. (2019). Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation. NMR in Biomedicine, 32, e3998.
- Rafael-Patino, J.(2020). Robust Monte-Carlo simulations in diffusion-MRI: Effect of the substrate complexity and parameter choice on the reproducibility of results. Frontiers in Neuroinformatics, 14, Article 8.