APART-QSM: An improved sub-voxel quantitative susceptibility mapping for susceptibility source separation using an iterative data fitting method

In the CNS, iron in several proteins is involved in many important processes such as oxygen transportation, oxidative phosphorylation, myelin production, and the synthesis and metabolism of neurotransmitters. Abnormal iron homoeostasis can induce cellular damage through hydroxyl radical production, which can cause the oxidation and modification of lipids, proteins, carbohydrates, and DNA. During ageing, different iron complexes accumulate in brain regions associated with motor and cognitive impairment. In various neurodegenerative diseases, such as Alzheimer's disease and Parkinson's disease, changes in iron homoeostasis result in altered cellular iron distribution and accumulation. MRI can often identify these changes, thus providing a potential diagnostic biomarker of neurodegenerative diseases. An important avenue to reduce iron accumulation is the use of iron chelators that are able to cross the blood-brain barrier, penetrate cells, and reduce excessive iron accumulation, thereby affording neuroprotection.

This paper is devoted to a theory of the NMR signal behavior in biological tissues in the presence of static magnetic field inhomogeneities. We have developed an approach that analytically describes the NMR signal in the static dephasing regime where diffusion phenomena may be ignored. This approach has been applied to evaluate the NMR signal in the presence of a blood vessel network (with an application to functional imaging), bone marrow (for two specific trabecular structures, asymmetrical and columnar) and a ferrite contrast agent. All investigated systems have some common behavior. If the echo time TE is less than a known characteristic time tc for a given system, then the signal decays exponentially with an argument which depends quadratically on TE. This is equivalent to an R2* relaxation rate which is a linear function of TE. In the opposite case, when TE is greater than tc, the NMR signal follows a simple exponential decay and the relaxation rate does not depend on the echo time. For this time interval, R2* is a linear function of a) volume fraction sigma occupied by the field-creating objects, b) magnetic field Bo or just the objects' magnetic moment for ferrite particles, and c) susceptibility difference delta chi between the objects and the medium.