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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5255_Библиотеки_им_академика_М_И_Перельмана
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402
MR Imaging - Basic Concepts
just the applied steady magnetic field, but also the small local magnetic field set up by
neighboring nuclear magnets, B
local
.
B. Chemical shift: Magnetic coupling of the electrons to the nucleus arises from the
magnetic fields originating either from the motion of the electrical charges or from the
magnetic moment associated with the electron spins. The former gives rise to chemical shift
effects, while the latter to the Knight shifts in metals, and to an indirect coupling between
nuclear spins (6).
For a nucleus embedded in bulk matter, the total field seen by the nucleus is,
B
= B0+Bd+Bp = B0 (1-) (2)
eff
where, Bd is the magnetic field produced at the nucleus by Larmor precession of the electronic
charges around it and Bp is the magnetic field created at the nucleus due to the polarization
of the electronic shells by B0. Both Bp and Bd are proportional to B0. is called the
shielding constant and depends on the electronic or chemical environment of the nuclei.
Although the shielding parameter is constant, the measured chemical shifts increase linearly
with field strength. To make chemical shift () independent of the field strength, it is
expressed in parts per million (ppm) of the resonance frequency, measured with respect to a
known standard reference,
= (
- o) . 106/
ref
ref
(3)
This shift is termed as the chemical shift and is due to the orbital effects of the surrounding
electrons and is therefore dependent upon the distribution. It has different values for different
chemical compounds.
Relaxation and FID – a classical treatment
In case of a spin 1/2 system, non-interacting spins remain randomly aligned in absence
of external magnetic field and there is no net magnetization. In an external field B0 along z
direction, the spins precess around B0 at the Larmor frequency to yield a net macroscopic
equilibrium magnetization, M0, along z direction (figure 1). In a rotating coordinate system
with z’ collinear to z axis, this magnetic moment is static while the field along z’ axis
vanishes. For an additional RF field B1 (small as compared to B0) applied along x’ direction,
with frequency of rotation (matching that of the Larmor frequency 0), the effective field
in the rotating frame is only B1.
MR Imaging - Basic Concepts
403
Figure 1: (a) Precessional motion of spin around external magnetic field, B0 with equilibrium
magnetization M0, (b) Static magnetization vector, M0, along z’ axis (rotating frame), (c) Application
of /2 pulse tips M0 along y’ axis (rotating frame), (d) Spin- spin relaxation in progress, (e), (f)
and (g) Spin-lattice relaxation in progress alongwith recovery of longitudinal magnetization, (h)
Recovery of longitudinal magnetization in the classical frame - a combination of (e), (f) and (g).
An RF pulse with appropriate width which can tip the magnetization through 90° is
termed as a /2 pulse. It shifts the magnetization to x or y direction (perpendicular to z).
A pulse, which inverts the magnetization along the -z direction through 180° is called the
pulse.
Considering the classical frame of reference, following application of 90° pulse, the
magnetization component Mxy rotates coherently about B0 at the Larmor frequency. Once B
is turned off at the end of a /2 pulse, dephasing of the spins occurs due to spin-spin
interaction (figure 1). The magnetization in the xy plane decay back to equilibrium value
while precessing about B0 with an angular velocity of ( B0). While sweeping through the
direction of receiver coil surrounding the sample volume, it induces a voltage in the coil.
The detected sinusoidal emf is called the Free Induction Decay (FID). The maximum
amplitude of the FID is proportional to the magnetization in the direction B0 prior to the
application of the /2 pulse. The amplitude (Mxy) further decays exponentially with a time
constant which is the transverse relaxation time (T2), described by equation (3). The
exponential decay curve of T2 (figure 2a) shows that after every interval of T2 (ms), 37% of
the magnetization remains in the xy plane. The FID duration is additionally influenced by
1
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MR Imaging - Basic Concepts
field inhomogeneities over sample volume, causing an additional spread in Larmor
frequencies, which leads to a faster decay of FID. The observed FID is now shorter than T
and is a measure of T2*. The output of the pickup coil will thus be a sinusoidal wave whose
amplitude decays in accordance with exp (-t/T2*).
Thus, besides precessing about the applied magnetic field, M relaxes back to equilibrium
value M0 along the z direction with a time constant, T1. Longitudinal magnetization recovers
by (1- (1/e)) or 63% during each time period of T1 (figure 2b) and is considered to be almost
recovered (99.3%) at 5T1 periods. Relaxation times in the solid and gaseous phases differ
significantly from those in liquids, due to the differing degrees of molecular motion. In
biological systems, in case of solids, the T2 relaxation is very short (< 1 ms) and T1 relaxation
time can be very long (>1 minute), e.g., the signals from macromolecules and cortical bone
decay too fast to produce a detectable signal. The T1 and T2 relaxation times of some of the
important human tissues at 1 Tesla are shown in table 1.
