Optimize the Flip Angle on gradient echo scans
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Optimizing the Flip Angle on gradient echo scans
The best signal to noise ratio in gradient echo scans (EPI or otherwise) is achieved with a flip angle , a equal to the so-called Ernst angle:
where T1 is the T1 of the object you are imaging (the T1 of the brain at 3T is about 1400 msec). You can calculate this on your pocket calculator, or you can use the handy utility, flip
The program will ask the tr and will give you the optimal brain flip angle. It lives in /usr/users/bin.
Note that the shorter the tr, the more the improvement to be had with smaller flip angles. In all cases, scanning at short tr, however, results in less signal than scanning with a long tr.
> flip Enter the TR you wish to use (in msec) '''200''' Assuming a brain t1 of 1400 msec, the optimum flip angle is '''29.90''' degrees. SNR improvement by using this flip angle: '''73%''' Relative signal (compared to infinite tr): '''26.70%''' >
The simple source for flip.c is:
#include <stdio.h> #include <stdlib.h> #include <string.h> #include <math.h> #define T1 1400.0 #define pi 3.141592654 int main() { char input[25]; float tr; float flipAngle; float Ratio; printf( "Enter the TR you wish to use (in msec) " ); scanf( "%s", input ); tr = atof( input ); flipAngle = acos( exp(-tr / T1)); printf( "\nAssuming a brain t1 of 1400 msec, the optimum flip angle is " ); printf( "%0.2f degrees.\n", 180 * flipAngle / pi ); Ratio = sin( flipAngle ) / ( 1-cos(flipAngle) * exp( -tr/T1 ) ); printf( "\nSNR improvement by using this flip angle: %0.2f%%\n", 100.0 * (Ratio - 1) ); printf( "Relative signal (compared to infinite tr): " ); printf( "%0.2f%%\n\n", 100 * Ratio * (1-exp( -tr/T1 )) ); return 0; }
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flip (°)
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