Numerical Simulation of Bloch Equation for Protons in Water and Fat Molecules
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Date
2018-07-03
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Addis Ababa University
Abstract
The phenomenological time dependent Bloch equations have been a source of insight
about the magnetic resonance phenomena and the purpose of this study was to
solve the Bloch equations in the laboratory frame. First, the time- dependent Bloch
equations were reduced to a homogeneous linear differential equation, and then a
simple equation was derived to solve it using a matrix operation (diagonalization
method). Then, as an example, this method is applied to the time dependent
Bloch equations for protons in water and fat molecules in uniform static field. The
radiofrequency (RF) pulse is first applied to disturb the protons so that they fall out
of alignment with the static magnetic field. This disturbance occurs through the
transfer of energy from the RF pulse to the protons, that can only occur when the
RF pulse has the same frequency as the Larmor frequency of the protons. The
representative trajectories of transverse component describe the complete time
evolution of magnetization in the transverse component. The transverse magnetization
behaviour can be described by transient sinusoidal oscillation. This has been
observed due to the interaction with neighbouring spin, the amplitude magnetization
damped and oscillates sinusoidal with time that can considerably vary for different
matters, depending on the size of the time constant T2 . For example, for water,
T2 are quite high, dephasing of the transverse magnetization are slow. For fat,
however, relaxation process are considerably faster. Hence, this work clearly describes
the effect of tissue properties (T2 relaxation time) of the proton of both water
and fat if they are exposed in a homogeneous field in the sample. The Fourier
transformation of the time domain leads Lorentzian peak in the frequency spectrum
in given sample.The matlab simulation results give the more physical insight about
the behaviour of magnetization.
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Keywords
Numerical Simulation, Bloch Equation, Protons in Water and Fat Molecules