T2 Relaxation, Spin-spin Relaxation, Free Induction Decay, Transverse Decay | MRI Physics Course #4

hello everybody and welcome back so in the previous talk we looked at the process of nuclear magnetic resonance where we placed protons within an external magnetic field and they aligned with that magnetic field processing at a set frequency we then applied a perpendicular radiofrequency magnetic pulse that caused those protons to start resonating in Phase with one another and Fanning out away from that longitudinal magnetization Vector that net magnetization Vector then gained more and more transverse magnetization and if we flip that net magnetization Vector to 90 degrees we completely lost the z-axis magnetization the longitudinal magnetization

and at the same point we've completely gained transverse magnetization at 90 degrees we have our maximum transverse magnetization Vector so that process of nuclear magnetic resonance and the application of a radio frequency pulse caused loss of longitudinal magnetization and gain of transverse magnetization in the next two talks we're going to look at the process of relaxation which happens in two separate independent mechanisms the first is the loss of transverse magnetization otherwise known as T2 relaxation the second process which is independent of that first process is what's known as T1 relaxation or the gaining regaining of

longitudinal magnetization so in today's lecture we're going to look at T2 relaxation which is the loss of transverse magnetization now there are multiple different terms for this that I want to introduce you to the first is what's known as spin spin relaxation we've seen in previous talks that the loss of transverse magnetization comes from this spins going out of phase with one another as we stop that radio frequency pulse the spins that were resonating in Phase start to de-phase from one another and the rate at which they defaze depends on which tissue they're in now

that dephasing is primarily caused by spins interacting with one another the way I to remember this is that spin spin has two s's here so spin spin is related to T2 relaxation now if you take that analogy of spinning a basketball on your finger if I had many people in the room and everyone was spinning a basketball on their finger and the basketballs bumped into one another those basketballs will start to lose some of their Spin and they will be de-phasing or spinning at different rates from the basketballs in the room that is the process

for the loss of phase in T2 relaxation another term that you may come across is what's known as transverse Decay and this makes sense as protons defaze they lose their transverse or their net transverse magnetization vector and we get a loss of signal because it's a transverse signal that we're measuring in our MRI machine so if you imagine these as basketballs these protons here and they're bouncing into one another and as the spins interact with one another the spins with different energy levels as well the energy is transferred and those spins become out of phase

and that's the predominant mechanism for the loss of transverse magnetization so let's have a look at an example here we have a unit of fat represented by this orange color here and a unit of CSF represented by this blue color here we've applied a radio frequency pulse that matches the processional frequency of these net magnetization vectors and we flip that net magnetization Vector to 90 degrees our maximum signal now what happens when we turn off that radio frequency pulse while those processing spins will now start to de-phase and if you think about what fat is

made up of it's made up of long chains of triglycerides where all the molecules are joined together they can bump into each other really easily if we take our room full of people with basketballs on their hands fat has got chains of people holding hands with one another and as they move around the room they're much more likely to have their spins or the basketballs bump into one another water or CSF has free people walking around in the room free to move as they please they're not joined to other people in these long chains of

fatty acids so water they're less likely for the spins to interact with one another there's more free movement in the room so you'll see that the phase of water or CSF stays much more in Phase than fat does let's have a look at these two separate tissues and see how they behave differently as they start to lose phase in the transverse plane as you see in CSF here the net magnetization Vector is staying much more in Phase the spins aren't interacting as much as they are in fattier and we see that the signal generated from

fat is lost much more quickly than the signal generated from CSF so now we can draw these curves here which are our T2 relaxation curves that are dependent on the type of tissue through which the spins are spinning look in fact here how outer phase those spins are and as we know as we get out of phase our magnetization vectors in the X Y plane start to cancel each other out and after a period of time we're getting complete loss of that signal in fat the water has stayed relatively in Phase with one another and

although we're still getting lots of signal because they're not perfectly in Phase that loss is much slower and for each tissue we can plot that free induction Decay curve for the different tissues now you'll see that I've written T2 star Decay here and not T2 Decay now whenever you put an asterisk somewhere it means that there's some terms and conditions and the reason for this T2 star Decay is because the actual measurable Decay that we measure on the MRI machine the drop off of signal that we were looking at at the previous slide is not

