The Frequency Encoding Gradients and Phase Encoding Gradients - Essay Example

? Physics Assignment This paper seeks to respond to a number of questions touching on among other factors, the frequency encoding gradients, phase encoding gradients (question one), Nyquist’s theorem (question two), Radiofrequency pulse (RF), the slice select gradient, Readout (frequency encoding) gradient, as well as signal acquisition (question three). These questions have been responded to in a certain chronological order as follow. Response to Question 1: Frequencies encoding gradients, as well as phase encoding gradients areboth essential part of the spatially encoded data. It is, thus, true that using the induced differences in the frequency and the phase of precession, makes the data amenable for analysis by the Fourier transform(the read of the MR signal which stored in the K-space represent the Fourier plane). (Kaut-Roth et al, 2005). Frequency encoding gradient helps locate signals along the long axis of the part that is imaged.In the event that the slice is selected, the signal that originates from the slice should always be positioned on both axis of the image.In respect to this, the signal position along the axis of the gradient can be determined from its frequency. This is achieved through establishing a difference in the frequency either linearly fashion or through a shift in the signal along the gradient axis, in which case the frequency encoding gradient is turning on.In the course of acquiring the signal it is often the frequency encoding gradient that is turned on. This is explains why it is often referred to asa readout gradient. As has been established through research, the degree of the steepness of the frequency encoding gradient slope often determines the field of view of the anatomy that undergoes scanning and it is known to be the last period of spatially encoding the signal (Kaut-Roth et al, 2005). Phase encoding gradient is used in locating signals throughout the short axis on the image.The process of turning on the phase encoding gradient takes place following the application of RF pulse. The magnetic field strength of the nuclei and its precessional frequency gets altered linearly through switching on the phase encoding gradient.In the event that the pace of the nuclei precession is changed, the resultant magnetic moments phase is altered as well, and it is because of this alteration that the precessional frequency path is changed. In this respect, Nuclei that are accelerated by the effect of the gradient tend to move faster than their precessional path as opposed to the case in which the phase encoding gradient is switched on. On the contrary, for nuclei that are slowed down, the reverse is true. It is the degree of the steepness in the phase encoding gradient slopethat detects the amount of phase shift between the two different points throughout the axis of the gradient. In essence, it implies that a steep gradient creates a large shift in the phase between these two points along the gradient axis. However, the shallow gradient create smaller shift between these two points (Kaut-Roth et al, 2005). Response to Question 2: This part deals with the Nyquist’s theorem. This is a theorem that is used for determining accurately the speed of digitizing frequency of the sine curve. For this to apply, the process of sampling the signal should always be equal or larger than double the signal frequency. When such happens, more points acquired results in better defined frequency. Dwell time is experessed mathematically as: Dwell time = 1/ (2?sweep width) (MRES7004, 2012). Dwell time = 1/(2?20,000) = 2.5 microseconds While acquisition time is, on the other hand, expressed mathematically as: Acquisition time = dwell time ?no. of data points Acquisition time = 0.64 miliseconds. Response to Question 3 This question is based on analyzing diagram of five lines have five processes. The 90 degrees RF pulse (excitation pulse) causes the longitudinal magnetization vector to move along the Z axis into the x-y plane (transverse plane). Due to the magnetic field inhomogeneity on the transverse plane magnetization, it becomes dephased. In such a case, a180 degrees pulse is required in order to rephrase them and make them reappear (Kaut-Roth et al, 2005). In regard to the slice select gradientin the diagram, turning on the gradient of slice selection coil causes the local magnetic field strength and the processional frequency of the nuclei that existed along the gradient axis to change linearly. This way, there is always the specific area along the gradient axis with a particular processional frequency. In respect to this, the particular alteration specifies the slice that need be excited. This is done through sending the RF pulse that has a range of frequencies that match the spins frequencies within the selected slice. During this process, the Nuclei within other slices and along the gradient axis do not