This document provides an overview of the physics principles behind Magnetic Resonance Imaging (MRI). It discusses how MRI works by using strong magnetic fields to align the spin of hydrogen protons in the body. When radiofrequency pulses are applied, the protons absorb energy and their spins are tipped into the transverse plane, generating a signal that is picked up by the MRI machine. The signal provides information used to create grayscale images of tissues and organs. The document also introduces key MRI concepts like spin states, precession, T1 and T2 relaxation times, and basic pulse sequences. An experiment is described that allows students to collect MRI data using a pulsed nuclear magnetic resonance spectrometer in order to better understand the physics behind the imaging process.

1. Lab Exploring the Fundamental Physics
Behind Magnetic Resonance Imaging
By
MARISSA S. MURAOKA
Department of Physics
PACIFIC UNIVERSITY
A thesis submitted to Pacific University in accordance with
the requirements of the degree of BACHELOR OF SCIENCE IN
PHYSICS WITH HEALTH EMPHASIS.
MAY 2015

3. ABSTRACT
A
n increase in the use of Magnetic Resonance Imaging (MRI) in the health care field has
inspired more students to understand and explore the physics behind the imaging process.
As an addition to the Modern Physics with Health Applications course offered at Pacific
University, a complete laboratory experiment was designed to enable students to stake data
from small-scale MRI simulations using a Teach Spin PSI-A Pulsed Nuclear Magnetic Resonance
Spectrometer. The lab consists of prerequisite assignments, lab activities, and homework made
for future students and faculty. The primary objective of the experiment is to obtain the two
times a MRI uses to create an image: spin-lattice relaxation time (T1) and spin-spin relaxation
time (T2). Completion of the lab activities will help students to make data-supported conclusions
about the physics concepts and principles involved in MRI based on their own findings.
i

5. DEDICATION AND ACKNOWLEDGEMENTS
T
hank you to the Pacific University Physics Department.
iii

7. AUTHOR’S DECLARATION
I
declare that the work in this dissertation was carried out in accordance with the
requirements of the University’s Regulations and Code of Practice for Research
Degree Programmes and that it has not been submitted for any other academic
award. Except where indicated by specific reference in the text, the work is the
candidate’s own work. Work done in collaboration with, or with the assistance of,
others, is indicated as such. Any views expressed in the dissertation are those of the
author.
SIGNED: .................................................... DATE: ..........................................
v

9. TABLE OF CONTENTS
Page
List of Tables ix
List of Figures xi
1 Introduction & Background 1
1.1 An MRI Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Magnet Composition 9
3 Contrast Determinants in MRI 11
3.1 T1: Spin-Lattice Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 T2: Spin-Spin Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Basic MRI Pulse Sequences 15
4.1 Spin-Echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Inversion Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5 Equipment Used in Experiment & their Relation to the MRI Process 19
5.1 Magnetic Torque Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2 Pulsed Nuclear Magnetic Resonance Spectrometer . . . . . . . . . . . . . . . . . . . 22
6 Conclusion: Testing & Future Directions 25
A Appendix A: Finding T1: Spin-Lattice Relaxation Time 27
B Appendix B: Finding T2: Spin-Spin Relaxation Time 29
C Appendix C: How to Use a Digital Oscilloscope 31
D Appendix D: MRI Terminology Glossary 33
Bibliography 35
vii

11. LIST OF TABLES
TABLE Page
3.1 T1 Signal Differences in Tissues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 T2 Signal Difference in Tissues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
ix

13. LIST OF FIGURES
FIGURE Page
1.1 Spin Up & Spin Down State of Hydrogen Nuclei . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 The Proton as a Mini-Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Precession Frequencies of Isotopes Imaged in MRI . . . . . . . . . . . . . . . . . . . . . 5
1.4 Magnetic Resonance Imaging Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Nuclear Precession Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Parallel and Anti-Parallel Alignment, Revisited . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 The Dangers of MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1 Lewis Structure of a Fat Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Lewis Structure of a Water Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.1 Example Spin-Echo Pulse Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.1 Teach Spin Magnetic Torque Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.2 Permanent Magnets of Magnetic Torque Apparatus . . . . . . . . . . . . . . . . . . . . . 21
5.3 Teach Spin PSI-A PNMR Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.4 Teach Spin PSI-A Power Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
xi

