It has recently been shown that, using the Spherical Mean Technique (SMT)¹, single diffusion encoding is capable of revealing microscopic diffusion anisotropy in tissue with complex directional structure. The present work extends this technique and introduces a multi-compartment microscopic diffusion model. In particular, we will provide estimates of microscopic features specific to the intra- and extra-neurite compartments unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The new imaging technique is demonstrated in a large cohort of healthy young adults as well as for the detection of microstructural tissue alterations in a preclinical animal model of tuberous sclerosis complex (TSC).

SMT is based on the insight that for any fixed gradient magnitude and timing, hence fixed b-value, the spherical mean of the diffusion signal over the gradient directions does not depend on the neurite orientation distribution¹. Rather, the mean diffusion signal is only a function of the microscopic diffusion process. The general approach consists of three steps: First, we need to formulate a model for the microscopic diffusion signal. Second, the spherical mean signal is computed by averaging the T₂-normalised diffusion signal acquired with uniformly sampled gradient directions for each b-shell separately. Third, the model parameters are estimated using a least-squares method that fits the spherical mean version of the microscopic diffusion model to the measured mean signals for a given set of b-values.

Here we propose a multi-compartment microscopic model that takes the presence of multiple tissue components at the (sub-) cellular level into account. Acknowledging the clinical time constraints, we describe the intra-neurite diffusion signal with a stick model, setting the transverse intra-neurite microscopic diffusivity to zero. The extra-neurite diffusion signal is modelled by a rotationally symmetric microscopic tensor, assuming that the transverse extra-neurite microscopic diffusivity is a function of the intra-neurite volume fraction v_int and intrinsic diffusivity λ, here the simple tortuosity model² $$\lambda_\perp^\mathrm{ext}(v_\mathrm{int},\lambda)=(1-v_\mathrm{int})\lambda.$$ Then the spherical mean version of this multi-compartment microscopic model is, for a fixed b-value, $$\bar{e}_b=v_\mathrm{int}\bar{e}_b^\mathrm{int}+(1-v_\mathrm{int})\bar{e}_b^\mathrm{ext}$$ with the intra-neurite mean signal $$\bar{e}_b^\mathrm{int}=\frac{\sqrt{\pi}\,\mathrm{erf}(\sqrt{b\lambda})}{2\sqrt{b\lambda}}$$ and the extra-neurite mean signal $$\bar{e}_b^\mathrm{ext}=\exp\left(-b\lambda_\perp^\mathrm{ext}(v_\mathrm{int},\lambda)\right)\frac{\sqrt{\pi}\,\mathrm{erf}(\sqrt{b(\lambda-\lambda_\perp^\mathrm{ext}(v_\mathrm{int},\lambda))})}{2\sqrt{b(\lambda-\lambda_\perp^\mathrm{ext}(v_\mathrm{int},\lambda))}}.$$ Unlike existing techniques such as NODDI³, we do not make any assumptions about the neurite orientation distribution (e.g. Watson/Bingham distributions) and estimate the microscopic diffusion coefficients from the data.

We used high-quality diffusion data acquired with a bespoke 3 T scanner from the Human Connectome Project (HCP), 500 Subjects Data Release⁴. The 1.25 mm-isotropic image data consist of 270 gradient directions evenly distributed over three b-shells of 1000, 2000 and 3000 s/mm². Moreover, we conducted an ex-vivo study with conditional knockouts (CKO) of Rictor and Tsc2 in Olig2-Cre mice, which both impact the myelination in the central nervous system⁵. Eight normal, five Rictor and five Tsc2 P60 mouse brains were scanned on a 15.2 T Bruker system using a diffusion sequence with 30 gradient directions for each b-value of 3000 and 6000 s/mm² (150 µm isotropic resolution).

Figure 1 maps the intra-neurite volume fraction v_int and intrinsic diffusivity λ in a human subject. Note that in cerebrospinal fluid λ approaches the diffusion coefficient of free water and v_int tends to zero. Figure 2 shows that SMT produces reliable results with just 45 diffusion gradients. After spatial normalisation, Figure 3 establishes the normative values of the new microscopic diffusion indices over a cohort of 100 unrelated healthy adults (aged 29.1 ± 3.7 years) coming from the HCP data set. Once the microscopic diffusion process has been recovered, we estimate the fibre orientation distribution using spherical deconvolution^6,7 with a spatially varying impulse response function. Figure 4 maps the orientation dispersion entropy, i.e. the Kullback–Leibler divergence of the neurite orientation distribution with respect to the uniform distribution. Furthermore, Figure 5 shows that for Rictor CKO, which results in a phenotype with moderate adverse effects, we observe only minor deviations, whereas Tsc2 mice exhibit a significant loss of axon density in wide areas of the brain white matter, presumably leading to the severe adverse effects seen in this model. Quantitative histology agrees with these findings (not shown, data publicly available⁸).

We have developed multi-compartment microscopic diffusion anisotropy imaging, which uses a standard sequence with two (or more) b-shells runnable within clinically feasible scan times. This simple, fast and robust method enabled us to recover the neurite density and intrinsic diffusivity unconfounded by and without knowledge of the fibre orientation distribution. The ex-vivo mouse study demonstrated that the microscopic diffusion indices are well suited for the evaluation of diffuse alterations in the white matter microstructure, thus offering great potential for clinical translation.