Nguyên lý tạo ảnh trong MRI (MRI dx rad imaging physics course)

Stewart, PhD, DABMP 4 Magnetic Field Gradients ¬ Linear magnetic field gradients with prescribed directionality and strength are produced in paired wire coil configurations energized wit

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Magnetic Resonance Imaging – Chapter 15

Brent K Stewart, PhD, DABMPProfessor, Radiology and Medical EducationDirector, Diagnostic Physics

a copy of this lecture may be found at:

http://courses.washington.edu/radxphys/PhysicsCourse04-05.html

Take Aways: Five Things You should be able

to Explain after the MRI Lectures

¬ How the MR signal is localized within the patient (2D)

¬ How the collected FID echoes are collected (‘k-space’

data acquisition) and how these are reconstructed into the grayscale image data visualized on PACS (2D)

¬ How 3D volume data is acquired and reconstructed

¬ What factors of the MRI data collection process play into the resulting quality of reconstructed image slices and volumes

¬ How consideration of artifacts, safety/bioeffects and instrumentation play into the decisions you will be making in the future with regards to image interpretation, magnet operation and system purchase

Localization of the MR Signal

¬ Spatial localization requires the imposition of magnetic

nonuniformities

¬ Linear gradients are superimposed on the homogeneous

and much stronger main magnetic field (B0)

¬ The change in Larmor frequency of the precessing nuclei

are used to distinguish position of the NMR signal within

the object

¬ Conventional MRI involves RF excitations (NMR)

combined with magnetic field gradients to localize the

signal from volume elements (voxels) within the patient

Magnetic Field Gradients

¬ Linear magnetic field gradients with prescribed directionality and strength are produced in paired wire coil configurations energized with a DC current of specific polarity and amplitude

¬ Gradient null point; reverse grad polarity w/ opp current

¬ Linear over a predefined field

of view (FOV)

¬ Three sets: x, y and z; can also generate oblique w/ superpos

c.f Bushberg, et al The Essential Physics

of Medical Imaging, 2 nd ed., p 416-7.

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¬ Larmor freq changes along gradient: e.g., Gz= ∂B/∂z, Gx= ∂B/∂x

¬ Location of nuclei along gradient is determined by their frequency

(∆f = (γ/2π)··∂∂B/∂z·∆z)and phase (∆φ= 2π·∆f∆t)

¬ Peak amplitude of gradient (G) field (‘steepness’): [1,80] mT/m

¬ Slew rate (‘quickness’ of gradient ramping): [5,200] mT/m/msec

of Medical Imaging, 2 nd ed., p 417.

c.f Hashemi, et al MRI the

¬ Gradient amplitude and number of samples over the FOV determines the frequency bandwidth across each pixel

¬ 10 mT/m · 42.58 MHz/T· 1T/1,000 mT· 1 m/100 cm = 4258 Hz/cm

¬ Localization of nuclei in 2D requires the application of three distinct and orthogonal gradients during the pulse sequence: slice select, frequency encode and phase encode gradients

From the above calculation, it’s easy to see that with gradients our old friend: γ/2π =

426 Hz-cm -1 /mT-m -1 ,

so then it’s just a matter of multiplying the number of mT/m

by this factor to get the bandwidth (Hz)/cm.

Slice Select Gradient (SSG)

¬ RF pulse antennas can’t spatially direct the RF energy within FOV

¬ In conjunction with a selective frequency narrowband RF pulse

applied to the entire volume, the SSG determines the imaging slice

¬ Slice thickness (ST) determined by:

¬ Applied RF pulse bandwidth (BW)

¬ Gradient strength across the FOV

¬ For a given gradient strength,

waveform: sinc(t) = sin(t)/t

¬ Need an infinitely long sinc pulse to get a perfectly rectangular slice

¬ Truncation in time of sinc pulse leads to rounded slice profiles

of Medical Imaging, 2 nd ed., p 419-20.

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¬ Width of sinc pulse determines

the output frequency BW

¬ Both narrow BW w/ weak

gradient and wide BW w/

strong gradient same ST

¬ SNR ∝[SQRT(BW)]-1

¬ Narrow BW chemical shift

¬ Gradients cause spin

dephasing: phase important!

