Medical Imaging Systems: MRI Image Formation Instructor: Walter F. Block, PhD 1-3 Notes: Walter Block and Frank R Korosec, PhD 2-3 Tuesday 9 August 1994 at 17h36 S.F. Hilton and Towers, Continental question period Pulse Sequences for Fluid Shear Measurement using Fourier-encoded Velocity Imaging. Session: Flow Quantification Chairs: D. Saloner and L. Frank Departments of Biomedical Engineering 1, Radiology 2 and Medical Physics 3 University of Wisconsin - Madison

But so far RF coils only integrate signal MRI Physics: So far... What we can do so far: 1) Excite spins using RF field at o 2) Record time signal (Known as FID) 3) Mxy decays, Mz grows 4) Repeat. But so far RF coils only integrate signal from entire body. We have no way of forming an image. That brings us to the last of the three magnetic fields in MRI. S?

Image Formation Overview Gradient fundamentals Slice Selection Limit excitation to a slice or slab Can be in any orientation Gradient echo in-plane spatial encoding Frequency encoding Phase encoding Spin echo formation SNR Generalized encoding

3nd Magnetic Field Static High Field Radiofrequency Field (RF) Termed B0 Creates or polarizes signal 1000 Gauss to 100,000 Gauss Earth’s field is 0.5 G Radiofrequency Field (RF) Termed B1 Excites or perturbs signal into a measurable form O.1 G but in resonant with signal Gradient Fields 1 -4 G/cm Used to determine spatial position of signal MR signal not based directly on geometry

Gradient Coils Fig. Nishimura, MRI Principles

X Gradient Example: Gx Magnetic field all along z, but magnetic strength can varies spatially with x. Stronger at right, no change in middle, weaker at left.

Gradient Coil Fundamentals Gradient strength directly proportional to current in coil On the order of 100 amps peak Performance Power needed proportional to radius5 Tight bore for patient Strength – G/cm or mT/m 4 G/cm is near peak now for clinical scanners Higher strength with localized gradients (research only) Slew rate Need high voltages to change current quickly 100- 200 T/m/s is high performance Rise to 1 G in .1 ms at 100 T/m/s Limited by peripheral nerve stimulation

Magnetic Field Gradient Timing Diagrams

B0 (t)(B0 + Gx(t)x) Before, only B0 Now with Gx Larmor Equation B0 Before, only B0 Precessional Frequency Static Magnetic Field (t)(B0 + Gx(t)x) Now with Gx

Gx, Gy, Gz: One for each spatial dimension Magnetic field all along z, but magnetic strength can vary spatially with x, y, and/or z.

Two Object Example of Spatial Encoding sr(t) Receiver Signal: No gradient Gx On: Beat Frequency Demodulated Signal x m(x) Water

Gz Gradient Example L31, slides 10-12 repeated here: first imaging method, basic procedure, projection reconstruction. The effects of the main magnetic field and the applied slice gradient. In this example, the local magnetic field changes in one-Gauss increments accompanied by a change in the precessional frequency from chin to the top of the head. Image, caption: copyright Proruk & Sawyer, GE Medical Systems Applications Guide, Fig. 11

Selective RF Excitation Recall frequency of RF excitation has to be equal or in resonance with spins Build RF pulse from sum of narrow frequency range

Frequency profile of modulated RF pulse Slice Selection - Consider a pulse B1(t) that is multiplied by cos(ot). This is called modulation . B1(t) is called the RF excitation. o is the carrier frequency = g B0. Mixer B1(t) cos(ot) A(t) cos(ot) Frequency profile of modulated RF pulse o = 2fo wo f

Frequency Encoding Spin Frequency (x) Image each voxel along x as a piano key that has a different pitch. MR coil sums the “keys” like your ear. Fig. 14.28 from Illustrator, mag 100% then shrunk in powerpoint

Frequency Encoding

GRE Pulse Sequence Timing Diagram rf Slice Select Freq. Encode Signal TE

Frequency Encoding & Data Sampling Generated Signal DAQ Sampled Signal

In-plane Encoding MR signal in frequency encoding (x) is Fourier transform of projection of object Line integrals along y Encoding in other direction Vary angle of frequency encoding direction 1D FT along each angle and Reconstruct similar to CT Apply sinusoidal weightings along y direction Spin-warp imaging or phase-encoding By far the most popular

2D Projection Reconstruction MRI ky  kx Gx Gy DAQ Reconstruction: convolution back projection or filtered back projection

Central Section Theorem in MRI Object y’ y In MR, echo gives a radial line in spatial frequency space (k-space). x’ ky θ x θ x’ kx F.T. CT Projection MR Signal (t) Interesting - Time signal gives spatial frequency information of m(x,y)

k-Space Acquisition (Radial Sampling) Y readout X readout ky kx kx ky

In-plane Encoding MR signal in frequency encoding (x) is Fourier transform of projection of object Line integrals along y Encoding in other direction Vary angle of frequency encoding direction 1D FT along each angle and Reconstruct similar to CT Apply sinusoidal weightings along y direction Apply prior to frequency encoding Repeat several times with different sinusoidal weightings Spin-warp imaging or phase-encoding By far the most popular

Phase Encoding: Apply Gy before Freq. encoding Fig. 14.31 from Illustrator, mag 130%

GRE Pulse Sequence Timing Diagram rf Slice Select Phase Encode Freq. Encode Signal TE

k-Space Acquisition ky kx Phase Direction One line of k-space Encode Sampled Signal DAQ kx ky Phase Direction One line of k-space acquired per TR Frequency Direction

k-Space Signal ky kx

512 x 512 8 x 8

512 x 512 16 x 16

512 x 512 32 x 32

512 x 512 64 x 64

512 x 512 128 x 128

512 x 512 256 x 256

512 x 512 512 x 32

Scan Duration Scan Time = TR  PE  NEX TR = Repetition Time PE = Number of phase encoding values NEX = Number of excitations (averages)