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SANDI: a compartment-based model for non-invasive apparent soma and neurite imaging by diffusion MRI
Marco Palombo, Andrada Ianus, Daniel Nunes, Michele Guerreri, Daniel C. Alexander, Noam Shemesh, Hui Zhang
TL;DR
The paper addresses the standard DW-MRI microstructure model’s treatment of soma and its failure to describe high-b-value gray-matter data. It introduces SANDI, which explicitly models soma alongside neurites, and reports soma-sensitive signal signatures plus human maps consistent with histological and anatomical expectations.
Problem
The standard DW-MRI microstructure model does not explicitly represent soma, despite soma contributing to gray-matter signal and motivating unexplained high-b-value behavior.
Method
SANDI is a compartment model that explicitly includes non-exchanging soma and neurite contributions within the intra-cellular signal.
Results
The simulated soma-size and density signature is observable in measured signals, and estimated soma maps meet expectations from histological imaging and anatomical understanding.
Takeaways & Limitations
SANDI provides apparent soma and neurite density imaging and a novel contrast sensitive to neural tissue cytoarchitecture.
Takeaways & Limitations
Conventional clinical DW-MRI data are generally not suitable for SANDI.
Abstract
from arXiv · showhide
This work introduces a compartment-based model for apparent soma and neurite density imaging (SANDI) using non-invasive diffusion-weighted MRI (DW-MRI). The existing conjecture in brain microstructure imaging trough DW-MRI presents water diffusion in white (WM) and grey (GM) matter as restricted diffusion in neurites, modelled by infinite cylinders of null radius embedded in the hindered extra-neurite water. The extra-neurite pool in WM corresponds to water in the extra-axonal space, but in GM it combines water in the extra-cellular space with water in soma. While several studies showed that this microstructure model successfully describe DW-MRI data in WM and GM at b<3 ms/{\mum^2}, it has been also shown to fail in GM at high b values (b>>3 ms/{\mum^2}). Here we hypothesize that the unmodelled soma compartment may be responsible for this failure and propose SANDI as a new model of brain microstructure where soma (i.e. cell body of any brain cell type: from neuroglia to neurons) is explicitly included. We assess the effects of size and density of soma on the direction-averaged DW-MRI signal at high b values and the regime of validity of the model using numerical simulations and comparison with experimental data from mouse (bmax = 40 ms/{/mum^2}) and human (bmax = 10 ms/{\mum^2}) brain. We show that SANDI defines new contrasts representing new complementary information on the brain cyto- and myelo-architecture. Indeed, we show for the first-time maps from 25 healthy human subjects of MR soma and neurite signal fractions, that remarkably mirror contrasts of histological images of brain cyto- and myelo-architecture. Although still under validation, SANDI might provide new insight into tissue architecture by introducing a new set of biomarkers of potential great value for biomedical applications and pure neuroscience.
1. Introduction
SANDI extends diffusion-MRI microstructure modeling by explicitly representing soma alongside neurites, addressing the standard model’s unexplained high-b-value behavior in gray matter. Simulations and mouse and human data support estimating apparent soma size and density and characterizing brain cyto- and myeloarchitecture.
- Motivation: The standard model represents neurites as restricted-diffusion sticks and merges soma signal with the extra-cellular contribution.In gray matter, the extra-neurite pool combines extra-cellular water with water in cell bodies.
- Contribution: SANDI incorporates soma size and density alongside neurite density, enabling their joint non-invasive estimation from DW-MRI.The model treats soma as an explicit contributor to the intra-cellular signal.
- Motivation: High-b-value gray-matter data depart from the standard model, potentially because soma water does not diffuse like extra-cellular water.The authors hypothesize that explicitly modeling soma can account for this unexplained signal.
- Evaluation: Monte-Carlo simulations show that soma size and density produce a specific direction-averaged DW-MRI signature at high b-values consistent with observed departures.The simulations also investigate whether neurite–soma exchange can be neglected at short diffusion times.
- Scope: The authors do not establish whether DW-MRI can distinguish neuroglial from neuronal signal, so SANDI likely quantifies cell bodies collectively.The expected signal includes cell bodies from neuroglia and neurons.
- Evaluation: Mouse and human brain data support SANDI as a tool for estimating apparent soma size and density and characterizing cyto- and myeloarchitecture.The study evaluates healthy ex-vivo mouse and in-vivo human brains.
2. Theory
SANDI extends the standard two-compartment neural-tissue model by adding an explicit soma compartment to the intra-cellular signal. It uses direction-averaged signals and restricted-diffusion representations for neurites and spherical soma, with short-time non-exchange and relaxation-related assumptions.
- Standard model: The standard paradigm models intra-cellular water mainly in neurites represented as zero-radius cylinders, while merging soma signal with extra-cellular signal.Compartment models generally assume no water exchange between compartments.
