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The Basics Of MRI

Chapter 6

IMAGING PRINCIPLES

y Introduction

y Magnetic Field Gradient

y Frequency Encoding

y Back Projection Imaging

y Slice Selection

y Problems

Introduction

You learned in Chapter 1 that magnetic resonance imaging is an imaging modality which is primarily used to construct pictures of the NMR signal from the hydrogen atoms in an object. In

medical MRI, radiologists are most interested in looking at the NMR signal from water and fat,the major hydrogen containing components of the human body.

The principle behind all magnetic resonance imaging is the resonance equation, which shows

that the resonance frequency of a spin is proportional to the magnetic field, Bo, it is

experiencing.

= Bo

Recall from the spin physics chapter that is the gyromagnetic ratio.

For example, assume that a human head contains only three small distinct regions where there ishydrogen spin density. In reality the entire head would contain signal. When these regions of

spin are experiencing the same general magnetic field strength, there is only one peak in the NMR spectrum.

Magnetic Field Gradient

If each of the regions of spin was to experience a unique magnetic field we would be able to

image their positions. A gradient in the magnetic field is what will allow us to accomplish this. Amagnetic field gradient is a variation in the magnetic field with respect to position. A one-

dimensional magnetic field gradient is a variation with respect to one direction, while a two-dimensional gradient is a variation with respect to two. The most useful type of gradient in

magnetic resonance imaging is a one- dimensional linear magnetic field gradient. A one-

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dimensional magnetic field gradient along the x axis in a magnetic field, Bo, indicates that themagnetic field is increasing in the x direction. Here the length of the vectors represent the

magnitude of the magnetic field. The symbols for a magnetic field gradient in the x, y, and zdirections are Gx, Gy, and Gz.

Frequency Encoding

The point in the center of the magnet where (x,y,z) =0,0,0 is called the isocenter of the magnet.

The magnetic field at the isocenter is Bo and the resonant frequency is o. If a linear magneticfield gradient is applied to our hypothetical head with three spin containing regions, the three

regions experience different magnetic fields. The result is an NMR spectrum with more thanone signal. The amplitude of the signal is proportional to the number of spins in a plane

perpendicular to the gradient. This procedure is called frequency encoding and causes theresonance frequency to be proportional to the position of the spin.

= ( Bo + x Gx ) = o + x Gx

x = ( - o ) / ( Gx )

This principle forms the basis behind all magnetic resonance imaging. To demonstrate how an

image might be generated from the nmr spectra, the backprojection method of imaging is presented in the next section.

Back Projection Imaging

Backprojection imaging is a form of magnetic resonance imaging. It was one of the first forms

of magnetic resonance imaging to be demonstrated. Backprojection is an extension of thefrequency encoding procedure just described. In the backprojection technique, the object is first

placed in a magnetic field. A one-dimensional field gradient is applied at several angles, andthe NMR spectrum is recorded for each gradient. For example, say you wished to produce an YZ

plane image of an object. A magnetic field gradient in the +Y direction is applied to the objectand an NMR spectrum is recorded.

A second spectrum is recorded with the gradient now at a one degree angle to the +Y axis. The

process is repeated for the 360o between 0o and 359o. Once this data has been recorded thedata can be backprojected through space in computer memory.

Once the background intensity is suppressed an image can be seen. The actual backprojectionscheme is called the inverse Radon transform.

In a conventional 90-FID imaging sequence this procedure might be applied with the aid of the

following pulse sequence. Varying the angle of the gradient is accomplished by theapplication of linear combinations of two gradients. Here the Y and X gradients are applied in

the following proportions to achieve the required frequency encoding gradient Gf .

Gy = Gf Sin Gx = Gf Cos

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For the backprojection technique to be a viable tomographic imaging technique we need to havethe ability to image the spins in a thin slice. The Gz gradient in the last graphic accomplishes this.

The following section will describe how slice selection is accomplished.

Slice Selection

Slice selection in MRI is the selection of spins in a plane through the object. The principle behind slice selection is explained by the resonance equation. Slice selection is achieved by

applying a one-dimensional, linear magnetic field gradient during the period that the RF pulse isapplied. A 90

opulse applied in conjunction with a magnetic field gradient will rotate spins which

are located in a slice or plane through the object. Picture what this would look like if we had acube of small net magnetization vectors. To understand this we need to examine the frequency

content of a 90o

pulse. A 90o

pulse contains a band of frequencies. This can be seen byemploying the convolution theorem. The frequency content of a square 90o pulse is shaped as a

sinc pulse. The animation window displays the real components of this pulse. The amplitudeof the sinc function is largest at the frequency of the RF which was turned on and off. This

frequency will be rotated by 90

o

while other smaller and greater frequencies will be rotated bylesser angles.

