Learn More
In this high-resolution magnetic resonance imaging (MRI) study at 17.6 Tesla of a fixed rat brain, we used the continuous time random walk theory (CTRW) for Brownian motion to characterize anomalous diffusion. The complex mesoporus structure of biological tissues (membranes, organelles, and cells) perturbs the motion of the random walker (water molecules in(More)
PURPOSE In diffusion-weighted MRI studies of neural tissue, the classical model assumes the statistical mechanics of Brownian motion and predicts a monoexponential signal decay. However, there have been numerous reports of signal decays that are not monoexponential, particularly in the white matter. THEORY We modeled diffusion in neural tissue from the(More)
Systemic lupus erythematosus (SLE) is an autoimmune disease with multi-organ involvement and results in neurological and psychiatric (NP) symptoms in up to 40% of the patients. To date, the diagnosis of neuropsychiatric systemic lupus erythematosus (NPSLE) poses a challenge due to the lack of neuroradiological gold standards. In this study, we aimed to(More)
Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue.(More)
In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and(More)
In this paper we use fractional calculus to characterize diffusion in brain tissue by generalizing Fick's 2<sup>nd</sup> Law. This approach, rooted in the physics of the Continuous Time Random Walk (CTRW) Theory expresses separate measures of tissue complexity through the fractional order of the time derivative, &#x03B1;, and the space derivative, &#x00DF;.(More)
In this study, we applied continuous random walk theory (CTRW) to develop a new model that characterizes anomalous diffusion in magnetic resonance imaging experiments. Furthermore, we applied a classification scheme based on information theoretic a techniques to characterize the degree of heterogeneity and complexity in biological tissues. From a CTRW(More)
  • 1