Introduction to MRI Physics for the Undergraduate Med Student by the Undergraduate Med Student

8/3/2019 Introduction to MRI Physics for the Undergraduate Med Student by the Undergraduate Med Student

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Introduction to MRI Physics for the Undergraduate Med Student by the Undergraduate Med Student

By Juan Janse van Rensburg

Introduction

This guide is intended to improve an undergraduates understanding of how an MRI machine

functions. It contains the very basics of NMR imaging. The information herein is compiled from

various sources (listed below). It has not been reviewed by any person. It is not intended as a study

aide, merely to help a student get to grips with the basic concepts which are used in NMR imaging.

Every atomic nucleus possesses angular momentum - it spins around an axis which transects its

centre. Every atomic nucleus is magnetically dipolar, meaning that it possesses both a positive

magnetic pole at one end of its axis and a negative magnetic pole at the opposite end of its axis.

When an atom is placed in external magnetic field, such as is produced by the earth, the atom tends

to align with the direction of the magnetic field which transects it (like the needle of a compass

does). When the atoms axis is not exactly in line with the external magnetic field, it starts to rotatearound the axis (which is in line with the direction) of the magnetic field which transects it. This

phenomenon is called precession. The greater the deviation of the atoms axis from the direction of

the magnetic field, the greater the circumference of the imaginary circle created by the precession

is, reaching a maximum when the axis of the atom is perpendicular to the direction of the external

magnetic field. The precession is also invisible when the axis of the atom points in the opposite

direction of the magnetic field. These concepts are used to create MRI images. Protons (hydrogen

atoms) are used in MRI imaging because of

An MRI machine consists of a number of coils. Electrical currents are applied to these currents to

create magnetic fields. Each individual coil has a different configuration and orientation in the MRI

machine. Each of these coils serves a unique function.

The largest coil (and the most expensive one) is used to create an extremely homogeneous magnetic

field in the bore. The purpose of this coil is to create a very strong field which will cancel the effects

of other unwanted external magnetic fields which may disturb the (close to) perfect alignment of all

the protons which is fundamental to the functioning of NMR imaging. This homogeneous external

magnetic field is a vector, represented by the symbol B. This field causes all the protons to align

with the magnetic field, either in the direction of the field (termed spin up) or in the exact

opposite direction (termed spin down). Protons in the spin up orientation have a low level of

potential energy in comparison with protons in the spin down orientation which have a high level of

potential energy. At room temperature the proportion of protons in these two orientations are

almost equal, with a very slight preponderance to the spin up state. The ratio of spin up protons to

spin down protons is called the Boltzmann factor and is determined by the strength of B and

temperature. The proportion of excess spin up protons (termed spin excess) is very small, but the

absolute number is massive and this spin excess produces the net signal that is measured during

NMR imaging (the signals of the other protons cancel each other out). If the strength of the

magnetic field increases, the Boltzmann factor increases, causing a greater spin excess and

consequently a greater signal, increasing the signal-to-noise ratio or SNR (see below). An increase in

temperature decreases the Boltzmann factor (the protons absorb the energy and deviate toward thehigher energy state of down spin), reducing spin excess and consequently the SNR. The vector of the


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magnetic field produced by the spin excess (which corresponds to the direction/axis of the angular

momentum) is represented by the symbol M.

The precession frequency of an atom is also known as the Larmor frequency or resonance frequency

and is represented by the symbol . The precession frequency of an atom is a product of the

strength of the magnetic field and the gyromagnetic ratio () of the atom in question.

= B.

Every atom has a unique gyromagnetic ratio. A proton has a very high gyromagnetic ratio which is

an important reason why it is the atom measured in NMR. All protons in an equal B precess at an

equal frequency. If the B is inhomogeneous this means that the field is stronger in some areas than

in others, therefore some protons will precess at a higher frequency and other protons will precess

at a lower frequency. This is the reason why the large NMR coil is so critical, because any significant

external, unwanted, unmeasured interference cannot be entered into the mathematical processesinvolved in NMR imaging and will therefore give inaccurate results.

Another important coil is the oscillating transverse magnetic field coil (OTMF). When an

electromagnetic radiofrequency is applied at a frequency equal to an atoms Larmor frequency,

these frequencies are said to resonate. The proton absorbs the electromagnetic energy and

consequently the protons spin tilts (it shifts to an orientation with a higher energy state, in the

direction of spin down). The angle of the tilt is proportional to the strength and the duration of the

applied electromagnetic pulse. The OTMF is applied for the exact time that it is necessary to tilt the

spin 90 degrees towards the xy-plane (transverse plane; the orientation at which precession causes

the greatest signal or, in other words, is most visible). This pulse ofelectromagnetic energy is

termed a 90 degree pulse. When the pulse is turned off, the vector of the spin gradually returns to

B (the direction of the B; also called the z-axis). This is called T1 relaxation. As the proton relaxes, it

emanates the energy as electromagnetic waves, known as an electromagnetic signal, which is

detected by a detector coil and gives information about the spins. Some of the energy is also

released in the form of heat to its environment (this environment is called the lattice). T1 relaxation

is therefore also known as spin-lattice relaxation. T1 is time it takes for the M to return to B. T1 is

unique to every type of tissue.