Table 1: T1 and T2 values for different human tissues at 1 Tesla
Tissue T1 (ms) T2 (ms)
Fat 241 85
Muscle 732 45
Brain- White matter 683 90
Brain- Grey matter 813 100
CSF 2500 1400
2
Figure 2. (a) Exponential decay of transverse magnetization Mxy with a time constant, T
(spin-spin relaxation time), (b) Recovery of the longitudinal magnetization characterised by a
time constant, T1 (spin lattice relaxation time).
2
MR Imaging - Basic Concepts
405
Magnetic Resonance Imaging
Magnetic Resonance Imaging was demonstrated by Raymond Damadian to distinguish
normal and cancerous tissue on the basis of T1 relaxation characteristics of the onedimensional NMR signal (7). Further in 1973, Paul Lauterbaur used NMR to create a 2
dimensional map of the density of nuclear spins within a sample (figure 3) (8). Lauterbaur
showed that by trading the homogeneity of magnetic field by using field gradients, it was
possible to encode position dependent information in the NMR signal, thus paving the way
for future clinical applications of the phenomena. Following this, rapid progress was made
in this field with the first live human MR images being reported in 1976, followed by hand
and thorax images in 1977, and head and abdomen images in 1978 (9,10).
Figure 3: Spatial encoding of position using field gradients: In the absence of the field gradient,
the FID signal has a single frequency component. On the application of gradient field the two
tubes have different Larmor frequencies that depends on their spatial position. The Fourier transform
of their FID is the projection onto the axis of the field gradient.
Image formation using MRI
Water (which contains two hydrogen atoms) is abundant in biosystems. Protons have the
highest natural abundance (percentage of atoms having NMR visible nuclei) of 99.98% and
the strongest NMR signal making it an excellent candidate for biomedical imaging and
spectroscopy. The imaging technique currently used in MRI originated from the work of
Ernst and Anderson (11). With the use of an external magnetic field gradient (a small static
magnetic field that can be varied spatially), the spatial information from the imaging plane
is encoded into the signal, from which a 2D image may be reconstructed. This is based upon
the dependence of Larmor frequency upon the magnetic field strength (equation 2). Hence,
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MR Imaging - Basic Concepts
making B0 slightly different at each point in the imaging volume associates the corresponding
spins with a different Larmor frequency.
The NMR absorption spectrum provides a projection of the sample spin density integrated
over planes perpendicular to the direction of gradient application. In order to reconstruct
tomographic slice images, it is necessary to have additional information, necessitating the
application of three orthogonal gradients for spatial encoding of data. These consist of the
slice selection gradient (typically Gz) applied alongwith the RF pulse, followed by phase
encoding (Gy) and read out or frequency encoding (Gx) gradients. Application of Gx and G
gradients encodes position information into each pixel: while one coordinate is encoded into
the phase, the other coordinate is encoded into the frequency. Following spin flip, pixel-bypixel magnetization in the selected slice initially rotates at the same phase (in-phase) and
frequency (time, t = 0). Application of the phase encoding gradient for time ty, affects the
precessional frequency, so that rates of rotation change and become dependent upon their
positions along the phase encoding gradient. A constant phase difference between spins in
neighboring lines is introduced that is maintained even after the gradient is switched off.
During read out, the frequency-encoding gradient is turned on for a time tx. This gives the
position information for each pixel. Figure 4 shows a T2 weighted image and a diffusion
weighted image, showing gray, white matter and csf.
y
Figure 4: (a) T2 weighted image and a (b) diffusion weighted image (b=1000) in a multiple
sclerosis patient
The modified Larmor equation for nuclei and hence precessional frequency for spins at
each pixel in the presence of a static magnetic field B0, upon which linear field gradients
along the x, y direction are superimposed, is given by
(x,y) = (B0 + xGx + yGy) (4)
MR Imaging - Basic Concepts
407
where, Gx= (Bx /x), Gy = (By /y).
The MR signal acquired is localised onto an imaging slice (2-D plane) by initial
application of the slice selection gradient. Simultaneous application of Gz gradient to the
external magnetic field alongwith the slice selective RF pulse ensures excitation of only
those nuclei whose bandwidth falls within the pulse bandwidth. Each plane of constant z
now corresponds constant precessional frequency given by,
0 = (x,y) + Gz z (5)
The location and thickness of the region of excitation is determined by the axial field
gradient (Gz), and the central frequency and bandwidth of the RF pulse.