¬ Re-establish original phase

with opp polarity gradient with

½integrated area (∆f ∝G·∆t)

Frequency Encode Gradient (FEG)

¬ FEG aka readout gradient

¬ Applied to SSG

¬ ∆f = (γ/2π)·Gx·∆x ∆f ∝∆x

¬ Applied throughout formation and decay of the FID echo from slab excited by the SSG

¬ Demodulation of the composite signal produces a net

frequency variation that is symmetrically distributed from +fmaxto –fmaxat FOV edges

¬ Spatial projection: column sum

Frequency Encode Gradient (FEG)

¬ Composite signal is amplified,

digitized and decoded by

Fourier Transform (FT)

¬ ∆f = (γ/2π)·Gx·∆x ∆f ∝∆x

¬ Rotation of FEG direction

provides projections through

object as a function of angle

¬ Like CT: filtered backprojection

¬ However, due to sensitivity to

motion artifacts phase

encoding gradients used

Phase Encode Gradient (PEG)

¬ Short duration gradient applied before FEG and after SSG to provide 3rdspatial dimension

¬ After SSG all spins in φ coherence

¬ During PEG application linear variation in precessional frequency introducing a persistent phase shift across the slice slab (∆φ∝By·∆y·)

¬ After all FID data collected, a FT is applied to decode the spatial position along the PE direction

¬ Motion during data collection produces ghosting in along PE

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Gradient Sequencing

¬ For the SE pulse sequence

¬ Timing of the gradients in conjunction with RF excitation pulsesand

data acquisition during echo evolution and decay

¬ Sequence repeated periodically (TR) with only slight changes in the

PEG amplitude to provide the 3D identity of protons of the object in

the resulting image

Raphex 2001 Diagnostic Questions

¬ D43. In MRI, the RF frequency is dependent on the:

¬ A Diameter of the body part being imaged

¬ B Magnetic field strength

¬ C Pulse sequence

¬ D Relaxation time

¬ E RF coil

¬ A Eliminate perturbations in the magnetic field due to

site location

¬ B Maintain a uniform magnetic field in the field of view

¬ C Measure the spin coupling

¬ D Provide spatial localization

¬ E Shorten T1 to reduce scan time

¬ D48 In MRI images, motion during the scans results in ghost images which appear in the direction.

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‘K-space’ Data Acq and Image Reconstruction

¬ MRI data initially stored in a

‘k-space’ matrix (spatial

frequency domain corr time

domain; x : k, f : t –FT pairs;

Larmor relation through

gradients: ∆f = (γ/2π)·Gx·∆x)

¬ k-space divided into 4

quadrants w/ origin at center

¬ FID data encoded in kxby FEG

and in kyby PEG

¬ Spat Freq enc.: [-kmax,kmax]

¬ Complex conjugate symmetry:

only ½matrix + one line req

adapted from Bushberg, et al The Essential

Physics of Medical Imaging, 2 nd ed., p 426.

adapted from Hashemi, et

al MRI the Basics, p 140.

Max signal in center of k-space

+k

+k -k

Two-dimensional Data Acquisition

¬ Example: 3 cycles/sec in kx

¬ MR data acquired as a complex, composite frequency waveform

¬ With methodical variations of the PEG during each excitation, the space matrix is filled (or partially filled) to produce the desired variations across the FE and PE directions

k-c.f Bushberg, et al The Essential Physics

Pulse Sequences

¬ Tailoring pulse sequences

emphasizes the image contrast

dependent on ρ, T1 and T2

¬ Timing, order, polarity, pulse

shaping, and repetition

frequency of RF pulses and x,

y and z gradient application

¬ Major pulse sequences

¬ Spin Echo (SE)

¬ Inversion recovery (IR)

¬ Fast Spin Echo (FSE)

¬ Gradient Recalled Echo

(GRE)

¬ Echo Planar Image (EPI)

c.f http://www.indianembassy.org/dydemo/page3.htm

Amendment to Bushberg Figure 15-15

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Summary of 2D SE Acquisition Steps

¬ (1) Narrowband RF pulse applied

simultaneously with SSG (center

t=0); SSG: ∂(∆f)/∂z

¬ (1) Mzconverted to Mxy, the extent

determined by the flip θ

¬ (2) PEG applied to SSG for short

time (encoding precessional ∆φ

along PE grad.) and with differing

amplitudes for each repetition to

create ∂(∆φ)/∂yalong PE direction:

multiple views along ky

¬ (3) Refocusing 180°RF pulse

delivered at t = TE/2: inverting

spins

¬ (4) Re-establishment of phase coherence at t = TE (FID echo)

¬ (4) During echo formation and subsequent delay, FEG (∂(∆f)/∂x) applied to both SSG and PEG, encoding precessional frequency along the readout gradient

