Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain

Abstract

High b value diffusion-weighted images sampled at high angular resolution were analyzed using a composite hindered and restricted model of diffusion (CHARMED). Measurements and simulations of diffusion in white matter using CHARMED provide an unbiased estimate of fiber orientation with consistently smaller angular uncertainty than when calculated using a DTI model or with a dual tensor model for any given signal-to-noise level. Images based on the population fraction of the restricted compartment provide a new contrast mechanism that enhances white matter like DTI. Nevertheless, it is assumed that these images might be more sensitive than DTI to white matter disorders. We also provide here an experimental design and analysis framework to implement CHARMED MRI that is feasible on human clinical scanners.

Introduction

Magnetic Resonance Imaging (MRI) has significantly improved the radiological assessment of white matter (Filley, 2001). T₁- and T₂-weighted and magnetization transfer (MT) MRI have been used to increase image sensitivity to lipids or macromolecules in white matter, which has been attributed to the myelin sheath surrounding axons (Tofts, 2003). Another MR method, diffusion tensor imaging (DTI), increases white matter conspicuity primarily through its sensitivity to the geometrical packing and architectural organization of white matter fibers (Basser, 2002; Basser and Pierpaoli, 1996; Basser et al., 1994; Pierpaoli et al., 1996).

DTI yields a diffusion tensor from measurements of the apparent diffusion coefficient (ADC) of water molecules obtained along multiple directions. This measurement can be used to estimate the principal diffusivities parallel and perpendicular to coherent fiber bundles (Basser and Jones, 2002, Basser and Pierpaoli, 1996, Basser et al., 1994, Pierpaoli et al., 1996). Due to the high packing density of axons in fasciculi, the motion perpendicular to axons is more tortuous than that parallel to them. Using the principal diffusivities, it is also possible to calculate the orientationally averaged (or mean) ADC and the degree of diffusion anisotropy (Basser et al., 1994), for which the most popular parameter used presently is the fractional anisotropy (FA) (Basser, 1995).

A typical voxel in a diffusion MRI experiment is of the order of 10 mm³, and thus contains thousands of cells and tissue components. The diffusion of water molecules in each compartment (e.g., extracellular space, cell soma, axons, dendrites) is affected by the local viscosity, composition, geometry, and membrane permeability. Of these factors, geometry and permeability appear to have the most pronounced effect on the measured signal because the path that molecules traverse within typical diffusion times in a DTI experiment is larger than these compartment sizes, so that the long-time (tortuosity) limit is achieved. Indeed, since the first applications of diffusion imaging to neuronal tissue in the mid-80s, a significant amount of data has led to the observation that besides the cellular viscosity, permeability and tissue geometry significantly affect water diffusion. It is well known that the diffusivity across red blood cells that are very permeable to water molecules is much higher than other tissue cells (e.g., neurons). Furthermore, the fact that fiber directionality can be measured in white matter implies that the geometrical arrangement of the tissue also contributes significantly to the observed diffusivity.

Diffusion experiments are usually performed by spatially labeling spins at two different times during an MR experiment. These labeling periods are separated by a time interval (known also as the diffusion time, Δ) during which we measure the spin's displacement. The measured signal decay will depend on the strength of the labeling (referred to as the q value) and the diffusion time. Sometimes, the signal decay is characterized by a b value (b = q²Δ). An analytic relation between the signal decay and the diffusivity can be found for cases of free, Gaussian diffusion where we use the b factor to calculate the diffusivity (E = e^−bD, also known as the Stejskal–Tanner equation). In cases of non-Gaussian diffusion, however, it is preferable to describe the signal decay as a function of the q value. Conventional diffusion MRI (including DTI) averages random motions of water molecules in all tissue compartments and is insensitive to exchange (Basser and Jones, 2002). Yet, a Gaussian displacement distribution adequately describes the random motion of water molecules in brain tissue (both gray and white matter) only at low b or q values (Basser, 2002), so that over that range of b (or q) values, the description of the diffusion process using the Stejskal–Tanner equation is meaningful. However, these observations preclude the possibility that DTI alone can tease apart contributions from the intra- and extra-axonal compartments in white matter.

Several years ago, non-Gaussian diffusion was observed in neuronal tissues using strong diffusion weighting (DW) that sensitizes the image to molecular motions on a small length scale (<2 μm) (Assaf and Cohen, 1998, Assaf et al., 2002a, Niendorf et al., 1996). This approach revealed a pool of water molecules that is highly anisotropic and restricted, which was attributed mainly to water residing in the intra-axonal space (Assaf and Cohen, 2000). The measurement of water diffusion at high b values was first quantified using q space MR, a model-free analysis of the signal decay, which can provide a displacement probability distribution function in three dimensions (Callaghan, 1991, Cory and Garroway, 1990, King et al., 1997). High b value diffusion imaging complements DTI, in particular, providing information about water mobility in highly restricted compartments (Assaf et al., 2002a). This additional information has been useful in detecting several white matter pathologies (Assaf et al., 2002a, Assaf et al., 2002b, Assaf et al., 2002c). If a significant portion of the signal observed at high b value originates from restricted motion of intra-axonal water, then it could provide new information about axonal morphology and microstructure not provided by DTI, and could potentially improve the delineation of white matter tracts, as well as white matter assessment in disease and development.

Recently, a composite hindered and restricted model of diffusion (CHARMED) was proposed to provide a more complete physical description of the diffusion process in white matter, expressing the signal decay observed in white matter in terms of Gaussian (hindered) and non-Gaussian (restricted) contributions (Assaf et al., 2004). The model assumes that one contribution to the net signal decay arises from hindered diffusion in the extra-axonal volume (including extra- and intracellular spaces), while another contribution to the net signal decay arises from restricted diffusion in the intra-axonal volume.

In this work, we use CHARMED MRI to characterize 3-D hindered and restricted diffusion in human brain in vivo. Here, we propose an experimental framework for performing CHARMED MRI in vivo within a clinically feasible timeframe, which entails acquiring DW MRIs with multiple b values and multiple gradient directions. We compare the ability of CHARMED MRI and DTI to separate multiple fiber orientations within a single voxel, and describe the biological significance of different microstructural and physical parameters measured (estimated) from CHARMED MRI.