- 1.The Study Sr. Secondary School Badi, Udaipur Project to be
submitted for the partial fulfillment of CBSE, Class XII, Practical
Examination 2006-07 Magnetic Resonance Imaging Submitted by:Kartik
Gupta Submitted to:Mr. Mukesh Shrimali
2. Curriculum Vitae
- Fathers Name:Lt Col Jayant Gupta
- Name of the School:The Study Senior SecondarySchool,
Udaipur
- CBSE Roll Number: 1228536
- CBSE Registration Number:A/05/03732/059693
- Address:12-B, Pologround, Saheli Marg, Udaipur
3. Certificate This is to certify that Mr.Kartik Guptaof Class
XII has satisfactorily completed the course of experiments and the
project report in practical Physics prescribed by the Central Board
of Secondary Education in the laboratory ofThe Study Senior
Secondary School, Udaipur in the year2006-07 . Date :Signature of
the Teacher-in-chargeSignature of the Principal 4.
Acknowledgement
- This project was made under the able guidance of Mr. Mukesh
Shrimali. It was through his untiring efforts that I have been able
to present my work with such clarity and precision.
5. Preface
- Magnetic resonance imaging (MRI), formerly referred to as
magnetic resonance tomography (MRT) or nuclear magnetic resonance
(NMR), is a method used to visualize the inside of living organisms
as well as to detect the composition of geological structures. It
is primarily used to demonstrate pathological or other
physiological alterations of living tissues and is a commonly used
form of medical imaging. MRI has also found many novel applications
outside of the medical and biological fields.
- NMR studies a magnetic nucleus, like that of a hydrogen atom
(protium being the most receptive isotope at natural abundance) by
aligning it with a very powerful external magnetic field and
perturbing this alignment using an electromagnetic field. The
response to the field by perturbing is what is exploited in nuclear
magnetic resonance spectroscopy and magnetic resonance
imaging.
6. Magnetic Resonance Imaging Above: Magnetic Resonance
Imageshowing a vertical (sagittal) cross section through a human
head. 7. Contents
- MRI: Basic Theoretical Working
- Imaging using an MRI(Sequential & Graphical Display)
- The Physical Aspect Of MRI
- A Diagrammatic Representation of the Physical Aspect of
MRI
- Applications of MRI in Medicine
8. Credit of Discovery The foundations for imaging using
magnetic resonance were laid in 1946 by Bloch and Purcell; Bloch at
Stanford, studying liquids, and Purcell at Harvard, in solids.
Though they received Nobel prizes for their discovery, it was not
until 1973 that nuclear magnetic resonance (NMR) was used to
generate images. 9. Background
- Magnetic resonance imaging was developed from knowledge gained
in the study of nuclear magnetic resonance.
- The original name for the medical technology is nuclear
magnetic resonance imaging ( NMRI ), but the wordnuclearis almost
universally dropped.
- Nuclear magnetic resonance (NMR) is a physical phenomenon based
upon the magnetic property of an atom's nucleus.
- All nuclei that contain odd numbers of nucleons and some that
contain even numbers of nucleons have an intrinsic magnetic moment.
The most often-used nuclei are hydrogen-1 and carbon-13, although
certain isotopes of many other elements nuclei can also be
observed.
10.
- NMR studies a magnetic nucleus, like that of a hydrogen atom
(protium being the most receptive isotope at natural abundance) by
aligning it with a very powerful external magnetic field and
perturbing this alignment using an electromagnetic field. The
response to the field by perturbing is what is exploited in nuclear
magnetic resonance spectroscopy and magnetic resonance
imaging.
- NMR spectroscopy is one of the principal techniques used to
obtain physical, chemical, electronic and structural information
about a molecule. It is the only technique that can provide
detailed information on the exact three-dimensional structure of
biological molecules in solution. Also, nuclear magnetic resonance
is one of the techniques that has been used to build elementary
quantum computers.
11. A Typical MRI Machine 12. MRI: Basic Theoretical Working
- Like X ray, MRI is based on a discovery in the physic lab: when
the nuclei of hydrogen atoms--single protons, all spinning
randomly--are caught suddenly in a strong magnetic field, they tend
to line up like so many compass needles.
- If the protons are then hit with a short, precisely tuned burst
of radio waves, they will momentarily flip around.
- Then, in the process of returning to their original
orientation, they resound with a brief radio signal of their
own.
- The intensity of this emission reflects the number of protons
in a particular "slice" of matter.
13. Imaging using an MRI(Sequential & Graphical Display)
- Step One : A tomographic image is taken. A tomographic imageis
an image of a thin slice through an object.
14.
- Step Two:The signal in a Voxel (Volume Element) is mapped to
the intensity of a Pixel (The smallest element of a digital
picture).