¬ (5) Simultaneous to application

of FEG and echo formation, the computer acquires the time-domain signal (FID echo) using ADC

¬ (5) ADC sampling rate determined

by the excitation BW

¬ (6) Data stored in k-matrix row (kx)

the position (ky) determined by the

PEG magnitude

¬ (6) Inc changes in PEG mag fills

matrix one row at a time (may be

non-sequential)

¬ (6) When filled partially then copy

complex conjugate data into

remaining blank rows

¬ (7) 2D FT decodes time (spatial

frequency -k) domain data

piecewise along the rows (kx) and

then columns (ky)

¬ (8) Object spatial and contrast characteristics manifested in the resulting image

¬ (8) Final image a spatial representation of the ρ, T1, T2 and flow characteristics of the tissues in each voxel using a gray-scale range

¬ Voxel thickness determined by SSG and RF freq bandwidth

¬ Pixel dimension determined by varying PEG magnitudes and readout digitization ratec.f Bushberg, et al The Essential Physics

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¬ Bulk of information representing lower spatial frequencies near

center of k-space –provides large area contrast in the image

¬ Higher spatial frequency nearer the periphery –provides resolution

and detail in the image

adapted from Hashemi, et

al MRI the Basics, p 140.

Max signal in center of k-space

+k

+k -k

Two-dimensional Multi-planar Acquisition

¬ Axial (SSG: z, PEG: y, FEG: x)

¬ Coronal (SSG: y, PEG: x, FEG: z)

¬ Sagittal (SSG: x, PEG: y, FEG: z)

¬ Oblique (SSG: a1x + a2y + a3z, etc.)

¬ Data acquisition into the k-space matrix same for all

x y

x

y

Acq Time, 2DFT SE and Multislice Acq.

¬ Acq time = TR ·no PE steps·

NEX (number of excitations)

¬ Example (256x192 matrix,

TR=600, NEX=2) 230 sec

¬ PE along lesser matrix

dimension to speed acquisition

¬ Multiple slice acquisition also

speeds image collection

¬ Max number slices =

TR/(TE+C)

¬ C dependent on MRI system

capabilities

¬ Longer TR more slices

¬ In FE direction ‘fractional echo’

and ‘read conjugate symmetry’

shorten FID echo sampling time

¬ Both SNR and artifacts

With quadrature detection, have real and “imaginary” (90° out of phase) components of induced voltage from FID (t):

V(t) = V1·cos(2πft) + i·V2·sin(2πft).

Two data values per digitized FID sample Complex conjugate =

V1·cos(2πft) – i·V2·sin(2πft)

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Inversion Recovery (IR) Acquisition

¬ 180-(TI)-90-(TE/2)-180-(TR)

¬ SSG, PEG and FEG as SE

¬ TR long many slices per TR

Fast Spin Echo (FSE) Acquisition

¬ FSE uses multiple PE steps w/

multiple 180°pulses per TR

¬ First echos placed near ky=0

¬ Best SNR least T2 decay

¬ Immunity from B0inhomogen

with up to 16x faster collection

¬ Lower SNR for high-freq ky

¬ Fewer slices collected per TR

¬ SE: 8.5 min (TR=2000, 256 PE)

¬ FSE: 2.1 min (TR=2000, 256

PE steps and 4 echos per TR)

¬ aka: ‘turbo SE’& RARE (Rapid Acq w/ Refocused Echoes)c.f Bushberg, et al The Essential Physics

Gradient Recalled Echo (GRE) Acquisition

¬ Similar to SE but with readout

gradient reversal for 180°pulse

¬ Repetition of acq for each PE

¬ With small flip angles and gradient

reversals large reduction in TR

and TE fast acq

¬ PEG rewinder pulse (opp polarity)

to maintain φrelationship between

pulses (due to short TR)

¬ Acq time=TR·no PE steps ·NEX

¬ Example (256x192 matrix,

TR=30): 15.5 sec

¬ SNR and artifacts; one slice

¬ GRASS, FISP, FLASH, etc

Echo Planar Image (EPI) Acquisition

¬ Extremely fast imaging

¬ Single (1 TR) and multi-shot

¬ 90°flip, PEG/FEG, 180°flip

¬ Oscillating PEG/FEG ‘blips’

stimulate echo formation

¬ Rapid ‘zig-zag’ k-space filling

¬ Acq occurs in a period < T2*:

