[MUSIC] Okay, let's talk about the Slice Selection here. The Slice Selection means it determines the position of a slice to be excited by an RF pulse. And the slice was, let's consider what slice selection created to. The gradient linearly changes, the precession frequency of the magnetic momentums along a specific selection. For instance, if that is applied along g direction, and that is combined, with RF pulse so is now combined with slice selection gradient they applied at the same time. And then what happens both frequency, preferential frequency, will be specially modulated as shown in the figure. So, this figure will be typically used to represent what gradient does for spatial frequency, and both goes direction, to present frequency. And which is same as magnetic field or b field, so because Omega equals comma B, they have a linear relationship. So this Omega equals comma B, that relationship is going to be maintained along the spatial direction in a linear way as shown in the figure. So to each slice positions, so this position projection represent spatial position. And that have each of them would have different precession frequency if that RF pulse is combined with this gradient applied at the same time. And then, so without this slice selection gradient, all the proton spins within the body will have the same precession frequency and that is not actually true but you can assume like that. That is true in some sense, so if we excite, if we apply for RF pulse, Omega 2 in this case at this Larmor frequency without this gradient then all the body part is going to be excited. But if we want to excite at a specific position as shown in this figure here and then we can change this modulation frequency of this RF pulse. So this RF pulse represent the envelope shape of the RF pulse and in fact, inside this envelope is modulated with Larmor frequency, okay? And that Larmor frequency can be changed. To change it, the excitation position, so as shown here, so Omega 0 is going to be the same as Larmor frequency and then we can slightly change the transmission RF pulse modulation frequency from Omega 2 to Omega 1 to change the location of excitation as shown in this figure, okay. So without this gradient, if we applied for Omega 0, then all the body part is going to be excited. But if we apply for RF pulse, we need the frequency Omega 1 with no gradient, then none of the spins is going to be excited. So in case of axial imaging, G gradient is used as a slice selection, okay? And the sagittal imaging then X gradient is used for slice selection and for quarterline imaging, the Y gradient is used for slice selection. So since the ideal excitation profile in the frequency domain is a rectangular pulse as shown here, we want to excite only a specific region of interest in a rectangular shape. So typically, the RF pulse shape in the time domain looks like a sinc-like pulse shape as shown here. Nothing exactly syncs like sinc pulse but the sinc pulse is typically used for RF excitation, and also slightly modified and windowed the sync function is typically used for RF excitation. Okay, let's talk a little bit more detail about the slice selection, so when strong gradient is combined with RF pulse and also lets take the another case when weak gradient is combined, with RF pulse. And then these two cases will have different effect.as shown in this figure, strong gradient means slope in this figure. So frequency particular direction of frequency and spatial [INAUDIBLE] direction is a special domain. And in this field again, the slope is going to be steeper when strong gradient is used compared to the weaker gradient is used. So when strong gradient used, for the given RF pulse, the same RF pulse shape and duration. So which means, bandwidth of the excitation RF pulse is fixed on the frequency domain, and then stronger gradient will excite a with thinner thickness than the case with lower gradient. Okay, weaker gradient, and then the slope is going to be less steeper and then the more bigger area is going to be excited on the spatial domain. So that is going to be the difference. But still the location of the excitation can be changed by changing the transmission or modulation frequency, okay? So the sliced transmission frequency will determine sliced position, so which part is going to be excited. So again another factor that we have to consider is, the case with the stronger gradient and the weaker gradient, if we want to excite the same position, then the transmission frequency should also change for two different cases. So that can be exactly calculated so which part should be excited, and that can be determined based on the gradient strength and the offset position, so that can be exactly calculated based on the relationship to Omega equals g Gamma Beta. And also thickness, slice thickness also can be calculated exactly based on the RF pulse bandwidth in this case. So slice selection gradient strength also affects the slice thickness as I mentioned based on the figure. So, that is, that follows exactly the Larmor equation. So, Omega equals comma B. And in this case, B field is going to be determined by a gradient strength which is G multiplied by special location g. So here, the thickness over the slice can be determined. So, that is Delta Omega here. Delta Omega = Delta G, so which is thickness. So thickness is going to be Delta Omega, which is bandwidth of this RF pulse divided by as shown here. So that is going to determine the thickness. So in reality for the most clinical MRI scanners, the RF pulse shape and duration is typically fixed for specific scan protocol. So the RF bandwidth typically fixed. And that is just a matter of convenience so that this shape and duration is typically fixed, that the region z, you don't want to change the timing by changing the slice thickness. So if the thickness is changed and the timing can change and that makes operator very confused. So for a matter of convenience, we typically fix RF pulse shape and the duration for a given scan protocol. And then generally, these are pre-determined. And then the slice thickness And position so that is determined by the operator that can determine that determines the gradient strength as shown here. So the sequence determines gradient strengths and then that gradient strength and space the location to be excited determines transmission frequency. Okay, that can be also calculated based on the Larmor equation, omega = comma B, or comma G, G, as shown here. So another thing we have to consider for the slice selection is a little bit more complicated than slice selection concept itself. Okay, the slice selection gradient enables us to selectively excite a slice of interest, so that is essential part of slice selection but that also cause a problem for a nonuniform precession frequencies within the excited slice. So as shown in this figure, so this slice selection gradient and the RF pulse this combination enables us to excite only the region of interest. The slice of interest. But we didn't excite this slice, each location along G direction so this slice selection direction, so the spins we didn't excite the slice, we will have a different procession frequency because of this gradient as shown in this field. So we didn't excite [INAUDIBLE]. Each spins will have different precession frequency, which will make excited spins to be out of phase. So we cannot observe signal the signal because all these spins within the excited slice will have different phase. So, to make this excited spins to be in phase along this G direction, so we have to apply for a gradient called slice refocusing gradient, which will make these protons, the space dephased because of these RF pulse and gradient combination to make in phase. So we have to apply for gradient with opposite polarity in the same half the duration of this RF pulse. So the reason is we can assume this RF pulse is obliged during this time period as shown in this figure but we can assume that actual RF excitation happened within the middle of this RF pulse. Okay, so this point is considered to be the time point of RF excitation, that is representative, effective point. So, because of that we have to refocus the phase, we have to apply for gradient in the amount of the gradient applied during this period. So the phase induced by the nonlinear precession frequencies is proportional to comma Gz 2 Tao over 2. So here Tao is the RF pulse duration. Sorry comma Gz G Tao over 2, okay? So the same phase with opposite polarity can be induced by applying a negative gradient with half the area of the slice gradient. Okay, so this is called the slice refocusing gradient. Okay so this part completes the slice selection, so by applying for this RF slice refocusing gradient all the excited spins going to be in phase at the slice selection, so this is going to complete slice selection part.
