Optimize the Flip Angle on gradient echo scans

From Center for Cognitive Neuroscience
Jump to navigation Jump to search

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:

a = acos( exp( -tr/T1) )

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;
}

tr (ms)
flip (°)
SNR gain
tr (ms)
flip (°)
SNR gain
50
15.2
87%
1000
60.7
41%

File:Flip.png

100
21.4
81%
1100
62.9
39%
150
26.1
77%
1200
64.9
36%
200
29.9
73%
1300
66.7
34%
250
33.2
70%
1400
68.4
32%
300
36.2
67%
1500
70.0
30%
350
38.8
65%
1750
73.4
26%
400
41.3
62%
2000
76.1
22%
450
43.5
60%
2250
78.4
18%
500
45.6
58%
2500
80.3
16%
600
49.3
54%
2750
81.9
13%
700
52.7
51%
3000
83.3
11%
800
55.6
47%
3250
84.4
9%
900
58.3
44%
3500
85.3
8%