Magnetic Resonance Imaging
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Magnetic Resonance Imaging
- Outline
• Review nuclear magnetic moments and the precession of the magnetization vector
about the static magnetic field.
• Hit the sample with a pulse of RF energy at a specific frequency called the Larmor
frequency and make the magnetization vector undergo nutation.
• Nutation is the changing of the precession angle (with respect to the external field)
by applying another force to the system (the RF pulse) and this varies the
longitudinal component of the magnetization.
• Investigate the relaxation times of the transverse and longitudinal magnetization
vectors for the time varying spin states.
• Briefly look at the ideas behind image formation,
which is a complex process.
Physics of Radiology, Anthony Wolbarst
Origin of the MRI Signal
- A review
• So, we have that the protons align in an external magnetic field and that their angular
momentum causes them to precess about the external field.
• Putting these protons into the external magnetic field produces a two state system of
energies that are split by the external field (the Zeeman Effect).
• A RF pulse applied perpendicular to the external field and this causes absorption of
photons by nuclei in the low energy state and the spin vector of the protons flips and this
causes a nutation of the magnetization vector that is precessing about the external field.
• The protons are all in precessing in phase and when the RF field is switched off the
protons relax and transition back to lower energy states with an emission of energy.
• But how do you know that for a given proton system in a static magnetic field that the
frequency of the RF is identical to the Larmor precession frequency?
• If and only if the RF happens to be oscillating at the Larmor frequency then I can cause the
net magnetization vector to precess at larger and larger angles (away from the static
field) until it is swinging in a transverse plane.
• This is the resonance of NMR and can be detected with a detection coil of wire
Magnetization
Physics of Radiology, Anthony Wolbarst
Physics of Radiology, Anthony Wolbarst
In the externally applied field the
magnetic moments try to align with the
field. There is a difference in numbers of
nuclei in the spin up versus spin down
states and the difference in number gives
rise to the magnetization.
Here the difference is illustrated.
A single nuclei precesses about
the magnetic field at frequency
f0 (the Larmor frequency).
For a collection of nuclei the
magnetization vector (which
represents the net magnetic
moment precesses about the
applied field.
Nutation – The Resonance in NMR
A tangentially applied force (one that is 90o
to the external force) causes nutation and
the object precesses at a larger angle with
respect to the applied force.
Here for the top, the external force is
gravity, and the tangential force is say
tension in an attached string.
For the proton precessing in a magnetic
field, the external force is due to the
magnetic field and the tangential force is a
90o RF pulse.
Physics of Radiology, Anthony Wolbarst
I’m applying a perpendicular B field to the
static field in NMR.
If the frequency of this field BRF is above or below the Larmour frequency not much
happens. If it is at the Larmour frequency then I case a resonance in the system.
Origin of the MR Signal
Physics of Radiology, Anthony Wolbarst
Physics of Radiology, Anthony Wolbarst
• The magnetization vector M precessing about the external magnetic field has both a longitudinal
component (parallel to the applied field) and a transverse component (perpendicular to the
applied
field).
• For M along the “z-axis” there is no change in voltage (or induced current) in the detection coil.
• For M precessing in or near the transverse plane the changing magnetic field produces a voltage
across (and a current through) the detection coil that changes in time.
• The shape is periodic and the amplitude of the voltage (and current) change as M moves in and out of
the transverse plane (relaxations).
• This only happens if you hit the proton sample at the correct frequency – system is tunable and the
system is said to be in resonance!
1 Dimensional Imaging: T1 Spin Relaxation
• When the RF is “off” the system tends to return to equilibrium (actually a thermal
equilibrium) and the nuclear spins tend to relax.
• There is a rate of relaxation that occurs with this process
depends on the magnetization vector.
• The magnetization vector has a longitudinal component (Mz)
and a transverse component (Mxy) and thus can have a
longitudinal and transverse nuclear spin relaxations.
• Immediately after an external static magnetic field is switched
on the magnetization of the protons grows from zero (no
spins aligned with B) to it’s final equilibrium value (a net
magnetization with more protons in the lower energy state)
after some time.
Physics of Radiology, Anthony Wolbarst
• Since the low energy configuration is when the proton dipoles
align with the field, there are generally more of them in the low energy state than
the high energy state.
• We arbitrarily define a time T1 as the time required to get 63% of the way from zero
magnetization to full magnetization, or equilibrium.
1 Dimensional Imaging: T1 Spin Relaxation
• The main interest in MRI is NOT the equilibrium state itself, but the moving
toward equilibrium through nuclear spin relaxation and the rate at which
this occurs.
• Equilibrium is when the RF field is off.
• So, when the external B-field is turned ON there is a time, T1, that
characterizes how long it takes for the net magnetization to grow from
zero to its equilibrium value of more protons aligned than anti-aligned
with the external field.
• Actually T1 is defined to be 63% of this total time.
• For pure water at body temperature, T1is several seconds in a 1.5T field
while its protons in water in tissue it’s much shorter, say by 5 to 10 times.
• When a sample of nuclei in a magnetic field are disturbed from equilibrium
the magnitude and direction of the magnetization vector vary with time.
1 Dimensional Imaging: T1 Spin Relaxation
• T1 is called the longitudinal relaxation
time.
• It characterizes the re-growth of the
longitudinal component of the
magnetization and involves
transitions between the spin-up and
spin-down states.
Physics of Radiology, Anthony Wolbarst
Physics of Radiology, Anthony Wolbarst
• 1/T1 is the rate at which the system
comes into thermal equilibrium.
• The RF pulse disturbs the system and as
the RF oscillates in time, M changes
with time and we could use this to
measure T1.
• To measure T1 we do a saturationrecovery pulse sequence and keep
track of Mz(t).
  t 
M z (t)  M o 1 e T1 


