TY - JOUR
AU - Kurz, Felix T.
AU - Kampf, Thomas
AU - Buschle, Lukas R.
AU - Schlemmer, Heinz-Peter
AU - Bendszus, Martin
AU - Heiland, Sabine
AU - Ziener, Christian H.
PY - 2016
M3 - 10.3389/fphy.2016.00046
SP - 46
TI - Generalized Moment Analysis of Magnetic Field Correlations for Accumulations of Spherical and Cylindrical Magnetic Perturbers
JO - Frontiers in Physics
UR - https://www.frontiersin.org/article/10.3389/fphy.2016.00046
VL - 4
SN - 2296-424X
N2 - In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin dephasing in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows deriving analytical expressions of the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.
ER -