Fig. 9. Illustration of the effects of a transient gradient on the angle or phase of the vector magnetization. After the gradient is briefly turned on and off, there is a temporary increase in frequency; when the field returns to B0, the frequency returns to the original value but with a 90° phase shift.

Fig. 9. Illustration of the effects of a transient gradient on the angle or phase of the vector magnetization. After the gradient is briefly turned on and off, there is a temporary increase in frequency; when the field returns to B0, the frequency returns to the original value but with a 90° phase shift.

accordingly along this axis. Even though the x-position can be sorted out by different frequencies, that still leaves a whole column along the y-axis that all have the same frequency and are therefore unable to be differentiated into their individual positions. To circumvent this, the y-gradient is turned on very briefly and then shut off after the 90° RF pulse but before the 180° and readout step. This causes the spins to undergo an extra positive or negative rotation depending on their position and leading to a shift of phase or angle of the vector (Fig. 9). In order for Fourier transformation to resolve and localize each voxel in the y-axis, this step has to be repeated many times (corresponding to the number of y pixels or the matrix size in the final image, often in multiples of 128 such as 256 or 512, and so on), with a minimum of 128 times while using a different y-gradient strength each time (14).

It is also necessary at this time to introduce the concept of k-space, a mathematical construct or the Fourier transformation data plane that illustrates the spatial frequency of a process spread out in space with a sinusoidal shape and consisting of signal pattern at different spatial frequencies. Spatial frequency is therefore measured in cycles per unit length and is what a phase-encoding gradient pulse imposes on the spin vectors. In other words the fc-space is a 2D array of raw data with the data placed one line at a time during each readout pulse for each different y-gradient. A very important point to note is that there is not a one-to-one correlation between a point in fc-space and the final image. Every point in fc-space contributes to every pixel of the image and vice versa. It also turns out that the points at the edges of fc-space determine resolution or sharpness of the image whereas the points near the center of fc-space are responsible for the brightness or contrast of the final image (Fig. 10). The number of phase-encoding steps (y-gradient) determines the number of lines in fc-space, the value of the steps contributes to the closeness of the lines, and the maximum (positive

High Resolution Low Contrast

2D Fourier transform

Low Resolution High Contrast

Fig. 10. In k-space kx and ky define the spatial frequency; the center of k-space contributes to contrast, whereas the periphery contributes to the resolution of the final image.

or negative) value defines the size of k-space. The length or duration of the line in k-space is proportional to the product of duration and strength of the readout or x-gradient.

The way that the data points are filled in k-space and the order in which they are filled can also be manipulated by the way the pulse sequence is designed and thus allows one to control the resolution and contrast of the image acquired. There is also a direct one-to-one relationship between data points in k-space and gradient strength. A larger negative or positive gradient fills the lower left and upper right edges of k-space, respectively, contributing to higher resolution of the image. A large k-space also gives the image a higher resolution, but if only the central part of k-space is filled the resolution will decrease. After the filling of k-space, 2D or sometimes 3D Fourier transformation can be performed to give the final MR image (15).

From the above discussion, one notes that the time to fill k-space will equal N x TR x NEX where N is the number of phase-encoding steps, TR the repetition time, and NEX the number of times the slice is sampled. The essence of MRI and pulse sequence design is the balancing and optimizing of the amount of imaging time and final image quality. A shorter acquisition time will minimize the potential for patient motion, increase throughput, and decreases strain on the gradient coils. All the different pulse sequences that are discussed in the following sections such as fluid-attenuated inversion recovery (FLAIR), fat suppression, diffusion, perfusion, fast scan, MR angiogram (MRA), and MR venogram (MRV) are designed to optimize certain data acquisitions but often also come with the penalty of time.

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