Stretched-Exponential Modeling of Anomalous T1{rho} and T2 Relaxation in the Intervertebral Disc In Vivo

PurposeIntervertebral disc degeneration (IVDD), resulting in the depletion of hydrophilic glycosaminoglycans (GAGs) located in the nucleus pulposus (NP), can lead to debilitating neck and back pain. Magnetic Resonance Imaging (MRI) is a promising means of IVD assessment due to the sensitivity of MRI tissue relaxation properties to matrix composition. Furthermore, anomalous (i.e. non-monoexponential) relaxation models have shown higher sensitivity to specific matrix components compared to conventional monoexponential models. Here, we extend the use of the stretched exponential model, an anomalous relaxation model, to IVD relaxometry data. Theory and MethodsT1{rho} and T2 relaxation data were measured in the cervical IVDs of healthy volunteers and IVDs adjacent to cervical fusion, and analyzed using both conventional and stretched-exponential (SE) models. Model differences were evaluated via goodness of fit in the healthy data. Normalized histograms of the resultant quantitative MRI (qMRI) maps were described using stable distributions, and data were compared across adjacent disc segments. ResultsIn the healthy IVDs, we found lower mean squared error in the SE relaxation model fitting behavior compared to monoexponential models, supporting anomalous relaxation behavior in healthy IVDs. SE model parameter T1{rho} increased level-wise in the caudal direction, especially in the nucleus pulposus, while conventional T1{rho} and T2 monoexponential measures did not vary. For IVDs adjacent to cervical fusion, SE parameters deviated near the fusion site compared with those in the healthy population. ConclusionSE modeling of T1{rho} relaxation provides greater sensitivity to level-wise variation in IVD matrix properties compared with conventional relaxation modeling, and could provide improved sensitivity to early stages of IVD degeneration. The improved model fit and correlation between the SE T1{rho} parameter with IVD level suggests SE modeling may be a more sensitive method for detection of GAG content variation.