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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

• 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

Origin of the MRI Signal- A review

Magnetization

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.

I’m applying a perpendicular B field to the static field in NMR. Physics of Radiology, Anthony Wolbarst

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

• 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.

• 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.


• 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.

• 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 saturation-recovery pulse sequence and keep track of Mz(t).



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Mz(t) = Mo 1− e−

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• 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

• 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.

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MZ = M0 1− e−

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T1 ⎛

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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.


• 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.

Bz

Bxy

An Introduction to MRI Physics and Analysis Michael Jay Schillaci, PhD


• 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.

• 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.


• Integrate magnetization to get MRI signal• Select a z “slice” and form image of xy plane variations where S is the

intensity

• 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.

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T2 Weighted Image (T2WI)(Gray Matter – CSF Contrast)

T1 Weighted Image (T1WI)(Gray Matter – White Matter)


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

• 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.

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Mxy = M0e−

t

T 2

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rf field

external magnetic field

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static field

static magnetic field

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perpendicular b field