ELEG 479 Lecture #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 transmitter Step #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 images Step#7: Allow subject to leave scanner (this is optional)

Equipment B0 Magnet Gradient Coil RF Coil 4T magnet RF Coil (inside) Magnet Gradient Coil RF Coil

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? Let’s first look at a simple hydrogen atom without any applied external magnetic field. electron Quantum mechanical property called electron spin Quantum mechanical property called proton spin proton

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 applied external magnetic field. electron Quantum mechanical property called electron spin Quantum mechanical property called proton spin proton 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 applied external magnetic field. electron Quantum mechanical property called electron spin Quantum mechanical property called proton spin Belectron proton Bproton 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.

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 applied external magnetic field. electron N S S N Belectron proton Bproton 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.

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 applied external magnetic field. electron Quantum mechanical property called electron spin Quantum mechanical property called proton spin Belectron proton Bproton 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.

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 applied external magnetic field. electron Quantum mechanical property called electron spin Quantum mechanical property called proton spin proton Question: So do the nucleus of all atoms possess this magnetic property or is hydrogen special?

To be imaged, nuclei must: 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? These guys will also possess a non-zero magnetic spin. H 1 C 13 6 O 17 8 F 19 9 Na 23 11 P 31 15 K 39 19 1.0 .016 .093 .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 applied external magnetic field. electron Quantum mechanical property called electron spin Quantum mechanical property called proton spin Belectron proton Bproton 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?

= No Net Magnetization Random Orientation So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? 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? = No Net Magnetization Random Orientation

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 First The 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 First The 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 Second The 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 Precession 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? Precession Demo

Magnetic Moment Vector of Proton Components of the Precessing Proton Z (longitudinal) x y z f a y xy (transverse plane) x Magnetic moment vector

Magnetic Moment Vector of Proton x y z f a (longitudinal magnetization vector) (transverse magnetization vector)

Net Magnetization Add all the magnetic moments from all the protons together at some instant in time x y z x y z x y z z z x y x y

Net Magnetization Add all the magnetic moments from all the protons together at some instant in time x y z x y z x y z z z x y x y Net Magnetization Vector

Net Magnetization Question: Anything we can say about Mxy? z z z y y x Net Magnetization Vector

Net Magnetization Question: Anything we can say about Mxy? 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! x y z (longitudinal magnetization vector) Another Question: What can we do to get a net magnetization vector in the transverse plane? (transverse magnetization 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!

RF Excitation 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. B1 time x y z x y z B1 x y x y

RF Excitation B1 + = + = B1 time t=0 z z z t=0 y y y x x x z z z t=Dt

RF Excitation B1 + = + = B1 time t=0 z z z t=2Dt y y y x x x z z z

Bo  = DtB1Dt Larmor Equation Tip Angle Tip Angle DC or static external magnetic field (the big one) Resonant Larmor frequency Bo Tip Angle  = DtB1Dt Tip Angle Amplitude of RF Pulse Time of Application of RF Pulse

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 Gradient Coil RF Coil Bo B1 4T magnet RF Coil gradient coil (inside)

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 At this time we turn off the RF excitation and use the coil as a receiver B1 time Question: What happens to the all the little spinning protons when we turn off the RF excitation?

MR Signal At this time we turn off the RF excitation and use the coil as a receiver B1 time Question: What happens to all the little spinning protons when we turn off the RF excitation? Answer: Two things The M vector starts uncoiling back to its position without any RF excitation 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).

Net Magnetization z (longitudinal magnetization vector) a y f x (transverse magnetization vector) (longitudinal magnetization vector) Simple Bloch Equation