15. Step Three: Zooming in on a Voxel Increasing Magnification
at each Step 16. The Physical Aspect of MRI
- Electrons, neutrons and protons, the three particles which
constitute an atom, have an intrinsic property called spin. This
spin is defined by the fourth quantum number for any given wave
function obtained by solving relativistic form of the Schrdinger
equation (SE). It represents a general property of particles which
we can describe using the properties of electrons. Electrons
flowing around a coil generate a magnetic field in a given
direction; this property is what makes electric motors work. In
much the same way electrons in atoms circulate around the nucleus,
generating a magnetic field. This generated field has an angular
momentum associated with it. It so turns out that there is also an
angular momentum with the electron particle itself, denoted the
spin, and this gives rise to the spin quantum number,m s .
- Spin angular momentum is quantized and can take different
integer or half-integer values depending on what system is under
study. If we solve the relativistic SE for the electron we get the
values + and -. Since the Pauli principle states that no two
fermions can have the same quantum number, it is why only two
electrons, paired antiparallel (one with positive spin and one
negative with negative spin), can appear in a single atomic
orbital.
17.
- Like the electron, protons and neutrons also have a spin
angular momentum which can take values of + and . In the atomic
nucleus, protons can pair with other antiparallel protons much in
the same way that electrons pair in a chemical bond. Neutrons do
the same. Paired particles, with one positive and one negative
spin, thus have a net spin of zero "0". We can see that a nucleus
with unpaired protons and neutrons will have an overall spin, with
the number unpaired contributing to the overall nuclear spin
quantum number,I . When this is larger than zero, a nucleus will
have a spin angular momentum and an associated magnetic moment, ,
dependent on the direction of the spin.It is this magnetic moment
that we manipulate in modern NMR experiments .
- It is worth noting here that nuclei can have more than one
unpaired proton and one unpaired neutron, much in the same way that
electronic structures in transition metals can have many unpaired
spins. For example 27Al has an overall spin I=5/2.
- A technique related to nuclear magnetic resonance is electron
spin resonance that exploits the spin of electrons instead of
nuclei. The principles are otherwise similar.
18.
- Values of spin angular momentum
- The spin angular momentum of a nucleus can take ranges from +
Ito Iin integral steps. This value is known as the magnetic quantum
number,m . For any given nucleus, there is a total (2 I +1) angular
momentum states. Spin angular momentum is a vector quantity.
Thezcomponent of which, denotedI z , is quantized:
-
- I z=mh /2 wherehis Planck's constant.
- The resultant magnetic moment of this nucleus is intrinsically
connected with its spin angular momentum. In the absence of any
external effects the magnetic moment of a spin nucleus lies
approximately 52.3 from the angular momentum axis or 127.7 for the
opposing spin. This magnetic moment is intrinsically related
toIwith a proportionality constant , called the gyromagnetic
ratio:
19.
- Spin behaviour in a magnetic field
- Consider the case of nuclei which have a spin of a half, like
1H, 13C or 19F. The nucleus thus has two possible magnetic moments
it could take, often referred to as up or down, + or - , which are
also called the spin states and . The energies of each state are
degenerate - that is to say that they are the same. The effect is
that the number of atoms, theirpopulation , in the up or state is
the same as the number of atoms in the state.
- If a nucleus is placed in a magnetic field, the angular
momentum axis coincides with the field direction. The resultant
magnetic momenta, space quantized from the angular momentum axis,no
longer have the same energysince one state has a z-component
aligned with an external field and are lower in energy (positive I
values) and the other opposes the external field and is higher in
energy. This causes a population bias toward the lower energy
states.
- The energy of a magnetic moment when in a magnetic fieldB 0 ,
the zero subscript is used to distinguish this magnetic field from
any other applied field, is the negative scalar product of the
vectors:
- We've already defined z =I z . So placing this in the above
equation we get:
20.
- The energy gap between our and states is ( hB 0 )/2. We get
resonance between the states, therefore equalizing populations, if
a radiofrequency is applied with the same energy as the energy
difference E between the spin states. The energy of a photon isE =h
, whereis its frequency.
- Thus, the frequency of electromagnetic radiation required to
produce resonance of a specific nucleus in a fieldBis:
- It is this frequency that we are concerned with, and detect in
NMR. And it is this frequency which describes the sample we are
observing. But importantly, it is this resonance that gives rise to
the nuclear magnetic resonance spectrum.
21.
- It would appear from the above equation that all nuclei of the
same nuclide, which have same the gyromagnetic ratio (y), resonate
at the same frequency. This is not the case. Since the gyromagnetic
ratio of a given nuclide does not change, we conclude that the
effect of the external magnetic field is different for different
nuclei. Local effects of other nuclei, especially spin-active
nuclei, and local electron effects shield each nucleus differently
from the main external field.
