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

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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!

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

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Overview of 2D FT Slice selection Phase encoding Frequency encoding

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

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RF profile I

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

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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.

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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 + )

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

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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

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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

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

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

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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.

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Basic Spin Echo N phase encodes

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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!!

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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

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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

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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

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Importance of k-space FT http://www.leedscmr.org/images/mritoy.jpg S(k x,k y ) s(x,y) = M (x,y) FT

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Filling k-space Frequency encode Phase encode N phase encodes

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

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http://www.radinfonet.com/cme/mistretta/traveler1.htm#part1 k-space Contribution to Image Properties Center - contrast Periphery - resolution

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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.

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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.

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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

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T1 Contrast TR MzMz short T 1 long T 1

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

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T2 Contrast TE MzMz short T 2 long T 2

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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

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Proton

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T1

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T2

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T1 Proton T2

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Introduction to Contrast Agents

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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 *).

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

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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).

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Gd Enhanced Brain Malignancy

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

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Negative Contrast From Iron Oxide

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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

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