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Magnetic Resonance Imaging
P. Ravikumar, Lect./BME
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Introduction
In 1933, Stern and associates discovered that theproton had a magnetic moment and would thereforeinteract with a magnetic field.
In 1939 Rabi, designed an apparatus to examine the
interaction of magnetic nuclei with time-varyingmagnetic fields.
He found that a certain frequency of the magnetic fieldwas required to obtain the strongest interaction withan atom or molecule and that this frequency varied foreach type of atom.
Rabi demonstrated the principle of magneticresonance (MR) and linked resonance frequencies tospecific nuclei.
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Introduction
The emission of radio signals from nuclei was
demonstrated independently by Bloch and Purcell in
1945.
The frequency shifts were found to be characteristic
for individual molecules.
This finding identified nuclear magnetic resonance
(NMR) as a method for identifying minute amounts
of chemicals in unknown samples and led to thedevelopment of NMR in the 1950s as a standard tool
for research in analytical chemistry
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INTERACTION OF NUCLEI WITH A
STATIC MAGNETIC FIELD
Magnetic Resonance first presents the classicalinterpretation of the behavior of nuclearmagnetic moments by using the hydrogennucleus (i.e., a single proton) as a model.
In the classical interpretation the position of thehydrogen nucleus can be specified with anydesired degree of precision, and its movementsare assumed to be continuous and completely
predictable. Each proton behaves as a small magnet with a
magnetic moment that has both magnitude anddirection.
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INTERACTION OF NUCLEI WITH A
STATIC MAGNETIC FIELD
A: Proton magnetic moment direction is indicated by arrow.
B: In a typical material, magnetic moments are oriented randomly.
C: If a magnetic field is applied, magnetic moments align themselvesalong the direction of the field. Note that some are parallel, whileothers are antiparallel.
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INTERACTION OF NUCLEI WITH A
STATIC MAGNETIC FIELD In a typical sample of hydrogen-containing material
(such as the human body), the magnetic moments ofthe individual hydrogen nuclei are oriented in randomdirections.
If a strong magnetic field is applied to the sample, thenuclei align their magnetic moments with thedirection of the magnetic field in a manner similar to acompass needle aligned with the earths magneticfield.
The earths magnetic field (0.5 gauss) is not strongenough to bring protons in a tissue sample intoalignment.
The field supplied by an MR system (e.g., 20,000 gauss)is strong enough to produce alignment.
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ROTATION AND PRECESSION
In addition to aligning with a magnetic field, amagnetic moment also precesses about the field.
A spinning top, for example, will wobble about avertical axis defined by the earths gravitational field.
This wobbling motion is precession.
Precession is a type of motion that is distinct fromrotation.
Rotation is the spinning of an object about its axis (animaginary line through the center of mass of the
object). The rapid spin of a top that causes its surface to blur is
rotation.
Precession is a second-order motion. It is therotation of a rotating object.
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Rotation or spin of the top about its own axis is first-order
motion.
Precession of the top about the vertical axis (axis
of gravity) is second-order motion.
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ROTATION AND PRECESSION
In the macroscopic world, rotating objectshave the property of angular momentum.
Nuclei react to forces in the microscopic world
just as objects with angular momentumrespond to forces in the macroscopic world.
Protons and other subatomic particles are
assumed to rotate about their axes and aredescribed as having spin.
Precession results from the interaction of
forces with a rotating object.
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Diagram of forces acting to cause precession.
Angular momentum and gravity interact to cause
precession of a gyroscope.
Magnetic moment and a magnetic field interact to cause
precession of a proton.
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The frequencyfof precession of a proton in
units of megahertz (106 cycles or rotations persecond) depends upon its gyromagnetic ratio
(in megahertz pertesla) and the strength B
(in tesla, T) of the static magnetic field.
This relationship is described by the Larmor
equation.
f = B
The frequency of precession is known as the
Larmor frequency.
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Gyromagnetic ratios for a number of nuclei are
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INTERACTION OF NUCLEI WITH A RADIO
FREQUENCY WAVE: NUTATION
There is a third-order property of an object
that is rotating (first-order property) and
precessing (second-order property).
This property, called nutation, is the result of
forces that rotate with the precession of the
object.
When force is applied to an object with
angular momentum, the object tends to move
at right angles to the force.
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Attempting to push a gyroscope in the direction of
precession causes the gyroscope to change its angle of
precession. Change in the angle of rotation is referred
to as nutation.
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if we push in the direction of precession, the
gyroscope precesses at a greater angle until it
finally lies flat on the table.
Precessing object responding to a force by
moving at a right angle to the force, thereby
changing its angle of precession. This change in angle, called nutation, is a
third-order circular motion (after rotation and
precession). In magnetic resonance of protons, the force
that causes nutation is provided by a second
magnetic field that varies with time.
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Each time the protons magnetic moment
comes around during precession, the second
magnetic field is switched on.
As the magnetic moment rotates away, the
magnetic field is switched off.
More precisely, the ons and offs are the
peaks and valleys of a continuously varying
magnetic field.
Larmor equation may be used to predict thefrequency of precession of a proton in a
magnetic field.
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The range of static field strengths employed in clinical
MRI, 0.1 to 3.0 tesla, corresponds to precessional
frequencies of 4.3 to 129 MHz for hydrogen nuclei.
The time-varying magnetic field of an electromagnetic
wave with a frequency in the megahertz range is a
suitable source for inducing nutation.
When this wave has a frequency that matches the
precession of protons in a particular magnetic field, it
is said to be in resonance.
This is the origin of the term magnetic resonance. Appropriate frequencies are in the FM radio portion of
the electromagnetic spectrum. Thus, we refer to the
use of RF pulses in MR.
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Rotation: Cyclical motion of an object about
an axis.
Precession: Compound motion of a rotating
object about an axis other than its axis of
rotation. The angle between the axis of
rotation and the axis of precession is known as
the angle of precession.
Nutation: Change in the angle ofprecession.