15. CHAPTER
1
INTRODUCTION & BACKGROUND
N
uclear Magnetic Resonance, or the ability of atoms to emit and absorb radiation when
immersed in an external magnetic field, was discovered independently in liquids and
solids by Edward Purcell & Felix Bloch in 1946. In 1950, Erwin Hahn found that this
technology could be honed further by implementing radiofrequency pulses to correct for magnetic
field inhomogeneities, and used to create one-dimensional images. The imaging process was
refined by Paul Lauterbur in 1972 and his findings are used widely in present times to generate
two dimensional gray-scale images. The word nuclear was removed, and the technology coined
Magnetic Resonance Imaging (abbreviated MRI), has become one of the most widely used forms
of medical imaging due to its lack of invasive procedural techniques. The imaging process relies
on interactions that can be explained in terms of physics and thus can be analyzed for educational
purposes.
Each year, approximately 30 million people in the United States receive an MRI. Therefore,
understanding how an MRI works can prove of interest to health care professionals and the
general public alike. Pacific University offers a course titled "Modern Physics with Health
Applications" alternate fall semesters that aims to expose students to the physics involved in the
world of medicine. Existing course lab activities include a nuclear medicine analysis, a radiation
therapy simulation, and partial exposure to the underlying physics behind MRI. As a complement
to the pre-existing MRI course material, a lab was created for the course that will allow students
to delve deeper into the physics involved in the MRI process and will prove beneficial for those
seeking to pursue a career in the health care field.
1

16. CHAPTER 1. INTRODUCTION & BACKGROUND
1.1 An MRI Overview
Everything in our world is made up of atoms. Atoms are made up of protons (positive charge),
neutrons (no charge), and electrons (negative charge). Atoms of each element are made unique by
their characteristic amount of protons, which give them a unique signature as evidenced by the
Periodic Table of the Elements. The MRI machine generates a gray-scale image of the desired
part of the body by measuring timed quantities and interactions between protons in the body
part and an extremely powerful magnetic field.
Each atom possesses angular momentum, a result of the sum of the angular momentum
of all its constituents. The protons and neutrons (called nucleons) housed in the nucleus have
angular momentum, which is described as spin in Quantum Mechanics. The "Quantum" term
in Quantum Mechanics alludes to the fact that amounts of any property are quantized. Each
unpaired electron, proton, and neutron has a spin quantized as +1/2 or -1/2. This is shown in
Figure 1.1.
The protons and neutrons, moving charges, generate a dipole magnetic field around them as
they move. For purposes of simplicity, one can think of each proton as a mini magnet, illustrated
in Figure 1.2. The net magnetization of all the protons in a single nucleus is represented by the
vector quantity µ. The sum of all µ for a sample is represented by the Net Magnetization Vector
which is abbreviated by NMV or the vector M.
Due to its natural abundance, the most commonly imaged element is Hydrogen. This is shown
in Figure 1.1. Hydrogen has one unpaired proton, so the terms Hydrogen, proton, and nuclei are
used interchangeably when dealing with MRI.
When placed in a magnetic field (B0), any particle with spin can absorb a photon. To be ab-
sorbed, the photon must be emitted at an isotope-specific frequency called the Larmor Frequency
ωL. It is made isotope-specific by the constant of proportionality, γ, The Gyromagnetic Ratio. γ
measured in MHz/T, is the ratio of an object’s µ to its Moment of Inertia, I. This is shown in
Equation (1), and Equation (2), respectively. Absorption of the photon at the ωL causes the nuclei
of the sample to switch spin states. This means that protons that have a -1/2 spin can absorb
a photon and switch the sign of its spin to +1/2. Likewise, protons with a +1/2 spin can emit a
photon and have a spin of -1/2.
(1) ωL = γ×B0
(2) γ = µ/I
When a person is first placed in into the MRI machine shown in Figure 1.1, they are exposed
to B0. The earth is known to have a magnetic field strength of approximately 0.5 Gauss (G). MRI
machines utilize magnets that have a field strength of 1.5 Tesla (T), where 1 Tesla = 10,000 Gauss.
2

17. 1.1. AN MRI OVERVIEW
FIGURE 1.1. Two hydrogen nuclei, one in the spin up state, and one in the spin down
state. The spin up state is synonymous with parallel alignment & the spin down
state is synonymous with anti-parallel alignment. The two spin states are related
to the intrinsic energy of each nucleus. Nuclei in the parallel energy state do not
possess enough energy to overcome B0. As a result, spin up nuclei are designated
as lower in energy than those in spin down states.
3