The application of this 90o

pulse with a magnetic field gradient in the x direction will rotate some

of the spins in a plane perpendicular to the x axis by 90o. The word some was used because some

of the frequencies have a B1 less than that required for a 90orotation. As a consequence the

selected spins do not actually constitute a slice.

A solution to the poor slice profile is to shape the 90o

pulse in the shape of a sinc pulse. The sinc

pulse, as first seen in Chapter 5, has a square frequency distribution. The animation windowdisplays the real components of this function.

A backprojection tomographic image can be achieved by the application of the following

pulses. An apodized sinc pulse shaped 90o

pulse is applied in conjunction with a slice selectiongradient. A frequency encoding gradient is turned on once the slice selection pulse is turned off.

The frequency encoding gradient is composed of a Gx and Gy gradient in this example. The FIDsare Fourier transformed to produce the frequency domain spectrum, which is then backprojected

to produce the image.

The backprojection imaging technique is highly educational but never used in state of the artimagers. Instead, Fourier transform imaging techniques are used. These techniques are described

in the next chapter.

Problems

1. A sample contains water at two locations, x = 0 cm and x = 2.0 cm. A one-dimensional

magnetic field gradient of 1 G/cm is applied along the x-axis during the acquisition of an

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FID. What frequencies (relative to the isocenter frequency) are contained in the Fourier transformed spectrum?

The frequency encoding equation is

(R = K x G

where:(R = frequency offset from isocenter

K = gyromagnetic ratio, 42.58 MHz/TG = frequency encoding gradient = 0.0001 T/cm

x = position relative to isocenter

x = 0 cm, (R = 0

x = 2.0 cm, (R = 8.516 kHz

2. An NMR spectrum is recorded from a sample containing two water locations. The

frequency encoding gradient is 1 G/cm along the y-axis. The spectrum containsfrequencies of +1000 Hz and -500 Hz relative to the isocenter frequency. What are thelocations of the water?

(R = K y Gwhere:

(R = frequency offset from isocenter

K = gyromagnetic ratio, 42.58 MHz/TG = frequency encoding gradient = 0.0001 T/cm

y = position relative to isocenter

y = (R / (K G)

y = 0.235 cm y = - 0.117 cm

3. You want to excite spins in an xy-plane located at z = -5.0 cm. The resonance frequencyat the isocenter is 63.85 MHz and your slice selection gradient is 1 G/cm. Describe in

detail the RF pulse which should be used.

We need to find the frequency of the RF that needs to be turned on and off in the shape of an apodised sinc function. If the slice is to be located at Z=-5.0 cm, the slice selection

gradient must be applied along the +z-axis. The frequency is calculated as follows.R - Ro = K z G

where:

R = frequency for slice

Ro = frequency at isocenter = 63.85 MHz

K = gyromagnetic ratio, 42.58 MHz/T

G = slice selection gradient = 0.0001 T/cmz = position relative to isocenter = -5 cm

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R = Ro + K z G

R = 63.85 MHz + (42.58 MHz/T)(-5 cm)(0.0001 T/cm)

R = 63.85 MHz - 0.21 MHz

63.829 MHz

4. A sample contains water at two locations, y = 1.0 cm and y = -2.0 cm. A one-dimensional

magnetic field gradient is applied along the y-axis during the acquisition of an FID. Thefrequency encoding gradient is 1 G/cm. What frequencies (relative to the isocenter

frequency) are contained in the Fourier transformed spectrum?5. An NMR spectrum is recorded from a sample containing two water locations. The

frequency encoding gradient is 0.5 G/cm along the z-axis. The spectrum containsfrequencies of -1000 Hz and +500 Hz relative to the isocenter frequency. What are the

locations of the water?6. You want to excite spins in an xy-plane located at z = -2.0 cm. The resonance frequency

at the isocenter is 63.85 MHz and your slice selection gradient is 2 G/cm. Describe indetail the RF pulse which should be used.

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