D eTRT1x y sin a MX y M0x y 11 etrtxy cos a339

For a given repetition time and flip angle, the image intensity is determined by the local longitudinal relaxation time T1(x, y). Since at short repetition times with small flip angles a large signal can still be obtained, this pulse sequence is often

Fig. 3.14. DESS steady-state sequence employing a combination of FISP and PSIF.

referred to as FLASH (fast low angle shot; Haase et al., 1986). With FLASH imaging it is assumed that the phase memory of the transverse nuclear magnetization has been lost at the end of the repetition interval; since this is not true when the repetition interval is smaller than the transversal relaxation time, spoiling gradient pulses must be applied at the end of each interval in order to prevent the emergence of coherent image artifacts. An alternative is to add a stochastically varying jitter to the repetition interval.

In order to obtain an imaging sequence that actually uses the phase memory of the spins in order to yield a stronger signal at rapid repetition, and also to obtain information on the local transversal relaxation time, instead of applying a spoiler gradient the encoding gradient Gy can be reversed at the end of the repetition interval (Fig. 3.14). Thus, the spin phase before the RF-pulses is always the same, establishing a steady-state magnetization. Such a sequence is referred to as FISP (fast imaging with steady precession) or GRASS (gradient recalled acquisition in the steady state).

In steady-state sequences such as FISP or GRASS, the phase variation of the transverse magnetization is always the same between the RF-pulses. Without preparation gradients (i.e., the gradient pulses applied before the data are sampled) in x- and z-directions, one would observe a focused magnetization before and after the RF-pulse (Freeman and Hill, 1971). Graphically, one can consider the signal after the RF-pulse as an FID, and that before as one-half of an echo with an amplitude reduced by the factor e~2TR/T2 compared to the FID. In FISP, the steady-state FID is used to obtain an image, but the steady-state half-echo signal can also be used to obtain a FISP-like image with additional T2 weighting (though this is not a strong effect at the short repetition times applied in steady-state sequences.) In this case the time course of the imaging sequence must be reversed, therefore, and is termed PSIF (Fig. 3.14). It is even possible to combine FISP and PSIF in a single sequence to give two images differing in T2 contrast (DESS, double echo in the steady state). In very homogeneous B0-fields and with very short repetition times, it is also possible to set up a sequence that superposes the FISP and the PSIF signal to give a better S/N ratio. This sequence, originally proposed as FISP (Oppelt et al., 1986), is now termed ''trueFISP''. The signal intensity of trueFISP is determined by the ratio T1/T2

for example, for fluids such as water, where T1 a T2, a signal equivalent to half of the maximum nuclear magnetization can be obtained using 90° pulses with rapid pulse repetition.

With gradient echo sequences, rapid image acquisition in less than 1 s is possible, but the contrast between different tissues is normally low. This can be enhanced by inverting the nuclear equilibrium magnetization using a 180° RF-pulse before the imaging sequence is started (Haase et al., 1989). Thus, during the fast imaging experiment the longitudinal magnetization undergoes relaxation back to its equilibrium state, producing image contrast with respect to tissues having different longitudinal relaxation times T1 (x, y).

Because gradient echo sequences are so fast, they are very well-suited for 3D-data acquisition. Either the RF-pulses are applied nonselectively (i.e., without a slice selection gradient), or a very thick slice is excited. Spatial resolution is then achieved by successively encoding the nuclear magnetization with the gradients Gz and Gy in the y- and z-directions and reading out the signal in the gradient Gx. Since each volume element is repeatedly measured according to the number of phase-encoding steps, the S/N ratio is improved considerably. Image reconstruction is performed with a fast 3D-Fourier transformation, resulting in a block of images that can be displayed as slices through the three main coordinate axes. Image postprocessing also allows the display of images of arbitrary planes (multiplanar reformatting = MPR).

Gradient echo sequences require homogeneous B0-fields in order to avoid signal loss due to dephasing of the transverse nuclear magnetization; the contrast with respect to tissues differing in T2 is generally low. With so-called spin echo sequences utilizing an additional 180° pulse, there is greater flexibility with respect to the manipulation of image contrast, though generally at the expense of acquisition time. Spin echo sequences are also much more stable against inhomogene-ities of the B0-field, since inhomogeneities in the direction of the phase-encoding gradient have no effect.