18. CHAPTER 1. INTRODUCTION & BACKGROUND
Figure 1.2: Each proton generates a magnetic field around it as it moves inside the nucleus. The
magnetic field has two poles, just like a basic magnet. For purposes of simplicity, we can think
of each proton in the sample as a mini magnet, whose net magnetization is represented by the
vector quantity µ, the nuclear Magnetic Moment. The sum of all µ in a sample is expressed as
the Net Magnetization Vector (NMV), or M.
B0 causes the protons in the body to align parallel (the same direction) or anti-parallel (the
opposite direction) to the magnetic field. The two alignments are related to the two spin states of
the nuclei: spin up (spin of +1/2) is another term used to reference parallel alignment. Spin down
(spin of -1/2) is synonymous with anti-parallel alignment. Alignment is related to energy levels
(E) of the nuclei. Spin down nuclei have E = −µ×B and spin up nuclei have E = µ×B.
More nuclei prefer the parallel alignment state because it is lower in energy. Protons in the
anti-parallel state possess intrinsic energy at the time B0 is applied, so they are able to overcome
the magnetic field and align against it. Nuclei in the parallel state are unable to overpower the
magnetic field, and thus are forced to go along with it. For every one million nuclei in the sample,
about 3 more will prefer the parallel state. Any pair of parallel/anti-parallel magnetic moments
will neutralize each other in terms of magnetization. More nuclei prefer the parallel state so M
will align along the positive z-axis after the nuclei have all finished aligning - a state referred to
as Thermal Equilibrium. 1019
protons exist in one cubic centimeter of tissue, so there is never a
shortage of nuclei to supply M. [3]
4

19. 1.1. AN MRI OVERVIEW
Figure 1.3: Precession frequencies of Isotopes most commonly used in MRI. Hydrogen is the most
commonly imaged element, due to its natural abundance of 99.98 %. [6]
The number of nuclei that align with the spin up state over the spin down state is proportional
to strength of B0. The stronger the field, the more nuclei that end up in the parallel alignment.
In fields outside of health care such as research, magnets of up to 60 Tesla are used to generate
the best quality image possible. [5]
Alignment of the nuclei is also accompanied by a Torque-induced (τ) effect called precession.
This can be thought of as what happens to a toy top when it is spun on a tabletop. Before it falls
to its side, the top begins to wobble - the wobbling effect of the top caused by gravitational torque
is analogous to the precession the nuclei experience around the z-axis as a result of B0. This
is illustrated in Figure 1.5, and is represented by Equation (3). The nuclei precess constantly
throughout the MRI process from the moment B0 is applied. This is what generates a signal,
which is picked up on by the MRI’s pickup coils and read to generate an image.
(3) τ = µ×B0
This changes the understood definitions of parallel and anti-parallel alignment. Not only are
the µ of the nuclei aligned in the same or opposite direction to B0, they are also offset by an angle
θ, and are precessing around the axis of magnetization, as shown in Figure 1.6.
From thermal equilibrium, a radiofrequency (RF) pulse is applied to the nuclei, and causes
M to be tipped into the transverse (xy-plane). The RF pulse is generated by coils oriented
perpendicular to B0. The nuclei absorb this energy and switch spin states, and as a result become
5

20. CHAPTER 1. INTRODUCTION & BACKGROUND
Figure 1.4: The Magnetic Resonance Imaging apparatus. The permanent magnets of the MRI,
and the coils that generate the RF pulse are housed in the doughnut-shaped portion of the
machine. The flat attachment is where the patient is positioned to receive the scan.[5]
"in phase" in with one another. In phase means that all the nuclei’s µ are pointing in the same
direction. It is the point at which the M has it’s greatest strength. The energy-induced state is
temporary and the nuclei eventually make their way back to their original alignment once the
RF pulse is turned off & emit a signal as they do so. The MRI machine’s pickup coils, which can
only measure transverse magnetization, pick up on the signal and match it to a contrast gradient
which produces a gray-scale image.
6

21. 1.1. AN MRI OVERVIEW
Figure 1.5: A toy top, experiencing precession due to the torque imposed on it by the force of
gravity. τ imposed on the top as a result of the gravitational field is analogous to the τ imposed
on the nuclei by B0. L, the angular momentum of the top corresponds to µ of the nuclei.
7

