Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange

• The white-matter Standard Model describes non-exchanging compartments with Gaussian diffusion, while gray-matter soma occupy about 10–20% of tissue volume and may need explicit modeling.SANDI represents soma as impermeable spheres and partially circumvents exchange using short diffusion times (t < 20 ms).Source: §1 · pp. 2–3
• Gray matter modeling must consider neurite-membrane exchange, disorder-driven non-Gaussian diffusion along cellular processes, and signal from cell bodies.The introduction describes gray matter as morphologically distinct from white matter, motivating a different simplified microgeometry.Source: §1 · p. 2
• Prior reports span exchange times of 3–5 ms ex vivo to 100–150 ms in cultures and rat studies, while cortical kurtosis time-dependence could not rule out exchange.The cited disorder account describes distinct long-time kurtosis trends for one-dimensional neurites and three-dimensional extracellular diffusion.Source: §1 · pp. 2–3
• Rat brain data showed negligible diffusivity time-dependence and time-dependent kurtosis compatible with t^-1; exchange better accounted for high-b signal decay than adding soma.These observations apply within the explored diffusion-weighting and diffusion-time ranges.Source: §1 · p. 4
• NEXI implements the anisotropic Kärger exchange model as a minimal gray-matter model, and simulations show multi-b multi-t data are critical for reliable parameter estimation, especially exchange time.The proposed model accounts for neurite membrane exchange; fit stability permitting, it could be extended with a soma fraction.Source: §1 · p. 4
• Experiments used strong preclinical gradients to probe diffusion times of 10–45 ms and b-values up to 10 ms/μm^2 in rat cortex and hippocampus, with white-matter regions as references.The study used 1 T/m gradients and selected rat anatomy to reduce partial-volume effects in cortex.Source: §1 · p. 4

2.1. Theory

• NEXI models barrier-limited exchange between neurites and extracellular space with an anisotropic Kärger model, then powder-averages the signal assuming isotropic extracellular diffusion.The four fitted parameters are f, D_i,∥, D_e, and t_ex; the model assumes exchange within local neurite–extracellular units, while exchange across multiple neurites is expected at longer times.Source: §2.1 · pp. 5–6
• The theory also defines exchange-related kurtosis decay and high-b signal scaling, while identifying structural disorder and soma models as alternative contributions to test.Kurtosis can include a residual offset, and disorder-related kurtosis may decay as t^-1/2 or (ln t)/t; SANDI represents sticks, spheres, and extracellular diffusion without exchange.Source: §2.1 · pp. 5–7

2.2. Experimental

• Six rats underwent 14T diffusion MRI across multiple b-values and diffusion times; all datasets assessed time-dependent diffusion and kurtosis, while four supported high-b and model analyses.Images were denoised and corrected for Rician bias, Gibbs ringing, and motion, and ROIs included cortex, hippocampus, and white-matter regions.Source: §2.2 · p. 7

2.3. Impact of each contribution (i)-(iii): exchange, structural disorder & soma

• Analyses estimated Standard Model parameters by diffusion time and b-range, and compared diffusivity and kurtosis time-dependence with exchange and structural-disorder decay forms.Shell-averaged signals were also fit with SANDI separately at each time and NEXI jointly across times to compare soma and exchange explanations.Source: §2.3 · pp. 8–9

2.4. NEXI parameter estimation

• NEXI parameters were estimated from synthetic and experimental signals using nonlinear least squares, with joint multi-time fits and tests of b-range and deep-learning estimation.Experimental fits used all shells and diffusion times jointly, including voxel-wise maps; initialization sensitivity was assessed with 100 random starts before narrowing the initialization ranges.Source: §2.4 · pp. 9–10

2.5. Histology

• Histology used immunostaining for microglia, astrocytes, neuronal microfilaments, and neuronal nuclei, with staining patterns compared against NEXI parameters, especially neurite density f.Source: §2.5 · p. 10

3.1.1. Time-dependent Standard Model parameters in GM and WM

• In gray matter, SM fraction f decreased and alignment c2 increased with diffusion time, while parallel diffusivities decreased most markedly at bmax ≥ 6; white-matter diffusivity trends were weaker.The f decrease was (2–3) ·10^-3 ms^-1 across ROIs; extra-neurite radial diffusivity increased with time only at bmax ≥ 6.Source: §3.1.1 · p. 11, Figure 2 · p. 11

3.1.2. Exchange vs structural disorder: Time-dependent diffusion and kurtosis

• Across 10–45 ms, diffusivities showed no significant time dependence, whereas mean kurtosis declined markedly in gray matter, supporting inter-compartment exchange as a sustained source of kurtosis change.The observed decay was close to t^-1, but the available interval did not conclusively distinguish exchange from 1D structural disorder; enforcing K∞=0 gave the best fit at the longest times. Exchange estimates were 21 ± 4 ms in cortex and 16 ± 3 ms in hippocampus, versus >80 ms in the internal capsule and corpus callosum and 43 ± 24 ms in cingulum.Source: §3.1.2 · pp. 11–12

