In diagnostic medical imaging with expensive imaging systems, such as MRI, diagnosis speed can be life or death and time is money. In these respects, faster is better but in general image quality is inversely related to image acquisition speed. Many approaches have been developed to improve image acquisition speed and a few are presented here.
The imaging sequences mentioned thus far have one major disadvantage. For maximum signal, they all require the transverse magnetization to recover to its equilibrium position along the Z axis before the sequence is repeated. When the T1 is long, this can significantly lengthen the imaging sequence. If the magnetization does not fully recover to equilibrium the signal is less than if full recovery occurs. If the magnetization is rotated by an angle θ that is less than 90° its Mz component will recover to equilibrium sooner, but there will be less signal since the signal will be proportional to the Sinθ. So we trade off signal for imaging time. In some instances, several images can be collected and averaged together and make up for the lost signal.To see this possibility, consider the following example while referring to the plot of relative signal vs. rotation angle θ for various TR/T1 values. For simplicity, letís imagine a fixed T1 of 1s. As TR is decreased, the θ value at which we see the maximum signal, as well as the maximum signal itself decrease. To maximize the signal for a given TR/T1 we must decrease the rotation angle θ. If we go from a TR/T1=5 to a TR/T1=0.01 the signal diminishes by a factor of 0.0707 according to the plot. However, the imaging time decreases by a factor of 500. If we could fit 500 of these shorter TR images in the longer TR period and signal average the images them we could obtain a signal-to-noise ratio improvement proportional to the square root of 500 or 22. The product of 22 and 0.0707 gives us 1.55 times the SNR. In this slightly unrealistic example we have improved the SNR by taking more images with a smaller rotation angle.
The gradient echo imaging sequence is the application of these principles. Here is its timing diagram. In the gradient echo imaging sequence a slice selective RF pulse is applied to the imaged object. This RF pulse typically produces a rotation angle of between 10° and 90°. A slice selection gradient is applied with the RF pulse.
A phase encoding gradient is applied next. The phase encoding gradient is varied between Gm and -Gm in 128 or 256 equal steps as was done in all the other sequences.
A dephasing frequency encoding gradient is applied at the same time as the phase encoding gradient so as to cause the spins to be in phase at the center of the acquisition period. This gradient is negative in sign from that of the frequency encoding gradient turned on during the acquisition of the signal. An echo is produced when the frequency encoding gradient is turned on because this gradient refocuses the dephasing which occurred from the dephasing gradient. This type of echo is called a gradient echo.
A period called the echo time (TE) is defined as the time between the start of the RF pulse and the maximum in the signal. The sequence is repeated every TR seconds. The TR period could be as short as tens of milliseconds.
It may be helpful at this point to emphasize the differences between the gradient echo sequence and the spin echo sequence. In a gradient echo, a gradient is used instead of a 180 degree RF pulse to rephase the spins. Imaging with a gradient echo is intrinsically more sensitive to magnetic field inhomogeneities because of the use of the refocusing gradient. The use of a small flip angle and of a gradient for the refocusing of magnetization vectors give this sequence a time advantage. Therefore it is widely used for fast scan images, including 3D acquisitions.
There several imaging techniques that may be used to shorten the image acquisition time without shortening TR. Two techniques, fractional Nex imaging and fractional echo imaging, are presented in this section, while others will be presented in subsequent sections in this chapter. Before fractional Nex or fractional echo imaging can be understood, it is first necessary to examine a relationship between the data in different halves of k-space.
K-space data is made up of complex data representing the Mx and My components of magnetization. The complex data in the right half of k-space is the complex conjugate of the data in the left half of k-space. Similarly, the data in the top half of k-space is the complex conjugate of the data in the bottom half of k-space.Fractional Nex Imaging
Fractional Nex imaging takes advantage of this complex conjugate relationship between the top and bottom halves of k-space to reduce the number of phase encoding steps. In half-Nex imaging, phase encoding steps +8 through -128 of +128 to -128 are recorded. Steps -128 through 0 are generated from the complex conjugate relationship between the halves of k-space. Phase encoding steps -8 through 0 are recorded to assure the center of k-space is at 0 and there is a smooth transition between the halves. Fractional Nex imaging sequences use Nex values between Nex=1 and Nex=1/2. Because fewer data points are collected in fractional Nex imaging, the signal-to-noise ratio becomes poorer as Nex is decreased. The advantage of fractional Nex imaging is that an image can be recorded faster than with Nex=1 but with the same contrast between the tissues as in the Nex=1 case.Fractional Echo Imaging
Fractional echo imaging is similar to fractional Nex imaging in that the complex conjugate relationship between the left and right halves of k-space is used to shorten the echo time in an imaging sequence. If the entire echo does not need to be recorded, the minimum TE value is decreased and more signal may be achieved. In some instances, shorter acquisitions times may result.