25-50 msec

¬ High demands on sampling rate, gradient coils and RF deposition limitations

¬ Poor SNR, low res (642) and many artifacts

¬ ‘Real-time’ snapshotc.f Bushberg, et al The Essential Physics

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Spiral K-space Acquisition

¬ Simultaneous oscillation of

PEG/FEG to sample data

during echo formation in a

spiral starting at k-space origin

¬ Regridding to 2D k-space

array for 2D FT

¬ Efficient method placing

maximum samples in the

low-frequency are of k-space

¬ Like EPI sensitive to T2*: field

inhomogeneities and

susceptibility agents

Gradient Moment Nulling

¬ In SE and GRE SSG/FEG balanced so that the uniform dephasing caused by the initial gradient application is rephased by an opposite polarity gradient of equal area

¬ Moving spins phase dispersal not compensated

¬ Constant flow: spins can be rephased with a gradient triplet

¬ Higher-order corrections

¬ Applied to both SSG/FEG to correct motion ghosting and pulsatile flow

A = -1, B = 3 and C = -3

¬ D50 Which of the following does NOT generally affect

the total exam time of an MRI study?

¬ A # of acquisitions

¬ B # of frequency encoding steps

¬ C # of phase encoding steps

¬ D # of pulse sequences in the study

¬ E TR

3D Fourier Transform Image Acquisition

¬ Uses a broadband, selective RF pulse to excite a large spin volume

non-¬ Acq time = TR ·no PE steps (z) ·no PE steps (y) ·NEX

¬ SE: TR=600, 1283 164 min

¬ GRE: TR=50, 1283 14 min

¬ Isotropic or anisotropic (<time)

¬ High SNR thin slice recon

¬ prob for motion artifacts

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Image Characteristics and Quality

¬ Spatial Resolution and Contrast Sensitivity

¬ RF Coil Quality Factor

¬ Magnetic Field Strength

¬ Cross Excitation

¬ Image Acquisition and Reconstruction Algorithms

Spatial Resolution

¬ Dependent on

¬ FOV: pixel size

¬ Gradient strength: FOV

¬ Receiver coil characteristics

¬ Sampling bandwidth

¬ Image matrix: 1282through 1024 x 512

¬ In plane: 0.5-1.0 mm (0.1-0.2 mm surface coil)

¬ Slice thickness: 5-10 mm

¬ Higher B0 larger SNR thinner slices

¬ However, RF heating, T1, T1 contrast and artifact

Contrast Sensitivity

¬ Major attribute of MR = f (ρ, T1, T2, flow, pulse param.)

¬ MR contrast agents, usually susceptibility agents disrupt

local B field to enhance T2 decay or provide additional

relaxation mechanisms for T1 decay important

enhancement agents for differentiation of normal and

diseased tissues

¬ Absolute contrast sensitivity of an MR image is ultimately

limited by the SNR and presence of image artifacts

Signal-to-Noise Ratio (SNR)

¬ I = intrinsic signal intensity based on pulse sequence

¬ NEX = number of excitations

¬ BW = freq BW of RF transmitter/receiver

¬ f1(QF) = func of coil quality factor param (tuning coil)

¬ f2(B) = function of magnetic field strength

¬ f3(slice gap) = function of interslice gap effects

¬ f4(recon.) = function of reconstruction algorithm

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No pixels x No pixels y

Signal Averages (NEX)

¬ Doubling SNR requires NEX = 4

¬ NEX < 1: ½ or ¾ NEX

¬ ½ NEX: half Fourier imaging ½PE-matrix dimension + 1

¬ ¾ NEX: ¾ PE-matrix dimension

¬ Missing data synthesized from the k-space matrix

¬ BW = 1/∆T (dwell time –time

between FID sampling)

¬ Narrow BW ∆T noise

(SNR ∝SQRT[∆T])

¬ BW gradient strength

chem shift artifacts)

¬ Also requires longer sampling

time and affects TEminwhich in

turn may affect num slices/TR

BW = (γ/2π)·Gx·FOVxremember: γ/2π =

426 Hz-cm -1 /mT-m -1

RF Coil Quality Factor

¬ Indication of RF coil sensitivity to induced currents in response to signal emanating from the patient

¬ Patient loading: electrical impedance characteristics of the body variation of B field, different for each patient

¬ Tuning the receiver coil to ω0mandatory

¬ Also dependent on volume of subject : coil volume

¬ Body coil positioned in magnet bore: moderate QF

¬ Surface coil: high QF

¬ Trade-off with FOV uniformity

¬ Body coil: relatively uniform over FOV

¬ Surface coil: signal falls off abruptly (1/r3-5)

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