Can T ₂ -Spectroscopy Resolve Submicrometer Axon Diameters?

Abstract

The microscopic geometry of white matter carries rich information about brain function in health and disease. A key challenge for medical imaging is to estimate microstructural features noninvasively. One important parameter is the axon diameter, which correlates with the conduction time delay of action potentials and is affected by various neurological disorders. Diffusion magnetic resonance (MR) experiments are the method of choice today when we aim to recover the axon diameter distribution, although the technique requires very high gradient strengths in order to assess nerve fibers with one micrometer or less in diameter. In practice in-vivo brain imaging is only sensitive to the largest axons, not least due to limitations in the human physiology which tolerates only moderate gradient strengths. This work studies, from a theoretical perspective, the feasibility of T ₂ -spectroscopy to resolve submicrometer tissue structures. Exploiting the surface relaxation effect, we formulate a plausible biophysical model relating the axon diameter distribution to the T ₂ -weighted signal, which is based on a surface-to-volume ratio approximation of the Bloch–Torrey equation. Under a certain regime of bulk and surface relaxation coefficients, our simulation results suggest that it might be possible to reveal axons smaller than one micrometer in diameter.