Abstract
Quasi-diffusion imaging (QDI) is a novel quantitative diffusion magnetic resonance imaging (dMRI) technique that enables high quality tissue microstructural imaging in a clinically feasible acquisition time. QDI is derived from a special case of the continuous time random walk (CTRW) model of diffusion dynamics and assumes water diffusion is locally Gaussian within tissue microstructure. By assuming a Gaussian scaling relationship between temporal (α) and spatial (β) fractional exponents, the dMRI signal attenuation is expressed according to a diffusion coefficient, D (in mm2 s−1), and a fractional exponent, α. Here we investigate the mathematical properties of the QDI signal and its interpretation within the quasi-diffusion model. Firstly, the QDI equation is derived and its power law behaviour described. Secondly, we derive a probability distribution of underlying Fickian diffusion coefficients via the inverse Laplace transform. We then describe the functional form of the quasi-diffusion propagator, and apply this to dMRI of the human brain to perform mean apparent propagator imaging. QDI is currently unique in tissue microstructural imaging as it provides a simple form for the inverse Laplace transform and diffusion propagator directly from its representation of the dMRI signal. This study shows the potential of QDI as a promising new model-based dMRI technique with significant scope for further development.
Highlights
Quasi-diffusion imaging [1] is a novel diffusion magnetic resonance imagingtechnique based on a special case of the continuous time random walk (CTRW) diffusion model [2,3,4,5]
Outside the CTRW model, techniques have been developed that assume the underlying diffusion process to be Gaussian. These include representing the diffusion signal attenuation as a second moment expansion known as Diffusional Kurtosis Imaging (DKI) [24,25], or as a signal in the experimentally acquired “q-space” from which, via application of the inverse Fourier transform leads to a Mean apparent diffusion propagator (MAP) of molecular displacement [26,27,28] allowing measurement of the length scale of the diffusion environment
T1wGd image (Figure 6a), the hyperintense region is typical for glioblastoma multiforme (GBM) and indicates the high-grade tumour core region that would be the target for resection and/or highest radiotherapy dose; the central dark region is necrotic tissue
Summary
Quasi-diffusion imaging [1] is a novel diffusion magnetic resonance imaging (dMRI). technique based on a special case of the continuous time random walk (CTRW) diffusion model [2,3,4,5]. Outside the CTRW model, techniques have been developed that assume the underlying diffusion process to be Gaussian These include representing the diffusion signal attenuation as a second moment expansion known as Diffusional Kurtosis Imaging (DKI) [24,25], or as a signal in the experimentally acquired “q-space” from which, via application of the inverse Fourier transform leads to a Mean apparent diffusion propagator (MAP) of molecular displacement [26,27,28] allowing measurement of the length scale of the diffusion environment. Examples of quasi-diffusion MAP imaging are given in which we show the technique can be performed using a clinical MR scanner and that dMRI data for analysis of quasi-diffusion can be acquired in a clinically feasible scan time
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