22. CHAPTER 1. INTRODUCTION & BACKGROUND
Figure 1.6: It is important to recognize that the nuclei, which align in parallel or anti-parallel
to B0 shown on the left, are also precessing around the z-axis, at an angle θ off of the axis of
magnetization. This is due to τ imposed on them from B0. Precession occurs throughout the
entire MRI process from the moment B0 is applied.
8

23. CHAPTER
2
MAGNET COMPOSITION
M
agnets can be made of various metals, but the most commonly used in Magnetic
Resonance Imaging are iron, cobalt, and nickel. Often alloys of these metals are used,
with the most common being a combination of aluminum, nickel, and cobalt called
AlNiCo.
One way magnetic fields are generated in MRI is through electromagnets. Electromagnets
use the movement of current through wires to create a magnetic field. There are different types
of electromagnets used in MRI, and these magnets are responsible for generating the RF pulse
applied to the nuclei of the sample.
Resistive magnets generate a magnetic field of strength proportional to the amount of current
flowing through its wires. The field that is generated is perpendicular to B0. Ideally, wires with
the least amount of resistance are preferred so that less energy can be used to power the RF
pulse(s). The pulses of energy through these coils are responsible for the loud noises a patient will
hear while undergoing an MRI. The noise comes from the circulation of large pulses of electricity
flowing through the coils.
The strength of the magnetic field generated by the magnets, though necessary for creating
a quality image, poses one of the biggest dangers of receiving an MRI. Metal tools, or metal
embedded in the body can easily become deadly once the magnetic field is turned on. An example
of this is shown in Figure 2. [5]
All the energy rushing into the coils has to go somewhere, and it is released as heat. To
remedy for the heat that is created in the MRI process, the wires are cooled in a process called a
cryogen bath. The cryogen bath is either liquid helium or liquid nitrogen that surrounds the coils,
and is housed in a vacuum so that it doesn’t instantly evaporate.
9

24. CHAPTER 2. MAGNET COMPOSITION
Figure 2.1: A person shown holding a scissors in free-float in the magnetic field generated by
the permanent magnets of an MRI. Because the field is so strong, any type of metal should be
removed from the imaging area. [5]
10

25. CHAPTER
3
CONTRAST DETERMINANTS IN MRI
T
he differences in color in the gray scale image created in MRI are related to the signal
given off by the tissue. The image will show up as light, aka hyperintense, if there is a
large transverse component of magnetization when the signal is measured. Parts of the
image will show up as black (hypointense) if it has a small transverse component of magnetization
at the time the signal is measured.
Although there are many different types of contrast determinants in MRI, the most commonly
used are called T1 and T2. In a T1 weighted image, fats show up as bright. So T1 weighted images
are preferred for imaging soft, fatty-filled tissues like the brain. It is also used to view areas with
high protein content or slow blood flow. In a T2 weighted image, fluids show up as bright. T2
weighting is preferred when imaging diseased tissues, as diseased tissues typically have higher
water content. [3] T2 is the contrast determinant chosen to image tumors, edemas, and inflamed
areas in the body. In real MRI, T1 and T2 happen simultaneously - in fact, some MRI images are
a blend of T1 and T2 weighting. For purposes of this experiment, it is useful to understand the
two weightings independently.
3.1 T1: Spin-Lattice Interaction
T1, also referred to as spin-lattice recovery/relaxation/interaction/delay time is the time constant
needed for the M to realign along the z-axis to 63% of its value at thermal equilibrium following
the removal of the RF pulse. It is a measure of how the energy given to the nuclei by the original
RF pulse is released to the surrounding environment. Not all tissues return to equilibrium at an
identical rate, so a tissue’s T1 allows the MRI to identify the tissue being imaged.
To understand why fats show up as bright in a T1 weighted image, one must consider their
11

