MRI Physics II: Gradients, Imaging

MRI Physics II: Gradients, Imaging Douglas C., Ph.D. Dept. of Biomedical Engineering University of Michigan, Ann Arbor

Magnetic Fields in MRI B 0 The main magnetic field. Always on (0.5-7 T) Magnetizes the object to be imaged After excitation, the magnetization precesses around B 0 at ω 0 = γb 0 B 1 The rotating RF magnetic field. Tips magnetization into transverse plane Performs excitation On for brief periods, then off

Gradient Fields The last magnetic field to be used in MRI are the gradient fields 3 of them: G x, G y, G z These are for localization Make the magnetic field different in different parts of the body, e.g. for the x-gradient: B(x) ) = B 0 + G. x Observe the field points in the same direction as B 0 so it adds to B 0.

x z y Gradients x-gradient (G( x ) z x y y-gradient (G( y ) z x y z-gradient (G( z )

Imaging Basics To understand 2D and 3D localization, we will start at the beginning with one- dimensional localization. Here we image in 1D - the x-direction. (e.g. the L-R direction) We start with the simplest form of localization called frequency encoding.

1D Localization We acquire data while the x-gradient (G( x ) is turned on and has a constant strength. Recall that a gradient makes the magnetic field vary in a particular direction. In this case, having a positive x-gradient implies that the farther we move along in the x-direction (e.g. the farther right we move) the magnetic field will increase. B(x) ) = B 0 + G. x

Frequency Encoding A fundamental property of nuclear spins says that the frequency at which they precess (or emit signals) is proportional to the magnetic field strength: ω = γb - The Larmor Relationship This says that precession frequency now increases as we move along the x- direction (e.g. as we move rightwards). ω(x) ) = γ (B 0 + G. x).

Frequency Encoding Low Frequency B Mag. Field Strength Low Frequency Object High Frequency x Position High Frequency x Position

Spins in a Magnetic Field ω(x) γg x x

Fourier Transforms The last part of this story is the Fourier transform. The Fourier transform is the computer program that breaks down each MR signal into its frequency components. If we plot the strength of each frequency, it will form a representation (or image) of the object in one-dimension.

Fourier Transforms Low Frequency MR Signal Fourier Transform Object High Frequency time 1D Image x Position

1D Pulse Sequence Now we put this together with excitation: TR RF TE Gx Data Acq. B(x) x

Alternate Method for 1D Localization In the case just described, the frequency encoding gradient was constant. At different locations spins precessed at different frequencies. This was true as long as the gradient was on. on. We now look at an alternate situation where the gradient is turned on and off rapidly. At different locations spins will precess at different frequencies, but only during the times that the gradient is on. on.

Alternate Method for 1D Localization RF Gx Data Acq.

On/Off Gradients in 1D Localization In the case previously described, the spins precessed smoothly. In this case, the spins precess in a stop- action or jerky motion. What is different here is that we sample the MR signal while it has stopped precessing. At each step, the spatial information has been encoded into the phase. This is a form of phase encoding.

Movement of Magnetization with Constant Gradient M Smooth precession of magnetization

Stop-Action Movement of Magnetization M STOP STOP Sample 1 Sample 2 Sample 3

Different 1D Localization Methods RF Gx Data Acq. Upper - smooth precession at different frequencies. (frequency encoding) RF Gx Data Acq. Lower - precession in small steps, phase contains location info. (phase encoding).

Different 1D Localization Methods RF Gx Data Acq. RF Gx Data Acq. Are the sampled data the same? Yes, if we neglect T2. In both cases, the Fourier transform creates the 1D image.

Alternate Method #2 for 1D Localization In the above cases, gradients were turned on and samples were acquired following a single RF excitation pulse. At different locations spins precessed at different frequencies. Motion was either smooth or stop-action. stop-action. We now look at a situation where a single sample is acquired after each RF pulse. Spins precess for a particular length of time and then a single sample is acquired.

