Quantitative MRI and the Aging Brain*

 

Myelin is a protein- and lipid-rich substance that potentiates electrical impulse transmission along axons. Myelination disorders are central to a number of pathologies, including multiple sclerosis in the CNS and Guillain-Barre syndrome in the peripheral nervous system, and implicated in many others, including cognitive impairment and Alzheimer’s disease. However, conventional MRI provides maps only of relatively non-bound water, with image contrast provided by appropriate implementation of pulse sequence parameters.  This leads to sensitive, but non-specific, measures of myelin.  Macromolecular mapping has been developed as a more specific, direct, alternative for studies of myelin and other macromolecules and related structures.  This approach focuses on detection and quantification of less-mobile water associated with the macromolecule of interest, typically through relaxation or diffusion properties.  This requires multi-component mathematical analysis of the MRI signal to distinguish between relatively unbound water and water with more limited mobility.  This leads to a mathematically difficult inverse problem in which the effect of noise in the data is greatly amplified in the resulting parameter estimates. One important version of this is multiexponential analysis via the inverse Laplace transform, a form of the classically ill-posed inverse problem of solving the Fredholm equation of the first kind. Specialized methods developed within the inverse problems perspective have been developed to address the problem of noise sensitivity.  We show applications to myelin mapping in the CNS and proteoglycan mapping in cartilage, and describe a number of methodologic advances.  The goals of our work are twofold: to improve the capacity of MR to evaluate tissue pathology, and to develop methods for application to inverse problems more generally.