Assignment about MRI Physics
The magnetic moment is considered as a vector quantity whose direction is perpendicular to the current loop in a right-hand-rule direction. The magnetic moment of nuclei are the magnetic moment of the nucleus that arises from a spin of protons and neutrons. A magnetic moment of nuclei is dipole moment – the quadrupole moment causes a shift in the hyperfine structure (Mangrum, 2012).
Nuclei with non-zero spin have a non-zero magnetic moment while that have zero spins have zero magnetic moments. Different isotopes of an element have a different nuclei magnetic moment.
A nucleus with an even number of protons and neutrons have a ground state that is, lie in the lowest energy state, nuclear spin and magnetic moment in them is zero. If the nucleus has an odd number of both protons and neutrons, the nuclei spin is nonzero. Thus, there are nuclei magnetic moment. In the magnetic materials, nuclei magnetic moment is caused by the spin and the orbital angular momentum states of the electrons of the element, and whether the atoms of one region are aligned with the atoms in another atom. Poles using electrostatics analogy can illustrate the cause of nuclei magnetic moment. In a bar magnet, the poles are the sources of magnetic force. The forces cancel out partially as one pole attracts while the other repel. The cancellation depends on the strength of poles and vector separating them. The nuclei magnetic moment can be illustrated as:
1
Energy difference between the parallel and antiparallel states of hydrogen nucleus when placed in a 1.5 T magnetic field
Hydrogen atoms nuclei (protons) have a simple spin, therefore, align themselves in either parallel or antiparallel to a magnetic field. The MRI signal depends on the spin polarization. In protons, it depends on the population difference of two energy states associated with parallel and antiparallel proton spin alignment in a magnetic field. In a magnetic field of 1.5 Tesla and at room temperature, thermal energy exceeds the difference between parallel and antiparallel states. The vast quantity of nuclei produces a detectable change in the field. The nuclei align parallel and antiparallel with the magnetic field. Because of quantum mechanical relationship, individual nuclei are set at an angle from the direction of magnetic field. Bulk collection of nuclei is partitioned into a set whose sum spins are aligned parallel and another set whose sum spins are antiparallel.
Given that the frequency (f) of an x-ray is 2 x 1019Hz, the energy of the photon can be calculated as:
Solution
With the resonance frequency given, we refer it to energy using the formula
, where h is the planks constant, h = and represents the resonant frequency
Converting the frequency in Hz to rad/s
,
Where h =
Energy € = hw
h =
Converting joules to
The significance of relative energies used in MRI and CT
The significance of relative energies used in MRI and CT is that in MRI, the behavior of nuclei in the body to align with the magnetic field is used. If someone is subjected to a robust scanner, protons in the body react with the magnetic field in the scanner. In other words, MRI is significant in that it is used to view the body status depending on the location of protons.
Description of how MRI sequences spatially encode nuclei in the read and phase direction
Signals from the slice are recorded in K-space, they are then processed to form an image of slice plane. The spatial frequency encoding takes a few milliseconds of reading a signal. The phase spatial encoding involves repeatedly imaging the sequence. A single phase encoding step in a classic spin echo sequence is performed in every repetition time (TR). As the repetition time, values can be of up to three seconds; the phase encoding is much longer than the frequency encoding.
The final step in spatial encoding involves the application of frequency encoding gradient, once the signal is received, in the last direction. This modifies the frequencies in the horizontal direction throughout the period. It, therefore, creates columns of protons that have an identical Larmor frequency.
Discussion of how two Fourier transforms are required to convert k-space data to an image
A Fourier change is an operation that changes over capacities from time to time. An inverse Fourier transform (IFT) changes over from frequency domain to time domain Fourier transform is a mathematical technique (method) that converts time domain data into a frequency domain data.
The Fourier transform is a principal method of the decay/decomposition of a confounded sign and complicated signal that permits mathematicians and scientists to see plainly the frequency and amplitude parts covered up inside. During the time spent creating an MR picture, the Fourier change determines the recurrence and stage encoded MR flags that form k-space. The 2D opposite Fourier change of k-space is the MR image we see. A grip of the Fourier change is key to comprehension a few MR antiques and the heap of strategies for sign procurement by and by today (Bright, 2011).
References
Bright, A. (2011). Planning and positioning in MRI. Sydney, Churchill Livingstone Elsevier. Mangrum, W. (2012). Duke review of MRI principles. Philadelphia, PA, Elsevier/Mosby.