Thus, the information of each phase and frequency is encoded into the signal. For
acquiring a matrix of data elements (m,n), it is thus finally required to collect a series of ‘n’
points in the presence of a read-out gradient that encodes the frequency of the signal and
produces a series of ‘n’ spatially encoded data points, following Fourier transformation.
Repetition of the procedure spaced out by the time parameter TR (TR= repetition time or
time to repeat a pulse sequence) with a progressively increasing phase-encode gradient G
pulses yields a new set of ‘m’ time domain points, producing a data set consisting of ‘m’
rows and ‘n’ columns. Usually the variable along the rows is the time and down the columns
is the phase. On Fourier transformation along the rows and down the columns, a map or
image of intensity within the two axes defined by the two applied gradients is produced in
the Fourier space or k-space (represented in spatial frequency, cycles/cm). This acts as a
Fourier transform plane of the acquired signal intensity patterns, each at different spatial
frequencies, which is inverse Fourier transformed to yield the image (11,12). Signals
corresponding to low spatial frequencies are concentrated near the origin of k-space.
y
Figure 5: Collection of the necessary Fourier coefficients as a function of their kx and ky coordinates
enables the generation of an image as a function of its x and y coordinates.
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MR Imaging - Basic Concepts
Information about high spatial frequencies is spread farther away from the origin. The
manner in which data at every point in k-space contributes to the image depends upon its
location in the Fourier transform plane or k-space. Points at the edge of the Fourier space
determine image resolution while those towards the center contribute to image contrast
(figure 5) (13].
Different combinations of Gx, Gy, tx and ty accumulate data over a grid in k-space. Since
these integrals evolve over time, the position of MR signal on the k-space plane describes a
trajectory. Thus magnitude, direction and period of application of the gradient determine the
manner in which k-space is traversed. Altering any of these parameters changes the k-space
scan path, leading to different imaging sequences such as spin echo, fast imaging with
steady-state precession, echo planar imaging (EPI), spiral imaging, etc (figure 6).
Figure 6: The k space trajectories for different pulse sequences: (a) 2D Fourier Transform Imaging,
(b) Echo Planar Imaging and (c) Square Spiral Imaging.
Pulse sequences
One of the strengths of MRI is the myriad measurement technique available for image
acquisition. Image acquisition involves the use of various electrical and electronic components,
particularly the transmitter, receiver, gradient coils and associated hardware components,
which have to be timed and applied according to the specific requirement of the study. All
hardware aspects of the signal detection process are controlled by pulse sequences. Depending
upon the contrast parameter and applications, different pulse sequences have been
implemented, which are named differently by various vendors. The major categories of
pulse sequences are Spin echo, Gradient echo, Inversion recovery and Ultrafast techniques.
Spin echo pulse sequence
The refocusing of the spins to form an echo is widely used for multi-echo acquisition,
with modifications proposed by Carr-Purcell and refined by Meiboom and Gill (14,15). The
MR Imaging - Basic Concepts
409
sequence is characterized by the use of a slice selective 90° excitation pulse and one or
more 180° pulses for refocusing the transverse magnetization to form a spin echo (figure
7a). This echo is detected in the presence of a readout gradient of constant amplitude after a
time TE (echo time) from the initial 90° pulse. The excitation-detection process is repeated
many times with amplitude of the phase-encoding gradient being different each time. Thus,
we directly acquire a line in k space for each phase-encoded projection acquired.
Figure 7: (a) Spin-echo pulse sequence timing diagram: A slice-selective 90o pulse followed by
a 180º refocusing pulse to form an echo. (b) Gradient Echo pulse sequence timing diagram: A
gradient reversal is used to replace the 180º rephasing pulse to form an echo.
The choice of TE controls T2 dependence, while TR exerts primary control over T
dependence. M0 corresponds to net magnitude of magnetization and cannot be controlled at
a given B0 field. The pulse sequence timing and parameters can thus, be adjusted to give
either T1-weighted, Proton density, or T2-weighted images to enhance the diagnostic value
(table 2).
