Diffusion-weighted magnetic resonance imaging (DW-MRI) is a powerful tool to probe the diffusion of water through tissues. Through the application of magnetic gradients of appropriate direction, intensity and duration constituting the acquisition parameters, information can be retrieved about the underlying microstructural organization of the brain. In this context, an important and open question is to determine an optimal sequence of such acquisition parameters for a specific purpose. The use of simulated DW-MRI data for a given microstructural configuration provides a convenient and efficient way to address this problem. We first present a novel hybrid method for the synthetic simulation of DW-MRI signals that combines analytic expressions in simple geometries such as spheres and cylinders and Monte Carlo (MC) simulations elsewhere. Our hybrid method remains valid for any acquisition parameters and provides identical levels of accuracy with a computational time that is 90% shorter than that required by MC simulations for commonly-encountered microstructural configurations. We apply our novel simulation technique to estimate the radius of axons under various noise levels with different acquisition protocols commonly used in the literature. The results of our comparison suggest that protocols favoring a large number of gradient intensities such as a Cube and Sphere (CUSP) imaging provide more accurate radius estimation than conventional single-shell HARDI acquisitions for an identical acquisition time.
Diffusion-weighted imaging is sensitive to the movement of water molecules through the tissue microstructure and can therefore be used to gain insight into the tissue cellular architecture. While the diffusion signal arising from simple geometrical microstructure is known analytically, it remains unclear what diffusion signal arises from complex microstructural configurations. Such knowledge is important to design optimal acquisition sequences, to understand the limitations of diffusion-weighted imaging and to validate novel models of the brain microstructure. We present a novel framework for the efficient simulation of high-quality DW-MRI signals based on the hybrid combination of exact analytic expressions in simple geometric compartments such as cylinders and spheres and Monte Carlo simulations in more complex geometries. We validate our approach on synthetic arrangements of parallel cylinders representing the geometry of white matter fascicles, by comparing it to complete, all-out Monte Carlo simulations commonly used in the literature. For typical configurations, equal levels of accuracy are obtained with our hybrid method in less than one fifth of the computational time required for Monte Carlo simulations.