Determination of the distribution of magnetic resonance (MR) transverse relaxation times is emerging as an important method for materials characterization, including assessment of tissue pathology in biomedicine. These distributions are obtained from the inverse Laplace transform (ILT) of multiexponential decay data. Stabilization of this classically ill-posed problem is most commonly attempted using Tikhonov regularization with an L 2 penalty term. However, with the availability of convex optimization algorithms and recognition of the importance of sparsity in model reconstruction, there has been increasing interest in alternative penalties. The L 1 penalty enforces a greater degree of sparsity than L 2 , and so may be suitable for highly localized relaxation time distributions. In addition, L p penalties, 1 < p < 2, and the elastic net (EN) penalty, defined as a linear combination of L 1 and L 2 penalties, may be appropriate for distributions consisting of both narrow and broad components. We evaluate the L 1 , L 2 , L p , and EN penalties for model relaxation time distributions consisting of two Gaussian peaks. For distributions with narrow Gaussian peaks, the L 1 penalty works well to maintain sparsity and promote resolution, while the conventional L 2 penalty performs best for distributions with broader peaks. Finally, the L p and EN penalties do in fact outperform the L 1 and L 2 penalties for distributions with components of unequal widths. These findings serve as indicators of appropriate regularization in the typical situation in which the experimentalist has a priori knowledge of the general characteristics of the underlying relaxation time distribution. Our findings can be applied to both the recovery of T 2 distributions from spin echo decay data as well as distributions of other MR parameters, such as apparent diffusion constant, from their multiexponential decay signals. K E Y W O R D Sinverse Laplace transform, inverse problems, NMR relaxometry, non-negative least squares, regularization

Purpose we applied a recently introduced method to achieve clinically-feasible in-vivo mapping of the proteoglycan water fraction (PgWF) of human knee cartilage with improved spatial resolution and stability as compared to existing methods. Material and Methods Multicomponent driven equilibrium single-pulse observation of T1 and T2 (mcDESPOT) datasets were acquired from the knees of two healthy young subjects and one older subject with previous knee injury. Each dataset was processed using Bayesian Monte Carlo (BMC) analysis incorporating a two-component tissue model. We assessed the performance and reproducibility of BMC and of the conventional analysis of stochastic region contraction (SRC) in the estimation of PgWF. Stability of the BMC analysis of PgWF was tested in two independent high-resolution (HR) datasets from each of the two young subjects. Results Unlike SRC, the BMC-derived maps from the two HR datasets were essentially identical. Furthermore, SRC maps showed substantial random variation in estimated PgWF, and mean values that differed from those obtained using BMC. In addition, PgWF maps derived from conventional low-resolution (LR) datasets exhibited partial volume and magnetic susceptibility effects. These artifacts were absent in HR PgWF images. Finally, our analysis showed regional variation in PgWF estimates, and substantially higher values in the younger subjects as compared to the older subject. Conclusions BMC-mcDESPOT permits HR in-vivo mapping of PgWF in human knee cartilage in a clinically-feasible acquisition time. HR mapping reduces the impact of partial volume and magnetic susceptibility artifacts compared to LR mapping. Finally, BMC-mcDESPOT demonstrated excellent reproducibility in the determination of PgWF.

Purpose Magnetic resonance imaging of ex vivo cartilage measures parameters such as T2 and magnetization transfer ratio (MTR), which reflect structural changes associated with osteoarthritis. Samples are often immersed in aqueous solutions to prevent dehydration and to to improve susceptibility matching. This study sought to determine the extent to which T2 and MTR changes are attributable to immersion alone and to identify immersion conditions to minimize this confounding factor. Methods T2 and MTR were measured before and after immersion for up to 24 hours at 4°C. Bovine nasal and articular cartilage and human articular cartilage were studied. Experimental groups included undisturbed immersion in Fluorinert FC‐770, a susceptibility‐matched, hydrophobic liquid with minimal tissue penetration, and immersion in Fluorinert, Dulbecco’s phosphate‐buffered saline (DPBS), or saline, with removal from the magnet between scans. 19F and 1H‐MRI were used to detect cartilage penetration by Fluorinert and swelling, respectively. Results Saline and DPBS immersion rapidly increased T2, wet weight and cartilage volume and decreased MTR, suggesting increased water content for all cartilage types. Fluorinert‐immersed samples exhibited minimal changes in T2 or MTR. No ingress of Fluorinert was detected after 2 weeks of continuous immersion at 4°C. Conclusion Ex vivo quantitative MR studies of cartilage may be confounded by the effects of immersion in aqueous solution, which may be comparable to or larger than effects attributed to pathology. These effects may be mitigated by immersion in perfluorocarbon liquids such as Fluorinert FC‐770.