- SANDI model: SANDI hierarchically separates tissue into intra-cellular and extra-cellular compartments, then divides the intra-cellular signal into neurite and soma contributions.The corresponding relative signal fractions within each hierarchy sum to unity.
- Assumptions: At short diffusion times of at most 20 ms, soma and neurite sub-compartments are approximated as non-exchanging.The model also neglects soma–extra-cellular exchange under the stated short-time conditions.
- SANDI model: The SANDI fractions are relative MRI signal fractions rather than voxel volume fractions because intra- and extra-cellular T2 values may differ.Myelin water is additionally neglected when the echo time sufficiently attenuates its contribution.
- Assumptions: The first implementation does not include CSF contributions and expects residual CSF signal to be captured by the extra-cellular compartment.Myelin water is also omitted through relaxation-based attenuation.
- Direction averaging: Direction averaging targets orientation-independent microstructure features and removes dependence on the fibre orientation distribution function.The powder-averaged signal averages measurements over uniformly distributed gradient directions.
- Compartment signals: Neurites are modeled as long thin cylinders, extra-cellular water as isotropic Gaussian diffusion, and soma as closed impermeable spheres.The soma signal uses a generalized-pulsed-gradient expansion and volume averaging over soma radii.
3. Methods
The study tests SANDI through simulations and mouse and human DW-MRI experiments, focusing on neurite–soma exchange, high-b-value signal sensitivity to soma properties, and model evaluation. The workflow uses simplified digital geometries, signal dictionaries, and region-of-interest comparisons.
- Simulation setup: Simplified simulations use non-branching neurites and isolate the intra-cellular signal, testing only selected assumptions of the intra-cellular model.The experiments assess sticks, spherical soma, and negligible exchange rather than the full generative morphology.
- Simulation setup: Synthetic geometries vary soma radius from 2 to 10 μm and soma volume fraction from 0.1 to 0.9 alongside cylindrical neurites.These configurations mimic a range of possible brain cell types.
- Simulation 1–2: Monte-Carlo simulations evaluate the non-exchange approximation between neurites and soma across diffusion times and b-values.Signals with and without exchange are compared through apparent diffusion coefficients and their relative difference.
- Simulation 1–2: A relative ADC difference below 10% is used as a sensible regime for treating neurite and soma compartments as non-exchanging.The simulations compare short and long diffusion-time conditions, including 10 ms and 80 ms.
- Simulation 3: Simulation 3 builds a dictionary of signals for different soma-size and soma-density configurations and compares it with experimental regional signals.Gray-matter cortex and white-matter corpus callosum ROIs are selected because they are expected to differ in soma properties.
- Experimental evaluation: Mouse DW-MRI acquired at ultra-high b-values tests whether the simulated soma-size and density signature agrees with measured data.Human high-b-value DW-MRI is analyzed to produce soma-density maps and assess sensitivity to cytoarchitecture.
4. Results
The simulations identify diffusion-time conditions under which a two-compartment intra-cellular model approximates exchanged soma–neurite signals, while longer times produce clear model mismatch. Results also show that SANDI distinguishes cellular configurations and better describes both WM and GM data.
- Regime of validity: td≤20 ms is the suitable regime for neglecting soma–neurite exchange and modeling intracellular signal as non-exchanging intra-neurite and intra-soma compartments.At td=10 ms, exchange, no-exchange, and simple-compartment signals nearly overlap; at td=80 ms, they clearly diverge.
- Regime of validity: At td=10 ms, the analytical model describes signal attenuation up to b=60 ms/μm^2 except for the smallest simulated cellular domain.At td=80 ms, the model also fails for larger cellular domains and soma.
- Sensitivity to soma size and density: SANDI simulations distinguish WM-like configurations with fis~1–5% and rs=2 μm from GM-like configurations with fis~60–65% and rs=6–10 μm.These configurations mirror the reported cellular compositions of the corpus callosum and cortex ROIs.
- Sensitivity to soma size and density: Different cellular configurations produce distinct signal variations, including configurations not matching the investigated WM and GM ROIs.The differing signals correspond to combinations of cellular-domain size and soma volume fraction.
- Experimental comparison: SANDI describes WM and GM data better than the dot-compartment variant, with ΔAICc>2 for both tissue types.At b-values as low as 3 ms/μm^2, extra-cellular water contributes negligibly in the comparison described.
5. Discussion
SANDI explicitly models soma alongside neurites, improving interpretation of high-b-value DW-MRI and enabling apparent soma and neurite measurements. Human and mouse results show biologically plausible contrasts that correspond with histological and anatomical patterns, while validation and acquisition constraints remain.
