Can T 2 -Spectroscopy Resolve Submicrometer Axon Diameters? [chapter]

Enrico Kaden, Daniel C. Alexander
2013 Lecture Notes in Computer Science  
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,
more » ... lthough 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 T2-spectroscopy to resolve submicrometer tissue structures. Exploiting the surface relaxation effect, we formulate a plausible biophysical model relating the axon diameter distribution to the T2-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. especially their spatial variation and the differences between subjects, are less known. These parameters are crucial markers towards the understanding of brain function, since the conduction time delay of action potentials, hence the speed of information transmission between remote brain areas, is largely determined by the axon radius [2] . Moreover, the fiber microanatomy is affected by various neurological disorders. In multiple sclerosis it is well known that during the typical course of the disease the thin axons are preferentially damaged [3] . Nowadays diffusion MR experiments are the method of choice when we aim to recover the axon diameter distribution in brain white matter noninvasively. This technique allows us to encode the diffusion process of water molecules through the external application of time-dependent magnetic fields, which are under control of the experimenter. Considerable effort over the past few years [4] has gone into devising biophysical models or acquisition protocols for estimating the axon diameter from diffusion MR measurements. For instance, Stanisz et al. [5] proposed a tissue model that provides an estimate of the mean axon diameter and demonstrated their approach in bovine optic nerve. The AxCaliber framework describes the restricted diffusion process within the axons and the hindered water diffusion in the space between the nerve fibers [6, 7] . The axon diameter distribution, which is parameterized by a Gamma density, was then estimated in excised nerve tissue and in the corpus callosum of living rat brain, respectively, thereby assuming parallel fibers with a single known orientation. The ActiveAx technique [8] allows orientationally invariant estimates of the axon diameter and shows the first in-vivo human maps of an index of axon diameter. This method still assumes that the nerve fibers in a voxel are parallel to each other. More recently, Zhang et al. [9] relaxed the assumption by allowing a Watson distribution of axon orientations to describe fiber dispersion known to exist even in the corpus callosum [10] . A key limitation of diffusion MR experiments is that the gradient strength places a lower bound on the measurable axon diameter [8, 11] . The gradient systems available on human scanners are sensitive only to the largest nerve fibers. Moreover, the human physiology tolerates only moderate gradient strengths, suggesting that in-vivo diffusion imaging has fundamental limitations upon the resolution power. Even on dedicated animal systems we cannot distinguish diameters less than one or two micrometers where the bulk of the axon distribution resides. Also unduly long gradient durations are prohibitive because of the short T 2 -relaxation time of white matter tissue. Here we consider, from a theoretical viewpoint, an alternative MR modality, T 2 -spectroscopy, and its potential to resolve submicrometer axon diameters. Instead of the displacement of the diffusing water molecules, this method measures their interaction with the cellular boundaries, which may contain paramagnetic impurities that give rise to fluctuating microscopic fields. As a consequence, the water molecules close to the axonal membranes partially loose their phase coherence and thus the T 2weighted signal attenuates faster. This surface relaxation effect is the contrast mechanism that gives the potential to measure axons with one micrometer or less in diameter. Intuitively, for a tissue sample of thin nerve fibers a large volume
doi:10.1007/978-3-642-38868-2_51 pmid:24684003 fatcat:4pxmv3nqibddhl3yi53cnjrswa