Name

Professor

Institution

Physics in (MRI) Magnetic Resonance Imaging

Date

Physics in Magnetic Resonance Imaging (MRI)

Instruction

An MRI is the image produced by a complex interplay that occurs between the RF pulses and the other intermittently activated fields. Both factors in play are under the control of a computer. For an MR image to be generated there must be a combination of both the spatial and the intensity information.

Figure SEQ Figure * ARABIC 1

The spatial information are recorded in various frequencies that must comprise of the spin echo signal. However, it is necessary to assume that the frequency of the true resonance will depend on the actual value (local) of the magnetic field in operations. On the other hand, McRobbie, et al, (2004) argues that it is also necessary to note that the magnetic field must be uniformly designed, and temporarily superimposed on the focal static field

Q1: Describe how MRI sequences spatially encode nuclei in the read and phase direction.

Based on the key principles of MRI such as relaxation, selective excitation, phase encoding and frequency encoding, it is easy to note that when a receiver coil set alongside an object, a current is induced in the object’s coil by a transverse magnetization. The signal is an integral of the real magnetization on throughout the volume. Therefore:

The spatial encoding has to vary the frequency of w(x; y; z; t) and the phase above the volume form each measurement to help in the recovery of the initial magnetization from the group of integrals. To achieve this, the variable (stationary in time) is applied to induce spatial distribution of frequencies over the whole volume. It is also noticeable that the spatial derivatives of: is responsible for the determination of the local resolution of the final image. However, since the constant gradients usually yield a uniform resolution all over the entire volume and the optimal bandwidth characteristics of the real current pattern in the gradient coils, it is quite easy to find that the linear magnetic fields are used in the MRI. In the light of the above statement, it is noteworthy to indicate that the selective excitation, frequency encoding and phase encoding are useful in MRI (McRobbie, et al, 2004)

Q2: Why are two Fourier transforms required to convert k-space data to an image?

Two Fourier transformations are required to convert k-space data to an image because the first Fourier transformation is in the read direction while the second one is n the phase direction of the K space data.

Explanation

After the first Fourier transformation, it is imperative to note that the intensity profiles that occur I the read direction is only a graphical representation of the of the real signal intensity in the Fourier’s read direction, as shown in figure 2 bellow:

Figure SEQ Figure * ARABIC 2: k space after the first Fourier transformation

If the information is to be viewed in reference to the phase direction, the intensity of the signal variation is likely to remain in an echo form as shown below:

Figure SEQ Figure * ARABIC 3: Data as echo

However in this direction, the spins are usually spatially encoded by just incrementing the actual phase of the spins. In the phase direction, the spins are spatially encoded by incrementing the phase of the spins. As the magnetic field is passing through zero, which is at the centre of the imaging magnet used, it is necessary to add the magnetic field strength to the spins occurring at the axis of the applied gradient. This may result in no change in phase for the nuclei positioned at the midpoint of the applied phase gradient. In the second Fourier transformation, the actual position of the nuclei in the frequency, as well as direction is easily determined. It is also healthy to state that the image of the actual nuclear spin density is generated inside the slice with respect to its position inside the same slice (Vinitski, et al, 2003pp, 501-511).

Q3: Draw a pulse program diagram for a spin echo pulse sequence. Discuss how each component of the MRI experiment affects transverse spin coherence and how this affects the lines of k-space data

Spin Echo Sequence

In the in echo pulse sequence diagram bellow, the pulse sequence is easily timed by adjusting to provide the T1-weighted, the Proton or spin density, as well as the T2-weighted images. However, the Dual echo as well as the multiecho sequences can easily be employed to obtain proton density as well as the T2-weighted images at the same time (simultaneously).

Avram et al., (2006, pp, 891-895) states that there are mainly two variables that are of interest, the TR (repetition time) and the echo time (TE). All of the sequence of the spin echo sequences usually have a slice selective 90 degree pulse, and the 180 degree refocusing pulses respectively(see figure 4 below)

Figure SEQ Figure * ARABIC 4: pulse diagram

However, Low, et al, (1994, pp, 637-645) in argues that, the RF (RF is the radio frequency pulse) which is a slice selective 90 degree pulse, is usually followed by either two or multiple 180 degree refocusing pulses. It is essential to note that the GS, GP, and GF are mainly slice selective, phase encoding, and the frequency encoding gradients, correspondingly. However, the echo in the diagram represents all the signals that are received from the actual slice succinct in the body. It is also advisable to note that if the TR and the TE are short, they will give a T1-weighted image (McRobbie, et al, 2004)

On the other hand, long TR and short TE are likely to give a proton density image. However, a long TR and TE give a T2-weighted image. These changes in the net magnetization are shown bellow as they occur for s spin echo sequence

Figure SEQ Figure * ARABIC 5: Typical T1’s, T2’s and ρ’s for Brain Tissues at 1.5 T

Selective irradiation is critical in reducing a three dimensional sample must be reduced into a one dimensional component. This is also referred to as slice selection. The effects are also felt as there is the need to saturate all the spins that are outside the actual area of interest (see below)

Then the unsaturated spins must also be tipped into another transverse plan by applying a gradient along an x-axis, then again along the y axis: The Fourier method is efficient for this as it helps in eliminating the limitation of fast imaging sequences like the EPI, especially when implementing and switching the gradients at a faster rate. This is achieved by use of spiral imaging as it covers the k-space. The spiral imaging is also useful for sampling the real center of K-space first and low spatial frequencies that are likely to affect the image (Lenz, 1994, p. 779).

Figure SEQ Figure * ARABIC 6: The pulse sequence diagram and coverage of k-space for spiral imaging

Bibliography

Avram et al., (2006). “Conjugation and Hybrid MR Imaging,” Radiology 189:891-895.D. W. McRobbie, E. A. Moore, M. J. Graves, M. R. Prince. (2003). MRI – From Picture to Proton. Cambridge University Press.Lenz, G.W., (1994). “Dual Contrast Turbose Sequence Optimized For Low Field Strength,” Medical Engineering Group, Siemens AG, Erlangen, Germany, SMRM, p. 779.

Low, et al., (1994). “Fast Spin-Echo MR Imaging Of The Abdomen: Contrast Optimization and Artifact Reduction,” SMR, vol. 4, No. 5, JMRI, pp. 637-645.

Vinitski, et al. (2003). “Conventional and Fast Spin-Echo MR Imaging: Minimizing Echo Time,” JMRI ; 3:501-511.