Spin, Precession, Resonance and Flip Angle | MRI Physics Course | Radiology Physics Course #3

hello everybody and welcome back today we're going to discuss the phenomenon of nuclear magnetic resonance in the previous talk we looked at the various different magnets that were required to generate the magnetic fields in MRI imaging and we saw that certain nuclei responded in a very particular way to those external magnetic fields now that response is what's governed by nuclear magnetic resonance and in order to understand nuclear magnetic resonance we first need to understand a concept known as spin now throughout your studying you're going to come across two separate models the first is what's known

as the classical model and the second is the quantum mechanical model now the classical model is more intuitive and it describes a Charged particle rotating around its own axis with angular momentum that movement of charge with angular momentum induces a magnetic field around that charged particle and the strength and direction of that magnetic field can be represented by what's known as the Magnetic Moment which we represent with this Arrow here the longer the arrow these stronger the magnetic field around this spinning particle now importantly this classical model is not actually what's happening within the particles

within the body it's a good way to think about what's happening but these particles aren't actually spinning and you'll see this model will fall short when we describe certain phenomena later on in this course for example a neutron has no charge yet it has a Magnetic Moment an uncharged Neutron if it was rotating on its own axis it wouldn't make a Magnetic Moment yet it's what we observe in the physical world now how do we go about describing that Magnetic Moment within a neutron well we need quantum physics in order to do that quantum physics

is a bizarre world it's less intuitive than the classical model and within quantum physics every property can be broken down into a discrete measurable value when we think about Quantum properties of an atom such as charge Mass color and now spin these are all properties that have distinct measurable values the way I like to think about it is looking at other Quantum properties if we look at an electron for example it has a Quantum property known as charge now charge is very difficult to describe to someone what exactly is charge it's very difficult to actually

say what it is what it does do though is it describes how that subatomic particle will react to other subatomic particles we know that other subatomic particles with a negative charge will be repelled from the electron and we know that opposite charges will attract so the quantum property there has described how that subatomic particle will react to an external Force the same thing is happening with spin it describes types how that subatomic particle or that particle will react to an external magnetic field we call this spin value spin angular momentum and they have discrete measurable

values protons for example like this proton here is made up of quarks two up quarks and one down clock which each have their own spin values and they are connected by gluons that hold those quarks tightly together in the proton the proton itself has a net spin value of a half and this spin value represents this spin angular momentum within the proton itself now you might be thinking that that's quite a difficult concept to get around we can't make an electron more or less negatively charged it has a set charge the same as a proton

has a set spin in fact electrons have a spin of a half and neutrons have a spin of a half now when two neutrons are within the same nucleus they both have a spin value of a half but they have what's known as spin up and spin down the two magnetic moments are in opposite direction and cancel each other out in a nucleus it has an even number of protons and an even number of neutrons The Net Spin value of that nucleus will be zero those proton Pairs and neutron pairs would have canceled one another

out and the nucleus of that atom would have a net spin value of zero now any atom that has a spin value of zero will be unaffected by an external magnetic field now if you think about the types of atoms within the human body we think about oxygen think about carbon and think about hydrogen now both Oxygen 16 and carbon-12 both have an even number of protons and neutrons and those even numbers mean that the spin values within those protons and neutrons cancel each other out in hydrogen we only have one proton there's no Neutron

now that proton has a spin value of a half meaning the proton has its own Magnetic Moment and will be influenced by an external magnetic field now what I'm describing here is really only scraping the surface and if you want to understand this in more depth I'm going to link some articles and videos that you can read in your own time now those principles that are linked below the Pali Exclusion Principle the Heisenberg uncertainty principle the Schrodinger equation and entanglement all of those are far beyond the scope of this course fortunately when we're not trying

to measure a single Magnetic Moment of a single proton itself but rather measure a group of protons we can take the net magnetization Vector the sum of all those magnetic moments and use that net magnetization Vector to calculate the MRI signal that we're generating and that net magnetization Vector acts very similarly to the classical model in physics and later if we come across a concept that is not explained by that classical model I will refer back to this quantum mechanical model to explain how those phenomena are occurring so why exactly do we use hydrogen well

