Magnetic Resonance Imaging
297
Here, we briefly present a simplified version of the reconstruction method, specialized toward the MR images. To have a simpler notation, we restrict ourselves to the
one-dimensional (1-D) case where we would like to find the proton density along
a line. Note that the time frequency of the precision in the FID signal is directly
proportional to the magnetic field strength, where the angular frequency and the
standard frequency are linked as described in Equation 15.15:
w = 2pf
(15.14)
specifically,
w x = gxG x
(15.15)
Now, if the density of the proton at each point is shown as ρ(x), the measured signal
f(t) is related to this intensity according to the following simplified line integral:
−i xG t
g x
f t
( ) =
∫
r( )
x e
dx
(15.16)
x
This is a typical tomographic equation. In the previous chapter, we described how
the Fourier slice theorem can be used to solve such equations. The preceding equation can be interpreted as a Fourier relationship between FID in the time domain f(t)
and a spin density profile along the x-direction.
Typical MR images files are often limited to 256 × 256 pixel matrices. In these
cases, the pixel size is in the order of 1 mm. The third dimension introduced by the
slice thickness can range from 1 to 10 mm. Larger matrix arrays are becoming available in the order of 512 × 512 pixels that provide better resolution. Image resolution
is steadily falling below 1 mm. Under MRI, the gray matter appears in the medium
range of gray values on T 1 -weighted images. Under MRI, the white matter then has
higher amplitudes than the gray matter.
Knowing the physical concepts of MRI and the general reconstructions methods
applied to form the images, we will next focus on f MRI and its applications.
Examples of various imaging techniques and 3-D rendering of the inner ear are
illustrated in Figure 15.13.
15.5 FUNCTIONAL MRI
A major field of study in medicine is the study of the function(s) of each part of the
brain. The “brain mapping” has been the main ultimate goal of neuroscience as well
as cognitive science. While sometimes researcher would like to know the functions
of a specific part of the brain, the reverse question has been more intriguing: If we
focus on one specific function, such as visual recognition, how can we identify the
parts of the brain that are directly involved in the process?
The fMRI is in principle the best tool available to perform brain mapping. This
technology allows observing the brain while a certain task is performed. The parts
297
Here, we briefly present a simplified version of the reconstruction method, specialized toward the MR images. To have a simpler notation, we restrict ourselves to the
one-dimensional (1-D) case where we would like to find the proton density along
a line. Note that the time frequency of the precision in the FID signal is directly
proportional to the magnetic field strength, where the angular frequency and the
standard frequency are linked as described in Equation 15.15:
w = 2pf
(15.14)
specifically,
w x = gxG x
(15.15)
Now, if the density of the proton at each point is shown as ρ(x), the measured signal
f(t) is related to this intensity according to the following simplified line integral:
−i xG t
g x
f t
( ) =
∫
r( )
x e
dx
(15.16)
x
This is a typical tomographic equation. In the previous chapter, we described how
the Fourier slice theorem can be used to solve such equations. The preceding equation can be interpreted as a Fourier relationship between FID in the time domain f(t)
and a spin density profile along the x-direction.
Typical MR images files are often limited to 256 × 256 pixel matrices. In these
cases, the pixel size is in the order of 1 mm. The third dimension introduced by the
slice thickness can range from 1 to 10 mm. Larger matrix arrays are becoming available in the order of 512 × 512 pixels that provide better resolution. Image resolution
is steadily falling below 1 mm. Under MRI, the gray matter appears in the medium
range of gray values on T 1 -weighted images. Under MRI, the white matter then has
higher amplitudes than the gray matter.
Knowing the physical concepts of MRI and the general reconstructions methods
applied to form the images, we will next focus on f MRI and its applications.
Examples of various imaging techniques and 3-D rendering of the inner ear are
illustrated in Figure 15.13.
15.5 FUNCTIONAL MRI
A major field of study in medicine is the study of the function(s) of each part of the
brain. The “brain mapping” has been the main ultimate goal of neuroscience as well
as cognitive science. While sometimes researcher would like to know the functions
of a specific part of the brain, the reverse question has been more intriguing: If we
focus on one specific function, such as visual recognition, how can we identify the
parts of the brain that are directly involved in the process?
The fMRI is in principle the best tool available to perform brain mapping. This
technology allows observing the brain while a certain task is performed. The parts