Mean apparent propagator (MAP) MRI: A novel diffusion imaging method for mapping tissue microstructure

Abstract

Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in “q-space,” and the corresponding “mean apparent propagator (MAP)” describing molecular displacements in “r-space.” We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit “displacement” sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions—the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.

Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

“…The EAP contains the full 3D information about the water molecule diffusion within the imaging voxel, which goes beyond principal directions that can be used for tractography (Merlet et al, 2012b). The EAP can serve to estimate parameters that reflect the microstructural environment, such as axonal diameter in recent works (Assaf et al, 2008;Ozarslan et al, 2013).…”

Efficient experimental designs for isotropic generalized diffusion tensor MRI (IGDTI)

“…Future studies will optimize the number of b-values and gradient orientations to achieve required levels of sensitivity, accuracy, precision, rotation invariance, robustness, and scan duration for specific clinical applications. The insights from this work will help improve and accelerate experimental designs for many clinical diffusion MRI applications, such as fast DKI (14), mean apparent propagator MRI (23,37), and GDTI (10,13), and may enable new clinical applications, such as isotropic diffusion relaxometry imaging (38,39) at the whole-brain level.…”

Multi-Spherical Diffusion MRI: Exploring Diffusion Time Using Signal Sparsity

“…In this case, given infinite gradient strength and some assumptions on tissue composition [12,13], q-space indices such as the Return-ToAxis Probability (RTAP) are related to the mean apparent axon diameter. -{q = 0, τ }: When q = 0 there is no diffusion sensitization so E(q = 0, τ ) = 1.…”

“…[8,9,12,14]. Of these bases, we use the Mean Apparent Propagator (MAP) basis [12] as it neatly fulfills all four previously stated requirements; (1) being an orthogonal basis, it can accurately represent any signal over q using few coefficients; (2) it allows to impose smoothness using analytic Laplacian regularization [13]; (3) the isotropic MAP implementation was successfully used to obtain sparse signal representation [8] and (4) MAP's signal basis is a product of three orthogonal Simple Harmonic Oscillatorbased Reconstruction and Estimation (SHORE) functions φ n (u) [15]:…”

“…As in MAP [12], before fitting, the data is rotated such that the DTI eigenvectors are aligned with the coordinate axis and we can use the datadependent scaling matrix A = Diag(u 2 x , u 2 y , u 2 z ) to scale the MAP basis functions according to the anisotropy of the data. The zeroth order is a purely Gaussian function while higher orders use the Hermite to correct this approximation to the true shape of the data.…”