3.1.3. Exchange vs soma

• SANDI parameters were generally similar between 12 and 20 ms, except R_s, which increased with diffusion time; this suggests limited exchange bias below about 20 ms except for R_s.For parameters other than R_s and f, mean absolute percentage differences were within 10% at 20 ms; D_i,∥ and D_e were within ±5%.Source: §3.1.3 · p. 13
• A short-time SANDI fit predicted higher signal at longer diffusion times, opposite to the measured trend, while NEXI explained the multi-time signal decay better.Agreement with NEXI was poorer at the highest b-values, potentially because of Rician noise-floor correction or soma.Source: §3.1.3 · p. 13, Figure 6 · p. 14

3.2.1. Simulations

• Joint fitting across diffusion times improved simulated precision for f and t_ex, restored some sensitivity to D_i,∥, and required bmax above 2.5 ms/μm2 for accuracy.Increasing bmax from 6 to 10 ms/μm2 further improved accuracy and precision, though less substantially.Source: §3.2.1 · p. 15

3.2.2. Experimental: in vivo rat GM

• With b-values up to 10 ms/μm2 and three to four diffusion times, all NEXI parameters were estimable in rat gray matter at ROI and single-voxel levels.Mean intra-neurite diffusivity was 2.5 μm2/ms, extra-neurite diffusivity 0.75 μm2/ms, and neurite fraction around 0.3; maps differentiated gray and white matter and gray-matter subregions.Source: §3.2.2 · p. 16, Figure 9 · p. 17
• NEXI exchange-time estimates were 25–65 ms in cortex and 25–65 ms in hippocampus for Datasets 1–3, while Dataset 4 estimates ranged 10–30 ms and agreed better with the comparison approach.The estimates were higher than the comparison values for Datasets 1–3; Dataset 4 had 2.5 times the voxel volume of Datasets 1–3.Source: §3.2.2 · p. 17
• NEXI neurite-fraction contrast was higher in central cortical layers, consistent with neurofilament staining, and in the dorsal dentate gyrus, where astrocyte density was higher.The authors suggest astrocytic processes may contribute to the NEXI neurite-fraction parameter because of their similar long, thin geometry.Source: §3.2.2 · p. 18, Figure 10 · p. 18

4. Discussion

• NEXI is proposed as the minimal gray-matter model, with estimated exchange times of 15–60 ms; simulations support intra-/extracellular exchange as dominant, though K(t) cannot identify the mechanism directly.The exchange-time estimates are reported for cortex and hippocampus; the discussion notes that other exchange mechanisms cannot be directly ruled out.Source: §4 · pp. 19, 21, 22
• In gray matter, exchange makes Standard Model parameters time-dependent and difficult to interpret; in thick white-matter bundles the model remains applicable, with estimates affected by b-value range and diffusion time.The apparent intra-neurite fraction decreased and neurite alignment increased with longer diffusion times; higher b-values also affected apparent compartment diffusivities, particularly in the intra-neurite space.Source: §4 · p. 19
• Across rat gray matter at 20–45 ms, mean diffusivity showed negligible time dependence while kurtosis decreased, supporting exchange over structural disorder, though broader time ranges are needed to distinguish decay laws.The discussion says the observed flat diffusivity supports treating tissue as Gaussian compartments within the cumulant regime; it notes that the long-time kurtosis limit may not have been reached.Source: §4 · pp. 19–20
• For diffusion times above 20 ms, SANDI parameters showed time dependence, while NEXI better predicted longer-time signal decay from short-time fits; SANDI agreed with NEXI and SM on several parameters.The discussion says short diffusion times (≤20 ms) did not challenge SANDI’s non-exchanging-compartment assumption, but longer times may bias its estimates through unaccounted exchange.Source: §4 · p. 21
• Joint fitting across four diffusion times improved NEXI parameter accuracy and precision; b-values up to 6 ms/μm2 were suggested as sufficient, while exchange times ≥80 ms were difficult to estimate with the simulated time range.Single-time data were insufficient for estimating exchange time and intra-neurite diffusivity, and broader multi-shell multi-time protocols may require scan-time optimization.Source: §4 · pp. 21–22, Limitations · p. 23
• Experimental NEXI estimates gave intra-neurite diffusivity of 2.2–2.5 μm2/ms, extra-neurite diffusivity of 0.75 μm2/ms, and neurite fraction about 0.3, below histological estimates.The neurite fraction was time-independent in NEXI, but may pool neuronal and astrocytic processes; high SNR (>20–30 in an individual b=0 image) was important for reliable estimation.Source: §4 · pp. 22–23

Limitations

• NEXI omits soma and assumes Gaussian compartments and exchange within each neurite’s local extracellular ensemble; non-Gaussian neurite effects and more general sequential exchange may limit its estimates.The discussion identifies extending NEXI to include exchange with soma and developing models of intra-compartment non-Gaussian effects as future work.Source: Limitations · pp. 23–24