I've alluded to it in the first place there are many different atoms that will undergo nuclear magnetic resonance all of these atoms here have a net spin that is not equal to zero we mentioned carbon 12 and Oxygen 16 earlier these Isotopes because of the extra particle within the nucleus mean that they have a NetSpend value and will ultimately undergo a nuclear magnetic resonance however we use hydrogen one because it's the most abundant isotope in the body and two because the Magnetic Moment that vector-like quality of the hydrogen proton itself is the largest out of

all of these Isotopes here it makes it a great candidate for MRI imaging and not only is hydrogen abundant but it's also abundant in various different tissues so we can compare tissues to one another now we've seen that the hydrogen proton itself has a non-zero spin value it's got a spin value of a half and because it has a non-zero spin value it will have a magnetic moment that vector-like property describing the magnetic field around that proton now throughout this course I'm going to refer to hydrogens either as free hydrogens or as protons because a

hydrogen is just one proton or I will refer to them as spins all three of those are synonyms that you will see used interchangeably so when we look at the hydrogen proton itself we say it has a net Magnetic Moment now in fact in the quantum world that hydrogen proton can exist both to spin up and spin down States simultaneously and only when we go about measuring that Magnetic Moment can we say with certainty whether that hydrogen is spin up or spin down we should rather think about the net Magnetic Moment of a group of

hydrogens where we submit all those little magnetic moments to get one net magnetization vector and that's why I'll represent a net magnetization Vector without the proton attached when you see a vector like this I'm talking about a group of hydrogen protons now the Magnetic Moment describes how those hydrogen protons will respond to an external magnetic field so it goes without saying that the Magnetic Moment and the spin value of the proton itself are linked in some way now in order to link the magnitude of the Magnetic Moment to the spin of the proton itself we

use a value that's known as the gyromagnetic ratio now this is a value that's worth learning if you're studying for an MRI physics exam this kind of question comes up a lot the hydrogen atom has a gyromagnetic ratio of 42.5 megahertz per Tesla and if we times the gyromagnetic ratio by the Spin we will get a Magnetic Moment value here now you'll see later that the gyromagnetic ratio becomes really important when determining the processional frequency of those hydrogen atoms in a magnetic field now the gyromagnetic ratio as you can see here links a specific atom

to that atom Spin and gives us the magnitude of the Magnetic Moment now we've said that when an atom with a non-zero spin is placed in a magnetic field that atom will align with the magnetic field and it will process at a certain frequency now the frequency at which that atom will process I've mentioned before is related to the strength of the magnetic field and the type of atom that it is now we can use the gyromagnetic ratio and the strength of the magnetic field strength in order to calculate what's known as the Lama frequency

if we take the specific gyromagnetic ratio of the atom of interest and we times it or multiplied by the strength of the magnetic field we will get a frequency value that's known as the Llama frequency and this is a key principle in MRI imaging if we know the magnetic field strength say it's one Tesla and we know the gyromagnetic ratio of the proton or atom that we are trying to image we can calculate the processional frequency of that hydrogen proton that becomes really important because when we start adding that RF pulse we want the radio

frequency poles to match the processional frequency if the main magnetic field strength went to 1.5 Tesla our frequency would increase by 50 you can see that multiplying a Tesla value with the gyromagnetic ratio means that the Tesla in the unit here will be canceled out and our frequency will be in megahertz now importantly what the Llama frequency is calculating is the processional frequency of the atom of interest in our case it's hydrogen now if you think about spinning a basketball on your finger firstly if the basketball wasn't spinning it would just fall off we need

that angular momentum in order for that basketball to stay on our finger as it's pulled down by gravity and you'll see when people spin a basketball on their finger they move their finger from side to side ever so slightly in order to keep that basketball spinning you can think of that as the processional frequency if that basketball were to change if you were to make it a tennis ball your frequency would have to change the frequency is dependent on the type of atom that is in that magnetic field now as those protons line with the

magnetic field we've said that some will be spin up and some will be spin down and there will be an energy difference between these two where the net magnetization Vector will lie parallel to the external magnetic field and we'll get what is known as a net magnetization vector as you can see these processing protons are processing out of phase they're at the same frequency but different phase because they're in different phases the X Y the transverse magnetization values cancel each other out and we have a net magnetization that is directly along the longitudinal or Z

axis now if we take this net magnetization vector and place it within the MRI machine this should not be processing and I want to make this clear throughout this course whenever I show a net magnetization Vector that is processing within the MRI scanner I am not saying that this net magnetization Vector has any transverse magnetization yet what I want to show you here is that the hydrogen atoms that are causing this net magnetization Vector are processing at a set frequency the magnetization vector itself should be dead still because those transverse magnetization values are canceling each

other out those hydrogen atoms are out of phase now this frequency becomes really important for when we want to induce transverse magnetization so we can calculate the specific frequency of the net magnetization vector by using the Llama equation here now once we've calculated that specific precession frequency we can apply a radio frequency pulse that matches that frequency that radio frequency pulse as we've seen is called B1 it's perpendicular to the main magnetic field if I'm spinning that basketball on my finger like this and someone gives a force to my arm perpendicular to the gravitational field

