Diffusion Weighted Imaging of Human Articular Cartilage Using Fractional Calculus Model: Preliminary Study

Xu Feng¹, Richard L. Magin¹, Jun Li², Carol Muehleman²

Restricted diffusion doesnt follow the mono-exponential decay. Some reports have suggested using bi-exponential model. However, bi-exponential fitting is nontrivial and needs some experience to get fast and slow diffusion coefficients. In this paper, we generalize a spatial Laplacian in the Bloch-Torrey equation to incorporate a fractional order Brownian model of diffusivity. A new parameter was derived from the new equation of Stejskal-Tanner gradient pulses. We fitted the signal attenuation obtained from the diffusion-weighted images of Sephadex gels and human articular cartilages using fractional order diffusion model. The results show that can be used to reflect the structure of the tissue. The value obtained from the osteoarthritis (OA) cartilage was larger than from the normal cartilage. Future development of this approach may be useful for detecting the early degeneration of OA.