ELEG 479Lecture #9

Magnetic Resonance (MR) Imaging

Mark Mirotznik, Ph.D.Professor

The University of Delaware

Process of MR Imaging Step#1: Put subject in a big magnetic field (leave him there)Step#2: Transmit radio waves into subject (about 3 ms)Step #3: Turn off radio wave transmitterStep #4: Receive radio waves re-transmitted by subject

– Manipulate re-transmission with magnetic fields during this readout interval (10-100 ms: MRI is not a snapshot)

Step#5: Store measured radio wave data vs. time– Now go back to transmit radio waves into subject and get more data.

Step#6: Process raw data to reconstruct imagesStep#7: Allow subject to leave scanner (this is optional)

Equipment

Magnet Gradient Coil RF Coil

RF Coil

4T magnet

gradient coil(inside)

B0

Magnetic Fields are Huge!Typical MRI Magnet: 0.5-4.0 Tesla (T)Earth’s magnetic field: 50 mTesla

So what happens to things that are normally non-magnetic when you

put them inside big magnetic fields?

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

proton

electron

Quantum mechanical property called proton spin

Quantum mechanical property called electron spin

Let’s first look at a simple hydrogen atom without any appliedexternal magnetic field.

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Let’s first look at a simple hydrogen atom without any appliedexternal magnetic field.

proton

electron

Quantum mechanical property called proton spin

Quantum mechanical property called electron spin

We can think of spin from a classical point of view as the proton or electron rotating about some axis.

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Let’s first look at a simple hydrogen atom without any appliedexternal magnetic field.

proton

electron

Quantum mechanical property called proton spin

Quantum mechanical property called electron spin

Since both the proton and electron are electrically charge when they spin they look like a tiny current loop (called a magnetic dipole). We know that a current loop produces a magnetic field.

Belectron

Bproton

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Let’s first look at a simple hydrogen atom without any appliedexternal magnetic field.

proton

electron

Since both the proton and electron are electrically charge when they spin they look like a tiny current loop (called a magnetic dipole). We know that a current loop produces a magnetic field.

Belectron

Bproton

S

N

N

S

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Let’s first look at a simple hydrogen atom without any appliedexternal magnetic field.

proton

electron

Quantum mechanical property called proton spin

Quantum mechanical property called electron spin

Since the proton is so much larger than the electron it will produce a much larger magnetic dipole. So most practical applications of this phenomenon relate to the nuclear magnetic properties.

Belectron

Bproton

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Let’s first look at a simple hydrogen atom without any appliedexternal magnetic field.

proton

electron

Quantum mechanical property called proton spin

Quantum mechanical property called electron spin

Question: So do the nucleus of all atoms possess this magnetic property or is hydrogen special?

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Question: So do the nucleus of all atoms possess this magnetic property or is hydrogen special?

• To be imaged, nuclei must:– have an odd number of neutrons, protons, or both– be abundant in the body

• Hydrogen in the water molecule satisfies both: – The hydrogen nucleus is composed of a single proton (odd

number of nucleons)– Water comprises 70% of the body by weight (very

abundant)– Most widely imaged

• Termed spins in MRI

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Question: So do the nucleus of all atoms possess this magnetic property or is hydrogen special?

H11 C13

6 O178 F19

9 Na2311 P31

15 K3919

These guys will also possess a non-zero magnetic spin.

.093.0161.0 .066

Relative sensitivity compared to hydrogen

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Let’s first look at a simple hydrogen atom without any appliedexternal magnetic field.

proton

electron

Quantum mechanical property called proton spin

Quantum mechanical property called electron spin

Question: So if all hydrogen atoms possess this magnetic property and we have lots of hydrogen atoms (we are mostly water) then why are we not magnetic?

Belectron

Bproton

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

RandomOrientation

= No NetMagnetization

Question: So if all hydrogen atoms possess this magnetic property and we have lots of hydrogen atoms (we are mostly water) then why are we not magnetic?

