Introduction

Many diffusion MRI (dMRI) techniques aim to reveal tissue structure at microscopic scale^1,2. A recent approach, called Temporal Diffusion Ratio (TDR³), maps restricted diffusion inside large axons and/or cell bodies, employing dMRI measurements with high b-value (>6000s/mm² to attenuate fast (extracellular) diffusion) and two HARDI shells with different diffusion times. TDR employs standard acquisition sequences, makes no assumptions of the underlying tissue structure and requires no model fitting.

We optimise gradient timings for TDR mapping, present a novel strategy for calculating TDR using subsets of full HARDI acquisitions and demonstrate optimised TDR using human and mouse brain-data.

Methods

TDR is computed by contrasting two direction-averaged dMRI signals using $$$\text{TDR}=\frac{(S_1-S_2)}{S_1}$$$ (S₁>S₂ in restrictions)³. Originally, the two signal acquisitions assumed equal gradient-pulse-duration 𝛿, and were not optimised³, hence limiting TDR contrast⁴.

Simulations: Here, we optimise both the 𝛿 and the diffusion-time Δ of each acquisition to maximise TDR contrast. We consider substrate configurations for distributions of: a) parallel impermeable cylinders (~axons), and b) impermeable spheres (~cell bodies). We assume fixed b-values=8000s/mm², limiting G≤600mT/m and Δ+δ≤45ms, ensuring sequence parameters achievable on preclinical scanners. Optimisations for Connectome are performed but not illustrated. Simulations use MISST (http://www.nitrc.org/projects/misst)⁵; optimisation is automated using an interior-point algorithm.

We use our optimal sequences to simulate TDR values across varied cylindrical and spherical distributions, demonstrating structures visible through TDR. Finally, we optimise the number of HARDI directions, taking subsets of our HARDI acquisitions that provide the highest signals given noise (SNR=10).

Human application: We use optimised TDR to map restriction in the human brain, in-vivo on data acquired on a healthy 35yo male participant under local ethics approval using a Siemens 3T-Connectome-scanner with HARDI protocol: TE=88ms, TR=4100ms, MB=2, BW=2272Hz, isotropic voxel size 2mm, 64 diffusion directions and 7 interleaved b0s. Acquisition parameters replicate the original TDR implementation³ and the proposed optimised one: constant b-value=8000s/mm² with G/δ/Δ=150mT/m/10ms/54ms; G/δ/Δ=258mT/m/10ms/21ms and G/δ/Δ=85mT/m/21ms/43ms. To account for susceptibility distortions, 4 b=0 images were acquired with alternating EPI-PE directions. Data are preprocessed as in [3]. We compare optimised and non-optimised acquisitions alongside the effects of using highest-signal HARDI direction subsets in the TDR estimation.

Preclinical application: We investigate TDR contrast in the mouse brain, ex-vivo. All experiments were preapproved by the competent institutional and national authorities and were carried out in accordance with European Directive 2010/63.

Ex-vivo dMRI data was acquired on a 16.4T Bruker scanner using PGSE-EPI (TE=53ms, TR=3s, 12 averages, slice-thickness=0.5mm, in-plane-resolution=0.15x0.15mm, matrix-size=106x64). Data was acquired with b-value=8000s/mm² and 60 directions. The following δ/Δ combinations were used: [Optimised TDR: δ/Δ={6.9/9;14/27.5}ms, Non-optimised TDR: δ/Δ={6.9/9;6.9/27.5}ms]. Gradient strength was artificially limited to 600 mT/m.

Results

As in [4], we find maximising TDR requires a short-δ, high-G sequence contrasted with a long-δ, lower-G sequence [here: S₁:Δ=30.92ms,δ=14.08ms; S₂:Δ=8.87ms,δ=6.87ms]. Fig.1 illustrates that the optimised Δ/δ combination maximises signal difference between the two acquisitions. The optimised sequences are extremely similar for cylinders and spheres, as well as for substrates with other size distributions (data not shown).

Fig.2 shows how TDR varies across a range of differently-sized structures, showing TDR’s suitability for imaging structures containing large restrictions.

Fig.3 shows that in the presence of noise, using 12/60 of the highest-signal directions provides more accurate TDR than when using all 60 directions across most cylinder distributions. For all structures, using more directions improves the precision.

Fig.4 shows that optimised TDR provides higher contrast when imaging the human brain. In some areas of white matter, TDR values are higher when using fewer HARDI directions, supporting our simulations.

Fig.5 shows optimised and non-optimised TDR contrast in the mouse-brain, ex-vivo, illustrating the contrast improvement from optimisation. Positive TDR highlights areas of restriction in white matter and grey matter.

Discussion and Conclusions

We show that optimised TDR requires short-δ, high-G sequences contrasted with long-δ, low-G sequences[Figure1]. When imaging anisotropic structures (e.g. axons), using a subset of the highest-signal HARDI directions is optimal in the presence of noise, while for isotropic structures (e.g. cell bodies) all directions contribute to TDR.

At G_max=600mT/m, TDR provides good contrast to a range of structures, consistent with previous axon diameter imaging⁶. In human and mouse data, TDR values in white matter are positive, but low (<0.1), corresponding to small restriction sizes, as indicated by simulations. TDR values in gray matter are larger; optimised TDR offers an effective way to image spherical cells, such as granular layer cells in the olfactory bulb or cerebellum.

In this work only simple impermeable geometrical substrates are considered, so an exploration of negative TDR values is impossible. These are likely due to unmodelled exchange effects^7,8. TDR contrast could be further improved by including other gradient shapes, such as oscillating gradients⁹.

Acknowledgements

This work is supported by an ESPRC studentship (EP/R513143/1); by ”la Caixa” Foundation (ID 100010434) and European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 847648, fellowship code CF/BQ/PI20/11760029; by a Wellcome Trust Investigator Award (096646/Z/11/Z) and a Wellcome Trust Strategic Award (104943/Z/14/Z); by an EPSRC equipment grant (EP/M029778/1); by a Siemens Healthcare Limited grant; and by UKRI Future Leaders Fellowship (MR/T020296/1).