Alternate Method #2 for 1D Localization RF Gx Data Acq.

Phase Encoding in 1D Again, spins precess only as long as gradient is turned on. on. If we look spins after each step (sample location), the precession will again appear as stop-action motion. Again, spatial information has been encoded into the phase of spin. Another form of phase encoding.

Phase Encoding in 1D M STOP STOP Phase Encode 0 Phase Encode 1 Phase Encode 2

Three Methods for 1D Localization 1D Localization: Frequency encoding Phase encoding following a single RF pulse A single phase encode following each of many RF pulses Sampled data is the same (if we neglect T2). The Fourier transform creates the 1D image.

Three Methods for 1D Localization Frequency Encoding RF Gx Data Acq. Phase Encoding Method #1 RF Gx Data Acq. Phase Encoding Method #2 RF Gx Data Acq.

2D Localization In general, we will combine two 1D localization methods to create localization in two dimensions (2D). The spin-warp method (used in almost all anatomical MRI) is a combination of : Frequency encoding in one direction (e.g. Left-Right) Phase encoding in the other direction (e.g. Anterior-Posterior)

2D Localization - Spin Warp RF Gx Frequency Encoding (in x direction) Data Acq. RF Gy Gx Data Acq. RF Gy Data Acq. Phase Encoding Method #2 (in y direction)

Spin-Warp Imaging For each RF pulse: Frequency encoding is performed in one direction A single phase encoding value is obtained With each additional RF pulse: The phase encoding value is incremented The phase encoding steps still has the appearance of stop-action motion

Spin-Warp Pulse Sequence RF Phase Enc. Gy Gx Freq. Enc. Data Acq.

Spin-Warp Data Acquisition In 1D, the Fourier transform produced a 1D image. In 2D, the Fourier transform is applied in both the frequency and phase encoding directions. This is called the 2D Fourier transform. Commonly we structure the samples in a 2D grid that we call k-space. k-space. One line of k-space is acquired at a time.

Spin-Warp Data Acquisition Each line has a different phase encode ky kx Frequency encoding along each line 2D Fourier Transform

Echo-Planar Imaging As with spin-warp imaging, echo-planar imaging (EPI) is just the combination of two 1D localization methods EPI is also a combination of : Frequency encoding in one direction (e.g. Left-Right) Phase encoding in the other direction (e.g. Anterior-Posterior) EPI uses a different phase encoding method.

Echo-Planar Imaging RF Gx Frequency Encoding (in x direction) Data Acq. Phase Enc. RF Gy Gx Freq. Enc. Data Acq. RF Gx Data Acq. Phase Encoding Method #1 (in y direction)

Echo-Planar Imaging For each RF pulse: Frequency encoding is performed many times All phase encoding steps are obtained The entire image is acquired With each additional frequency encoding (each additional line in the k-space grid): The phase encoding value is incremented The phase encoding steps still has the appearance of stop-action motion

EPI Pulse Sequence Phase Enc. RF Gy Gx Freq. Enc. Data Acq.

EPI Data Acquisition As with Spin-Warp imaging, we put the acquired data for the frequency and phase encoding into the 2D grid called k-space. Also, the 2D Fourier transform is used to create the image. In EPI, the data is filled into k-space in a rectangular zig-zag -like-like pattern.

EPI Data Acquisition Changing the sign of the frequency enc. changes the direction that the data is placed into this 2D grid. Each line has a different phase encode ky kx Frequency encoding along each line

EPI Imaging In summary, EPI data is in many ways like Spin-Warp imaging: They are combinations of two kinds of 1D localization. They have both frequency and phase encoding. Data are acquired on a 2D grid called k-space. Images are reconstructed by a 2D Fourier transform.

EPI Imaging It is also different from Spin-Warp Imaging: The image can be acquired with a single RF pulse. The phase encoding steps all happen in rapid succession. The frequency direction alternates in sign. The time needed to acquire data after each RF pulse is very long. Special hardware is required.

