Terry M. Button, Ph.D. Principals of Magnetic Resonance Image Formation

General Signal Localization Region of interest is excited with f L. Magnetic field is modified in a planned way using gradients. Emitted frequency is now dependent on location. Signal vs. time is collected, FT provides signal vs. f which is also signal vs. location!

2D FT Initial approach will be descriptive and non- mathematical. The second approach will be semi- mathematical.

Overview of 2D FT Slice selection Phase encoding Frequency encoding

Slice selection Apply a gradient along z Excite with RF which covers  ( B o -  ) to  ( B o +  ) Bo+Bo+ Bo+Bo+ Z

RF profile I

Slice Thickness is Determined by Bandwidth and Gradient Strength x B f l = (B o -  )  f h = (B o +  )  x2x2 t T

Slice Selection Excite bandwidth (kHz) is usually fixed and gradient strength used to change slice thickness. Slice orientation is controlled using the gradients; oblique is one gradient tilted by a second gradient. Slice position is moved by changing reference frequency.

Frequency Encode Frequency encoding is accomplished during signal acquisition (read) by application of a gradient. B o -  BoBo B o +  f l = (B o -  )  f o = B o  f h = (B o +  ) 

Frequency Encoding Gradient Provides a Simple Projection BoBo S t I f FFT

Sample Collection Signal is sampled N times (128, 256, 512, 1024) Sample collection time is  t (1-100  sec) –SNR   t Total collection time T = N  t –T< TE Bandwidth = 1/  t –  t = 50  sec, BW = 20 kHz S t

FOV Field of view (FOV) is controlled by: –Gradient strength –Bandwidth From the last slide; BW = 20 kHz –Nyquist criteria; max freq 10 kHz –If the read gradient is 1mT/m then the FOV is: 42 MHz/T x 0.001T/m = 42 kHz/m –The FOV is: (10 kHz)/(42 kHz/m) = 24 cm

Phase Encode Phase encoding is accomplished by applying a gradient for a time . B o -  BoBo B o +  t = 0 t = 

Slice Image formation Frequency encode Phase encode fn,nfn,n f1,1f1,1

Must Satisfy Nyquist Sampling: Phase Encode Suppose a 60 o phase difference at each voxel: –60 o,120 o,180 o, 240 o, 300 o, 360 o, 60 o –Phase encode is not unique; must repeat with incremented phase encoding gradient strength.

Basic Spin Echo N  phase encodes

Image Acquisition Time Suppose TE = 20 msec, TR = 500 msec, N  = 256 and only one average is required. T = TR x N  x Avg T = 0.5 sec x 256 x 1 = 128 sec = 2 min 8 sec This is the time to make one slice!!

Multi-slice In the previous example, collected data for slice in 20 msec but had to wait 480 msec before re- excite. Acquire additional slices during this time. Max slices = TR/(TE+  ). 480 ms 20 ms

Image Reconstruction After demodulation, the frequency for any column along the frequency encoded axis is: f(x) =  G x x And the phase along any row in the phase encoded axis is:  (y) =  G y y  The sinusoidal signal detected from any element is: S(x,y) = M (x,y) e [2  i (f(x)+  (y))] t

Image Reconstruction The total signal collected as a function of time is then: S(t 1, t 2 ) =   M (x,y) e 2  i [f(x)t1+  (y) t2] dx dy Substituting: S(t 1, t 2 ) =   M (x,y) e 2  i [  Gx x t1+  Gy y t2] dx dy Let: k x =  G x t 1 k y =  G y t 2 Substituting: S(k 1, k 2 ) =   M (x,y) e 2  i [kx x+ ky y] dx dy Recognized as a 2D FT! Therefore: M(x,y) = s( k x, k y ) =   S(k x, k y ) e -2  i [kx x+ ky y] dk x dk y

Importance of k-space FT S(k x,k y ) s(x,y) = M (x,y) FT

Filling k-space Frequency encode Phase encode N  phase encodes

k-space Contribution to Image Properties Center of k-space controls contrast Periphery of k-space controls resolution

k-space Contribution to Image Properties Center - contrast Periphery - resolution

k-space Applications Conjugate symmetry –Acquire only half of k-space and employ symmetry. –Cuts acquisition time in half. –Reduces SNR by 40%. Centric ordering –Acquire center of k-space as contrast arrives to ensure maximum contrast enhancement.

Spin Echo Contrast SE image contrast can be weighted to provide T 1, T 2 and   dependence Weighting is adjusted by modifying TE and TR.

Spin Echo T 1 Weighting Long T 1 Short T 1 t t For T 1 weighting short* TR is required. Low signal High signal

T1 Contrast TR MzMz short T 1 long T 1

Spin Echo T 2 Weighting Long T 1 Short T 1 For T 2 weighting long* TE is required. High signal Low signal

T2 Contrast TE MzMz short T 2 long T 2

Spin Echo Contrast T 1 - short TR and short TE –TR = 500 ms, TE = 10 ms T 2 - long TR and long TE –TR = 2500 ms, TE = 100 ms Proton density (  H ) – not T 1 or T 2 –longTR and short TE –TR = 2500 ms, TE = 10 ms Long TR and long TR are never used –T 1 and T 2 contrast conflicts

Proton

T1

T2

T1 Proton T2

Introduction to Contrast Agents

Magnetic Properties of Materials Weakly repel: water and tissue Weakly attract: Gd T 1 and T 2 Reducing agents Interact strongly: Fe susceptibility agents (T 2 *).

Contrast Agents Contrast agents can function by altering: –T1 – Paramagnetic agents –T2 – Paramagnetic and Susceptibility agents –T2* – Susceptibility agents –proton density – hormones and diuretics

Paramagnetic Molecular tumbling results in reduced T1 and T2. –Shorten T2 => reduced signal –Shorten T1 => increased signal Gd chelate –Used as an enhancing agent (T1 weighted sequence).

Gd Enhanced Brain Malignancy

Superparamagnetic Susceptibility agents –Cause local field inhomogeneity and very short T 2 *. –Used to remove signal on T 2 or T 2 * weighted images.

Negative Contrast From Iron Oxide

Factors controlling SNR Basic factors –Field strength –Coil tune and match –Magnet shim Setup factors: –Coil selection (Filling factor) –Sequence selection (longer TR/shorten TE) Sequence variables: –Voxel volume –Averages –Bandwidth –Gap