Visualisation of Fractal Fingering using NMR Imaging
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Visualisation of Fractal Fingering using NMR Imaging ELEANOR S. DAVIES', T.ADRIAN CARPENTER-, LAURANCE D. HALL* and CHRISTOPHER HALLt * Herchel Smith Laboratory for Medicinal Chemistry, University of Cambridge Clinical School, University Forvie Site, Robinson Way, Cambridge, CB2 2PZ, U.K. t Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge, CB3 QEL, U.K.
ABSTRACT Fractal fingering is a well known phenomenon, ususally visualised using photography t . Previous experiments have shown that the patterns can be visualised using NMR imaging 2, and in this paper we show that the fractal dimension of such a pattern can be easily calculated.
NMR DATA ACQUISITION TECHNIQUES All data were acquired using an Oxford Research Systems Biospec 1 console, controlled by a Bruker Aspect 3000 computer, interfaced with an Oxford Instruments 2T, 31cm horizontal-bore, superconducting magnet with 20cm purpose built Helmholtz-Golay gradient coils.
A sine-spaced birdcage radiofrequency probe3 , was used.
All data
processing, except where stated otherwise was performed on a Sun4/150 workstation with a TAAC accelerator board, using in-house software. The image of the cell was obtained using a prefocused gradient-recalled echo imaging sequence 4 (Fig 1.) which allows fast 2D images to be obtained, which display a T1 -dependent signal intensity. Such prefocused pulses excite longitudinal components of the magnetization whilst "spoiling", or dephasing, existing transverse components. As a result, the peak amplitude of the gradient recalled echo formed after each pulse depends on the proportion of the excited magnetization which has undergone longitudinal relaxation in the inter-pulse interval (TR). In contrast, conventional FLASH imaging 5 requires additional sl)oiling mechanisms to dephase transverse magnetization Mat. Res. Soc. Symp. Proc. Vol. 290. 01993 Materials Research Society
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and prevent it giving rise to spurious echos which intefere with the desired echoes and degrade the image contrast. Consequently, if TR (and so the overall imaging time) is kept short, species with short longitudinal relaxation times will appear relatively bright, whilst species with longer T-'s will appear dimmer. The signal intensity from a gradient recalled echo formed a time (TG) after the puse application is given by the equation:
S a p(l
-
e-TR/TI )e-TGITm
TG is therefore kept as short as possible (,-.1 ms) to minimize the effect of Tý on the image contrast. This condition is easily satisfied in this case since the aqueous sodiumcarboxymethylcellulose(CMC) had a line width of -30Hz.
This corresponds
to T; of about lOOms and relaxation during the gradient echo time may therefore be neglected.
PULSE
ECHO
4A4
'"
RF
7- 1 *
*6
Slice Gradient I
I
Phase encode
Read
LY1
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