- It was stated that the energy of a spin state is defined by E=-
z B 0 . It can be seen that by shielding the strength of the
magnetic field, the experienced effect, oreffective magnetic
fieldat the nucleus is lower:B effective< B 0 . Thus the energy
gap is different, and hence the frequency required to achieve
resonance deviates from the expected value.
- These differences due to nuclear shielding give rise to many
peak frequencies in a nuclear magnetic resonance spectrum. It can
be seen why nuclear magnetic resonance is a direct probe of
chemical structure.
- It is possible for the shielding to change as the orientation
of the molecule, this is called chemical shift anisotropy, and can
even be used in some types of experiment. Especially if the sample
is solid, the external fields of the crystal structure interfere
with the nuclear field too much for the spectrum to be of any use.
Anisotropy is usually averaged out by spinning the sample. For
liquids, anisotropy is often relatively small, but the accuracy is
increased by using a pneumatic spinner to rotate the sample. For
solids, magic angle spinning at very high angular velocities (20
kHz) is used, since the anisotropy is often very large.
22.
- The process called population relaxation refers to nuclei that
return to the thermodynamic state in the magnet. This process is
also called T 1relaxation, where T 1refers to the mean time for an
individual nucleus to return to its equilibrium state. Once the
population is relaxed, it can be probed again, since it is in the
initial state.
- The precessing nuclei can also fall out of alignment with each
other (returning the net magnetization vector to a nonprecessing
field) and stop producing a signal. This is calledT 2 relaxation .
It is possible to be in this state and not have the population
difference required to give a net magnetization vector at its
thermodynamic state. Because of this,T 1is always larger (slower)
thanT 2 . This happens because some of the spins were flipped by
the pulse and will remain so until they have undergone population
relaxation. In practice, the T 2time is the life time of the
observed NMR signal, the free induction decay. In the NMR spectrum,
meaning the Fourier transform of the free induction decay, the T
2time defines the width of the NMR signal. Thus, a nucleus having a
large T 2time gives rise to a sharp signal, whereas nuclei with
shorter T 2times give rise to more broad signals. The length of T
1and T 2is closely related to molecular motion.
23. A Diagrammatic Representation of the Physical Aspect Of MRI
24. 25. Applications of MRI in Medicine
- In clinical practice, MRI is used to distinguish pathologic
tissue (such as a brain tumor) from normal tissue. One advantage of
an MRI scan is that it is harmless to the patient. It uses strong
magnetic fields and non-ionizing radiation in the radio frequency
range. Compare this to CT scans and traditional X-rays which
involve doses of ionizing radiation and may increase the chance of
malignancy, especially in a fetus.
- While CT provides good spatial resolution (the ability to
distinguish two structures an arbitrarily small distance from each
other as separate), MRI provides comparable resolution with far
better contrast resolution (the ability to distinguish the
differences between two arbitrarily similar but not identical
tissues). The basis of this ability is the complex library ofpulse
sequencesthat the modern medical MRI scanner includes, each of
which is optimized to provideimage contrastbased on the chemical
sensitivity of MRI.
26.
- For example, with particular values of theecho time(T E ) and
therepetition time(T R ), which are basic parameters of image
acquisition, a sequence will take on the property of T 2
-weighting. On a T 2 -weighted scan, fat-, water- and
fluid-containing tissues are bright (most modern T 2sequences are
actuallyfast T 2sequences). Damaged tissue tends to develop edema,
which makes a T 2 -weighted sequence sensitive for pathology, and
generally able to distinguish pathologic tissue from normal tissue.
With the addition of an additional radio frequency pulse and
additional manipulation of the magnetic gradients, a T 2 -weighted
sequence can be converted to a FLAIR (Fluid Light Attenuation
Inversion Recovery) sequence, in which free water is now dark, but
edematous tissues remain bright. This sequence in particular is
currently the most sensitive way to evaluate the brain for
demyelinating diseases, such as multiple sclerosis.
- The typical MRI examination consists of 5-20 sequences, each of
which are chosen to provide a particular type of information about
the subject tissues. This information is then synthesized by the
interpreting physician.
27.
Some Diagnostic Images
- Magnetic Resonance Imageshowing a vertical (sagittal) cross
section through a human head.
- Magnetic resonance angiography
- A fMRI scan showing regions of activation in orange, including
the primary visual cortex
28. Conclusion
- Nuclear Magnetic Resonance is the safest and the most advanced
diagnostic imaging instrument available in the international
market. Although its reach is limited to top class medical
institutions because of it its high price [costing approximately
US$1 million per tesla for each unit (common field strength ranges
from 0.3 to 3 teslas)] with several hundred thousand dollars per
year of upkeep costs], it still remains as one of the most reliable
tools of a neurologist.
29. Bibliography And References
- This project has been made with references made from:
30. The Study Sr. Secondary School Badi, Udaipur