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Measurement of compartment size in q ‐space experiments: Fourier transform of the second derivative
Author(s) -
Kuchel Philip W.,
Eykyn Thomas R.,
Regan David G.
Publication year - 2004
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.20219
Subject(s) - fourier transform , space (punctuation) , k space , compartment (ship) , derivative (finance) , fourier analysis , physics , nuclear magnetic resonance , mathematics , mathematical analysis , biological system , computer science , biology , geology , oceanography , financial economics , economics , operating system
Restricted diffusion in compartmentalized systems can lead to spatial coherence phenomena being observed in q ‐space plots from pulsed field gradient spin‐echo (PGSE) nuclear magnetic resonance (NMR) experiments. The underlying features observed in these plots contain information on the geometry of the compartments that is otherwise difficult to obtain. A numerical procedure is proposed that accentuates these coherence features: the data are weighted with a bell‐shaped window function, interpolated with a shifting cubic spline, and then the second derivative is taken prior to Fourier transformation. The window function provides apodization of the noisy data at high q values, while it and the second derivative are equivalent to applying a high‐pass filter to remove the zero‐ or low‐frequency components in the echo‐signal attenuation. Using a combination of theory, Monte Carlo simulations, and data from PGSE NMR experiments on human red blood cells, we demonstrate this to be a valuable processing tool for delineating the underlying coherence features. It should prove particularly useful where the coherence features are poorly defined or where more than one pattern is present in a q ‐space plot. Magn Reson Med 52:907–912, 2004. © 2004 Wiley‐Liss, Inc.