26. CHAPTER 3. CONTRAST DETERMINANTS IN MRI
molecular structure. The molecule is large, and the atoms are closely packed together. Because of
this, the molecules are not able to move very quickly, and therefore do not possess much inherent
energy. When the RF pulse is removed, the Hydrogen nuclei are able to release the energy into
the fat molecule (their surroundings), which efficiently absorbs the energy. A lewis structure of a
fat molecule illustrating the network of Hydrogen with other elements is shown in Figure 3.1.
In contrast, fluids like water shown in Figure 3.1, are made up of molecules that are very
small. This means that the water molecules have a lot of space to move, and thus more inherent
energy. The nuclei don’t have as much "free-space" to put the energy received by the RF pulse,
and thus T1 is longer in fluids, as the nuclei take longer to disperse the energy to the water
molecule. In Table 3.1, contrast signals of different tissues are described.
T1 Signals of Different Tissues
Signal Tissue Being Imaged
High Cysts with Proteinaceous Fluid
High Methaemoglobin
Low Infections
Low Tumors
None Air
None Scar Tissue/Calcification
Table 3.1: T1 signals of different tissues. In a T1 weighted image, fatty-filled tissues/tissues with
high protein content show up as hyperintense, while tissues with high fluid content show up as
dark. Tissues with no fatty or proteinaceous content do not show up in a T1 weighted image. [5]
T1 also depends on how closely the motion of the molecules matches ωL. If there is a good
match between ωL and the molecular tumbling, then energy is effectively exchanged between
Hydrogen and the surrounding molecular lattice.
In a T1 weighted image, a short TE and short TR are desirable. TE, known as the "time to
echo" is the time between the RF pulse and the maximum signal received by the MRI. TR is
called the repetition time and is the time between RF pulses. In T1 weighting, the differences
between T1 and T2 readings have to be exaggerated to form a contrast. To reduce the effects of
T2, the TE has to be short.
3.2 T2: Spin-Spin Interaction
T2, which is known as spin-spin relaxation/interaction/decay time is the amount of time it takes
for the nuclei’s magnetic moments to become out of phase with one another in the transverse
plane. This corresponds to 63 % of the transverse magnetization being lost. The nuclei, all as
individual precessing mini-magnets, generate magnetic fields that influence the magnetic fields
of the nuclei around them. This causes their magnetic moments to point in different directions
12

27. 3.2. T2: SPIN-SPIN INTERACTION
Figure 3.1: The Lewis Structure of a fat molecule. The molecule is a large chain of atoms. Because
of their spacing, the nuclei do not possess much inherent energy.
than along the net magnetization vector. The loss of phase coherence causes the decay signal
of M in the transverse plane, whose time constant is T2. In Table 3.2, differences in signal of
T2-weighted images are described.
TE in T2 decay must be long (>70 mS) because water and fats both take a substantial amount
of time to decay in the transverse plane. The effects of T1 must also be extinguished as much as
possible. To cause this, TR in a T2-weighted is also quite long (>2000 mS).
13

28. CHAPTER 3. CONTRAST DETERMINANTS IN MRI
Figure 3.2: The Lewis Structure of a water molecule. The molecule is small, with only 3 atoms.
Because of it’s size, the nuclei possess greater inherent energy in comparison to large molecules
like fat.
T2 Signals of Different Tissues
Signal Tissue Being Imaged
High Infection
High Haemorrhage
Low Calcification
Low Deoxyhaemoglobin
None Air
None Scar Tissue/Calcification
Table 3.2: T2 signals of different tissues. In a T2 weighted image, fluid-filled tissues/tissues with
high water content show up as hyperintense, while tissues with low fluid content show up as
dark. Tissues with no fluid content do not show up in a T1 weighted image. [5]
14

29. CHAPTER
4
BASIC MRI PULSE SEQUENCES
Usually, before T2 can be measured, a process called T2* occurs. T2* is another timed property of
the nuclei that results from the magnetic field being inhomogenous in some areas. Unfortunately
there is no such thing as a completely homogenous magnetic field in MRI. Hypothetically speaking,
if a sample were to be placed in a completely uniform magnetic field, then T2=T2∗ The differences
in magnetic field affect the proton’s rate of precession, and cause them to precess at different
rates. We can verify through Equation (1). The difference in rates of precession cause the µ of the
nuclei to "fan out" around the z-axis and cancel out the signal of M.
The exponential loss of signal strength is remedied by a pulse sequence, a series of RF pulses.
The RF pulses refocus the nuclei and cause them to be in phase so that a signal can be read by
the MRI’s pickup coils. The pulses can also manipulate the NMV into different planes.
4.1 Spin-Echo
T
he most basic pulse sequence in MRI is called "Spin-Echo". Spin Echo involves the
incorporation of two RF pulses. The first pulse in any sequence referred to as the "A"
pulse. Any subsequent pulse following the A pulse is referred to as a "B" pulse. The
A pulse in a Spin Echo pulse sequence tips the NMV 90 degrees, and can also be referred to
as a π/2 pulse. It flips the NMV from the positive z-axis into the transverse plane. Next, any
subsequent pulse called a B pulse of magnitude 180 degrees (also called a π pulse) causes the
nuclei to partially re-phase, and produces an observable signal called an "echo". An example
pulse sequence is shown in Figure 4.1. The relationship between T2 and T2* is illustrated by
Figure 4.1. The 180 degree RF pulse used to generate the echo re-phases the spins that have
undergone T2* decay. The signal decay from subsequent echos is from T2.
15