become excited. This is because of their having different frequencies (Kaut-Roth et al, 2005). In practice, there are three gradients that select slice during the RF pulse. They include the gradient in z axis for axial slices, the X gradient in x axis for sagittal slices, and the gradient in y axis for coronal slices (Kaut-Roth et al, 2005).Occasionally, it is switched on during the period of the 90 degrees RF pulse application. The function of the gradient, in such applications causes the nuclei magnetization to lose their coherence quickly along the transverse plane. In order to regain the coherence magnetization of the spins, another gradient is applied along the opposite direction for purposes of rephrasingthem.In this regard, the same time, as well as the amplitude used in the first gradient need to be used in the opposite gradient. In such cases, it is worth noting that each line of the K space represents one slice with the position of slice select gradient at the center of the K space (Kaut-Roth et al, 2005).The slope of the select gradient helps in distinguishing different values in the processional frequency for two different points along the gradient.This, thus, implies that when the steepness of the gradient slope is high, it gives vast difference between the two points in their processional frequencies along the gradient axis. Using shallow gradient slope leads to small difference being created in the resultant processional frequency between the two points. This, therefore, means, in order to scan thin slices, steep gradient need to be used. On the contrary, in order to scan thick slices shallow gradients need to be used (Kaut-Roth et al, 2005). For the case of the Phase encoding gradient in the diagram, the gradient is to be applied immediately prior to the application of the 180 degrees RF pulse. Whenever it is applied, the net magnetization phase (lose coherence) leading to signal reduction. The phase gradient is altered in every repetition time (TR), following the use of rephrasing gradients for filling different lines in the K space with data. Using the high phase encoding gradient causes a decrease in the signal intensity. Clearly, this show that highest signals are often gained in the absence of phase encoding gradients application (Kaut-Roth et al, 2005). Research show that Readout (frequency encoding) gradient is the gradient that is applied through the period of the signals acquisition, once frequency encoding gradient is turned on, the magnetic field strength of the nuclei and, therefore, their processional frequency is changed linearly along the frequency encoding gradient axis and these frequency changes are characterized by where those nuclei are located along the frequency encoding gradient. In this case, the signal dephases quickly whenever the readout gradient is switched on because of the phase coherence losing and the signal approaching zero. In order to regain the signal, another gradient, which is always acting in the opposite direction to the first gradient (called preparation gradient), is applied. In this case, this preparation gradient can be positioned either prior or after the application of the 180 degrees RF pulse. If the preparation gradient is to be applied before the application of 180 degrees RF pulse, the preparation gradient direction must always be in the same direction as the primary gradient. This is due to rephrasing of the spins by the 180 degrees RF pulse. The positive gradient prior to the 180 degrees RF pulse equals the negative gradient applied after the 180 degrees RF pulse. The magnitude of the preparation gradient has to be equal to halfthe magnitude of the frequency (readout) encoding gradient.In such cases, each echo acquired during the frequency encoding (readout) gradient is positioned in a separate line in the K space. In a case such as the 256?256 matrix,there are 256 points to be located in one line of the K space (Kaut-Roth et al, 2005). When dealing with the signal, it is worth noting that high signal acquisition is obtained when the echo reaches the peak, as well as when each echo acquired during each TR and after each application of 90 degrees RF pulse is followed by application of 180 degrees RF pulse. In this case, each echo is to be positioned in a different K space line and the number of echoes entirely depend on the number of phase encoding gradients applied (Kaut-Roth et al, 2005).Moreover, two dimension inverse Fourier transform is needed to get an MR image from K space data (Denis H, 2009). References Denis, H. (2009). K- space exploration. Retrieved on 19th Sept 2012 from http://www.imaios.com/en/e-Courses/e-MRI/The-Physics-behind-it-all/K-space. Kaut-Roth, et al.(2005).MRI in Practice (3rd Edition).New York: American Registry for Radiologic Technologists (ARRT). The University of Queensland, 2012. Standard Imaging sequences, image reconstruction and applications. Retrieved on 19th Sept 2012 from MRES7004. Read More