A Fractional-Order Model for T2 Relaxation in Normal & Degraded Cartilage

David a Reiter¹, Richard L. Magin², Weiguo Li², Maria Pilar Velasco³, Juan Trujillo⁴, Richard G. Spencer¹

We previously derived a fractional-order relaxation model through incorporating a memory kernel into the Bloch equations. This leads to transverse relaxation decay according to a stretched-exponential (Str-Exp) function. We apply this to cartilage degeneration by fitting Str-Exp functions to decay curves from normal and enzymatically degraded cartilage. We find that the fractional-order parameter, , is sensitive to, and increases with, proteoglycan loss. We interpret this in terms of a reduction in microstructural tissue complexity. In contrast to multiexponential analysis, Str-Exp fits describe cartilage degradation using a single parameter and may be of particular utility in the setting of limited SNR.