purely due to the spins interacting with one another T2 relaxation in an ideal world would only be getting loss of that transverse magnetization Vector from spins interacting with one another spin spin relaxation now in the real world we get loss of signal because of spin spin relaxation but we also get loss of signal due to magnetic field in homogeneities which we're going to look at next before we move into that I want to draw your attention to these T2 star time constants here at the beginning of our radio frequency pulse once we flip those net

magnetization vectors to 90 degrees we have maximum signal and all those protons are in Phase with one another we have a hundred percent of the transverse signal at 90 degrees this is our transverse magnetization vector now as time goes by we get lots of that signal because of the dephasing of those atoms and it happens at different rates depending on the tissue we're in when 63 of that signal has been lost or we have 37 of the transverse magnetization Vector left that time constant the amount of time it takes to get to that point is

what's known as T2 star or T2 star Decay and we can use these values to get contrast in our tissues later now in an Ideal World we wouldn't want T2 star we would want a T2 value which would represent 63 loss in the transverse magnetization Vector purely due to spin spin interactions not due to magnetic field in homogeneities and this curve here would be known as our T2 relaxation curve we've seen that the t2 star relaxation curve happens much quicker in tissues now if we have a look at our MRI machine here in an Ideal

World the magnetic field would be homogeneous it would be exactly the same no matter where the protons are within this magnetic field now there are three separate mechanisms that make this magnetic field inhomogeneous and cause that T2 star Decay the first is that the MRI scanner itself can't make a perfect strength magnetic field that's equal all the way through the transverse plane the coils are going to have differing magnetic field strains the further away from the coils you get so that's the first reason for magnetic field in a motor geneties the second mechanism is that

there could be a substance within the patient either metal or calcium or dense cortical bone that causes disruption in the local magnetic fields here and that's why in a patient that has a metal device you'll often see T2 signal is completely lost around that device that's because of the localized changes in the magnetic field strength and the last thing is when spins start to de-phase with one another the magnetization vectors are becoming out of phase with one another and they can disrupt the local magnetic field as well and so we don't get perfect magnetic field

lines in the longitudinal plane here so all three of those mechanisms cause the magnetic field to be in homogeneous now because the field is inhomogeneous a proton that is sitting here will experience a different magnetic field strength to a proton that is sitting at a different location and we've seen that when protons or spins experience different magnetic field strands they will spin at different rates we look back to our alarm frequency a different magnetic field strength will cause the dephasing to be increased because the rates of change of those processional values will be different between

those two protons and that's what's responsible for this T2 star effect occurring now our T2 star or the free induction Decay Curve will always be less than the t2 value the t2 relaxation value and in imaging we want to try and compensate for this reduction or increased rate of loss of transverse magnetization and there actually is a mechanism for which we can compensate for these local field in homogeneous 80s so let's have a look at how we go about compensating for that T2 star decay when we are trying to produce an image the first thing

we need to do is apply a 90 degree RF pulse that is perpendicular to the main magnetic field once we've applied that 90 degree RF pass and turn it off we will get relaxation T2 relaxation where we get loss of transverse magnetization now in an Ideal World the transverse magnetization loss will be June only due to spin spin interactions where spins are transferring energy and they start becoming out of phase because of that transfer of energy between the two spins that is what's known as our T2 Decay or T2 relaxation now what actually happens in

the real world is we get spin spin interactions which cause that loss of transverse magnetization and we get local magnetic field in homogeneities which causes this T2 star Decay to occur so this is what we want this T2 relaxation this is what we actually measuring because of the inhomogeneities within the magnetic field so what has actually happened here well we've taken our longitudinal net magnetization vector and flipped it to 90 degrees with that 90 degree RF pulse we've completely lost longitudinal magnetization and we've now got a maximum transverse magnetization we've got maximum T2 signal here

now what's going to happen is these spins in the same voxel within our image are going to defaze with one another if we look at it end on they're going to D phase like this some of them will move faster than others and that's mainly due to the spin spin interaction between the different spins but we've also seen that there is differing strengths of magnetic field strength because of that local inhomogeneity in the magnetic field now the one that's experiencing a higher magnetic field strength is going to defaze quicker than the one that's experiencing a

