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Imagen de resonancia magn

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Magnetic resonance imaging, G.A. WRIGHT IEEE ... 1946 MR phenomenon - Bloch & Purcell. 1952 Nobel Prize - Bloch & Purcell. 1950 NMR developed as analytical tool ... – PowerPoint PPT presentation

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Title: Imagen de resonancia magn


1
Imagen de resonancia magnética
  • http//www.cis.rit.edu/htbooks/mri/inside.htm
  • Magnetic resonance imaging, G.A. WRIGHT IEEE
    SIGNAL PROCESSING MAGAZINE pp56-66 JANUARY 1997

2
  • MRI Timeline
  • 1946 MR phenomenon - Bloch Purcell
  • 1952 Nobel Prize - Bloch Purcell
  • 1950 NMR developed as analytical tool
  • 1960
  • 1970
  • 1972 Computerized Tomography
  • 1973 Backprojection MRI - Lauterbur
  • 1975 Fourier Imaging - Ernst
  • 1977 Echo-planar imaging - Mansfield
  • 1980 FT MRI demonstrated - Edelstein
  • 1986 Gradient Echo Imaging NMR Microscope
  • 1987 MR Angiography - Dumoulin
  • 1991 Nobel Prize - Ernst
  • 1992 Functional MRI
  • 1994 Hyperpolarized 129Xe Imaging
  • 2003 Nobel Prize - Lauterbur Mansfield

3
Modelos de scanners
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5
Algunas bobinas de GE
6
Doty coils
7
Tomographic imaging
Magnetic resonance started out as a tomographic
imaging modality for producing NMR images of a
slice through the human body.
8
Magnetic resonance imaging is based on the
absorption and emission of energy in the radio
frequency range of the electromagnetic spectrum.
Many scientists were taught that you can not
image objects smaller than the wavelength of the
energy being used to image. MRI gets around
this limitation by producing images based on
spatial variations in the phase and frequency of
the radio frequency energy being absorbed and
emitted by the imaged object.
9
Microscopic Property Responsible for MRI
The human body is primarily fat and water. Fat
and water have many hydrogen atoms which make the
human body approximately 63 hydrogen atoms.
Hydrogen nuclei have an NMR signal. For these
reasons magnetic resonance imaging primarily
images the NMR signal from the hydrogen
nuclei. The proton possesses a property called
spin which 1. can be thought of as a small
magnetic field, and 2. will cause the nucleus
to produce an NMR signal.
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11
Basic physics
  • Magnetic resonance imaging, G.A. WRIGHT IEEE
    SIGNAL PROCESSING MAGAZINE pp56-66 JANUARY 1997

12
The relevant property of the proton is its spin,
I, and a simple classical picture of spin is a
charge distribution in the nucleus rotating
around an axis collinear with I. The resulting
current has an associated dipole magnetic moment,
p, collinear with I, and the quantum mechanical
relationship between the two is
where h is Plancks constant and y
is the gyromagnetic ratio. For protons, y/2n
42.6 MHz/T.
13
In a single-volume element corresponding to a
pixel in an MR image, there are many protons,
each with an associated dipole magnetic moment,
and the net magnetization, M Mx j Myi Mzk,
of the volume element is the vector sum of
the individual dipole moments, where i, j, and k
are unit vectors along the x, y , and z axes,
respectively. In the absence of a magnetic
field, the spatial orientation of each dipole
moment is random and M 0.
14
This situation is changed by a static magnetic
field, Bo Bok. This field induces magnetic
moments to align them- selves in its direction,
partially overcoming thermal randomization so
that, in equilibrium, the net magnetization, M
M0k, represents a small fraction (determined
from the Boltzmann distribution) of times
the total number of protons. While the
fraction is small, the total number of
contributing protons is very large at
approximately 10'' dipoles in a S mm3 volume.
15
Equilibrium is not achieved instantaneously.
Rather, from the time the static field is turned
on, M grows from zero toward its equilibrium
value M, along the z axis that is, where T1
is the longitudinal relaxation time. This
equation expresses the dynamical behavior of the
component of the net magnetization Mz along the
longitudinal (z) axis.
16
The component of the net magnetization, Mxy,
which lies in the transverse plane orthogonal to
the longitudinal axis, undergoes completely
different dynamics. Mxy, often referred to as
the transverse magnetization, can be described
by acomplex quantity where
This componentprecesses about Bo, i.e., The
precession frequency is proportional to B, and
is referred to as the Larmor frequency (Fig. 1
b). This relation holds at the level of
individual dipoles as well, so that
17
Accompanying any rotating dipole magnetic moment
is a radiated electromagnetic signal circularly
polarized about the axis of precession this is
the signal detected in MRI. The usual receiver
is a coil, resonant at w0 , whose axis lies in
the transverse plane-as Mxy, precesses, it
induces an electromotive force (emf) in the coil.
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If Bo induces a collinear equilibrium magnetizatio
n M, how can we produce precessing magnetization
orthogonal to Bo?
The answer is to apply a second, time-varying
magnetic field that lies in the plane transverse
to Bo
This field rotates about the static field
direction k at radian frequency w0 If we then
place ourselves in a frame of reference (x'y'z)
that also rotates at radian frequency w0, this
second field appears stationary.
20
Moreover, any magnetization component orthogonal
to B0, no longer appears to rotate about Bo.
Instead, in this rotating frame, M appears to
precess about the "stationary" field B1, alone
with radian frequency. One can therefore
choose the duration of B1, so that M is rotated
into the transverse plane. The corresponding B1
waveform is called a 90" excitation pulse
21
  • The signal from Mxy will eventually decay.
  • Part of this decay is the result of the drive to
    thermal equilibrium where M is brought parallel
    to Bo, as described earlier.
  • Over time, the vector sum, M, decreases in
    magnitude since the individual dipole moments no
    longer add constructively.
  • The associated decay is characterized by an
    exponential with time constant T2