I'm going to Fan my finger out in order to carry on balancing that basketball and the axis of that basketball is also going to change the same thing happens when we apply a radio frequency magnetic force at the same frequency as those atoms are processing energy will be applied into the system and that net magnetization Vector will be knocked off the longitudinal or Z plane we will gain some transverse magnetization now importantly this radio frequency pulse needs to match the processional frequency of those hydrogen atoms in order to induce this resonance now resonance is two

things the first is it's applying energy to cause that net magnetization Vector to Fan out the second is that because the radio frequency pulse matches the processional frequency those hydrogen spins start to spin in Phase with one another they are no longer out of phase and because they are in Phase with one another we actually get a vector forming where we can measure the X Y plane or the transverse magnetization now importantly we only get transverse magnetization when the hydrogen nuclei are in phase and when they're in Phase they're undergoing what is known as resonance

now if we apply a radio frequency pulse for a certain period of time we are flipping that net magnetization vector by a certain angle known as the flip Angle now at a flip angle of say 60 degrees here we will measure a certain signal if we place a coil transverse to our main magnetic field here and that signal can be read out the signal strength the amplitude of that signal is proportional to the transverse magnetization of those in-phase processing hydrogen atoms now if we apply that radio frequency pulse for a longer period of time that

flip angle will keep getting bigger until it reaches 90 degrees that is when we get the maximum signal for our hydrogen nuclei the net magnetization Vector is now 90 degrees to our main magnetic field and you can see the amplitude of this signal is higher here so the application of a radio frequency pulse allows us to induce resonance resonance allows us to get transverse magnetization and transverse magnetization allows us to measure a signal now when we are looking at a gradient that's applied in the longitudinal direction we can calculate the specific frequency with the Lamar

equation for a specific point along this gradient if we know the magnetic field strength here we will know that the Llama frequency will be higher for these hydrogen atoms along this X Y plane here the gyromagnetic ratio for the hydrogen atoms or hydrogen protons within the sample Remains the Same but the magnetic field strength changes that changing magnetic field strength changes the frequency of the hydrogen protons that are processing within the tissues and we can select a specific slice that matches that frequency and have a radio frequency pulse that selects for just that specific slice

again the radio frequency pulse will only work if you are pushing it at the processional frequency if my professional frequency is different to my radio frequency poles they are not going to match up and that energy is not going to be transferred to those processing and now a resonant hydrogen protons so not only does resonance allow us to measure signal but it also allows us to select a specific group of hydrogen atoms based on the Llama frequency of those hydrogen atoms now what I've alluded to is that when we apply a radio frequency pulse it

takes time for those now in Phase processing hydrogen atoms to gain transverse magnetization that takes a period of time if we apply a radio frequency pulse that matches the processional frequency for a certain period of time that makes that net magnetization Vector 45 degrees we will get a certain signal if we wait that exact same period of time continually applying that radio frequency pulse that magnetization Vector will now be 90 degrees we'll have gained maximum transverse magnetization interestingly this takes half the time to generate the signal but the signal generated at 45 degrees is 70

percent of the signal generated at 90 degrees and we're going to come across sequences later where we need to measure the signal quickly and we need to use short flip angles we can't afford to wait all that time for the radio frequency pulse to get into 90 degrees and despite using small flip angles we are still generating a proportionally higher signal for the time it took to flip that net magnetization Vector 45 degrees now when we looked at the classical model with that actual spinning charged particle creating a magnetic moment we would think that the

radio frequency pulse could only flip those protons to 90 degrees if we tried to flip in more than 90 degrees the magnetic dipole of that specific proton would be opposite to the main magnetic field and we wouldn't be able to push it past 90 degrees now the quantum properties of a proton means that if we apply the radio frequency pulse for double the amount of time that it took to flip the net magnetization Vector to 90 degrees we can in fact flip that net magnetization Vector a full 180 degrees we've again lost all transverse magnetization

but now this Vector is sitting in the higher energy state anti-parallel to the main magnetic field and this is because the proton can exist in both the spin up and spin down States and you'll see as we go on throughout this course there are multiple pulse sequences when we are required to flip the net magnetization Vector a full 180 degrees and and then we wait for that net magnetization Vector to return to its resting state and you'll see why that's extremely helpful when trying to generate a true T2 signal instead of a T2 star free

induction Decay signal but that is for another talk I hope nuclear magnetic resonance has made some sense to you spin angular momentum is responsible for a Magnetic Moment within a proton that Magnetic Moment means that proton will align with an external magnetic field and process at a frequency that's dependent on the strength of that magnetic field and the type of atom that we're looking at and we can then use that processional frequency to apply a force perpendicular to that processional frequency and induce resonance within those hydrogen atoms that entire process is what's known as nuclear

magnetic resonance so I'll see you all in the next talk where we're going to look at the loss of transfer signal once we flip that net magnetization Vector 90 degrees how then do we go about measuring the loss of that net magnetization Vector so I'll see you all in that talk goodbye everybody