Multi-shot EPI While possible to acquire an entire image with a single RF pulse (single-shot), it is sometimes necessary to use multiple shots. There are two common ways of doing this: Interleaving Mosaic Multi-shot EPI is useful to: Improve spatial resolution Reduce artifacts

Multi-shot EPI ky ky kx kx #2 #1 #1 #2 Interleaved EPI Mosaic EPI

Spin-Warp vs. EPI Pulse Sequences Spin-Warp EPI RF Gy RF Gy Gx Data Acq. Gx Data Acq. Many acquisitions to make a one image. One acquisition to make one image.

Spiral Imaging One method that has very similar properties to EPI is Spiral Imaging. Like EPI: All image data can be acquired in a single-shot. Multi-shot variants also exist. Many of the artifacts are similar. But: Image reconstruction is different. Some artifacts are different.

Spiral Imaging RF ky Gy Gx kx Data Acq. Pulse Sequence k-space Data

Fourier Representation of Images Decomposition of images into frequency components, e.g. into sines and cosines. 1D Object Fourier Data

1D Fourier Transform 0 th Frequency Component New Components Cumulative Sum of Components

1D Fourier Transform 1 st Frequency Component New Components Cumulative Sum of Components

1D Fourier Transform 2 nd Frequency Component New Components Cumulative Sum of Components

1D Fourier Transform 3 rd Frequency Component New Components Cumulative Sum of Components

1D Fourier Transform 5 th Frequency Component New Components Cumulative Sum of Components

1D Fourier Transform 20 th Frequency Component New Components Cumulative Sum of Components

1D Fourier Transform 63 rd Frequency Component New Components Cumulative Sum of Components

Fourier Acquisition In MRI, we are acquiring Fourier components Remember, we take the FT of the acquired data to create an image The more Fourier components we acquire, the better the representation

Spatial Frequencies in 2D Full Low Freq High Freq Fourier Data Image Data Low Res (contrast) Edges

Resolution and Field of View Resolution is determined by size of the area acquired: k y Δx = 1 / W k x Field of view is determined by spacing of samples: Δk FOV = 1 / Δk W

Goals of Image Acquisition Acquire samples finely enough to prevent aliasing Acquire enough samples for the desired spatial resolution Acquire images with the right contrast Do it fast as possible Do it without distortions and other artifacts

Single-shot Imaging Hardware Single-shot imaging is an extremely rapid and useful imaging method. It does, however, require some special, high performance hardware. Why? In spin-warp, we acquire a small piece of data for an image with each RF pulse. However in EPI and spiral, we try to acquire all of the data for an image with a single RF pulse.

Single-shot Imaging Hardware Need powerful gradient amps. Limitations: Peripheral nerve stimulation Acoustic noise Increased noise Heating and power consumption in gradient subsystem

T2 Decay and Acquisition Time In spin-warp imaging, only a single phase encode need to be acquired. Only takes a short time. In EPI, all phase encode lines need to be acquired. Takes longer. Without special hardware - 100 ms to 1 second. T2 decay reduces signal throughout data acquisition.

T2 Decay and Acquisition Time RF Gy Gx Data Acq. Signal Strength Signal decays away during acquisition. Data Acq. takes longer.

Other Limitations Single-shot imaging has a variety of limitations Hardware T2 Decay B 0 inhomogneity Consequences: Limited spatial resolution Image distortions Some limits on available contrast

Some Common Imaging Methods Conventional (spin-warp) Imaging Echo Planar Imaging (EPI) Spiral Imaging

Conventional (Spin-Warp) Imaging k y k x One Line at a Time 128x128 FLASH/SPGR TR/TE/flip = 50ms/30ms/30º 0.2 slices per sec, single slice

Conventional (Spin-Warp) Imaging k y k x Known as: GRE, FLASH, SPGR Typically matrix sizes for fmri 128x64, 128x128 Acquisition rates 3-10 sec/image 1-4 slices One Line at a Time Usually best for structural imaging

