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 MagnetGradient CoilRF Coil 4T magnet gradient coil (inside) B0B0

Magnetic Fields are Huge! Typical MRI Magnet: 0.5-4.0 Tesla (T) Earths magnetic field: 50 Tesla

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 Lets first look at a simple hydrogen atom without any applied external magnetic field.

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Lets first look at a simple hydrogen atom without any applied external 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? Lets first look at a simple hydrogen atom without any applied external 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. B electron B proton

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Lets first look at a simple hydrogen atom without any applied external 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. B electron B proton S N N S

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Lets first look at a simple hydrogen atom without any applied external 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. B electron B proton

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Lets first look at a simple hydrogen atom without any applied external 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? H 1 1 C 13 6 O 17 8 F 19 9 Na 23 11 P 31 15 K 39 19 These guys will also possess a non-zero magnetic spin..093.016 1.0.066 Relative sensitivity compared to hydrogen

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Lets first look at a simple hydrogen atom without any applied external 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? B electron B proton

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Random Orientation = No Net Magnetization 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, lets look at a proton when we apply an external static magnetic field B o Bore (55 60 cm) Shim (B 0 uniformity) Magnetic field (B 0 ) Body RF (transmit/receive)Gradients

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Now, lets look at a proton when we apply an external static magnetic field B o First The protons magnetic dipoles tend to orient themselves in 1 or 2 states (spin and spin - 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, lets look at a proton when we apply an external static magnetic field B o First The protons magnetic dipoles tend to orient themselves in 1 or 2 states (spin and spin - 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 dont 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, lets look at a proton when we apply an external static magnetic field B o Question: So if the magnetic dipoles align both up and down why dont 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, lets look at a proton when we apply an external static magnetic field B o

So what happens to things that are normally non-magnetic when you put them inside big magnetic fields? Now, lets look at a proton when we apply an external static magnetic field B o 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, lets look at a proton when we apply an external static magnetic field B o 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, o.

Larmor Precession Now, lets look at a proton when we apply an external static magnetic field B o

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 xy (transverse plane) x y z Magnetic moment vector

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

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

z x y x y z x y z z x y x y z Net Magnetization Vector Net Magnetization

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

Question: Anything we can say about M xy ? 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 (transverse magnetization vector) (longitudinal 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! Net Magnetization

RF Excitation time B1B1 x y x y z x y z x y B1B1 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 B1B1 x y z x y z B1B1 t=0 x y z =+ t= t x y z x y z x y z =+

RF Excitation time B1B1 x y z x y z B1B1 t=0 t=2 t x y z =+ t=3 t x y z x y z x y z =+

B o t B 1 t Tip AngleAmplitude of RF Pulse Time of Application of RF Pulse Larmor Equation Tip Angle DC or static external magnetic field (the big one) Resonant Larmor frequency

RF Excitation transmission coil: apply magnetic field along B1 (perpendicular to B 0 ) 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: childrens swingset final angle between B 0 and B 1 is the flip angle B 1 is small: ~1/10,000 T RF Excitation transmission coil: apply magnetic field along B1 (perpendicular to B 0 ) 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: childrens swingset final angle between B 0 and B 1 is the flip angle B 1 is small: ~1/10,000 T

Equipment RF Coil 4T magnet gradient coil (inside) Gradient CoilRF Coil BoBo B1B1

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 B1B1 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 B1B1 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). 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).

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

Documents

ELEG 479 Lecture #9 Magnetic Resonance (MR) Imaging Mark Mirotznik, Ph.D. Professor The University of Delaware