30. CHAPTER 4. BASIC MRI PULSE SEQUENCES
Figure 4.1: Example Spin-Echo pulse sequence. After the initial π/2 pulse,the nuclei are in phase.
As they start to de-phase, they emit a signal called the Free Induction Decay. Then, before
dephasing completely occurs, the nuclei are re-phased by a 180 degree pulse. This is applied at
time interval τ after the π/2 pulse. As the nuclei make their way back to thermal equilibrium,
they emit a signal that is called an echo. The echo is smaller in magnitude than the original
RF pulse. Note that the lower part of the figure, which shows the re-phasing of the nuclei, is
illustrated from the point of view of the rotating reference frame [2]
16

31. 4.2. INVERSION RECOVERY
Erwin Hahn, who originally thought of implementing a Spin-Echo pulse sequence to account
for inhomogeneities in the magnetic field, described the re-phasing using this analogy:
Let a team of runners with different but constant running speeds start off at a time
t = 0 as they would do at a track meet... At some time T these runners would be
distributed around the race track in apparently random positions. The referee fires
his gun at a time t = τ > T, and by previous arrangement the racers quickly turn
about-face and run in the opposite direction with their original speeds. Obviously, at
a time t = 2τ , the runners will return together precisely at the starting line. [1]
In simple terms, even though some nuclei begin to get "ahead" and precess faster than other
nuclei, they all end up back in the same place due to the re-phasing pulse.
4.2 Inversion Recovery
Inversion recovery sequences can be thought of as the direct opposite of Spin-Echo in terms of
how the RF pulses are applied. The A pulse in an Inversion Recovery sequence is the 180 degree
pulse. This flips the NMV from the positive z-axis to the negative z-axis. The B pulse moves the
NMV into the transverse plane (a π/2 pulse), which allows the pickup coils of the MRI to generate
a reading as it moves back to thermal equilibrium.
17

33. CHAPTER
5
EQUIPMENT USED IN EXPERIMENT & THEIR RELATION TO THE
MRI PROCESS
5.1 Magnetic Torque Apparatus
The Magnetic Torque Apparatus manufactured by Teach Spin will give students a "warm up" in
understanding Magnetic Resonance Imaging. Shown in Figure 5.1, it comes with four components:
a power supply, a set of magnetic coils, a set of external permanent magnets, and a yellow magnetic
cueball.
The cueball represents a single proton. Its black handle represents µ. The set of Helmholtz-
like coils carry a current that can be controlled from the power supply. The current creates a
magnetic field whose positive z-axis is straight up from the center of the top coil (by the right
hand rule). When the students spin the cueball in its holder when the field is turned on, they find
that the cueball will begin to precess along the positive z-axis of the coils. The torque imposed on
the cueball parallels B0 of the MRI imposed on the protons in the body. The permanent magnets
of the Magnet Torque apparatus, which have a field strength of 1 mT, will be used to represent
the RF pulse. When the permanent magnets are rotated at the Larmor Frequency around the
cueball bearing, the cueball will tip into the horizontal plane and begin to precess around the
permanent magnet’s field. The time it takes to rotate the magnets until the tipping occurs is
representative of the pulse width used in a pulse sequence.
An essential piece of knowledge that the students will gain from this series of lab activities is
recognizing that there are two different types of precession occurring. Each magnetic field causes
τ that induces precession. The original applied external magnetic field, B0 from the coils, causes
the nuclei to precess around the z-axis. The second magnetic field, in the form of the RF pulse
generated by the permanent magnets, causes the nuclei to precess in the transverse plane as
19

