Magnetic Resonance Relaxometry and Macromolecular Mapping: An Inverse Problem Framework, with Applications to Alzheimer's Disease and Osteoarthritis*

Quantification of changes in the macromolecular constituents of tissue is a major theme in biomedical magnetic resonance (MR). In many cases, constituents can only be distinguished through their differing water transverse relaxation times, instead of by frequency differences as is more familiar in MR spectroscopy. However, this requires implementation of multiexponential transverse relaxation analysis (METRA), a special case of the inverse Laplace transform, a notoriously ill-posed and unstable inverse problem. Our work in this area combines basic science studies with methodologies that carry immediate translational potential. We will discuss METRA as a means to quantify the myelin water fraction (MWF) of total brain water as a marker for myelin, a critical element of signal transmission within the central nervous system, in the mathematical setting of a linear inverse problem. In addition, we have stabilized MWF estimates using a rapid steady-state MR pulse sequence through Bayesian analysis of the corresponding non-linear inverse problem. With this, we provide the first report of myelination deficits using direct MWF measurements in subjects with mild cognitive impairment and Alzheimer's disease. We have implemented similar methods to map cartilage proteoglycan, the macromolecule most vulnerable to loss in osteoarthritis, obtaining results indicating the potential for improved detection of this condition. Finally, we describe extensions of METRA to higher dimensional experiments, with two or more independent time variables. We discuss the stability of parameter estimates from these experiments, as well as correlation experiments providing insight into chemical exchange between macromolecular constituents. All of these studies are directed toward the clinical goal of improving the ability of MR to diagnose pathology and monitor disease progression, and to define therapeutic targets for treatment.