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Now, let’s look at a proton when we apply an external static magnetic field Bo

Bore(55 – 60 cm)

Shim(B0 uniformity)

Magnetic field (B0)

Body RF(transmit/receive)

Gradients

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Now, let’s look at a proton when we apply an external static magnetic field Bo

FirstThe proton’s magnetic dipoles tend to orient themselves in 1 or 2 states (spin ½ and spin - ½ or spin parallel and spin anti-parallel) with respect to the external magnetic field

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Now, let’s look at a proton when we apply an external static magnetic field Bo

FirstThe proton’s magnetic dipoles tend to orient themselves in 1 or 2 states (spin ½ and spin - ½ or spin parallel and spin anti-parallel) with respect to the external magnetic field

Question: So if the magnetic dipoles align both up and down why don’t they just cancel each other out and again give a zero net magnetization?

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Now, let’s look at a proton when we apply an external static magnetic field Bo

Question: So if the magnetic dipoles align both up and down why don’t they just cancel each other out and again give a zero net magnetization?

Answer: At any temperature above absolute zero we get a few more in one state than the other.

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?Now, let’s look at a proton when we apply an external static magnetic field Bo

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?Now, let’s look at a proton when we apply an external static magnetic field Bo

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?Now, let’s look at a proton when we apply an external static magnetic field Bo

Enough to get a measurable net magnetization! This is called the longitudinal magnetization.

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Now, let’s look at a proton when we apply an external static magnetic field Bo

SecondThe proton is spinning (think of a spinning top) so it has a non-zero angular momentum, J. When we place it in the magnetic field the proton experiences a torque.

This torque causes the tip of the magnetic field vector to precess at some angular frequency, wo.

Larmor PrecessionNow, let’s look at a proton when we apply an external static magnetic field Bo

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

Precession Demo

Magnetic Moment Vector of Proton

Components of the Precessing Proton

Z (longitudinal)

x

yxy (transverse plane)

x

y

z

zm m

xymf

a

zzytxtt zxyzyx ˆˆˆ)(ˆ)()( mmmmmm

Magnetic moment vector

zzytxtt zxyzyx ˆˆˆ)(ˆ)()( mmmmmm

x

y

z

zm m

xymf

a

(longitudinalmagnetization vector)

(transverse magnetization vector)

Magnetic Moment Vector of Proton

Net Magnetization

z

x

y

zm m

xym

Add all the magnetic moments from all the protons together at some instant in time

x

y

z

zm

m

xym

x

y

z

zm m

xym

z

x

y

zm

m

xymx

y

z

zm

m

xym

z

x

y

zm m

xym

Add all the magnetic moments from all the protons together at some instant in time

x

y

z

zm

m

xym

x

y

z

zm m

xym

z

x

y

zm

m

xymx

y

z

zm

m

xym

Net Magnetization Vector

zMtMtM

tzyxtM

zxy

N

nnnnn

ˆ)()(

),,,()(1

m

Net Magnetization

z

x

y

zm m

xym

Question: Anything we can say about Mxy?

x

y

z

zm

m

xym

x

y

z

zm m

xym

z

x

y

zm

m

xymx

y

z

zm

m

xym

Net Magnetization Vector

zMtMtM

tzyxtM

zxy

N

nnnnn

ˆ)()(

),,,()(1

m

Net Magnetization

Question: Anything we can say about Mxy?

zMtM

tzyxtM

z

N

nnnnn

ˆ)(

),,,()(1

m

Answer: At any instant in time the magnetic dipoles are precessing at the same frequency but all out of phase. The net summation of all those vectors in the transverse plane is zero!

Another Question: What can we do to get a net magnetization vector in the transverse plane?

x

y

z

zM M

xyM

(transverse magnetization vector)

(longitudinalmagnetization vector)

Net Magnetization

Answer: At any instant in time the magnetic dipoles are precessing at the same frequency but all out of phase. The net summation of all those vectors in the transverse plane is zero!

Another Question: What can we do to get a net magnetization vector in the transverse plane?