Echo Planar Imaging (EPI) k y k x Zig-Zag Pattern Single-shot EPI, TE = 40 ms, TR = 2 s, 20 slices

Echo Planar Imaging (EPI) k y k x Single-shot acquisition Typically matrix sizes for fmri 64x64, 96x96 128x128 interleaved Acquisition rates TR = 1-2 sec 20-30 slices Zig-Zag Pattern Suffers some artifacts Distortion, ghosts

EPI Geometric Distortions high res image field map warped epi image unwarped epi image Courtesy of P. Jezzard Jezzard and Balaban, MRM 34:65-73 1995

EPI Nyquist Ghost Courtesy of P. Jezzard

Spiral Imaging k y k x Spiral Pattern Single-shot spiral, TE = 25 ms, TR = 2 s, 32 slices

Spiral Imaging k y k x Single-shot acquisition Typically matrix sizes for fmri 64x64, 96x96 128x128 interleaved Acquisition rates TR = 1-2 sec 20-40 slices Spiral Pattern Suffers some artifacts Blurring

Spiral Off-Resonance Distortions Courtesy of P. Jezzard perfect shim poor shim

Pulse Sequences Two Major Aspects Contrast (Spin Preparation) What kind of contrast does the image have? What is the TR, TE, Flip Angle, etc.? Localization (Image Acquisition) How is the image acquired? How is k-space sampled?

Pulse Sequences Spin Preparation (contrast) Spin Echo (T1, T2, Density) Gradient Echo Inversion Recovery Diffusion Velocity Encoding Image Acquisition Method (localization, k-space sampling) Spin-Warp EPI, Spiral RARE, FSE, etc.

Localization vs. Contrast In many cases, the localization method and the contrast weighting are independent. For example, the spin-warp method can be used for T1, T2, or nearly any other kind of contrast. T2-weighted images can be acquired with spin-warp, EPI, spiral and RARE pulse sequences.

Localization vs. Contrast But, some localization methods are better than others at some kinds of contrast. For example, RARE (FSE) is not very good at generating short-tr, T1-weighted images. In general, however, we can think about localization methods and contrast separately.

The 3 rd Dimension We ve talked about 1D and 2D imaging, but the head is 3D. Solution #1 3D Imaging Acquire data in a 3D Fourier domain Image is created by using the 3D Fourier transform E.g. 3D spin-warp pulse sequence Solution #2 Slice Selection Excite a 2D plane and do 2D imaging Most common approach

Slice Selection The 3 rd dimension is localized during excitation Slice selective excitation Makes use of the resonance phenomenon Only on-resonant spins are excited

Slice Selection With the z-gradient on, slices at different z positions have a different magnetic fields: B(z) ) = B 0 + G. z z and therefore different frequencies: B(z) Slice 1 Slice 2 Slice 3 ω(z) ) = ω 0 + γg. z z G z ω(z 1 ) < ω(z 2 ) < ω(z 3 ) z

Slice Selection Slice 1 is excited by setting the excitation frequency to ω(z 1 ) Slice 2 is excited by setting the excitation frequency to ω(z 2 ) and similarly for other slices. B(z) Slice 1 Slice 2 Slice 3 G z Interesting note: Exciting a slice does not perturb relaxation processes that are occurring in the other slices. z

Slice Thickness Slice thickness is adjusted by changing the bandwidth of the RF pulse Bandwidth ~ 1 / (duration of RF pulse) E.g., for duration = 1 ms, BW = 1 khz ω(z) Δω γg z Δz z

Multi-Slice Imaging Since T1 s s are long, we often would like to have long TR s (500-4000 ms) While one slice is recovering (T1), we can image other slices without perturbing the recovery process

Multi-Slice Imaging RF pulses ω(z 1 ) Data acquisition Slice 1 RF pulses ω(z 2 ) Data acquisition Slice 2 RF pulses Data acquisition ω(z 3 ) TR Slice 3