Principles of MRI Physics and Engineering Allen W. Song Brain Imaging and Analysis Center Duke University

Part III.1 Some fundamental acquisition methods And their k-space view

k-Space Recap Kx =  /2  0 t  Gx(t) dt Ky =  /2  0 t  Gx(t) dt Equations that govern k-space trajectory: These equations mean that the k-space coordinates are determined by the area under the gradient waveform

A 2x2 Matrix I(1,1) I(1,2) I(2,1) I(2,2) S(1,1) S(1,2) S(2,1) S(2,2) Image Space k-Space (data space) S(1,1)S(1,2) S(2,1)S(2,2)

Gradient Echo Imaging  Signal is generated by magnetic field refocusing mechanism only (the use of negative and positive gradient)  It reflects the uniformity of the magnetic field  Signal intensity is governed by S = So e -TE/T2* where TE is the echo time (time from excitation to the center of k-space)  Can be used to measure T2* value of the tissue

MRI Pulse Sequence for Gradient Echo Imaging digitizer on Excitation Slice SliceSelection Frequency Encoding Encoding Phase Phase Encoding Encoding Readout

K-space view of the gradient echo imaging Kx Ky n n

Spin Echo Imaging   Signal is generated by radiofrequency pulse refocusing mechanism (the use of 180 o pulse )   It doesn’t reflect the uniformity of the magnetic field   Signal intensity is governed by S = So e -TE/T2 where TE is the echo time (time from excitation to the center of k-space)   Can be used to measure T2 value of the tissue

MRI Pulse Sequence for Spin Echo Imaging digitizer on Excitation Slice SliceSelection Frequency Encoding Encoding Phase Phase Encoding Encoding Readout

K-space view of the spin echo imaging Kx Ky n n

Inversion Recovery Imaging Inversion Recovery Imaging

Time History of MR Signal -S -S o SSoSSo S = S o * (1 – 2 e –t/T1 ) S = S o * (1 – 2 e –t/T1’ )

Pulse Sequence for Inversion Recovery RF Gz GRE or SE Readout 180 o

Part III.2 Image Contrast Mechanisms

The Concept of Contrast (or Weighting)  Contrast = difference in RF signals — emitted by water protons — between different tissues  T1 weighted example: gray-white contrast is possible because T1 is different between these two types of tissue

T2 Decay MR Signal T1 Recovery MR Signal 50 ms 1 s

Proton Density Contrast   Technique: use very long time between RF shots (large TR) and very short delay between excitation and readout window (short TE)   Useful for anatomical reference scans   Several minutes to acquire 256  256  128 volume   ~1 mm resolution

T2 Decay MR Signal T1 Recovery MR Signal 50 ms 1 s Proton Density Contrast

Proton Density Weighted Image

T2* and T2 Contrast   Technique: use large TR and intermediate TE   Useful for anatomical and functional studies   Several minutes for 256x256X128 volumes, or ~several seconds to acquire 64  64  20 volume   1mm resolution for anatomical scans or 4 mm resolution [better is possible with better gradient system, and a little longer time per volume]

T2 Decay MR Signal T1 Recovery MR Signal 50 ms 1 s T2* and T2 Contrast

T2 Weighted Image

T1 Contrast  Technique: use intermediate timing between RF shots (intermediate TR) and very short TE, also use large flip angles  Useful for anatomical reference scans  Several minutes to acquire 256  256  128 volume  ~1 mm resolution

T2 Decay MR Signal T1 Recovery MR Signal 50 ms 1 s T1 Contrast

T1 Weighted Image

-S -S o SSoSSo S = S o * (1 – 2 e –t/T1 ) S = S o * (1 – 2 e –t/T1’ ) Inversion Recovery for Extra T1 Contrast

T2 Inversion Recovery (CSF Attenuated)

In summary, TR controls T1 weighting and TE controls T2 weighting. Short T2 tissues are dark on T2 images, but short T1 tissues are bright on T1 images.

Other Imaging Methods  Can “prepare” magnetization to make readout signal sensitive to different physical properties of tissue  Flow weighting (bulk movement of blood)  Diffusion weighting (scalar or tensor)  Perfusion weighting (blood flow into capillaries)  Magnetization transfer (sensitive to proteins in voxel)  Temperature

MR Angiogram Time-of-Flight ContrastTime-of-Flight Contrast Phase ContrastPhase Contrast

Time-of-Flight Contrast No Flow Medium Flow High Flow No Signal Medium Signal High Signal Vessel Acquisition Saturation Excitation Vessel

90 o Excitation Image Acquisition RF Gx Gy Gz 90 o Saturation Time to allow fresh flow enter the slice Pulse Sequence: Time-of-Flight Contrast

Phase Contrast (Velocity Encoding) Externally Applied Spatial Gradient G Externally Applied Spatial Gradient -G Blood Flow v Time T 2T 0

90 o Excitation Phase Image Acquisition RF Gx Gy Gz G -G-G Pulse Sequence: Phase Contrast