Assume these kids are all swinging at the same frequency but out of phase. How can we get them all in phase?

Net Magnetization

Answer: At any instant in time the magnetic dipoles are precessing at the same frequency but all out of phase. The net summation of all those vectors in the transverse plane is zero!

Another Question: What can we do to get a net magnetization vector in the transverse plane?

Assume these kids are all swinging at the same frequency but out of phase. How can we get them all in phase? You push them at the same time and at the same frequency!

Net Magnetization

RF Excitation

time

B1

x

y

zm m

xym

x

y

z

zm

m

xym

x

y

z

zm m

xym

x

y

zm

m

xym

B1

Add a RF field whose frequency is the same as the Lamor resonant frequency of the proton and is oriented in the xy or transverse plane.

RF Excitation

time

B1

x

y

z

zm

xym

x

y

z

zm

xym

B1

t=0

t=0

x

y

z

M

xyM

=+

t=Dt

x

y

z

zm

xym

x

y

z

zm

xym

x

y

zM

xyM

=+

RF Excitation

time

B1

x

y

z

zm

xym

x

y

z

zm

xym

B1

t=0

t=2Dt

x

y

z

M

xyM

=+

t=3Dt

x

y

z

zm

xym

x

y

z

zm

xym

x

y

z

M

xyM

=+

wBo

wDtB1Dt

Tip Angle Amplitude of RFPulse

Time of Applicationof RF Pulse

Larmor Equation

Tip Angle

DC or static external magnetic field(the big one)

Resonant Larmorfrequency

RF Excitation

RF Excitation• transmission coil: apply magnetic field

along B1 (perpendicular to B0)• oscillating field at Larmor frequency• frequencies in RF range• tips M to transverse plane – spirals

down• gets all the little magnetic moments to

precess at the same phase: analogy: children’s swingset

• final angle between B0 and B1 is the flip angle

• B1 is small: ~1/10,000 T

Equipment

RF Coil

4T magnet

gradient coil(inside)

Gradient Coil RF Coil

BoB1

Radiofrequency Coils

Other kinds of RF Coils

Summarize A large DC magnetic field applied to a patient aligns his/her protons and gets them precessing like a top at the lamor resonant frequency.The net magnetization in the transverse plane is zero because they are all out of phase. If we apply a RF field at the same Lamor resonant frequency and oriented orthogonal to the large DC field then we can get them all moving together (i.e. coherent rotation). The tip angle is a function of the amplitude of the RF pulse and how long it is applied for.

Summarize A large DC magnetic field applied to a patient aligns his/her protons and gets them precessing like a top at the lamor resonant frequency.The net magnetization in the transverse plane is zero because they are precessing all out of phase. If we apply a RF field at the same Lamor resonant frequency and oriented orthogonal to the large DC field then we can get them all moving together (i.e. coherent rotation). The tip angle is a function of the amplitude of the RF pulse and how long it is applied for.

That is all well and good but how do we get out a signal we can measure for imaging?

MR Signal

time

B1

Question: What happens to the all the little spinning protons when we turn off the RF excitation?

At this time we turn off the RF excitation and use the coil as a receiver

MR Signal

time

B1

Question: What happens to all the little spinning protons when we turn off the RF excitation?

At this time we turn off the RF excitation and use the coil as a receiver

Answer: Two things(1) The M vector starts uncoiling back to its position

without any RF excitation(2) The phase coherence between all the spinning

protons starts go away (i.e. they get out of phase again).

This process is called relaxation

Signal Detection via RF coil

As the net magnetization changes we can use a detector coil (often the same coil used for excitation) to sense it. This is the same idea as a electric generator (i.e. time varying magnetic fields cutting through a coil of wire produces a voltage).

zMMzMytMxtMtM

BtMdttMd

zxyzyx

o

ˆˆˆ)(ˆ)()(

)()(

Simple Bloch Equation

x

y

z

zM M

xyMf

a

(transverse magnetization vector)

(longitudinalmagnetization vector)

Net Magnetization