The electromagnetic waves emitted by the precessing protons causes a potential difference in the

detector coil (according to the laws of electromagnetic induction) and produces the signal which is

measured in the NMR computer system. As the proton precesses, the direction of its magnetic field

(corresponding with the axis of its angular momentum) also rotates. This causes an oscillating

voltage in the detector coil. When M is aligned in the xy-plane, the oscillating voltage is at its

greatest. As relaxation takes places, this oscillating voltage/signal decreases. This decrease in signal

is termed free induction decay.

After a 90 degree pulse, a certain period of time (called half echo time) elapses in which the protons

relax toward the z-axis and also go out of phase in the xy-plane (due to the magnetic field gradient

and minor inhomogeneity). Before the vector reaches to the z-axis, another electromagnetic pulse isapplied the 180 degree pulse (which is twice as long as a 90 degree pulse). The axes of angular


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momentum of each proton is displaced to the exact opposite direction and the protons commence

relaxation towards the direction of B. The direction of precession is reversed and at echo time

(which is half echo time after the 180 degree pulse), the axes of angular momentum are once again

in phase and Mis in the transverse plane. The signal is at its greatest again. The protons relax

further until they align with Bagain. The form of the signal forms an echo and this process is

called spin echo.

When spin echoes are performed repeatedly the amplitudes of the echoes are seen to decrease

gradually. This is because the axes of angular momentum go out of phase in the transverse plane for

reasons other than differences in the external magnetic field. This loss of phase is irreversible and is

because of the effect of the magnetic fields caused by the atoms surrounding the protons. Because

the composition of tissues differs, these effects vary and cause differences in Larmor frequencies.

This effect is termed T2-relaxation. T2 is the time it takes for signal amplitude to decrease with36,8%.

The T2 is dependent on the chemical milieu of the protons is thus relatively characteristic of a certain

type of tissue - this permits the identification of tissue on the NMR image.

A third major coil, the magnetic field gradient coil, produces a magnetic field which varies linearly in

three orthogonal directions (along the x-, y- and z-axis).Two solenoids of equal strength are placed at

opposing points of the bore (a pair along each axis). They create equal but opposite magnetic fields

and this creates a gradient in the magnetic field. Because the Larmor frequency of the proton is

proportional to the magnitude of the external magnetic field, the gradient causes a linear variation

in precession frequencies, with the greatest frequency at and the smallest at a wanted and

predictable variation in magnetic field (as opposed to unwanted, unpredictable inhomogeneity). The

Larmor frequency of the proton is thus dependent on its position. This allows the computer to

calculate the position of signal in each of the 3 planes.

The magnetic field gradient coil also corrects minor distubances of B, primarily caused by the

Earths magnetic field. As mentioned earlier, if certain areas of the magnetic field are stronger than

others, the protons precess at different frequencies, causing the vectors of the individual protons

dipoles(axes of angular momentum) to point in different directions, causing the vector of M (the

total magnetization vector) to decrease and consequently a decrease in signal. The free induction

decay occurs more rapidly (because of lower initial signal amplitudes). The magnetic field gradient

coil decreases the effects of external unwanted disturbances this process is called shimming. The

field is more homogeneous, the strength of the signal greater and the free induction decay is longer.

All the signals received by the detector coil are organized into a virtual matrix, called the k-space.

This matrix represents the manner in which the signals are gathered spatially (only in two

dimensions in the axial plane or slices). The process of gathering the signals is called encoding

and three different types of encoding exist and these represent the three gradients which are

applied by the magnetic field gradient coil.

The first encoding gradient is the slice encoding gradient. A gradient is applied along the z-axis (i.e.

along the length of the bore) or B which is in the cephalic direction. Consequently the magnetic

field is greatest at the head of the patient (only slightly stronger than B) and gradually decreasesuntil it is at its weakest at the feet of the patient (only slightly weaker than B). When the


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electromagnetic pulses are applied, they only resonate with the protons precessing at their specific

frequency. Consequently only spins at that axial level will produce a signal. The matrix represents a

specific slice.

The phase encoding gradient is applied along the y-axis. Phase encoding is only done one row (of

the matrix or k-space) at a time. This gradient is applied for a small period and then switched off. The

result is that protons along the y-axis are out of phase in a predictable pattern. When this gradient is

switched off, the phase difference remains constant. Phase encoding produces the columns of the

k-space.