MR Angiogram

Diffusion Weighted Imaging Sequences Externally Applied Spatial Gradient G Externally Applied Spatial Gradient -G Time T 2T 0

Pulse Sequence: Gradient-Echo Diffusion Weighting 90 o Excitation Image Acquisition RF Gx Gy Gz G -G-G

90 o Excitation Image Acquisition RF Gx Gy Gz G 180 o G Pulse Sequence: Spin-Echo Diffusion Weighting

Advantages of DWI 1.The absolute magnitude of the diffusion coefficient can help determine proton pools coefficient can help determine proton pools with different mobility with different mobility 2. The diffusion direction can indicate fiber tracks

Diffusion Anisotropy

Determination of fMRI Using the Directionality of Diffusion Tensor

Display of Diffusion Tensor Using Ellipsoids

Diffusion Contrast

Perfusion/Flow Weighted Arterial Spin Labeling Transmission Imaging Plane Coil Tagging

AlternatingInversion Pulse Tagging AlternatingInversion Imaging Plane FAIR Flow-sensitive Alternating IR EPISTAR EPI Signal Targeting with Alternating Radiofrequency Perfusion/Flow Weighted Arterial Spin Labeling with Pulse Sequences

RF Gx Gy Gz Image 90 o 180 o Alternating opposite Distal Inversion Odd Scan Even Scan 180 o RF Gx Gy Gz Image 90 o 180 o Alternating Proximal Inversion Odd Scan Even Scan Pulse Sequence: Perfusion Imaging

Advantages of ASL Perfusion Imaging 1.It can non-invasively image and quantify blood delivery blood delivery 2.Combined with proper diffusion weighting, it can assess capillary perfusion it can assess capillary perfusion

Perfusion Contrast

Perfusion Diffusion Diffusion and Perfusion Contrast

Other Interesting Types of Contrast  Perfusion weighting: sensitive to capillary flow  Diffusion weighting: sensitive to diffusivity of H 2 O  Very useful in detecting stroke damage  Directional sensitivity can be used to map white matter tracts  Also useful in functional MRI to determine the signal origin  Flow weighting: used to image blood vessels (MR angiography)  Magnetization transfer: provides indirect information about H nuclei that aren’t in H 2 O (mostly proteins)

Part III.3 Introduction to Fast Imaging Very useful techniques for fMRI, Diffusion, Perfusion, etc. when brain functions are being investigated

Fast Imaging How fast is “fast imaging”? In principle, any technique that can generate an entire image with sub-second temporal resolution can be called fast imaging. For fMRI, we need to have temporal resolution on the order of a few tens of ms to be considered “fast”. Echo-planar imaging, spiral imaging can be both achieve such speed.

Echo Planar Imaging (EPI)  Methods shown earlier take multiple RF shots to readout enough data to reconstruct a single image  Each RF shot gets data with one value of phase encoding  If gradient system (power supplies and gradient coil) are good enough, can read out all data required for one image after one RF shot  Total time signal is available is about 2  T2* [80 ms]  Must make gradients sweep back and forth, doing all frequency and phase encoding steps in quick succession  Can acquire low resolution 2D images per second

GE-EPI Pulse Sequence Actually have 64 (or more) freq. encodes in one readout (each one < 1 ms) [only 13 freq. encodes shown here]

K-space view of the echo-planar imaging ….. Kx Ky

Why EPI?  Allows highest speed for dynamic contrast  Highly sensitive to the susceptibility-induced field changes --- important for fMRI  Efficient and regular k-space coverage and good signal-to-noise ratio  Applicable to most gradient hardware

Spiral Imaging t = TE RF Gx Gy Gz t = 0

K-Space Representation of Spiral Image Acquisition

Why Spiral? More efficient k-space trajectory to improveMore efficient k-space trajectory to improve throughput. throughput. Better immunity to flow artifacts (no gradient atBetter immunity to flow artifacts (no gradient at the center of k-space) the center of k-space) Allows more room for magnetization preparation,Allows more room for magnetization preparation, such as diffusion weighting. such as diffusion weighting.

Under very homogeneous magnetic field, images look good …

Gradient-Recalled EPI Images Under Homogeneous Field

Gradient Recalled Spiral Images Under Homogeneous Field

However, if we don’t have a homogeneous field … (That is why shimming is VERY important in fast imaging)

Magnetic Field Inhomogeneity Introduced by x-Shim Coil

Distorted EPI Images with Imperfect x-Shim

Distorted Spiral Images with Imperfect x-Shim

Magnetic Field Inhomogeneity Introduced by y-Shim Coil

Distorted EPI Images with Imperfect y-Shim

Distorted Spiral Images with Imperfect y-Shim

Magnetic Field Inhomogeneity Introduced by z-Shim Coil

Distorted EPI Images with Imperfect z-Shim

Distorted Spiral Images with Imperfect z-Shim