Table 2: Contrast manipulations by selection of sequence parameters (TR,TE)
Repetition time, TR, ms
Short Long
Echo time, Long Poor S/N ratio Mixed (Spin density,T2)
TE, ms Short Mixed (Spin density, T1) Proton density (H)
Gradient echo pulse sequence
The sequence has a slice selective 90º excitation pulse followed by a reversal of gradient
pulses to refocus the transverse magnetization, avoiding the use of an additional RF pulse
1
410
MR Imaging - Basic Concepts
(figure 7b). Gradient echo (GE) sequences are more sensitive to sources of dephasing such
as field inhomogeneity and differences in magnetic susceptibility, i.e., more sensitive to T2*
effect than T2. These sequences enable acquisition of high contrast images with very short
TR (<300ms). The image contrast is also much more dependent upon the excitation pulse
angle.
Variations of gradient echo sequence include spoiled gradient echo, refocused gradient
echo, magnetization prepared gradient echo, etc. Spoiled gradient echo sequences enable
acquisition of T1 weighted or intermediate weighted images and are particularly suited for
breath-hold studies following administration of a contrast agent in abdominal imaging.
Inversion recovery pulse sequence
This sequence is derived from spin echo sequence and is used mainly to detect long T
relaxing tissues. 180º RF pulse is applied prior to the primary excitation pulse to invert the
net magnetization. Following this, a 90º RF pulse brings the residual longitudinal
magnetization into the x-y or transverse plane where it can be detected by an RF coil. In
tissues, following this pulse, T1 relaxation occurs in which the net magnetization from each
tissue passes from an inverted condition through zero net magnetization to a relaxed condition
(equilibrium magnetization, M0). The signal is subsequently refocused with a 180º pulse as
in a spin echo sequence. The time between the initial 180º pulse and the 90º pulse is the
inversion time (TI). It is user definable and determines how much time is allowed for T
relaxation.
Choice of TE controls T2 dependence, while TI exerts primary control over T1 dependence.
Major applications of inversion recovery sequences are in tissue suppression. Selecting a TI
value so that a tissue has no net magnetization in z-axis will cause the tissue to generate no
signal. Most commonly used inversion recovery sequences are (1) short TI inversion recovery
technique (STIR) for fat suppression and (2) fluid attenuation inversion recovery (FLAIR)
technique for cerebrospinal fluid suppression.
Ultrafast Imaging
Faster acquisition times may be required for imaging dynamic processes by repeated
acquisitions and increasing patient comfort and throughput. The net acquisition time (T
acq
for any MR image is given by,
1
1
)
T
= TR no. of phase encoding steps (m) no. of averages (6)
acq
Here, it is assumed that only one phase encoding or Fourier line is acquired during each
TR interval. For reduction in acquisition time, fast scan pulse sequences employ alternative
spatial encoding methods with acquisition of more than one Fourier line after each excitation
pulse [acquisition of many phase encoding lines during each TR (fast spin echo), or acquisition
of all phase encoding lines during one TR (echo planar imaging), etc]. Sequences that
employ a reduced TR and TE alongwith added preparative pulses to provide contrast have
MR Imaging - Basic Concepts
411
also been developed. Magnetization prepared methods include TurboFLASH or snapshot
FLASH sequences, T1 weighted MPRAGE, etc. In the Echo planar technique, complete 2D
encoding process is completed during the free induction decay following a single excitation
pulse (16). Variations of this technique include FLEET (Fast Low-angle Excitation Echo
planar Technique), BEST (Blipped Echo-planar Single-pulse technique), MBEST (Modulus
Blipped Echo-planar Single-pulse technique), etc.
Contrast mechanisms
Pixel-by-pixel variations in signal intensity are termed as contrast. In other radiological
techniques like Ultrasound and CT, contrast depends only on a single parameter, i.e. acoustical
impedance and x-ray attenuation coefficients of the tissue, respectively. Image contrast in
MRI depends on a combination of physical (T1 and T2 relaxation times, proton density,
diffusion, etc), chemical (molecular environment of the nuclei) and biological (tissue type,
flow, etc) properties. These parameters can be broadly divided into intrinsic and extrinsic
imaging parameters. The intrinsic parameters are proton density and relaxation times. In
general, contrast can be given by the weighted sum of the spin density, T1 and T2 differences
(17). The value of the weighting factors depend upon the type of pulse sequence used and
the value of timing parameters (TR, TE, TI) as compared to T1 and T2, which can be
modified to obtain optimum results.
System hardware
The main requirements of an MRI system are magnet for inducing the Zeeman splitting,
shim coils for homogenizing the magnetic field in the selected field of view, gradient system
to choose the region of interest, transmitter to tip the nuclear spin system with the RF
Figure 8: MR Scanner, alongwith necessary hardware infrastructure.
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