The frequency encoding gradient is applied along the x-axis. This gradient is applied after the

phase encoding gradient is halted. This causes a further deviation in phasealignment along the x-

axis which is also predictable. Frequency encoding produces the rows of the k-space.

By consolidating the data gathered during the various encodings, the NMR computer is able tocalculate the position of a signal. Fourier transformation (a mathematical process) is applied to the

data which are arranged in the k-space and a two-dimensional image is formed.

Different sequences

T1 weighted: better to view disruption in anatomy

T2 weighted: better to view pathological changes in tissue

STIR (fat-suppression): decreases intensity of adipose tissue, to differentiate it from other

hyperintense tissue, especially in the case of a history of cancer and trauma.

Field of view:

Field of view is the specific volume which is to be detected by the receiver coil. A greater field of

view means more electromagnetic waves to be detected, i.e. a greater signal, but a decrease in

resolution (if the matrix size is constant, because slices are thicker).

SNR

The signal to noise ratio is the ratio between the strength of the signal from the area of interest and

the signal from background electromagnetic activity (termed noise). A low SNR causes images to

appear grainy. The SNR is proportional to the size of the voxel. An increase in field of view, slice

thickness, phase steps and a decrease in matrix size cause an increase in SNR. The inverse applies for

a decrease in SNR. The SNR is proportional to the acquisition time.

Resolution

Resolution determines the sharpness or pixelated appearance of an NMR image. The resolution is

inversely proportional to the voxel. A decrease in the field of view, slice thickness and an increase in

matrix size cause an increase in resolution.

Voxel size

The size of the voxel is equal to the field of view divided by the matrix size. The depth of the voxel is

always the largest dimension, therefore the resolution perpendicular to the image plane is alwaysthe poorest.


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Acquisition time

Acquisition time is equal to repetition time (TR) multiplied by the number of phase encoding steps

multiplied by the number of averages (NSA or NEX).

Performing an MRI

Initially only an overview image is taken. This image is of poor resolution, but is used to plan the

definitive imaging study. In the imaging application, frames are placed and cropped to fit over the

areas of interest in the sagittal and axial plane. A number of parameters (e.g. field of view, number

of slices, etc.) are entered and the definitive imaging process is commenced. The imaging is repeated

for every sequence requested by the requesting physician. When the image collection is complete,

the radiographer annotates the images and digitally sends them to the radiologists job list as well as

the archive.

The duration of an MRI study is dependent on the anatomical area of interest, the number of

sequences requested, whether contrast is used and whether a dynamic study is performed.

Depending on the anatomical area of interest, different receiver coils are used during NMR imaging.

There are a number of special coils: brain coil, neck coil, torso coil, cardiac coil, breast coil, knee coil,

wrist coil and spinal coil. Some of these coils are place over the area of interest, e.g. the brain coil;

and some rest beneath the area of interest, e.g. the torso coil.

Special anaesthetic equipment, ECG machines, pulse oximeters, capnography machines,

defibrillators etc. are used in the MRI room. This is necessary because standard equipment will be

strongly attracted by the bore, causing objects to move rapidly and adhere to the bore. This causes a

great hazard for persons in the MRI room and may damage the bore.

Switching the large electromagnetic coil on is not a simple, quick or cheap procedure. It make take

days from initiation for the MRI machine to be fully functional. Therefore the MRI machine is not

switched of for any folly. In the event of an emergency necessitating the deactivation of the bore

(such as a large magnetic object which cannot otherwise be removed or an object impinging a

person), a procedure called quenching is performed.


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Sources

1. The knowledge and experience of the employees of Schnetler, Corbett and Partners2. Introductory NMR and MRI with Paul Callaghan (video series)3. www.mritutor.org4. Introduction to MRI Physics (www.simplyphysics.com)5. MRI Physics (www.hsc.csu.edu)6. MRI Physics (www.mri-physics.net)7. The Basic Principles of MRI (www.spinwarp.ucsd.edu)8. Basic Principles of MRI by Wm. Faulkner (www.e-radiography)
http://www.mritutor.org/http://www.mritutor.org/http://www.simplyphysics.com/http://www.simplyphysics.com/http://www.simplyphysics.com/http://www.hsc.csu.edu/http://www.hsc.csu.edu/http://www.hsc.csu.edu/http://www.mri-physics.net/http://www.mri-physics.net/http://www.mri-physics.net/http://www.spinwarp.ucsd.edu/http://www.spinwarp.ucsd.edu/http://www.spinwarp.ucsd.edu/http://www.spinwarp.ucsd.edu/http://www.mri-physics.net/http://www.hsc.csu.edu/http://www.simplyphysics.com/http://www.mritutor.org/

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Introduction to MRI Physics for the Undergraduate Med Student by the Undergraduate Med Student