In the standard spin echo imaging sequence, slice-selective 90° and 180° RF-pulses are used with phase-encoding gradients between them (Fig. 3.15); the echo signal is readout in the frequency-encoding (or projection) gradient. Two parameters are available for signal manipulation, the sequence repetition time TR and the echo time TE. The use of a long echo time allows transverse relaxation of the spin system before signal acquisition, whereas rapidly repeating the pulse sequence prevents longitudinal magnetization from being re-established. This effect is sin a sin a

Fig. 3.15. Standard spin echo imaging sequence. The compensation of the twisted transversal magnetization caused by the selective 90° pulse is achieved here with the prolonged slice selecting gradient pulse after the selective 180° pulse.

called saturation (see also Section 3.2.4). The signal intensity in a pixel is given by

M?(x, y) = M0(x, y)(1 - e-TR/T'(x'y))e-TE¡T2(x'y) (3.41)

The repetition time and the echo time can be adjusted so that the image contrast due to different types of tissue is determined by either M0, T1 or T2. Short values of Te and Tr give T1-weighted images, while a long TE and a short TR give spin density or Mo-weighted images, and long values of both TE and TR give T2-weighted images. For imaging of the heart, no fixed TR is chosen, but the sequence is triggered by the R-wave of the ECG.

Contrast between adjacent anatomic structures can be further enhanced by means of contrast agents. Since the addition of other magnetic moments increases magnetic interactions during the collisions between molecules in a fluid, a paramagnetic agent dispersed in the tissue accelerates the relaxation of excited spins, longitudinally as well as transversely. One commonly used contrast agent is Gd-DTPA (gadolinium diethylenetriaminepentaacetic acid) (Weinmann et al., 1984). When administered into the bloodstream, this contrast agent will accumulate at various levels in tissue due to the different microvascular structures.

The standard spin echo imaging sequence can be modified in several ways. At long repetition times, images of several different slices are acquired in no longer an acquisition time than for a single slice, when the different slices are addressed during the waiting interval. In order to obtain information on transverse relaxation, the NMR signal can be recovered several times by repeating the 180° pulses. Thus, several images are reconstructed with varying T2 weighting for a single slice;

Fig. 3.16. Echo planar imaging (EPI) sequence employing a blipped phase encoding gradient (upper plot) and the according trajectory in Fourier space (lower plot).

the transversal relaxation time can be calculated in each pixel and even displayed as an image.

When each echo of a multi-echo sequence is encoded in the y-direction with a different gradient pulse, several lines in Fourier-space are recorded during one pulse sequence, significantly reducing the time of measurement (TSE = Turbo Spin Echo); it is even sufficient to scan only half of the Fourier space (HASTE = Half Fourier Acquired Single Shot Turbo Spin echo). When the 180° pulses are omitted and the polarity of the projection gradient is alternately reversed (Mansfield, 1977), a complete image can be acquired in less than 100 ms. Such a sequence (termed echo planar imaging; EPI) is the quickest way to obtain an MR image. Sir Peter Mansfield, the eminent NMR scientist and Nobel Prize winner in 2003, had proposed the principle as early as 1978, but it lasted until the 1990s that standard MR system hardware was capable of generating and switching the strong gradients required for execution. A pulse diagram together with the resulting trajectory in Fourier space is shown in Figure 3.16.

The sensitivity of gradient echo sequences (especially of echo planar imaging) to magnetic field inhomogeneities can be exploited to image effects in the human body which respond sensitively to changes in magnetic susceptibility. An example of this is perfusion of the human brain cortex, which varies according to certain actuating or perceptive tasks. If a certain region of the brain is activated (e.g., the visual cortex) when a subject under study sees light flashes, the local oxygen requirement increases. The circulatory system reacts by increasing the local blood supply even more than necessary. Consequently, the activation process results in an increased oxygen content of the venous blood flow. Oxygen is transported by hemoglobin that is confined to the red blood cells. Oxygenated hemoglobin (HbO2)

is diamagnetic, while deoxygenated hemoglobin (Hb) is paramagnetic due to the presence of four unpaired electrons. These different magnetic susceptibilities lead to different signal intensities in susceptibility-sensitive (i.e. T2 *-weighted sequences as EPI). Blood oxygen level-dependent (BOLD) contrast serves as the foundation of functional MRI (Ogawa et al., 1992).

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