Non-invasive estimation of axon diameter plays an important role in biomedical imaging. For instance, the conduction velocity of signal transmission throughout the nerve pathways in the central nervous system (CNS) [1] is directly influenced by axon diameter. Thus, estimating this tissue feature can provide essential information on the performance and function of white matter pathways [2]. Moreover, changes

L.S. Kakkar (H) • A. Ianus • I. Drobnjak

Centre for Medical Image Computing, University College London, London, UK e-mail: lebina.shrestha.
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D. Atkinson • R.W. Chan

Centre for Medical Imaging, Wolfson House, 4 Stephenson Way, London, UK B. Siow

A. Fuster et al. (eds.), Computational Diffusion MRI, Mathematics

and Visualization, DOI 10.1007/978-3-319-54130-3_7

in axon diameter estimates can be used to study the effect of ageing [3], as well as of various CNS diseases, such as amyotrophic lateral sclerosis [4], autism [5], and schizophrenia [6], where axonal degeneration can lead to abnormal axon diameters.

A number of methods for estimating axon diameter using diffusion weighted magnetic resonance imaging (DW-MRI) have been proposed. These include q-space imaging (QSI) [7], double pulsed field gradient (dPFG) [8, 9], AxCaliber [10] and ActiveAx [11]. The majority of these techniques are based on single diffusion encoding (SDE) sequences. However, various authors suggest that oscillating gradient spin echo (OGSE ) offers benefits over SDE for imaging fibre diameter [12-15].

A common argument is that high-frequency OGSE sequences provide shorter effective diffusion time than SDE and hence are able to probe smaller length scales. This is clearly an advantage for measuring the free diffusivity in small fibres because it minimises the effects of restriction [16, 17]. However, it is not clear whether it is advantageous for measuring fibre diameter where contrast at the long diffusion time limit may be more informative.

Recently, a thorough numerical approach has been used to compare directly the sensitivity to axon diameter of SDE and OGSE sequences in a wide space of clinically plausible sequence parameters [12]. The research showed that for the simple case of diffusion gradient direction perfectly perpendicular to straight parallel fibres, SDE with the longest gradient duration always gives maximum sensitivity for small diameters. However, in real-world scenarios where fibres have unknown and/or dispersed orientation, OGSE provides higher sensitivity. This happens because the oscillating waveforms can achieve high sensitivity to fibre diameters at a modest b-value, which in turn enables OGSE sequences to retain their sensitivity by avoiding excessive signal attenuation from unrestricted displacements along the fibre direction. These results were confirmed analytically in a recent study by Nillson et al. [18]. Both groups also found diameter resolution limits for a range of different gradient strengths and SNRs. Their results show that on typical clinical scanners the limit is around 6 |xm, i.e. axon diameters below that limit are undistinguishable from zero.

This study aims to explore experimentally, on a clinical scanner, the sensitivity of OGSE sequences to fibre diameter in a phantom consisting of cylindrical microcapillaries with unknown orientation. We use water-filled micro-capillaries array plates as a model for axons, and fit a single restricted component. We use a rotationally invariant HARDI acquisition with 32 directions as we assume microcapillaries of unknown orientation. The micro-capillary diameters used here are 5, 10 or 20 |xm, which is within the limits of axon diameters in the body (0.2-20 |i,m) [2]. We use a trapezoidal OGSE with a range of frequencies for imaging and OGSE ActiveAx [14, 19] for the estimation of microstructure parameters.