Let's talk about the concept of relaxation here. So, as I mentioned before, so when RF energy is applied along x-prime direction, transverse magnetization is flipped towards y-prime direction. So, in case of 90 degree RF flipping, then it will be completely moved to transverse direction. And when we stop applying RF energy, magnetization will return back to original state, and this is called relaxation. So, in the viewpoint of transverse direction, the transverse component will get in-phase originally and then these fields will get dephased back to original state. So, after magnetization, the longitudinal component is completely moved to transverse direction, which maximizes the in-phase component along the transverse direction. Now, those in-phase component, get out of phase. That is the signal decay in the viewpoint of transverse direction. And along the longitudinal direction, there's a longitudinal magnetization, it becomes zero after magnetization and then return back to original high longitudinal component. So, that is about relaxation along the longitudinal direction. So, the application of alpha pulse generates transverse magnetization, and it can be detected as an exponentially-decaying sinusoidal signal, which is called the free induction decay in an RF coil. And then, the magnetization returns back to the original state, which is called relaxation. So, this is the signal component as a function of time that we can detect in the RF coil, which is called free induction decay. And then, as I mentioned, there are two relaxation mechanisms. One is a transverse relaxation, it is called a T2 relaxation, which is also called a spin-spin relaxation, and the reason is that signal decay is about the interaction between the proton spins and then makes the proton spins out of phase and the signal decays. So, this is the decay of transverse magnetization by random dephasing, and this is irreversible because this is caused by random spin-spin interaction. And the longitudinal relaxation is called a T1 relaxation or a spin-lattice relaxation, and it's about the recovery of the longitudinal magnetization. And it's related to the energy so we absorb energy and then the longitudinal component gets recovered back to original by emitting the energy to the surrounding tissue. So, it's about the spin-lattice relaxation, so energy emitting procedure. So, these two relaxation phenomenons are completely independent to each other, and we can consider these two as flushing a toilet. So, when we flush a toilet, and then the water cleans the toilet and that is related transverse relaxation. So, that is about action time of the toilet. And then after that, the water should refill the toilet and then it takes time, and then that is about the longitudinal relaxation. And then, sooner water is partly refilled. And then, if we flush again, and then the actual water that can be used for the cleaning the toilet will get reduced if we don't wait long enough. So, the actual MR signal that can be detected is only for the transverse component. But this longitudinal component is also very important because that longitudinal component will be used to generate the next transverse component of the MR signal. So anyway, these transverse relaxation and longitudinal relaxation are completely independent. And also, transverse relaxation is linked to the MR signal decay, right? So, the faster the transverse relaxation, the faster the magnetization decay. And this longitudinal relaxation is recovery of the actual MR signal for the next excitation. So, this is related to the recovery of the MR signal. So, the faster the longitudinal relaxation, the higher the MR signal for the next magnetization. And magnetization for the MR imaging, we have to repeat this procedure multiple times to generate imaging. So, this recovery is directly related to the MR signal. So, you may have to remember for the period after the next week. So, let's talk about the relaxation or even more. And T2 star relaxation is actually measured MR signals actually decay faster than T2 decay, and because of magnetic field inhomogeneity, T2 star is shorter than T2. So, it can be presented in this equation. So, one over T2 star equals one over T2 plus one over T2 prime. And then here, the T2 prime is decay associated with the magnetic field inhomogeneity. Relaxation due to T2 prime is reversible and this one here. So, there's a T2 decay, and T2 star decay is a little bit faster. Well, this T2 star decay can be recovered by using 180 degree pulse. I'm not going to talk detail about that here but we will explain that later much more detailed. So, when there is a start line and there are a few students, and each of them may have a different speed. And some students may run fast and some students may run slow. Okay. But that is related to the pre-cession speed, which is related to magnetic field strength. So, M_0 equals gamma B_0. So, that determines our pre-cession speed. So, it can be considered here for the students. Some of them may run fast, some of them may run slow. If we let them start all together, and then they run together, and then at some point we may ask them to come back. And then, they will return back to the original state at the same time, and that they will return back to the original state at the same position. So, this location of the students get dephased. But once we ask them to come back, and they will get in-phased. Well, so, this procedure can be reversible. So, the speed due to magnetic field inhomogeneity can be considered as a speed in balance, and they can be recovered by applying for 180 degree pulse, which is the same as asking the students, "Come to back to the original state." They will get in-phased again. But, if those students can interact each other, some of them may push them, or some of them may just interact each other very randomly. Then some students may get a position in a slightly different location. Some of them may get faster or some of them may get slowed. And then after that, we ask them to return back to the original state and then they may not be in-phase, slightly out of phase. Okay. As shown here. So, there will be certain dephase because of the random interaction between the students. So, the dephasing due to random interaction between the students can be considered as a T2 relaxation. So, T2 relaxation is about interaction between the proton spins in a random manner. So that is irreversible. But, the decay due to magnetic field inhomogeneity, which means M-0 equals to gamma B_0. In that equation, B_0 is not uniform. So the M_0. The precession frequency is not uniform and that can be reversed by applying for 180 degree pulse. Okay. That is the concept of the T2 star. So, that is a combination of those two components. So here, the relaxation time constant, T1 and T2 are tissue-specific parameters, and serve as a source of MR signal contrast as they are depending on B_0 but not on scan parameters. So, this is intrinsic parameters specific to our tissue of interest, an important parameters to determine MR signal strengths and contrast. And T2 star and T2 prime are tissue-specific but they may depend on scan parameters because they depend on magnetic field inhomogeneity. And this magnetic field inhomogeneity can be determined. How big is the MR imaging pixel? So, how uniform within the MR pixel, and that determines the parameter of magnetic field inhomogeneity. So, they are tissue-specific component, T2, plus non-specific component, T2 prime. So they are a combination. So, MR signals transverse component can be represented as a M_ xy equals M_xy0 original component, T2 minus T Plus T2, those MR signals gets decay following this time constant, T2. So in fact, the decay is faster than T2 because of magnetic field inhomogeneity, and then this transverse component can be represented as a M_xy0, original state multiplied by etomized T2 star. And then, the longitudinal component can be represented as M_2 minus M_0 minus M_00. And then, this component is the flipped component, and this flipped component will decay following etomized T1 following T1 recovery, which means the signal gets closer to the original M_0. So, this equation represent the MR signal behavior along the longitudinal direction, which can be presented following T1 time constant. And the transverse component is MR signal decay, which can be represented by T2 or T2 star. Okay. Here is the summary of the content in this week. The MRI is concerned about the charge and angular momentum of nuclei of atoms. And when protons are placed in a strong external magnetic field, the magnetic moments tend to align parallel or anti-parallel to the field, and the magnetic moment rotates, which is called pre-cession, and it rotates along the axis over the magnetic field at a frequency proportional to the external magnetic field, which is called Larmor frequency, and the equation is called Larmor equation. So, M_O equals gamma B_0. And then, magnetization caused by slightly higher number of spins parallel to the field is called a spin excess. And there are a majority of the spins parallel to the field and anti-parallel to the field, they cancel each other. And this small number of spin excess generates the magnetization, and it's the source of the MRI signals. When RF energy is applied at the pre-cession frequency of proton spins and some spins parallel to the field move to the state of anti-parallel to the field, and then generating in-phase transverse component, which is detectable in the RF coil. And that's the mechanism of generating MR signal, and when application of the RF energy stops and the net magnetization returns back to the original state, which is called relaxation. And the relaxation time constant tissue-specific and sources of image contrast. Okay. These are the summary of the content in this week. See you next week.