34. CHAPTER 5. EQUIPMENT USED IN EXPERIMENT & THEIR RELATION TO THE MRI
PROCESS
Figure 5.1: The Teach Spin Magnetic Torque Apparatus. Described from left to right: The two
coils responsible for generating the magnetic field, B0 (with the cueball shown inside), and the
power supply. Students will complete a series of mini-experiments to understand how different
aspects of an MRI process affect a single Hydrogen nucleus, represented by the yellow cueball.
The cueball rests on a bearing that allows it to move with as little friction as possible. The black
handle on the cueball represents the magnetic moment of the nucleus. The Magnetic Torque
Apparatus also has a strobe light that allows the students to measure the rotational frequency of
the cueball. The permanent magnets are shown in Figure 5.1.
The magnetic field is analogous to the magnetic field generated by electromagnets in MRI.
well. Both of these precessions are occurring at the same time, which is precisely why T1 and T2
effects happen simultaneously in MRI and PNMR.
Until now, the topic and concept of spin and precession has always been addressed in the
outside/laboratory frame. But if data is taken from a rotating frame of reference, it is easier
to take data measurements. We can think of two rotating frames of reference in this lab. One
rotating frame is taken from the NMV as it returns to thermal equilibrium. If data is taken
from the rotating frame, then NMV’s path as it makes its way to thermal equilibrium represents
exponential recovery, whose time constant is T1. Another rotating frame can be placed on the
transverse magnetization as de-phasing occurs. If the rotating frame moves at the mean frequency
of the de-phasing nuclei, then the "fanning-out" that occurs as the nuclei de-phase makes it easier
to measure T2 as the nuclei’s magnetic moments align themselves in random orientations around
20

35. 5.1. MAGNETIC TORQUE APPARATUS
Figure 5.2: Permanent Magnets of the Magnetic Torque Apparatus shown around the ball bearing
hosting the magnetic cueball. The permanent magnets, which create a field strength of 1 mT
(milliTesla), cause the cueball to "tip" into the transverse plane. The students will manually
rotate the permanent magnets at the Larmor Frequency to observe the tipping. The time it takes
to rotate the magnets until the tipping occurs is analogous to the pulse width of PNMR.
21

36. CHAPTER 5. EQUIPMENT USED IN EXPERIMENT & THEIR RELATION TO THE MRI
PROCESS
the z-axis.
The permanent magnets, analogous to the RF pulse in actual MRI and PNMR, trick the
nucleus into falling into a moving frame of reference. This is why the cueball precesses around
the field of the permanent magnets when they are rotated at the Larmor Frequency.
Understanding the concepts of how magnetic fields induce τ on the cueball, how the nucleus
behaves when the spins are tipped, how the RF pulse causes the spins to tip (or flip in PNMR/MRI),
and how the incorporation of a rotating frame of reference can be useful in data collection will
give students a solid foundation to start working with the PNMR Spectrometer.
5.2 Pulsed Nuclear Magnetic Resonance Spectrometer
Although students will be unable to generate T1 and T2 gray-scale images using the PSI-A model
PNMR Spectrometer manufactured by Teach Spin, they’ll still be able to use the equipment
to pick up on T1 and T2 signals because PNMR and MRI both rely on the same fundamental
technology.
The Pulsed Nuclear Magnetic Resonance Spectrometer includes a permanent magnet, cross
coil sample probe, and three electronic modules that produce a signal shown on a digital oscillo-
scope. The setup is shown in Figure 5.2.
Quoted from Teach Spin’s conceptual introduction to the equipment:
The three electronic modules are a receiver, pulse programmer, and mixer. The
receiver amplifies the signal coming from the pickup coil, which measures transverse
magnetization. The mixer multiplies the RF signal from the transmitter coil with the
actual precession frequency of the protons as sensed by the pick up coil. This allows
the experimenter to see if they are the same. When the oscillator is properly tuned to
the resonant frequency, the signal output of the mixer should show no “beats." [7]
No beats refers to a Free Induction Decay Signal shown on the oscilloscope. The frequency
adjust tuning can then be used to match the frequency of the RF pulse to the nuclei’s precession
frequency. The precession frequency drifts because the temperature of the permanent magnet is
not absolutely constant. Any change in magnet temperature causes a change in B0 and thus in
the precession frequency."
The pulse programmer of the apparatus allows the student to implement their designed pulse
sequence with a series of A and B pulses. The pulse width of each pulse can be changed along
with the delay time between pulses. Repetition time allows the students to change how often the
pulse sequence is repeated.
As mentioned by Teach Spin’s conceptual introduction, the magnetic field is extremely tem-
perature dependent. The students will realize this as they complete a pre-requisite lab activity
that requires them to plot the magnetic field at various locations over a period of time. To remedy
this, a cooler can be placed around the permanent magnets so that the temperature remains
22