Value

• The authors argue that exchange should be modeled in gray matter at typical clinical diffusion times (>20 ms), and that exchange-time estimates could serve as proxies for membrane permeability or myelin thickness.They also note potential complications for b-tensor encoding when free gradient waveforms span long diffusion times, where exchange may not be negligible.Source: Value · p. 24

• In rat GM in vivo, exchange dominates structural disorder, and NEXI explains diffusion-time signal decay better than adding a soma compartment.Source: §5 · p. 24
• At long diffusion times, filtering suggests only myelinated, non-exchanging neurites remain in the intra-neurite Standard Model compartment, while unmyelinated neurites with stronger dispersion are attributed to extra-neurite space.Source: §5 · p. 24
• For cortical microstructure at t > 20 ms, NEXI is better suited than a three-compartment soma model and provides exchange time as a proxy for membrane permeability.Source: §5 · p. 24
• Future models should ideally account for both soma and exchange when data support estimating the larger number of parameters.Source: §5 · p. 24

Appendix: DKI(t) for the orientationally-averaged anisotropic KM

• K(τ)=K0F(τ), with F(τ)=2(e^-τ−1+τ)/τ², describes kurtosis decay over time in the scalar Kärger model.The supplied expression gives K0 as proportional to 2f(1−f)(D1−D2)².Source: Appendix: DKI(t) for the… · p. 26
• For a fascicle at angle θ, the compartment diffusivities are D1=Di,∥x² and D2=De,⊥+Δe x², with x=cos θ.The derivation averages the signal over orientations by expanding in b-moments through b² and integrating term by term.Source: Appendix: DKI(t) for the… · p. 26
• The orientationally averaged expression includes 3f(1−f)[De,⊥²+(2/3)De,⊥(Δe−Di,∥)+(1/5)(Δe−Di,∥)²].Source: Appendix: DKI(t) for the… · p. 26
• At long times, residual kurtosis K∞ corresponds to an isotropic mixture of diffusion tensors with specified effective axial and radial diffusivities.The main text sets Δe=0 and De,⊥=De,∥=De, then neglects K∞ because the model does not adequately describe mixing between differently oriented sticks at sufficiently long times.Source: Appendix: DKI(t) for the… · p. 26

Supplementary Methods

• The estimator used three fully connected layers, each with 16 times the number of b-values times the number of diffusion times units.Leaky ReLU activations provided the nonlinearities.Source: Supplementary Methods · p. 33
• Network inputs were log(S̅), and target parameters were scaled to the [-1, 1] range.Source: Supplementary Methods · p. 33
• Training used 10^5 simulated signals and corresponding parameters, with mean-squared error between estimates and ground truth as the loss.Source: Supplementary Methods · p. 33
• The network was trained for both noiseless and noisy parameter estimation.For noisy training, SNR ranged from 80 to 120 to represent multiple noise levels in experimental datasets.Source: Supplementary Methods · p. 33

Supplementary Results: Figures and Tables

• For bmax=10 ms/μm2, c2 increased with diffusion time in the corpus callosum and cingulum, with GM rates of increase 2–6 times faster.The SM parameter time-dependence was also assessed across maximum b-values in the internal capsule, corpus callosum, and cingulum.Source: Table S1 · p. 34, Figure S1 · p. 34
• Across t=10–45 ms, diffusivity slopes were inconclusive around zero, whereas MK time-dependence was significant in all ROIs and strongest in GM.In WM, MK decayed throughout the interval; KM with K∞=0 and 1D disorder fits were similar, while freeing K∞ produced poorer parameter estimates.Source: Table S2 · p. 34, Figure S2 · p. 35
• SANDI diffusion-time effects were assessed using percentage changes from 12 ms, pairwise ANOVA with Bonferroni correction, and weighted linear trends, with p<0.05 treated as significant.The supplementary table reports parameter-rate units and identifies significant trends using 95% confidence intervals and an F-test.Source: Table S3 · p. 35, Figure S3 · p. 36, Figure S4 · p. 36
• With finite SNR=100, fitting each diffusion time separately could not estimate Di,∥ or tex, whereas joint multi-shell multi-time fitting estimated tex, De, and f accurately but biased Di,∥ toward its mean.Without noise, joint fitting estimated all parameters with high accuracy and precision.Source: Figure S5 · p. 37, Figure S6 · p. 37
• Increasing both shell count and maximum b-value improved NEXI estimate accuracy and precision; with seven shells, the benefit of bmax=10 over 5.5 ms/μm2 was marginal.Across 100 random NLLS initializations, the solution with Di,∥>2 and De<1 was dominant despite several local minima.Source: Figure S7 · p. 38, Figure S8 · p. 38
• At t=40 ms, NEXI fit the cortical signal better than SANDI, while the impermeable-stick model failed to capture its curvature against b−1/2.The NEXI low-b and high-b approximations were reasonable in their respective regimes.Source: Figure S9 · p. 39