- Human brain findings: 25 healthy human subjects showed apparent soma density and size maps matching histological imaging and anatomical expectations, including cortical correspondence with Brodmann-area patterns.Soma signal fractions followed Brodmann boundaries and showed similar distributions across the cortical surface, including at the individual-subject level.
- Model and motivation: SANDI introduces soma as an explicit restricted spherical compartment alongside neurites, challenging the standard model’s treatment of soma contribution.The model separates cell-body signal from elongated cellular projections and represents soma water diffusion in geometries of non-zero size.
- Model and motivation: At bmax > 3,000 s/mm2, soma size and density produce a specific direction-averaged DW-MRI signal signature, increasing sensitivity to apparent soma properties.This regime is especially relevant because the conventional model fails in grey matter at high b values.
- Model comparison: SANDI fits measured signals better than the dot-compartment model in both GM and WM, with ΔAICc>2, while dot-model fractions can conflict with expected neuroanatomy.In WM, both models provide similar estimates, consistent with WM’s low soma density, but SANDI still gives a better fit.
- Human brain findings: Estimated human soma radii ranged from 2 to 12 μm, with mean±std 10±3 μm, close to the expected neural-soma radius of 11±7 μm.The maps also showed higher soma signal fractions in GM and neurite fractions highlighting major WM tracts.
- Implications and limitations: SANDI’s soma and neurite signal-fraction maps may support non-invasive cyto- and myelo-architecture mapping, new cortical parcellations, and improved delineation of difficult GM sub-regions.The authors also describe potential applications to developmental, disease-related, and other microstructural changes, but emphasize that validation is still in progress.
- Implications and limitations: Interpretation remains limited by imperfect MRI–histology concordance, different subjects and resolutions, non-optimal human acquisition, and conventional clinical DW-MRI b values typically no higher than 3,000 s/mm2.Human soma-radius estimates are neither very accurate nor particularly precise because of limited b values and only one diffusion time.
6. Conclusion
The paper proposes SANDI, a compartment-based model that explicitly separates intra-neurite and intra-soma signals to estimate apparent soma and neurite properties non-invasively. Simulations and mouse and human DW-MRI analyses support new contrasts related to brain cyto- and myeloarchitecture, while validation and acquisition constraints remain.
- 6. Conclusion: High-b DW-MRI modeling motivates the new tissue picture because the preceding microstructure model fails at b >> 3,000 s/mm2.The earlier model was successful at relatively low b values but failed at high b values.
- 6. Conclusion: SANDI subdivides the intracellular compartment into non-exchanging intra-neurite and intra-soma sub-compartments, whose signals form a weighted sum.The total MRI signal is modeled as a weighted sum of signals from water diffusing in each compartment.
- 6. Conclusion: SANDI accounts for soma abundance in grey matter relative to white matter, enabling non-invasive estimation of apparent soma density and size.The model introduces soma explicitly into the tissue microstructure representation.
- 6. Conclusion: Numerical simulations identify the validity regime for treating neurites and soma as non-exchanging intracellular sub-compartments, and the model is demonstrated in mouse and human data.The demonstrations use ex-vivo mouse DW-MRI and in-vivo human acquisitions.
- 6. Conclusion: SANDI produces contrasts that provide complementary information on brain cyto- and myeloarchitecture, although the reported maps remain under validation.The work presents these contrasts as potential sources of insight into tissue architecture and biomarkers for biomedical applications and neuroscience.
Figures
The figures introduce SANDI’s compartment structure, test when it approximates cellular diffusion, and evaluate parameter estimation against simulations and brain data. Human maps and mouse comparisons assess whether soma-sensitive contrasts reflect tissue architecture.
- Model: SANDI divides the voxel into intracellular and extracellular compartments, with intracellular signal further separated into neurite and soma sub-compartments.The total signal is represented as weighted sums of non-exchanging compartment signals.
- Model validity: Simulations compare exchange, no-exchange, and compartment-model ADCs across diffusion times, using a 10% difference threshold to define the model’s validity regime.The analysis varies overall cellular size and soma size or density.
- Model validity: At 10 ms diffusion time, exchange and no-exchange signals are similar, whereas at 80 ms they clearly diverge from the compartment approximation.Figure 4 evaluates direction-averaged normalized signal versus b^-1/2 under the same three conditions.
- Parameter estimation: Simulation fits estimate soma signal fraction, soma size, and intra-neurite diffusivity by comparing fitted parameters with ground-truth values and Monte Carlo uncertainties.The figure evaluates fitting of the compartment relation without an extracellular compartment.
- Validation and contrasts: Mouse data are compared with simulations spanning soma radius and fraction, while human maps report soma and neurite signal fractions alongside anatomical and histological contrasts.Additional figures examine model-versus-dot-compartment fits, validity for different diffusivities, training-set effects, and cortical soma-fraction maps across 25 subjects.