lower magnetic field strength so we've flipped it to 90 degrees and we're getting de-phasing of these spins now what happens is over time these spins will defaze with one another and they will also start gaining longitudinal magnetization now the one is dephasing faster than the other what we want to do is be able to re-phase these two spins with one another and the way we do that is by applying what's known as a 180 degree radio frequency pulse it's the same radio frequency pulses this 90 degree radio frequency pulse same magnitude but for twice the

duration so what has happened now one spin is de-phasing faster than another Spin and we apply a 180 degree RF pole so let me get this right here this is the faster one the blue is the slower one we apply a 180 degree radio frequency pulse we are flipping those spins now 180 degrees here is our main magnetic field now the leading spin is the slow Spin and the trailing spin is the fast spin we're spinning or processing in this direction now what is going to happen over time is the faster spin is going to

catch up with the slower or the lagging Spin and if we wait the exact same period of time between our 90 and 180 degree pulse what will happen is those spins will now become in Phase with one another because of that 180 degree spoon and we have gained now that net magnetization Vector in the transverse plane our spins have re-phased with one another and you can see that represented by this graph here is that as the spins start to re-phase with one another we get an increase in that transverse magnetization Vector because of that 180

degree flip and then allowing those spins now to catch up with one another and sync up giving us a maximum net transverse magnetization vector and what we can do then is sample the signal at this point and if we sample the signal at this point you'll notice that that signal is the same as the t2 relaxation the signal we're measuring now at the time to Echo and you can see now why it's called an echo is the same as what we would have gotten if the loss of transverse magnetization was only because of spin to

spin interactions or T2 relaxation and it's this mechanisms which we're going to look at later in a pulse sequence called spin Echo sequences that allows us to regain that T2 relaxation and account for those local inhomogeneities in the magnetic field and we can do this for all the different tissues all the different voxels within our patient and plot these values over time now importantly we can place this 180 degree RF pulse wherever we want to place it and then measure the echo at the same distance between the 90 degree RF pulse and the 180 degree

RF boss this distance and this distance is the same we can make this te time much shorter or or we can make it much longer a shorter te time will give us higher signal and a longer te time is going to give us lower signal and if we plot those signals over time depending on the different tissues that we're trying to image we can see that T2 relaxation curve it takes much longer in CSF because those hydrogen protons are able to move freely in fact you think of people holding hands in the room spinning basketballs

in those long triglyceride change the basketballs are going to bump into each other and that spin spin interaction is going to cause a loss of transverse magnetization and that happens even faster in muscle now we've seen that we can choose the time to Echo when we're going to sample this tissue if we sample really early a short time to Echo we flip that longitudinal magnetization Vector into 90 degrees switch off the RF pulse and immediately sample the tissue what we get is a short time to Echo now you'll see that the signal here is high

for the muscle for the fat and for the CSF we're going to have a high signal and there's going to be no contrast between these tissues we've got very little difference in the t2 relaxation times between these tissues if we wait a longer period of time and make our Echo slightly longer you'll see that the signal has decreased but the contrast between the various different tissues has increased our muscle signal is going to be much lower it's going to be represented darker on the MRI fat is lower than CSF but higher than muscle and now

CSF is still giving us a bright signal value waiting or prolonging the t2 times going to increase the contrast between those two tissues so you can see how changing te time changes the contrast and that contrast is based on the t2 relaxation differences between these tissues now we can wait even longer and have a third time to Echo here where we've now got very little signal and again we've lost contrast here there's very slight grayscale differences but now it's difficult to tell the CSF from the fat and from the muscle so if you wait too

long without time to Echo we're going to lose that transverse magnetization vector and not have any signal to detect now hopefully this graph shows you that change in the te will highlight the differences in T2 relaxation differences between the various different types of tissues in the next talk we're going to be looking at T1 relaxation and I'm going to show you how we can use T1 relaxation differences in order to see the T1 differences between tissues so until that talk I'll see you all then goodbye everybody