A fast spin echo imaging sequence is a multi-echo spin-echo sequence where different parts of k-space are recorded by different spin-echoes. For example we might have a four echo spin-echo sequence with a TE of 15 ms. The k-space will be divided into four sections. The first echo is used to fill the central part, lines 96-160, of k-space. The second echo is used for lines 64-96 and 160-192. The third echo fills lines 32-64 and 192-224. The last echo fills lines 1-32 and 224-256 of k-space. There are some problems with the steps between the parts of k-space, but since there is little data in these regions the steps can be corrected for. The benefit of the technique is that a complete image can now, as was shown in this example, be recorded in one fourth of the time.
Echo-planar imaging is a rapid magnetic resonance imaging technique which is capable of producing tomographic images at video rates. The technique records an entire image in a TR period. To understand echo planar imaging it is helpful to understand the concept of k-space. A magnetic resonance image is referred to as image space. Its Fourier transform is referred to as being k-space. In magnetic resonance imaging, k-space is equivalent to the space defined by the frequency and phase encoding directions. Conventional imaging sequences record one line of k-space each phase encoding step. Since one phase encoding step occurs each TR seconds the time required to produce an image is determined by the product of TR and the number of phase encoding steps. Echo planar imaging measures all lines of k-space in a single TR period.
A timing diagram for an echo planar imaging sequence looks as follows. There is a 90° slice selective RF pulse which is applied in conjunction with a slice selection gradient. There is an initial phase encoding gradient pulse and an initial frequency encoding gradient pulse to position the spins at the corner of k-space. Next there is a 180° pulse. Since the echo planar sequence is typically a single slice sequence, the 180° pulse need not be a slice selective pulse. The phase and frequency encoding directions are next cycled so as to traverse k-space. This is equivalent to putting 128 or 256 phase and frequency encoding gradients in the usual period when the echo is recorded. If we zoom into this region of the timing diagram it will be clearer. You can see that there is a phase encoding gradient, followed by a frequency encoding gradient, during which time a signal is recorded. Next there is another phase encoding gradient followed by the reverse polarity frequency encoding gradient during which time a signal is recorded.
Looking at the k-space trajectory map at the same time as we are zoomed into the phase and frequency encoding gradient area we can see how the gradients trace out k-space. The rate at which k-space is traversed is so rapid that it is possible, depending on the image matrix, to obtain 15 to 30 images a second. This is video rate acquisition.
Sensitivity encoding for MRI (SENSE), simultaneous acquisition of spatial harmonics (SMASH), and sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE-RIP) are MRI techniques designed to reduce the scan time. The reduction is achieved by under sampling k-space and recording images simultaneously from multiple imaging coils. Under sampling reduces the acquisition time and the use of multiple RF coils eliminates the wraparound caused by the under sampling. To fully appreciate how this is possible, please review sampling error in Chapter 5, the wrap around artifact in Chapter 11, and surface coil sensitivity under RF coils in Chapter 9.
If an image space is under sampled in the phase encoding direction by a factor of two, it will take half the time to acquire the image, but every pixel in the image will represent data from two points in space. To represent this as an equation, f is defined as the actual sampling frequency and fo as the optimal sampling frequency for an image. The image space is under sampled if f < fo, and over sampled if f > fo. Defining the sampling factor as,
a k<1 conveys under sampling. In an under sampled image, the number of points in space represented per pixel is 1/k. The reduction in imaging time from under sampling is k.
Image A is taken using fo and B using fo/2 or k=1/2. Note in image B that there are portions of the image that are wrapped around. Pixels in the top half of image B contain information from both the bottom ľ and top middle forth of image A. Pixels in the bottom half of image B contain information from both the top ľ and bottom middle forth of image A. With SENSE, SMASH, or SPACE-RIP imaging it is possible to decode the information in image B and obtain image A in half the imaging time.
Letís examine the process in detail with a specific example. Assume an abject, S, is imaged with four imaging coils (A, B, C, and D) at a sampling frequency fo/4. The imaged object will experience wrap around of the four sections defined by the red lines and be one forth of its original size. Each of the four coils will produce an image (IA, IB, IC, and ID) that is one forth of the optimal size and is made up of the overlap of the four sections (S1, S2, S3, and S4) of the optimally imaged object S. Each of the four imaging coils will have a sensitivity map (CA, CB, CC, and CD). The signals form the respective coils are given by the following equations.
By solving these simultaneous equations, it is possible to solve for S1, S2, S3, and S4 and hence piece them together to form S.
There are some additional costs associated with this imaging technique. There needs to be 1/k imaging coils, signal channels, and signal digitizers on the imager. Some researchers are working on 32 channel systems. There is some image degradation associated with this process due to the added noise from the four channels and the propagation of errors in the solution of the simultaneous equations. However, the time savings makes the process worth while.
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