Measurement of compartment size in q-space experiments: Fourier transform of the second derivative

Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine
P W KuchelDavid G Regan

Abstract

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.

References

Jun 1, 1990·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·D G Cory, A N Garroway
May 1, 1997·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·P W KuchelP Stilbs
Jan 5, 2002·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Y AssafY Cohen
Jun 25, 2002·Biophysical Journal·David G Regan, Philip W Kuchel

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Citations

Apr 29, 2009·European Biophysics Journal : EBJ·Timothy J Larkin, Philip W Kuchel
May 31, 2012·European Biophysics Journal : EBJ·Timothy J LarkinPhilip W Kuchel
Oct 19, 2010·Bulletin of Mathematical Biology·Huaxiong HuangRobert M Miura
Mar 3, 2007·Magnetic Resonance in Medical Sciences : MRMS : an Official Journal of Japan Society of Magnetic Resonance in Medicine·Eizou UmezawaEiji Tanaka
Nov 29, 2007·IEEE Transactions on Medical Imaging·Jimmy LättSara Brockstedt
Apr 4, 2013·Journal of Magnetic Resonance·Dan Benjamini, Uri Nevo
Jun 22, 2007·Magnetic Resonance Imaging·Jimmy LättSara Brockstedt
Nov 26, 2008·Journal of Magnetic Resonance Imaging : JMRI·Guilhem PagesPhilip W Kuchel
Sep 2, 2010·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Guilhem PagesPhilip W Kuchel
Jul 22, 2014·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Wilfred W LamKarla L Miller

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