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Magnetic Resonance Imaging Part 2

Pål Erik Goa Associate Professor in Medical Imaging

Dept. of Physics, NTNU pal.e.goa@ntnu.no

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Spatial encoding

•  The acquired signal in MRI originates from all the excited spins.

•  No spatial information as such. •  By exploiting the resonance condition (ω0=γB0) in

different ways we can obtain spatial information. •  This is achieved by use of gradient coils (x, y and z

direction). •  A gradient coil is designed to create a linear variation

in the magnetic field (and thereby the resonant frequency) along a given physical axis.

RF System

RF Transmitter RF Receiver

Magnetic Field

RF Pulse

N

S NMR Signal

NMR Signal Intensity

Frequency

NMR Spectrum Fourier Transformation

FID (Free Induction Decay)

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Three principles of spatial coding

•  Slice selection –  Gradient applied during rf transmission

•  Frequency encoding –  Gradient applied during rf-signal reception

•  Phase encoding –  Gradient applied between transmission and reception

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Slice selection gradient •  B0 varies linearly along

the z-axis. •  Rf-pulse with limited

bandwidth. •  Only areas where the

resonance frequency fits the RF-pulse-frequencies, are excited.

•  RF bandwidth determines the slice-thickness.

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Slice gradient example •  Gradient amplitude (Gz):

–  10 mT/m •  Rf-bandwidth (Δf):

–  2.1 kHz •  Resulting slice thickness (Δz):

•  Note that this is independent of B0 itself. •  Position of slice is determined by center frequency.

!z =!f"Gz

=2.1kHz

42.58MHz /T #10mT / m= 5mm

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Effect of slice select gradient

•  The received signal is now coming only from a thin slice of the object

•  Still no spatial information within the slice

•  X-axis: Frequency direction

•  Y-axis: Phase direction

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Frequency gradient

•  Gradient in X-direction during signal acquisition.

•  Protons spin at different frequencies depending on their position along the X-axis (Frequency direction)

Without frequency encoding

Z

Y

X

Without gradients both samples feel the same fieldstrength….

Intensity

Intensity

Frequency

Time

Fourier Transform

……Resulting in a signal containing one frequency

When gradients is applied, the samples will feel different magnetic field...

…resulting in a signal containing two frequencies.

Intensity

Fourier Transformation

Frequency Time

Intensity

ZY

X

With frequency encoding

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Effect of frequency encoding

•  Each frequency in the signal corresponds to one specific location along x-axis.

•  Use Fourier transform to get the amplitude of each frequency = the signal at a given x-position

•  Result: 1D Image

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Phase encoding gradients •  Y-gradient is turned on for a

short while after the excitation •  Protons spin with different

frequency •  After the gradient is switched

off, all protons will spin with the same frequency again, but a phase shift is introduced along the Y-axis (Phase direction)

•  The sequence is repeated several times with different gradient strength. A resolution of 128 pixels, requires 128 different gradient values.