37. 5.2. PULSED NUCLEAR MAGNETIC RESONANCE SPECTROMETER
Figure 5.3: The TeachSpin PSI-A Permanent Magnet Apparatus. Shown from left to right in the
image: The permanent magnets (housing the cross-coil sample probe), the three-module power
supply, and on top of it, a digital oscilloscope that displays T1 and T2 signals obtained from the
sample. A close up view of the power supply is shown in Figure
uniform. If a cooler is not used, the temperature measurements should be made quickly to prevent
disparities in the data.
23

38. CHAPTER 5. EQUIPMENT USED IN EXPERIMENT & THEIR RELATION TO THE MRI
PROCESS
Figure 5.4: A close up view of the three electronic modules that are used to measure T1 and
T2 times of a sample. The receiver amplifies the signal coming from the pickup coil. The pulse
programmer allows the student to implement their own pulse sequence with a series of A and B
pulses. The oscillator allows the student to adjust the applied frequency, which can vary based on
temperature.
24

39. CHAPTER
6
CONCLUSION: TESTING & FUTURE DIRECTIONS
T
he completed lab documents are now in the testing phases, and can be found attached in
the Appendices. The versions attached are the faculty versions, that contain the questions
asked, and answers. The completed documents are available in a Google Drive Folder.
First, the students will use a Quizlet program file to familiarize themselves with MRI
terminology. There is also a handout, which was obtained from Massachusetts Institute of
Technology’s MRI website, that has a glossary of all the terms used for purposes of reference.
Once they’ve played the online learning game on Quizlet, they’ll complete the pre-requisite lab
activities using the Magnetic Torque Apparatus. These lab activities are already in existence and
are not included in the google drive folder.
Then, once they’ve completed the Magnetic Torque pre-labs, they’ll use the PNMR Spectrome-
ter to find the T1 and T2 times of various liquids. The liquids chosen for experimental purposes
are at the discretion of the instructor. The guide written for finding T1 and T2 times is written
for water, mineral oil, or vegetable oil.
Two student testers were able to test the lab - one will be taking Modern in fall. The measured
T2 was not within the accepted range for mineral oil, which is around 15 µseconds. But, we are
currently in the process of retaking data and refining the process so that more accurate T1 and
T2 times can be recorded in the future.
It is my hope that by completing these lab activities, students will be able to understand more
about the physics behind Magnetic Resonance Imaging by allowing them to delve deeper into
exploring the physics involved in the MRI process.
25

41. APPENDIX
A
APPENDIX A: FINDING T1: SPIN-LATTICE RELAXATION TIME
The documents are included as screenshots of a PDF format because incorporating them into this
Latex document made the file size too large to compile. Page breaks correspond to page breaks in
the lab, not in the design of the thesis.
27

43. APPENDIX
B
APPENDIX B: FINDING T2: SPIN-SPIN RELAXATION TIME
The documents are included as screenshots of a PDF format because incorporating them into this
Latex document made the file size too large to compile. Page breaks correspond to page breaks in
the lab, not in the design of the thesis.
29

45. APPENDIX
C
APPENDIX C: HOW TO USE A DIGITAL OSCILLOSCOPE
The documents are included as screenshots of a PDF format because incorporating them into this
Latex document made the file size too large to compile. Page breaks correspond to page breaks in
the lab, not in the design of the thesis.
31

47. APPENDIX
D
APPENDIX D: MRI TERMINOLOGY GLOSSARY
The documents are included as screenshots of a PDF format because incorporating them into this
Latex document made the file size too large to compile. Page breaks correspond to page breaks in
the lab, not in the design of the thesis. This document was found online, on MIT’s website. [4]
33

49. BIBLIOGRAPHY
[1] E. L. HAHN, Free nuclear induction, Physics Today, (1953), p. 8.
[2] R. V. D. J. STOLTENBERG, D. PENGRA AND O. VILCHES, Pulsed Nuclear Magnetic Resonance,
PhD thesis, Rutgers, feb 2006.
[3] J. B. J. SWAIN, K. BUSH, Diagnostic Imaging for Physical Therapists, Saunders Elsevier.
[4] R. S. . J. JOVICICH, Mri glossary.
Obtained from Massachusetts Institute of Technology, Fall 2011.
[5] C. WESTBROOK, MRI at a Glance, Wiley Blackwell, 2010.
[6] T. A. WILKINSON, Mri latex table.
http://tinkertailorsoldiersponge.com/tag/mri/, jul 2003.
[7] B. WOLFF-REICHERT, Conceptual tour of pnmr.
Instruction Manual From Teach Spin, mar 2003.
35