1 Dimensional Imaging: T1 Spin Relaxation
• The RF pulse disturbs the system of nuclei from equilibrium.
• When the system is disturbed the magnetization vector, M(t), changes with time.
• Suppose that you have a sample of water and you put it between the poles of a magnet,
which provides an external field.
• The protons in the sample orient themselves along or against the external field (with
more aligned with the field) and over time the magnetization reaches an equilibrium
value of M0 according to
  t 
MZ  M01 e T1 


• This is called the longitudinal magnetization, or the component of the magnetization
lying along the “z-axis”. (Remember M precesses about the B field.)
• The system relaxes into this equilibrium state.

• The actual time T1 depends on cellular physiology and pathologic conditions.
T1 Mapping
• We can map out Mz for different environments of tissues.
• Each tissue has a different T1 relaxation time, determined
by its physiological characteristics.
• The longitudinal component of M, Mz, detected in the detector coils produces intensities
that are proportional to the Mz from the different tissues.
• The MRI map reflected the difference between two regions in the value of Mz and the
difference occurs because the T1’s are not the same for all tissues.
• Fatty tissue equilibrates more readily than say white/gray matter
in the brain because the magnetic environments are
different. The shorter T1 the brighter the signal.
• The contrast in the figure are due to differences in T1
relaxation times and this is said to be T1-weighted.
T1 weighted images
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Left image is a T1 weighted sagittal image of the human brain showing left
hemisphere, lateral ventricles, cerebellum and sinus cavities.
The right image is also a sagittal image of the cervical spine. You can also
clearly see the spinal cord and part of the cerebellum.
Magnetic Resonance Imaging
- Image formation & reconstruction
• The MRI image reflects spatial distribution of T1, T2 or proton density within a slice of
tissue.
• This involves the NMR signal from differing volume elements of protons caries
information that allows for its localization within the body.
• The static magnetic field points along the patients body, taken to be the z-axis.
• The transverse plane is a slice through the body, generally.
• Other slices, like coronal or sagittal are possible with good image resolution.
• Most commercial machines have resolutions on the order of a millimeter.
• The most critical and expensive component is the main magnet with fields in the 0.3 –
1.5T range.
• The fields need to be stable and very uniform over the imaging region – not trivial.
Magnetic Resonance Imaging
- Image formation & reconstruction
• The RF coils are used to produce and detect the MRI signals.
• The weak resonance signals produced with in the body are amplified, digitized and
computer manipulated to generate an image.
• The orientation of the RF coils (which some are able to be manipulated) generate
other slices of the body.
Bxy
An Introduction to MRI Physics and Analysis Michael Jay Schillaci, PhD
Bz
Magnetic Resonance Imaging
- Image formation & reconstruction
• The RF signals from the detector coils given information about the magnetization
vector in the transverse plane as a function of time.
• We scan over a section of tissue and compare the
signals received in the detector coils and
“actually” calculate the magnetization.
• The value of the magnetization gives us a measure
of T1 as well as spatial information about the
proton density and magnetic field environments
of the nuclei.
• The differences in T1 timesprovide contrast.
• The signals are mixtures of many frequency photons.
Physics of Radiology, Anthony Wolbarst
• The signals are “deconvoluted” and analyzed using Fourier analysis. Then they
are reconstructed to form an image. This is a highly non-trivial process, but it
works along the same lines as CT.
Magnetic Resonance Imaging
- Image formation & reconstruction
Integrate magnetization to get MRI signal
• Select a z “slice” and form image of xy plane variations where S is the
intensity

  
t

i
xG



yG



dt
X
Y
0


S
(
t
)

M
x
,
y
,
t
e
XY

dxdy
Area
•
Contrast is due to differences in magnetization intensities in space
• Image at several times
• Scanner acquires K-Space weights (Fourier transforms of
frequencies.)
• Construct image and average slices from differences in T1.
Horizontal density

Vertical density
•

An Introduction to MRI Physics and Analysis Michael Jay Schillaci, PhD
Magnetic Resonance Imaging
- Image formation & reconstruction
T1 Weighted Image (T1WI)
T2 Weighted Image (T2WI)
(Gray Matter – White Matter)
(Gray Matter – CSF Contrast)
An Introduction to MRI Physics and Analysis Michael Jay Schillaci, PhD
T2 scans are almost the photographic negative of T1 scans. We make dark areas
white and white areas dark to enhance fluid filled areas.
T1 and T2 Relaxation
• Recall that M has a component in the transverse plane as well, Mxy.
• As M oscillates (and Mz relaxes back to equilibrium and then away,) the transverse
magnetization also changes.
• The signal in the detection coil decreases with time due to T1 relaxation effects.
• The transverse magnetization decays exponentially with time approximately
according to
M xy  M 0e

t
T2
• T2 is called the spin-spin or transverse relaxation time.
• Of course this all assumes that everything is perfect.

• Inhomogeneities in the magnetic fields effect T2.
• The net magnetization vector is not constant in length but can vary due to the
inhomogeneous magnetic fields.