22
the loss of transverse magnetization due to
dephasing can be recovered to some extent by
inducing a spin echo. Specifically, let the
dipole moments evolve for a time t after
excitation. At this time apply another B1 field
along y' to rotate the dipole moments 180" around
B1. This occurs in a time that is very short
compared to t. This pulse effectively negates
the phase of the individual dipole moments that
have developed relative to the axis of rotation
of the refocusing pulse. Assuming the precession
frequencies of the individual dipole moments
remain unchanged then at a time ,t, after the
spin-echo or 180" pulse, the original
contributions of the individual dipoles refocus
(Fig. 2a). Hence, at a time TE 2t after the
excitation, the net magnetization is the same as
it was just after excitation.
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25
If one applies a periodically spaced train of
such 180" pulses following a single excitation,
one observes that the envelope defined by
at each echo time steadily decays (Fig. 2b).
This irreversible signal loss is often modeled
by an exponential decay with time constant T2.
the transverse relaxation time
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28
Before the experiment can he repeated with
another excitation pulse, sufficient time must
elapse to re-establish equilibrium magnetization
along k. As indicated in Eq. (l), a sequence
repetition time, TR, of several Tls is necessary
for full recovery of equilibrium magnetization,
Mo, along Mz, between excitations. Bloch
equation
29
Imaging, contrast and noise
30
  • Imaging spatial resoltion of the signal
  • Two-step process
  • exciting the magnetization into the transverse
    plane over a spatially restricted region, and
  • (ii) encoding spatial location of the signal
    during data acquisition.

31
Spatially Selective Excitation The usual goal in
spatially selective excitation is to tip
magnetization in a thin spatial slice or section
along the z axis, into the transverse plane.
Conceptually, this is accomplished by first
causing the Larmor frequency to vary linearly in
one spatial dimension, and then, while
holding the field constant, applying a
radiofrequency (RF) excitation pulse crafted to
contain significant energy only over a limited
range of temporal frequencies (BW) corresponding
to the Larmor frequencies in the slice.
32
To a first approximation, the amplitude of the
component at each frequency in the excitation
signal determines the flip angle of the protons
resonating at that frequency. If the temporal
Fourier transform of the pulse has a rectangular
distribution about w0, a rectangular
distribution of spins around zo is tipped away
from the z axis over a spatial extent
33
For small tip angles we can solve the Bloch
equations explicitly to get the spatial
distribution of Mxy following an RF pulse, B1(t),
in the presence of a magnetic field gradient of
amplitude Gz
Assume that all the magnetization initially lies
along the z axis. Under these conditions, a
rectangular slice profile is achieved if
34
Image Formation Through S p a t i a l Frequency
Encoding The Imaging Equation Once one has
isolated a volume of interest using
selective excitation, the volume can be imaged by
manipulating the precession frequency (determined
by the Larmor relation), and hence the phase of
Mxy. For example, introduce a linear magnetic
field gradient, Gx, in the x direction so that
each dipole now contributes a signal at a
frequency proportional to its x-axis coordinate.
35
In principle, by performing a Fourier transform
on the received signal, one can determine Mxy as
a function of x. An equivalent point of view
follows from observing that each dipole
contributes a signal with a phase that depends
linearly on its x-axis coordinate and time.
Thus, the signal as a whole samples the
spatial Fourier transform of the image along the
kx spatial frequency axis, with the sampled
location moving along this axis linearly with
time.
36
A more general viewpoint can be developed
mathematically from the Bloch equation. Using
spatially selective excitation only protons in a
thin slice at z zo are tipped into the
transverse plane so that
Let the magnetic field after excitation be
37
Assume is relatively constant during
data acquisition (i.e. acquisition duration ltlt
Tl,T2,T2) and let the time at the center of the
acquisition be tacq. During acquisition
38
The signal received, S(t), is the integral of
this signal over the xy plane.
39
If this signal is demodulated by w0 then the
resulting baseband signal, Se(kx(t), ky(t)), is
the 2D spatial Fourier transform of
at spatial frequency coordinates kx(t) and ky(t).
One chooses Gx(t) and Gy(t) so that, over the
full data acquisition, the 2D frequency domain is
adequately sampled and the desired image can be
reconstructed as the inverse Fourier transform of
the acquired data.
40
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