BE 581

Lecture 3- Intro to MRI

BE 581

Lecture 3 - MRI

Block Equation - T1 decay

90 pulse

180 pulse

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Mz t( ) = Mo 1− e−t

T1 ⎛

⎝ ⎜

⎞

⎠ ⎟

Mz t( ) = Mo 1− 2e−t

T1 ⎛

⎝ ⎜

⎞

⎠ ⎟

T1 relaxation (slow) (longitudinal or spin-lattice)

0.5T 1.5T

Fat 200 ms 260

Liver 320 490

Kidney 500 650

White m. 530 780

Grey m. 650 920

Cerebrospinal fluid 2,000 2,400

T2 relaxation (quick)

1.5T

Fat 60-80

Liver 40

Kidney 60

White m. 90

Grey m. 100

Cerebrospinal fluid 160

How to measure T1 & T2?

• Sequence of RF pulses with a specific• TE: Echo Time- time after 90o RF pulse until

readout. Determines how much spin-spin relaxation will occur before reading one row of the image.

• TR: Repetition Time– time between successive 90o RF pulses. Determines how much spin-lattice relaxation will occur before constructing the next row of the image

Measuring T1

• Magnetization Mz• A 90o RF pulse Mz->My• Wait for a t time• Send a new 90o RF• How long does it take for

Mz to recover?

• Generate the Mz recovery curve

Measuring T1

• Energy transfer works when the frequency of precession of the protons overlaps with vibrational freq. of lattice

• Large molecules->low vibrational freq->longT1

• Small molecules->broad vibrational freq->long T1

• Medium/viscous fluid-> intermediate freq ->short T1

Large molecules

small molecules

Measuring T1

• Large molecules->low vibrational freq -> small overlap with o

• Small molecules->broad vibrational freq-> larger overlap with o

• Medium/viscous fluid->intermediate freq.->largest overlap with o

Large molecules

small molecules

T1 and T2

Molecule size

T1 T2

Small Long Long

Medium Small Small

Large Longest Small

T1 and T2 relaxation time

Spin echo

• First 90o nutate magnetization – spin in phase T2 and T2* impact signal

• Second 180 re-phasing pulse– applied at time T ->re-phases spins

Spin echo

• The 180o pulse has the function of rotating the magnetization vector to the opposite direction of the first 90o pulse.

• Spins experience OPPOSITE magnetic field inhomogeneities -> cancel its effect

• T2* is cancelled

Spin echo contrast

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S ∝ ρ HA 1− e−TR /T1[ ]e−TE /T2

h proton densityTR repetition timeTE echo time

Using the same pulse seq.We get different S depending on T1 and T2

Inversion recovery

• Emphasizes T1 relaxation time

• Extends longitudinal recovery time by a factor of 2

• 180 pulse Mz => -Mz• wait TI (time of inversion)• 90 pulse -Mz => Mxy => FID• Wait TE/2• 180 pulse produces echo at TE

Inversion recovery

Inversion recovery

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S ∝ ρ HA 1− 2e−TI /T1 + e−TR /T1( )

• No T2• A factor of 2 (-Mz to Mz)

How do you generate images?

• Spatial Encoding

• Generate magnetic gradient across the patient

B decreases

Spatial encoding

• Frequency of precession vary with B

• Resonance frequency will also vary

• A wise choice of RF frequency can give just one slice

B decreases

f1 f2

Bo

Spatial encoding

• You can do this in all 3 planes

• The intersection of all planes gives us a location (voxel)

• A voxel becomes a value of intensity on the MRI image

Sensitive point technique (se)

• Apply slice select gradient

• No effect everywhere else• The location is established by RF central

frequency• Slice thickness is established by RF bandwidth

Phase encoding

• Protons at the end of a gradient (strong B) go faster than the one at the other end (weak B).

• Protons where B was higher are ahead of protons where B was slower

B ON

B OFF

WE GET A PHASE GRADIENT

Frequency encoding

Gradients

Spatial encoding

• You can do this in all 3 planes

• The intersection of all planes gives us a location (voxel)

• A voxel becomes a value of intensity on the MRI image

• Fourier transforms are used to go from time to frequency

Spatial encoding

• Apply slice select gradient while transmitting an RF pulse

• Apply phase encoding gradient

• Apply frequency encoding gradient

• Fourier transform received signal

• Repeat with different phase

Spatial encoding

• Slice -> Z axis

• Frequency of returned RF signal -> x axis

• Phase of returned RF signal -> y axis

• The intersection of all planes gives us a location (voxel)

MRI instrument

MRI

Magnets and coils

Main magnet

• 1 Tesla = 10,000 Gauss• Earth 0.5 µT - 0.5G• Magnet can be

– Resistive -can be turned on and off, consume a lot of electricity (0.35T)

– Permanent-cannot be turned off (0.5T)– Superconducting - best performance need

to be cooled

Superconducting magnet

• Several tesla

• Conduct electrical current with little resistance

• Wire- wrapped cylinder (solenoid)

• Need high cooling (4.2K)

Gradient coils

• Up to 60 mT/m

• In the z direction are called Helmholtz coils

• X and y are Saddle coils

• Fast switch on/of 500 µs

RF coils

• Frequencies 1 MHz - 10GHz

• Transmitter coil - sends RF pulse

• Receive coils (can be same as transmitter) - receive RF signal

Magnetic Shielding

• Layers of steel plates around the magnets

• RF shielding - faraday cage (copper sheet metal all around the MRI room.

Homework

• Please write a short description of – T1 Weighting– T2 Weighting– Spin Proton Weighting

• (Matlab should be used to generate graphs that will help your description)

Images References

• The essential physics of medical imaging (Bushberg)

• Lucas Parra CCNY

Matlab exercise

Pulse effect

• We start by assuming that the equilibrium magnetization vector is – [0, 0, 1]' – If we had a perfect 90-degree excitation,

about the y axis, then the vector becomes [1, 0, 0]'

– Try defining M=[1, 0, 0]' in Matlab, and notice the result.

Transverse relaxation

• Transverse relaxation • Exponential decay process of the x and y

components of magnetization• Mathematically this means

• Mx(t)=Mx(0)exp(-t/T2) • My(t)=My(0)exp(-t/T2).

Transverse relaxation

• Assume M consists of only an x component.

• Let's say that T2=100 ms.

• Ignoring other effects, what is the magnetization vector due to T2-decay after 50 ms?

Answer

• [ 0.61 0 0 ];

Transverse relaxation

• What matrix do you need to do this in vector form? (remember your homework)

Answer

• [ exp(-50/100) 0 0;

0 exp(-50/100) 0;

0 0 1];